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In order to calculate the auxiliary loss between the feature maps of intermediate layers and the ground truth in the field of semantic segmentation, the size of each feature map must match the ground truth. In all studies using the auxiliary losses with the segmentation models, from what we have investigated, they either use a down-sampling function to reduce the size of the ground truth or use an upsampling function to increase the size of the feature map in order to match the resolution between the feature map and the ground truth. However, in the process of selecting representative values through down-sampling and upsampling, information loss is inevitable. In this paper, we introduce Class Probability Preserving (CPP) pooling to alleviate information loss in down-sampling the ground truth in semantic segmentation tasks. We demonstrated the superiority of the proposed method on Cityscapes, Pascal VOC, Pascal Context, and NYU-Depth-v2 datasets by using CPP pooling with auxiliary losses based on seven popular segmentation models. In addition, we propose See-Through Network (SeeThroughNet) that adopts an improved multiscale attention-coupled decoder structure to maximize the effect of CPP pooling. SeeThroughNet shows cutting-edge results in the field of semantic understanding of urban street scenes, which ranked #1 on the Cityscapes benchmark. + +# 1. Introduction + +Increasing the depth of the convolutional neural network can introduce optimization difficulties as shown in [6, 24]. To solve this vanishing gradient problem in the field of image classification, directly connected auxiliary classifiers were used to provide extra gradients into some intermediate layers. The auxiliary classifiers have been widely used in the variations of the Inception architecture of GoogLeNet + +![](images/2e508954efa64c4dcf88812a17eca915051b92cad422d6a3381f26c134e230cd.jpg) + +![](images/a1e5ea5868d919a34e78f82ad38c7f07a6155b4f69b91b42782e7ecb36b46d42.jpg) + +![](images/778a837b8502d85fb40dc7a6221005003e0ae9b3baf2c3dcd0a9268fd718626c.jpg) +Image +DeepLabV3+ + +![](images/e803426b0e549f82aac17a5dfd6898f096acd2dfcc81faa45188e098c3d2c216.jpg) +Ground Truth + +![](images/8bd144ec823bf9712e0427644828ffb1b58b0ca73ecd7ff2e56627806b2a0cbe.jpg) +pLabV3+ w/ CPP +Figure 1. Visualizations of the effect of Class Probability Preserving (CPP) pooling. The images are from Cityscapes. For the occluded train (in the red box), the occluded building (the bus stop in the orange box), and the poles in the distance (in the yellow box), the DeepLabV3+ [5] model w/ CPP shows finer and stronger activation in the Grad-CAM [34] visualization (the left column) than the DeepLabV3+ original model. In the inference results (the right column), the w/ CPP model shows correct and fine segmentation. The enlarged views are provided (the yellow box). + +![](images/46ef065512fe95dadf9ec336fdf11b67463f66f80ee52aa738f248ca5f83287e.jpg) + +[38] and ResNet [18], where the motivation was to provide useful gradients directly to intermediate layers as extra supervision during training to resist the vanishing gradient problem in very deep networks. + +Similar attempts have been made in the field of semantic segmentation. For example, [53, 55, 56] used ResNet-101 as a backbone and adopted an auxiliary head in the intermediate layer as specified in [53]. Since the feature map of the auxiliary head connected layer and ground truth are used to calculate the auxiliary loss, their resolutions should be the same. The auxiliary head is responsible for re-sizing the resolution of the intermediate feature map to that of the ground truth through a re-sizing operation. + +![](images/76fca676a5694fe0537b0c459d5e974c8ad09d876a357435d0e5f0db452b1e21.jpg) +Figure 2. Visualization of the effects of the conventional pooling (i.e. nearest neighbor [NN] pooling) and CPP pooling. NN pooling has been widely used for down-sampling ground truth for segmentation task since the ground truth ids are integer. A semantic ground truth from the Cityscapes dataset is used. As the scale factor of the pooling increases, more information is lost. Especially, in NN pooling, far object and boundary information are lost a lot, while they still remain as a probability in CPP pooling. + +However, designing the auxiliary loss with the re-sizing operations has an inevitable flaw. Each layer in deep neural networks learns different data-driven features. For example, closer layers to the input image learn simpler low-dimensional features. As one moves away from the input layer, higher-order complex features are learned. If we resize the ground truth resulting in one-dimensional pixelwise class information to get the auxiliary loss for the intermediate layers, it would not be enough to guide the various-order features of each layer. For this reason, researchers in this field decorate these re-sizing guided losses with the word auxiliary and use them as auxiliary solutions rather than complete solutions. For the same reason, the majority of scene segmentation papers [5, 14, 17, 29, 46, 48] that have been published recently do not aggressively use auxiliary loss (mostly using no or one auxiliary head). + +Motivated by this limitation, we introduce Class Probability Preserving (CPP) pooling to provide well-designed auxiliary guides, which help optimize the training process of the networks. CPP pooling keeps the class information within a receptive field as a probability preventing the information loss (Figure 3). Through the comprehensive experiments with seven popular semantic segmentation models on various datasets such as Cityscapes [9], Pascal VOC [11], Pascal Context [26] and NYU-Depth-v2 [28], we demonstrated that the proposed method is a model agnostic method that is simply applicable to any model but effective. In addition, we introduce See-Through Network (SeeThroughNet) with an improved multi-scale attention-coupled decoder structure to maximize the effect of CPP pooling. SeeThroughNet shows state-of-the-art results in the field of semantic understanding of high-resolution urban street scenes. The results of ablation and transfer learning experiments are also provided. + +The main contributions of this paper are: + +- We introduce Class Probability Preserving (CPP) pooling to alleviate information loss, where it keeps the class information within a receptive field as a probability. +- We demonstrated seven popular semantic segmentation models with CPP pooling on Cityscapes, Pascal VOC, Pascal Context, and NYU-Depth-v2 datasets to show the effect of the proposed method. +- We propose SeeThroughNet with multi-scale attention-coupled decoder maximizing the effect of CPP pooling, and achieved the first place on the Cityscapes leaderboard. + +# 2. Related Work + +Pooling Methods. Variants of pooling methods have been proposed with convolutional neural networks, which can be categorized into four groups following [1]. Value-based pooling methods [10,21,30,37,47] pick a single representative value based on the significance of the values in the region for down-sampling. Max and average pooling are widely used ones in this category. Patch or multi-sampling approach has been proposed to complement the information loss of the value-based pooling methods, where values in patches or in multi-scale sub-maps are processed. Probability-based pooling methods [16,22,43,45,51] evaluate the probability for the representative values in the region, which helps to prevent overfitting. Various approaches based on probability have been proposed, including stochastic, dropout max, failure density, hybrid, and mixed gated pooling methods. In rank-based pooling methods [19,20,35], weights are learned during training, which + +are used as a weighted sum in the pooling region. Multi-partite, ordinal, and global weighted rank approaches have been demonstrated, in which the multipartite feature ranking in pooling layers, different weights to all feature activations, and estimated scores associated with a class were used, respectively. For transformed domain pooling methods, [44] discarded the first-level and only used the second-level wavelet decomposition to reduce the feature dimensions, which resulted in fewer artifacts. [32] truncated the lower frequencies in power spectrum to reduce the dimensions that preserved more information per parameter than other pooling methods. + +These pooling methods used various approaches to decide representative values in the corresponding receptive fields for down-sampling. However, to the best of our knowledge, none of the pooling methods used an approach preserving class information as a probability. + +Label Smoothing. CPP pooling could be seen as a variation of the label smoothing proposed in [39]. Compared to the label smoothing, our method uses it for down-sampling process and follows the class distribution of the pixels in the receptive field, instead of using a predefined distribution such as the uniform distribution used in [39]. Therefore, CPP pooling is an improved version in that the class probability distribution for each pixel follows data adaptively. + +Semantic Segmentation Architectures. Fully Convolutional Networks (FCNs) [25] have demonstrated significant improvement adopting deep convolutional neural networks (CNNs) in semantic segmentation, by replacing fully connected layers (FCs) with convolutional layers at the end of CNN architectures. Based on this improvement, other advanced techniques such as skip-connections in encoder-decoder architecture [2, 5, 33], a pyramid pooling module [53], and an atrous convolution with atrous spatial pyramid pooling (ASPP) [4] have shown remarkable improvements. + +Recent works have focused on relational context to improve performance, not multi-scale context. [12,49,52] considered the similarity between pixels using a self-attention method and performs a similarity-weighted aggregation. Boundary-aware methods also have been applied to improve semantic segmentation performance. For example, Gated-SCNN [40] used the shape stream network that takes image gradients and features to produce semantic boundaries as output. It used a pixel-based loss to train the shape stream network. InverseForm [3] employed the inverse-transformation network to model the spatial distance-based metric into the loss function. [41, 48, 53] used the auxiliary losses with the up-sampled logits instead of the conventional pooling methods to mitigate the information loss. + +In this work, we show that when using auxiliary losses, the performance is further improved by using the proposed CPP pooling instead of using the conventional up-sampling or down-sampling methods. + +![](images/e95563695d42f55ccdc54909d885e166e5ba165a2fbfdf73192490ae27aca129.jpg) +Figure 3. Illustration of Class Probability Preserving (CPP) pooling. It shows 1/4 pooling where the 4x4 grids information is downsampled to one grid. The number of channels of the output equals to the total number of classes (e.g. 20 classes for Cityscapes including the ignore class), where each channel represents the class probability of the corresponding grid. + +# 3. Method + +# 3.1. Class Probability Preserving Pooling + +Conventional pooling methods (e.g., max-pooling, average-pooling, nearest neighbor pooling, etc.) have been commonly used to down-sample features and ground truth. However, this potentially degrade performance for semantic segmentation task due to the information loss when selecting the representative values from the corresponding receptive regions. The top row of Figure 2 shows an example of information loss from down-sampling, where as the scale factor of the pooling increases, more information loss is observed to down-sample the semantic ground truth. + +We propose Class Probability Preserving (CPP) pooling, a novel pooling method preserving class information minimizing information loss (Figure 3). Instead of deciding one representative value from the corresponding receptive region in the input map, CPP pooling counts the number of grids (or pixels) that match each class in the region, then use the number as a probability for each class. For example, Figure 3 shows $1/4$ CPP pooling where $4 \times 4$ grids are down-sampled to one grid. In the input map, the number of class 0 (road) in the $4 \times 4$ region is counted, which becomes the probability value of the corresponding grid of the output channel of the class 0 (road). The same calculations are processed for the other classes (i.e. total 20 classes for Cityscapes including the ignore class). As shown, each location in the output grid keeps a certain class probability. + +In more details, in CPP pooling, a grid of the output $Y_{k_{(l,m)}}'$ of a class $k$ is computed as: + +$$ +Y _ {k _ {(l, m)}} ^ {\prime} = \frac {1}{s ^ {2}} \sum_ {(i, j)} \mu_ {i, j}, \text {w i t h} \mu_ {i, j} = \left\{ \begin{array}{l l} 1 & \text {i f} Y _ {(i, j)} = k \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {1} +$$ + +, where $Y_{(i,j)}$ is the grids (or pixels) of the input feature + +![](images/741cea04087322a62e3516708a2e392a865883f011c8c0ebd8483893ecba8ec9.jpg) +HRNetV2 +See-Through Decoder + +![](images/fe942209786c189b37b7ab5e2c4b5af51ab0ed7fe3c5f1cda2ccfa0afb85fe29.jpg) +Multi-Scale Attention Module +(MSAM) +Figure 4. SeeThroughNet Architecture. The architecture consists of CPP pooling with 3 auxiliary heads combined with multi-scale attention. To make better use of CPP pooling, See-Through Decoder was designed to include the multi-scale attention that allows CPP pooling to be used for each scale. See Section 3.2 for detail. + +![](images/5fe143ee97519f071a2950c17fe2e1ac369080a26bb3e3a373321e107f82d7d9.jpg) +Multi-Scale Attention Mask +(A.MASK) + +map, $k \in K$ is the object class, $Y$ is the input feature map, and $Y'$ is the output of the CPP pooling. $Y_{k(l,m)}'$ is the grid $(l,m)$ of the class $k$ channel map in the output $Y'$ . Given a scale factor $1 / s$ , the range of $Y_{(i,j)}$ are $s \times l \leq i < s \times (l + 1)$ and $s \times m \leq j < s \times (m + 1)$ for the corresponding area of the input feature map. Finally, to compute the output grid value $Y_{k(l,m)}'$ , we compute each class $k$ probability by counting the matching class at target grids (or pixels), then normalize it by $s^2$ . After down-sampling semantic segmentation labels by CPP pooling, we get two probability distributions (i.e. CPP pooling result from the ground truth and the semantic prediction output from the layer). To measure the difference between two probability distributions, we use Kullback-Leibler (KL) divergence [13], written as $D_{KL}$ in Equation 2. Let $p_i(x)$ and $q_i(x)$ are the semantic prediction output of the layer and the CPP pooling result from the semantic ground truth, respectively, the loss function is: + +$$ +L _ {c p p} = \frac {1}{H \times W} \sum_ {h, w \in H, W} D _ {K L} (p (x) | | q (x)) \tag {2} +$$ + +, where the KL divergence result is normalized by all element $H\times W$ ; $H$ for the height of $p_i(x)$ and $W$ for the width of $p_i(x)$ . + +# 3.2. SeeThroughNet + +To adopt the benefit of CPP pooling for semantic segmentation task, we propose our state-of-the-art semantic segmentation network called SeeThroughNet (Figure 4). We dubbed Seethrough Network since the class probability information is seen through the CPP output channels (Figure 3), while only a representative class is shown with the hard labels of the existing down-sampling methods. + +Backbone. We use HRNetV2-W48 [36] as a backbone, where the outputs of the final stage with four different scale features are used for the SeeThrough decoder. + +See Through Decoder. The coarse semantic predictions $X_S'$ (the pink boxes in Figure 4) are created from each of four different scales $S = [s_{32}, s_{16}, s_8, s_4]$ . The coarse semantic segmentation head consists of (3x3 conv) → (BN) + +$\rightarrow$ (ReLU) $\rightarrow$ (1x1 conv). We use three auxiliary losses, which take the label $Y'$ generated by CPP pooling. Thanks to the class probability preserved labels, the decoder learns potentially existing information from the larger scale image that disappears when down-sampling is used instead. + +To create larger and fine semantic segmentation prediction, we sequentially combine from the smaller scale semantic map to the larger scale semantic map. When combining the two semantic segmentation predictions with different scales, we use the trainable relative attention mask $\alpha_{s}^{d}$ in the decoder between the adjacent scale semantic segmentation maps, and the bilinear up-sampling operation $\mu$ on the smaller map to match resolution (Multi-Scale Attention Module [the blue boxes] in Figure 4). [41] introduced the related attention mask, which was originally used to combine multi-scale predictions at training and inference phase but not in the decoder. To generate the attention mask for each scale in the SeeThrough decoder, we use the same scale of the backbone features and coarse segmentation map (Multi-Scale Attention Mask in Figure 4). The multi-scale coarse segmentations $X_{S}^{\prime}$ with $S = [s_{32}, s_{16}, s_{8}, s_{4}]$ are aggregated sequentially as in Equation 3 to get the fine segmentation feature $X^{\prime}$ . + +$$ +X ^ {\prime} = \sum_ {s \in S} \left(\mu \left(\alpha_ {s} ^ {d} * X _ {s} ^ {\prime}\right) + \left(\left(1 - \mu \left(\alpha_ {s} ^ {d}\right)\right) * X _ {s + 1} ^ {\prime}\right)\right) \tag {3} +$$ + +, where $*$ and $+$ are pixel-wise multiplication and addition. + +OCR Head. We adopt OCR Head [48] to predict the final semantic segmentation output $X$ . It takes the multi-scale aggregated segmentation prediction $X'$ from the SeeThrough decoder and the concatenated features of the backbone's final stage outputs. + +Two-resolution training. For training, a given input image is resized by factor $r$ , where $r = 0.5$ means down-sampled by factor 2. As introduced in [41], we follow the scale factor $r$ as $r = 0.5$ and $r = 1.0$ for the two-resolution training. For each scale factor, the output of the SeeThrough decoder are combined as follows. To get the final aggregated semantic segmentation prediction $X_{agg}$ from the results of the + +Table 1. The results of the CPP pooling experiments with the seven segmentation models on the various validation datasets such as Cityscapes (trained with fine annotation only), Pascal VOC 2012, Pascal Context, and NYU-V2. All models with CPP pooling (w/ CPP) show performance improvement over the Baseline models. + +
ModelCityscapes (mIoU %)PASCAL VOC (mIoU %)PASCAL Context (mIoU %)NYU-V2 (mIoU %)
Baselinew/ CPPGainBaselinew/ CPPGainBaselinew/ CPPGainBaselinew/ CPPGain
OCRNet [48]81.1781.79+0.6277.4378.43+1.0045.9646.72+0.7658.0958.59+0.50
DeepLabV3+ [5]79.7781.07+1.3078.3579.89+1.5445.6948.23+2.5454.6655.71+1.05
UPerNet [46]79.1379.59+0.4676.3278.95+2.6344.1346.89+2.7653.6055.22+1.62
DMNet [14]78.1579.69+1.5478.1978.94+0.7545.3647.95+2.5954.0855.07+0.99
CCNet [17]77.4779.64+2.1776.9079.51+2.6143.7646.24+2.4853.6354.10+0.47
PSPNet [53]78.3479.85+1.5177.4479.56+2.1245.1147.77+2.6654.5155.14+0.63
ANN [56]78.3178.93+0.6277.4578.59+1.1444.4247.19+2.7754.5055.44+0.94
+ +See Through decoder from the two resolutions, we merge $X_{0.5}$ and $X_{1.0}$ with the trainable attention mask $\alpha_{0.5}^{m}$ as written in Equation 4. + +$$ +X _ {a g g} = \mu (\alpha_ {0. 5} ^ {m} * X _ {0. 5}) + ((1 - \mu (\alpha_ {0. 5} ^ {m})) * X _ {1. 0}) \quad (4) +$$ + +Overall objective function. To compute the loss of the final semantic segmentation prediction $X$ and the label $Y$ , we use RMI loss $L_{rmi}$ following [54] as Equation 5. $L_{ce}$ is the cross entropy loss. $I$ represents the mutual information, $b$ is the batch size, and $c$ is the class. For $\lambda$ , we use 0.5 as in [54]. $L_{rmi}(X,Y) = \lambda L_{ce} +$ + +$$ +(1 - \lambda) \frac {1}{B} \sum_ {b} ^ {B} \sum_ {c} ^ {C} \left(- I _ {l} ^ {b, c} (X: Y)\right) \tag {5} +$$ + +Additionally, we compute the auxiliary loss (Aux. w/ CPP in Figure 4) in the SeeThrough decoder with the three different scales $(X_{s_{16}}^{\prime}, X_{s_{8}}^{\prime}$ , and $X_{s_4}^{\prime}$ ), which are sequentially aggregated to get $X^{\prime}$ . We use KL divergence (Equation 2) to get the auxiliary loss $L_{decoder}$ in Equation 6. + +$$ +L _ {\text {d e c o d e r}} (X, Y) = \sum_ {s \in S} L _ {\text {c p p}} \left(X _ {s}, Y _ {s} ^ {\prime}\right) \tag {6} +$$ + +, where $S = [s_{16}, s_8, s_4]$ . Finally, the overall objective function used of SeeThroughNet is: + +$$ +\begin{array}{l} L _ {\text {o v e r a l l}} = L _ {r m i} (X, Y) + \sum_ {r} ^ {R} \sum_ {s} ^ {S} L _ {\text {d e c o d e r}} \left(X _ {r, s}, Y\right) \tag {7} \\ + \gamma L _ {c e} \left(X _ {1. 0}, Y\right) + \gamma L _ {c e} \left(\mu \left(X _ {0. 5}\right), Y\right) \\ \end{array} +$$ + +, where $R = [r_{0.5}, r_{1.0}]$ , $S = [s_{16}, s_{8}, s_{4}]$ , and $\gamma$ is the constant (0.05) as in [41]. + +# 4. Experimental Results + +In this section, we present experimental results to validate the proposed CPP pooling and SeeThroughNet. To see the effect of the CPP pooling, we experimented with seven popular semantic segmentation models on Cityscapes, Pascal VOC, Pascal Context, and NYU-Depth-v2 datasets. We evaluated SeeThroughNet on the Cityscapes dataset. Implementation details can be found in the Appendix. + +![](images/93cebfa71de999dced199a6675403887f9a43e4ae56c4b552c7c9b66df638c01.jpg) +(a) Aux. losses with up-sampling +Figure 5. The results of the ablation experiments with different numbers of the auxiliary losses (w/ up-sampling and w/ CPP) on the Pascal VOC 2012 val set. The number of auxiliary losses are 0, 1, 2, 3, 4 for both conditions. (Enlarged view is recommended.) + +![](images/03f58677da33a9a0a6ca94576e812526d208919cf4967db3398cbe0721a6cf4d.jpg) +(b) Aux. losses with CPP pooling + +# 4.1. Effect of CPP pooling + +Auxiliary heads. To apply CPP pooling on the seven conventional semantic segmentation models, we employed auxiliary heads on the backbone. For the HRNetV2 backbone of OCRNet, we added four auxiliary heads to the four different scales of the final outputs. For the ResNet101 backbone of the other six models, we added four auxiliary heads to the final outputs of each stage. The auxiliary head consists of (3x3 conv) $\rightarrow$ (BN) $\rightarrow$ (ReLU) $\rightarrow$ (1x1 conv). + +CPP pooling performance for various models. Table 1 shows the results of the CPP pooling experiments with the conventional segmentation models on Cityscapes, Pascal VOC, Pascal Context, and NYU-Depth-v2 datasets. We used the models from MMSegmentation [8] and trained them from scratch. The models have the ResNet101 backbone except OCRNet. For Baseline models, we applied four auxiliary heads in the backbone with up-sampled logit with Cross Entropy (CE) loss as implemented in [8]. For w/ CPP models, we applied four auxiliary heads with CPP pooling with the KL loss (Equation 2). For all the models and datasets in Table 1, the models w/ CPP pooling outperform the baseline models. These results indicate that CPP pooling can be applied to various segmentation models to enhance performance. + +Ablation experiment of CPP pooling. We conducted the ablation experiment of CPP pooling, where the number + +Table 2. Class-wise comparison between the baseline models and the w/ CPP models on the Cityscapes validation set. The seven popular semantic segmentation models are compared. More improvement are observed with the instance classes (i.e. person, rider, car, truck, bus, train, motorcycle, and bicycle) than with the non-instance classes. + +
MethodClass IoU (%)
Non-InstanceInstance
roadswalkbuildwallfencepolethightfisternvegterrainskypersonridercartruckbustrainmocbicycle
OCRNet [48]Base98.385.793.658.165.571.776.383.493.263.895.685.167.595.879.591.286.370.980.7
CPP98.587.293.759.465.372.476.883.693.264.395.684.766.596.186.292.587.170.280.8
Diff.0.21.50.11.3-0.20.70.50.20.00.50.0-0.4-1.00.36.71.30.8-0.70.1
Diff. Avg.0.440.89
DeepLabV3+ [5]Base98.486.593.153.262.070.075.381.992.963.495.284.467.495.479.890.277.269.180.1
CPP98.486.393.251.463.370.075.682.093.064.095.484.867.696.187.092.687.172.080.7
Diff.0.0-0.20.1-1.81.30.00.30.10.10.60.20.40.20.77.22.49.92.90.6
Diff. Avg.0.063.04
PSPNet [53]Base98.285.292.954.461.767.173.580.292.662.795.082.965.695.274.788.374.564.679.2
CPP98.285.693.054.261.366.973.880.792.865.395.183.365.295.784.790.483.468.179.7
Diff.0.00.40.1-0.2-0.4-0.20.30.50.22.60.10.4-0.40.510.02.18.93.50.5
Diff. Avg.0.313.19
UPerNet [46]Base98.385.992.850.960.868.774.580.392.761.995.283.664.695.679.290.181.767.379.5
CPP98.386.392.851.359.868.173.780.792.863.094.983.465.095.683.790.781.371.379.6
Diff.0.00.40.00.4-1.0-0.6-0.80.40.11.1-0.3-0.20.40.04.50.6-0.44.00.1
Diff. Avg.-0.031.13
CCNet [17]Base98.385.992.651.157.966.872.280.192.463.295.082.966.595.070.486.270.666.378.6
CPP98.386.692.952.160.366.873.880.292.663.695.183.967.295.883.791.981.467.579.4
Diff.0.00.70.31.02.40.01.60.10.20.40.11.00.70.813.35.710.81.20.8
Diff. Avg.0.624.29
DMNet [14]Base98.385.892.951.159.367.173.880.692.663.094.983.365.195.675.587.072.367.779.4
CPP98.385.892.952.660.366.873.780.992.764.094.983.664.595.985.291.583.667.379.7
Diff.0.00.00.01.51.0-0.3-0.10.30.11.00.00.3-0.60.39.74.511.3-0.40.3
Diff. Avg.0.323.18
ANN [56]Base98.184.992.753.360.166.872.980.092.562.495.182.963.895.680.387.272.368.279.0
CPP98.285.192.853.459.267.273.481.392.562.394.883.364.495.681.890.677.866.979.3
Diff.0.10.20.10.1-0.90.40.51.30.0-0.1-0.30.40.60.01.53.45.5-1.30.3
Diff. Avg.0.131.30
+ +Table 3. The distribution of the classes in the Cityscapes fine training dataset (2975 images). The table lists the number of images containing each class object in the training set. The images with the truck, bus, and train classes are significantly lacking compared to the other classes. + +
Classroadswalkbuildwallfencepolelighttsignvegterrainskypersonridercartruckbustrainmecybicycle
Counts29342811293497012962949165828082891165426862343102328323592741425131646
+ +of auxiliary heads for the models are varies from 0 to 4 with up-sampling (i.e. bilinear up-sampling) and with CPP pooling. As in Figure 5, the results show that adding the auxiliary heads with up-sampling does not help to improve the performance, and sometimes even degrade the performance compared to the model without the auxiliary head (0 Aux). On the other hand, adding auxiliary heads with CPP pooling improves performance over the models without the auxiliary head (0 Aux) and the auxiliary heads with up-sampling. Note that we believe that adding auxiliary heads with down-sampling degrades the performance further because more information loss occurs with down-sampling with the conventional methods than up-sampling. + +This implicates why the recently proposed semantic segmentation architectures did not aggressively use auxiliary heads (mostly using one auxiliary head). Adding more aux + +iliary heads with the conventional down-sampling and upsampling methods does not help the performance improvement because of the information loss. + +Performance with the class distribution. We compared the class-wise results of the seven semantic segmentation models between the baseline and the w/ CPP models. As shown in Table 2, the instance classes, such as the person, rider, car, truck, bus, train, motorcycle, and bicycle classes, generally show more improvement than the non-instance classes. We speculate that CPP pooling makes the model more robust for occluded and long-distance objects that often appear with instance classes. The Grad-CAM [34] visualizations of the distant and occluded objects are in Figure 6 for qualitative analysis. + +In addition, we observed that the truck, bus, and train classes show especially more improvement than the other + +![](images/a86dd7edab321f19c8ef46fe70d064f7eb3147e5b05dbbdce09c781dfe703553.jpg) +Image + +![](images/26e1917bfb1dc6592f62990032237e1eaa39c4201d3da3d59a3e966096fd2b23.jpg) +Ground Truth + +![](images/29189dba3453d41a586ea5655acf498466025d3c3e80b03d9e67ee0972a6ee8f.jpg) +Without CPP pooling + +![](images/d96a3205fee56eba61e269abee3be09cb2a90b7c78a1052e43ecf8cc71015650.jpg) +With CPP pooling + +![](images/667a8e80ca6534f96227864f07760905bac4c5e25bfd716f9860c882cce1a602.jpg) +Image + +![](images/303fef1972ef1db70e16c9a2ea56021cb8550810b9df3d1d8d7d7ea4241c439d.jpg) +Ground Truth + +![](images/974497c7f15dc9b61ce399576f5e52a5154686078a20d5c4dec013e4e6911cf8.jpg) +Without CPP pooling + +![](images/fc015321144e3c368b631154be1294a4f33a2f2dbc078b3054c3d14cba2ed257.jpg) +With CPP pooling +Figure 6. Grad-CAM [34] visualizations of the train (top) and person (bottom) class. The occluded and distant objects (in the orange boxes) show stronger activation with CPP pooling than the baseline (without CPP pooling). + +classes for all results from the seven semantic segmentation models. This follows the class distribution in the Cityscapes fine training dataset. We counted the images containing each class object from the fine training dataset (2975 images), and list them in Table 3. The images with the truck, bus, and train classes are markedly lacking compared to the other classes. This implicates that CPP pooling also could address the class imbalance problem. The potential reason for dealing with the class imbalance problem is that such soft labels prevent the network from over-confidence by providing noise distribution [27]. Thus the soft labels generated by CPP pooling encourage higher probability predictions for minority classes. This performance improvement for the scarce classes was also observed in the SeeThroughNet experiment. After adding the Mapillary dataset, the SeeThroughNet model showed $4\%$ improvement in the train class, even if the Mapillary dataset had no train class label. + +# 4.2. SeeThroughNet Results on Cityscapes + +SeeThroughNet ablation study. To see the effect of CPP pooling on SeeThroughNet, we conducted the ablation experiments with the SeeThrough Decoder. In Table 4, both w/ CPP pooling and w/ multi-scale (MS) attention show improvement over the baseline, where w/ CPP pool + +Table 4. SeeThroughNet ablation study. Trained and evaluated on the Cityscapes fine and validation set. CPP pooling is our proposed method. MS attention indicates multi-scale attention mask used to combine semantic map in the Seethrough decoder. + +
CPP poolingMS AttentionIOU (%)Gain
84.06
✓84.690.63
✓84.370.31
✓✓85.291.23
+ +Table 5. SeeThroughNet feature transfer learning for object detection task. The SeeThroughNet encoder (HRNetV2-48) trained on Cityscapes were transferred to the detection models. The three detection models loaded the encoder weight and trained on the detection data with and without freezing the encoder. The detection data labels were parsed from the Cityscapes instance dataset to utilize the SeeThroughNet encoder weight trained on the Cityscapes semantic segmentation data. Bold - the highest numbers (not including the En.frozen results). Highlighted in blue - the highest for all numbers (including the En.frozen results). + +
ModelPre-trainedAP\( AP_{50} \)\( AP_s \)\( AP_m \)\( AP_l \)
Mask-RCNN [15]ImageNet(En.frozen)41.0(36.6)65.8(65.6)18.7(16.8)39.9(37.1)60.6(53.8)
SeeTh. w/o CPP(En.frozen)44.6(42.1)69.1(69.7)20.2(21.9)42.7(40.9)64.3(59.0)
SeeTh. w/ CPP(En.frozen)45.9(46.1)71.3(75.1)22.3(32.3)43.9(47.0)65.3(61.8)
FCOS [42]ImageNet(En.frozen)37.7(32.4)62.4(59.6)15.2(13.8)35.2(31.1)55.9(49.8)
SeeTh. w/o CPP(En.frozen)42.3(39.2)67.7(66.1)19.7(19.8)41.8(38.2)59.8(53.9)
SeeTh. w/ CPP(En.frozen)44.2(43.8)70.7(72.3)20.7(22.0)43.4(44.2)61.8(58.1)
Faster-RCNN [31]ImageNet(En.frozen)39.4(34.0)64.7(62.1)17.5(16.5)39.3(34.5)58.1(49.6)
SeeTh. w/o CPP(En.frozen)43.4(39.7)68.4(69.0)20.3(20.1)41.2(39.4)63.0(55.3)
SeeTh. w/ CPP(En.frozen)44.7(44.8)71.6(75.7)22.4(31.5)43.4(45.9)61.7(58.4)
+ +ing enhanced more. A synergistic effect was observed when CPP pooling and MS attention were used together. The qualitative results are shown in the Appendix. + +Cityscapes benchmark. SeeThroughNet achieved state-of-the-art results (mIoU $86.12\%$ ) on the Cityscapes benchmark. For the inference, we used the scales = {0.5, 1.0, 2.0} and the input image flipping. Table 6 shows the comparison between the SeeThroughNet and other semantic segmentation models on the Cityscapes test set. In Figure 7, SeeThroughNet shows finer and more accurate results for the occluded and distant objects than another state-of-the-art model InverseForm [3]. For example, the GradCAM visualizations show stronger and finer activation for the corresponding classes resulting in better inference results. In addition, in row 2 in Figure 7, the SeeThroughNet is able to segment the occluded rider in the distance. + +Table 6. Comparison between SeeThroughNet and other methods on the Cityscapes leaderboard (test set). The Map. column indicates whether Mapillary Vista was used for pretraining. + +
MethodMap.roadswalkbuiltwallfencepolehighplainvegferrierskypersonridercarfruexbustrainmecycbicycle
PSPNet [53]No98.6886.9293.4658.3863.6767.6776.1280.4793.6372.2095.2986.8371.9196.2177.6991.5183.6470.8077.53
DeepLabv3+ [5]No98.6987.0493.9159.4763.7371.3978.1682.1593.9673.0395.8487.9573.2696.4078.0290.9183.9073.8378.87
OCRNet [48]Yes98.8288.2994.2666.8866.6973.2880.2183.0494.2074.1095.9788.5075.7896.5178.5191.7890.1273.4079.31
DecoupleSegNet [23]Yes98.7987.7894.3766.0764.7772.3278.7982.6194.2073.9796.1288.6775.8896.5880.1993.7891.5574.3279.53
SegFix [50]Yes98.8888.3394.3967.9767.8273.5980.6083.9294.3574.4596.0689.2175.8596.8383.6294.1791.2874.0280.09
Panoptic Deeplab [7]Yes98.8488.4094.4464.3168.3475.3281.0484.1994.1973.7396.0989.6978.6496.7382.1993.6990.1676.4079.80
HMSA [41]Yes98.9789.3894.9071.8368.3875.8582.1885.2794.4974.9796.3090.1479.7196.9682.5894.6087.8077.1581.70
InverseForm [3]Yes98.6089.4594.6171.8069.2475.8482.3885.5394.3275.0095.8390.1779.7896.9284.4595.5888.6576.6881.76
SeeThroughNet (Ours)Yes98.9489.0995.0473.7671.3576.1082.4185.1394.5275.2696.2590.0679.6397.0484.2595.0792.6877.8581.76
+ +![](images/d954c928700747d338bd2ac4612c52ab9123f015277a23d83fe4e8ee5e8764a5.jpg) + +![](images/e446e59ff12d162ec87909d57d20a999255897e2cc885e3452956e0cb1a4f0a7.jpg) + +![](images/2c6ef571b6696a6be2afe7c38c567252a72f19f246b1c70efdace2505cf3c60e.jpg) +Image + +![](images/ab37f8e9dbe19ec566a4aa3ac2b7caae57b1979ce201042e283022402ec60a97.jpg) + +![](images/46c693c554cc5d4fc1c82e2a2f5269b792bdc87cc10a0da1cd79fd251527532f.jpg) + +![](images/8c22ac65e8abafdb7f8aec5cbfe1afd4cdf547b253221e95bb36b13abfd65659.jpg) +InverseForm + +![](images/06851dfe312b01e7f78cfa33625ac0cc9442618ac661e3acb4e57964942416a3.jpg) + +![](images/69f4e6920a1517a0faa934e40dad35b10b02f1bc455068fc38b488b949e9211b.jpg) + +![](images/8d99550492dd12aa62dd95030e5766b1fffd825681f8570f87d7917c1552cb6e.jpg) +Figure 7. SeeThroughNet qualitative results on the Cityscapes test set. The inference results and Grad-CAM [34] visualizations of the SeeThroughNet and another state-of-the-art model InverseForm [3] are compared. The SeeThroughNet shows finer and more accurate results for the occluded and distant objects. The Grad-CAM classes are marked in the right-bottom corner of the Grad-CAM images. The enlarged views are provided. More examples are in the Appendix. + +![](images/1c5c78dbd75959f6e6bda24909f379eb373f7a229a88ea3832173f30bb43a603.jpg) + +![](images/c70273601a22708fbc320ae1de174e41a49bd0f3e226875a52f765953501b0b5.jpg) + +![](images/eb72a53c19d55385c537f68d87d19c11618fe39a4a8f0688a00bad5f32d900af.jpg) +SeeThroughNet + +![](images/b109422a8182086e5fe3d29caa0b582adaf979a4996e8b336b1972fa7e77cb17.jpg) + +![](images/6d15223b7e6956c7257a52885a1468d724519917141832ab1e6ee7cb0818a2dc.jpg) + +![](images/d9b46fed1bae186186b07584b723919141c1750da6ad9bed237ffcee131a56c0.jpg) + +SeeThroughNet feature transfer learning for object detection task. We transferred the encoder (HRNetV2-48) of the trained SeeThroughNet on Cityscapes to the detection task to see how the learned features with CPP from SeeThroughNet could affect the detection task. The detection labels were parsed with the Cityscapes instance dataset to utilize the SeeThroughNet encoder weight trained on the Cityscapes semantic segmentation data. As in Table 5, the detection models trained with the pre-trained SeeThroughNet w/ CPP encoder shows better accuracy than the other two conditions. Also, for comparing the encoder frozen and not-frozen models, the results of the freeze models for the SeeThroughNet w/ CPP encoder show similar or higher accuracy than the not-freeze models, while the other two conditions show more improvement with the not-frozen models. These results indicate that the auxiliary loss with CPP pooling help to learn feature representations for another task such as object detection even without further training. In addition, the encoder frozen scores with SeeThroughNet w/ CPP show more improvements in $\mathrm{AP}_s$ than the others implying the effectiveness of CPP pooling for handling distant (small) and occluded objects. + +# 5. Conclusion + +In this paper, we propose a novel model-agnostic pooling methods called Class Probability Preserving (CPP) pooling to minimize information loss. To show the effect of the CPP pooling, we experimented with seven popular segmentation models on Cityscapes, Pascal VOC, Pascal Context, and NYU-Depth-v2 datasets, where our proposed CPP pooling consistently improved the models by simply applying it with auxiliary losses. The ablation experiments and class-wise analysis are demonstrated as well. In addition, we introduce the SeeThroughNet utilizing CPP pooling with auxiliary heads combined with multi-scale attention. The results of the ablation experiments and feature transfer learning experiments with the SeeThroughNet encoder are provided. 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In IEEE ICCV, 2019. 1, 5, 6 \ No newline at end of file diff --git a/seethroughnetresurrectionofauxiliarylossbypreservingclassprobabilityinformation/images.zip b/seethroughnetresurrectionofauxiliarylossbypreservingclassprobabilityinformation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ca7280b1091c97880bab711dcb833ba03b2b6110 --- /dev/null +++ b/seethroughnetresurrectionofauxiliarylossbypreservingclassprobabilityinformation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dc826dab4a5da2e8a64d7881da51c170be75c4ce42689290d82e90ccbf71ba60 +size 995782 diff --git a/seethroughnetresurrectionofauxiliarylossbypreservingclassprobabilityinformation/layout.json b/seethroughnetresurrectionofauxiliarylossbypreservingclassprobabilityinformation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..92629d0f3c30074ecef3e051e74a15e177fbedce --- /dev/null +++ b/seethroughnetresurrectionofauxiliarylossbypreservingclassprobabilityinformation/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:06d99a904e5345af77a9a8cbe102dbc19c00872df1248c4120e5d6ab0dfdb564 +size 427830 diff --git a/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_content_list.json b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..27822a7bb9fee0907b1647a0aab0626195f4ebfd --- /dev/null +++ b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e2e7550c348e576521cfa17874358df820d0252833743c694e3aad240a2c083a +size 79747 diff --git a/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_model.json b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fd9e1bb62ebbd0829032666f46b33a0d8ed69609 --- /dev/null +++ b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a77a35baeab3bf307f208a24232cb05dce9d467b14e354f428c362b354799e81 +size 98693 diff --git a/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_origin.pdf b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ce2f30e2485c5fc2ef2bdf2d0b756e40510454f4 --- /dev/null +++ b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/0aeacc17-5308-4568-8581-a22da120ad50_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4a6b92149ab6218043de1a56fd48906183711c45d6e2275b78bd2418940e5120 +size 7983785 diff --git a/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/full.md b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..14dff879090cd721c7bedd21d9dabf1bf9413ccb --- /dev/null +++ b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/full.md @@ -0,0 +1,339 @@ +# Segment and Complete: Defending Object Detectors against Adversarial Patch Attacks with Robust Patch Detection + +Jiang Liu1, Alexander Levine2, Chun Pong Lau1, Rama Chellappa1, Soheil Feizi2 +1Johns Hopkins University, 2University of Maryland, College Park + +{jiangliu, clau13, rchella4}@jhu.edu, {alevine0,sfeizi}@cs.umd.edu + +# Abstract + +Object detection plays a key role in many security-critical systems. Adversarial patch attacks, which are easy to implement in the physical world, pose a serious threat to state-of-the-art object detectors. Developing reliable defenses for object detectors against patch attacks is critical but severely understudied. In this paper, we propose Segment and Complete defense (SAC), a general framework for defending object detectors against patch attacks through detection and removal of adversarial patches. We first train a patch segmenter that outputs patch masks which provide pixel-level localization of adversarial patches. We then propose a self adversarial training algorithm to robustify the patch segmenter. In addition, we design a robust shape completion algorithm, which is guaranteed to remove the entire patch from the images if the outputs of the patch segmenter are within a certain Hamming distance of the ground-truth patch masks. Our experiments on COCO and xView datasets demonstrate that SAC achieves superior robustness even under strong adaptive attacks with no reduction in performance on clean images, and generalizes well to unseen patch shapes, attack budgets, and unseen attack methods. Furthermore, we present the APRICOT-Mask dataset, which augments the APRICOT dataset with pixel-level annotations of adversarial patches. We show SAC can significantly reduce the targeted attack success rate of physical patch attacks. Our code is available at https://github.com/joellliu/SegmentAndComplete. + +# 1. Introduction + +Object detection is an important computer vision task that plays a key role in many security-critical systems including autonomous driving, security surveillance, identity verification, and robot manufacturing [42]. Adversarial patch attacks, where the attacker distorts pixels within a region of bounded size, pose a serious threat to real-world object detection systems since they are easy to implement physi- + +![](images/fa8f72d5a53e95d6a23d7c4b88f6d0363ed61090c58a24e1547858bf40b79975.jpg) +Figure 1. We adopt a "detect and remove" strategy for defending object detectors against patch attacks. Left: Predictions on a clean image; middle: predictions on an adversarial image; right: predictions on SAC masked image. + +cally. For example, physical adversarial patches can make a stop sign [40] or a person [41] disappear from object detectors, which could cause serious consequences in security-critical settings such as autonomous driving. Despite the abundance [9,22,23,25,29,39-41,43,45,51] of adversarial patch attacks on object detectors, defenses against such attacks have not been extensively studied. Most existing defenses for patch attacks are restricted to image classification [16, 17, 24, 32, 34, 44, 46, 49]. Securing object detectors is more challenging due to the complexity of the task. + +In this paper, we present Segment and Complete (SAC) defense that can robustify any object detector against patch attacks without re-training the object detectors. We adopt a "detect and remove" strategy (Fig. 1): we detect adversarial patches and remove the area from input images, and then feed the masked images into the object detector. This is based on the following observation: while adversarial patches are localized, they can affect predictions not only locally but also on objects that are farther away in the image because object detection algorithms utilize spatial context for reasoning [38]. This effect is especially significant for deep learning models, as a small localized adversarial patch + +can significantly disturb feature maps on a large scale due to large receptive fields of neurons. By removing them from the images, we minimize the adverse effects of adversarial patches both locally and globally. + +The key of SAC is to robustly detect adversarial patches. We first train a patch segmenter to segment adversarial patches from the inputs and produce an initial patch mask. We propose a self adversarial training algorithm to enhance the robustness of the patch segmenter, which is efficient and object-detector agnostic. Since the attackers can potentially attack the segmenter and disturb its outputs under adaptive attacks, we further propose a robust shape completion algorithm that exploits the patch shape prior to ensure robust detection of adversarial patches. Shape completion takes the initial patch mask and generates a "completed patch mask" that is guaranteed to cover the entire adversarial patch, given that the initial patch mask is within a certain Hamming distance from the ground-truth patch mask. The overall pipeline of SAC is shown in Fig. 2. SAC achieves $45.0\%$ mAP under $100 \times 100$ patch attacks, providing $30.6\%$ mAP gain upon the undefended model while maintaining the same $49.0\%$ clean mAP on the COCO dataset. + +Besides digital domains, patch attacks have become a serious threat for object detectors in the physical world [9, 23, 39-41, 43, 45]. Developing and evaluating defenses against physical patch attacks require physical-patch datasets which are costly to create. To the best of our knowledge, APRICOT [6] is the only publicly available dataset of physical adversarial attacks on object detectors. However, APRICOT only provides bounding box annotations for each patch without pixel-level annotations. This hinders the development and evaluation of patch detection and removal techniques like SAC. To facilitate research in this direction, we create the APRICOT-Mask dataset, which provides segmentation masks and more accurate bounding boxes for adversarial patches in APRICOT. We train our patch segmenter with segmentation masks from APRICOT-Mask and show that SAC can effectively reduce the patch attack success rate from $7.97\%$ to $2.17\%$ . + +In summary, our contributions are as follows: + +- We propose Segment and Complete, a general method for defending object detectors against patch attacks via patch segmentation and a robust shape completion algorithm. +- We evaluate SAC on both digital and physical attacks. SAC achieves superior robustness under both non-adaptive and adaptive attacks with no reduction in performance on clean images, and generalizes well to unseen shapes, attack budgets, and unseen attack methods. +- We present the APRICOT-Mask dataset, which is the first publicly available dataset that provides pixel-level annotations of physical adversarial patches. + +# 2. Related Work + +# 2.1. Adversarial Patch Attacks + +Adversarial patch attacks are localized attacks that allow the attacker to distort a bounded region. Adversarial patch attacks were first proposed for image classifiers [7, 14, 20]. Since then, numerous adversarial patch attacks have been proposed to fool state-of-the-art object detectors including both digital [22, 25, 29, 38, 51] and physical attacks [9, 23, 39-41, 43, 45]. Patch attacks for object detection are more complicated than image classification due to the complexity of the task. The attacker can use different objective functions to achieve different attack effects such as object hiding, misclassification, and spurious detection. + +# 2.2. Defenses against Patch Attacks + +Many defenses have been proposed for image classifiers against patch attacks, including both empirical [16, 17, 32-34, 44] and certified defenses [24, 46, 49]. Local gradient smoothing (LGS) [33] is based on the observation that patch attacks introduce concentrated high-frequency noises and therefore proposes to perform gradient smoothing on regions with high gradients magnitude. Digital watermarking (DW) [17] finds unnaturally dense regions in the saliency map of the classifier and covers these regions to avoid their influence on classification. LGS and DW both use a similar detect and remove strategy as SAC. However, they detect patch regions based on predefined criteria, whereas SAC uses a learnable patch segmenter which is more powerful and can be combined with adversarial training to provide stronger robustness. In addition, we make use of the patch shape prior through shape completion. + +In the domain of object detection, most existing defenses focus on global perturbations with the $l_{p}$ norm constraint [8,10,50] and only a few defenses [19,38,47] for patch attacks have been proposed. These methods are designed for a specific type of patch attack or object detector, while SAC provides a more general defense. Saha [38] proposed Grad-defense and OOC defense for defending blindness attacks where the detector is blind to a specific object category chosen by the adversary. Ji et al. [19] proposed Ad-YOLO to defend human detection patch attacks by adding a patch class on YOLOv2 [35] detector such that it detects both the objects of interest and adversarial patches. DetectorGuard (DG) [47] is a provable defense against localized patch hiding attacks. Unlike SAC, DG does not localize or remove adversarial patches. It is an alerting algorithm that uses an objectness explainer that detects unexplained objectness for issuing alerts when attacked, while SAC solves the problem of "detection under adversarial patch attacks" that aims to improve model performance under attacks and is not limited to hiding attacks, although the patch mask detected by SAC can also be used as a signal for issuing attack alerts. + +![](images/9749ce97361351582ec5ea72cab116d8b2dc05a1420f2ee7c1e8ccc30ba529be.jpg) +Figure 2. Pipeline of the SAC approach. SAC detects and removes adversarial patches on pixel-level through patch segmentation and shape completion, and feeds the masked images into the base object detector for prediction. + +# 3. Preliminary + +# 3.1. Faster R-CNN Object Detector + +In this paper, we use Faster R-CNN [36] as our base object detector, though SAC is compatible with any object detector and we show the results for SSD [28] in the supplementary material. Faster R-CNN is a proposal-based two-stage object detector. In the first stage, a region proposal network (RPN) is used to generate class-agnostic candidate object bounding boxes called region proposals; in the second stage, a Fast R-CNN network [15] is used to output an object class and refine the bounding box coordinates for each region proposal. The total loss of Faster RCNN is the sum of bounding-box regression and classification losses of RPN and Fast R-CNN: + +$$ +\mathcal {L} ^ {\text {F a s t e r R - C N N}} = \mathcal {L} _ {\text {r e g}} ^ {\text {R P N}} + \mathcal {L} _ {\text {c l s}} ^ {\text {R P N}} + \mathcal {L} _ {\text {r e g}} ^ {\text {F a s t R - C N N}} + \mathcal {L} _ {\text {c l s}} ^ {\text {F a s t R - C N N}} \tag {1} +$$ + +# 3.2. Attack Formulation + +In this paper, we consider image- and location-specific untargeted patch attack for object detectors, which is strictly stronger than universal, location invariant attacks. Let $x \in [0,1]^{H \times W \times 3}$ be a clean image, where $H$ and $W$ are the height and width of $x$ . We solve the following optimization problem to find an adversarial patch: + +$$ +\hat {P} (x, l) = \underset {P \in \left\{P ^ {\prime}: \| P ^ {\prime} \| _ {\infty} \leq \epsilon \right\}} {\arg \max } \mathcal {L} \left(h \left(A (x, l, P)\right); y\right), \tag {2} +$$ + +where $h$ denotes an object detector, $A(x,l,P)$ is a "patch applying function" that adds patch $P$ to $x$ at location $l$ , $\| \cdot \|_{\infty}$ is $l_{\infty}$ norm, $\epsilon$ is the attack budget, $y$ is the ground-truth class and bounding box labels for objects in $x$ , and $\mathcal{L}$ is the loss function of the object detector. We use $\mathcal{L} = \mathcal{L}^{\mathrm{Faster~R - CNN}}$ for a general attack against Faster R-CNN. We solve Eq. (2) using the projected gradient descent (PGD) algorithm [30]: + +$$ +P ^ {t + 1} = \prod_ {\mathbb {P}} \left(P ^ {t} + \alpha \operatorname {s i g n} \left(\nabla_ {P ^ {t}} \mathcal {L} \left(h (A (x, l, P ^ {t}); y)\right)\right), \right. \tag {3} +$$ + +where $\alpha$ is the step size, $t$ is the iteration number, and $\prod$ is the projection function that projects $P$ to the feasible set + +$\mathbb{P} = \{P: \| P \|_{\infty} \leq \epsilon$ and $A(x, l, P) \in [0, 1]^{H \times W \times 3}\}$ . The adversarial image $x_{\mathrm{adv}}$ is given by: $x_{\mathrm{adv}} = A(x, l, \hat{P}(x, l))$ . + +We consider square patches $P \in \mathbb{R}^{s \times s \times 3}$ , where $s$ is the patch size, and apply one patch per image following previous works [20, 23, 29, 49]. We use an attack budget $\epsilon = 1$ that allows the attacker arbitrarily distort pixels within a patch without a constraint, which is the case for physical patch attacks and most digital patch attacks [7, 22, 25, 29, 38, 51]. + +# 4. Method + +SAC defends object detectors against adversarial patch attacks through detection and removal of adversarial patches in the input image $x$ . The pipeline of SAC is shown in Fig. 2. It consists of two steps: first, a patch segmenter (Sec. 4.1) generates initial patch masks $\hat{M}_{PS}$ and then a robust shape completion algorithm (Sec. 4.2) is used to produce the final patch masks $\hat{M}_{SC}$ . The masked image $\hat{x} = x \odot (1 - \hat{M}_{SC})$ is fed into the base object detector for prediction, where $\odot$ is the Hadamard product. + +# 4.1. Patch Segmentation + +Training with pre-generated adversarial images We formulate patch detection as a segmentation problem and train a U-Net [37] as the patch segmenter to provide initial patch masks. Let $PS_{\theta}$ be a patch segmenter parameterized by $\theta$ . We first generate a set of adversarial images $\mathcal{X}_{\mathrm{adv}}$ by attacking the base object detector with Eq. (2), and then use the pre-generated adversarial images $\mathcal{X}_{\mathrm{adv}}$ to train $PS_{\theta}$ : + +$$ +\min _ {\theta} \sum_ {x _ {\mathrm {a d v}} \in \mathcal {X} _ {\mathrm {a d v}}} \mathcal {L} _ {\mathrm {B C E}} \left(P S _ {\theta} \left(x _ {\mathrm {a d v}}\right), M\right) \tag {4} +$$ + +where $M$ is the ground-truth patch mask, $PS_{\theta}(x_{\mathrm{adv}})\in [0,1]^{H\times W}$ is the output probability map, and $\mathcal{L}_{\mathrm{BCE}}$ is the binary cross entropy loss: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {B C E}} (\hat {M}, M) = - \sum_ {i} ^ {H} \sum_ {j} ^ {W} \left[ M _ {i j} \cdot \log \hat {M} _ {i j} \right. \tag {5} \\ + (1 - M _ {i j}) \cdot \log (1 - \hat {M} _ {i j}) ]. \\ \end{array} +$$ + +Self adversarial training Training with $\mathcal{X}_{\mathrm{adv}}$ provides prior knowledge for $PS_{\theta}$ about "how adversarial patches look like". We further propose a self adversarial training algorithm to robustify $PS_{\theta}$ . Specifically, we attack $PS_{\theta}$ to generate adversarial patch $\hat{P}_{s - \mathrm{AT}}\in \mathbb{R}^{s\times s\times 3}$ : + +$$ +\hat {P} _ {\mathrm {s - A T}} (x, l) = \underset {P \in \left\{P ^ {\prime}: \| P ^ {\prime} \| _ {\infty} \leq \epsilon \right\}} {\arg \max } \mathcal {L} _ {\mathrm {B C E}} \left(P S _ {\theta} (A (x, l, P)), M\right), \tag {6} +$$ + +which is solved by PGD similar to Eq. (3). We train $PS_{\theta}$ in self adversarial training by solving: + +$$ +\begin{array}{l} \min _ {\theta} \left[ \lambda \mathbb {E} _ {x \sim \mathcal {D}} \mathcal {L} _ {\mathrm {B C E}} \left(P S _ {\theta} (x), M\right) \right. \\ \left. + (1 - \lambda) \mathbb {E} _ {x \sim \mathcal {D}, l \sim \mathcal {T}} \mathcal {L} _ {\mathrm {B C E}} \left(P S _ {\theta} \left(A (x, l, \hat {P} _ {\mathrm {s - A T}} (x, l))\right), M\right) \right], \tag {7} \\ \end{array} +$$ + +where $\mathcal{T}$ is the set of allowable patch locations, $\mathcal{D}$ is the image distribution, $M$ is the ground-truth mask, and $\lambda$ controls the weights between clean and adversarial images. + +One alternative is to train $PS_{\theta}$ with patches generated by Eq. (2). Compared to Eq. (2), Eq. (6) does not require external labels since the ground-truth mask $M$ is determined by $l$ and known. Indeed, Eq. (7) trains the patch segmenter in a manner that no external label is needed for both crafting the adversarial samples and training the model; it strengthens $PS_{\theta}$ to detect any "patch-like" area in the images. Moreover, Eq. (6) does not involve the object detector $h$ , which makes $PS_{\theta}$ object-detector agnostic and speeds up the optimization as the model size of $PS_{\theta}$ is much smaller than $h$ . + +The patch segmentation mask $\hat{M}_{PS}$ is obtained by thresholding the output of $PS_{\theta}$ : $\hat{M}_{PS} = PS_{\theta}(x) > 0.5$ + +# 4.2. Shape Completion + +# 4.2.1 Desired Properties + +If we know that the adversary is restricted to attacking a patch of a specific shape, such as a square, we can use this information to "fill in" the patch-segmentation output $\hat{M}_{PS}$ to cover the ground truth patch mask $M$ . We adopt a conservative approach: given $\hat{M}_{PS}$ , we would like to produce an output $\hat{M}_{SC}$ which entirely covers the true patch mask $M$ . In fact, we want to guarantee this property - however, if $\hat{M}_{PS}$ and $M$ differ arbitrarily, then we clearly cannot provide any such guarantee. Because both the ground-truth patch mask $M$ and the patch-segmentation output $\hat{M}_{PS}$ are binary vectors, it is natural to measure their difference as a Hamming distance $d_{H}(\hat{M}_{PS}, M)$ . To provide appropriate scale, we compare this quantity to the total magnitude of the ground-truth mask $\|M\|_H \coloneqq d_H(\mathbf{0}, M)$ . We therefore would like a patch completion algorithm with the following property: + +$$ +\text {I f} \frac {d _ {H} \left(\hat {M} _ {P S} , M\right)}{\| M \| _ {H}} \leq \gamma \text {t h e n} \forall i, j: \hat {M} _ {S C (i, j)} \geq M _ {(i, j)} \tag {8} +$$ + +![](images/381a62801df268d94e875a9a436eb1c3be90502f2e50c9c93a9d0b0f4a63ada0.jpg) +Figure 3. Construction of $\hat{M}_{SC}$ in Eq. (9): $\hat{M}_{SC}$ is the union of all candidate masks $M^{s,(i,j)}$ which are $\gamma$ -close to $\hat{M}_{PS}$ . If $M$ is $\gamma$ -close to $\hat{M}_{PS}$ , this guarantees that $M$ is covered by $\hat{M}_{SC}$ . + +# 4.2.2 Proposed Method + +If the size of the ground-truth patch is known, then we can satisfy Eq. (8), minimally, by construction. In particular, suppose that $M$ is known to be an $s \times s$ patch, and let $M^{s,(i,j)}$ refer to the mask of an $s \times s$ patch with upper-left corner at $(i,j)$ . Then Eq. (8) is minimally satisfied by the following mask: + +$$ +\hat {M} _ {S C (i, j)} := \left\{ \begin{array}{l l} 1 & \text {i f} \exists i ^ {\prime}, j ^ {\prime}: M _ {(i, j)} ^ {s, \left(i ^ {\prime}, j ^ {\prime}\right)} = 1 \text {a n d} \\ & \frac {d _ {H} \left(\hat {M} _ {P S} , M ^ {s , \left(i ^ {\prime} , j ^ {\prime}\right)}\right)}{s ^ {2}} \leq \gamma \\ 0 & \text {o t h e r w i s e .} \end{array} \right. \tag {9} +$$ + +where we have used that $\| M\| _H = s^2$ . In other words, we must cover every pixel within any $s\times s$ patch $M^{s,(i^{\prime},j^{\prime})}$ that is $\gamma$ -close to the observed mask $\hat{M}_{PS}$ , because any such patch may in fact be $M$ : a mask consisting of only these pixels is therefore the minimal mask necessary to satisfy Eq. (8). See Fig. 3 for an example. While Eq. (9) may appear daunting, there is a simple dynamic programming algorithm that allows the entire mask $\hat{M}_{SC}$ to be computed in $O(H\times W)$ time: this is presented in the supplementary material. + +# 4.2.3 Unknown Patch Sizes + +In Eq. (9), we assume that the ground-truth patch size $s$ is known; and is further parameterized by the distortion threshold $\gamma$ . Let $\hat{M}_{SC}(s, \gamma)$ represent this parameterized mask, as defined in Eq. (9). If we do not know $s$ , but instead have a set of possible patch sizes $S$ such that the true patch size $s \in S$ , then we can satisfy Eq. (8) by simply combining all of the masks generated for each possible value of $s$ : + +$$ +\hat {M} _ {S C} (S, \gamma) _ {(i, j)} := \bigvee_ {s \in S} \hat {M} _ {S C} (s, \gamma) _ {(i, j)} \tag {10} +$$ + +Eq. (10) is indeed again the minimal mask required to satisfy the constraint: a pixel $(i,j)$ is included in $\hat{M}_{SC}(\gamma)$ if and only if there exists some $M^{s,(i',j')}$ , for some $s\in S$ , such + +that $(i,j)$ is part of $M^{s,(i',j')}$ and $M^{s,(i',j')}$ is $\gamma$ -close to $\hat{M}_{PS}$ . In practice, this method can be highly sensitive to the hyperparameter $\gamma$ . To deal with this issue, we initially apply Eq. (10) with low values of $\gamma$ , and then gradually increase $\gamma$ if no mask is returned - stopping when either some mask is returned or a maximum value is reached, at which point we assume that there is no ground-truth adversarial patch. The details can be found in the supplementary material. + +# 4.2.4 Unknown Patch Shapes + +In some cases, we may not know the shape of the patch. Since the patch segmenter is agnostic to patch shape, we use the union of $\hat{M}_{PS}$ and $\hat{M}_{SC}$ as the final mask output: $\hat{M} = \hat{M}_{PS} \cup \hat{M}_{SC}$ . We empirically evaluate the effectiveness of this approach in Sec. 5.3.4. + +# 5. Evaluation on Digital Attacks + +In this section, we evaluate the robustness of SAC on digital patch attacks. We consider both non-adaptive and adaptive attacks, and demonstrate the generalizability of SAC. + +# 5.1. Evaluation Settings + +We use COCO [27] and xView [21] datasets in our experiments. COCO is a common object detection dataset while xView is a large public dataset of overhead imagery. For each dataset, we evaluate model robustness on 1000 test images and report mean Average Precision (mAP) at Intersection over Union (IoU) 0.5. For attacking, we iterate 200 steps with a set step size $\alpha = 0.01$ . The patch location $l$ is randomly selected within each image. We evaluate three rounds with different random patch locations and report the mean and standard deviation of mAP. + +# 5.2. Implementation Details + +All experiments are conducted on a server with ten GeForce RTX 2080 Ti GPUs. For base object detectors, we use Faster-RCNN [36] with feature pyramid network (RPN) [26] and ResNet-50 [18] backbone. We use the pretrained model provided in torchvision [31] for COCO and the model provided in armory [1] for xView. For patch segmenter, we use U-Net [37] with sixteen initial filters. To train the patch segmenters, for each dataset we generate $55\mathrm{k}$ fixed adversarial images from the training set with patch size $100 \times 100$ . Training on pre-generated adversarial images took around three hours on a single GPU. For self adversarial training, we train each model for one epoch by Eq. (7) using PGD attacks with 200 iterations and step size $\alpha = 0.01$ with $\lambda = 0.3$ , which takes around eight hours on COCO and four hours on xView using ten GPUs. For patch completion, we use a square shape prior and the possible patch sizes $S = \{25, 50, 75, 100\}$ for xView and + +$S = \{25, 50, 75, 100, 125\}$ for COCO. More details can be found in the supplementary material. + +# 5.3. Robustness Analysis + +# 5.3.1 Baselines + +We compare the proposed method with vanilla adversarial training (AT), JPEG compression [13], spatial smoothing [48], and LGS [33]. For AT, we use PGD attacks with thirty iterations and step size 0.067, which takes around twelve hours per epoch on the xView training set and thirty-two hours on COCO using ten GPUs. Due to the huge computational cost, we adversarially train Faster-RCNN models for ten epochs with pre-training on clean images. More details can be found in the supplementary material. + +# 5.3.2 Non-adaptive Attack + +The defense performance under non-adaptive attacks is shown in Tab. 1, where the attacker only attacks the object detectors. SAC is very robust across different patch sizes on both datasets and has the highest mAP compared to baselines. In addition, SAC maintains high clean performance as the undefended model. Fig. 4 shows two examples of object detection results before and after SAC defense. Adversarial patches create spurious detections and hide foreground objects. SAC masks out adversarial patches and restores model predictions. We provide more examples as well as some failure cases of SAC in the supplementary material. + +# 5.3.3 Adaptive Attack + +We further evaluate the defense performance under adaptive attacks where the adversary attacks the whole object detection pipeline. To adaptively attack preprocessing-based baselines (JPEG compression, spatial smoothing, and LGS), we use BPDA [4] assuming the output of each defense approximately equals to the original input. To adaptively attack SAC, we use straight-through estimators (STE) [5] when backpropagating through the thresholding operations, which is the strongest adaptive attack we have found for SAC (see the supplementary material for details). The results are shown in Tab. 1. The performances of preprocessing-based baselines drop a lot under adaptive attacks. AT achieves the strongest robustness among the baselines while sacrificing clean performance. The robustness of SAC has little drop under adaptive attacks and significantly outperforms the baselines. Since adaptive attacks are stronger than non-adaptive attacks, we only use adaptive attacks for the rest of the experiments. + +# 5.3.4 Generalizability of SAC + +Generalization to unseen shapes We train the patch segmenter with square patches and use the square shape prior + +Table 1. mAP (%) under non-adaptive and adaptive attacks with different patch sizes. The best performance of each column is in bold. + +
DatasetMethodCleanNon-adaptive AttackAdaptive Attack
75×75100×100125×12575×75100×100125×125
COCOUndefended49.019.8±1.014.4±0.69.9±0.519.8±1.014.4±0.69.9±0.5
AT [30]40.223.5±0.718.6±0.813.9±0.323.5±0.718.6±0.813.9±0.3
JPEG [13]45.639.7±0.337.2±0.333.3±0.422.8±0.918.0±0.813.4±0.7
Spatial Smoothing [48]46.040.4±0.638.1±0.634.3±0.123.2±0.717.5±1.013.5±0.6
LGS [33]42.736.8±0.135.2±0.632.8±0.920.8±0.715.9±0.512.2±0.9
SAC (Ours)49.045.7±0.345.0±0.640.7±1.043.6±0.944.0±0.339.2±0.7
DatasetMethodCleanNon-adaptive AttackAdaptive Attack
50×5075×75100×10050×5075×75100×100
xViewUndefended27.28.4±1.67.1±0.45.3±1.18.4±1.67.1±0.45.3±1.1
AT [30]22.212.1±0.48.6±0.17.2±0.712.1±0.48.6±0.17.15±0.7
JPEG [13]23.319.3±0.417.8±1.015.9±0.411.2±0.39.5±1.08.3±0.3
Spatial Smoothing [48]21.816.2±0.714.2±1.112.4±0.811.0±0.77.9±0.66.5±0.2
LGS [33]19.111.9±0.510.9±0.39.8±0.58.2±0.86.5±0.45.4±0.5
SAC (Ours)27.225.3±0.323.6±1.223.2±0.324.4±0.823.0±0.922.1±0.6
+ +![](images/d361025d132904a14c6c399b60e3293b77fe616f75e12eb5e24ed1fc8d70c043.jpg) + +![](images/cc03740fe0fcc826ad49d48ab49629e03dff35b5fb308d2f1f77eae57d5f3bae.jpg) +(a) Ground-truth on clean image. + +![](images/3468ac251e778602965c2debe8d2bc3ff7341dec48561a0e0b209a05a280c816.jpg) + +![](images/43e9503592d3ba1fef61f75a4b4b44de6e539ff5fd34f393cf45651db25f37cc.jpg) +(b) Predictions on clean image. + +![](images/5bf277a876c5da15dee4a13bfdb3d6b21e681f68a7fc9e51b57751d5f161121f.jpg) + +![](images/126789911b0aa8f37ca94e16a0ad97547a8a3f58ff9d0b8b693dbcfe58f7c1d0.jpg) +(c) Predictions on adversarial image with a $100 \times 100$ patch. +Figure 4. Visualization of object detection results with examples from COCO dataset (top) and xView dataset (bottom). Adversarial patches create spurious detections, and make the detector ignore the ground-truth objects. SAC masks out the patch and restores model predictions. + +![](images/dca2b977923371bfa9caf0c1fed35c9c2fd41914cee0d412295f3aa3facc83f5.jpg) + +![](images/9fec3a3262f8e22fb7cafdf7374735a892e5db6df9bdbfba2b59f71df7bad0a4.jpg) +(d) Predictions on SAC masked image. + +in shape completion. Since adversarial patches may not always be square in the real world, we further evaluate square-trained SAC with adversarial patches of different shapes while fixing the number of pixels in the patch. The details of the shapes used can be found in the supplementary material. We use the union of $\hat{M}_{PS}$ and $\hat{M}_{SC}$ as described in Sec. 4.2.4. The results are shown in Fig. 5. SAC demonstrates strong robustness under rectangle, circle, diamond, triangle, and ellipse patch attacks, even though these shapes + +mismatch with the square shape prior used in SAC. + +Generalization to attack budgets In Eq. (2), we set $\epsilon = 1$ that allows the attacker to arbitrarily modify the pixel values within the patch region. In practice, the attacker may lower the attack budget to generate less visible adversarial patches to evade patch detection in SAC. To test how SAC generalizes to lower attack budgets, we evaluate SAC trained on $\epsilon = 1$ under lower $\epsilon$ values on the xView dataset. We set + +![](images/2db8df0a093cb37a4a232c06fa724e98d1fdd23f60e07d2793bcfc99eab68ace.jpg) +(a) xView dataset. + +![](images/cd8dc7066c7a7b5a57eea0a63d9f8124508920aa374f98f8ae53d827440d9cc5.jpg) +(b) COCO dataset. +Figure 5. Performance of SAC under adaptive attacks with different patch shapes and sizes. SAC demonstrates strong robustness under rectangle, circle and ellipse patch attacks, even though these shapes mismatch with the square shape prior used in SAC. + +![](images/630add66b5a29bcd82a3ccaa198750636e5855d79c31f5993c17763a0d72f7f9.jpg) +Figure 6. SAC performance under different attack budgets on xView dataset. SAC is trained with $\epsilon = 1$ . + +iteration steps to 200 and step size to $\epsilon / 200$ . Fig. 6 shows that SAC remains robust under a wide range of $\epsilon$ . Although the performance of SAC degrades when $\epsilon$ becomes smaller because patches become imperceptible, SAC still provides significant robustness gain upon undefended models. In addition, SAC is flexible and we can use smaller $\epsilon$ in training to provide better protection against imperceptible patches. + +Generalization to unseen attack methods In the previous sections, we use PGD (Eq. (3)) to create adversarial patches. We further evaluate SAC under unseen attack methods, including DPatch [29] and MIM [12] attack. We use 200 iterations for both attacks, and set the learning rate to 0.01 for DPatch and decay factor $\mu = 1.0$ for MIM. The performance is shown in Tab. 2. SAC achieves more than $40.0\%$ mAP on COCO and $21\%$ mAP on xView under both attacks, providing strong robustness upon undefended models. + +# 5.4. Ablation Study + +In this section, we investigate the effect of each component of SAC. We consider three models: 1) patch segmenter trained with pre-generated adversarial images (PS); 2) PS further trained with self adversarial training (self AT); 3) Self + +Table 2. mAP (%) under adaptive unseen attack methods with different patch sizes. + +
AttackMethod75×75100×100125×125
COCODPatch [29]Undefended33.6±0.829.1±0.625.0±1.7
SAC (Ours)45.3±0.344.1±0.642.1±0.8
MIM [12]Undefended20.1±1.214.2±0.810.5±0.2
SAC (Ours)42.2±0.943.5±1.040.0±0.2
AttackMethod50×5075×75100×100
xViewDPatch [29]Undefended16.0±0.513.4±0.911.1±0.9
SAC (Ours)25.3±0.522.7±1.121.8±0.5
MIM [12]Undefended8.3±0.47.3±0.86.5±1.5
SAC (Ours)24.7±0.723.0±0.922.1±0.6
+ +Table 3. mAP (%) under adaptive attacks of ablated models. + +
Method75×75100×100125×125
COCOUndefended19.8±1.014.4±0.69.9±0.5
PS23.3±0.718.7±0.313.1±0.3
+ self AT41.5±0.240.5±0.636.6±0.1
+ SC43.6±0.944.0±0.339.2±0.7
Method50×5075×75100×100
xViewUndefended8.4±1.67.1±0.45.3±1.1
PS16.8±0.613.6±0.411.1±0.3
+ self AT20.6±0.417.6±0.515.4±0.6
+ SC24.4±0.823.0±0.922.1±0.6
+ +AT trained PS combining with shape completion (SC), which is the whole SAC defense. The performance of these models under adaptive attacks is shown in Tab. 3. PS alone achieves good robustness under adaptive attacks (comparable or even better performance than the baselines in Tab. 1) thanks to the inherent robustness of segmentation models [3, 11]. Self AT significantly boosts the robustness, especially on the COCO dataset. SC further improves the robustness. Interestingly, we find that adaptive attacks on models with SC would force the attacker to generate patches that have more structured noises trying to fool SC (see supplementary material). + +# 6. Evaluation on Physical Attack + +In this section, we evaluate the robustness of SAC on physical patch attacks. We first introduce the APRICOT-Mask dataset and further demonstrate the effectiveness of SAC on the APRICOT dataset. + +# 6.1. APRICOT-Mask Dataset + +APRICOT [6] contains 1,011 images of sixty unique physical adversarial patches photographed in the real world, of which six patches (138 photos) are in the development + +set, and the other fifty-four patches (873 photos) are in the test set. APRICOT provides bounding box annotations for each patch. However, there is no pixel-level annotation of the patches. We present the APRICOT-Mask dataset1, which provides segmentation masks and more accurate bounding boxes for adversarial patches in the APRICOT dataset (see two examples in Fig. 7). The segmentation masks are annotated by three annotators using Labelbox [2] and manually reviewed to ensure the annotation quality. The bounding boxes are then generated automatically from the segmentation masks. We hope APRICOT-Mask along with the APRICOT dataset can facilitate the research in building defenses against physical patch attacks, especially patch detection and removal techniques. + +![](images/4f5b38a28f7943174840cb1d759fa161e242a24d054284a95d7e6a30a0a8a8c6.jpg) +Figure 7. Images and patch annotations from the APRICOT and APRICOT-Mask datasets. Left: adversarial images from the APRICOT dataset; middle: patch bounding boxes provided by the APRICOT dataset; right: patch bounding boxes and segmentation masks provided by the APRICOT-Mask dataset. + +![](images/915d5efb993f8d34da667cf9c1a3461da7e04d0bc7501bf0616ff93fcab46a31.jpg) + +![](images/c584a1bf944d47e1000ace8695e01c32b18fe5952b3ec6222221b5cdee285b45.jpg) + +# 6.2. Robustness Evaluation + +Evaluation Metrics We evaluate the defense effectiveness by the targeted attack success rate. A patch attack is "successful" if the object detector generates a detection that overlaps a ground truth adversarial patch bounding box with an IoU of at least 0.10, has a confidence score greater than 0.30, and is classified as the same object class as the patch's target [6]. + +Evaluation Results We train the patch segmenter on the APRICOT test set using the segmentation masks from the APRICOT-Mask dataset. The training details can be found in the supplementary material. Since APRICOT patches are generated from three detection models trained on the COCO dataset targeting ten COCO object categories, we use a Faster-RCNN model pretrained on COCO [31] as our base object detector, which is a black-box attack setting with target and substitute models trained on the same dataset. We evaluate the targeted attack success rate on the development + +![](images/77b1f426902522f445b8fb645c8f9880693f0869010e807f0baa58d612034f06.jpg) +Figure 8. Targeted attack success rates on the APRICOT dataset. + +set and compare SAC with the baselines as in Sec. 5.3.1. For AT, we use the Faster-RCNN model adversarially trained on the COCO dataset (AT-COCO) as the size of the APRICOT dataset is not enough to retrain an object detector. The results are shown in Fig. 8. SAC significantly brings down the targeted attack success rate of the undefended model from $7.97\%$ to $2.17\%$ , which is the lowest among all defense methods. AT has a slightly higher targeted attack success rate than the undefended model, which may be due to the domain gap between COCO and APRICOT datasets. + +# 7. Discussion and Conclusion + +In this paper, we propose the Segment and Complete defense that can secure any object detector against patch attacks by robustly detecting and removing adversarial patches from input images. We train a robust patch segmenter and exploit patch shape priors through a shape completion algorithm. Our evaluation on digital and physical attacks demonstrates the effectiveness of SAC. In addition, we present the APRICOT-Mask dataset to facilitate the research in building defenses against physical patch attacks. + +SAC can be improved in several ways. First, although SAC does not require re-training of base object detectors, fine-tuning them on images with randomly-placed black blocks can further improve their performance on SAC masked images. Second, in this paper, we adopt a conservative approach that masks out the entire patch region after we detect the patch. This would not cause information loss when the attacker is allowed to arbitrarily distort the pixels and destroy all the information within the patch such as in physical patch attacks. However, in the case where the patches are less visible, some information may be preserved in the patched area. 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Object hider: Adversarial patch attack against object detectors. arXiv preprint arXiv:2010.14974, 2020. 1, 2, 3 \ No newline at end of file diff --git a/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/images.zip b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..58f431b2e1fde535f9f4bddeb512085e19c20a32 --- /dev/null +++ b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cdb71d7b2d8f62714576bf966b81a86ae37de73c5d5a051e145da30bf01c9fc9 +size 735144 diff --git a/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/layout.json b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d753aafd5122702816f012355d95b4d167cd4760 --- /dev/null +++ b/segmentandcompletedefendingobjectdetectorsagainstadversarialpatchattackswithrobustpatchdetection/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:60ad77950183b34f1f4be70a93fb03657336b0bd0c755b966cfac082d3336fd0 +size 451164 diff --git a/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_content_list.json b/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..63bda7e7a2856e048eca67d5f730dca5d2beaf13 --- /dev/null +++ b/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:16c84533e84f720d5c2f9b13abc17da5ac668856947097443003a91836c30af2 +size 74314 diff --git a/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_model.json b/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f342f0d539c17408a50737f9863c90deeb6a6de2 --- /dev/null +++ b/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5f56b53c8045d5f95cea811b02f936c88a39626c60508265f7e6753dfea95b0b +size 90917 diff --git a/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_origin.pdf b/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1cc4d21c1033d075065dc25cb20e7eab89521a08 --- /dev/null +++ b/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/7a0dc952-63c4-42c6-88dc-54474cb84c0a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:de1381a5b0aace71bc5accbfa4efd262f7c1d793f4c9551c84cecbe38d6223b5 +size 2250549 diff --git a/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/full.md b/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ab0672c521874c75642f8ba4caed1ad83a812091 --- /dev/null +++ b/segmentfusionhierarchicalcontextfusionforrobust3dsemanticsegmentation/full.md @@ -0,0 +1,304 @@ +# Segment-Fusion: Hierarchical Context Fusion for Robust 3D Semantic Segmentation + +Anirud Thyagharajan1, Benjamin Ummenhofer2, Prashant Laddha1, Om Ji Omer1, Sreenivas Subramoney1 +{1Processor Architecture Research Lab India, 2Autonomous Agents Lab Germany}, Intel Labs + +# Abstract + +3D semantic segmentation is a fundamental building block for several scene understanding applications such as autonomous driving, robotics and AR/VR. Several state-of-the-art semantic segmentation models suffer from the part-misclassification problem, wherein parts of the same object are labelled incorrectly. Previous methods have utilized hierarchical, iterative methods to fuse semantic and instance information, but they lack learnability in context fusion, and are computationally complex and heuristic driven. This paper presents Segment-Fusion, a novel attention-based method for hierarchical fusion of semantic and instance information to address the part misclassifications. The presented method includes a graph segmentation algorithm for grouping points into segments that pools point-wise features into segment-wise features, a learnable attention-based network to fuse these segments based on their semantic and instance features, and followed by a simple yet effective connected component labelling algorithm to convert segment features to instance labels. Segment-Fusion can be flexibly employed with any network architecture for semantic/instance segmentation. It improves the qualitative and quantitative performance of several semantic segmentation backbones by upto $5\%$ on the ScanNet and S3DIS datasets. + +# 1. Introduction + +The growing resolution and availability of 3D visual sensors in recent years (e.g. Kinect, RealSense, Xtion) have enabled high fidelity representation of real world scenes using 3D data, allowing machines to understand 3D scenes with higher accuracy. One of the most important tasks in scene understanding includes 3D semantic segmentation, which aims to recognize the object class that each point in the scene belongs to. 3D semantic segmentation is fundamental to various applications, such as autonomous driving, robotic navigation and AR/VR [11,28,31,38]. + +![](images/db4a7f61c6ef06909080392cc83c0b43f98d0207935cfe3003356d93222065da.jpg) +Figure 1. Semantic labels with baseline [37] and our Segment-Fusion approach on a sample point cloud from ScanNet Validation set [5]. The circled regions highlight how well Segment-Fusion addresses the part misclassification problem prevailing in many state-of-the-art semantic segmentation methods. + +Recent advancements in 3D scene understanding have been greatly influenced by deep neural networks achieving state-of-the-art results [3,9,10,15-17,20,23,34,37] on multiple benchmarks and wide range of datasets [1, 5]. However, many of these methods are often plagued by the part-misclassification problem, where parts of the same object are labelled incorrectly as shown in Figure 1. This problem can be better addressed if object instance boundaries can be correctly estimated, which includes annotating points with object instance identifiers. This helps to group all points associated with an object instance and utilize consensus to rectify semantic mispredictions. + +Jointly solving semantic and instance segmentation has been explored by several previous works [2, 7, 12, 13, 18, 22, 24, 35, 36]. Many of these methods [13, 18, 24, 35, 36] focus on employing models for instance and semantic segmentation, before fusing pointwise features. However, they require higher compute resources as they fuse at a fine-grained level and do not exploit local continuities in scene structure. Methods such as [2, 7, 12, 22] include hierarchical pooling of features over a spatial region addressing the part misclassification problem by fusing these regions, with an assumption that these regions do not stretch over object boundaries. Such hierarchical methods are more efficient since they work with regions and not directly with points. While such methods are more efficient, they employ itera + +![](images/7297a884cc454aa27bd155a45ac40ece0fe4f3ff736caf20de0accf26c6df448.jpg) +Figure 2. Overview of the Segment-Fusion approach. The Graph Segmentation module (GS) groups points into segments and enables pooling pointwise semantic and instance features $\mathbf{S}$ , $\mathbf{I}$ into segment-wise features $\bar{\mathbf{S}}$ , $\bar{\mathbf{I}}$ . The Segment Fusion Network maps these features to a common feature space $\bar{\mathbf{F}}$ which is then used in the connected component labelling algorithm (CCL) to create the final set of segments. + +tive clustering and aggregation techniques that are known to be heuristic-driven, non-learnable and specific to the backbone models used for extracting semantic and instance features. They also use complex post-processing [6, 27] to transform instance features to labels. Thus, there is a need for hierarchical, learnable methods for fusing such regions with simple post-processing. + +Our prime objective is to improve semantic segmentation performance of a generic semantic segmentation model by using a hierarchical fusion of semantic and instance information. We use a graph segmentation algorithm to group points into regions and pool region-wise semantic and instance features but downstream, we propose a learnable clustering algorithm. It is desirable that the method should be learnable and agnostic to dataset specific heuristics. + +- We propose a graph segmentation algorithm optimized for semantic segmentation across datasets, which is used to compose semantic and instance features at a coarser level (which we term as segments). +- We propose a learnable attention based network, Segment Fusion, to hierarchically fuse segments based on the similarity of their semantic and instance features, thus understanding the appropriate granularity of context (local to global: points to instance to scene). +- Our approach offers the advantages of adapting to inputs from other datasets and other backbones, as well as offering the possibility to perform end-to-end training and maintain efficiency (while working on a hierarchically smaller representation, and not working on individual points). These proposals help ameliorate the problem of part-misclassification by improving the performance (mIoU) of multiple semantic backbones on datasets like ScanNet [5] and S3DIS [1] upto $5\%$ . + +We also compare the impact of our proposed method with the iterative clustering method proposed by Occuseg [12] and report $1 - 2\%$ mIoU improvement in semantic segmentation. + +# 2. Related Work + +3D Semantic Segmentation. Semantic segmentation techniques can be broadly classified into 2D projection based and 3D methods. Methods that use 3D processing are known to provide superior accuracy because they can naturally overcome occlusion or scale ambiguity [12]. Several 3D methods have been proposed for semantic segmentation, which can be further categorized into point-based [25, 26] and volumetric methods [3, 10, 15-17, 34]. Methods from the PointNet family [25, 26] work on unstructured point clouds directly, employing pointwise networks to extract features and using ball queries and hierarchical grouping to encode spatial locality. + +On the other hand, volumetric methods voxelize point clouds into regular grids and process them with regular structured computations. SparseConvNet [10] proposed submanifold sparse convolutions to process only the active voxels in a scene, while MinkowskiNet [3] generalized this concept with the help of hybrid kernels to express different types of local structure. Apart from these classes of methods, hybrid methods that utilize deformable/parametric convolutions [30] on points have been proposed, in addition to employing graph convolutions [14, 33, 39] on points. All the above models apply voxel/point-wise cross entropy loss to optimize the model weights. Even though they employ network topologies such as U-Nets that are intended to comprehend scale and local-to-global structure, they exhibit part-misclassification issues as observed in Figure 3. Therefore, the model needs additional information about which instance of the object each point is a part of. + +![](images/683d35be612ccb7a2dee73397923e1f4230be8b8cae57714aa9b150eed53c2cd.jpg) +Figure 3. Illustrations of the part misclassification problem while using SCN [10] ( $1^{\text{st}}$ row) and MinkowskiNet [3] ( $2^{\text{nd}}$ row) as backbones for semantic predictions on the ScanNet dataset [5]. + +Joint Semantic-Instance Segmentation. Instance segmentation techniques aim to predict features for every point that indicate the object with which it is associated. Several methods have been proposed to perform semantic and instance segmentation jointly, since there is shared context between two similar tasks. Methods such as ASIS [36], SGPN [35] and JSIS3D [24] exercise models to fuse semantic and instance features pointwise, and subsequently compute the instance labels through clustering algorithms; ASIS [36] uses mean-shift clustering, SGPN [35] uses NMS to filter proposals and JSIS3D [24] uses a CRF to cluster instance embeddings into labels. However, these methods are heuristic driven (eg. mean-shift clustering [6] depends upon the window size) and are computationally complex (since they work with the pointwise features). + +Works such as Occuseg, 3D-MPA, HAIS and SPG [2, 7, 21] simplify this complexity by grouping features at a higher abstractive level of surfaces (than points), thus proposing hierarchically fusing these features to form instances. Occuseg [12] computes instance and semantic features per supervoxel, where supervoxels are composed using a graph segmentation scheme [8], which are fed to an iterative clustering algorithm to merge supervoxels into instances. 3D-MPA [7] samples keypoints through a deep voting scheme, uses a graph convolutional network to refine the keypoint features, which are fed to DBSCAN [27] to obtain instance labels. HAIS [2] proposed a hierarchical method to generate point sets (based on the semantic features) and employ an iterative set aggregation algorithm to aggregate these point sets into instances. SST-Net [22] propose a tree classifier to hierarchically build a subtree of superpoint proposals. SPG [21] propose a graph convolutional network to learn relationships between abstracted surfaces. + +While these methods may be effective for certain datasets, they propose iterative algorithms, which are not learnable. This makes it difficult for the algorithm to generalize for multiple sets of input features and/or datasets. Eventhough 3D-MPA uses a graph convolutional layer to refine the higher-level features, (a) they work with a fixed number of proposals in a scene (due to the deep voting + +![](images/486740c09ad966d6d0aa7114c06a515082e55ea4c894de6a241a30237c9de004.jpg) +Figure 4. Impact of proposed J-GS method on an example S3DIS point cloud. As observed in (1) [8], graph segmentation purely based on difference in normals fails to recognise the boundary between the door and the wall, while augmenting it with color information helps in discerning this (J-GS (2)). + +scheme) which does not scale with scenes, and (b) they eventually use a heuristic driven classifier (DBSCAN [27]) after the refinement. SPG [21] utilizes only abstracted information at the level of surfaces and does not incorporate instance-level information. + +Graph Segmentation for hierarchical processing. As discussed above, graph segmentation algorithms [8] have been used previously to group points into larger regions (based on normal-similarity) and work at the abstraction level of these regions. It is observed that representations in higher-level abstractions such as these segments offer geometric continuity, since they ensures that the variation in point normals in a segment is bounded. Graph segmentation solely based on normals is effective but in some datasets, normals across object boundaries are not distinctive enough, as seen in Figure 4. This problem cannot be solved by lowering threshold for discriminating normals, because it leads to a highly over-segmented graph and defeats the purpose of hierarchical processing. Previous work [29] aims to solve this problem by performing segmentation using dissimilarity in normals and colors, but does not generalize for other kinds of features, or propose methods for selecting the thresholds for normals/colors. + +Ideally, a semantic-instance fusion algorithm should have the following desirable properties: + +- Hierarchical. To be efficient, the system should abstract features from the points level to a higher-level spatial representation (segments: eg. surfaces, groups of points) and process at this level. +- Learnable. The fusion of features from segments to instances should incorporate a learnable model to adapt to a variety of scenarios across datasets and underlying backbones for semantic and instance features. +- Non-heuristic labelling. The task of converting instance features to labels should be done simplistically + +to avoid imparting any heuristic driven processing and absorb learning to the learnable component. + +# 3. Methods + +We present an overview of our method in Figure 2 that incorporates the desirable properties discussed in Section 2. The proposed method assumes a (i) semantic model that emits per-point semantic features $\mathbf{S}$ and (ii) an instance model that emits per-point instance features $\mathbf{I}$ . Our method applies equivocally to those networks as well where these models could be sharing a common backbone network. For instance models like Occuseg [12] that emit multiple types of embeddings (eg. instance embeddings, centroid and occupancy estimates), $\mathbf{I}$ can be thought of as a concatenation of such features pointwise. In general, if $\mathbf{X}$ denotes any point-wise features, the corresponding segment-wise features are denoted by $\overline{\mathbf{X}}$ . + +# 3.1. Joint Graph Segmentation (J-GS) + +We propose a hierarchical strategy, segmenting points into 3D segments (surfaces or super-voxels) using efficient graph segmentation algorithms such as [8, 19, 29]. The input graph is defined by vertices (points $\mathcal{P}$ ) joined by edges (neighbors $E$ ), where the goal of the segmentation is to find a mapping $\mathcal{J}$ that assigns the same segment ID to a set of grouped points. It also records the connections $(\mathcal{E})$ between the segments, represented by an adjacency matrix $\mathbf{A}$ . + +To cover a gamut of datasets, we generalize our graph segmentation algorithm to work across two options: + +- Point clouds without mesh information. Datasets like ScanNet [5] have mesh information available, which allows us to compute per vertex normals $\mathcal{N}$ from the adjacent polygonal faces. However, for datasets like S3DIS [1] which do not have such connectivity information, we propose obtaining normals using plane-fitting techniques, as obtaining mesh information would incur additional expensive preprocessing (Figure 5). +- Indiscriminative Normals. We propose to generalize this method across datasets over previous work [29] by (a) allowing to use arbitrary pointwise features $\mathcal{F}$ (not specifically colors) in addition to normals, and then performing a joint segmentation over two spaces $(\mathcal{F}$ and $\mathcal{N})$ , as shown in Algorithm 1. An example using colors as $\mathcal{F}$ for the S3DIS dataset is shown in Figure 4. (b) we generalize sorting orders ( $s: \{\text{norm, feats}\}$ , choosing to sort edges along similarity in $\mathcal{N}$ or $\mathcal{F}$ ), and (c) we employ a voting-based methodology (see Algorithm 2) to decide the optimal similarity threshold for a generic dataset for the semantic segmentation task. + +In Algorithm 1, computeEdgeWeights computes dissimilarity scores along $\mathcal{N}$ (cosine product) and $\mathcal{F}(\ell_1 / \ell_2$ + +norms). updateThresh is similar to previous work [29] where the threshold slightly increases to accommodate a growing segment, where it approaches the largest intra-segment weight. + +Though the proposed method (shown in Figure 4) may lead to over-segmentation of input scene, it ensures that points belonging to different objects are allotted to different segments. It avoids segment boundaries to cross-over object instance boundaries. + +Algorithm 1 Proposed Graph Segmentation +Inputs: Normals $\mathcal{N}$ ,Features $\mathcal{F}$ ,Polygonal edges $E$ ,feature and normal similarity thresholds $(f_{th},n_{th})$ ,sort-flag (s) +1: function SEGMENTGRAPH(N,F,E,nth,fth,s) +2: $E_{wn},E_{wf}\gets$ computeEdgeWeights(N,F) +3: $E\gets$ sortEdgesByNormalsOrFeats(s) +4: $t h_{f},t h_{n}\gets f_{t h},n_{t h}$ initialize threshold vectors +5: $\mathcal{J}\gets$ initUnionFind(E) +6: for $e_{ij}\in E$ do edge joining ith and jth points +7: $S_{i}\gets \mathcal{J}$ .find(i) +8: $S_{j}\gets \mathcal{J}$ .find(j) +9: $e_{wn},e_{wf}\gets E_{wn}[i,j],E_{wf}[i,j]$ edge weights +10: if $(e_{wn} < th_n[i],th_n[j])$ and $(e_{wf} < th_f[i],th_f[j])$ then +11: $newID\leftarrow \mathcal{J}$ .join(i,j) +12: updateThresh(e wn,e wf,thn,thf,newID) +13: end if +14: end for +15: return $\mathcal{J}$ +16: end function + +Algorithm 2 Graph Segmentation based Voting algorithm +Inputs: List of J-GS Params $g_{j} = (n_{th},f_{th},s)$ , predicted semantic la- +bels S, groundtruth labels G function J-GSV(GP,S) init scores for $g_{j}$ in GP do $\mathcal{I}_j\gets$ SEGMENT.GRAPH $(g_j)$ $\mathbf{S}_{j,maj}\gets$ majorityVoting $(\mathcal{I}_j,\mathbf{S})$ scores[j] $\leftarrow$ getIoU(Sj,maj,G) end for return argmin(scores) end function Datasets with meshed faces (e.g. ScanNet) 1 +Points GS (original; internally +Features GS (direct +kNN neighbours LS $\rightarrow$ $\Phi (\mathcal{J})\rightarrow \bar{\mathbf{S}}$ +meshing info (faces) e.g. S3DIS I $\rightarrow$ $\Phi (\mathcal{J})\rightarrow \overline{\mathbf{I}}$ + +Figure 5. Proposed flow for generalizing graph segmentation across a variety of point cloud datasets. + +To select the right variant for given dataset, we enable quantitative comparison across the above options by proposing the J-GSV score (Joint Graph Segmentation-based Voting) (Algorithm 2). Across point clouds from the training set, for the $j$ -th variant, we obtain a list of sets of points $\mathcal{I}_j$ , with the $i$ -th set $\mathcal{I}_{j,i}$ containing points pertaining to the same segment. We compute the semantic predictions for the $j$ -th variant by pooling the per-point semantic predictions $\mathbf{S}$ for each segment, and broadcasting the majority label to all points in the segment. The mean Intersection-over-Union (mIoU) for the modified semantic predictions $\mathbf{S}_{j,maj}$ is the score associated with the $j$ -th variant. For the dataset, we select the variant with the highest score and denote by $\mathcal{I}^*$ . Consequently, we employ a differentiable function $\phi$ , to transform pointwise features to segment-wise features $(\overline{\mathbf{X}} = \phi(\mathbf{X}, \mathcal{I}^*))$ . To simplify, our implementation of $\phi(.)$ is the mean function, average-pooling across pointwise semantic and instance features $(\mathbf{S}, \mathbf{I})$ to obtain segment-wise features $(\overline{\mathbf{S}}, \overline{\mathbf{I}})$ , similar to [12]. For pointwise features $\mathbf{X}$ we get the feature for a segment as + +$$ +\overline {{\mathbf {X} _ {i}}} = \frac {1}{| \mathcal {J} _ {i} |} \sum_ {j \in \mathcal {J} _ {i}} \mathbf {X} _ {j}. \tag {1} +$$ + +Thus, the proposed joint graph segmentation hierarchically composes features of a scene at a coarse level to enable efficient fusion decisions of these segments. + +# 3.2. Segment-Fusion Network + +Having formed segments out of the underlying points, the next goal is to understand how to form objects out of these segments. To this effect, we train a network to jointly associate the instance-level and semantic-level information to essentially form decisions if a pair of segments belong to the same object (fusable) or not (separable). + +We project the instance and semantic features per segment $\{\bar{\mathbf{S}},\bar{\mathbf{I}}\}$ to a transformed set of features $\bar{\mathbf{F}}$ in the joint semantic-instance space using the Segment-Fusion network. We compose the Segment-Fusion network using a stack of attention encoder blocks (taking cues from a Transformer [32] block). Attention blocks are known to capture larger contextual information among different segments by extracting useful intermediate representations using scaled-dot-product attention. Additionally, in each block, we propose multiplying the attention-matrix element-wise with the adjacency matrix $\mathbf{A}$ describing the connections between the segments. This helps to constrain the interactions only between the segment pairs that are spatially connected. A more detailed description of the network architecture is provided in the supplementary material. + +To supervise this learning process, we propose two sets of losses - (i) Instance loss and (ii) Segment Loss: + +$$ +\mathcal {L} _ {S F} = \mathcal {L} _ {\text {i n s t a n c e}} + \mathcal {L} _ {\text {s e g m e n t}} \tag {2} +$$ + +# 3.2.1 SF-Instance Loss + +We propose attraction and repulsion instance losses at the segment level. These losses ensure that segments of the same instance are clustered together (Equation (4)), whereas the centroids of the instance features are repelled from each other (Equation (5)). While this appears similar to the instance losses employed at the per-point level [12, 36] in principle, but in our case, the losses are applied at the segment-level features. Additionally, we parameterise the thresholds for repulsion and attraction to be $\Delta_D$ and $\Delta_V$ respectively, essentially to unify the thresholds used in the SF-Segment loss and CCL algorithm. + +$$ +\mathcal {L} _ {\text {i n s t a n c e}} = \mathcal {L} _ {\text {a t t r a c t}} + \mathcal {L} _ {\text {r e p e l}} + \mathcal {L} _ {\text {r e g}} \tag {3} +$$ + +$$ +\mathcal {L} _ {\text {a t t r a c t}} = \frac {1}{K} \sum_ {i = 1} ^ {K} \frac {1}{N _ {i}} \sum_ {j = 1} ^ {N _ {i}} H \left(d \left(\bar {\mathbf {F}} _ {j}, \mu_ {i}\right) - \Delta_ {V}\right) ^ {2} \tag {4} +$$ + +$$ +\mathcal {L} _ {\text {r e p e l}} = \frac {1}{K (K - 1)} \sum_ {i = 1} ^ {K} \sum_ {j = 1; i \neq j} ^ {K} H \left(\Delta_ {D} - d \left(\mu_ {i}, \mu_ {j}\right)\right) ^ {2} \tag {5} +$$ + +$$ +\mathcal {L} _ {\text {r e g}} = \frac {1}{K} \sum_ {i = 1} ^ {K} | | \mu_ {i} | | _ {1} \tag {6} +$$ + +where $K$ denotes the number of ground truth instances in the scene; $||.||$ is the $\ell_1$ norm; $\mu_i$ is the average of the segment features across the segments belonging to the ith instance; $d(f_i, f_j)$ indicates feature distance using a suitable norm $(\ell_1 / \ell_2)$ , and $H(.)$ is the hinge loss; we set the values of the thresholds $\Delta_V$ and $\Delta_D$ to be 0.10 and 1 respectively. + +# 3.2.2 SF-Segment Loss + +The SF-instance losses aid in clustering segment features appropriately, but relying solely on them requires iterative post-processing clustering algorithms such as DBSCAN [27], mean-shift clustering [6] etc. In this work, we propose a much simpler the clustering algorithm for projecting features to labels (Section 3.3), by using penalties on pairwise distances in the segment feature metric space. To this end, we propose a loss function that focuses on fusable and separable edges independently (Equations (7), (8) and (9)). We reuse the same threshold $\Delta_V$ here to place constraints along the edges of the graph. + +$$ +\mathcal {L} _ {\text {s e g m e n t}} = w _ {\text {f u s e}} \mathcal {L} _ {\text {f u s e}} + w _ {\text {s e p}} \mathcal {L} _ {\text {s e p}} \tag {7} +$$ + +$$ +\mathcal {L} _ {\mathrm {s e p}} = \frac {1}{| \mathcal {E} _ {\mathrm {s e p}} |} \sum_ {e _ {i j} \in \mathcal {E} _ {\mathrm {s e p}}} H \left(\Delta_ {V} - d \left(\bar {\mathbf {F}} _ {i}, \bar {\mathbf {F}} _ {j}\right)\right) \tag {8} +$$ + +Table 1. Performance impact (mIoU) of Segment-Fusion on state-of-the-art semantic segmentation backbones on the ScanNet test set. + +
Modelwallfloorcabinetbedchairsofatabledoorwindowbookshelfpicturecounterdeskcurtainfridgeshowertoiletsinkbathroomfurnituremean
SparseConvNet82.99564.476.979.564.455.457.754.178.627.639.554.165.666.679.492.77178.14866.6
SparseConvNet + SF85.497.36779.98675.76060.561.479.628.144.861.979.770.588.795.77985.951.371.9
PointConv72.694.251.86477.47051.237.1546120.64046.157.355.958.287.856.17038.958.2
PointConv + SF75.996.85766.579.973.154.140.555.963.521.445.348.760.559.96292.862.781.741.462.0
MinkNet4283.995.471.182.484.576.1665966.88019.750.559.482.119.789.188.772.891.254.572.4
MinkNet42 + SF85.697.572.583.286.377.467.46367.781.22254.259.382.92293.492.677.697.456.174.7
VMNet85.995.474.582.184.281.961.862.371.683.92449.661.488.474.790.393.178.181.85874.2
VMNet + SF88.397.577.283.385.783.862.567.172.684.92855.161.689.977.193.696.985.285.459.276.7
+ +$$ +\mathcal {L} _ {\text {f u s e}} = \frac {1}{| \mathcal {E} _ {\text {f u s e}} |} \sum_ {e _ {i j} \in \mathcal {E} _ {\text {f u s e}}} H \left(d \left(\bar {\mathbf {F}} _ {i}, \bar {\mathbf {F}} _ {j}\right) - \Delta_ {V}\right) \tag {9} +$$ + +where $\mathcal{E}_{\mathrm{sep}}$ and $\mathcal{E}_{\mathrm{fuse}}$ denote the set of edges which should be kept separate and fused respectively, decided using ground truth instance information. + +Since the number of objects in a scene are finite, the number of edges between dissimilar objects are much lower than the edges within the same object. This influences the relative weighing of $w_{\mathrm{fuse}}$ and $w_{\mathrm{sep}}$ , which we set to be 1 and 0.01 respectively, to counter this imbalance. + +# 3.3. Connected Component Labelling (CCL) + +To convert the segment features $\bar{\mathbf{F}}$ to fusion decisions, we employ a connected component labelling algorithm over the feature space that $\bar{\mathbf{F}}$ resides in. Pairwise-distances are computed $d(\bar{\mathbf{F}}_i,\bar{\mathbf{F}}_j)\forall e_{ij}\in \mathcal{E}$ and thresholded using $\Delta_V$ , depicted through a piecewise function as in Equation 10. Thus, each positive entry of $\mathbf{B}_{ij}$ indicates a fusing decision between segments $i$ and $j$ . + +$$ +\mathbf {B} _ {i j} = \left\{ \begin{array}{l l} 1 & d \left(\bar {\mathbf {F}} _ {i}, \bar {\mathbf {F}} _ {j}\right) < \Delta_ {V} \forall e _ {i j} \in \mathcal {E} \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {10} +$$ + +For every pair of indices for which $\mathbf{B}_{ij} = 1$ , we use an efficient disjoint-set forest to implement Union-Find to record the connectivity information [4]. For every connected component composed of a set of segments, we compute the mean semantic probability vector of the component and identify the most probable semantic label for the entire component, thus forming the final set of predictions $\mathbf{S}_{SF}$ . This procedure enables us to (i) identify and assign a single label to an entire object, and (ii) allow the Segment-Fusion block to override erroneous point-wise semantic predictions for parts of the object by using consensus information across larger parts of the object. + +# 4. Evaluation + +# 4.1. Training Setup + +We apply and evaluate our method with multiple state-of-the-art backbones of semantic segmentation across Scan- + +Net1 and S3DIS datasets1 using the mean Intersection-over-Union (mIoU) metric. To assess qualitative improvements, we also compare results with and without Segment-Fusion (and show its effect in regions with part misclassification). + +# 4.2. ScanNet Dataset + +We pick four state-of-the-art semantic segmentation backbones - SparseConvNet [10], PointConv [37], MinkNet [3] and VMNet [16]. We augment each of these semantic backbones with an instance backbone trained with the losses proposed in Occuseg [12]. On the ScanNet test set, as shown in Table 1, we observe significant improvements of $5.3\%$ , $3.8\%$ , $2.3\%$ and $2.5\%$ respectively in mIoU scores. We notice a consistent upswing in IoU scores across all classes. Qualitative improvements are shown in Figure 6. Thus, we observe that the improvements provided by Segment-Fusion do not depend specifically on the choice of the semantic segmentation backbone used. The improvements in mIoU help move the MinkNet42 + SF and VMNet + SF variants to the $5^{th}$ and $2^{nd}$ positions on the leaderboard respectively. + +# 4.3. S3DIS Dataset + +To demonstrate the effectiveness of our approach on datasets that do not have mesh information, we evaluate Segment-Fusion on the Area 5 set from S3DIS. We choose three semantic backbone networks: MinkNet18 [3], KPConv [30] and ASIS [36] to show improvements with Segment-Fusion. Table 2 presents semantic segmentation results on the S3DIS Area 5 set on a variety of semantic backbones. We augment each of these semantic backbones with instance features from ASIS [36]. The results show that we obtain $1.5\%$ , $0.6\%$ and $0.8\%$ improvement in mIoU on using Segment-Fusion over MinkNet18 [3], KPConv [30] and ASIS [36] respectively. + +# 4.4. Comparisons with Occuseg clustering + +We also assess Segment-Fusion with heuristic driven graph clustering approach as employed in OccuSeg [12]. + +![](images/4cd949b57362f52ea3352426a84c4fec5e30180c29da7258c22993bd014524d5.jpg) +Figure 6. Qualitative results of Segment-Fusion on some sample point clouds of the ScanNet validation set using the MinkowskiNet-42 [3], PointConv [37] and SparseConvNet [10] semantic backbones. The highlighted regions indicate mispredictions in the base semantic model (S). Note how Segment-Fusion builds consensus using the instance features to correct the semantic predictions in these areas (without degrading the performance in the other regions). + +Table 2. Impact of Segment-Fusion on state-of-the-art semantic segmentation backbones on the S3DIS Area 5 + +
Modelclutterbeamboardbookcaseceilingchaircolumndoorfloorsofatablewallwindowmean
MinkNet1851.40.066.567.492.387.134.968.495.959.876.081.049.263.8
MinkNet18+SF52.40.069.367.293.088.437.667.796.767.776.581.651.265.3
KPConv54.30.060.972.592.389.720.273.296.870.177.980.152.064.6
KPConv+SF55.20.061.873.392.489.520.775.696.970.077.980.753.465.2
ASIS41.50.052.50.089.61.47.817.296.50.01.473.139.932.4
ASIS+SF43.20.061.60.089.70.02.916.996.60.00.074.543.433.2
+ +![](images/206274d0e177bdbc9e4eca40869fd682ce8b395092d537954fccd18ecf6cdeaf.jpg) +Figure 7. Performance comparison between Occuseg's clustering and Segment-Fusion's learnable fusion algorithm on ScanNet/val. + +For this we use semantic and instance backbones similar to OccuSeg, and compare the improvement in semantic segmentation performance obtained through the iterative clustering algorithm they propose, with that of Segment-Fusion. Figure 7 shows that Segment-Fusion outperforms the heuristic driven iterative clustering algorithm across semantic backbones; lending the conclusion that a learnable algorithm like Segment-Fusion may be more scalable and generic to apply on generic semantic and instance backbones as compared to a hand-crafted algorithm. + +# 4.5. Ablation Studies + +# 4.5.1 Impact of learning beyond J-GS + +To better understand the effectiveness of our approach, we study the individual contributions of the components of our system. Table 3 compares the mIoU of the 3 semantic segmentation backbones employing (i) only graph segmentation based voting (J-GSV) without any fusion network, (ii) J-GS + SF, but trained only with instance losses $(\mathcal{L}_{\mathrm{instance}})$ , and (iii) J-GS + SF trained with both segment and instance losses $(\mathcal{L}_{\mathrm{segment}} + \mathcal{L}_{\mathrm{instance}})$ . In J-GSV, we obtain semantic labels by performing majority voting within the segment; while in SF, semantic labels are computed as described in + +Section 3.3. Note that employing only $\mathcal{L}_{\mathrm{instance}}$ degrades performance, essentially because we use a simplistic CCL algorithm to compute labels from the features; using only instance loss results in over-fusion of segments, leading to poorer performance. We observe a significant performance improvement on adding segment losses to constrain individual edges. Thus, noting steady improvements in mIoU on account of J-GS and SF, we conclude that (i) a hierarchical approach consisting of abstracting pointwise features to segment-wise features and (ii) learnable methods to fuse these segments are both required and effective. + +Table 3. Impact of individual components of Segment-Fusion on overall mIoU (ScanNet validation set) ( $\mathcal{L}_{\mathrm{ins}} = \mathcal{L}_{\mathrm{instance}}$ , $\mathcal{L}_{\mathrm{seg}} = \mathcal{L}_{\mathrm{segment}}$ ) + +
ModelBaseBase + J-GSVBase + SF(Lins)Base + SF(Lins+Lseg)
SparseConvNet67.170.469.771.5
PointConv58.361.561.463.6
MinkNet4272.474.673.1175.2
+ +![](images/c470c275efc4907a5caba991b4e0c65b8de0457934d090d7f96dc5f838f60f61.jpg) +Figure 8. Top: Fraction of points in a point cloud where J-GSV is incorrect and the base semantic predictor is correct. Bottom: Fraction points in a point cloud where J-GSV is correct and the base semantic predictor is incorrect. + +# 4.5.2 Does J-GS result in over-fusion? + +While graph segmentation aids in abstracting the problem to a higher level spatially, it runs the risk of over-fusing points belonging to two different classes into one segment. We evaluate the impact of such occurrences on overall performance using the proposed J-GSV score. For each point cloud, we analyse the base semantic predictions $\mathbf{S}$ with the predictions after J-GSV $\mathbf{S}_{maj}$ (without Segment-Fusion Network) and count the number of points for which they disagree with each other. We define overfusion to occur when the J-GSV predictions are incorrect while the base predictor is correct. In Figure 8 we observe that J-GS based voting helps in an improvement of at least $2\%$ in $\sim 32\%$ of the point clouds in the validation set of the ScanNet dataset, while being $2\%$ incorrect in $\sim 1\%$ of the point clouds. This indicates that J-GSV is consistently beneficial across point clouds of the dataset and provides higher improvement than the degradation due to overfusion. + +# 4.5.3 J-GS on S3DIS + +We present an ablative study to describe the methodology of selecting the thresholds for the proposed J-GS method. Figure 9 illustrates the performance of J-GSV on the training and validation sets of the S3DIS dataset. As discussed in Section 3.1, we evaluate the performance of various J-GSV variants on the training set to select the J-GS parameters and apply them to the validation set. It is observed that on an average, sorting of edge weights along feature similarity performs better than sorting along similarity along normals. Also, relying solely on normals ends up reducing performance as compared to the base validation performance (without J-GSV). We observe that $(s:feats,f_{th}:0.5)$ provides optimal performance for the training set, and use this to apply J-GS on the validation set and generate segment-wise data for Segment-Fusion Network. To evaluate how well these parameters generalize from the training to the validation set, we evaluate the same parameter set + +![](images/63d8086a6e2942285ec180c918136b7b7f609e73e094fc10908a15e3e7d22092.jpg) +Figure 9. J-GS Voting Score results for the S3DIS validation set across a variety of feature thresholds. The threshold used in the normals space $n_{th}$ is 0.01; results along this axis are omitted here due to lack of sensitivity. + +on the validation set as well. Though $(s: \text{feats}, f_{th}: 2)$ performs better on the validation set, the difference with $f_{th}: 0.5$ is low (lower than the gains we see alongwith SF, Table 2). On the validation set, the sorting parameter $s$ has a higher sensitivity than the feature-threshold parameter. The ScanNet dataset has more distinctive normals, hence we did not observe much sensitivity with the $f_{th}$ threshold. + +# 5. Limitations and Future Work + +While we have demonstrated the effectiveness of our approach on multiple semantic and instance backbones, the method still requires supervision. There is also potential in exploring deeper and more complex network architectures in the Segment-Fusion network to increase improvements. In the future, we plan to extend this work by using similar strategies to fuse learnings from problems with shared context, along with focusing on semi/self-supervised learning. + +# 6. Conclusion + +We presented Segment-Fusion, a learnable, hierarchical method to fuse segments, aimed at improving semantic segmentation performance of generic base models. We proposed a voting based algorithm to select optimal graph segmentation hyperparameters for varying datasets. Our learnable method can be flexibly used in conjunction with existing semantic/instance models. Finally, we performed comprehensive evaluations to demonstrate the effectiveness of our methods on multiple types of semantic backbones. + +# 7. Acknowledgements + +We would like to thank Chris Choy for his help in setting up the MinkowskiNet baseline for semantic segmentation. + +# References + +[1] Iro Armeni, Sasha Sax, Amir R Zamir, and Silvio Savarese. Joint 2d-3d-semantic data for indoor scene understanding. arXiv preprint arXiv:1702.01105, 2017. 1, 2, 4 +[2] Shaoyu Chen, Jiemin Fang, Qian Zhang, Wenyu Liu, and Xinggang Wang. Hierarchical aggregation for 3d instance segmentation. 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Existing methods mainly leverage a single-stage detection fashion, while neglecting small objects with low-resolution fine edges requires more operations than the larger ones. To tackle camouflaged object detection (COD), we are inspired by humans' attention coupled with the coarse-to-fine detection strategy, and thereby propose an iterative refinement framework, coined SegMaR, which integrates Segment, Magnify and Reiterate in a multi-stage detection fashion. Specifically, we design a new discriminative mask which makes the model attend on the fixation and edge regions. In addition, we leverage an attention-based sampler to magnify the object region progressively with no need of enlarging the image size. Extensive experiments show our SegMaR achieves remarkable and consistent improvements over other state-of-the-art methods. Especially, we surpass two competitive methods $7.4\%$ and $20.0\%$ respectively in average over standard evaluation metrics on small camouflaged objects. Additional studies provide more promising insights into SegMaR, including its effectiveness on the discriminative mask and its generalization to other network architectures. Code is available at https://github.com/dlut-dimt/SegMaR. + +# 1. Introduction + +Camouflaged object detection (COD) is a task which aims to identify any object hidden in the background [8, 22, 29]. It has been commonly useful for many applications in different fields [9, 38], including agriculture (e.g. locust detection to prevent invasion), art (e.g. photo-realistic blending and recreational art) and medical diagnosis (e.g. polyp segmentation). Biological and psychological studies have shown that various camouflage strategies can easily deceive the human's visual perceptual system [38], since the camouflaged objects always have similar visual features as the background surroundings. The major difficulty in COD is + +![](images/83dff7b14388223749104c1b5d9926385daac5f7d2e8dd3ba7ebf184fedbfddd.jpg) +Figure 1. Illustration of our SegMaR (Segment, Magnify and Reiterate) framework for camouflaged object detection. Multiple stages are performed iteratively in the framework. Each stage involves two main steps: segment the camouflaged object (the solid line) and magnify the camouflaged object (the dotted line). + +how to accurately distinguish the subtle differences between the target object and the background in the image. + +Different from traditional methods [5, 29, 51], a number of recent works [4, 7, 8, 20, 28, 45], by making use of sophisticated deep learning techniques [3, 43, 53], have achieved new state-of-the-art performance on all the COD benchmarks. Despite the quantitative performance by the latest methods looks promising (e.g. 0.80 of $S_{\alpha}$ on COD10K test set [8]), several difficulties in COD are still remaining unsolved. Particularly, when one certain camouflaged object accounts for a very small proportion of the whole image, it becomes more difficult to detect accurate edges around the object. For instance the crab in the first column in Fig. 1, its size is much smaller than the beach in the background. Unfortunately, existing COD methods fail to detect small camouflaged objects accurately. + +Their detection and segmentation results lead to high deviation on low-resolution and small objects. One main reason is these methods employ a single-stage detection fashion, but many camouflaged objects are hardly detectable at the first time. In fact, when humans cannot watch any target object in the scene clearly, they will consciously move closer to the target till its resolution is large enough for visual recognition. We expect every person in front of the + +screen is using such a manner to observe the small crab in Fig. 1. Motivated by this human behavior, our work aims to address the research question: How to leverage more stages for gradually discovering more accurate camouflaged objects? + +To this end, we propose a new iterative refinement framework, coined SegMaR, which integrates Segment, Magnify and Reiterate via a multi-stage detection fashion, please see Fig. 2. First of all, our approach builds a new camouflaged segmentation network to generate an initial mask prediction. Next, an object magnification step takes as input both the original image and the mask prediction, and leverages an attention-based sampler to enlarge the camouflaged object adaptively. It can be observed that the image size is kept while the camouflaged object accounts for a larger proportion in the image. Moreover, we run iterative refinement by passing the image with magnified object back into the same network and fine-tuning the network parameters. After more refinement stages, SegMaR enables to refine and enrich the detected details, especially for small objects. + +Importantly, SegMaR is an unified and general framework which shall be applicable to various camouflaged segmentation networks. Considering the significance of object localization and edge extraction, we advocate several special designs on the segmentation network for improving the COD performance further. + +In particular, we introduce a distraction module to disentangle foreground and background features in order to capture more accurate edges. + +Besides, we present a new and non-binary ground truth called discriminative mask, which combines the fixation and edge annotations together. Beyond the original ground truth based on binary mask, our discriminative mask makes the network attend more on the most significant textures and edges associated with the camouflaged objects. + +The contributions in this work are three-fold: + +- Framework contribution: we propose SegMaR, which is the first to leverage an iterative refinement framework for camouflaged object detection. This work raises awareness of the importance of accomplishing COD in a multi-stage detection fashion. +- Network contribution: we implement an effective camouflaged segmentation network which introduces a distraction module to disentangle better object feature. In addition, we present a new discriminative mask to make the network attend on the most significant object regions. +- Empirical contribution: Our SegMaR achieves new state-of-the-art performance on three COD benchmarks, especially for small camouflaged objects. Besides, previous COD networks are easy to be applicable to SegMaR and witness remarkable accuracy boosts. + +# 2. Related Work + +Camouflaged Object Detection. Camouflaged or concealed objects [7, 18, 29, 51] are hardly detectable due to their subtle differences from the background surroundings. To overcome this difficulty, a increasing number of recent works [8, 20, 25, 28, 36] are devoted to adopting sophisticated SOD techniques [3, 42, 43, 53] for solving COD. For instance, SINet [8] was built on top of cascaded partial decoder [43] which has been widely used for SOD. The work in [25] introduced the reverse attention [3] in order to capture more spatial details. Besides, some other works [24, 49] focus on how to extract more accurate edges around the camouflaged objects. Zhai et al. [49] built an edge-Constricted Graph Reasoning module to guide feature representation learning of camouflaged objects. However, these existing methods are not robust to some more challenging yet practical cases, especially when the camouflaged objects are very small. Different from the single-stage framework used in previous works, our SegMaR refines and enriches camouflaged detection results iteratively in a multi-stage framework. + +Iterative Refinement. This is a common and effective learning process for a variety of vision-oriented applications like object detection [1, 12], semantic segmentation [34, 50] and object localization [32, 35]. On the one hand, some studies [2, 11, 23, 34] perform the refinement steps iteratively from shallow to deep convolutional layers within one single neural network. For example, the work in [34] addressed semantic segmentation with a refinement module and stacked such modules successively into a top-down refinement process. Likewise, Lin et al. [23] presented a multi-path refinement network which effectively combines high-level semantics and low-level features to generate high-resolution segmentation maps. On the other hand, several research works [47, 50] re-train the same network iteratively by passing the result of the last training iteration into the next iteration. Representatively, CANet [50] proposed an iterative optimization module to refine predicted results for few-shot semantic segmentation. + +Despite the significant improvements by iterative refinement, it has not been researched for solving COD yet. Besides, our SegMaR framework aims to magnify camouflaged objects gradually until capturing more accurate results. + +Object Magnification. To increase the resolution of the target objects, some tasks [14, 17, 21, 30, 40, 41, 48] crop or sample the original image into sub-regions at finer scales and train neural networks recurrently. To reduce expensive and redundant calculation cost caused by the sub-regions, Marin et al. [27] proposed a content-adaptive down-sampling technique to sample locations near semantic edges of target objects. However, the increase of the background resolution is useless. To this end, the method of [54] provided an attention-based sampler to enlarge at + +![](images/34429d83f2b3a4792716ab8662f2ecd54287c56f8053d976271db3b678635adf.jpg) +Figure 2. Pipeline of our SegMaR framework. The magnification module enlarges the proportion of the object while compressing that of the background, without increasing the image size. Due to limited space, we show the first stage only, while the following stages reiterate the same process. Please refer to the details in Section 3. + +tended parts and decrease the background resolution, meanwhile the image size can be kept. One similar work to ours is [44] where they introduced the attention-based sampler [54] for SOD, while their method only magnified the object once. Different from solving SOD, our work leverages more magnification steps for camouflaged objects and achieves further performance boosts. + +# 3. Segment, Magnify and Reiterate + +Overview. This section introduces the SegMaR framework designed for COD. As depicted in Fig. 2, one can observe SegMaR is an iterative refinement framework trained in a multi-stage fashion. First of all, the input image is fed into a camouflaged segmentation network to generate a mask prediction with respect to the camouflaged object. Then it combines the input image and its mask into an attention based object magnification module, so as to enlarge the object while the image size can be kept. Next, we reiterate the segmentation process by taking as input the image with the magnified object. Consequently, the camouflaged object becomes more and more detectable from the background surroundings (Fig. 1). + +Below, we detail the steps in the framework. + +# 3.1. Camouflaged Segmentation Network + +Like most of related works [8, 43], our camouflaged segmentation network is built on top of a two-branch network architecture, see the left in Fig. 3. (1) For the first branch (shown in blue), it consists of four convolutional blocks and a discriminative decoder that generates a mask prediction $P_{dis}$ . (2) The second branch (shown in green) adds three new convolutional blocks following the first block in the first branch. A binary decoder is responsible to inferring the final binary mask $P_{bin}$ for COD. In addition, it is encouraged to use the first branch to help improve the learning process of the second branch. To make it, we merge the feature maps from the second convolutional block and the discriminative decoder in the first branch with the second branch, by using a holistic attention (HA) module [43]. + +The discriminative and binary decoders have the same + +network structure, see the right in Fig. 3. The input feature maps are firstly followed by atrous spatial pyramid pooling (ASPP) components [46] with dilation rate $D_r = 3, 6, 12, 18$ , respectively. The aim is to achieve multi-scale receptive fields in the image. Then the pooling maps are concatenated together and passed into a distraction module (DM) [55]. DM is an effective technique to disentangle previous feature maps into foreground and background features, separately. We find this ability is significant particularly for recognizing the subtle differences between camouflaged objects and background surroundings. Different from [55], we tailor the DM module by adding two parallel residual channel attention blocks (RCAB) [52], which make the module concentrate more on informative channels and high-frequency information (e.g. edges, texture) in the feature maps. Afterwards, we use the element-wise subtraction to reverse the background feature and the element-wise addition to augment the foreground feature. The output feature $f_d$ by the distraction operation is formulated by + +$$ +f _ {d} = B R \left(\beta f _ {a} + B R (- \alpha f _ {b})\right), \tag {1} +$$ + +where $BR$ is the combination of batch normalization and ReLU, $f_{a}$ and $f_{b}$ represent the foreground and background features, respectively. $\alpha$ and $\beta$ are two learnable parameters and initialized with 1. Lastly, another ASPP component following DM is added to make the output features. + +Discriminative mask. In the wild, the fixation regions like the face or limbs, are the key clues for the predator being able to quickly locate camouflaged prey. Besides, the edge regions may also leak the location of the camouflaged objects, e.g. the hair of an animal. Thus, both fixation and edge regions are important to make the camouflaged object detectable. Typically, a binary mask (i.e. 255: object, 0: background) usually acts as the ground truth to train the COD model, which implies all the regions of the object weigh equally. However, this way neglects some important regions associated with the object. Although one recent work [25] adds new fixation annotations in addition to the binary mask, their fixation annotations have some wrong regions overflow the object region. + +![](images/89a912a3a0479e6d8a3738952c645d497d9fdc908960b3fa67b7660b059d8232.jpg) +Figure 3. Our camouflaged segmentation network (Left) and its decoder (Right). The prediction $P_{dis}$ by the first branch is supervised with the discriminative mask we present, while the prediction $P_{bin}$ from the second branch is trained with the original binary mask. HA is holistic attention, ASPP is atrous spatial pyramid pooling, and RCAB is residual channel attention block. + +![](images/4ab77128f51f6e7104df00b352c35ba04a8ee1d555be92fd4aae8aa76996a7be.jpg) + +![](images/fb2875c11945de68867c354508ca4ba95e6a7fae6edefcb90546ea9fae59a938.jpg) +Figure 4. The calculation process of our discriminative mask. Here we use the colormaps for clearer visualization. + +To solve this problem, we propose a richer and nonbinary ground-truth annotation called discriminative mask. Beyond the original binary mask, our discriminative mask supervise the network to attend more on the fixation and edge regions. As for any image, we capture its edge annotation based on the binary mask, and then dilate the edges with Gaussian operation. The dilated edge captures more information around the object boundary. Then we merge the fixation annotation and dilated edge, resulting a addition mask. Lastly, we use the binary mask to subtract the overflow fixation region. Our discriminative mask $G_{dis}$ is computed via + +$$ +G _ {d i s} = G _ {b i n} \cap \left(G _ {f i x} \cup A (\sigma , \lambda , G _ {e d g e})\right), \tag {2} +$$ + +where $A(\cdot)$ is the Gaussian function with Gaussian blur $\sigma = 15$ and kernel size $\lambda = 25$ . $G_{bin}$ is binary mask based ground truth, $G_{fix}$ and $G_{edge}$ are fixation and edge annotations. Since $G_{fix}$ is non-binary, $G_{dis}$ is a non-binary mask ranging from 0 to 255. Figure 4 depicts the process of computing the discriminative mask. We illustrate some discriminative mask instances in Fig. 6, which renders stronger attention on significant regions. + +![](images/685cf753524a236a57a1ecd241ed5868bc18ea704ba83084c2ea241d16fb8886.jpg) +(a) Original image +Figure 5. The attention based magnification process. + +![](images/416b41f61a844ff3d422a5ccb55172544b25f8ad895d23d9391af1b4f3fa7e6e.jpg) +(b) Attention map + +![](images/5e93fcd7f1c8f58f610de1f0a73f7f08f6711f8e465c8aaab182c579e1321575.jpg) +(c) Sampling points + +![](images/785c282a4c82513fb41ba2b2991dfc4123c696ae3343340d72aaee93ece2a008.jpg) +(d) Magnified image + +Loss function. The camouflaged segmentation network is trained end-to-end by two loss terms: the discriminative loss $L_{dis}$ and the binary loss $L_{bin}$ . $L_{dis}$ indicates the loss cost between $P_{dis}$ and $G_{dis}$ , and $L_{bin}$ is that between $P_{bin}$ and $G_{bin}$ . We adopt the structure loss in [42] to compute $L_{dis}$ and $L_{bin}$ . The structure loss $L_{str}(P, G)$ adds a weighted binary cross entropy (BCE) loss $L_{bce}^{w}$ and a IoU loss $L_{iou}^{w}$ by + +$$ +L _ {s t r} (P, G) = L _ {b c e} ^ {w} (P, G) + L _ {i o u} ^ {w} (P, G). \tag {3} +$$ + +This structure loss is beneficial to maintain both pixel and global restrictions between the prediction and the ground truth. Finally, our total loss function is + +$$ +L _ {t o t a l} = L _ {d i s} + L _ {b i n} = L _ {s t r} \left(P _ {d i s}, G _ {d i s}\right) + L _ {s t r} \left(P _ {b i n}, G _ {b i n}\right). \tag {4} +$$ + +# 3.2. Attention based Object Magnification + +Camouflaged objects normally accounts for a very small proportion of the whole images, which makes it difficult to detect accurate object edges. Motivated by the fact that humans always move closer to the target in order to watch it more clearly, we propose to enlarge the camouflaged object while compressing the background information, as shown in Fig. 5. + +Given the prediction mask $P_{bin}$ , we further dilate it to be an attention map $D$ via + +$$ +D = \operatorname {D i l a t i o n} (\sigma , \lambda , P _ {\text {b i n}}), \tag {5} +$$ + +where Gaussian blur $\sigma = 15$ and kernel size $\lambda = 75$ . The dilation operation aims to enlarge the original prediction area, and strengthen the integrity of the object region. In the second image of Fig. 5, the attention map completely covers the object. Then we employ an attention based sampler algorithm [54] to magnify the camouflaged object based on the attention map $D$ . The attention map is used to calculate the mapping function between the coordinates of the original image and the sampled image, and the area with larger attention value is more likely to be sampled. We first decompose the attention map into two dimensions and obtain the marginal distribution by calculating the max values of the attention map $D$ over x axis and y axis as + +$$ +D _ {x} = \max _ {1 \leq i \leq w} D _ {i}, D _ {y} = \max _ {1 \leq j \leq h} D _ {j}, \tag {6} +$$ + +where $w$ and $h$ is the width and height of $D$ . Given the original image $I$ , the sampling function $\text{Sampler}(I, D)$ is defined as + +$$ +\operatorname {S a m p l e r} (I, D) _ {i, j} = I _ {D _ {x} ^ {- 1} (i), D _ {y} ^ {- 1} (j)}, \tag {7} +$$ + +where $D^{-1}(\cdot)$ indicates the inverse function of $D(\cdot)$ . Figure 5 demonstrates the area with high values in the attention map is dense sampled and magnified with its shape unchanged. + +# 3.3. Iterative Refinement + +The main advantage of SegMaR is its iterative refinement by replaying the Segment and Magnify steps in a multi-stage fashion. As shown in Fig. 1, the camouflaged crab becomes more detectable in an increasing resolution across the stages. During training period, all the stages share the same network parameters. In addition, we use the same hyper-parameters such as the Gaussian blur and kernel size for object magnification. The iterative refinement will terminate when the loss differences between two successive stages become subtle. Algorithm 1 summarizes the training steps in the SegMaR framework. + +In terms of testing period, we need to restore the final mask prediction $P_{bin}$ to the original object size, so that it can be aligned with the ground truth of the test images. We leverage a reversed sampling strategy of Eq. (7), which is denoted as $R_{sampler}(\cdot)$ . The restored mask prediction is represented as $R_{sampler}(P_{bin})$ . + +# 4. Experiment Results + +# 4.1. Setup and Evaluation + +Dataset. We evaluate our method on three widely used datasets: CHAMELEON [37], CAMO [19], and COD10K [8]. CHAMELEON [37] includes 76 high-resolution images, which are collected from the Internet by using 'camouflaged animal' as the keyword. + +Algorithm 1 Training SegMaR via Iterative Refinement + +Input: Input images $I^{(i)}$ at the $i$ -th stage, binary mask $(G_{bin})$ , discriminative mask $(G_{dis})$ , $N$ stages + +Output: COD network (Net) + +1: for each stage $i \in [1, N]$ do +2: // Segment step +3: $Net^{(i)}\gets$ train network with $I^{(i)}$ as Eq. (4); +4: // Magnify step +5: $D^{(i)}\gets Dilation(\sigma ,\lambda ,G_{bin}^{(i)})$ as Eq. (5) +6: $I^{(i + 1)}\longleftarrow \text{Sampler}(I^{(i)},D^{(i)})$ as Eq. (7) +7: $G_{bin}^{(i + 1)}\longleftrightarrow \text{Sampler}(G_{bin}^{(i)},D^{(i)})$ as Eq. (7) +8: $G_{dis}^{(i + 1)}\longleftarrow \text{Sampler}(G_{dis}^{(i)},D^{(i)})$ as Eq. (7) +9: // Reiterate step +10: Initialize the next stage $Net^{(i + 1)}\gets Net^{(i)}$ +11: end for + +![](images/55ed6fb4521cdbf0035e9de9e84e7321ff51a42b2b45a50cdaf84bba7e09f7c7.jpg) + +![](images/28a5f58b6dae5e8534893c9b5c13ceb000172976633639d9ce2e15e7d6cfe3e9.jpg) + +![](images/514bc27403d03f4582b23856c0441e6ddd3a3649e70c3b5f1210d47247ef8a25.jpg) +Figure 6. From top to bottom: original image, discriminative mask and colormap visualization. It can be seen that the fixation and edge regions have stronger attention. + +CAMO [19] is a collection of 1,250 images with 8 categories. COD10K [8] is currently the largest benchmark, containing 10,000 images with 10 super-classes and 78 sub-classes collected from photography websites. Following previous works, our training includes 1,000 images from CAMO dataset, and 3,040 images from COD10K, and the test set merges 2,026 images from COD10K, 76 images from CHAMELEON and 250 images from CAMO. In addition to the binary mask based ground truth provided in the benchmarks, we also employ the discriminative mask when training the network, please see the examples in Fig. 6. + +Implementation details. A pretrained ResNet50 [13] on ImageNet dataset [16] is employed as the backbone of our camouflaged segmentation network. All input images are resized to $352 \times 352$ , and the output predictions are resized back to the original object sizes to compare with their binary ground truths. Bilinear interpolation is employed for image resizing. We adopt Adam optimizer [15] with learning rate + +
MethodCOD10K-Test (2,026 images)CAMO-Test (250 images)CHAMELEON-Test (79 images)
\(S_{\alpha}\uparrow\)αE↑wF↑M↓\(S_{\alpha}\uparrow\)αE↑wF↑M↓\(S_{\alpha}\uparrow\)αE↑wF↑M↓
CPD [43]0.7520.8200.5570.0490.7120.8130.5610.1080.8600.9080.7530.044
PraNet [9]0.7680.8360.5990.0470.7380.8140.6130.0980.8640.9180.7840.038
MINet-R [31]0.7590.8320.5800.0450.7490.8350.6350.0900.8440.9190.7460.040
SINet [8]0.7710.8070.5650.0480.7420.8340.6010.1010.8690.9030.7490.041
LSR [25]0.7670.8610.6110.0450.7120.7910.5830.1040.8460.9130.7670.046
PFNet [28]0.8000.8680.6600.0400.7820.8520.6950.0850.8820.9420.8100.033
C2F-Net [39]0.8100.8750.6740.0380.7910.8630.7060.0830.8860.9310.8240.032
MGL [49]0.8110.8650.6660.0370.7750.8470.6730.0880.8930.9230.8130.030
SegMaR (Stage-1)0.8130.8800.6820.0350.8050.8640.7240.0720.8920.9370.8230.028
SegMaR (Stage-2)0.8300.8900.7180.0340.8080.8630.7390.0740.9020.9440.8510.027
SegMaR (Stage-3)0.8330.8920.7250.0340.8100.8700.7450.0730.9050.9470.8580.027
SegMaR (Stage-4)0.8330.8950.7240.0330.8150.8720.7420.0710.9060.9540.8600.025
+ +Table 1. Comparison of our method with other state-of-the-art methods on three benchmarks in terms of $S_{\alpha}$ (larger is better), $\alpha E$ (larger is better), $wF$ (larger is better), and $M$ (smaller is better). Stage- $i$ ( $i = 1,2,3,4$ ) denotes the iterative stages of our multi-stage framework. The best scores highlighted in bold indicate our SegMaR outperforms other methods by achieving new top-performing accuracy. + +![](images/155667836893f83a2ffffada01d2a4484e7241eef826d6cacb581ab181b9247e.jpg) +Figure 7. Visual comparison of our multi-stage detection framework. The fist stage has a rough contour of the object, while the following stages refine it. Please zoom-in to see the details. + +of $2.5e - 5$ and decay rate of 0.9. + +We use PyTorch toolbox [33] to conduct the experiments on a GPU Tesla V100. Each training stage takes about 6 hours with batch size 24 and 50 epochs. + +Evaluation Metrics. We employ four evaluation metrics, including mean absolute error $(M)$ , structure measure $(S_{\alpha})$ [6], adaptive E-measure $(\alpha E)$ [10], and weight F-measure $(wF)$ [26]. $M$ is defined as element-wise difference between prediction map and binary ground truth. $S_{\alpha}$ is defined as $S_{\alpha} = \alpha S_{o} + (1 - \alpha)S_{r}$ , where $S_{o}$ denotes object-aware structural similarity and $S_{r}$ denotes region-aware structural similarity. $\alpha E$ evaluates the pixel-level similarity and the image level statistic simultaneously, which is related to human visual perception. $wF$ is a comprehensive measure on both precision and recall, and recent works [6, 10] suggest that $wF$ is more reliable than F-measure. + +# 4.2. Comparison with the State-of-the-arts + +We compare our SegMaR model with eight state-of-the-art COD methods, including CPD [43], PraNet [9], MINet [31], SINet [8], LSR [25], PFNet [28], $C^2 F$ Net [39] and MGL [49]. For a fair comparison, the results of these methods are directly provided by their authors or by their + +original trained model, and we test them with the same evaluation protocols. For our SegMaR model, we find the loss difference between two successive stages flattens within four stages for all three benchmarks. To validate the multistage learning framework, we list the performance of the proposed SegMaR in four stages, and compare them with other methods in Table 1. We can see the performance of SegMaR improves progressively with the increase of training stages, demonstrating the object magnification and iterative refinement help the model to achieve stronger detection ability. In addition to the quantitative results, Fig. 7 compares detection results across four stages qualitatively. Comparing with the ground truth in the last column, we can already obtain a rough area in the first stage. The detection results are improved with more details gradually in the following stages. + +From the results reported in Table 1, the performance of our 1-st stage already outperforms other methods, which verifies the advantage of our camouflaged segmentation network. Furthermore, our 4-th stage achieves new state-of-the-art performance on three benchmarks. Specifically, SegMaR outperforms previous methods by a large margin on the most challenging dataset COD10K, like surpassing MGL [49] $3.5\%$ on $\alpha E$ , and $8.7\%$ on $wF$ . We outperform MGL $2.0\%$ in average over all metrics on CAMO dataset, and $2.4\%$ in average on CHAMELEON dataset. Additionally, Fig. 8 shows the qualitative comparison of our method with other methods. We can see that our detection results are the closest to the ground-truth annotations, in terms of not only large camouflaged objects (e.g. the first row), but also small ones (e.g. the last four rows). This is mainly because the discriminative mask can provide the initial location of the camouflaged objects and enforce the attention on the contours. Moreover, benefited by the magnification process in the multi-stage training, our method can capture + +![](images/270f8d2e16b15e57dab12ce3c802e199699b0ae941d255cc546b462225411a14.jpg) +(a) Image + +![](images/ec0b470028c37daea3eaa9073c837df3d6891b83cc2473aca3019349696264e4.jpg) +(b) GT + +![](images/1eec349ecdfb5a557f9e4531f26aef82a9ec5a893e3c62fc31df353b78e28665.jpg) +(c) Ours + +![](images/1d3543e096756180c0fa71d716a9eeb487ceb4f1dbc7e234178e2e67adbaff92.jpg) +(d) SINet + +![](images/0ce9dcbaab066e2b023cd097f45ef3f3be94d8c311c1c424e7f8148c78ceaa38.jpg) +(e) LSR +Figure 8. Visual comparison of the proposed SegMaR with recent state-of-the-art methods. Our method can distinguish the edges of camouflaged objects more clearly than other methods. + +![](images/7f4ead3c073d45edc30862c151129c260c50c1fe7a0c65c4d0574c7500d261ec.jpg) +(f) MGL + +![](images/08328cf6064df8db92409533fbbe8a0097388713bfe519d40c3c4c5cc4813145.jpg) +(g)PFNet + +detailed distraction information and thus has the ability to finely segment the camouflaged objects with complex structures. The proposed SegMaR is far beyond other methods on the fine contour with only bits of pixels, such as the fingers of frog in the first row, the legs of spider in the second row, and crab's claws in the last two rows. + +# 4.3. Ablation Study + +We conduct ablation studies to validate our key components tailored specifically for accurate COD, including discriminative mask, small object detection, distraction module (DM) and generalization analysis. + +Effectiveness of discriminative mask. Table 2 compares the performance of training SegMaR in the first stage based on four different types of ground truth, including fixation annotation, edge annotation, binary mask and our discriminative mask. Notice that these ground-truths are used to train the discriminative decoder in our segmentation network, while the binary decoder is always trained with the binary mask for a consistent comparison with previous works. Our discriminative mask surpasses fixation annotation and binary mask across all metrics. Edge annotation achieves better performance sometimes, but still under-performs our discriminative mask. + +Small object detection. One can expect that it is challenging to segment small camouflaged objects with fine + +edges composed of limited pixels, such as fur or legs of living creatures. + +In order to validate the effectiveness of SegMaR on small objects, we divide the testing set on COD10K into 'small' and 'non-small' subsets. The small subset contains 1,084 images where the objects occupy less than $1/4$ of the image size, and the left 924 images belong to the 'non-small' subset. As shown in Table 4, we compare our performance at Stage-4 with two competitive methods, i.e. SINet and MGL. Our method has remarkable improvements over the two methods on small testing set, by surpassing SINet $8.0\%$ on $S_{\alpha}$ , $16.8\%$ on $\alpha E$ , $35.4\%$ on $wF$ , and outperforming MGL $7.4\%$ in average over three metrics. + +Effectiveness of distraction module (DM). To further investigate the effectiveness of the tailored components of our camouflaged segmentation network, Table 3 compares the performance with and without our distraction module. Specifically, adding the DM obtains $4.2\%$ performance gain in terms of $wF$ on COD10K test set. This validates the rationality of our design to learn distractions from the attentive input features. + +Generalization analysis of SegMaR framework. We state that, SegMaR is a unified and general framework which shall be applicable to other camouflaged segmentation networks. To validate its generalization ability, we reiterate the segmentation, magnification steps on SINet [8] + +
SegMaR (Stage-1)COD10K-Test (2,026 images)CAMO-Test (250 images)CHAMELEON-Test (76 images)
Sα↑αE↑wF↑M↓Sα↑αE↑wF↑M↓Sα↑αE↑wF↑M↓
fixation0.8060.8710.6690.0370.7840.8550.6930.0830.8840.9310.8080.032
edge0.8090.8820.6790.0360.7960.8630.7120.0750.8900.9440.8220.030
binary0.8100.8770.6800.0360.7990.8570.7190.0750.8870.9200.8180.031
discriminative0.8130.8800.6820.0350.8050.8640.7240.0720.8920.9370.8230.028
+ +Table 2. Ablation analysis of using different ground-truth annotations to train the network. 'fixation' and 'edge' indicate fixation and edge annotations. 'Binary' indicates the binary mask, while 'discriminative' is our discriminative mask. Overall, our discriminative mask achieves the best performance on almost all evaluation metrics. + +
SegMaR (Stage-1)COD10K-Test (2,026 images)CAMO-Test (250 images)CHAMELEON-Test (76 images)
Sα↑αE↑wF↑M↓Sα↑αE↑wF↑M↓Sα↑αE↑wF↑M↓
without DM0.7990.8660.6540.0390.7950.8650.7060.0770.8810.9260.7990.033
with DM0.8130.8800.6820.0350.8050.8640.7240.0720.8920.9370.8230.028
+ +Table 3. Ablation analysis of our distraction module (DM) and its effect on our SegMaR framework. Overall, introducing DM brings considerable performance gains across datasets and metrics. We show the results at Stage-1 only due to limited space, while other stages witness consistent improvements. + +
MethodCOD10K(2,026 images)
Small (1,084 images)Non-Small (924 images)
\( S_{\alpha} \uparrow \)\( \alpha E \uparrow \)\( wF \uparrow \)\( S_{\alpha} \uparrow \)\( \alpha E \uparrow \)\( wF \uparrow \)
SINet [8]MGL [49]0.7640.7430.5000.7790.8810.639
0.7960.8230.5980.8320.9110.743
SegMaRstage-10.7970.8520.6200.8320.9130.753
stage-20.8210.8660.6670.8410.9170.775
stage-30.8250.8710.6770.8430.9170.782
stage-40.8250.8680.6770.8420.9210.779
+ +Table 4. Performance results on small and non-small test sets. 'Small' indicates the region of the camouflaged object is less than $1/4$ of the image. We show the results of SegMaR at Stage-4. The best performance in bold demonstrates our method surpass SINet and MGL by a large margin, particularly for small objects. + +
MethodStageCOD10K-Test (2026 images)
Sα↑αE↑wF↑M↓
SINet [8] with SegMaR frameworkStage-10.7710.8070.5650.048
Stage-20.7950.8470.6390.043
Stage-30.8010.8620.6580.041
Stage-40.8050.8690.6670.041
+ +Table 5. Generalization analysis of the proposed SegMaR framework, by applying multi-stage iterative refinement to SINet [8]. + +which is a recent and competitive baseline in the field. Comparing the results from Stage-1 to Stage-4 in Table 5, SINet gains $4.4\%$ , $7.7\%$ , and $18.0\%$ improvements in terms of $S_{\alpha}$ , $\alpha E$ , and $wF$ , validating our potential and strong generalization to other alternatives. + +# 4.4. Limitations and Discussions + +We discuss two potential limitations in this work: + +Q1: Why the whole SegMaR framework is not end-to + +end trainable. The main reason is the object magnification module we introduce is a non-parametric approach. Alternatively, we did consider leveraging a neural network to implement the magnification module. However, this solution requires new ground-truth annotations with respect to the magnified objects. Otherwise, it is hard to supervise the magnification network and achieve desirable results. We will devote to learning an unsupervised magnification network, with no need of extra annotations. + +Q2: When to terminate the iterative refinement stages. Here, we terminate the iterative refinement when the loss difference between two successive stages is subtle. As a result, our SegMaR reaches saturation after four stages only. This training process is simple yet lacks theoretical evidence. Instead, it is promising to design new algorithms to optimize the multi-stage training process, so as to reiterate more stages and achieve better performance. + +# 5. Conclusion + +To simulate humans attention which segments camouflaged objects in a coarse-to-fine manner, we have proposed an iterative refinement framework SegMaR to integrate Segment, Magnify and Reiterate in a multi-stage detection fashion. We also designed a new discriminative mask and distraction module to make the network segment more object regions. Extensive experiments have demonstrated our top-performing performance on three benchmarks especially for small camouflaged objects. In the future, it is promising to study more sophisticated magnification algorithms. + +Acknowledgements. This work is partially supported by the NSF of China under grant Nos. 61876030, 61733002, 61572105, 61922019, 62027826 and 62102061. + +# References + +[1] Sayanti Bardhan. Salient object detection by contextual refinement. In CVPR, pages 1464-1472, 2020. 2 +[2] Arantxa Casanova, Guillem Cucurull, Michal Drozdal, Adriana Romero, and Yoshua Bengio. On the iterative refinement of densely connected representation levels for semantic segmentation. In CVPR Workshop, pages 978-987, 2018. 2 +[3] Shuhan Chen, Xiuli Tan, Ben Wang, and Xuelong Hu. Reverse attention for salient object detection. In ECCV, volume 11213, pages 236-252, 2018. 1, 2 +[4] Bo Dong, Mingchen Zhuge, Yongxiong Wang, Hongbo Bi, and Geng Chen. 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However, the capacities largely come from high-quality annotated labels, which are expensive to collect. Noisy labels are more affordable, but result in corrupted representations, leading to poor generalization performance. To learn robust representations and handle noisy labels, we propose selective-supervised contrastive learning (Sel-CL) in this paper. Specifically, Sel-CL extend supervised contrastive learning (Sup-CL), which is powerful in representation learning, but is degraded when there are noisy labels. Sel-CL tackles the direct cause of the problem of Sup-CL. That is, as Sup-CL works in a pair-wise manner, noisy pairs built by noisy labels mislead representation learning. To alleviate the issue, we select confident pairs out of noisy ones for Sup-CL without knowing noise rates. In the selection process, by measuring the agreement between learned representations and given labels, we first identify confident examples that are exploited to build confident pairs. Then, the representation similarity distribution in the built confident pairs is exploited to identify more confident pairs out of noisy pairs. All obtained confident pairs are finally used for Sup-CL to enhance representations. Experiments on multiple noisy datasets demonstrate the robustness of the learned representations by our method, following the state-of-the-art performance. Source codes are available at https://github.com/ShikunLi/SeL-CL. + +# 1. Introduction + +Deep networks are powerful in various tasks, e.g., image recognition [19, 62], object detection [58], visual tracking [11] and text matching [3]. The power is largely attributed to the collection of large-scale datasets with high-quality annotated labels. In supervised learning, with the + +![](images/7629a5f3ef3874fc5e92db8b619fa78c7278f4f51bf5b63cad630de4cf06546f.jpg) +Figure 1. Left: learning a classifier with ideal representations induced by clean labels; Right: learning a classifier with corrupted representations caused by noisy labels. Circles represent the representations of positive examples while triangles represent the representations of negative examples. When the representations are corrupted by noisy labels, the decision boundary of the classifier will be largely changed. Therefore, the learned classifier in this case cannot generalize well on test examples. + +data (i.e., the instance and label pairs) in such datasets, deep networks first learn ideal latent representations of the instances and then complete following tasks with the representations [14, 57]. However, it is extremely expensive to obtain large-scale high-quality annotated labels. Alternatively, we can collect labels based on web search and user tags [36, 55]. These labels are cheap but inevitably noisy. + +Noisy labels impair the generalization performance of deep networks [15, 60]. It is because, supervised by the datasets with noisy labels, the mislabeled data provide incorrect signals when inducing latent representations for the instances. The corrupted representations then cause inaccurate decisions for following tasks and hurt generalization [29, 52]. For example, as shown in Fig. 1, the corrupted representations result in an inprecise classification boundary. Therefore, it is crucial to induce robust latent representations of instances for learning with noisy labels, which is also our focus in this paper. + +Recent works [7, 8, 13, 18, 65] show that, working in a pair-wise manner, contrastive learning (CL) methods can bring good latent representations to help following tasks. Based on whether supervised information is provided, the + +CL methods can be grouped into supervised contrastive learning (Sup-CL) [27] and unsupervised contrastive learning (Uns-CL) [7, 8, 18]. It has been shown that Sup-CL can exploit the supervised information to learn better representations than Uns-CL, but relies on the quality of supervised information [41]. If the supervised information is corrupted by noisy labels, built pairs by training examples are noisy, following corrupted representations learned by Sup-CL. Motivated by this phenomenon, prior methods use general-purpose techniques in tackling noisy labels for robust representation learning with Sup-CL, e.g., introducing regularization [41] or generating pseudo-labels [32]. Although these methods can work fine in some cases, the general-purpose techniques fail to consider the remarkable pair-wise characteristic of Sup-CL in strengthening representation learning. The achieved performance by them is thus argued to be sub-optimal. + +In this paper, we propose selective-supervised contrastive learning (Sel-CL) to address the above issue. Sel-CL can make use of the pair-wise characteristic to learn robust latent representations. The core idea of Sel-CL is (1) select confident pairs out of noisy pairs; (2) employ the confident pairs to learn robust latent representations. Note that it is hard to identify confident pairs directly for representation learning. The main reason is that we always need to set a threshold with the noise rate for precise identification, e.g., see [15, 16, 26]. Nevertheless, it is difficult to estimate the noise rate of noisy pairs. To handle this problem, we propose to first employ confident examples [16, 41], which is much easier to identified, to build a reliable set of confident pairs at each epoch. Then, based on the representation similarity distribution of confident pairs in this set, we set a dynamic threshold to selected more confident pairs out of all noisy pairs. By this pair-wise selection, we can make better use of not only the pairs whose class labels are correct, but also the pairs whose class labels are incorrect, but the examples in them are misclassified to the same class. All selected confident pairs are utilized to enhance representation learning with Sup-CL. As the selected confident pairs are less noisy, the learned representations with this selective-supervised paradigm will be more robust, naturally following promising generalization. + +The main contributions of this paper are summarized as three aspects: 1) We propose selective-supervised contrastive learning with noisy labels, which can obtain robust pre-trained representations by effectively selecting confident pairs for performing Sup-CL. 2) Without knowing the noise rate of pairs, our approach selects the pairs built by identified confident examples, and the pairs built by the examples with high representation similarities. It fulfils a positive cycle, where better confident pairs result in better representations and better representations will identify better confident pairs. 3) We conduct experiments on synthetic + +and real-world noisy datasets, which clearly demonstrate our approach achieves better performance compared with the state-of-the-art methods. Comprehensive ablation studies and discussions are also provided. + +# 2. Related Works + +In this section, we review recent methods on learning with noisy labels and contrastive learning. + +# 2.1. Learning with Noisy Labels + +There are a large body of recent works on learning with noisy labels, which include but do not limit to estimating the noise transition matrix [9, 20, 53, 54], reweighting examples [38, 44, 45, 47], selecting confident examples [4, 25, 33, 56], designing robust loss functions [10, 12, 49, 64], introducing regularization [5, 23, 61], generating pseudo labels [17, 34, 46, 63, 66], and etc. In addition, some advanced start-of-the-art methods combine serveral techniques, e.g., DivideMix [30] and $\mathrm{ELR} +$ [37]. + +# 2.2. Contrastive Learning + +Recent works in unsupervised contrastive learning (Uns-CL) [7, 8, 18, 48] have demonstrated the potential of contrastive based similarity learning frameworks for representation learning. These methods maximize (minimize) similarities of positive (negative) pairs at the instance level. That is to say, the positive pair is only built by two correlated views of the same instance. The other data pairs are negative. To make use of supervised information for learning better representations, Uns-CL is extended to the fully-supervised setting, named supervised contrastive learning (Sup-CL) [27]. Sup-CL aims to make examples belonging to the same class lie closer in the representation space than those of examples from different classes. With clean labels, Sup-CL achieves promising performance. + +In consideration of the strong power of Sup-CL, some works tend to use it to learn latent representations and handle noisy labels. For example, the methods MOIT+ [41] and MoPro [32] work in two stages. First, they pre-train the networks with Sup-CL and use general-purpose techniques, e.g., adding regularization, to reduce the side effect of noisy labels. Second, the network is fine-tuned on a reliable dataset. Additionally, the methods ProtoMix [31] and NGC [51] work in one stage. They jointly perform the generation of pseudo labels and Sup-CL to combat noisy labels. In this paper, we follow the two-stage learning style. The pair-wise characteristic of contrastive learning is investigated to enhance representation learning and further better handle noisy labels. + +# 3. Selective-Supervised Contrastive Learning + +We begin by fixing notations. Scalars are in lowercase letters. Vectors are in lowercase boldface letters. Let $\mathbb{I}[A]$ + +![](images/5369ae7ebce141fcbd40a6feeb1539ef16f2292cc74e86c73c58bdd3209a0a3a.jpg) +Figure 2. The illustration of the proposed Sel-CL, which progressively selects better confident pairs $\mathcal{G}$ for supervised contrastive learning based on the representation similarity. Without the noise rate prior, confident examples $\mathcal{T}$ are also obtained to help identify the pairs. + +be the indicator of the event $A$ . Let $[z] = \{1, \dots, z\}$ . Consider a classification task, there are $C$ classes. We are given a noisily-labeled dataset $\widetilde{\mathcal{D}} = \{(x_i, \tilde{y}_i)\}_{i=1}^n$ , where $n$ is the sample size, $x_i$ is the instance of the $i$ -th example and $\tilde{y}_i \in [C]$ is the corresponding noisy label. For $\tilde{y}_i$ , the associated but unobservable true label is denoted by $y_i$ . + +Overview. Following the two-stage learning style [13, 32, 41, 65], our aim is to induce robust pre-trained representations of instances for learning with noisy labels. + +To achieve it, our approach progressively selects better confident pairs $\mathcal{G}$ out of noisy pairs for performing supervised contrastive learning at each epoch. Without the noise rate prior, to help identify the pairs, confident examples $\mathcal{T}$ are also obtained in this process. The used pre-training network consists of three components: (1) a deep encoder $f$ (a convolutional neural network backbone) that maps the instance $\boldsymbol{x}_i$ to a high-dimensional representation $\boldsymbol{v}_i$ ; (2) a classifier head (a fully-connected layer followed by the softmax function) that receives $\boldsymbol{v}_i$ as an input and outputs class predictions $\hat{\boldsymbol{p}}(\boldsymbol{x}_i)$ ; (3) a linear or non-linear projection that maps $\boldsymbol{v}_i$ into a low-dimensional representation $\boldsymbol{z}_i$ . The illustration of the proposed Sel-CL can be seen in Fig. 2. After that, with the robust representations, we only keep the pre-trained deep encoder, and apply one new classifier head on the top to output the predictions for fine-tuning stage. In the following, we present our method step by step. + +# 3.1. Selecting Confident Examples + +To help identify the confident pairs, we first select confident examples base on the representation similarity. In addition, we warm up the training in the first few epochs to ob + +tain low-dimensional representations of instances for identifying confident examples later. Specifically, we use UnsCL [7] for the warm-up training. Note that our method is robust to the choice of warm-up methods (See Section 4.6). + +The confident examples are identified by measuring agreements between the obtained low-dimensional representations and given labels. For this goal, given two low-dimensional representations $\mathbf{z}_i$ and $\mathbf{z}_j$ , we first calculate the representation similarity between them by the cosine distance, i.e., + +$$ +d \left(\boldsymbol {z} _ {i}, \boldsymbol {z} _ {j}\right) = \frac {\boldsymbol {z} _ {i} \boldsymbol {z} _ {j} ^ {\top}}{\| \boldsymbol {z} _ {i} \| \| \boldsymbol {z} _ {j} \|.} \tag {1} +$$ + +Then, to quantify the agreement, as did in [41], for each example $(\boldsymbol{x}_i,\tilde{\boldsymbol{y}}_i)$ , we aggregate the original label from its top- $K$ neighbors based on the representation similarity to create a pseudo-label $\hat{y}_i$ . That is to say, we count the original labels of its top- $K$ neighbors ( $K = 250$ in the experiments) and correct $\tilde{y}_i$ using the dominant class. In this way, we can better use of representation similarities to improve the detection of unlabeled examples [41]. We use the pseudo-labels to approximate clean class posterior probabilities, i.e., + +$$ +\hat {q} _ {c} \left(\boldsymbol {x} _ {i}\right) = \frac {1}{K} \sum_ {\substack {k = 1 \\ \boldsymbol {x} _ {k} \in \mathcal {N} _ {i}}} ^ {K} \mathbb {I} [ \hat {y} _ {k} = c ], c \in [ C ], \tag{2} +$$ + +where $\mathcal{N}_i$ denotes the neighbor set of $K$ closest instances to $\pmb{x}_i$ according to the learned representation. Following [16], we exploit the cross-entropy loss $\ell$ to identify confident examples. Denoted the set of confident examples belonging to the $c$ -th class as $\mathcal{T}_c$ , we have + +$$ +\mathcal {T} _ {c} = \left\{\left(\boldsymbol {x} _ {i}, \tilde {\boldsymbol {y}} _ {i}\right) \mid \ell \left(\hat {\boldsymbol {q}} \left(\boldsymbol {x} _ {i}\right), \tilde {\boldsymbol {y}} _ {i}\right) < \gamma_ {c}, i \in [ n ] \right\}, c \in [ C ], \tag {3} +$$ + +where $\gamma_{c}$ is a threshold for the $c$ -th class, which is dynamically defined to ensure a class-balanced set of identified confident examples. To achieve this goal, we use the $\alpha$ fractile of per-class agreements between the corrected label $\hat{y}_i$ and the original label $\tilde{y}_i$ across all classes to determine how many examples should be selected for each class, i.e., $\sum_{i=1}^{n} \mathbb{I}[\hat{y}_i = \tilde{y}_i][\tilde{y}_i = c], c \in [C]$ . Finally, we can get the confident example set including all classes, i.e., $\mathcal{T} = \cup_{c=1}^{C} \mathcal{T}_c$ . This set is less noisy than original noisy datasets and therefore more reliable. + +# 3.2. Selecting Confident Pairs + +As it is hard to achieve a precise estimation of the noise rate of noisy pairs, we use identified confident examples to help select confident pairs. Specifically, we transform identified confident examples into a set of associated confident pairs. Denoted this set by $\mathcal{G}'$ , we have + +$$ +\mathcal {G} ^ {\prime} = \left\{P _ {i j} \mid \tilde {y} _ {i} = \tilde {y} _ {j}, \left(\boldsymbol {x} _ {i}, \tilde {y} _ {i}\right), \left(\boldsymbol {x} _ {j}, \tilde {y} _ {j}\right) \in \mathcal {T} \right\}, \tag {4} +$$ + +where $P_{ij}$ is the pair built by the examples $(\pmb{x}_i,\tilde{\pmb{y}}_i)$ and $(x_j,\tilde{y}_j)$ . As $\mathcal{G}'$ is built by $\mathcal{T}$ , it is reliable. It should be noted that, even though two examples in one pair have incorrect class labels, the similarity labels are still correct when two examples are misclassified to the same class [50]. Such pairs are valuable for representation learning. We thus identify more confident pairs from noisy pairs. We define whether two instances $\pmb{x}_i$ and $\pmb{x}_j$ belong to the same class as their similarity label, i.e., $\tilde{s}_{ij} = \mathbb{I}[\tilde{y}_i = \tilde{y}_j]$ . Note that similarity labels are extremely imbalanced, i.e., the positive ones are less than negative ones [50]. For convenience, we consider the noisy pairs with positive similarity labels. Denoted by the set of confident pairs identified from noisy positive pairs by $\mathcal{G}''$ . We have + +$$ +\mathcal {G} ^ {\prime \prime} = \left\{P _ {i j} \mid \tilde {s} _ {i j} = 1, d \left(\boldsymbol {z} _ {i}, \boldsymbol {z} _ {j}\right) > \gamma \right\}, \tag {5} +$$ + +where $\gamma$ is a dynamic threshold to control the number of identified confident pairs; $i$ and $j$ are two indices sampled from all training data. To avoid the noise rate estimation of noisy positive pairs, we utilize the reliable information of $\mathcal{T}$ to set $\gamma$ . In more detail, the $\beta$ fractile of the representation similarities of the pairs in $\mathcal{G}'$ is used here. Finally, we can get the confident pair set $\mathcal{G} = \mathcal{G}' \cup \mathcal{G}''$ . + +# 3.3. Representation Learning with Selected Pairs + +After selecting confident pairs, we can learn representations by utilizing them with supervised contrastive learning at each epoch. As selected confident pairs can be less noisy, this selective-supervised paradigm can enhance representations to handle noisy labels. + +Contrastive learning. Following the original Sup-CL [27], we randomly sample $N$ instances in each mini-batch to apply two random data augmentation operations to each in + +stance, thus generating two data views. The resulting training mini-batch data is $\{(x_i,\tilde{y}_i)\}_{i = 1}^{2N}$ , where $i\in I = [2N]$ is the index of an arbitrary augmented instance. Given $\mathcal{G}$ , we perform supervised contrastive learning with selected confident positive pairs: + +$$ +\begin{array}{l} \mathcal {L} = \sum_ {i \in I} \mathcal {L} _ {i} (\boldsymbol {z} _ {i}) \\ = \sum_ {i \in I} \frac {- 1}{| \mathcal {G} (i) |} \sum_ {g \in \mathcal {G} (i)} \log \frac {\exp \left(\boldsymbol {z} _ {i} \cdot \boldsymbol {z} _ {g} / \tau\right)}{\sum_ {a \in A (i)} \exp \left(\boldsymbol {z} _ {i} \cdot \boldsymbol {z} _ {a} / \tau\right)}, \tag {6} \\ \end{array} +$$ + +where $A(i)$ means the set of indices excluding $i$ , i.e., $A(i) = I \setminus \{i\}$ ; $\mathcal{G}(i) = \{g \mid g \in A(i), P_{i'g'} \in \mathcal{G}\}$ , and $i'$ and $g'$ are the original indices of $\boldsymbol{x}_i$ and $\boldsymbol{x}_g$ in $\widetilde{\mathcal{D}}$ , respectively. $\tau \in \mathbb{R}^+$ is a temperature parameter. Note that expect for the examples that are involved in selected confident pairs, for the other examples, we perform unsupervised contrastive learning [7] on them. + +Additionally, to further make representation learning robust, following MOIT [41], a Mixup technique [61] is added into our framework. Mixup performs convex combination of pairs of examples as $\boldsymbol{x}_i = \lambda \boldsymbol{x}_a + (1 - \lambda)\boldsymbol{x}_b$ , where $\lambda \in [0,1] \sim \mathrm{Beta}(\alpha_m, \alpha_m)$ and $\boldsymbol{x}_i$ denotes the training example that combines two mini-batch examples $\boldsymbol{x}_a$ and $\boldsymbol{x}_b$ . A linear relation in the contrastive loss is imposed as + +$$ +\mathcal {L} _ {i} ^ {\operatorname {M I X}} \left(\boldsymbol {z} _ {i}\right) = \lambda \mathcal {L} _ {a} \left(\boldsymbol {z} _ {i}\right) + (1 - \lambda) \mathcal {L} _ {b} \left(\boldsymbol {z} _ {i}\right), \tag {7} +$$ + +where $\mathcal{L}_a$ and $\mathcal{L}_b$ have the same form as $\mathcal{L}_i$ in Eq. 6. It should be noted that the selection of positive/negative pairs involves considering a unique label for each mixed example [41]. Nevertheless, the input example always contains two labels, where $\lambda$ determines the dominant one. We assign this dominant label to every example for positive/negative sampling. + +Classification learning. A classification objective with confident examples is also employed to stabilize the convergence and achieve better representations. Given the confident examples of $\mathcal{T}$ , classification learning is conducted by using + +$$ +\mathcal {L} ^ {\mathrm {C L S}} = \sum_ {\left(\boldsymbol {x} _ {i}, \tilde {y} _ {i}\right) \in \mathcal {T}} \mathcal {L} _ {i} ^ {c l s} \left(\boldsymbol {x} _ {i}\right) = \sum_ {\left(\boldsymbol {x} _ {i}, \tilde {y} _ {i}\right) \in \mathcal {T}} \ell \left(\hat {\boldsymbol {p}} \left(\boldsymbol {x} _ {i}\right), \tilde {y} _ {i}\right), \tag {8} +$$ + +where $\pmb{x}_i$ can also refer to the augmented image. + +Moreover, inspired by recent methods [22, 50] that learn classifiers with similarity labels, we add a learning objective to directly learn from similarity labels using classifier predictions. Given a multiviewed mini-batch data $\{(x_i,\tilde{y}_i)\}_{i = 1}^{2N}$ , the added similarity loss is: + +$$ +\mathcal {L} ^ {\mathrm {S I M}} = \sum_ {i \in I} \sum_ {j \in A (i)} \ell (\hat {\boldsymbol {p}} (\boldsymbol {x} _ {i}) \hat {\boldsymbol {p}} (\boldsymbol {x} _ {j}), \mathbb {I} [ P _ {i ^ {\prime} j ^ {\prime}} \in \mathcal {G} ]). \tag {9} +$$ + +Lastly, combining the above analyses, the total objective loss is: + +$$ +\mathcal {L} ^ {\text {A L L}} = \mathcal {L} ^ {\text {M I X}} + \lambda_ {c} \mathcal {L} ^ {\text {C L S}} + \lambda_ {s} \mathcal {L} ^ {\text {S I M}}, \tag {10} +$$ + +where $\lambda_{c}$ and $\lambda_{s}$ are loss weights, which we set as $\lambda_{c} = 1, \lambda_{s} = 0.01$ in all experiments. Note that, by alternately identifying confident pairs and learning robust representations at each epoch, it fulfils a positive cycle that better confident pairs will result in better learned representations and better representations will identify better confident pairs. The similar idea of the positive cycle is shared by [2]. + +# 3.4. Classification Fine-tuning + +With the pre-trained robust representation before, we only keep the pre-trained deep encoder $f$ , and apply one new classifier head on top to form a classifier network $f'$ and output the predictions. The existing methods on handling noisy labels can be applied to fine-tune the classifier. To avoid the complexity of the method, we fine-tune the deep networks on identified confident examples, with a simple robust loss function [41]. In order to better distinguish the two stages in our framework, we call the proposed method with fine-tuning as Sel-CL+. Also, we empirically verify that our method is also applicable with complex fine-tuning algorithms, e.g., DivideMix [30] and ELR+ [37]. + +# 4. Experiments + +In this section, we employ comprehensive experiments to verify the effectiveness of our method. + +# 4.1. Datasets and Implementation Details + +Simulated noisy datasets. We validate our method on two simulated noisy datasets, i.e., CIFAR-10 [28] and CIFAR-100 [28]. Both CIFAR-10 and CIFAR-100 contain 50k training images and 10k test images of the size $32 \times 32 \times 3$ . Following previous works [30,41,46], we consider two settings of simulated noisy labels: symmetric and asymmetric noise. Symmetric noise is generated by randomly replacing the labels for a percentage of the training data with all possible labels. Asymmetric noise uses label flips to incorrect classes: "truck $\rightarrow$ automobile, bird $\rightarrow$ airplane, deer $\rightarrow$ horse, cat $\leftrightarrow$ dog" in CIFAR-10, whereas in CIFAR-100 label flips are done circularly within the super-classes. + +For CIFAR-10/100 datasets, we use a PreAct ResNet-18 network, and train it using SGD with a momentum of 0.9, a weight decay of $10^{-4}$ , and a batch size of 128. The network is trained for 250 epochs and the warm-up training has 1 epoch. We set the initial learning rate as 0.1, and reduce it by a factor of 10 after 125 and 200 epochs. The fine-tuning stage of Sel-CL+ has 70 epochs, where the learning rate is 0.001. We always use the Mixup parameter $\alpha_{m} = 1$ , scalar temperature $\tau = 0.1$ , and loss weights $\lambda_{c} = 1$ , $\lambda_{s} = 0.01$ . The noise detection fractiles on the synthetic datasets are + +Table 1. Noise detection fractiles on simulated noisy CIFAR-10 and CIFAR-100. + +
FractilesCIFAR-10CIFAR-100
Sym.Asym.Sym.Asym.
α50%50%75%25%
β25%25%35%0%
+ +Table 2. Weighted KNN evaluations $(\%)$ on CIFAR-100. The best results are in bold. + +
MethodsCleanSymmetricAsymmetric
0%20%80%10%40%
Uns-CL [7]56.23----
Sup-CL [27]72.6658.3241.0071.1168.00
MOIT [41]77.4867.4255.5874.8672.60
Sel-CL77.9475.3662.4976.7772.71
+ +shown in Tab. 1. We apply the strong data augmentations SimAug [7] in the pre-training stage, and the standard weak data augmentations in the fine-tuning stage. To save computing resources, the MOCO trick [18] is used, and the size of queue is set to $30k$ . + +Real-world noisy dataset. We validate our method on a real-world noisy dataset, i.e., WebVision [35]. WebVision contains 2.4 million images crawled from the web using the 1,000 concepts in ImageNet ILSVRC12. Following previous works [30, 41], we compare baseline methods on the first 50 classes of the Google image subset, called WebVision-50. For WebVision-50, we use a standard ResNet-18, and train it using SGD with a momentum of 0.9, a weight decay of $10^{-4}$ , and a batch size of 64. The network is trained for 130 epochs and the warm-up training has 5 epochs. We set the initial learning rate as 0.1, and reduce it by a factor of 10 after 80 and 105 epochs. The fine-tuning stage has 50 epochs, where the learning rate is 0.001. We use the Mixup parameter $\alpha_{m} = 1$ , scalar temperature $\tau = 0.1$ , loss weights $\lambda_{c} = 1$ , $\lambda_{s} = 0.01$ . The noise detection fractiles are $\alpha = 40\%$ and $\beta = 0\%$ . The data augmentation techniques are similar to those of the CIFAR-10/100 datasets. The MOCO trick [18] also is used, and the size of queue is $60k$ . + +For all baselines, we use similar configurations for the same datasets for a fair comparison. We acquire the results of some baselines based on published codes. The results with underlines mean that we obtain them based on published codes. Implementation details for baselines are provided in Appendix B. We also borrow other experimental results from the related works [30, 37, 41, 42, 51, 65]. + +# 4.2. Representation Learning Evaluations + +We start by analyzing the behaviors of different contrastive learning methods in the presence of noisy labels. We show how the selective module for confident pairs im + +Table 3. Comparison with state-of-the-art methods in the test accuracy (%) on CIFAR-10 and CIFAR-100. The best results are in bold. + +
DatasetCIFAR-10CIFAR-100
Methods/Noise rateSymmetricAsymmetricSymmetricAsymmetric
20%50%80%90%10%20%30%40%20%50%80%90%10%20%30%40%
Cross-Entropy82.757.926.116.888.886.181.776.061.837.38.83.568.163.653.344.5
Mixup [61]92.377.646.743.993.388.083.377.766.046.617.68.172.465.157.648.1
Forward [43]83.159.426.218.890.486.781.976.761.437.39.03.468.763.254.445.3
GCE [64]86.681.954.621.289.585.680.676.059.247.815.87.268.058.651.442.9
P-correction [59]92.088.776.558.293.192.992.691.668.156.420.78.876.168.959.348.3
M-correction [1]93.891.986.668.789.691.892.291.273.465.447.620.567.164.558.647.4
DivideMix [30]95.093.792.474.293.893.292.591.474.872.157.629.269.569.268.351.0
ELR [37]93.892.688.063.394.493.391.585.374.570.245.220.575.874.873.670.0
GCE (Uns-CL init.) [13]90.089.373.936.591.187.382.278.168.153.322.18.970.260.252.644.1
ELR (Uns-CL init.)94.493.088.386.295.094.794.493.376.271.957.940.877.275.574.370.4
MOIT+ [41]94.191.881.174.794.294.394.393.375.970.647.641.877.476.475.174.0
Sel-CL+95.593.989.281.995.695.294.593.476.572.459.648.878.777.576.474.2
+ +![](images/543113d4747c954f230e772a66d1733fef00b4940af48ebb265f8d257b780f1a.jpg) +(a) + +![](images/632c38dc0f43fa1feb5f46b4b32b51c7992aa24068451be920bc832ac90b3271.jpg) +(b) + +![](images/6f37b9b5a42d0f758534b631c7cd2c139652ad5475386dd20b69c2ef5e624af2.jpg) +(c) + +![](images/94cbb9c1e54ffb26d4ceed26cbfef1b161bade297e2c6ab7f1e3491868234663.jpg) +(d) +Figure 3. The learning process of Sel-CL on CIFAR-100 with $20\%$ symmetric noise. (a) the number of selected examples vs. epochs; (b) the number of selected positive pairs vs. epochs; (c) the label precision of selected examples and pairs $(\%)$ vs. epochs; (d) weighted KNN evaluations of Sel-CL $(\%)$ vs. epochs. + +pacts the learned representations. We evaluate the quality of representations using a weighted KNN (K=200) evaluation in unsupervised learning [24]. + +The results are shown in Tab. 2. As can be seen, when there is no noise, MOIT greatly improves the quality of learned representations. Benifting from the application of the similarity loss, Sel-CL achieves $0.46\%$ quality gains. Then, for noisy datasets, Sup-CL is seriously affected by noisy labels. Although MOIT improves its robustness through the Mixup technique and semi-supervised strategy, its performance is still unsatisfactory. For example, in the case with $80\%$ symmetric noise, the weighted KNN accu + +racy of MOIT is $55.58\%$ , which is even less than the result of Uns-CL, i.e., $56.23\%$ . In contrast, our Sel-CL significantly alleviates the side effect of noisy labels, by selecting confident pairs for supervised contrastive learning. We can see that Sel-CL consistently outperforms baselines across different cases. + +We illustrate the numbers of the selected confident examples and pairs, the label precision of selected confident examples and pairs, and the quality of learned representations during training. The experiments are conducted with $20\%$ symmetric noise. The results are provided in Fig. 3. It can be seen that the selection of confident examples/pairs and representation learning form a positive cycle. Sel-CL can progressively achieve effective selection and improve learned representations. + +# 4.3. Results on Simulated Noisy Datasets + +We compare the proposed Sel-CL+ with multiple baselines. We report the averaged test accuracy over the last 10 epochs. All baselines use the PreAct ResNet-18 network. Note that for a fair comparison, we report the results of DivideMix [30] without model ensembles, and equip ELR [37] with Mixup and weight averaging techniques. + +As shown in Tab. 3, we first observe that the methods pre-trained by Uns-CL [7] can outperform the original ones, e.g., GCE vs. GCE (Uns-CL init.) and ELR vs. ELR (Uns-CL init.). When the noise level is high, e.g., $80\%$ and $90\%$ , the improvement is clearer, which is consistent with the observations in related works [13, 65]. For MOIT+ which exploits Sup-CL by adding regularization, its performance is promising. For symmetric noise, MOIT+ achieves comparable results with other state-of-the-art algorithms, e.g., ELR and DivideMix. For asymmetric noise, MOIT+ can perform better in most cases. As for our Sel-CL+, it achieves competitive performance with symmetric noise. For asymmetric noise, Sel-CL+ consistently achieves + +Table 4. Weighted KNN evaluation $(\%)$ of Sel-CL with different selected sets on CIFAR-10/100 with $40\%$ asymmetric noise. + +
Sel-CL with different selected setsCIFAR-10CIFAR-100
All examples and all pairs90.5868.66
Confident examples T and pairs G'90.6470.25
Confident examples T and pairs G' ∪ G''92.9772.71
Clean examples and associated pairs94.2171.45
Clean examples and all pairs94.7673.43
Clean examples and clean pairs95.5276.56
+ +the best performance over all baselines. The results verify the effectiveness of our method well. + +# 4.4. Pair-wise Selection Analysis + +As the results on simulated noisy datasets show that Sel-CL+ work better in the case of asymmetric noise, where label flips happens between semantically similar classes. It is because Sel-CL not only exploits confident pairs associated with $\mathcal{T}$ , but also extracts more confident positive pairs based on the representation similarity. To detail this phenomenon, we conduct some analysis about the pair-wise selection in our approach under the asymmetric noise cases. + +There are several observations provided in Tab. 4. The results show that, it is useful to employ the confident examples and associated positive pairs $\mathcal{G}'$ . However, the imporvement is limited compared with selecting clean examples and clean pairs. Our method further employs $\mathcal{G}''$ , which is based on the similarity representations. By this procedure, we can make better use of the confident pairs whose class labels are incorrect but similarity labels could be correct, which is much common in the asymmetric cases and real-world scenarios. Besides, an interesting phenomenon is that it is not bad for selecting clean examples and all pairs, since the noise rate of pairs is smaller. This phenomenon may explain why MOIT+ also has advantages with asymmetric noise, which uses all noisy pairs. + +# 4.5. Results on the Real-World Noisy Dataset + +We validate our method on the real-world dataset WebVision-50 [35], which contains noisily-labeled images collected from Flickr and Google. As shown in Tab. 5, Sel-CL+ achieves the best results on both top-1 and top-5 accuracy on the WebVision validation set and ImageNet ILSVRC12 validation set than the other state-of-the-art methods, including four recent methods that also utilize contrastive learning. The results mean that our method is better to handle realistic scenes. + +# 4.6. Ablation Study and Discussions + +Influence of each component. To study the impact of each component in our method, we use CIFAR-100 for evaluations. We report test accuracy/weighted KNN evaluations $(\%)$ for Sel-CL, and test accuracy $(\%)$ for Sel-CL+ + +Table 5. Accuracy (%) on the WebVision and ILSVRC2012 validation sets. The model is trained on WebVision-50. The best results are in bold. + +
MethodsWebVisionILSVRC12
top-1top-5top-1top-5
Forward [43]61.1282.6857.3682.36
Decoupling [40]62.5484.7458.2682.26
D2L [39]62.6884.0057.8081.36
MentorNet [26]63.0081.4057.8079.92
Co-teaching [16]63.5885.2061.4884.70
Iterative-CV [6]65.2485.3461.6084.98
DivideMix [30]77.3291.6475.2090.84
ELR [37]76.2691.2668.7187.84
ELR+ [37]77.7891.6870.2989.76
ELR (Uns-CL init.)79.9392.0071.2388.23
ProtoMix [31]76.391.573.391.2
MoPro [32]77.59-76.31-
NGC [51]79.1691.8474.4491.04
Sel-CL+79.9692.6476.8493.04
+ +Table 6. Ablation study for Sel-CL and Sel-CL+ on CIFAR-100. The best results are in bold. + +
MethodsSym. 20%Asym. 40%
Sel-CL w/o Mixup Data Aug.70.3/70.664.2/66.2
Sel-CL w/o MOCO Trick73.3/74.169.2/71.5
Sel-CL w/o Selection67.2/68.949.9/68.7
Sel-CL w/o Classifier Learning— /69.9— /70.2
Sel-CL w/o LSTM74.5/74.971.8/72.5
Sel-CL74.9/75.472.0/72.7
Sel-CL+ w/ Strong Data Aug.74.572.7
Sel-CL+ w/o Retraining Cls.76.473.4
Sel-CL+76.574.2
+ +in Tab. 6. It shows the contribution of each component into our method. + +Discussions on warm-up methods. We use different warm-up methods, i.e., Uns-CL [7] and Sup-CL [27] for Sel-CL+. The experiments are conducted on CIFAR-10 and CIFAR-100 with symmetric and asymmetric noise. The results in Tab. 7 demonstrate that Sel-CL+ is robust to the choice of warm-up methods. + +Discussions on fine-tuning methods. We further test two complex but advanced methods for fine-tuning stage, i.e., DivideMix [30] (be better with symmetric noise) and $\mathrm{ELR} +$ [37] (be better with asymmetric noise). As shown in Tab. 8, using more advanced fine-tuning methods can further improve the performance. Both the representations obtained by Uns-CL [7] and Sel-CL can promote the robustness of two methods, and our Sel-CL brings better results. + +Comparison with one-stage methods for handling noisy labels. We compare our method with two recent one-stage methods, which also employ contrastive learning to handle noisy labels. For a fair comparison, we use AugMix [21] + +Table 7. Comparison with different warm-up methods in the test accuracy $(\%)$ of Sel-CL+. + +
DatasetCIFAR-10CIFAR-100
Noise typeSym.Asym.Sym.Asym.
Noise rate20%90%40%20%90%40%
Uns-CL [7]95.581.993.476.548.874.2
Sup-CL [27]95.581.693.476.851.474.5
+ +Table 8. Comparison with using different fine-tuning methods in the test accuracy (\%). The best results are in bold. + +
DatasetCIFAR-10CIFAR-100
Noise typeSym.Asym.Sym.Asym.
Noise rate20%40%20%40%
DivideMix [30]95.792.176.953.8
ELR+ [37]94.693.077.572.2
DivideMix (Uns-CL init.) [65]96.290.878.352.9
ELR+ (Uns-CL init.) [65]94.894.377.772.3
DivideMix (Sel-CL init.)96.391.678.755.2
ELR+ (Sel-CL init.)95.294.677.772.9
+ +Table 9. Comparison with one-stage methods in the test accuracy $(\%)$ . † denotes fine-tuning using AugMix data augmentation. The best results are in bold. + +
DatasetCIFAR-10CIFAR-100
Noise typeSym.Asym.Sym.Asym.
Noise rate20%90%40%20%90%40%
ProtoMix [31]95.875.091.979.129.348.8
NGC [51]95.980.590.679.329.8-
Sel-CL+95.467.592.876.435.574.2
Sel-CL+†95.267.492.576.035.474.2
+ +Table 10. Comparison with different example selection strategies in the test accuracy/label precision $(\%)$ of Sel-CL+. + +
Noise typeSym.Asym.
Noise rate20%90%20%40%
w pseudo-labels76.5/99.148.8/62.077.5/97.574.2/92.2
w/o pseudo-labels76.5/99.146.2/55.476.8/96.669.4/83.9
+ +as data augmentations of the pre-training stage. As shown in Tab. 9, our approach has advantages in the asymmetric noise cases. In addition, we also try to adopt AugMix augmentation in the fine-tuning stage and find that the weak augmentation is more suitable, which is consistent with the ablation study. The results may reflect the difference between representation learning and classification learning. + +Role of pseudo-labels $\hat{y}$ . Following [41], we use the representation similarity with the weighted KNN to create pseudo labels. In this way, we can make better use of representation similarities. To make it clear, we use CIFAR-100 for evaluations. We report test accuracy/label precision evaluations (\%) for Sel-CL+ with and without pseudo-labels, and here label precision is the average over all epochs. As Tab. 10 shows, this practice results in better performance + +due to improved label precision. Besides, we also can just use the pseudo labels to define confident examples rather than to estimate clean class posterior probabilities. By comparing them from empirical observations, our method brings a higher label precision, which is shown in Fig. 4. + +![](images/d503a980e82f1db980014743c0edc86a0d0ee20638be5710efbde3947bacc933.jpg) +Figure 4. Comparison of label precision. The experiments are conducted on CIFAR-100 with $20\%$ asymmetric noise. + +The ablation studies about the hyperparameters are provided in Appendix A, which show that our method is robust to the choices of the hyperparameters. + +# 5. Limitations + +Our work still has certain limitations, including: 1) This work exploits contrastive learning, and therefore, the performance of our approach relies on adequate data augmentation and large amounts of negative samples. A larger batch size or memory bank is needed, which places higher demands on the storage of computing devices. 2) The use of the KNN algorithm brings greater computational consumption. In this work, we have used some faster KNN algorithms (see source codes) to alleviate the above issue, which facilitates the application of our method to large-scale datasets. + +# 6. Conclusion + +This paper proposes selective-supervised contrastive learning (Sel-CL), a new method to handle noisy labels in training data by learning robust pre-trained representations. We make use of the pair-wise characteristic of contrastive learning to better enhance network robustness. Without the noise rate prior, the confident pairs are selected out of noisy pairs for supervised contrastive learning. We demonstrate the state-of-the-art performance of our method with extensive experiments on multiple noisy datasets. For future work, we are interested in extending our method to other tasks such as object detection and text matching. + +Acknowledgements This work was partially supported by grants from the Beijing Natural Science Foundation (19L2040), National Key Research and Development Plan (2020AAA0140001), and National Natural Science Foundation of China (61772513). Shiming Ge was supported by the Youth Innovation Promotion Association, CAS. Xiaobo Xia was supported by ARC Projects DE-190101473. Tongliang Liu was partially supported by ARC Projects DP180103424, DE-190101473, and DP-220102121. + +# References + +[1] Eric Arazo, Diego Ortego, Paul Albert, Noel E. O'Connor, and Kevin McGuinness. Unsupervised label noise modeling and loss correction. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, ICML, pages 312-321, 2019. 6 +[2] Yingbin Bai and Tongliang Liu. Me-momentum: Extracting hard confident examples from noisily labeled data. In ICCV, 2021. 5 +[3] Haolan Chen, Fred X. 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Most of them simply formulate dehazing and rehazing cycles, yet ignore the physical properties of the real-world hazy environment, i.e. the haze varies with density and depth. In this paper, we propose a self-augmented image dehazing framework, termed $D^4$ (Dehazing via Decomposing transmission map into Density and Depth) for haze generation and removal. Instead of merely estimating transmission maps or clean content, the proposed framework focuses on exploring scattering coefficient and depth information contained in hazy and clean images. With estimated scene depth, our method is capable of re-rendering hazy images with different thicknesses which further benefits the training of the dehazing network. It is worth noting that the whole training process needs only unpaired hazy and clean images, yet succeeded in recovering the scattering coefficient, depth map and clean content from a single hazy image. Comprehensive experiments demonstrate our method outperforms state-of-the-art unpaired dehazing methods with much fewer parameters and FLOPs. Our code is available at https://github.com/YaN9-Y/D4. + +# 1. Introduction + +Haze is a kind of natural phenomenon caused by the scattering effect of aerosol particles in the atmosphere. It can cause severe disclarity to visual content, which brings trouble to both human observers and computer vision systems. + +Dehazing methods aim to remove the haze and improve the visual quality of real-world hazy images, which can benefit computer vision tasks like image segmentation [4, 38], object detection [15, 34] on the hazy weather. + +The degradation of haze effect can be formulated by Koschmieder's law [29, 30]: + +$$ +\mathbf {I} (z) = \mathbf {J} (z) \mathbf {t} (z) + \mathbf {A} (1 - \mathbf {t} (z)), \tag {1} +$$ + +where $\mathbf{I}(z)$ indicates the $z$ -th pixel of observed hazy image, $\mathbf{J}(z)$ and $\mathbf{A}$ are the scene radiance and global atmosphere light, respectively. Transmission map $\mathbf{t}(z) = e^{-\beta \mathbf{d}(z)}$ is defined by the scene depth $\mathbf{d}(z)$ and the scattering coefficient $\beta$ that reflects the haze density. + +With the great learning capability of deep neural networks [12, 13], plenty of methods were proposed to solve the image restoration tasks [3, 25, 35, 46, 48, 49], as well as image dehazing [7, 27, 31, 36], in a supervised manner. Through training on a large amount of synthetic hazy-clean image pairs, supervised deep dehazing methods achieved impressive results on specific test sets. + +However, there exists a relatively large domain gap between synthetic and real-world hazy images. Dehazing models that are solely trained on paired synthetic images are easy to over-fitting, and generalize poorly to real-world hazy conditions. + +Since the desired real-world hazy&clean image pairs are nearly unreachable, in recent years, many unpaired deep learning methods were proposed to explore the dehazing cues from unpaired training data. Among them, constructing the dehazing cycle and rehazing cycle is widely adopted [8,9,17,26,45,50] since it provides a simple and effective scheme for keeping content consistency while performing domain transformation. If the hazy and clean image domains can be accurately modeled, the cycle framework is expected to gain promising performance on unpaired dehaz- + +![](images/4a924513ee24bbd187c892fd022f51701804d7b0194ac841f9d5bd96c98a5602.jpg) +Figure 1. Illustration of (i) previous CycleGAN-based dehazing methods, (ii) our proposed method and, (iii) the results comparison. Compared to RefineDNet [51], our method can better remove the haze. The CycleGAN-based methods can only generate haze with fixed density for certain clean image, and the generated haze is not consistent with the depth. + +ing. However, we argue that simply inheriting the CycleGAN [52] framework from unpaired image-to-image translation methods would fail to handle unpaired image dehazing tasks. Existing cycle-based dehazing methods ignore the physical properties of real-world hazy environments, i.e. the real-world haze varies with density and depth. As shown in Fig. 1 (i) and (iii)-(e), CycleGAN-based methods easily collapse to synthesizing haze with fixed density, and may incorrectly model the haze effect, e.g. the haze should be thicker accompanied with the increasing of scene depth. + +In this paper, we propose a novel dehazing framework termed $D^4$ , i.e. Dehazing via Decomposing transmission map into Density and Depth, for unpaired haze synthesis and removal. Following the hazy image formation process, we explicitly model the scattering coefficient $\beta$ and depth map $\mathbf{d}(z)$ of the target scene. As shown in Fig. 1 (ii), on the Dehazing-Rehazing branch, our model is trained to directly estimate both transmission map and scattering coefficient from a hazy image. According to the physics process expressed in Eq. (1), scene depth and clean content then can be derived directly. On the Hazing-Dehazing branch, our model aims to estimate the depth information of the input clean image, then synthesize hazy images with different densities, i.e. scattering coefficients. Considering the fact that 'spatial-variant haze thickness provides an additional cue for perceiving scene depth', depth maps estimated from hazy images act as pseudo ground truth of the depth of clean images. Similarly, in the Hazing-Dehazing branch, the randomly sampled scattering coefficients $\beta$ in the Hazing step act as pseudo ground-truth of the density predicted in the Dehazing step. + +Finally, with our novel unpaired dehazing framework, we can (i) estimate depth maps from clean images (Fig. 1 + +(g)); (ii) synthesize realistic hazy images with various densities (data augmentation) (Fig. 1 (h),(i)); and (iii) achieve better dehazing performance than state-of-the-arts unpaired dehazing methods with less parameters and FLOPs. + +Overall, our contributions can be summarized as follows: + +- We propose a novel unpaired dehazing framework, which explicitly models the scattering coefficient (i.e. density) and the depth map of hazy scenes. The proposed physics-based framework largely alleviates the ill-posed problem that existed in existing unpaired dehazing methods. +- Inspired by the intuition: 'spatial-variant haze thickness reflect scene depth', our model learns to predict depth information from hazy images. Then, with only unpaired hazy and clean images, our model are trained to predict depth information from clean images. +- With estimated scene depth, our model is able to generate hazy images with different thickness by altering the scattering coefficient. Such characteristic acts as a self-argumentation strategy for better training the de-hazing network. +- Extensive experiments on both synthetic and real images are conducted to reveal the effectiveness of our design. The proposed $D^4$ framework shows clear advantages on generalization ability over state-of-the-art methods. + +# 2. Related Work + +This section briefly reviews previous dehazing works closely related to ours, which are grouped into prior-based, supervised and unsupervised learning-based methods. + +Prior-based approaches. To allviate the ill-posedness of + +single image dehazing, early attempts concentrated on discovering priors on haze-free images from statistic analysis or observation. Among them, He et al. [14] proposed the dark channel prior, which assumes that the locally lowest intensity in RGB channels should be close to zero in haze-free natural images. Zhu et al. introduced the color attenuation prior [53], they point that the difference between the value and saturation of pixels should be positively correlated to the depth of scene in a linear model. In [10], Fattal discovered that the values of small patches distribute largely along a 1-D line in the RGB space. As a serious drawback, these methods are all built upon handcrafted priors, which are not always in line with the complex real environments. + +Supervised learning approaches. Benfitting from the success of CNNs and the development of large-scale synthetic datasets, deep learning-based supervised methods relaxed the limitation of handcrafted priors, and have occupied the dominant position. For instance, [2] is the pioneer to estimate the transmission map from hazy images in an end-to-end manner by constructing a convolutional neural network. Ren et al. [36] proposed a multi-scale convolutional network to predict the transmission map from coarse to fine. However, these methods may suffer from the cumulative error when separately estimating the transmission and atmospheric light. To deal with this issue, Li et al. [22] reformulated Eq. (1) to simultaneously estimate the transmission map and atmospheric light together. Moreover, a number of methods [24, 27, 31, 32] directly estimate the clean image from hazy inputs without explicitly modeling the atmosphere scattering model. Recently, several attempts introduce the domain adaption methods into image dehazing tasks, they aim to shrink the domain gap between synthesized and real data [39, 41, 42]. Overall, although supervised methods have achieved remarkable performance on synthetic datasets, they are easy to overfit to the provided training data and generalizing poorly to other hazy images, specifically for real-world haze. + +Unsupervised learning approaches. Comparing to the supervised methods, the unsupervised learning methods do not rely on paired supervision. Some unsupervised methods can be directly trained on hazy images. For instance, [20, 21] perform dehazing in a zero-shot manner, which disentangle the hazy image into the clean image and other components. [11] trains a network by minimizing a DCP-based [14] loss on hazy images. In these methods, since the clean images are not involved in training, the intrinsic property of the clean image domain is not efficiently considered, thus limit their performance. + +The unpaired dehazing methods learn the dehazing mapping from unpaired clean and hazy images. Besides of a few methods [47, 51] that try to disentangle the clean component from the hazy image under GAN supervision, most unpaired dehazing methods are based on CycleGAN with + +other specific designs. For example, the CDNet [8] introduces the optical model into the CycleGAN. [50] adopts double-discriminator to stabilize the cyclic training. CycleDehaze [9] applies a Laplacian pyramid network to deal with high-resolution images and proposes a cycle perceptual loss for better structure preserving. [26] uses a two-stage mapping strategy in each branch of CycleGAN to enhance the effectiveness of fog removal. However, these methods usually ignore the depth information and the variousness of density when generating hazy images. The absence of these factors leads to unrealistic haze generation, which will further affect the dehazing performance. To deal with these issues, in our proposed $D^4$ framework, we focus on exploring both depth information and scattering coefficient contained in hazy and clean images. + +# 3. Proposed Method + +CycleGAN [52] is a broadly adopted framework for unpaired image-to-image translation. On one hand, the GAN loss is employed to enforce images translating between two domains. On the other hand, the cycle reconstruction loss works well to maintain the content consistency. For image dehazing, the CycleGAN-based methods [8, 9, 26] usually contain a dehazing network and a rehazing network, which predict the clean images and hazy images from their counterparts [9]. Here, we argue that such practice may be questionable. Two crucial properties, depth and density, are ignored in those methods. Consequently, the generated haze usually lacks of realism and variousness, which further affects the learning of dehazing network. To address these issues, we proposed a novel unpaired dehazing framework termed $D^4$ (Dehazing via Decomposing transmission map into Density and Depth). The overall framework and training procedures are detailed as follows. + +# 3.1. The Overall Framework + +Given a clean image set $\mathcal{X}_C = \{\mathbf{C}\}_{i=1}^{N_1}$ and a hazy image set $\mathcal{X}_H = \{\mathbf{H}\}_{i=1}^{N_2}$ , where $N_1$ and $N_2$ stand for the cardinal numbers of the two sets. Unlike the synthetic hazy-clean image datasets, there exists no paired information between two sets. As shown in Fig. 2, our $D^4$ framework consists of three networks: the dehazing network $\mathcal{G}_D$ , the depth estimation network $\mathcal{G}_E$ , and the refine network $\mathcal{G}_R$ . + +The dehazing network $\mathcal{G}_D$ is trained to estimate the transmission map $\hat{\mathbf{t}}$ and the scattering coefficient $\hat{\beta}$ from a hazy image $\mathbf{H}$ , which can be formulated as: + +$$ +(\hat {\beta}, \hat {\mathbf {t}}) = \mathcal {G} _ {D} (\mathbf {H}). \tag {2} +$$ + +According to Eq. 1, the depth map $\mathbf{d}$ of the hazy image can be calculated from the estimated transmission $\hat{\mathbf{t}}$ and scattering coefficient $\hat{\beta}$ by: + +$$ +\mathbf {d} (z) = \frac {\ln \hat {\mathbf {t}} (z)}{- \hat {\beta}}. \tag {3} +$$ + +![](images/9519e9af05402373fd7c7f895b5756b72e64bcfbe46ccfeb6d539497265ff300.jpg) +Figure 2. The architecture of our proposed network $D^4$ . The whole network comprises of the Dehazing-Rehazing branch and the Hazing-Dehazing branch. Both depth and density information are considered in haze generation. Two pairs of pseudo supervision are introduced to confirm the accuracy of estimated depth and scattering coefficient. + +The depth estimation network $\mathcal{G}_E$ aims to estimate the depth $\hat{\mathbf{d}}$ from a clean image $\mathbf{C}$ , which is formulated as + +$$ +\hat {\mathbf {d}} = \mathcal {G} _ {E} (\mathbf {C}). \tag {4} +$$ + +Note that our depth estimation network $\mathcal{G}_E$ shares the same function as other single image depth estimation networks [19,33], yet we do not employ any pretrained weights from existing depth estimators or ground truth depth supervision during training. In our $D^4$ framework, network $\mathcal{G}_E$ is trained using the pseudo supervision from the dehazing network $\mathcal{G}_D$ , more details are introduced in Sec. 3.3. + +The refine network $\mathcal{G}_R$ . Different from previous CycleGAN-based methods that directly synthesize a hazy image from an input clean image, the proposed $D^4$ models the rehazing process by considering two physical properties (density and depth). Specifically, we first derive a coarse fake hazy image by combining a clean image, its estimated depth and a scattering coefficient. Then, the refine network $\mathcal{G}_R$ works as an image-to-image translation network that maps coarse fake hazy images to hazy images that follow the distribution of real hazy images, i.e. + +$$ +\hat {\mathbf {H}} = \mathcal {G} _ {R} (\hat {\mathbf {H}} _ {\text {c o a r s e}}). \tag {5} +$$ + +In other words, the proposed refine network can be regarded as performing a conditional hazy image generation. Given the depth and density information, the refine network aims to generate visually realistic hazy images. + +In our proposed $D^4$ framework, both the dehazing network $\mathcal{G}_D$ and the depth estimation network $\mathcal{G}_E$ are based on the structure of EfficientNet-lite3 [43], and the refine network $\mathcal{G}_R$ has a UNet [37] structure. The detailed network architectures are provided in our supplementary material. + +# 3.2. Training Procedure + +As shown in Fig. 2, the training of our $D^4$ contains two branches: (i) the Dehazing-Rehazing branch and (ii) the Hazing-Dehazing branch. + +The Dehazing-Rehazing branch. By feeding a hazy image $\mathbf{H}$ into the dehazing network $\mathcal{G}_D$ , we can obtain the estimated transmission map $\hat{\mathbf{t}}$ , estimated scattering coefficient $\hat{\beta}_H$ and the calculated depth $\mathbf{d}_H$ . Meanwhile, the dehazed result $\hat{\pmb{c}}$ can be calculated by: + +$$ +\hat {\boldsymbol {c}} (z) = \frac {\mathbf {H} (z) - \hat {A}}{\hat {\mathbf {t}} (z)} + \hat {A}, \tag {6} +$$ + +where $\hat{A}$ is the atmospheric light estimated by the prior. + +With the dehazed image $\hat{c}$ , the depth estimator $\mathcal{G}_E$ predicts the depth $\hat{\mathbf{d}}_H$ from it. Then, we rehaze the dehazed image $\hat{c}$ with previously estimated scattering coefficient $\hat{\beta}_H$ and the estimated $\hat{\mathbf{d}}_H$ . Specifically, we first derive a coarse hazy image $\hat{\mathbf{H}}_{coarse}$ with the haze formation process: + +$$ +\hat {\mathbf {H}} _ {\text {c o a r s e}} (z) = \hat {\boldsymbol {c}} (z) e ^ {- \hat {\beta} _ {H} \hat {\mathbf {d}} _ {H} (z)} + A (\mathbf {1} - e ^ {- \hat {\beta} _ {H} \hat {\mathbf {d}} _ {H} (z)}), \tag {7} +$$ + +where we adopt the brightest pixel as the atmospheric light $A$ for haze generation. Then, the coarse hazy image $\hat{\mathbf{H}}_{coarse}$ is processed by the refine network to obtain the final rehazing image $\hat{\mathbf{H}} = \mathcal{G}_R(\hat{\mathbf{H}}_{coarse})$ . + +The Hazing-Dehazing branch. In this branch, we sample a clean image $\mathbf{C}$ from the set $\mathcal{X}_C$ . The depth estimation network $\mathcal{G}_E$ is employed to estimate the depth map $\hat{\mathbf{d}}_C$ from the image $\mathbf{C}$ . Then, we randomly sample a $\beta_C$ from a predefined uniform distribution. Following the same physical process presented in Eq. 7, we derive the coarse hazy image $\hat{\pmb{h}}_{coarse}$ with variable haze density, i.e. + +$$ +\hat {\boldsymbol {h}} _ {\text {c o a r s e}} (z) = \mathbf {C} (z) e ^ {- \beta_ {C} \hat {\mathbf {d}} _ {C} (z)} + A (\mathbf {1} - e ^ {- \beta_ {C} \hat {\mathbf {d}} _ {C} (z)}). \tag {8} +$$ + +Our fake hazy image $\hat{\pmb{h}}$ is then synthesized by the refine network $\mathcal{G}_R$ , and is further processed by the dehazed network $\mathcal{G}_D$ to predict the transmission $\hat{\mathbf{t}}_C$ , the scattering coefficient $\hat{\beta}_{C}$ . Finally, we can reconstruct the clean input using the same calculations presented in Eq. 6. It is worth noting that, in this branch, since $\beta_{C}$ is sampled from a predefined range, our hazing process can be regarded as a data augmentation operation for the following training of the dehazing network. + +# 3.3. Training Objectives + +In the proposed $D^4$ framework, we train the proposed three networks together to perform the dehazing and rehazing cycles. Similar to CycleGANs, the cycle-consistency loss and the adversarial training loss are employed to penalize the content consistency and data distribution, respectively. Differently, we propose novel pseudo scattering coefficient supervision loss and pseudo depth supervision loss for learning physical properties (density and depth) from unpaired hazy and clean images. + +Cycle-consistency loss imposes that an intermediate image transferred from one domain to another should be able to transfer back. In our $D^4$ framework, the reconstructed clean image $\hat{\mathbf{C}}$ and hazy image $\hat{\mathbf{H}}$ should be consistent with their input counterparts $\mathbf{C}$ and $\mathbf{H}$ , respectively. The cycle-consistency loss in our $D^4$ can be written as follows: + +$$ +L _ {c y c} = \mathbb {E} _ {\mathbf {C} \sim \mathcal {X} _ {C}} \| \mathbf {C} - \hat {\mathbf {C}} \| _ {1} + \mathbb {E} _ {\mathbf {H} \sim \mathcal {X} _ {H}} \| \mathbf {H} - \hat {\mathbf {H}} \| _ {1}, \quad (9) +$$ + +where $\| \cdot \| _1$ designates the $\ell_1$ norm. + +Adversarial learning losses evaluate whether a generated image belongs to a specific domain. In other words, it penalizes our dehazed and rehazed images should be visually realistic and following the same distribution as images in training sets $\mathcal{X}_H$ and $\mathcal{X}_C$ . We adopt the LSGAN [28] due to its promising stability and visual quality. For the dehazing network $\mathcal{G}_D$ and corresponding discriminator $\mathcal{D}_c$ , the adversarial loss can be expressed as follows: + +$$ +\begin{array}{l} L _ {a d v} (\mathcal {D} _ {c}) = \mathbb {E} \left[ \left(\mathcal {D} _ {c} (\boldsymbol {c}) - 1\right) ^ {2} \right] + \mathbb {E} \left[ \left(\mathcal {D} _ {c} (\hat {\boldsymbol {c}})\right) ^ {2} \right], \\ L _ {a d v} \left(\mathcal {G} _ {D}\right) = \mathbb {E} \left[ \left(\mathcal {D} _ {c} (\hat {\boldsymbol {e}}) - 1\right) ^ {2} \right], \tag {10} \\ \end{array} +$$ + +where $c$ is real clean sample from the clean image set $\mathcal{X}_C$ , $\hat{c}$ is the dehazing result from $\mathcal{G}_D$ , $\mathcal{D}_c$ is the discriminator judging if the input image belongs to the clean domain. The adversarial loss for the haze refine network $\mathcal{G}_R$ and corresponding discriminator $\mathcal{D}_H$ is in the same form. + +Pseudo scattering coefficient supervision loss penalizes the difference between $\beta_{C}$ (the randomly sampled scattering coefficient for haze generation in the Hazing-Dehazing branch) and $\hat{\beta}_{C}$ (the scattering coefficient estimated from the generated hazy image $\hat{h}$ ), + +$$ +L _ {s c a t t} = \left(\hat {\beta} _ {C} - \beta_ {C}\right) ^ {2}. \tag {11} +$$ + +For hazy images from the training set $\mathcal{X}_H$ , the ground truth scattering coefficient is unavailable. Therefore, we alternatively adopt the randomly sampled scattering coefficients and corresponding generated hazy images to train the proposed dehazing network. + +Pseudo depth supervision loss. According to the observation that 'spatial-variant haze thickness provides an additional cue for perceiving scene depth', we employ the depth map $\mathbf{d}_H$ predicted from the hazy image $\mathbf{H}$ as the pseudo ground truth. Then, we train the depth estimation network $\mathcal{G}_E$ to estimate the depth map $\hat{\mathbf{d}}_H$ from the dehazed image $\hat{c}$ , i.e. $\hat{\mathbf{d}}_H = \mathcal{G}_E(\hat{c})$ . Then, we define the training loss, + +$$ +L _ {\text {d e p t h}} = \left\| \hat {\mathbf {d}} _ {H} - \mathbf {d} _ {H} \right\| _ {1}. \tag {12} +$$ + +Overall, the depth estimation network $\mathcal{G}_E$ is optimized alone by the depth loss $L_{depth}$ . The rest modules are jointly optimized with a weighted combination of the cycle loss, adversarial loss and pseudo scattering coefficient loss as: + +$$ +L _ {\text {t o t a l}} = \lambda_ {\text {c y c}} L _ {\text {c y c}} + \lambda_ {\text {a d v}} L _ {\text {a d v}} + \lambda_ {\text {s c a t t}} L _ {\text {s c a t t}}, \tag {13} +$$ + +where $\lambda_{cyc}$ , $\lambda_{adv}$ and $\lambda_{scatt}$ are the weights balancing different terms. In our experiments, empirically setting $\lambda_{cyc} = 1$ , $\lambda_{adv} = 0.2$ and $\lambda_{scatt} = 1$ works well. + +# 4. Experiments + +# 4.1. Experimental Configuration + +Datasets. In this work, we adopt the RESIDE [23] dataset, I-HAZE [1] dataset and Fattal's dataset [10] to train and evaluate the performance of our model and other candidates. + +The RESIDE dataset [23] is a widely-used large-scale dehazing benchmark datasets which comprises of subsets including: (i) ITS/OTS, which contains 13990/313950 synthetic indoor/outdoor hazy images with ground-truth for training. (ii) SOTS-indoor/outdoor, which include 500 synthetic indoor/outdoor hazy images with ground-truth for testing. (iii) RTTS and URHI, which both contain over 4000 real hazy images without ground-truth clean images. The I-HAZE [1] dataset contains 35 image pairs of hazy and corresponding haze-free indoor images. The haze in this dataset is produced by professional haze generators. Fattal's dataset [10] includes 31 real hazy images without ground truth, and it is broadly used for visual comparison. + +Competitors & Metrics. We compare our method with several state-of-the-arts dehazing algorithms. Among those methods, some use paired data for training, including EPDN [32], HardGAN [6], FFANet [31], DADehaze [39], and PSD [5]. While other methods are trained without using paired data, including DCP [14], CycleGAN [52], CycleDehaze [9], DisentGAN [47], YOLY [20] and RefineDNet [51]. The metrics including PSNR, SSIM [44] and CIEDE2000 (CIEDE for short) [40] are adopted to quantitatively evaluate the performance. + +![](images/1c42ad2d889b6b8d3237689bd51f9507ae590c1ccd01a7c173b87eb9a0c56db1.jpg) +Figure 3. Visual comparison in haze removal on samples from the SOTS-indoor, SOTS-outdoor and I-HAZE dataset. FFANet only performs well on the first and second cases. All results of PSD, YOLY and CycleDehaze are hazy. The first, second and fourth cases of RefineDNet are hazy and the third case is over-dehazed. Our method dehazes well on all cases. + +Implementation details. In the training phase, we apply the discriminator proposed in [16] with the patch size of $30 \times 30$ . The Adam optimizer [18] with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ , learning rate $l_{r} = 10^{-4}$ , and a batch size of 2 is used to optimize the network. All training samples are resized to $256 \times 256$ , half of which are horizontally flipped for data augmentation. To estimate the atmospheric light, we adopt the method in [14] for outdoor and I-HAZE dataset. While for synthetic indoor scenes, the brightest pixel is regarded as atmospheric light. + +# 4.2. Performance Evaluation + +Comparisons on the benchmark dataset. To quantitatively evaluate the performance and the generalization ability of our $D^4$ , we first conduct experiments on the bench + +mark datasets. Specifically, we train our model and comparison methods on the ITS dataset. For fair comparisons, all supervised methods utilized pair training data within the ITS dataset, yet unpaired methods, including our $D^4$ , abandoned all paired information during training. Considering the SOTS-indoor is synthesised in the same way as ITS, we selected it as one of our test sets. While SOTS-outdoor and I-HAZE various on the scenes and haze types, the results on these two test sets can reflect the dehazing generalization ability of different models. Note that, since the I-HAZE dataset is not used for training, we adopt the entire I-HAZE dataset for testing. + +The quantitative comparisons are reported in Tab. 1. On SOTS-indoor test set, the supervised methods HardGAN [6] + +Table 1. The quantitative comparison results on SOTS-indoor, SOTS-outdoor and I-HAZE datasets. Higher PSNR, SSIM, and lower CIEDE2000, Params, FLOPs indicate better results. Paired and W/o Paired denote the method used or did not use paired data for training. Since DCP is not based on DNN and YOLY needs to iteratively process on single image, the parameters of DCP and the FLOPS of YOLY, DCP are not available. The best, second best and third best result are denoted in bold, underlined and italic, respectively. + +
MethodsSOTS-IndoorSOTS-OutdoorI-HAZEEfficiency
PSNR↑SSIM↑CIEDE↓PSNR↑SSIM↑CIEDE↓PSNR↑SSIM↑CIEDE↓Params (M)FLOPs (GMac)
PairedEPDN [32]25.060.9314.57820.470.8968.56615.020.76314.9617.384.826
FFANet [31]36.360.9931.10820.230.9056.90812.000.59220.334.456288.3
HardGAN [6]35.450.9911.26923.330.9375.34813.820.72017.542.54649.18
PSD [5]15.020.76413.8015.630.83412.6015.300.80014.8433.11182.5
W/o PairedDCP [14]13.100.6997.40420.150.9197.61313.100.69919.04--
CycleGAN [52]21.340.8987.00020.550.8569.29815.290.75619.5011.3856.89
CycleDehaze [9]20.110.8548.76121.310.8999.48114.690.75119.0511.3849.16
DisentGAN [47]21.510.8997.29418.450.83112.2414.480.67516.5211.4857.46
YOLY [20]15.840.81912.3714.750.85715.8514.740.68815.2432.00-
RefineDNet [51]24.360.9394.30519.840.8538.48113.600.66017.0865.8075.41
Ours25.420.9323.67025.830.9564.29515.610.78014.4510.702.246
+ +![](images/390a1de96f665b06316ea495fd6ba28b3af9efa92e5351910d0273eb31140edb.jpg) +Hazy image + +![](images/7679c0f74a97130d6c3d8920a08f8d9d1913bbb04ad3d0f520ac3abae3ed1069.jpg) + +![](images/3cf78a13bc6a814a40ec921064342c3d3ea04dd339e15154aa994a91e75ed3e1.jpg) +FFANet [31] + +![](images/25c0eac912358287999a37aab7d80c98c169a9a44cbb01951f883fe311278639.jpg) +PSD [5] + +![](images/0e561c104502e402b46989982abebc40c0dd9aa530e7e0c23429a69b8cd8108d.jpg) +Ours +Figure 4. Visual comparison on two real images from Fattal's dataset [10]. FFANet has minor effect on haze removal. PSD causes global color distortion and over-saturation. + +and FFANet [31] demonstrate their powerful fitting ability and rank the first and second places with absolute advantage. Our $D^4$ is the best among the methods without using paired training data. In contrast, since the samples in SOTS-outdoor dataset and I-HAZE dataset are inconsistent with training data, the FFANet and HardGAN lose their dominant positions. It partly reveals the overfitting issue of supervised dehazing methods. While our $D^4$ gets rid of such defect and outperforms other competitors on both datasets. Besides, we also provide several visual comparisons in Fig. 3. For the first and second synthetic indoor cases, both of FFANet and our $D^4$ can thoroughly remove the haze while other methods remain observable haze on the results. For the last two cases, FFANet remains dense haze on the results. Although PSD produces brighter results, it fails to remove the haze. CycleDehaze suffers from the color distortion and RefineDNet over-dehazes the third case and leaves obvious haze on the last case, while our $D^4$ successfully removes the haze without leaving obvious artifacts. All these results validate the better generalization ability of our $D^4$ . To summarize, although our result is not + +![](images/6870c074641f9a140c15a1d8d8923b36607b67876765906c2bf39c1830ff4edb.jpg) +Hazy image +Figure 5. Comparison on two real samples from URHI. HardGAN and DADehaze both leave observable haze on the results. + +![](images/60946cb5aa928be6477996b308fb843bcff8064d4538b865dd91f3b5edcddb0e.jpg) +HardGAN [6] + +![](images/974526ed61e2d497443202038c537e1c179d8213e52dfe415d5e4436a139d930.jpg) +DADehaze [39] + +![](images/36ed627f3cf4a77d0d978a37659ef0f8804c26abe9a8dda0575cd886fa8fecff.jpg) +Ours + +comparable with the supervised method in SOTS-indoor, it is outstanding among the methods without using paired data. Considering quantitative, visual results and model efficiency in all three datasets, our method is more appealing. Comparisons on real-world hazy images. To further evaluate the dehazing performance for real scenes, we conduct experiments on the Fattal's dataset [10] and URHI dataset. We finetune our model on unpaired outdoor clean and hazy images from OTs and RTTS. From indoor to outdoor, we employ an additional hyper-parameter for adjusting transmission estimator when extending to outdoor scene. For DADehaze [39], RefineDNet [51] and PSD [5], we use their released model which is pre-trained on real hazy images. For FFANet [31] and HardGAN [6], we adopt the model trained on paired synthetic images. The visual results on Fattal's dataset and URHI dataset are shown in Fig. 4 and Fig. 5, respectively. From Fig. 4, we can see that FFANet [31] has a very limited effect towards real hazy images. The results produced by PSD [5] suffer severe color distortion. While our method successfully removes the haze in the image. In Fig. 5, results of both HardGAN [6] and DADehaze [39] contain residual haze, while our result is sharp + +![](images/c02145ee7337f5165ab0392d0f671ed5b8a6c3bf713eb5c2f0a89953ae421867.jpg) +Input + +![](images/a1007406aaf9064d00345202347633ad48b15da4b00bd8398885505fef3d4382.jpg) +GT + +![](images/d3cc6ea29d0980dc8c5d99066b9132db0bc69122fa09e1e78abb4e22c849354f.jpg) +FCRN [19] + +![](images/e10810649cdc70795db2bdce1af5e25587644a7c41b6ca2081a81f234cdda077.jpg) +Ours + +![](images/26670a2dfb7630b852cd4cff72cab7949f49b97f42642d911f72ad75207acf47.jpg) +Input + +![](images/3df3d814e728ac8b81ca7c352e2afb76ca9203acefb51a0fc60ab08d4a388d0c.jpg) +Light + +![](images/0c631ed87da5b53e95ae311bf33c4bc47d5b2a27c9a9de7e09849aeba377603b.jpg) +Heavy + +![](images/88aaa4b72e47095d31a943e91f32951180ea3dbe067db316e891316b9b0d12f2.jpg) +CycleGAN [52] +Figure 6. Example of depth estimation and haze generation. Compared with GT and FCRN, our estimated depth is also visually reasonable. The haze generated by CycleGAN is not consistent with depth, while the haze from ours is more realistic and various. + +and clear. This part of experiment validates that our method generalizes well on real-world outdoor hazy images, + +Results on depth estimation and haze generation. We notice that without paired depth supervision, our method can learn to predict visually reasonable depth maps from unpaired hazy and clean images. Fig. 6 presents a few cases of depth estimation and haze generation, from which we can see that, although a gap between our depth estimation and the supervised FCRN exists, our method is acceptable without ground-truth depth information. Having the predicted depth, our network can produce more realistic and various hazy images on both indoor and outdoor images in comparison with CycleGAN. + +The comparison on the efficiency of the method. To measure the efficiency of the networks, we make comparison on the number of parameters, and the FLOPs of the dehazing models. Specifically, only the dehazing part of each model is taken into account. As shown in Tab. 1, our model has the lowest FLOPs and fewer parameters with a light-weight backbone [43]. With such a light-weight model, our method still outperforms other state-of-the-arts methods, which validates the effectiveness of our design. + +# 4.3. Ablation Study + +In this part, we validate the effectiveness of our proposed self-augmentation and pseudo supervision mechanism. For the self-augmentation, we replace the random generated $\beta$ in the Hazing-Dehazing branch with a fixed value, and keep other settings unchanged (denoted as w/o Aug). For the pseudo supervision, since the pseudo $\beta$ supervision and pseudo depth supervision are closely tied to each other, we have to add or remove them together. Without these two pseudo supervisions (w/o PS), we remove the function of estimate $\beta$ of the dehazing network $\mathcal{G}_D$ and change the depth estimation network $\mathcal{G}_E$ to directly estimating the transmission map. Overall, this setting makes our + +![](images/39c89d03bc5d6ba5a7dcd14553eec733de6349920c76c4008f20782811848a2f.jpg) +(a) Input + +![](images/bc0ec0f642da817f3dcc0eedf5d8110e4a29d1fa921915c1ef81b29ca0fc1359.jpg) +(b) w/o PS + +![](images/baf3510bf56fdbbe8dd31ce7091a797dc928e40905480df17ff3249a8894a729.jpg) + +![](images/853884c39710bbe9508b59a0ab0c6b85c87e699e9b01bb32089f478f55803e84.jpg) + +![](images/ff0805020efb633d43c97477f1d489eca52f115bb3c12cd1daf7e89edc10d542.jpg) +(e) GT + +![](images/5dc5f5eb38948b446c0d76e211322384d317c3fbd127010f2e8cbd58c96a9f4a.jpg) +(f) w/o PS +Figure 7. The images in (b)-(d) are the dehazed results of (a) by different network configurations, while (f)-(h) are generated hazy images from the clean image (e). + +![](images/ac5986dff7ab2d7717931cc0b5e59e10a7e94c5b2a6d19e9af4d8c103fd26b40.jpg) +(c) w/o Aug +(g) w/o Aug + +![](images/f69aa0a6f7c355f8f1761c4c70462f7af4cc5c9d348a39b9ffa19c2f5398ab15.jpg) +(d) Ours +(h) Ours + +Table 2. Ablation study on the SOTS dataset. + +
MetricsSOTS-indoorSOTS-outdoor
PSNR↑SSIM↑CIEDE↓PSNR↑SSIM↑CIEDE↓
w/o Aug23.150.91264.97524.080.94725.041
w/o PS20.020.85097.31522.950.91685.669
Ours25.420.93213.67025.830.95594.295
+ +framework degrade to a vanilla-CycleGAN-liked architecture. The quantitative and qualitative results are shown in Tab. 2 and Fig. 7, respectively. From Tab. 2, we can see that any ablation to our network causes an obvious drop in performance. Fig. 7 shows intuitive visual comparisons. From the images on the first row, we can infer that our complete $D^4$ removes the haze most thoroughly in comparison with the networks without self-augmentation and pseudo supervision mechanism. Besides, as shown in the images on the second row, our complete $D^4$ generates the most realistic hazy images. Specifically, the red boxed regions are near to the observer, so the haze at that area should be thinner. Such a property is more clearly reflected on the images produced by our complete model than those by the other configurations. The ablation study verifies that both self-augmentation and pseudo supervision are effective. + +# 5. Conclusion + +This paper has proposed a self-augmented unpaired image dehazing framework termed $D^4$ , which decomposes the estimation of transmission map into predicting the density and the depth map. With the estimated depth, our method is capable of re-rendering hazy images with various densities as self-augmentation to improve the dehazing performance by a large margin. Extensive experiments have validated the clear merits of our method over other state-of-the-arts dehazing methods. However, our method also has the limitation that, it usually over-estimates the transmission of extreme bright area, which will mislead the depth estimation network to predict low depth value for over-bright areas. Besides, we found that training data with low quality will make the training unstable. But it is positive that our thought of further decomposing variables in the physical model can be extended to other tasks, like low-light enhancement. 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Yet, employing a complex pre-trained teacher network or an ensemble of peer students in existing KD is both time-consuming and computationally costly. Various self KD methods have been proposed to achieve higher distillation efficiency. However, they either require extra network architecture modification or are difficult to parallelize. To cope with these challenges, we propose an efficient and reliable self-distillation framework, named Self-Distillation from Last Mini-Batch (DLB). Specifically, we rearrange the sequential sampling by constraining half of each mini-batch coinciding with the previous iteration. Meanwhile, the rest half will coincide with the upcoming iteration. Afterwards, the former half mini-batch distills on-the-fly soft targets generated in the previous iteration. Our proposed mechanism guides the training stability and consistency, resulting in robustness to label noise. Moreover, our method is easy to implement, without taking up extra run-time memory or requiring model structure modification. Experimental results on three classification benchmarks illustrate that our approach can consistently outperform state-of-the-art self-distillation approaches with different network architectures. Additionally, our method shows strong compatibility with augmentation strategies by gaining additional performance improvement. The code is available at https://github.com/Meta-knowledge-Lab/DLB. + +# 1. Introduction + +Knowledge Distillation (KD), first introduced by Bucilua et al. [2], was later popularized by Hinton et al. [10]. Numerous previous researches have demonstrated the success of KD in various learning tasks to boost the generalization ability. For example, in the case of network compression, the two-stage offline KD is widely used to transfer + +dark knowledge from a cumbersome pre-trained model to a light student model that learns from teachers' intermediate feature maps [21], logits [10], attention maps [40], or auxiliary outputs [43]. However, training a high-capacity teacher network heavily relies on large computational sources and run-in memory. To alleviate the time-consuming preparation of static teachers, online distillation is introduced [44], where an ensemble of peer students learns mutually from each other. Online KD achieves equivalent performance improvement, compared with offline KD, with higher computational efficiency. Thus, this line is subsequently extended by many following works to a more capable self-ensemble teacher [3,8,14,33]. Other applications of KD include semisupervised learning, domain adaptation, transfer learning and etc [18,26,28]. The main scope of this paper focuses on the KD paradigm itself. + +Conventional KD approaches, both online and offline, have achieved satisfying empirical performance [24]. Yet, existing KD approaches suffer from an obstacle in the low knowledge transferring efficiency [35]. Additionally, high computation and run-in memory costs restrict their deployment onto the end devices, such as mobile phones, digital cameras [4]. To cope with these limitations, self-knowledge distillation has received increasing popularity, which enables a student model to distill knowledge from itself. The absence of a complex pre-trained teacher and an ensemble of peer students in self-KD contributes to a marginal improvement in the training efficiency. + +One popular formulation of self KD, such as Be Your Own Teacher (BYOT), requires heavy network architecture modifications, which largely increases their difficulty to generalize onto various network structures [19,32,43]. In another line, history information, including previous training logits or model snapshots, is utilized to construct a virtual teacher for extra supervision signals as self distillation. Initially, born again networks (BAN) sequentially distill networks with identical parameters as its last generation [7]. An advancement achieved by snapshot distillation is to take the secondary information from the prior mini-generation i.e. a couple of epochs, within one generation [36]. This virtual teacher update frequency is further + +Table 1. A comparison with the state-of-the-arts in terms of computational cost and smoothed granularity. We compare our method with label smoothing regularization [27], teacher-free knowledge distillation (Tf-KDself, Tf-KDreg) [37], class-wise self-knowledge distillation (CS-KD) [39], progressive self-knowledge distillation (PS-KD) [12], memory-replay knowledge distillation (Mr-KD) [30], data-distortion guided self-knowledge distillation (DDGSD) [35], be your own teacher (BYOT) [43]. + +
CharacteristicLSRTf-KDselfTf-KDregCS-KDPS-KDMr-KDDDGSDBYOTOurs
Sample-level smoothing×✓✓✓✓✓✓✓✓
No pre-trained teacher✓×✓✓✓✓✓✓✓
No Architecture modification✓✓✓✓✓✓✓×✓
Forward times per batch12122≥2211
Backward times per batch1112112≥21
Number of involved networks121121111
Label update frequency-epoch--epochepoch--batch
+ +improved to epoch-level in progressive self-knowledge distillation [12] and learning with retrospection [5]. Yet, existing self KD methods have the following setbacks to be tackled. Firstly, the most instant information from the last iteration is discarded. Moreover, storing a snapshot of past models consumes an extra run-in memory cost, and subsequently increases the difficulty to parallelize [36]. Finally, computation of the gradient in each time backward prorogation is associated with twice the forward process on each batch of data, resulting in a computational redundancy and low computational efficiency. + +To address these challenges in existing self KD methods, we propose a simple but efficient self distillation approach, named as Self-Distillation from Last Mini-Batch (DLB). Compared with existing self KD approaches, DLB is computationally efficient and saves the run-in memory by only storing the soft targets generated in the last minibatch backup, resulting in its simplicity in deployment and parallelization. Every forward process of data instances is associated with a once backpropagation process, mitigating the computational redundancy. Major differences compared with the state-of-the-arts are summarized in Table 1. DLB produces on-the-fly sample-level smoothed labels for self-distillation. Leveraging the soft predictions from the last iteration, our method provides the most instant distillation for each training sample. The success of DLB is attributed to the distillation from the most immediate historically generated soft targets to impose training consistency and stability. To be more specific, the target network plays a dual role as teacher and student in each mini-batch during the training stage. As a teacher, it provides soft targets to regularize itself in the next iteration. As a student, it distills smoothed labels generated from the last iteration and minimizes the supervision learning objective e.g. the cross-entropy loss. + +We empirically illustrate the comprehensive effectiveness of our methods on three benchmark datasets, namely CIFAR-10 [13], CIFAR-100 [13], TinyImageNet. Our approach is both task-agnostic and model-agnostic i.e. with no requirement of model topological modifications. We + +select six representative backbone CNNs for evaluations, including ResNet-18, ResNet-110 [9], VGG-16, VGG-19 [25], DenseNet [11], WideResNet [41]. Experimental results demonstrate that our DLB can consistently improve the generalization ability. We also test the robustness of DLB on corrupted data. Training consistency and stability imposed by DLB on corrupted data results in higher generalization ability. + +The major contributions are three-fold. + +- We propose a simple but efficient consistency regularization scheme based on self-knowledge distillation, named as DLB. With no network architecture modifications, our method requires very few additional computation costs as well as the run-time memory to implement. Utilizing the latest update from the last iteration, our DLB is easy to implement for parallelization. Notably, the proposed method is also both model-agnostic and task-agnostic. +- Comprehensive experimental results on three popular classification benchmarks illustrate consistent generalization improvements on different models. We also empirically demonstrate the compatibility of DLB with various augmentation strategies. +- We systemically analyze the impact of our method on the training dynamics. Concretely, the success of its regularization effect is attributed to guidance towards training consistency, by leveraging on-the-fly sample-level smooth labels. The consistency effect is further amplified under label corruption settings, showing strong robustness to label noise. These empirical finds may shed light on a new direction to understand the effect of knowledge distillation. + +# 2. Related Works + +Knowledge distillations. Knowledge distillation (KD) targets to transfer 'knowledge', such as logits, or intermediate feature maps, from a high-capability teacher model + +![](images/5efce8d7f2870c8d3d22f597871fe325068adb79ed8a7951a3971457d3c98efd.jpg) +Figure 1. The overall architecture of our DLB. We write $\mathcal{B}_t, \phi_t, \theta_t$ for a mini-batch of data samples, random augmentation and the trainable parameters indexed in the $t^{\text{th}}$ iteration. + +to a lightweight student network [2, 10]. Despite its competitive performance improvement to generalization, pretraining a complex teacher model requires extra training time and computational cost. Another way to form an economic distillation is called mutual learning, also known as online distillation, where an ensemble of students learn mutually from each other [44]. This idea was popularized by many following works [3, 14, 33]. But, the optimization in peer learning involves multiple numbers of networks, which requires extra memory to store all parameters. + +Self Knowledge Distillation. To enhance efficiency and effectiveness in knowledge transferring, self knowledge distillation (SKD) is proposed to utilize knowledge from itself, without the involvement of an extra networks [31]. There are three popular ways to construct a SKD model i.e., 1) data distortion based self-distillation [15,35], 2) use history information as a virtual teacher, 3) distilling across auxiliary heads [17,43]. However, the first one marginally relies on the augmentation efficiency. The second one misses the latest update from the last mini-batch. And the last kind requires heavy network architecture modifications, which increase its difficulty for deployment. + +Distillations as regularization. KD is extensively used in many tasks, such as model compression, semi-supervised learning, domain adaptation and etc [18, 26, 28]. However, theoretical analysis of the success of KD remains a big challenge. Recently, Yuan et al. attributed the success of KD to its regularization effect as providing sample-level soft targets from the LSR perspective [37]. It reveals the large promise of applying KD to the regularization domain. In this line, class-wise self-knowledge distillation (CS-KD) is designed by evacuating a consistency between predic + +tions of two batches of samples identified with the same category [39]. Progressive self-knowledge distillation (PS-KD), more similar to our work, progressively distills past knowledge from the last epoch to soften hard targets in the current epoch [12]. Memory-replay knowledge distillation (Mr-KD) extends PS-KD by storing a series of abandoned network backups for distillation [30]. However, implementing PS-KD or Mr-KD both requires extra GPU memory to store the historical model parameters or the whole past predictions on the disk. The previous strategy is computationally costly for large models such as deep WRN [41], while the latter one is inefficient in training large datasets such as ImageNet [23]. The above-mentioned drawbacks result in low training efficiency, as well as the implementation difficulty on end devices such as mobile phones, digital cameras, etc [4], which restrict their applications for regularization. On the other hand, much recent information from the last several mini-batches is absent in these methods. To cope with these shortages, we propose a novel self-distillation framework named DLB, which will be elaborated on in the following section. + +# 3. Methods + +# 3.1. Preliminary + +In this work, we focus on a supervised classification task as case study. For a clear notation, we write a $K$ -classes labelled dataset as $\mathcal{D} = \{(\mathbf{x}_i,y_i)\}_{i=1}^N$ , where $N$ is the total number of training instances. In every mini-batch, a batch of $n$ samples $\mathcal{B} = \{(\mathbf{x}_i,y_i)\}_{i=1}^n \subseteq \mathcal{D}$ is augmented by data distortion $\phi$ to derive the distorted images $\mathcal{B}^\phi = \{(\phi(\mathbf{x}_i),y_i)\}_{i=1}^n$ . Afterwards, they are fed into target neural network $h_\theta$ to optimize the cross-entropy loss function, defined as follows + +$$ +\mathcal {L} _ {C E} = \frac {1}{n} \sum_ {i = 1} ^ {n} H \left(y _ {i}, \mathbf {p} _ {i}\right). \tag {1} +$$ + +Formally, the predictive distribution $\mathbf{p}_i = (p_i(1),\dots ,p_i(K))$ in a softmax classifier for class $k\in [K]$ is formulated as + +$$ +p _ {i} (k) = \frac {\exp \left(f _ {k} \left(\mathbf {x} _ {i} ; \theta\right) / \tau\right)}{\sum_ {j = 1} ^ {K} \exp \left(f _ {j} \left(\mathbf {x} _ {i}; \theta\right) / \tau\right)}, \tag {2} +$$ + +where $f_{k}$ writes for the $k^{\mathrm{th}}$ component of the logits from the backbone encoder parameterized by $\theta$ . Temperature $\tau$ is usually set to 1 in Eq. (2). To improve the generalization ability, vanilla knowledge distillation [10] transfers pre-trained teacher's knowledge by optimizing an additional Kullback-Leibler (KL) divergence loss between the softened outputs from teacher and student in every minibatch i.e. + +$$ +\mathcal {L} _ {K D} = \frac {1}{n} \sum_ {i = 1} ^ {n} \tau^ {2} \cdot D _ {K L} \left(\widetilde {\mathbf {p}} _ {i} ^ {\tau} \| \mathbf {p} _ {i} ^ {\tau}\right), \tag {3} +$$ + +where $\mathbf{p}_i^\tau$ , $\widetilde{\mathbf{p}}_i^\tau$ are the soften predictions, parameterized by temperature $\tau$ , from student and teacher respectively. A higher temperature results in a more uniform distribution, leading to a similar regularization effect as label smoothing [27, 37]. Compared with previous works where a complex network is pre-trained to generate $\widetilde{\mathbf{p}}_i^\tau$ , our work uses historic information from the last batch to efficiently generate $\widetilde{\mathbf{p}}_i^\tau$ as a more instant smoothed labels for regularization. + +# 3.2. Self-Distillation from Last Batch + +The overall training process for the proposed self-distillation is visualized in Figure 1. Instead of adopting a complex pre-trained teacher model to provide samplewise smoothed labels, our proposed framework utilizes the backup information from the last mini-batch to generate soft targets. It results in a regularization towards training consistency. For a clear notation, we denote the original batch of data sampled in the $t^{\text{th}}$ iteration as $\mathcal{B}_t = \{(\mathbf{x}_i^t,y_i^t)\}_{i = 1}^n$ , and the network parameters as $\theta_t$ . Formally, we substitute the $\widetilde{\mathbf{p}}_i^\tau$ in Eq. (3) by the soften labels $\mathbf{p}_i^{\tau ,t - 1}$ generated by the identical network at $t - 1^{\text{th}}$ iteration i.e. $f$ parameterized by $\theta_{t - 1}$ . Consequently, we introduce an extra last-batch consistency regularization loss to DLB as follows: + +$$ +\mathcal {L} _ {L B} = \frac {1}{n} \sum_ {i = 1} ^ {n} \tau^ {2} \cdot D _ {K L} \left(\mathbf {p} _ {i} ^ {\tau , t - 1} \| \mathbf {p} _ {i} ^ {\tau , t}\right). \tag {4} +$$ + +Rather than storing the whole $\theta_{t - 1}$ in the $t^{\mathrm{th}}$ iterations as designed in previous works [12], which is run-time memory consuming, we complete the computation of all $\mathbf{p}_i^{r,t - 1}$ in $t - 1^{\mathrm{th}}$ iteration. We employ a data sampler to obtain $\mathcal{B}_t$ and $\mathcal{B}_{t - 1}$ simultaneously at the $t - 1^{\mathrm{th}}$ iteration for implementation. Both the predictions from $\mathcal{B}_{t - 1}$ and $\mathcal{B}_t$ in $t - 1^{\mathrm{th}}$ + +iteration update the $\mathcal{L}_{CE}$ . Whereas predictions from $\mathcal{B}_t$ are smoothed by temperature $\tau$ and then stored for regularization in $t^{\mathrm{th}}$ iteration. Storage of a batch of smoothed labels requires very few extra memory cost, which is thus more efficient. Conclusively, the overall loss function is formulated by + +$$ +\mathcal {L} = \mathcal {L} _ {C E} + \alpha \cdot \mathcal {L} _ {L B}, \tag {5} +$$ + +where $\alpha$ is the coefficient to balance two terms. In short, we constrain half of each mini-batch coinciding with the previous iteration, and the rest half with the upcoming iteration. Afterwards, the former half mini-batch distills on-the-fly soft targets generated in the previous iteration. The overall training process is summarized in Algorithm 1. + +Algorithm 1 Pseudo code for DLB. +Input: balancing coefficient $\alpha$ +Input: distillation temperature $\tau$ +Require: dataloader samples batches as in Figure 1 +1: last_logits = None # initialization +2: for (x,gt_labels) in dataloader do +3: $\hat{n} = \mathrm{gt\_labels.size}(0)$ # batch size +4: logits = model.forward(x) +5: loss = CELoss(logits, gt_labels) +6: if last_logits != None then +7: soft_targets = Softmax(last_logits/ $\tau$ ) +8: pred = Softmax(logits[: $\hat{n} // 2$ ]/ $\tau$ ) +9: loss += $\alpha^{*}\mathrm{LBLoss}(\mathrm{pred},\mathrm{soft\_targets})^{*}\tau^2$ +10: end if +11: loss/backward() # update parameters +12: last_logits = logits[ $\hat{n} // 2$ ].detach() # no gradient +13: end for + +# 4. Experiments + +# 4.1. Datasets and Settings + +Datasets. We employed three multi-class classification benchmark datasets for comprehensive performance evaluations. The CIFAR-10/CIFAR-100 contain a total number of 60,000 RGB natural images of $32 \times 32$ pixels from 10/100 classes [13]. Each class includes 5,000/500 training samples and 1,000/100 testing samples. We followed the widely-used pre-processing from previous works [9,41]. More precisely, training samples were normalized by deviation and padded 4 pixels with zero-value on each side. A random crop of $32 \times 32$ region was generated from the padded image or its horizontal flip. The TinyImageNet is a subset of ILSVRC-2012, made up of 200 classes. Each class includes 500 training samples and 50 testing samples, scaled at $64 \times 64$ . All training images were randomly cropped and resized to $32 \times 32$ after the normalization. The test images were only normalized. + +Table 2. Performance comparison with label smoothing regularization and state-of-the-art self-distillation methods on CIFAR-10, CIFAR-100 and TinyImageNet in terms of average top-1 error rate (\%). We calculated the average and deviation over three runs. The best and second best performance were highlighted in Red and Green respectively. + +
DatasetMethodsVgg-16Vgg-19ResNet-32ResNet-110WRN20-8DenseNet-40-12
CIFAR-10Baseline6.03±0.226.04±0.106.54±0.105.21±0.245.47±0.087.09±0.28
LSR5.91±0.406.05±0.066.73±0.175.60±0.174.76±0.067.47±0.27
Tf-KDself5.92±0.155.91±0.016.32±0.014.92±0.085.33±0.137.03±0.14
Tf-KDreg6.12±0.076.25±0.186.60±0.055.48±0.184.79±0.017.38±0.16
CS-KD6.22±0.206.38±0.116.88±0.156.12±0.054.89±0.197.85±0.17
PS-KD5.90±0.046.07±0.575.96±0.065.09±0.684.99±0.016.77±0.28
DLB5.38±0.015.58±0.085.85±0.024.85±0.114.46±0.016.57±0.02
(0.65↑)(0.46↑)(0.70↑)(0.37↑)(1.01↑)(0.53↑)
CIFAR-100Baseline26.37±0.1927.16±0.4228.26±0.1823.64±0.2522.42±0.2328.31±0.35
LSR25.81±0.0226.75±0.4528.21±0.1323.32±0.1622.17±0.0129.07±0.01
Tf-KDself25.94±0.1127.46±0.8226.09±0.2427.02±0.0121.88±0.3428.40±0.09
Tf-KDreg25.85±0.3026.82±0.5928.29±0.0723.54±0.0422.28±0.0528.92±0.04
CS-KD25.81±0.4326.65±0.4929.21±0.2123.41±0.2821.75±0.2629.65±0.51
PS-KD25.95±0.7426.36±0.7627.49±0.7522.85±0.6521.26±0.1128.48±0.53
DLB23.88±0.0624.53±0.1326.00±0.0321.82±0.1920.79±0.3327.48±0.21
(2.50↑)(2.63↑)(2.26↑)(1.83↑)(1.63↑)(0.83↑)
TinyImageNetBaseline48.83±0.3350.02±0.1250.38±0.3843.20±0.5643.72±0.2850.94±0.56
LSR47.95±0.3248.86±0.7852.75±0.6942.18±0.5743.51±0.1351.01±0.16
Tf-KDself46.76±0.1047.25±0.0649.48±0.1641.31±0.0141.13±0.1150.78±0.01
Tf-KDreg48.31±0.0649.54±0.1650.97±0.0241.88±0.9142.85±0.0751.47±0.10
CS-KD46.95±0.1547.89±0.1353.99±0.0343.06±0.2242.04±0.4254.93±0.25
PS-KD48.39±0.2349.77±0.2350.28±0.1742.22±0.7243.37±0.0151.57±0.05
DLB45.66±0.0146.68±0.0948.66±0.0740.39±0.0141.03±0.0250.13±0.01
(3.17↑)(3.35↑)(1.72↑)(2.81↑)(2.69↑)(0.81↑)
+ +Implementations. All experiments were performed on one NVIDIA Tesla V100 GPU with 32Gb memory. The proposed DLB and compared methods were all implemented on Pytorch 1.6.0 in Python 3.7.0 environment. The hyper-parameters for the training scheme followed a consistent setting for a fair comparison. CIFAR-100/10: We followed the settings in previous works [29, 34]. Specifically, every backbone network was trained for 240 epochs with a batch size of 64. The initial learning rate was set to 0.05, and decayed by a factor of $10\%$ at $150^{\mathrm{th}}$ , $180^{\mathrm{th}}$ and $210^{\mathrm{th}}$ epoch. We employed a stochastic gradient descent (SGD) optimizer with 0.9 Nesterov momentum, where the weight decay rate was set to $5 \times 10^{-4}$ . TinyImageNet: We also followed the settings in previous works [42]. Concretely, we set the maximal epoch number to 200, the batch size to 128. The initial learning rate was set to 0.2 with a decayed factor of $10\%$ at $100^{\mathrm{th}}$ , $150^{\mathrm{th}}$ epoch. The weight decay rate and the momentum in the SGD optimizer were set to $1 \times 10^{-4}$ and 0.9 respectively. We fixed the temperature $\tau$ at 3 and coefficient $\alpha$ in DLB to 1, where the dependence of hyper-parameters is explored in the next subsection. The + +temperature setting in DLB followed suggests from previous work [44], and we did not manually tune it for our approach. We used the top-1 error rate (\%) on the test set as the evaluation metric. For reproducibility, we fixed the random seed at 95 in all experiments. We also measured the average and the associated standard deviation over three runs. Importantly, for a fair comparison in terms of computation cost, the proposed method (DLB) was evaluated on half of the total training interactions/epochs than the compared approaches. Although our method comes to a doubled batch size by duplicating half of the last mini-batch, it brings no extra computation cost with halving total training iterations. + +Backbone architectures. We employed six representative architectures [3, 33] for evaluation, namely Vgg-16, Vgg-19 [25], ResNet-32, ResNet-110 [9], WRN20-8 [41], DenseNet-40-12 [11]. + +Compared methods. Hard labels were utilized in the baseline to train the target network directly. We also compared the proposed method with label smoothing regulariza + +Table 3. Performance compatibility with augmentation-based regularization methods including CutOut [6], CutMix [38] and DDGSD [35] on CIFAR-10/100. We calculated the average top-1 error rate (\%), standard deviation of three runs, written in the form of 'avg ± std'. The best result in each category was highlighted in **boldface**. + +
DatasetMethodsVgg-16Vgg-19ResNet-32ResNet-110WRN20-8DenseNet-40-12
C10Baseline6.03±0.226.04±0.106.54±0.105.21±0.245.47±0.087.09±0.28
+ DLB5.38±0.015.58±0.085.85±0.024.85±0.114.46±0.016.57±0.02
+ CutOut4.93±0.045.10±0.055.91±0.124.64±0.144.88±0.116.68±0.11
+ CutOut + DLB4.48±0.034.46±0.405.18±0.053.78±0.094.12±0.095.54±0.04
+ CutMix5.29±0.045.41±0.035.96±0.284.82±0.104.89±0.316.76±0.17
+ CutMix + DLB5.20±0.135.21±0.015.22±0.664.41±0.254.29±0.205.28±0.06
+ DDGSD5.65±0.145.79±0.085.96±0.044.77±0.044.72±0.136.83±0.21
+ DDGSD + DLB5.31±0.075.52±0.055.75±0.254.45±0.594.14±0.035.74±0.23
C100Baseline26.37±0.1927.16±0.4228.26±0.1823.64±0.2522.42±0.2328.31±0.35
+ DLB23.88±0.0624.53±0.1326.00±0.0321.82±0.1920.79±0.3327.48±0.21
+ CutOut25.76±0.1626.19±0.6927.72±0.0222.09±0.1821.14±0.3728.58±0.47
+ CutOut + DLB23.02±0.0823.62±0.1725.93±0.2820.27±0.3320.30±0.0127.04±0.43
+ CutMix24.07±1.0225.67±0.0427.31±0.4221.42±0.120.57±0.2728.27±0.42
+ CutMix + DLB23.48±0.2924.06±0.0125.77±0.6420.93±0.0420.10±0.1126.82±0.12
+ DDGSD24.36±0.0424.69±0.0126.32±0.2322.55±0.1720.83±0.0827.69±0.32
+ DDGSD + DLB23.81±0.1124.20±0.2825.98±0.0421.18±0.4220.28±0.0127.25±0.28
+ +![](images/17ef375f6c4571ac68ee6698417b3a714aa3a62fd755618ed1a2151544a4dbfd.jpg) +(a) CIFAR-100 + +![](images/2fc018ff1d85397e83731a2771e18af45d67adc5cd8015bb0007bd64bdbe200e.jpg) +(b) CIFAR-10 +Figure 2. Performance on training with label noise. (a) CIFAR-100. (b) CIFAR-10. The line shows the top-1 validation error rate (\%) on corrupted data at different percentage $(p)$ of the noisy label i.e., $p \in \{0, 10\%, 20\%, 30\%, 40\%, 50\%, 60\}$ . The bar illustrates the improvement of our approach, compared with baseline. + +tion (LSR) [27] and self-knowledge distillation regularization approaches, including teacher-free knowledge distillation (Tf-KD $_{self}$ , Tf-KD $_{reg}$ ) [37], class-wise self-knowledge distillation (CS-KD) [39], progressive self-knowledge distillation (PS-KD) [12]. The above methods focus on logit-level regularization. Data-distortion guided self-knowledge + +distillation (DDGSD) is a data augmentation based distillation approach [35], which was compared and tested the compatibility with DLB. We removed the feature-level supervision in DDGSD [35] i.e. MMD loss, for a fair comparison. As DDGSD is an augmentation based method, we explore the performance compatibility between DLB and + +![](images/bcc24da6ca13ede605f117aedfa928a4bb1f0c708dca62f102f5c9a406363c06.jpg) +(a) Vgg-16 + +![](images/c065172f828dba27fba7cdc398fcd270c3ed4dc2012471f7114d9584d3214a6d.jpg) +(b) Vgg-19 + +![](images/909c2232a71733d7d37217b8e8fbff917bd685b00e999e062724f7054e2ba34d.jpg) +(c) WRM + +![](images/396865a8ef7ed99411500129fcb03fb7bb970e515353da089530442731ddb20b.jpg) + +![](images/a0ddf596ea755f5107e10b6f712b14f69bf7f86cffab4082bbc1d20b0e33dc6f.jpg) +(e) Vgg-16 + +![](images/0107b8e33d12fdf714cf6f0809a3e4cfab89dbfbfbf2bfa7c362940e71dd7865.jpg) +(f) Vgg-19 + +![](images/3063fb266149318797259fd3a23a26f3cb8f590265939b2810f01482e13ec4e6.jpg) +(g) WRM +Figure 3. The training performance of Vgg-16, Vgg-19, WRN, DenseNet on corrupted data. (a)-(d) Results on data corruption rate $p \in \{0.1, 0.3, 0.5\}$ ; (e)-(h) Results on data corruption rate $p \in \{0.2, 0.4, 0.6\}$ . + +![](images/8ab981de8e338cc7b4feccee465d91dda999481fa64acd4a0f814f0c5f31906b.jpg) +(d) DenseNet +(h) DenseNet + +DDGSD. All the extra hyper-parameters involved in the compared methods were retained as their original settings. + +# 4.2. Classification Results + +As illustrated in Table 2, our method (denoted as DLB) consistently improved the performance on various backbones (baseline). To be more specific, the averaged error rate improvement achieved by DLB ranged from $0.83\%$ to $2.50\%$ on CIAFR-100, $0.37\%$ to $1.01\%$ on CIFAR-10, and $0.81\%$ to 3.17 on TinyImageNet. It shows the effectiveness of DLB that can significantly improve the generalization ability on various classification tasks. Moreover, DLB outperformed the state-of-the-art approaches, achieving the lowest top-1 error. The best and second-best performances on each set were highlighted in red and green respectively. + +![](images/826143e8c4b1f78ca755f4fda18000b6e31a44fc104432a1f30929552470bffa.jpg) +(a) Temperature +Figure 4. Impact of hyper-parameters in DLB on CIFAR-100 to ResNet-32 and Vgg-16. (a) Impact of temperature $\tau \in \{1,2,3,4,5,10,20\}$ , with a fixed $\alpha = 1$ . (b) Impact of balancing coefficient $\alpha \in \{0.1,0.2,0.5,1.0,2.0,5.0,10.0\}$ with fixed temperature 3. The best performance in each controlled experiment is marked out by red. + +![](images/5c65a2f55ec2290a27e0436a997cf5d0f58c94fa12607227a1e4ba679a519ae3.jpg) +(b) Alpha + +We can observe that DLB on CIFAR-10 succeeded the state-of-the-arts by $0.30\%$ with WRN20-8; whilst on CIFAR100 by $0.47\%$ . These improvements are attributed to the self-distillation regularization from the last mini-batch. We notice that DLB significantly outperformed Tf-KD [37], and PS-KD [12]. It demonstrates the performance advantage of DLB to generalize CNN. Furthermore, the identical teacher from the last mini-batch provides dynamically updated smoothed labels that fit the training process better than a pre-trained teacher or the last-epoch backup. Conclusively, DLB can efficiently serve as a universal regularization to normally train neural networks. + +# 4.3. Compatibility with Augmentations + +Previous work claims that data augmentation and distillation provide an orthogonal improvement [22]. To evaluate the compatibility of DLB with data augmentation based regularization, we combined our method with CutMix [38], CutOut [6] and DDGSD [35] on CIFAR-10/100. + +CutOut. CutOut randomly masks a square region in the training samples [6], we set the number of holes to 1 and the hole size to 16. Combining DLB with CutOut is straightforward. As shown in Table 3, DLB can progressively improve CutOut by $0.45\%$ to $1.14\%$ on CIFAR-10 and $0.84\%$ to $2.74\%$ on CIFAR-100. The performance enhancement was slightly higher than itself on the baseline. It suggests that DLB works in conjunction with CutOut. + +CutMix. CutMix randomly cuts and pasts patches in a mini-batch for regularization, where we follow the addi + +tional hyper-parameters setting as its original work [38] i.e., $\beta = 1$ for beta distribution and augmentation probability $p = 0.5$ . CutMix improved the baseline by approximately $0.52\%$ on CIFAR-10 and $1.48\%$ on CIFAR-100. We plugged CutMix into our approach by performing self-distillation on a batch of images distorted by the same CutMix operation. It resulted in an extra $0.42\%$ improvement on CIFAR-10 and $1.02\%$ on CIFAR-100. + +DDGSD. DDGSD is a self-distillation scheme, excavating a consistency between different distorted versions of the same images [35]. We plugged DLB into DDGSD by distilling the last mini-batch for both two predictions from different augmented versions. As demonstrated in Table 3, DLB slightly outperforms DDSGD. Moreover, combining DLB with DDSGD can obtain observable improvements. + +Discussion. We empirically show that DLB and augmentation regularization work orthogonally. To be more specific, an extra performance gain can be achieved by combining DLB with augmentation based regularization. These finds indicate that using DLB as a plugged-in regularization can enhance the generation of other approaches. + +# 4.4. Robustness to Data Corruption + +In this section, we try to understand how DLB works by empirically exploring its regularization effect on a corrupted setting. DLB is expected to impose training stability and consistency. The superiority of DLB is its simplicity for implementation and parallelization. Additionally, DLB is expected to amplify the robustness of the target neural network, especially in noisy data. It results in a stronger tolerance to the corrupted data, by mitigating the over-fitting to label noise [16]. To prove this statement, we kept the experimental settings aligned with previous works [1, 20, 42] by randomly injecting symmetric label noise at different rate $p \in \{0.1, 0.2, 0.3, 0.4, 0.5, 0.6\}$ to CIFAR-100/CIFAR-10 before the training process. Whilst, the test set was kept clean. In Figure 2 (a)-(b), we can observe a stable performance improvement on different models. For example, on CIFAR-100, DLB improved baseline by $2.38\%$ at $p = 0.1$ and $4.44\%$ at $p = 0.6$ . The generalization improvement went increasingly higher with a higher label noise rate $p$ . These observations demonstrate that DLB can effectively mitigate a neural network to fit label noise and improve the overall performance. The training performance of Vgg-16, Vgg-19, WideResNet, DenseNet are visualized in Figure 3. + +# 4.5. Impact of Hyper-parameters + +To analyze the impact of two hyper-parameters in DLB, namely the temperature $\tau$ in Eq. (4) and balancing coefficient $\alpha$ in Eq. (5), we carried out controlled experiments. Firstly, we fixed $\alpha$ to 1 and assigned $\tau$ with different values + +ranged in $\{1,2,3,4,5,10,20\}$ to evaluate the performance of ResNet-32, Vgg-16 on CIFAR-100. As plotted in Figure 4 (a), DLB achieved lowest error rate with a temperature $\tau = 3$ . The performance reliance on $\alpha$ is demonstrated in Figure 4 (b), with a fixed $\tau = 3$ . We observe that DLB performs well when $\alpha$ changes in [0.5, 2.0]. + +# 4.6. Ablation Study + +We removed the last batch distillation loss and only retained the cross-entropy loss for ablation on CIFAR-100. Specifically, ResNet-32 achieved a $28.01\%$ test top-1 error rate, which performs slightly better than the baseline $(28.26\%)$ . However, it was far worse than our DLB $(26.00\%)$ . These findings show the significance to include the distillation loss as well as the effectiveness of our method. Detailed ablation results on all models are reported in the Table 4. + +Table 4. Ablation study on CIFAR-100. + +
NetworksBaselineloss in (4) removedAll settings
Vgg-1626.37±0.1925.45±0.1323.88±0.06
Vgg-1927.16±0.4225.73±0.2824.53±0.13
ResNet-3228.26±0.1828.01±0.0226.00±0.03
ResNet-11023.64±0.2522.65±0.2321.82±0.19
WRN20-822.42±0.2321.18±0.0120.79±0.33
DenseNet-40-1228.31±0.3528.30±0.2427.48±0.21
+ +# 5. Limitation and Conclusion + +In this research, we introduce an efficient self-distillation mechanism for consistency regularization. Without the involvement of a complex pre-trained teacher model or an ensemble of peer students, our method (DLB) distills the on-the-fly generated smooth labels in the previous iteration after rearranging the sampling sequence. DLB regularizes network by imposing training consistency, which is further amplified under data corruption settings. Thus, it boosts the robustness to label noise. Experimental results on three benchmark datasets suggest that our method can consistently outperform the state-of-the-art self-distillation mechanism. Moreover, DLB, as a universal regularization approach, works in conjunction with augmentations techniques, bringing additional performance gain. However, due to the limitation of computational resources, we did not evaluate the performance on large-scale datasets such as ImageNet, which is left to future work. 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Learning From Unlabeled Data Facilitates Scalable Navigation Decision-Making. Our goal is to develop robust, generalized, and easily deployable decision-making policies for navigation. Our key insight is to make use of the hours of freely available and highly diverse navigation data from the web in order to augment the knowledge and robustness of an initially trained navigation policy. + +# Abstract + +Effectively utilizing the vast amounts of ego-centric navigation data that is freely available on the internet can advance generalized intelligent systems, i.e., to robustly scale across perspectives, platforms, environmental conditions, scenarios, and geographical locations. However, it is difficult to directly leverage such large amounts of unlabeled and highly diverse data for complex 3D reasoning and planning tasks. Consequently, researchers have primarily focused on its use for various auxiliary pixel- and image-level computer vision tasks that do not consider an ultimate navigational objective. In this work, we introduce SelfD, a framework for learning scalable driving by utilizing large amounts of online monocular images. Our key idea is to leverage iterative semi-supervised training when learning imitative agents from unlabeled data. To handle unconstrained viewpoints, scenes, and camera parameters, we train an image-based model that directly learns to plan in the Bird's Eye View (BEV) space. Next, we use unla + +beled data to augment the decision-making knowledge and robustness of an initially trained model via self-training. In particular, we propose a pseudo-labeling step which enables making full use of highly diverse demonstration data through "hypothetical" planning-based data augmentation. We employ a large dataset of publicly available YouTube videos to train SelfD and comprehensively analyze its generalization benefits across challenging navigation scenarios. Without requiring any additional data collection or annotation efforts, SelfD demonstrates consistent improvements (by up to $24\%$ ) in driving performance evaluation on nuScenes, Argoverse, Waymo, and CARLA. + +# 1. Introduction + +How can we learn generalized models for robust vision-based navigation in complex and dynamic settings? While humans can effortlessly transfer general navigation knowledge across settings and platforms [36, 46, 52, 53], current real-world development of navigation agents generally deploys within a fixed pre-assumed setting (e.g., ge + +ographical location, use-case) and carefully calibrated sensor configurations. Consequently, each autonomy use-case generally requires its own prohibitive data collection and platform-specific annotation efforts [4, 6, 19, 56, 79]. Due to such development bottlenecks, brittle navigation models trained in-house by various developers (e.g., Tesla's Autopilot [23], Waymo's Driver [4], Amazon's Astro [69], Fedex's Roxo [25], etc.) are easily confounded by the immense complexity of the real-world navigation task, e.g., rare scenarios, novel social settings, geographical locations, and camera mount perturbations. Yet, every minute, a vast amount of highly diverse and freely available ego-centric navigation data containing such scenarios is uploaded to the web. In this paper, we work towards effectively utilizing such freely available demonstration data to improve the efficiency, safety, and scalability of generalized real-world navigation agents. + +There are two key challenges to employing the large amounts of unconstrained and unlabeled online data for training robust vision-based navigation policies. First, while online images may be collected in various layouts and camera settings, existing monocular-based prediction and decision-making methods tend to rely on restrictive assumptions of planar scenes [22, 70] and known camera parameters [13, 28, 41, 55, 59, 71, 77]. Towards a dataset and platform-agnostic navigation agent, our proposed architecture does not explicitly rely on such assumptions. Second, due to safety-critical requirements, methods for learning decision-making in complex navigation settings generally also assume access to highly curated benchmarks with clean annotations [4, 7, 10, 13, 17, 20, 26, 33, 64, 74]. Consequently, such methods must be revisited when learning from unlabeled and diverse internet videos, e.g., with various quality demonstrations [74]. To effectively utilize such data, we propose to leverage recent advances in iterative semi-supervised learning [8, 38, 60]. Yet, as such techniques are studied within pixel and image-level tasks [14, 29, 41], their utility for learning complex and safety-critical 3D reasoning and planning tasks is not well-understood. + +Contributions: Motivated by how humans are able to effortlessly learn and adapt various skills using online videos, our SelfD approach introduces three main contributions. First, to facilitate learning from unconstrained imagery, we develop a model for mapping monocular observations directly to a Bird's Eye View (BEV) planning space (i.e., without requiring camera calibration). Second, we introduce a novel semi-supervised learning approach incorporating self-training with "hypothetical" data augmentation. We demonstrate the proposed sampling step to be essential for making use of highly diverse demonstration data. Third, we perform a set of novel cross-dataset experiments to analyze the ability of an initially trained decision-making model to self-improve its generalization capabilities using minimal + +assumptions regarding the underlying data. We evaluate across various datasets with complex navigation and harsh conditions to demonstrate state-of-the-art model generalization performance. + +# 2. Related Work + +Observational Imitation Learning: Our key idea is to leverage the scale and diversity of easily available online ego-centric navigation data to learn a robust conditional imitation learning policy [13, 17]. While learning from labeled demonstrations can significantly simplify the challenging vision-based policy learning task [3, 6, 11, 12, 30, 31, 39, 42, 47, 48, 52, 56, 58, 78, 81, 82], observed images in our settings are not labeled with corresponding actions of a demonstrator. We therefore work to generalize current conditional imitation learning (CIL) approaches [13, 17, 18] to learn, from unlabeled image observations, an agent that can navigate in complex urban scenarios. To address this challenging observational learning task, prior work has recently explored introducing various restrictive assumptions, including access to a hand-designed reward function [9], an interactive environment for on-policy data collection [66], or demonstrator optimality [66, 67]. Moreover, due to unconstrained and dynamic scenes in our settings, learning an inverse model [9, 65-67] (i.e., the visual odometry task of recovering actions from observation sequences) becomes challenging and may result in noisy trajectories. To facilitate scalable training from diverse data sources, our proposed semi-supervised learning approach does not leverage such assumptions. Nonetheless, our resulting model can also be used to bootstrap other methods for policy training, e.g., model-based or model-free reinforcement learning approaches [12, 42, 51, 68]. + +Semi-Supervised Learning for Navigation: CIL generally involves learning from known actions of human experts [17, 18, 58], which is not applicable to our settings. Yet, the recent work of Chen et al. [13] utilizes a multi-stage training step, where a privileged (i.e., 'teacher') CIL agent is employed to provide supervision to a non-privileged (i.e., 'student') visuomotor CIL agent. As the privileged agent is given access to extensive ground truth information about the world in training and testing, it produces highly plausible and clean trajectories. In contrast, SelfD leverages the same visuomotor architecture as teacher and student. We also train in inherently noisy settings, as teacher inference is performed on diverse out-of-distribution image data and not on the original training dataset. Consequently, our approach goes beyond prior policy distillation approaches to handle scenarios where supervision by the teacher model may be potentially noisy and unsafe. We also note the relationship between such distillation and semi-supervised training via pseudo-labeling [8,38,43,60,62]. However, as far as we are + +aware, we are the first to develop a pseudo-labeling based self-training method for learning safe driving policies from complex scenes with diverse navigation data, camera perspectives, geographical locations, and weathers. In contrast, prior work [38, 60] emphasizing semi-supervised learning for image- and object-level recognition tasks [8, 76] has limited utility for complex decision-making tasks as further discussed in Sec. 4. + +Self-Supervised Visual Learning: Our approach aims to directly leverage experience from large amounts of unlabeled video data to learn complex 3D navigation. An alternative approach to our proposed semi-supervised framework involves learning visual representations from the large unlabeled data [15, 27, 29, 32, 44, 45, 54, 63]. These generic representations can then be transferred to the policy learning task [29]. However, visual representation learning from unlabeled data often relies on various auxiliary image-level data augmentation strategies [2, 50, 72, 80], e.g., Jigsaw or Colorization [29] tasks, that are indirect to the ultimate navigation task. Thus, such methods are limited in utility for elaborate spatial navigation tasks in dynamic settings. Indeed, the utility of image augmentation-based methods beyond navigation in simple static environments (e.g., [29]) has yet to be demonstrated, i.e., for autonomous driving. In contrast, SelfD's learning and augmentation strategies directly optimize for BEV (map) planning. Moreover, our approach is orthogonal to the aforementioned studies as indirect visual tasks can be leveraged as further pre-training prior to the proposed self-supervised pseudo-labeling step. + +# 3. Method + +Our goal is to facilitate training driving policies at scale. To efficiently make use of the broad and diverse experience found in large amounts of unlabeled videos, we follow three main steps. We first propose to use a monocular image-based behavior cloning planner that reasons directly in the BEV (Sec. 3.3). Our proposed planner can therefore better generalize across arbitrary perspectives. Next, we introduce a data augmentation step for obtaining multiple plausible pseudo-labels when self-training over unlabeled internet data (Sec. 3.4). Finally, we re-train the model over the larger dataset to learn a more robust and generalized vision-based navigation policy (Sec. 3.5). + +# 3.1. Problem Setting + +We consider the task of learning from observations $\mathbf{x} = (\mathbf{I}, v, c) \in \mathcal{X}$ of a single front camera image $\mathbf{I} \in \mathbb{R}^{W \times H \times 3}$ , ego-vehicle speed $v \in \mathbb{R}$ , and a categorical navigational command $c \in \mathbb{N}$ (e.g., turn left, turn right, and forward [17]). Our agent learns to map such observations to a navigational decision. In general, the decision may either be a low-level vehicle control action [18] (e.g., steering, throt + +tle) or a desired future trajectory relative to the ego-vehicle, i.e., set of $K$ waypoints $\mathbf{y} \in \mathcal{V}$ [13, 47] in the BEV (map) space. In the latter case, future waypoints may be paired with a hand-specified or learned motion controller to produce the low-level action [13, 47]. In this work, we focus on the latter representation due to its interpretability and generalizability [47]. Thus, our goal is to obtain a waypoint prediction function $f_{\theta} \colon \mathcal{X} \to \mathcal{Y}$ , with learnable parameters $\theta \in \mathbb{R}^d$ , i.e., the decision-making policy. Without loss of generality, we will slightly augment the output space of this function in Sec. 3.3. Next, we build on recent advances in driving policy learning, in particular CIL [13, 17, 18], to develop a general approach for learning to drive from unlabeled data. + +Conditional Imitation Learning: Navigational demonstrations can be collected by logging the sensor data of a manually operated system, as often done by researchers and developers. Such demonstrations can then be utilized for training decision-making policies through various learning techniques [1, 4, 16, 17, 52, 56, 61]. In its most straightforward implementation, training the mapping function $f_{\theta}$ can be simplified to supervised learning via an i.i.d. data assumption [5, 56]. More robust policies can be trained by going beyond such schemes, e.g., through online and interactive learning strategies [52, 57, 61]. In our work, we leverage off-line demonstrations and do not assume access to an interactive environment. Nonetheless, our proposed data augmentation techniques in Sec. 3.4 can significantly improve policy robustness, as will be demonstrated in Sec. 4. + +Given a collected dataset of observations and corresponding actions, $\mathcal{D} = \{(\mathbf{x}_i,\mathbf{y}_i)\}_{i = 1}^N$ , supervised training can be achieved by optimizing an imitation objective + +$$ +\underset {\boldsymbol {\theta}} {\operatorname {m i n i m i z e}} \mathbb {E} _ {(\mathbf {x}, \mathbf {y}) \sim \mathcal {D}} \left[ \mathcal {L} (\mathbf {y}, f _ {\boldsymbol {\theta}} (\mathbf {x})) \right] \tag {1} +$$ + +with $\mathcal{L}$ being a suitable loss function, e.g., $L_{1}$ regression distance to the waypoint targets. Despite widespread use in academia [18, 34, 75] and industry [4, 6], the standard CIL formulation significantly limits scalability. Specifically, approaches for imitation learning generally require having direct access to optimal target action labels. Consequently, they cannot be applied towards learning from the vast and diverse unlabeled data that is uploaded online. + +Conditional Imitation Learning from Observations: To make full use of unlabeled data in demonstrations containing diverse navigational experience, we develop a framework for Conditional Imitation Learning from Observations (CILfO), i.e., assuming only data of the form $\mathcal{U} = \{\mathbf{I}_i\}_{i=1}^M$ . Within this more generalized yet difficult learning task, a key challenge lies in recovering suitable label targets $\hat{\mathbf{y}}$ , navigational command $\hat{c}$ and speed $\hat{v}$ to construct a dataset + +$$ +\hat {\mathcal {D}} = \left\{\left(\mathbf {I} _ {i}, \hat {v} _ {i}, \hat {c} _ {i}\right), \hat {\mathbf {y}} _ {i}) \right\} _ {i = 1} ^ {M} \tag {2} +$$ + +over which Eqn. 1 can then be used to train a policy. + +Initial Data Assumption: In order to address the challenging CILfO learning task, our key idea is to leverage a small labeled dataset to learn an initial policy mapping using human expert demonstrations. We then sample from this trained function to obtain pseudo-labels [38] over the unlabeled data. This assumption is reasonable considering that there are several publicly available driving datasets with included action labels [7,26,33,73]. Alternatively, a preliminary dataset with a novel platform setup or use-case may be initially collected. + +Sequential Data Assumption: We note that although sequential video data is used in our ablation, our generic and scalable CILfO formulation does not assume access to temporal data. The reason for this is three-fold. First, while sequential observations may be potentially beneficial for disambiguation of various decision-making factors [21], generalization results for learning temporal sensorimotor driving policies have been inconclusive [21, 48, 70]. Second, while sequential data is assumed in most prior observational imitation learning settings [9, 66] recovering the underlying demonstration actions (e.g., using monocular visual odometry [71]) in arbitrary scenes is challenging. Due to the difficulty and noise in sequential action recovery, our proposed single-frame formulation in Sec. 3.2 is shown to significantly outperform such baselines in Sec. 4. Third, we do not make any assumptions regarding the optimality of the demonstrations in the unlabeled dataset $\mathcal{U}$ [49, 67]. Consequently, our generalized method is suitable for scalable learning from videos with complex scenes, environmental conditions, arbitrary viewpoints, and diverse demonstration quality. As our learning task lies well beyond the capabilities of existing CIL and observational methods, we next develop a generalized training method for leveraging unconstrained and unlabeled demonstration data. + +# 3.2. SelfD Overview + +Through a semi-supervised policy training process, our proposed SelfD navigation policy model can be learned in three summarized steps: + +1. Use a small, labeled domain-specific dataset $\mathcal{D}$ to learn an initial observations-to-BEV policy $f_{\theta}$ via imitation. +2. Obtain a large pseudo-labeled dataset $\hat{\mathcal{D}}$ by leveraging sampling from $f_{\theta}$ . +3. Pre-train a generalized policy $f_{\theta}$ on $\hat{\mathcal{D}}$ and fine-tune on the clean labels of $\mathcal{D}$ . + +Note that we re-use the parameter symbol $\theta$ throughout the steps to simplify notation. Our iterative semi-supervised training enables effectively augmenting the knowledge and robustness of an initially trained policy. As described + +next, our proposed initial step facilitates learning a platform and perspective-agnostic policy during subsequent training steps by directly reasoning in a BEV planning space. + +# 3.3. BEV Plan Network + +In this section, we propose a suitable output representation to account for arbitrary cameras, viewpoints and scene layouts. Current monocular planners generally predict waypoints in the image plane to align with an input image [13, 47]. The waypoints are then transformed to a BEV plan using carefully calibrated camera intrinsic and extrinsic (e.g., rotation, height) parameters [13]. Thus, policy models are often trained and evaluated within a fixed pre-assumed setup. In contrast, SelfD predicts a future plan parameterized by waypoints in the BEV plan space directly. Based on our experiments in Sec. 4, we demonstrate this choice to be crucial for real-world planning across settings. The predicted generalized BEV waypoints can be paired with a low-level controller, e.g., a PID controller [13, 47]. + +Due to the difficulty in learning a monocular-to-BEV plan mapping, we follow recent work in confidence-aware learning [37] to train an augmented model $f_{\theta} \colon \mathcal{X} \to \mathcal{Y} \times \mathcal{R}$ with quality estimates $\sigma \in \mathcal{R}$ . Our training loss function in Eqn. 1 is defined as + +$$ +\mathcal {L} = \mathcal {L} _ {\text {p l a n}} + \lambda \mathcal {L} _ {\text {q u a l i t y}} \tag {3} +$$ + +where $\mathcal{L}_{\mathrm{plan}}$ is the $L_{1}$ distance between ground-truth and predicted waypoints, $\mathcal{L}_{\mathrm{quality}}$ is a binary cross-entropy loss [37, 76], and the $\lambda$ hyper-parameter balances the tasks. + +# 3.4. "What If" Pseudo-Labeling of Unlabeled Data + +Given a set of unlabeled images $\mathcal{U}$ , we sample from the trained conditional policy $f_{\theta}$ in a semi-supervised training process. While the speed and command inputs to $f_{\theta}$ can be recovered through visual odometry techniques [71], these result in highly noisy trajectories in our online video settings (discussed in Sec. 4). As the demonstrations in our data may be unsafe or difficult to recover, we propose to leverage a single-frame pseudo-labeling mechanism. Our key insight is to employ the conditional model $f_{\theta}$ to generate multiple hypothetical future trajectories in a process referred to as "what if" augmentation. Beyond resolving the missing speed and command inputs, our proposed augmentation provides additional supervision, i.e., a conditional agent that better reasons on what it might need to do, for instance, if it had to turn left instead of right at an intersection (Fig. 2). In contrast to related work in policy learning and distillation [13], sampling from the teacher agent is more challenging as the agent is not exposed to extensive 3D perception knowledge about the world and is being evaluated outside of its training settings. + +We repeatedly sample $\hat{v}$ and $\hat{c}$ uniformly and rely on the conditional model to provide pseudo-labels $(\hat{\mathbf{y}},\hat{\pmb{\sigma}}) =$ + +![](images/8125dba229733dd4300f9c8ca803af72a4f3596495e007070774c8cabd810a30.jpg) + +![](images/c2d729da9234649983eba41dcf7d52028931155fbc1676716edbe796553aee26.jpg) + +![](images/e46e15ceb8d6fd7f1f946841c96cc136103775bbe2a0dc21f98ad42e39cf89d3.jpg) +Figure 2. "What If" Hypothetical Pseudo-Labeling. We generate multiple plausible future trajectories (units are meters in BEV) as pseudo-labels for each unlabeled frame by sampling the conditional planner from Sec. 3.3. We depict two scenarios from our dataset with inference shown for various inputs. Speed is in meters per second and conditional commands are either left (1), forward (2), or right (3). + +![](images/92c9bb76ca4cb98e02de9b5a5f15e98b5841159b922b3c5c544afd5c4469e78b.jpg) + +$f_{\theta}(\mathbf{I}, \hat{v}, \hat{c})$ for additional supervision across all conditional branches and speed observations. In this manner, querying the "teacher" model $f_{\theta}$ enables us to generate various scenarios beyond the original demonstration. In particular, as discussed in Sec. 4, we find self-training strategies to provide limited generalization gains without this "what if" data augmentation step. This augmentation strategy enables our single-frame pseudo-labeling approach to significantly outperform approaches that are more elaborate to train at scale, as they may involve additional modules relying on approximating $\hat{\mathbf{y}}$ , $\hat{c}$ , and $\hat{v}$ from video. Finally, to avoid incorporating potentially noisy trajectories, the corresponding quality estimates $\hat{\sigma}$ can be used to process and filter examples in the pseudo-labeled dataset $\hat{\mathcal{D}}$ . + +# 3.5. Model Pre-Training and Fine-Tuning + +As a final training step, we re-train the waypoint network $f_{\theta}$ from scratch over the large and diverse dataset $\hat{\mathcal{D}}$ . The pre-trained policy can then be further fine-tuned over the original dataset $\mathcal{D}$ , thus leveraging the additional knowledge gained from $\hat{\mathcal{D}}$ to improve its performance. We note that we employ separate training over the two datasets $\hat{\mathcal{D}}$ and $\mathcal{D}$ and rely on knowledge transfer through learned representations as it reduces the need for any careful hyperparameter tuning beyond the overall learning rate. For instance, Caine et al. [8] empirically demonstrate the importance of delicately optimizing the ratio of labeled to pseudo-labeled data when mixing the datasets for a 3D object detection task, while also showing it to vary among object categories, e.g., pedestrians vs. vehicles. Thus, through a pre-training mechanism, we avoid the need to carefully mix the cleanly + +labeled and pseudo-labeled datasets [8,63,76]. + +# 3.6. Implementation Details + +We implement our BEV waypoint prediction network $f_{\theta}$ leveraging a state-of-the-art conditional sensorimotor agent [13]. However, as discussed in Sec. 3.2, we do not assume a fixed known BEV perspective transform. Thus, we remove the fixed perspective transformation layer which restricts scalability and replace it with a per-branch BEV prediction module (see supplementary for additional implementation and architecture details). During training we use a learning rate of $1\mathrm{e} - 3$ and resize images to $400\times 225$ . + +# 4. Experiments + +# 4.1. Experimental Setup + +To obtain large amounts of driving data, we downloaded 100 hours of front view driving videos from popular driving channels on YouTube (across cities, weathers, and times of day, as shown in Fig. 1). In our real-world evaluation, we use the nuScenes [7], Waymo [64] and Argoverse [10] datasets. While nuScenes is a highly instrumented and annotated dataset, it is primarily used for perception tasks without an official benchmark for future waypoint planning. The recent work by Hu et al. [35] uses a random split, yet this is not suitable for studying generalization (the method also employs LiDAR input whereas we do not). We create a geography-based split into nuScenes Boston (nS-Boston) and nuScenes Singapore (nS-Singapore) which is challenging due to the significant domain shift. To further evaluate generalization, we also utilize the Waymo and Argoverse datasets which were collected across 8 different cities. Specifically, we construct a future waypoint prediction benchmark from the Waymo perception testing set and the Argoverse 3D tracking training set. Note that in our evaluation we do not assume any access to the target domain's pseudo-labels, as often done in related research. Overall, our split results in $13K$ , $11K$ , $11K$ , and $26K$ samples from nS-Boston, nS-Singapore, Argoverse and Waymo, respectively. + +The open-loop real-world evaluation compares predictions to an expert driver in complex interactions (i.e., diverse maneuvers, yielding, merging, irregular intersections). To analyze the impact of the proposed approach during closed-loop driving, we further perform interactive on-policy evaluation in CARLA [18, 24]. We replicate our training settings in simulation and predict a final low-level action by employing a PID controller [13]. In particular, we train on labeled data from Town 1 and evaluate on Town 2 in regular traffic (following NoCrash [18]). To understand the impact of pseudo-labeling on the close-loop driving metrics we keep a portion of the training town data for pseudo-labeling. The evaluation is conducted over 25 pre + +defined routes in Town 2 under four different weathers, one of which is not seen in annotated data. Additional details regarding the experimental setup can be found in the supplementary. + +Evaluation Metrics: We follow standard open-loop evaluation and use Average and Final $L_{2}$ Displacement Error (ADE and FDE, respectively) over future waypoints in the BEV [40]. We also compute a collision rate [34] which measures collisions along the predicted waypoints with other vehicles (we are only able to compute this metric on nuScenes and Argoverse due to the provided annotations for the surrounding vehicles). In our CARLA experiments we also report agent Success Rate (SR), Route Completion (RC), and Collision (Coll.) frequency per 10km. + +# 4.2. Results + +Model Architecture: We first analyze the proposed BEV planning model architecture on the nuScenes cross-town split. The architecture is then fixed for subsequent experiments. As shown in Table 1, the state-of-the-art CIL model [13] achieves a 1.86 ADE on the cross-town training and testing split. We emphasize that the CIL baseline [13] predicts the waypoints in 2D images and transform the predicted waypoints into BEV through a perspective transformation. However, such transformation may not be accurate in the real-world. We can therefore see the benefits of the BEV planner, even before pseudo-labeling techniques have been applied. Our proposed BEV planner achieves a 1.14 ADE (a nearly $40\%$ reduction in error compared to CIL). Given prior work on nuScenes primarily relies on non-conditional approaches based on LiDAR [34], we also ablate over different inputs to the model. Intuitively, we find the speed measurements to be critical to BEV waypoint prediction. Our proposed BEV planner with both speed and conditional command input gives the best ADE performance on nS-Singapore. We now continue to analyze the benefits of a semi-supervised learning step to improve policy performance. + +Pseudo-Labeling Approaches: We consider various approaches for leveraging the unlabeled YouTube data (we select 10 driving hours for the ablation). To emphasize generalization, we do not pseudo-label the unseen test datasets or incorporate their unlabeled samples into the self-training in any way. We report waypoint prediction performance before and after the final fine-tuning step on nS-Boston across all test sets. As shown in Table 2, pre-training over the pseudo-labeled YouTube data and fine-tuning on the clean dataset consistently improves ADE, FDE, and collision metrics across evaluation settings. We see how leveraging a state-of-the-art Visual Odometry (VO) model [71] as a teacher for SelfD instead of the proposed pseudo-labeling mechanism results in reduced performance. As recovering + +Table 1. Model Architecture. The CIL baseline [13] predicts waypoints in the image and relies on perspective transform with known camera calibration, while our proposed monocular-to-BEV planner does not have access to camera intrinsic or extrinsic parameters. All models are trained on nuScenes Boston and evaluated on nuScenes Singapore. + +
ModelsCommandSpeedADE (meters)
CIL Baseline [13]✓✓1.86
BEV Planner✓4.77
4.64
✓1.33
✓✓1.14
+ +the camera motion in dynamic scenes with unknown camera parameters is difficult, leveraging this model results in noisy and unsafe trajectories. While we find limited utility in leveraging temporal data, this may be alleviated by improved visual odometry methods in the future. As such methods become more robust to arbitrary settings, they may be integrated to complement our method, e.g., to leverage both rollouts as well as the proposed data augmentation. We also find our pre-training pipeline to improve over mixing-based approaches [63]. + +What If Augmentation: Results in Table 2 demonstrate how self-training without the proposed data augmentation results in limited gains. Here, we experiment with pseudolabeling using various sampling strategies for speed measurements and conditional commands. In addition to uniform and prior-based sampling (determined empirically based on the training data), we also report findings using the visual odometry [71] model estimates for the speed and conditional command. We find uniform sampling to outperform more informed prior and visual odometry-based sampling due to the extensive speed profile and multi-branch supervision it provides. We can see how a model learned through self-training but without such powerful augmentation (i.e., SelfD without What if in Table 2) results in worse performance compared to the baseline BEV planning model, e.g., 1.18 vs. 1.14 ADE and 2.23 vs. 2.16 FDE. We also find the augmentation to improve safety of the predicted trajectories, as shown by reduced collision rates. This is affirmed in our closed-loop evaluation shown in Table 5. + +Generalization to Harsh Settings: We stress test SelfD in Table 3 under the most challenging subsets across the datasets, as selected by video episodes collected in certain environmental conditions. Interestingly, we find SelfD to efficiently reduce error on nighttime conditions, which is only seen in YouTube videos. However, as nS-Boston already contains some scenes with cloudy and light rain settings, the improvement on rainy conditions on Waymo is + +Table 2. Pseudo-Labeling Approaches. We compare various pseudo-labeling approaches by varying the underlying sampling mechanism for the speed and conditional inputs. These may either be estimated with visual odometry [71] (i.e., SelfD without "what if" augmentation) or sampled from a prior distribution (i.e., uniformly or with a prior). We find uniform sampling to work best as a form of data augmentation. We also compare to a baseline using a state-of-the-art visual odometry method for pseudo-labels. Note that DVO-based approaches utilize sequential video data while the rest are single-frame. "Coll." refers to collision rate and "nS" to nuScenes (see Sec. 4.1). + +
MethodnS-SingaporeArgoverseWaymo
ADEFDEColl. (%)ADEFDEColl. (%)ADEFDE
BEV Planner (nS-Boston)1.142.169.501.072.1616.502.173.87
Pre-Trained (YouTube)SelfD (VO)4.638.0712.914.357.5431.875.169.02
SelfD (w/o What If)1.322.4510.021.272.4613.922.434.28
SelfD (What If-Prior)1.192.4010.011.122.3416.512.103.94
SelfD (What If-Uniform)1.192.2810.101.132.2815.702.244.01
Fine-Tuned (YouTube & nS-Boston)FixMatch [63]1.182.2212.021.102.2415.202.183.88
SelfD (VO)1.092.099.331.032.1117.522.013.62
SelfD (w/o What If)1.182.239.341.092.1816.262.033.62
SelfD (What If-Prior)1.092.109.471.002.0615.712.103.73
SelfD (What If-Uniform)1.001.939.300.992.0514.201.653.02
+ +Table 3. Generalization to Harsh Conditions. We analyze the impact of SelfD on generalization from nS-Boston to specific environmental conditions. We compute the performance over domain subsets within each dataset. While insightful for the larger nuScenes and Waymo splits, we note that this splits leads to a small dataset on Argoverse with limited insights. + +
MethodnS-Singapore NightArgoverse RainyArgoverse NightWaymo RainyWaymo Night
ADEFDEADEFDEADEFDEADEFDEADEFDE
BEV Planner (nS-Boston)1.673.050.811.710.781.610.701.281.813.25
SelfD (Pre-Trained)1.733.170.841.850.941.940.771.421.963.55
SelfD (Fine-Tuned)1.282.420.791.710.911.800.671.321.532.80
+ +Table 4. Impact of Initial Training Dataset. We analyze the impact of different datasets for training the initial BEV planner model. + +
Initial DatasetMethodnS-Singapore
ADEFDE
ArgoverseBEV Planner1.422.58
SelfD (w/o FT)1.382.52
SelfD (w/ FT)1.182.23
WaymoBEV Planner1.082.03
SelfD (w/o FT)1.132.14
SelfD (w/ FT)0.911.81
+ +limited. While we show results on similar Argoverse settings for consistency and completeness, our harsh settings split results in very few samples (in particular for Argoverse Night). Hence, results become less meaningful. While insightful, this experiment demonstrates the difficulty in obtaining diverse annotated data, further motivating our SelfD approach for development and real-world scalability. + +Impact of Initial Training Data: We further investigate the role of the initial training dataset on the pseudo-labeling step and resulting model generalization performance in + +Table 5. Closed-Loop Evaluation in CARLA. We analyze the impact of the proposed self-training step on closed-loop metrics of Success Rate (SR), Route Completion (RC), and Collision frequency (Coll.) per $10\mathrm{km}$ . + +
MethodADE ↓FDE ↓SR (%) ↑RC (%) ↑Coll. ↓
CIL Baseline [13]0.571.301666.8810.71
BEV Planner0.661.321265.6611.33
SelfD (Town 1)0.561.302571.8411.51
SelfD (Town 1 & 2)0.551.242674.505.18
+ +Table 4. Here, we repeat the experiments by replacing nS-Boston with Argoverse and Waymo and test on nS-Singapore (i.e., for direct comparison with Table 2). We keep all hyper-parameters fixed. While models trained on different dataset may bias differently the pseudo-labels on the YouTube dataset, overall we find similar trends in performance regardless of the original training dataset. + +Closed-Loop Evaluation in CARLA: We show our analysis in CARLA in Table 5. We report both open-loop and closed-loop metrics for completeness. In this experiment, we train our BEV planner using an annotated portion of Town 1, and test on Town 2. We note that while our CIL + +![](images/6c8c793425dd1527d8c6f9852e8ccf96c75f2cad4016b0d6ec7b89b79d515bb9.jpg) + +![](images/3dff77780c88d3ae1631cd95d7021672b9245e8be0fcde67fe48b9d81ba8adfc.jpg) + +![](images/47d04c41277c8f02fdefdca6d236580fa19b168fcd8b0c8e86ee54fa12a9ed9b.jpg) +Figure 3. Qualitative Results. We compare predicted waypoints in BEV for the ground truth trajectory, the baseline model (trained on nS-Boston), and SelfD (pre-trained on YouTube, fine-tuned on nS-Boston). Results are shown on Waymo (left) and nS-Singapore (right). The SelfD model (green) is shown to generalize well across unusual scenarios due to the proposed pseudo-labeling mechanism. We also observe improved robustness to rare command and speed inputs. Units are meters for the BEV plan plots. + +![](images/a5a5d14d321738e3467449c975ed191ad174910327a6d20dc136e1f9495ca54c.jpg) + +![](images/38fd7d509ec234ad16608a8af8bd60e9789af4eaa521c3ce78968d32ef811653.jpg) + +![](images/0ba227881ff5e75dd1cbc29a77abf0f1569d11c35ee0a5c0fc285a32bebf6fd0.jpg) + +![](images/c5e4438c1e3ed933ed239024680d1fcdd444f8170b0abd0219ac9f47fa4c3f14.jpg) + +![](images/7c091f80fcae7232cab48b7e58a4d71f5ce2a3ad041128ed96eda7b60309d1d3.jpg) + +![](images/40254ab14be43c471e53f9a6ce616457094e348afc949c459caaee5bcfdb8d22.jpg) +Figure 4. Additional Unlabeled Data. Results when increasing the amount of pseudo-labeled YouTube driving data up to 100 hours. As our proposed self-training pipeline facilitates scalable learning from large amounts of data, the model can continue to improve with additional YouTube data. + +![](images/bf977bf391fd5827bdf68d187f0d609c0530893025da76768ee48dc14ee46811.jpg) + +Baseline benefits from the known fixed perspective transform assumption the BEV planner has no knowledge of camera parameters and must learn it from the data. When training SelfD using pseudo-labeled data from Town 01, we achieve a near doubling in the success rate, from $12\%$ to $25\%$ . This increase in model performance using the most difficult closed-loop evaluation metric highlights the benefits of the proposed approach. We further pseudo-label and use in pre-training an unlabeled dataset from Town 2 (i.e., SelfD - Town 1 & 2), showing additional gains in driving performance across metrics. This experiment suggests multiple ways in which the proposed approach may be leveraged in real-world generalization and adaptation settings. + +Additional YouTube Pre-Training Data: While we leverage 10 hours of YouTube data in our ablation analysis, we provide results with additional YouTube data of up to 100 hours. The results, shown in Fig. 4, suggest further gains can be made with larger and more diverse pre-training + +datasets from the web. As our proposed self-training pipeline facilitates scalable learning from large amounts of data, the model may continue to improve with additional YouTube data. However, this requires further study in the future, e.g., with respect to larger network capacity. + +# 5. Conclusion + +We envision broad and easily deployable autonomous navigation systems. However, access to resources and data limits the scope of the brittle autonomous systems today. Our SelfD approaches enables to significantly improve an initially trained policy without incurring additional data collection or annotation efforts, i.e., for a new platform, perspective, use-case, or ambient settings. Crucially, due to the proposed underlying model architecture, we do not incorporate camera parameters or configuration assumptions into the monocular inference. As SelfD is self-improving, a future direction could be to continue and learn from increasingly larger online datasets beyond what is described in our study. While we emphasized efficient large-scale training in our model development, how to best extend SelfD to more explicitly leverage temporal demonstration data is still an open question which could be studied further in the future. 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Explicit methods require a predefined template mesh for a given sequence, while the template is hard to acquire for a specific subject. Meanwhile, the fixed topology limits the reconstruction accuracy and clothing types. Implicit representation supports arbitrary topology and can represent high-fidelity geometry shapes due to its continuous nature. However, it is difficult to integrate multi-frame information to produce a consistent registration sequence for downstream applications. We propose to combine the advantages of both representations. We utilize differential mask loss of the explicit mesh to obtain the coherent overall shape, while the details on the implicit surface are refined with the differentiable neural rendering. Meanwhile, the explicit mesh is updated periodically to adjust its topology changes, and a consistency loss is designed to match both representations. Compared with existing methods, SelfRecon can produce high-fidelity surfaces for arbitrary clothed humans with self-supervised optimization. Extensive experimental results demonstrate its effectiveness on real captured monocular videos. The source code is available at https://github.com/jby1993/SelfReconCode. + +# 1. Introduction + +Clothed body reconstruction has been an important and challenging research topic in the community for years. In the film and gaming industry, high-fidelity human reconstruction usually requires pre-captured templates, multicamera systems, controlled studios, and long-term works of talented artists. However, these requirements exceed the application scenarios of general customers, such as personalized avatars for telepresence, AR/VR, anthropometry, and virtual try-on, etc. Therefore, directly reconstruction high-fidelity digital avatar from monocular video will have significant practical application value. + +The state-of-the-art marker-less monocular human performance capture approaches [17, 18, 52] are mainly designed based on explicit mesh representation. They require actor-specific rigged templates and utilize detected 2D/3D joints and silhouettes to estimate per frame's posture and non-rigid deformation. DeepCap [18] additionally uses multi-view information during training to resolve deep ambiguity and improve tracking accuracy for monocular inference. The explicit representation has some advantages, including space-time coherence and compatibility with existing graphics control pipelines, like texture editing and reposing. Moreover, skinning deformation is suitable under this paradigm to model the body's large-scale articulated deformations. However, actor-specific templates limit the extension of these methods to unseen human sequences. For videos of self-rotation humans under rough Apose, VideoAvatar [2] can estimate general clothed humans with the SMPL+D parametric representation [1-3,6,31,49], while it can not recover folds and loose clothing, like skirts. + +Recently, some neural implicit representation based monocular human reconstruction approaches have demonstrated compelling results [10, 20, 21, 23, 41, 42, 46, 50, 55, 56]. These methods can handle various topologies, and thus can represent various clothing and hairstyles. However, they require high-quality 3D data for supervision, and they only reconstruct for a specific frame and can not keep the space-time coherence of surface vertices for the whole sequence. A simple solution to guarantee the coherence and correct body structure is to maintain an implicit template surface in the canonical space, and then utilize backward deformation fields to map current points to canonical space to assist their implicit function queries. The backward deformation strategy has been widely applied recently and works well for small-scale deformations [29, 36, 40, 45]. However, it is not very suitable for articulated skinning deformation due to its irreversibility in some parts of current space [11, 24]. To this end, technologies such as pose-related skinning weights prediction [24, 38, 47] and specific inverse articulated deformation design [13] are proposed at the cost of high complexity and poor generalization. + +In this work, we propose SelfRecon, which combines the explicit and implicit representations together to reconstruct + +high-fidelity digital avatar from a monocular video. Specifically, SelfRecon utilizes a learnable signed distance field (SDF) rather than a template with fixed topology to represent the canonical shape. To improve the generalization of the deformation and reduce the optimization difficulty, we adopt the forward deformation to map canonical points to the current frame space [11, 54]. During optimization, we periodically extract the explicit canonical mesh and warp it to each frame with the deformation fields. For these meshes, we utilize mask loss and smooth constraints to recover the overall shape. For the implicit part, a differential formulation is designed to intersect the deformed surface and follow IDR's neural rendering [53] to refine the geometry. A consistency loss is designed to match both geometric representations as close as possible. + +SelfRecon alleviates the dependence on actor-specific templates and extracts a space-time coherent mesh sequence from a monocular video. Extensive evaluations on self-rotating human videos demonstrate that it outperforms existing methods. We believe that SelfRecon will inspire more studies on combining implicit and explicit representations for 3D reconstruction for articulated object. + +# 2. Related Work + +Implicit Human Reconstruction. PIFu [41] adopts a deep network to extract image features and concatenates pixel's feature and its corresponding 3D point depth information as the input of a Multi-Layer Perceptron (MLP) to obtain high-fidelity 3D clothed human occupancy field. However, it may generate incorrect body structures for humans under challenging poses. StereoPIFu [22] aims at binocular images, utilizes volume alignment feature and predicted high-precision depth to guide implicit function prediction, can effectively alleviate the depth ambiguity and restore absolute scale information. PIFuHD [42] utilizes higher resolution features and predicted normal information to refine the geometric details of PIFu. PaMIR [55] utilizes parameterized human body to decrease the influence of deep ambiguity in implicit function training, reduces the occurrence of abnormal human body structure, and improves the reconstruction accuracy. These methods train an MLP to represent the human's implicit geometry from single or several images and achieve impressive results. However, they require the corresponding high-quality 3D data of color images to train the model, which is hard to obtain and thus limits their generalization to in-the-wild images. + +Besides, overfitting the implicit neural representation of a person's movement sequence to acquire actor-specific reconstructions becomes popular. NASA [13] coarsely models the naked body as the union of articulated parts, and each part is an implicit occupancy field. SCANimate [43] proposes an end-to-end trainable framework that turns raw 3D scans of a clothed human into an animatable avatar. + +SNARF [11] learns a forward deformation field to improve its generalization for unseen human poses. All these methods need 4D scan data to train their clothed body representation, and thus are difficult to be widely used for general image data. + +Recently, some implicit representation methods, which can extract geometry and synthesize novel views based on multi-view images, attract researchers' attention. NeuralBody [39] reconstructs per frame's NeRF [34] field conditioned at body structured latent codes and utilizes the NeRF field to synthesize new images. However, the extracted geometry from NeRF suffers from noise. H-NeRF [51] utilizes an implicit parametric model [4] to reconstruct the temporal motion of humans. Neural Actor [30] integrates texture map features to refine volume rendering. IDR [53] combines implicit signed distance field and differential neural rendering to generate high-quality rigid reconstruction from multi-view images. Concurrent IMAAvatar [54] expand IDR to learn implicit head avatars from monocular videos. + +Explicit Human Reconstruction. With the help of human statistical model [5, 25, 31], some works utilize image cues to automatically obtain model parameters [9, 16, 28, 35]. To represent human clothing, some methods add displacements on SMPL [31] vertices to model tight clothing [2, 7, 33, 37]. However, this SMPL+D representation can only support tight clothing types and recover coarse level geometry shape. To improve the representation ability, some works adopt separate clothing representation and combine with SMPL body to do reconstruction [26, 32], but they need clothing type and high-quality 3D supervision. + +Besides, to capture the performance of a specific person, many prior works use an actor-specific template to assist tracking. Monoperfcap [52] optimizes the deformation of template mesh to match 2D cues. LiveCap [17] refines the optimization pipeline and achieves real-time tracking for a specific person with monocular RGB input. DeepCap [18] adopts a network to predict per frame's template deformation for a specific person. However, the requirement for pre-defined templates limits their broader applications. + +# 3. Method + +SelfRecon aims to reconstruct a high-fidelity and space-time coherent clothed body shape from a monocular video depicting a self-rotating person, and the whole algorithm pipeline is given in Fig. 1. Both explicit and implicit geometric representations are utilized to achieve the above target. Specifically, we utilize the forward deformation field to generate space-time coherent explicit meshes. The deformation fields are decomposed into two parts, where the first one represents per frame's non-rigid deformation with a learnable MLP, and the second is the skinning deformation field. Differentiable masks, regular and smooth losses are adopted to control the shape of explicit meshes. To + +![](images/077c5fe651fcd5c31f075305a564804483bb281f82a2ddb7b1edafbb5fd75712.jpg) +Figure 1. The pipeline of SelfRecon. We simultaneously maintain the explicit and implicit geometry representations and use forward deformation fields to transform canonical geometry to the current frame space. For explicit representation, we mainly use differentiable mask loss to recover the overall shape. As for implicit representation, sampled neural rendering loss and predicted normals are used to refine geometry details. Finally, a consistency loss is used to keep both geometric representations matched. + +update the shape of implicit neural representation, we use non-rigid ray-casting (sec 3.3) to find the differentiable intersection points of rays and the deformed implicit surface. Then, the implicit rendering network (sec 3.4) will utilize the rays' color information to improve the geometry. Unless otherwise indicated, we also utilize the predicted normal map [42] to refine the details. Finally, a consistency loss is designed to match both representations. + +For a self-rotating video with $N$ frames, we adopt the method described in VideoAvatar [2] to generate the initial shape parameter $\beta$ and per-frame's pose parameters $\{\theta_i|i\in \{1,\dots,N\}\}$ of SMPL model. We pre-defined a template pose and generate initial canonical SMPL body mesh $\mathcal{B}$ with $\beta$ and this pose parameter. Our implicit and explicit representations are both initialized with $\mathcal{B}$ . In the following, we present the algorithm details of each component. + +# 3.1. Canonical Implicit SDF + +In the similar work of VideoAvatar [2], they adopt the SMPL+D representation for clothed human body. However, SMPL+D has limited resolution and representation ability, and thus it can not represent high-fidelity geometry shape and various clothing types. In this work, we represent the canonical template shape $S_{\eta}$ as the zero isosurface of a SDF, which is expressed by an MLP $f$ with learnable weights $\eta$ : + +$$ +\mathcal {S} _ {\eta} = \left\{\mathbf {p} \in \mathbb {R} ^ {3} | f (\mathbf {p}; \eta) = 0 \right\}. \tag {1} +$$ + +To avoid unexpected solution, we use IGR [15] to initialize $S_{\eta}$ as the initial canonical body $\mathcal{B}$ . + +# 3.2. Deformation Fields + +Following prior works [21, 23], we utilize skeleton skinning transformation to control human body's large-scale movements due to the articulated structure. However, garments' non-rigid deformation cannot be fully represented by skinning transformation. Therefore, we extend to model non-rigid deformation with another MLP. + +Non-rigid Deformation Field. We use an MLP $d$ with learnable weights $\phi$ to represent the non-rigid deformation field. For $i$ -th frame, $d$ takes its optimalizable conditional variable $\mathbf{h}_i$ as input and deform points in the canonical space with $i$ -th frame's specific non-rigid deformation. + +Skinning Transformation Field. Given $i$ -th frame's pose parameter $\theta_{i}$ , we have to define a canonical-to-current space skinning transformation field $\mathcal{W}$ . As the initial template body $\mathcal{B}$ has well-defined skinning weights relate to its SMPL skeleton, an intuitive idea is to expand the skinning weights of $\mathcal{B}$ 's vertices to the whole canonical space to define the skinning transformation field. Specifically, we first pre-defined a sparse grid containing $\mathcal{B}$ in the canonical space. For each grid point, we find its nearest 30 vertices on $\mathcal{B}$ and average their skinning weights with IDW (inverse distance weight) as its initial weight. Then, we smooth all grid points' weights with Laplace smoothing. Finally, given + +a point in the canonical space, we compute its skinning weights by trilinear interpolation in the grid. During our optimization, the grid is pre-computed and fixed. This forward deformation design avoids the trouble of inverse skinning transformation [11, 13, 24, 47] and provides a regular constrain for human articulated movement. + +Finally, by compositing $d$ and $\mathcal{W}$ , we get the final deformation field $\mathcal{D} = \mathcal{W}(d(\cdot))$ . It takes $i$ -th frame's conditional variable $\mathbf{h}_i$ and SMPL pose parameter $\pmb{\theta}_i$ as input, and transform canonical points to the $i$ -th frame space. For brevity of description, we use $\mathcal{D}_i$ to denote $i$ -th frame's deformation field, $\mathcal{S}_i$ for $i$ -th frame's zero isosurface $\mathcal{D}_i(S_\eta)$ and $\psi_i$ for $\mathcal{D}_i$ 's estimizable parameters $\{\phi, \mathbf{h}_i, \pmb{\theta}_i\}$ . + +# 3.3. Differentiable Non-rigid Ray-casting + +For rigid scenes, the sphere tracing algorithm [19,27,53] is widely used to find the intersection point of a ray and the SDF. However, it is not feasible here due to the deformation fields. Inspired by the method in [44], which proposes a strategy to render a deformed SDF, we utilize the explicit mesh to help find the intersection point of a ray and $S_{i}$ . + +As shown in Fig 2, we extract an explicit template mesh $\mathbf{T}$ from the canonical surface $S_{\eta}$ . With deformation $\mathcal{D}_i$ , we can get $i$ -th frame's mesh $\mathbf{T}_i$ . Theoretically, $\mathbf{T}_i$ is a piecewise linear approximation of $S_i$ . Therefore, consider a ray emitted from the camera position $\mathbf{c}$ along the direction $\mathbf{v}$ , its first intersection $\hat{\mathbf{x}}$ with $\mathbf{T}_i$ is a good approximation of its intersection with $S_i$ . Moreover, with the intersected triangle on $\mathbf{T}_i$ , we can find $\hat{\mathbf{x}}$ 's corresponding point $\hat{\mathbf{p}}$ on the template $\mathbf{T}$ by consistent barycentric weights. Obviously, $\hat{\mathbf{p}}$ is close to $S_{\eta}$ and is a good approximation of $\mathcal{D}_i^{-1}(\hat{\mathbf{x}})$ . With $\hat{\mathbf{p}}$ as good initialization, we can find a point $\mathbf{p}$ on $S_{\eta}$ , whose deformed point $\mathbf{x} = \mathcal{D}_i(\mathbf{p})$ is exactly the intersection point of the ray $\mathbf{r}$ and $S_i$ . Specifically, we solve $\mathbf{p}$ by: + +$$ +\mathbf {p} = \underset {\hat {\mathbf {p}}} {\arg \min } \omega | f (\hat {\mathbf {p}}) | + \frac {\left\| \left(\mathcal {D} _ {i} (\hat {\mathbf {p}}) - \mathbf {c}\right) \times \mathbf {v} \right\| _ {2}}{\left\| \mathcal {D} _ {i} (\hat {\mathbf {p}}) - \mathbf {c} \right\| _ {2}}, \tag {2} +$$ + +where the first item constrains $\hat{\mathbf{p}}$ to be close with $S_{\eta}$ and the second item restricts $\mathcal{D}_i(\hat{\mathbf{p}})$ on the ray. In our implementation, we set $\omega = 3.05$ and execute 10 gradient descent iterations to solve $\mathbf{p}$ . To guarantee accuracy, we reject those samples with large losses. + +Differentiable Formula. The above-mentioned solving process of $\mathbf{p}$ is an iterative optimization process, which is not differentiable. For the ray in $i$ -th frame, camera position $\mathbf{c}$ , view direction $\mathbf{v}$ , $\mathcal{D}_i$ 's parameters $\psi_i$ and $f$ 's parameter $\eta$ uniquely determine the $\mathbf{p}$ . Therefore, $\mathbf{p}$ can be seen as a function of these parameters, and we need to compute partial derivatives of $\mathbf{p}$ to all these parameters. For brevity, we only clarify our calculation for $\eta$ here, and other partial derivatives are computed similarly. + +Through the above analysis, $\mathbf{p}$ satisfies the surface and ray constraints: $f(\mathbf{p})\equiv 0$ and $(\mathcal{D}_i(\mathbf{p}) - \mathbf{c})\times \mathbf{v}\equiv 0$ .We + +![](images/30deda7e0b92fa1f00d0456662168f62cadcd32e971b4c80e8ee8bf6bd2a5b44.jpg) +Figure 2. Some related symbols and illustration about differentiable non-rigid ray-casting and implicit neural rendering. + +differentiate these two equations w.r.t $\eta$ to get: + +$$ +\frac {\partial f}{\partial \mathbf {p}} ^ {T} \frac {\partial \mathbf {p}}{\partial \eta} = - \frac {\partial f}{\partial \eta} [ \mathbf {v} ] _ {\times} \frac {\partial \mathbf {x}}{\partial \mathbf {p}} \frac {\partial \mathbf {p}}{\partial \eta} = 0, \tag {3} +$$ + +where $\mathbf{x} = \mathcal{D}_i(\mathbf{p})$ and $[\mathbf{v}]_{\times}$ is $\mathbf{v}$ 's cross product matrix. We concatenate these two equations to get a $4\times 3$ linear system, then $\frac{\partial\mathbf{p}}{\partial\eta}$ is computed by solving its normal equation. + +# 3.4. Implicit Rendering Network + +IDR [53] proposes an MLP $M$ to approximate the rendering equation and demonstrates certain disentangle ability of lighting and material. In their rigid configuration, $M$ takes the zero isosurface's point, its normal, the view direction and its global geometry feature vector as input to estimate the point's color along the view direction. We subtly transfer their design to non-rigid scenarios by converting related current frame's attributes to canonical space. As shown in Fig. 2, considering a ray emitted from camera center $\mathbf{c}$ along a sampled pixel, whose direction $\mathbf{v}$ is determined by camera's intrinsic parameters $\tau$ , we compute its intersection point $\mathbf{p}$ on $S_{\eta}$ with the algorithm described in sec 3.3. In the meantime, we compute its normal $\mathbf{n_p} = \nabla f(\mathbf{p};\eta)$ by gradient calculation. Then, the view direction $\mathbf{v_p}$ in canonical space can be computed by transferring $\mathbf{v}$ with the Jacobian matrix $J_{\mathbf{x}}(\mathbf{p})$ of the deformed point $\mathbf{x} = \mathcal{D}_i(\mathbf{p})$ w.r.t $\mathbf{p}$ . As for the global geometry feature, we similarly use a larger MLP $F(\mathbf{p};\eta) = (f(\mathbf{p};\eta),\mathbf{z}(\mathbf{p};\eta))$ to additionally compute it, which implies the geometry information around $\mathbf{p}$ and can be used to help the prediction of global shadow [53]. + +Finally, we use an MLP $M$ with learnable weights $\gamma$ to compute $\mathbf{p}$ 's color $L_{\mathbf{p}}(\eta, \psi_i, \gamma, \tau)$ , formulated as: + +$$ +\begin{array}{l} L _ {\mathbf {p}} (\eta , \psi_ {i}, \gamma , \tau) = M (\mathbf {p}, \mathbf {n} _ {\mathbf {p}}, \mathbf {v} _ {\mathbf {p}}, \mathbf {z} (\mathbf {p}; \eta); \gamma) \\ \mathbf {n} _ {\mathbf {p}} = \nabla f (\mathbf {p}; \eta) \tag {4} \\ \mathbf {x} = \mathcal {D} _ {i} (\mathbf {p}) \\ \mathbf {v} _ {\mathbf {p}} = J _ {\mathbf {x}} (\mathbf {p}) ^ {- 1} \mathbf {v}, \\ \end{array} +$$ + +where related symbols have been described above. It can be seen that the color along direction $\mathbf{v}$ of the deformed point $\mathbf{x}$ in $i$ -th frame is determined by the MLP weights $\eta$ and $\gamma$ , camera parameters $\tau$ and deformation field parameters $\psi_{i}$ . + +# 3.5. Loss Function + +According to the description above, for a $N$ -frame self-rotating video, the set $\mathcal{X}$ of all estimizable parameters is: + +$$ +\mathcal {X} = \{\eta , \gamma , \phi , \tau \} \cup \left\{\mathbf {h} _ {i}, \boldsymbol {\theta} _ {i} | i \in 1, \dots , N \right\}, +$$ + +which includes camera parameters, the learnable weights of MLPs shared by the whole sequence and per frame's specific pose parameters and non-rigid deformation field's conditional variable. Our target is to design a loss function and optimize $\mathcal{X}$ to match the mask and RGB images $\{O_i,I_i|i\in 1,\dots,N\}$ of the input video. Besides, a predicted normal map $\{N_{i}|i\in 1,\dots,N\}$ is added to the optimization. As SelfRecon maintains both explicit and implicit geometry, the loss terms can be divided into two parts. + +# 3.5.1 Explicit Loss + +During the computation of explicit losses, we temporarily regard the canonical mesh vertices $\mathbf{T}$ as an estimizable variable and compute its gradient together with $\mathcal{X}$ . Then in the consistency loss, we associate its variations with our implicit representation. At present, explicit losses mainly include mask loss, deformation regularization loss, and the smoothness loss of the skeleton. + +Mask Loss. We utilize a differentiable renderer [48] based on point cloud to render the mask $O(\mathbf{T}_i)$ of $i$ -th frame's mesh $\mathbf{T}_i = \mathcal{D}_i(\mathbf{T})$ with camera parameters, and compute the IoU loss with target mask $O_i$ : + +$$ +l o s s _ {I o U} = 1 - \frac {\left\| O \left(\mathbf {T} _ {i}\right) \otimes O _ {i} \right\| _ {1}}{\left\| O \left(\mathbf {T} _ {i}\right) \oplus O _ {i} - O \left(\mathbf {T} _ {i}\right) \otimes O _ {i} \right\| _ {1}}, \tag {5} +$$ + +where $\otimes$ and $\oplus$ are the operators that perform element-wise product and sum respectively. + +Deformation Regularization Loss. As stated in Sec. 3.2, the $i$ -th frame's deformation field $\mathcal{D}_i$ contains variable $d$ and fixed $\mathcal{W}$ . $d$ represents the deformation that can not be represented by skinning transformation $\mathcal{W}$ , and this deformation should be relatively small. To associate the skeleton + +pose, we design the following regularization loss: + +$$ +\operatorname {l o s s} _ {\text {r e g u}} = \frac {1}{| \mathbf {T} |} \sum_ {\mathbf {t} \in \mathbf {T}} \rho \left(\left\| \mathcal {W} (\mathbf {t}; \boldsymbol {\theta} _ {i}) - \mathcal {D} _ {i} (\mathbf {t}) \right\| _ {2}\right), \tag {6} +$$ + +where $\mathbf{t}$ is a vertex coordinate of $\mathbf{T}$ , $|\mathbf{T}|$ is the vertices number of $\mathbf{T}$ , and $\rho$ is the Geman-McClure robust loss [14]. + +Skeleton Smoothness Loss. The motion trajectory of the joints should be low frequency. Similar with MonoP-erf [52], we smooth the skeleton coordinates of 30 consecutive frames by minimizing the distance to a 10 dimensional linear subspace $\mathbf{B} \in \mathbb{R}^{30 \times 10}$ spanned by the 10 lowest frequency basis vectors of the discrete cosine transform: + +$$ +l o s s _ {s k e} = \frac {1}{3 0} \| \mathbf {J N u l l} (\mathbf {B}) \| _ {F} ^ {2}. \tag {7} +$$ + +Here, $\mathrm{Null}(\mathbf{B})$ denotes the nullspace of the $\mathbf{B}$ matrix, the matrix $\mathbf{J} \in \mathbb{R}^{72 \times 30}$ stacks all skeleton coordinates of consecutive 30 frames, and $\| \cdot \|_F$ denotes the Frobenius norm. + +Finally, the loss for the explicit representation is: + +$$ +\operatorname {L o s s} _ {e x p} = \operatorname {l o s s} _ {I o U} + \lambda_ {e 1} \operatorname {l o s s} _ {r e g u} + \lambda_ {e 2} \operatorname {l o s s} _ {s k e}. \tag {8} +$$ + +$\lambda_{e1}$ and $\lambda_{e2}$ adjust the weights of related losses. After each iteration, we reserve $\mathcal{X}$ 's gradients and wait for the implicit loss iteration to update together. For canonical mesh vertices, we use SGD to update $\mathbf{T}$ to $\hat{\mathbf{T}}$ , which will be used in consistency loss to match two representations. + +# 3.5.2 Implicit Loss + +We sample pixels within the ground truth mask and utilize Sec. 3.3 to get the ray's intersection $\mathbf{p}$ on $S_{\eta}$ and its corresponding ground truth color $I_{\mathbf{p}}$ and predicted normal $N_{\mathbf{p}}$ if available. Then, based on this sampled points set $\mathbf{P}$ , we construct two losses. + +Color Loss. By referring to Eq. (4), we formulate the color loss as: + +$$ +\operatorname {l o s s} _ {R G B} = \frac {1}{| \mathrm {P} |} \sum_ {\mathbf {p} \in \mathrm {P}} \left| L _ {\mathbf {p}} (\mathcal {X}) - I _ {\mathbf {p}} \right|. \tag {9} +$$ + +Here, we use $\mathcal{X}$ to substitute related parameters in Eq. (4). Intuitively, this loss requires that the rendered images should match the input images. + +Normal Loss. We utilized the predicted normal map by PIFuHD [42] to further refine the geometry shape. Referring to Eq. (4), we can easily compute $\mathbf{p}$ 's normal $\mathbf{n_p}$ . Besides, we need to transform the corresponding predicted normal $N_{\mathbf{p}}$ from the space of current frame to canonical space, which can be computed with $J_{\mathbf{x}}(\mathbf{p})^T N_{\mathbf{p}}$ , where $J_{\mathbf{x}}(\mathbf{p})$ is the Jacobian matrix of the forward deformation field at $\mathbf{p}$ [44]. Thus, the normal loss is: + +$$ +\left. \operatorname {l o s s} _ {\text {n o r m}} = \frac {1}{| \mathrm {P} |} \sum_ {\mathbf {p} \in \mathrm {P}} \omega_ {\mathbf {p}} \| \mathbf {n} _ {\mathbf {p}} - \operatorname {u n i t} \left(J _ {\mathbf {x}} (\mathbf {p}) ^ {T} N _ {\mathbf {p}}\right) \| _ {2}. \right. \tag {10} +$$ + +Here, $unit(\cdot)$ means to normalize the vector. $\omega_{\mathbf{p}}$ is the weight defined by the cosine of angle between $\mathbf{n_p}$ and corresponding view direction. Since the predicted normals are noisy and inconsistent between frames, we use this weights to alleviate the impact of normal that deviates from its view direction and avoid geometry artifacts. + +We also design regular losses for the implicit representation, and these losses are defined on the set of sampled points $S$ near the implicit surface [15]. + +Rigidity Loss. We require the first deformation field $d$ to be as rigid as possible to avoid distortion. Following Park et al. [36], we design our loss as: + +$$ +\operatorname {l o s s} _ {\text {r i g i d}} = \frac {1}{| \mathrm {S} |} \sum_ {\mathbf {p} \in \mathrm {S}} \rho \left(\left\| \log \Sigma_ {\mathbf {p}} \right\| _ {F}\right), \tag {11} +$$ + +where $\Sigma_{\mathbf{p}}$ is the singular value diagonal matrix of the Jacobian of $d$ on $\mathbf{p}$ and $\rho$ is the robust function [14]. + +Eikonal Loss. We adopt the regular loss of IGR [15] to make $f$ to be sign distance function: + +$$ +l o s s _ {s d f} = \frac {1}{| \mathrm {S} |} \sum_ {\mathbf {p} \in \mathrm {S}} \left(\left\| \mathbf {n} _ {\mathbf {p}} \right\| _ {2} - 1\right) ^ {2}, \tag {12} +$$ + +where $\mathbf{n_p}$ is obtained by differentiating $f$ at $\mathbf{p}$ . + +Finally, the implicit loss can be represented as: + +$$ +L o s s _ {i m p} = l o s s _ {R G B} + \lambda_ {i 1} l o s s _ {n o r m} + \lambda_ {i 2} l o s s _ {r i g i d} + \lambda_ {i 3} l o s s _ {s d f}, \tag {13} +$$ + +where $\lambda_{i1},\lambda_{i2}$ and $\lambda_{i3}$ are balancing weights. + +# 3.5.3 Explicit/Implicit Consistency + +After explicit iteration, the canonical mesh has been updated to $\hat{\mathbf{T}}$ , to make the implicit SDF consistent with the updated explicit mesh during implicit iteration, we design a consistency loss: + +$$ +\operatorname {L o s s} _ {\text {c o n s}} = \frac {1}{| \hat {\mathbf {T}} |} \sum_ {\hat {\mathbf {t}} \in \hat {\mathbf {T}}} | f (\hat {\mathbf {t}}; \eta) |, \tag {14} +$$ + +where $\hat{\mathbf{t}}$ is a vertex coordinate of $\hat{\mathbf{T}}$ . Intuitively, the loss requires $\hat{\mathbf{T}}$ to match the implicit surface $S_{\eta}$ . + +In each optimization step, we first perform the explicit iteration to obtain $\hat{\mathbf{T}}$ and reserve $\mathcal{X}$ 's gradients. Then, we compute implicit and consistency losses to accumulate new $\mathcal{X}$ 's gradients. Finally, Adam is utilized to update $\mathcal{X}$ with computed gradients. + +# 4. Experiments + +We conduct quantitative and qualitative experiments to demonstrate the effectiveness of SelfRecon. For quantitative evaluation, we synthesize several sequences with commercial software due to the lack of high-quality geometry + +Table 1. The errors (cm) on the synthetic five sequences. We report three error metrics: the average distance from reconstructed to GT meshes (Recon), the average distance from GT to reconstructed meshes (GT), and the Chamfer distance. For each error metric, we report the values of VideoAvatar and ours in two consecutive rows. + +
Subjectf1f2f3m1m2mean
Recon1.591.711.931.811.271.66
1.671.321.631.531.171.46
GT2.081.502.401.921.421.86
1.621.161.921.531.171.48
Chamfer1.841.602.171.861.341.76
1.641.241.771.531.171.47
+ +data of human body with general clothing. For qualitative evaluation, we mainly utilize the PeopleSnapshot [2] dataset and several real sequences collected by ourselves. We also present ablation study for the loss term design and present an avatar generation application. + +# 4.1.Quantitative Evaluation + +We synthesize data to quantitatively evaluate our reconstruction algorithm. Specifically, we use Blender [8] to design the self-rotating motions for male and female avatars. Then, we utilize CLO3D [12] to design several clothes and animate the clothed body with motions. Finally, we synthesized two sets of male and three sets of female dressing sequences. We reconstruct these sequences with VideoAvatar [2] and our method, and report the registration error for the canonical posture results in Tab. 1. Compared with VideoAvatar, our method significantly reduces the values of various error metrics. In Fig. 3, we also present four group results and their error maps. Intuitively, our results capture the overall shape and have some reasonable details. As VideoAvatar is based on the SMPL+D representation, it has plausible results for tighter clothing, like the male examples, but lacks detailed reconstruction ability. Moreover, it can not correctly reconstruct loose clothing, especially for the females dressed in skirts. + +# 4.2. Qualitative Evaluation + +We also qualitatively compare SelfRecon with multi-frame prediction algorithm PaMIR [55], optimization method VideoAvatar [2] and NeRF [34] based neural rendering method NeuralBody [39] on several sequences of PeopleSnapshot dataset. In Fig. 4, we present the first frame of input video, our rendered image, and reconstruction results of all methods from two perspectives. And we compare with PaMIR in the first two rows and the others with NeuralBody. As we can see, VideoAvatar based on SMPL+D can only approximately capture the overall shape, but details such as hairstyle and clothing folds are lost. PaMIR uses multi-frame input to improve its results, + +![](images/70dfae8c716611bd6ff87f3edd27823c3ca730382f337d99e5f971a195c534fe.jpg) +Figure 3. Reconstructions in canonical pose and their error maps for four synthetic self-rotating sequences. In each group, we show the GT mesh, results of VideoAvatar and SelfRecon in turn (red means $\geq 6\mathrm{cm}$ ). + +![](images/55b8e58719d7de3669f8afd9806fefd4c1ea1ba3fcdb8aec35d62e99f76283cf.jpg) +Figure 4. Comparison results with methods that use video or multi-frame images, including PaMIR [55], NeuralBody [39] and VideoAvatar [2]. For the second comparison group, the method in the first two rows is PaMIR, and the rest is NeuralBody. We also present our rendered image as reference. SelfRecon can reconstruct high-fidelity geometry shape of standing posture, including facial features and clothing folds. + +but still suffers from the deep ambiguity. As in the second example, its reconstructed human is not upright from the side view. Besides, its results have some details but miss facial features, while our method has better details and can recover certain facial features. Similar with SelfRecon, NeuralBody also inputs a video to do self-supervised optimization. It mainly focuses on novel view synthesis, but still can extract geometry from underlying NeRF representation. We can see that its reconstructions alleviate deep ambiguity and conform to the human's overall structure while suffering from large noise on the surface, which may be caused by excessive freedom of volume rendering. Different from their method, implicit surface representation based SelfRecon can recover high-fidelity geometry shape without noises. + +![](images/eb86eb04a7d98306f114674409fc651a8553fc813eaf2a7c51568921d2c8414e.jpg) +Figure 5. Reconstruction results from videos taken by smartphones. Each group shows the first image of the video, corresponding neural rendered image and reconstructed shape. + +Fig. 5 shows reconstruction results on our collected videos with smartphones. For each group, we present the first frame of the video, our rendered image and reconstruction. Our results have high-fidelity geometry shapes for kinds of clothing and body, and our neural rendered images are also quite close to the input images. + +# 4.3. Ablation Study + +Our complete algorithm requires color images, masks and normal maps as inputs. Fig. 6 shows ablation experiments of two examples on three inputs. As the results show, if only using the mask loss, the recovered geometry shape is inside the convex hull formed by the silhouettes but lacks details and has noticeable concavities. After adding the color loss, it significantly improves the details and reduces the unnatural concavities. For the second example, the result has been very close to the result obtained by adding the normal loss. However, for the first example, it can not completely eliminate the depressed geometry with- + +![](images/b28dbd5b987fd380c71e219c74692d62bde128b55e9f25329362d43f1ab4592e.jpg) +Figure 6. Ablation study for color, mask and normal losses. With mask loss only, the results lack details and have much concave geometry. After adding color loss, geometry is significantly improved but can not completely eliminate the concavities. With the predicted normals, the results are further improved. In the last column, we also show the neural rendering images as reference. + +![](images/fcc1ae7587cd33bc5b8cf79121cef24a7b103b12cae27f73c88abe6f49044667.jpg) +Figure 7. Without the adaptive weights in Eq. (10) and small $\lambda_{i1}$ in Eq. (13), normal loss will result artifacts (middle). After adjusting the weights, the corresponding result (right) is more plausible. + +![](images/88abe8123d6ecec062b41751f31e36520ad60fe2109afb8901a819f7619a8a70.jpg) + +![](images/2add636844e784e8308b3daf55c83ceb715c190aa47a6571c67455f55ee66b91.jpg) + +out normal loss. This may be caused by lacking rich texture and multi-view observations in these areas. With the normal loss, our results are further improved, and the unnatural pits are eliminated while the details are preserved. + +Since the normal prediction network [42] is trained with synthetic images, its prediction may be not accurate for real tests and may be not consistent for different frames. As shown in Fig. 7, without the adaptive weights in Eq. (10), the normal loss might result unexpted results. + +# 4.4. Avatar Generation + +Thanks to our forward deformation field design, we can extract a mesh sequence with consistent topology. Based on the tracking results, we can extract a texture template mesh from the images with bound skinning weights from the skinning transformation field. Then, an animatable avatar is generated and can be driven with SMPL pose parameters. For texture extraction, we follow the method of VideoAvatar [2]. Fig. 8 shows two examples of texture generation and driving from the PeopleSnapshot dataset. Our method recovers better geometric details like facial, shoes + +![](images/cf4b85578a27e6d89de3e372bea78754d7df72ad26a7760e2afe57e7153f9009.jpg) +Figure 8. The reconstructed texture mesh and driving results. The left shows the reference image, texture meshes generated by VideoAvatar and SelfRecon. On the right, we use three pose parameters to drive our texture mesh and generate plausible results. + +and clothing folds thanks to more accurate tracking results. Besides, our driving results look plausible and may be of sufficient quality for some applications. + +# 5. Conclusion and Discussion + +We proposed SelfRecon, a self-supervised reconstruction method based on neural implicit representation and neural rendering. With forward deformation, our method can be easily applied to body movement and recover spacetime coherent surfaces, which is convenient for downstream applications. Moreover, combining the explicit representation, we proposed a non-rigid ray casting algorithm, which makes it possible for differentiable intersecting with the deformed implicit surface. SelfRecon can reconstruct high-fidelity clothed body shape from a self-rotating video without pre-computed templates. We also show high-fidelity avatar generation with our tracking results, demonstrating potential applications of SelfRecon. + +SelfRecon still has several limitations. First, it requires relatively long time to optimize, which limits its convenient applications. However, this problem can be alleviated with the help of body priors and the fast growing field of neural rendering. Second, current method relies on the predicted normal maps to improve the geometric details. How to recover the geometric details directly from the self-supervised rendering loss is worthy of future study. Third, the proposed method mainly works well for self-rotating motions, and it is worthy of study for more general motion sequences. + +Acknowledgement This research was supported by National Natural Science Foundation of China (No. 62122071), the Youth Innovation Promotion Association CAS (No. 2018495), "the Fundamental Research Funds for the Central Universities" (No. WK3470000021). + +# References + +[1] Thiemo Alldieck, Marcus Magnor, Bharat Lal Bhatnagar, Christian Theobalt, and Gerard Pons-Moll. Learning to reconstruct people in clothing from a single RGB camera. 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Most existing methods either take the end-to-end supervised learning based manner, where large amounts of pairs of sparse input and dense ground-truth are exploited as supervision information; or treat up-scaling of different scale factors as independent tasks, and have to build multiple networks to handle upsampling with varying factors. In this paper, we propose a novel approach that achieves self-supervised and magnification-flexible point clouds upsampling simultaneously. We formulate point clouds upsampling as the task of seeking nearest projection points on the implicit surface for seed points. To this end, we define two implicit neural functions to estimate projection direction and distance respectively, which can be trained by two pretext learning tasks. Experimental results demonstrate that our self-supervised learning based scheme achieves competitive or even better performance than supervised learning based state-of-the-art methods. The source code is publicly available at https://github.com/xnowbzhao/sapcu. + +# 1. Introduction + +Point clouds serve as a popular tool to represent 3D data due to their flexibility and compactness in describing objects/scenes with complex geometry and topology. They can be easily captured by modern scanning devices, and have been widely used in many applications, such as autonomous driving, robotics, etc. However, due to the inherent limitations of 3D sensing technology, raw point clouds acquired from 3D scanners are usually sparse, occluded and non-uniform. In many downstream applications, such as surface reconstruction and understanding, dense point clouds are desired for representing shapes with richer geometric details. Accordingly, people turn to develop a computational approach, referred to as point clouds upsampling, + +which has attracted extensive attention in both industry and academia [7, 8, 13, 20-22]. + +Unlike conventional grid based images, point clouds are irregular and unordered, which make point clouds upsampling a more challenging task than its 2D image counterpart. The goal of point clouds upsampling is two-fold: 1) generating a dense point set from the sparse input to provide richer details of the object; 2) generating a uniform and complete point set to cover the underlying surface faithfully. + +In recent years, deep neural networks based point clouds upsampling approaches emerge and become popular, which adaptively learn structures from data and achieve superior performance than traditional methods, such as optimization-based ones [1,5,6]. For instance, Yu et al. [21] propose to learn multi-level features per point and expand the point set via a multi-branch convolution unit implicitly in feature space, which is then split to a multitude of features for reconstruction of an upsampled point set. Wang et al. [20] propose to progressively train a cascade of patch-based upsampling networks on different levels of detail. Li et al. [7] apply generative adversarial network into point clouds upsampling, which constructs an up-down-up expansion unit in the generator for upsampling point features with error feedback and self-correction, and formulate a self-attention unit to enhance the feature integration. To better represent locality and aggregate the point neighborhood information, Qian et al. [13] propose to use a Graph Convolutional Network to perform point clouds upsampling. + +In summary, the outlined deep learning based methods take a general approach: first design an upsampling module to expand the number of points in the feature space, then formulate losses to enforce the output points to be as close as possible to the ground truth dense points. However, these methods suffer from the following two limitations: + +End-to-End Training. These methods are trained in an end-to-end supervised learning manner, which requires a large amount of pairs of input sparse and ground-truth dense point sets as the supervision information. The training data is constructed by sampling from synthetic models, whose distributions are inevitably biased from that of the real- + +scanned data. This would lead the trained models to have poor generalization ability in real-world applications. Thus, it is more desirable to develop self-supervised or unsupervised point cloud upsampling schemes. + +Fixed Upsampling Factor. Due to resource constraints, such as display resolution and transmission bandwidth, the required upsampling factor is usually various. These existing methods treat upscaling of different scale factors as independent tasks, which train a specific deep model for a pre-defined factor and have to build multiple networks to handle upsampling with varying factors. This manner is clumsy, which increases both model complexity and training time significantly. Thus, it is more desirable to develop unified point cloud upsampling schemes that can handle arbitrary scale factor. + +Some methods developed very recently [9,14,19,22] investigate the above limitations and attempt to address them: + +- Regarding self-supervised point cloud upsampling, Liu et al. [9] propose the coarse-to-fine framework, which downsamples the input sparse patches into sparser ones and then exploits them as pairs of supervision information to perform end-to-end training. [22] proposes an end-to-end self-supervised learning manner, in which the loss functions enforce the input sparse point cloud and the generated dense one to have similar 3D shapes and rendered images. However, these two methods are still limited to a fixed upsampling factor. +- Regarding arbitrary-scale upsampling, inspired by the counterpart Meta-SR in image [4], Ye et al. [19] propose Meta-PU for magnification-flexible point cloud upsampling, in which the meta-subnetwork is learned to adjust the weights of the upsampling blocks dynamically. Qian et al. [14] design a neural network to adaptively learn unified and sorted interpolation weights as well as the high-order refinements, by analyzing the local geometry of the input point cloud. However, these two methods still follow the end-to-end supervised learning manner, which need to construct a large-scale training set including ground truth dense point sets with scales within a wide range. + +In this paper, we propose a novel and powerful point clouds upsampling method via implicit neural representation, which can achieve self-supervised and magnification-flexible upsampling simultaneously. Specifically, to get rid of the requirement of ground truth dense point clouds, we do not directly learn the mapping between the input sparse and output dense point sets. Alternatively, inspired by the notion that an implicit surface can be represented by signed distance function (SDF) [10, 11, 15], we turn to seek the nearest projection points on the object surface for given seed points through two implicit neural functions, which are used to estimate projection direction and distance respectively. + +The two function can be trained by two constructed pretext self-supervised learning tasks. In the way, as long as the seed points are sampled densely and uniformly, we can produce high-resolution point clouds that are dense, uniform and complete. To guarantee the uniformity of seeds sampling, we exploit equally-paced 3D voxels to divide the space of point cloud. Experimental results demonstrate our self-supervised learning based scheme achieves competitive or even better performance that supervised learning based state-of-the-art methods. The main contributions of this work are highlighted as follows: + +- To the best of our knowledge, we are the first in the literature to simultaneously consider self-supervised and arbitrary-scale point clouds upsampling. +- We formulate point clouds upsampling as the task of seeking nearest projection points on the implicit surface for seed points, which can be done by two implicit neural functions trained by pretext tasks. From the generated dense point clouds, we can achieve arbitrary-scale upsampling by farthest point sampling. +- Although our method is self-supervised, it produces high-quality dense point clouds that are uniform and complete, and achieves competitive objective performance and even better visual performance compared with state-of-the-art supervised methods. + +# 2. Method + +Define $\mathcal{X} = \{\mathbf{p}_i\}_{i=1}^n \in \mathbb{R}^{n \times 3}$ as the input sparse point cloud. For a desirable scaling factor $r$ , we target to obtain a corresponding dense point cloud $\mathcal{Y} = \{\mathbf{p}_i\}_{i=1}^N \in \mathbb{R}^{N \times 3}$ including $N = \lfloor r \times n \rfloor$ points. $\mathcal{S}$ is defined as the underlying surface of the dense point cloud. The high-resolution point cloud $\mathcal{Y}$ is required to be dense and uniform, as well as be able to handle occlusion and noise, i.e., to be complete and clean. + +Unlike the existing methods that take the end-to-end training framework, we do not directly learn the mapping between the input sparse and output dense point sets, but instead seek the nearest projection point on the object surface for a given seed point in a self-supervised manner. By densely and uniformly sampling seed points in the space, we can obtain dense and approximately uniform projection points, which can describe the underlying surface faithfully. The proposed self-supervised point clouds upsampling strategy includes the four steps: + +- Seeds Sampling. We represent the geometric space of the point cloud by 3D voxel grid, from which we choose the centres of voxels that are close to the implicit surface $S$ as the seed points. + +- Surface Projection. For seed points, we project them to the implicit surface $S$ to obtain the projected points, which construct the generated dense point cloud. +- Outliers Removal. We further remove the projected points that are generated by far seed points to achieve cleaner point cloud. +- Arbitrary-Scale Point Cloud Generation. To obtain the desired upsampling factor, we adjust the number of vertices of the generated dense clouds by farthest point sampling. + +In the following, we introduce each step in detail. + +# 2.1. Seeds Sampling + +To obtain uniformly sampled seed points, given a point cloud, we divide the 3D space into equally spaced voxels $\{\mathbf{V}_{(x,y,z)}\}$ , where $\mathbf{V}_{(0,0,0)}$ represents the voxel locating in the origin of the 3D Cartesian coordinate system. We define the resolution of a 3D voxel volume as $l\times l\times l$ . The centre of a voxel $\mathbf{V}_{(x,y,z)}$ is thus $\mathbf{c}_{(x,y,z)} = [x + 0.5*l,y + 0.5*l,z + 0.5*l]$ . The centres of voxels are equally distributed in the space, which serve as good candidates of seed points. However, we do not use them all, but choose the ones that are closed to the underlying surface of the point cloud. + +A reasonable principle to choose centres is according to their distances to the surface $S$ . We choose a centre $\mathbf{c}_{(x,y,z)}$ as the seed if its distance to the surface within a preset range: $\mathrm{Dist}(\mathbf{c}_{(x,y,z)}, S) \in [D_l, D_u]$ . The difficulty lies in that we cannot directly compute the distance $\mathrm{Dist}(\mathbf{c}_{(x,y,z)}, S)$ , since the underlying surface $S$ is unknown. We propose an alternative strategy to approximate $\mathrm{Dist}(\mathbf{c}_{(x,y,z)}, S)$ . Specifically, from the input sparse point sets $\mathcal{X}$ , we choose $M$ points that are nearest to $\mathbf{c}_{(x,y,z)}$ , denoted as $\{\mathbf{p}_{c,1}, \mathbf{p}_{c,2}, \dots, \mathbf{p}_{c,m}, \dots, \mathbf{p}_{c,M}\}$ that are ordered from near to far. From these points, we can form a set of triangles $\{T_m = (\mathbf{p}_{c,1}, \mathbf{p}_{c,2}, \mathbf{p}_{c,m})\}_{m=3}^M$ . We then perform the following approximation: + +$$ +\operatorname {D i s t} \left(\mathbf {c} _ {(x, y, z)}, \mathcal {S}\right) \approx \min \operatorname {D i s t} \left(\mathbf {c} _ {(x, y, z)}, t\right), t \in \left\{T _ {m} \right\} _ {m = 3} ^ {M} \tag {1} +$$ + +where $t$ represents a point contained in the constructed triangles. Finally, we obtain the seed points set $C$ . By setting appropriate $l$ , we can generate dense and uniformly distributed seed points. + +# 2.2. Surface Projection + +With the sampled seed points, the next step is to seek the their projection points on the surface, which are the target points of the generated dense point cloud. + +In the field of 3D computer vision and graphics, it is well-known that an implicit surface can be defined as a signed distance function (SDF) [10, 11, 15]. SDF, when + +passed the coordinates of a point in space, outputs the closest distance of this point to the surface, whose sign indicates whether the point is inside or outside of the surface. Inspired by SDF, we propose the following feasible approach to estimate the projected point on the surface for a query seed point. + +It is worth noting that, the computation strategies of SDF, such as [10, 11, 15], cannot be directly applied for our purpose. For a 3D query point $\mathbf{x}$ , SDF outputs: $SDF(\mathbf{x}) = s$ , $s \in \mathbb{R}$ . The sign of $s$ only indicates it is inside or outside of a shape, but does not provide the direction to the surface. In our method, for a seed point $\mathbf{c} \in C$ , we divide the task of estimating projection point into two sub-tasks: 1) estimating the projection direction $\mathbf{n} \in [-1,1]^3$ ; 2) estimating the projection distance $d \in \mathbb{R}$ . Then the coordinate of the projection point of the seed point $\mathbf{c}$ can be obtained as: $\mathbf{c}_p = \mathbf{c} + \mathbf{n} * d$ . + +Projection Direction Estimation. We train a multi-layer fully-connected neural network $f_{n}(\cdot ;\Theta_{n})$ for this purpose, which takes the query point $\mathbf{c}$ and the sparse point cloud $\mathcal{X}$ as inputs: + +$$ +\mathbf {n} = f _ {n} (\mathbf {c}, \mathcal {X}; \Theta_ {n}) \tag {2} +$$ + +To reduce the computational complexity, we take $k$ nearest points to $\mathbf{c}$ in $\mathcal{X}$ instead of the whole $\mathcal{X}$ as input. We denote this subset of points as $\mathcal{X}_c = \{\mathbf{p}_1,\dots ,\mathbf{p}_k\}$ . Moreover, to facilitate the inference process of neural networks, we perform normalization on the point coordinates by setting $\mathbf{c}$ as the origin. In this way, we can simplify the estimation function as: + +$$ +\mathbf {n} = f _ {n} \left(\widehat {\mathcal {X}} _ {c}; \Theta_ {n}\right) \tag {3} +$$ + +where $\widehat{\mathcal{X}}_c = \{\mathbf{p}_1 - \mathbf{c},\dots ,\mathbf{p}_k - \mathbf{c}\} .$ + +Projection Distance Estimation. Similarly, for estimating the projection distance $\mathbf{d}$ , we also train a multi-layer fully-connected neural network $f_{d}(\cdot ;\Theta_{n})$ , which takes the query point $\mathbf{c}$ , the subset of nearest points $\mathcal{X}_c$ and the estimated projection direction $\mathbf{n}$ as inputs: + +$$ +d = f _ {d} \left(\mathbf {c}, \mathcal {X} _ {c}, \mathbf {n}; \Theta_ {d}\right) \tag {4} +$$ + +Normalization is also helpful for this network. Different from $f_{n}$ , here the input $\mathbf{n}$ involves direction. Therefore, it should perform normalization on both position and direction, which can be done in two stages: 1) moving $\mathbf{c}$ to the origin; 2) applying the rotation matrix $\mathbf{W}_r$ to rotate $\mathbf{n}$ to a specific direction $\mathbf{n}_t$ , i.e., $\mathbf{n}_t = \mathbf{W}_r\mathbf{n}$ . After normalization, $\mathcal{X}_c$ becomes $\widetilde{\mathcal{X}}_c = \{\mathbf{W}_r(\mathbf{p}_1 - \mathbf{c}),\dots ,\mathbf{W}_r(\mathbf{p}_k - \mathbf{c})\}$ , which is the only required input for $f_{d}$ : + +$$ +d = f _ {d} \left(\tilde {\mathcal {X}} _ {c}; \Theta_ {d}\right) \tag {5} +$$ + +# 2.3. Outliers Removal + +In the step of seeds sampling, some points that are actually far away from $S$ may be included into the seed points + +![](images/faf7f2f73ae67823ab9033668d4f3438a8405b36a196020d4ebab00e197af0d7.jpg) + +![](images/5ea021a7fb3eed0d80ca1c55beae821d5bd59b70f777deab2080ea69bf3ed92b.jpg) +Figure 1. The network architecture of implicit neural function. + +set $C$ due to the error in approximation. The normal vector and distance of these points cannot be well estimated, leading to outliers in the resulting dense point cloud. We turn to exploit the post-processing procedure to remove them. + +Specifically, for a projection point $\mathbf{c}_p$ , we find its $v$ nearest points $\{\mathbf{c}_{p,1},\dots ,\mathbf{c}_{p,v}\}$ . We then compute the average bias between $\mathbf{c}_p$ and them: + +$$ +b _ {p} = \frac {1}{v} \sum_ {i = 1} ^ {v} \operatorname {D i s t} \left(\mathbf {c} _ {p}, \mathbf {c} _ {p, i}\right) \tag {6} +$$ + +For all projection points, we do in the same way to get $\{b_p\}$ , the average of which is denoted as $\bar{b}$ . We determine a point as outlier if it satisfies $b_{p} > \lambda \bar{b}$ , where $\lambda$ is set as 1.5 in practical implementation. + +# 2.4. Arbitrary-Scale Point Cloud Generation + +Note that the above process cannot accurately control the number of vertices generated. Thus, it is necessary to adjust the number of vertices to achieve upsampling with the desired scale factor. In our context, we first perform inverse normalization on the generated point cloud, and then adjust the number of vertices to $N$ by the farthest point sampling algorithm [12]. + +# 3. Implicit Neural Networks Training + +In this section, we introduce the architecture of implicit neural networks and the training strategy. + +# 3.1. Architectures + +The networks $f_{n}$ and $f_{d}$ share the same architecture as shown in Figure 1, which borrows the idea of encoder-decoder framework [10]. The network takes the normalized subset of points as input, which are feed into the encoder to obtain a 2048-dimensional feature vector. Here we employ a state-of-the-art method DGCNN [17] as the encoder + +to preserve surface information in multi-levels. The feature vector is then passed through 4 full-connected (FC) layers with batch normalization and ReLU, the output dimensional of which are 1024, 512 and 128 respectively. The output dimensional of the last FC layer is 3 for the projection direction $\mathbf{n}$ and 1 for the projection distance $d$ . Note that the design of the network is not the main contribution of this paper. We can exploit any suitable network for our purpose. + +# 3.2. Training Data Preparation + +To train the two implicit neural functions, we construct two pretext tasks, for which we prepare training samples that consist of 3D points and the corresponding ground truth projection direction and distance values. We train with normalized watertight meshes that are constructed by the TSDF-Fusion presented in [10, 16] from a subset of the ShapeNet [2] that consists of 13 major categories. Since $f_{n}$ and $f_{d}$ are designed with different purposes, we prepare different training pairs for them: + +- For preparing the training data of $f_{n}$ , we firstly generate the seed points: 50K seed points are randomly selected around the mesh surface by limiting that the distances between them and the surface are within a preset range $[D_{l} - \epsilon, D_{u} + \epsilon]$ , where $\epsilon$ is introduced to increase robustness. For a seed point $\mathbf{c}$ , we find the nearest point on the mesh and sample 5 points around it, then compute the average vector $\mathbf{d}$ between $\mathbf{c}$ and them. In this way, we can effectively handle the error in mesh reconstruction. The ground truth $\widehat{\mathbf{n}}$ is finally derived as the normalization of $\mathbf{d}$ . Secondly, for every 16 seed points, we randomly select 2048 points as the corresponding sparse point cloud $\mathcal{X}$ . +- For preparing the training data of $f_{d}$ , 50K seed points are randomly selected around the mesh surface in the + +
Scale2×4×
Metric (10-3)CD ↓EMD ↓F-score ↑mean ↓std ↓CD ↓EMD ↓F-score ↑mean ↓std ↓
Fixed ScalePU-Net [21]12.9 (6)6.75 (6)334 (5)4.02 (5)5.62 (4)11.3 (7)7.02 (7)462 (7)5.05 (7)6.81 (6)
MPU [20]-----10.4 (4)5.64 (5)527 (4)3.61 (4)5.50 (3)
PU-GAN [7]12.7 (5)5.09 (5)326 (6)4.32 (6)6.01 (5)10.9 (5)6.66 (6)484 (6)4.66 (6)6.56 (5)
PU-GCN [13]12.2 (3)4.94 (4)360 (3)3.47 (2)5.09 (2)10.2 (3)5.50 (4)537 (3)3.35 (2)5.01 (2)
PU-DR [8]11.0 (1)3.55 (1)409 (1)2.30 (1)4.05 (1)8.71 (1)3.98 (2)625 (1)2.24 (1)3.89 (1)
Arbitrary ScaleMeta-PU [19]12.6 (4)3.94 (2)339 (4)3.77 (4)5.41 (3)10.9 (5)3.56 (1)506 (5)3.89 (5)5.60 (4)
Proposed12.1 (2)4.93 (3)371 (2)3.49 (3)10.2 (6)10.1 (2)4.87 (3)561 (2)3.49 (3)9.35 (7)
Scale8×16×
Metric (10-3)CD ↓EMD ↓F-score ↑mean ↓std ↓CD ↓EMD ↓F-score ↑mean ↓std ↓
Fixed ScalePU-Net [21]9.67 (5)8.91 (6)611 (6)4.85 (6)6.81 (5)9.25 (7)10.4 (7)632 (7)6.04 (7)8.04 (6)
MPU [20]-----8.12 (5)7.74 (6)727 (5)4.01 (6)6.11 (5)
PU-GAN [7]8.82 (4)5.05 (3)676 (4)3.76 (4)5.51 (3)7.52 (2)6.02 (4)770 (3)3.14 (2)4.92 (2)
PU-GCN [13]8.78 (3)6.41 (5)678 (3)3.33 (2)5.06 (2)7.80 (4)7.44 (5)749 (4)3.39 (4)5.11 (3)
PU-DR [8]8.34 (1)3.95 (1)708 (1)2.99 (1)4.97 (1)7.29 (1)4.51 (1)779 (1)2.92 (1)4.72 (1)
Arbitrary ScaleMeta-PU [19]9.71 (6)4.33 (2)625 (5)3.95 (5)5.68 (4)8.96 (6)5.62 (2)676 (6)3.87 (5)5.59 (4)
Proposed8.70 (2)5.53 (4)706 (2)3.48 (3)8.84 (6)7.65 (3)5.98 (3)772 (2)3.35 (3)8.34 (7)
+ +Table 1. Objective performance comparison with respect to CD, EMD, F-score, mean and std with state-of-the-art methods. The ranking numbers are also provided. + +same way as $f_{n}$ . We then find the corresponding nearest projection points on the surface. The distance between a seed point and the projection point is used as the ground truth $\widehat{d}$ . The generation of $\mathcal{X}$ is in the same way as $f_{n}$ . + +It is worth noting that, although the training data are generated from watertight meshes, our scheme is capable to handle non-watertight point clouds, which can be observed in the real-world cases shown in Figure 6. + +# 3.3. Training Details + +The training of $f_{n}$ and $f_{d}$ is done by minimizing the sum over losses between the predicted and real direction/length values under the mean squared error (MSE) loss function. The training process is conducted on a server with two Tesla V100 GPUs. The networks are trained for 1200 epochs with a batch size of 64, using the Adam algorithm. Following [10], the learning rate is set as $10^{-4}$ , and the other hyperparameters of Adam are set as $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ , $epsilon = 10^{-8}$ , weight decay $= 0$ . + +# 4. Experiments + +In this section, we provide extensive experimental results to demonstrate the superior performance of our method. + +# 4.1. Comparison Study + +We compare the proposed self-supervised arbitrary-scale point clouds upsampling (SSAS) method with several state-of-the-art works, which can be divided into two categories in term of the scale factor: 1) fixed scale methods, including PU-Net [21], MPU [20], PU-GAN [7], PU-GCN [13], PU-DR [8]; 2) arbitrary scale method, including Meta-PU [19]. + +Note that these methods are all supervised learning based. The compared models are trained with the released codes by their authors, following the default settings in their papers. + +We train all these compared methods following the approach mentioned in [19] for fair comparison. The test samples are from the dataset adopted by [19, 21]. We nonuniformly sample 2048 points using Poisson disk sampling from 20 test models to form the test set. + +# 4.2. Parameters Setting + +The side length of voxel $l$ and the range of the distance between seed point and surface $[D_l, D_u]$ decide the number of seed points. However, the number is also depended on the shape of input point cloud. To ensure that enough points are generated, we set $l = 0.004$ and $[D_l, D_u] = [0.011, 0.015]$ . Under this condition, the minimum number of generated points is 99001 (Chair), which meets the demands of $16 \times$ or higher scale upsampling. The specific direction $\mathbf{n}_t$ in normalization can be arbitrarily chosen. We set $\mathbf{n}_t = (1, 0, 0)$ in our experiments. The number of nearest points $k$ is set as 100 in Section 2.2 and 30 in Section 2.3. The number of nearest point $M$ for computing $\mathrm{Dist}(\mathbf{c}_{(x,y,z)}, S)$ affects the number of outliers and continuity of seed points. We set $M = 10$ and further discuss the effect of different $M$ in ablation study. + +# 4.3. Objective Performance Comparison + +Objective Evaluation. We employ six popular metrics for objective evaluation: 1) Chamfer Distance (CD) and Earth Mover Distance (EMD) [21]: which evaluate the similarity between the predicted points and ground truth one in the Euclidean space. For both metrics, smaller is better. 2) F-score [18]: which treats upsampling as a clas + +
Scale2×4×
p (10-2)0.2% ↓0.4% ↓0.6% ↓0.8% ↓1.0% ↓0.2% ↓0.4% ↓0.6% ↓0.8% ↓1.0% ↓
Fixed ScalePU-Net [21]3.05 (6)2.33 (6)2.03 (6)1.86 (6)1.75 (6)2.72 (7)2.19 (7)1.97 (7)1.84 (7)1.76 (7)
MPU [20]-----2.53 (6)2.03 (6)1.80 (6)1.67 (6)1.59 (6)
PU-GAN [7]2.46 (3)1.86 (3)1.62 (4)1.50 (4)1.43 (4)2.45 (4)1.94 (5)1.73 (5)1.62 (5)1.56 (5)
PU-GCN [13]2.68 (5)2.06 (5)1.80 (5)1.65 (5)1.57 (5)2.40 (3)1.93 (4)1.72 (4)1.61 (4)1.54 (4)
PU-DR [8]1.83 (1)1.34 (1)1.17 (1)1.09 (1)1.06 (1)1.77 (2)1.46 (2)1.34 (2)1.28 (2)1.24 (2)
Arbitrary ScaleMeta-PU [19]2.53 (4)1.86 (3)1.58 (3)1.43 (3)1.35 (3)2.50 (5)1.87 (3)1.60 (3)1.45 (3)1.37 (3)
Proposed1.96 (2)1.50 (2)1.33 (2)1.25 (2)1.21 (2)1.72 (1)1.40 (1)1.27 (1)1.21 (1)1.19 (1)
Scale8×16×
p (10-2)0.2% ↓0.4% ↓0.6% ↓0.8% ↓1.0% ↓0.2% ↓0.4% ↓0.6% ↓0.8% ↓1.0% ↓
Fixed ScalePU-Net [21]2.64 (5)2.21 (6)2.02 (6)1.91 (6)1.84 (6)2.86 (6)2.42 (6)2.22 (7)2.10 (7)2.02 (7)
MPU [20]-----2.30 (4)1.96 (4)1.82 (4)1.73 (4)1.69 (4)
PU-GAN [7]1.72 (2)1.47 (3)1.38 (3)1.34 (3)1.32 (3)1.79 (3)1.57 (3)1.48 (3)1.44 (3)1.41 (3)
PU-GCN [13]2.31 (4)1.93 (4)1.75 (4)1.65 (5)1.59 (5)2.42 (5)2.07 (5)1.91 (5)1.82 (5)1.76 (5)
PU-DR [8]1.42 (1)1.20 (1)1.13 (1)1.11 (1)1.11 (1)1.56 (1)1.38 (1)1.32 (1)1.29 (1)1.28 (1)
Arbitrary ScaleMeta-PU [19]2.72 (6)2.05 (5)1.76 (5)1.60 (4)1.51 (4)3.27 (7)2.51 (7)2.14 (6)1.93 (6)1.79 (6)
Proposed1.72 (2)1.45 (2)1.34 (2)1.29 (2)1.27 (2)1.75 (2)1.51 (2)1.41 (2)1.36 (2)1.33 (2)
+ +Table 2. Uniformity performance comparison with respect to NUC scores. The ranking numbers are also provided. + +![](images/6fe9cb38c68045f1507bc998312b7afde77d94fcf877b9ea604e2a2b4c380f7f.jpg) +Figure 2. $4\times$ point upsampling results of Chair, Camel and Fandisk. (a) the input point cloud; (b) the ground truth; (c) to (i) the results of PU-Net [21], MPU [20], PU-GAN [7], PU-GCN [13], PU-DR [8], Meta-PU [19] and ours. Please enlarge the PDF for more details. + +sification problem. For this metric, larger is better. 3) mean and std [21]: which evaluate the distance between the predicted point cloud and ground truth mesh. For both metrics, smaller is better. 4) Normalized Uniformity Coefficient (NUC) [21]: which evaluates the uniformity of points on randomly selected disk with different area percentage $p = 0.2\%$ , $0.4\%$ , $0.6\%$ , $0.8\%$ , $1.0\%$ . For this metric, smaller is better. + +In Table 1, we offer the comparison results for four scale + +factors $[2\times ,4\times ,8\times ,16\times ]$ with respect to CD, EMD, F-score, mean and std. Surprisingly, it can be found that, although our model is trained in a self-supervised manner without accessing to the ground-truth, it achieves competitive performance with those supervised learning based ones with respect to metrics CD, EMD, F-score and mean. Taking CD for example, our method is ranked #2, #2, #2 and #3 among seven compared methods for $[2\times ,4\times ,8\times ,16\times ]$ respectively. Similar results can be found for F-score, for + +![](images/3474d10798a5ad8f05ba8d6ad0fc254318df61eb9d45ee364bfc102dbe825808.jpg) +Input + +![](images/355dd2efbbcb8a7488b669ceaa5f1ced53e9b992df9e1ed3b5580d4df16daa3a.jpg) +$4\times$ + +![](images/591cb61b36d00d7ff466a290bfeef374278335ec29afeab47105f7fdd05943e1.jpg) +$16\times$ + +![](images/207d3e9582570db22d0a1d8e6588972ab87db6354cf115f3dcc7051265e3ba5c.jpg) +$64\times$ +Figure 3. $4 \times$ , $16 \times$ and $64 \times$ upsampling results of Moai. + +which our method is ranked #2 for all cases. Note that our method performs worst with respect to std, which is because that outliers cannot be completely removed. + +Table 2 shows the uniformity evaluation results with respect to NUC. Our method is ranked #2 for $[2\times ,8\times ,16\times ]$ just blow PU-DR [8]. In the case of $4\times$ our method is ranked #1. These results demonstrate that the proposed method produces dense and uniform point clouds. + +Inference Time Cost Comparison. This experimental analysis is conducted on a server with two 1080Ti GPU. In our inference process, estimation of direction and length are the most time-consuming steps. According to the experiments, generating 40000 projected points by our method would cost 46s in average. As a comparison, the time costs of generating 40000 points $(16\times)$ are 342.4s by MPU [20] and 0.228s by Meta-PU [19]. It should be noticed that the estimation of each point is independently performed and thus can be done in parallel to speed up significantly. + +# 4.4. Subjective Performance Comparison + +Visual Comparison. Figure 2 illustrates the $4 \times$ upsampling results generated by our method and the compared state-of-the-art methods on three models Chair, Camel and Fandisk. The results show that our method achieves better visual performance than other methods. The produced high-resolution point clouds are dense and uniform, which also have continuous and complete contours. Specifically, results of the highlighted part of Chair show that our method succeeds in recovering structure from very few points; results of the highlighted part of Camel show that our method can handle complex contour. Furthermore, our method can reconstruct the edge region very well, as demonstrated in the highlighted part of Fandisk. The above visual comparisons verify the superiority of our proposed method. + +Results on Variable Scales. Figure 3 shows the upsampling results of Moai with different scale factors. It can be observed that the contours of all the results are consistent, and the uniformity of points is well preserved. + +Robustness against Varying Sizes of Input. Figure 4 shows the $4 \times$ upsampling results of Eight with different + +![](images/9033eac5a75a15334559b2b6a16f7547792f224ca09ef1006bffb1da7ab00223.jpg) +Figure 4. $4 \times$ Upsampling results of $Eight$ with varying size of input. The first row are the inputs, the second row are the corresponding upsampling results. + +![](images/94ef610aab75823bb9b85d93dc395e83434f432d7efaf6bb56045552882eebe6.jpg) +Figure 5. $4 \times$ Upsampling results of Star with different additive Gaussian noise level. + +sizes of input point sets. Our method generates consistent outlines regardless of the number of input points. Figure 5 shows the $4 \times$ upsampling results of star with noise level $0\%$ , $1\%$ and $2\%$ . Our scheme also works well on the noisy input while the uniformity is well preserved. Overall, our method is robust to the input size and noise. + +Result on Real-world Sample. We choose one real-world sample from KITTI [3] to evaluate the generalization capability of our method. In Figure 6, the upsampling results + +![](images/734b9d04e78b2abe8ff8af421aa87379c5cc6728f184ddc668c2c475b40aaaa8.jpg) +Figure 6. $8 \times$ Upsampling result on a real-world sample from KITTI. Please enlarge the PDF for more details. + +![](images/79402efa12ac4343ea523b2fdd08131b8d1cffa35081a74a68a4e7151a0cf04c.jpg) + +![](images/36e125f4ff5f275458aac8b9667212f2bf649d988f696f697c9850b00d6a0e38.jpg) + +![](images/dc410b769287250e8c6a4997e583b39a41f8ec0b8fe96e61eec22c87ebfd0acd.jpg) + +![](images/49afa5a5db91a9ff5bbf8b9fb1959d6ba17611bc9647fcb9e32676fbd75ca953.jpg) +Figure 7. Ablation on the choice of $M$ . (a) input point cloud, (b) $M = 3$ , (c) $M = 10$ . + +![](images/ff021c954ff3f7c7eeeaf63dd9337faf8188d8160abd3f5c6459eee1a2ccd2d0.jpg) +Figure 8. Ablation on the outliers removal. (a) input point cloud, (b) without outliers removal, (c) with outliers removal. + +of three different regions are presented. It can be found that, even though the input point cloud is sparse and nonuniform, our scheme can still recover the high-resolution one very well. + +# 4.5. Ablation Study + +About the choice of $M$ . $M$ works in the distance approximation of a seed point to the underlying surface, which affects the number of outliers and the continuity of projected points. When $M$ increases, both the continuity and the number of outliers increase. To show the effect of different $M$ , we provided the $4 \times$ upsampling result of cow with $M = 3$ and $M = 10$ . The results are shown in Figure 7. It can be observed that, when $M = 3$ , no outlier is introduced to the blue box. However, the surface is discontinuous in the red box. When $M = 10$ , the surface in the red box becomes continuous, however, a few amount of outliers is still introduced to the blue box after outliers removal. + +About the necessity of outliers removal. To show the ef- + +fect of outliers removal, we provide the $4 \times$ upsampling result of cow with and without outliers removal. The results are shown in Figure 8. It can be observed that the outliers removal does not affect the smooth region in the red box, while it can remove most of the outliers in the blue box. + +# 4.6. Limitations + +The limitation of our method are two-fold. Firstly, even outliers removal is performed, there still exist a certain number of outliers. Secondly, our method cannot precisely control the number of upsampled point set. We have to first generate a dense one with over-sampled points and then adjust the number of vertices to the target number by the farthest point sampling algorithm. + +# 5. Conclusion + +In this paper, we present a novel and effective point clouds upsampling method via implicit neural representation, which can achieve self-supervised and arbitrary-scale upsampling simultaneously. We formulate point clouds upsampling as the task of seeking nearest projection points on the implicit surface for seed points, which can be done by two implicit neural functions trained without the ground truth dense point clouds. Extensive experimental results demonstrate that our method can produce high-quality dense point clouds that are uniform and complete, and achieves competitive objective performance and even better visual performance compared with state-of-the-art supervised methods. + +# 6. Acknowledgements + +This work was supported by National Key Research and Development Project under Grant 2019YFE0109600, National Natural Science Foundation of China under Grants 61922027, 6207115 and 61932022. + +# References + +[1] Marc Alexa, Johannes Behr, Daniel Cohen-Or, Shachar Fleishman, David Levin, and Claudio T. Silva. Computing and rendering point set surfaces. 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The image quality of OCTA, however, is often degraded by Bulk Motion Artifacts (BMA), which are due to micromotion of subjects and typically appear as bright stripes surrounded by blurred areas. State-of-the-art methods usually treat BMA removal as a learning-based image inpainting problem, but require numerous training samples with nontrivial annotation. In addition, these methods discard the rich structural and appearance information carried in the BMA stripe region. To address these issues, in this paper we propose a self-supervised content-aware BMA removal model. First, the gradient-based structural information and appearance feature are extracted from the BMA area and injected into the model to capture more connectivity. Second, with easily collected defective masks, the model is trained in a self-supervised manner, in which only the clear areas are used for training while the BMA areas for inference. With the structural information and appearance feature from noisy image as references, our model can remove larger BMA and produce better visualizing result. In addition, only 2D images with defective masks are involved, hence improving the efficiency of our method. Experiments on OCTA of mouse cortex demonstrate that our model can remove most BMA with extremely large sizes and inconsistent intensities while previous methods fail. + +# 1. Introduction + +As a fast and non-invasive optical imaging technology with high spatiotemporal resolution, optical coherence tomography (OCT) is an emerging medical imaging modality not only for laboratory research but also for clinical applications [8]. Optical coherence tomography angiography (OCTA) has been reported to effectively diagnose and + +![](images/2e57120ef34d330df400210df683dc4dfd481c8bdcb3f7663af221943f49e329.jpg) +Figure 1. Illustration of OCTA affected by Bulk Motion Artifacts (BMA). Our work focuses on the BMA removal task in vessel mask (blue rectangle in dashed line). The enhanced OCTA after BMA removal has better visualization quality. + +assess many retinal conditions, such as diabetic retinopathy [21], macular degeneration [23] and choroidal neovascular membrane [19]. Not only in ophthalmology, OCT has also been employed to visualize the prognosis of tumor vasculature for a better understanding of microenvironment [22]. Benefitting from high spatiotemporal resolution and non-invasive features, OCT has been utilized to study neurovascular changes and brain function in vivo. + +A typical OCTA image of mouse cortex is shown in Fig. 1. Previous approach [15] employed image enhancement to remove background noises for better qualitative and quantitative analysis. Specifically, a vessel mask was generated to highlight vasculature while suppressing the background noise. Unfortunately, this approach failed to remove Bulk Motion Artifact (BMA), which was caused by micromotion of the object, as highlighted with double arrows in Fig. 1. + +BMA is one of the most frequent artifacts affecting many + +medical imaging modalities (CT, MRI and OCT), which seriously degrades image quality and affects quantitative analysis. Over decades of research, numerous models have been developed to remove BMA, but effective solutions for all circumstances remain missing. In OCTA, BMA causes a severely blurred image and usually appears as horizontal stripes of different widths with high-intensity in the center and low contrast in the surrounding area. As illustrated in Fig. 1, the horizontal stripes across OCTA are the areas affected by BMA. In the following sections, we use BMA and stripe (artifacts) interchangeably. + +Previous approaches remove BMA with image registration or supervised denoising models, requiring duplicate scans or numerous training data with annotations. The current state-of-the-art model [14] inpaints the BMA-affected areas to generate a clear vasculature mask for enhancement. However, the inpainting model abandons the information in noisy areas so has limited capability to fill large gaps. Besides, lots of images with annotations are needed for training. We observed that, even if the intensity value of BMA is far stronger than normal area, there were still textures within BMA. Furthermore, BMA only affects vertical gradient rather than horizontal ones due to the OCTA imaging process. These features could serve as structural references of vasculature in noisy BMA area. However, there are three main challenges for BMA removal: (1) information within the motion artifacts is too noisy; (2) how to inject structure information from the BMA area into the recovery framework; and (3) OCTA data are limited and the pixel-level annotations are difficult to acquire. + +In this paper, we propose a self-supervised BMA removal method to solve the issues above. First, the gradient-based structural information and appearance feature are extracted from BMA and injected into the model to capture more connectivity. Specifically, we keep the BMA-affected area, even the noisy one, as an input channel instead of discarding it directly. Furthermore, based on the observation that BMA mainly affects vertical gradients rather than horizontal ones, we introduce horizontal gradients to make our model aware of potential structures under BMA. Adding the gradient map makes the training stabler and convergence faster. With structural and appearance information and easily collected defective masks, we train our model in a self-supervised manner that the clear areas are used for training while the BMA areas are only for inference. + +With the rich structural and appearance information carried in the BMA stripe region as reference, our model can remove large BMA and handle the background noise at the same time. Our BMA removal model is end-to-end and only requires 2D image with defective mask, which is more practical. Compared with other context-guided denoising models, our content-aware model can learn guidance directly from noisy images and is thus more robust. Experiments on + +a mouse cortex OCTA dataset demonstrate that our model can remove most BMA under different intensities and extreme area sizes while existing methods fail. The specific contributions of our paper are: + +- We propose a new structural denoising model that can leverage the rich structural and appearance information carried in the BMA stripe region. +- Our model is trained in a self-supervised manner, and training does not involve manual annotation. +- For image enhancement, our method can alleviate BMA and background noises simultaneously, and thus significantly improve image quality. + +# 2. Related Work + +In this section, we will first discuss OCTA and BMA. Then, we will briefly introduce some general denoising methods followed by related OCT denoising methods. + +# 2.1. OCTA and BMA in Awake Animal Study + +OCT is a high-speed 3D imaging technique with micron-level resolution. Previous methods employ gradient-based filters [7, 11, 12] to generate vessel masks to highlight vasculature for better analysis. However, the image reconstruction is sensitive to micromotion caused by heartbeat, respiration, and mechanical vibration. Such motions lead to misalignment and phase noise which cause BMA. Severe BMA usually results in extremely high-intensity noise. Previous gradient-based approaches [7, 12] can not handle such artifacts because BMA has similar gradient information with vessel branches. Moreover, long-lasting BMA could result in a broad and blurred area, making it hard to correct. Last but not least, BMA is often accompanied by background noise, which makes it even harder to find vessels within the affected area. The interleaved background noise and BMA could lead to poor visualization and erroneous quantification. + +# 2.2. General Denoising Method + +BM3D [4] is a classic denoising model based on sparse representation. Inspired by the observation that natural images consist of repeated textures, BM3D groups related image patches and filters them together to shrink noise. It handles Gaussian noise well but fails to remove structural noise. After convolutional neural network (CNN) is firstly applied for the denoising task in [9], lots of works have been proposed to keep updating the state-of-the-art performance [3, 25, 29, 30]. Recently, Wu et al. [26] propose a single image dehazing method based on contrastive learning and achieves state-of-the-art performance on both synthetic and real-world datasets. Still, this method is trained + +![](images/d33d47245ce36eeb8eef21c019fd117bf669b54b16f60fd478eb10cb127d7b46.jpg) +Figure 2. Framework of the proposed Content-Aware BMA Removal model (CABR). + +in a supervised manner. It is not the case for some medical image modalities without ground truth. + +More and more unsupervised learning based denoising methods [6, 10, 13] have been proposed and achieved promising performance. However, these approaches are not intended to remove structural noise. Broaddus et al. [1] employ structural kernels to remove spatially correlated noise in fluorescence microscope images. However, the performance of this method depends on the selection of blind mask, which is not fully automatic and needs prior knowledge for noise distribution. + +# 2.3. OCT Denoising Method + +Most traditional OCTA denoising methods [2, 24] are based on duplicate sampling, in which BMA-affected area is replaced by BMA-free area at the same location but different sampling period. The downside of such approaches is the considerably long sampling time, which reduces the practicability for researches and clinical diagnoses. Devalla et al. [5] propose a deep learning based OCT denoising model for retinal images. It is relatively easier to denoise OCT images of the retina than other tissues, such as mouse bladder and cortex, because of shallower imaging depth, less background noise, and BMA. Li et al. [16] remove BMA in an enhancement approach. Firstly, this method applies optimally oriented flux (OOF) [11, 12, 15] to generate vessel mask with defects in BMA areas and then employs tensor voting [18] to restore the defective mask. Finally, an OCTA image is enhanced with the corrected mask for BMA removal. However, this method may fail to remove moderate and severe BMA. + +The current state-of-the-art model [14] removes BMA with the combination of a BMA detection module, a vessel segmentation module and a mask inpainting module [28]. The BMA detection module predicts BMA affected rows in OCTA. The segmentation module takes OCTA with BMA + +![](images/9293a8b6ce5566d7d53f5f5422a548a7595337515f3334467f7a5ab578ab88e9.jpg) +Figure 3. Deconvolution layer with GatedConv. + +areas removed as input and produces a corrupted mask. After that, the mask inpainting module takes the probability map of the segmentation module as input and fills the missing mask. Manually annotated masks are used to train the segmentation module and inpainting module. The whole pipeline [14] is relatively ad-hoc and the performance depends on every step. Furthermore, numerous 2D and 3D training data are involved in training. Last but not least, this model learns only from surrounding BMA-free areas while ignoring the structural information within noisy data. So this context-based model often fails when dealing with severe BMA. + +# 3. Method + +In this section, we will start with problem formulation and challenges. Then, to deal with the context learning issue, we will discussing two sets of information injection and the proposed Content-Aware BMA Removal Model (CABR). Finally, we will illustrate a self-supervised training strategy to solve data insufficiency. + +# 3.1. Problem Formulation + +We first define the BMA-affected OCTA image as $\pmb{I} \in \mathbb{R}^{H \times W}$ , the defective vasculature mask $M \in \{0,1\}^{H \times W}$ + +the Gradient Statistics $\pmb{G} \in \mathbb{R}^{H \times W}$ (See Sec. 3.2), and the corresponding row label $l \in \{0,1\}^H$ , where $W$ and $H$ are image width and height, respectively. $l_i = 0$ means the $i$ -th row of $\pmb{I}$ is clear while $l_i = 1$ for BMA. For each $\pmb{I}$ , the corresponding mask $M$ is automatically generated with OOF [11, 12]. The BMA affected region can be discerned easily and the row label $l$ indicates which rows in image are affected by BMA. The proposed BMA removal framework takes $(\pmb{I}, \pmb{M}, \pmb{G}, l)$ as input and outputs the vasculature prediction $M'$ with BMA removed: + +$$ +M ^ {\prime} = f (M, I, G, l). \tag {1} +$$ + +The main issue of previous context-guided inpainting models is that little information from noisy area is automatically learned. Therefore these surrounding-based generative models produce plausible but unconvincing results, especially for large missing areas. But the certainty is just what medical image researchers demand. So the information within noisy area should be utilized to improve the prediction confidence. + +Data insufficiency is another issue to apply supervised methods in medical images sometimes. It is difficult or even impossible to get noise-free or ground truth for some imaging modalities. Supervised methods may not work well under this condition. So we should leverage any available information to solve the data insufficiency. These two issues will be solved in the following parts. + +# 3.2. Content-Aware BMA Removal + +The uncertainty of context-guided inpainting models is the main drawback for the tasks demanding accurate results rather than plausible ones. We have observed that, even with heavy noise, some structure and texture information exist in BMA affected areas. To leverage such vessel clues, we introduce two information injection approaches, e.g. Gradient Statistics (GS) and Appearance Feature (AF). The proposed CABR can automatically learn reliable references from the injected information for BMA removal. The framework of CABR is illustrated in Fig. 2. + +Gradient Statistics (GS). BMA usually causes high-intensity horizontal stripes in OCTA images. We observed that the horizontal gradients are hardly affected by BMA so we introduce the horizontal gradients as the structural information for CABR. Specifically, we apply the vertical Sobel operator in BMA areas to extract GS. The absolute value of response is injected into the model to capture more reference for BMA removal. Sobel operator is linear and efficient so only marginal computational cost is involved. + +Appearance Feature (AF). GS provides a good reference for branch vessels but may not discern capillaries at relatively low intensities. Inspired by the deep denoising models, we define the BMA-affected areas as AF and keep AF, even noisy ones, as the additional input. With sufficient + +training samples, the BMA removal model can automatically learn the texture information to capture better vessel connectivities. The generation of training samples is discussed in Sec. 3.3. + +Model Design. To overcome the limitations of context-guided inpainting model, we propose the content-based CABR for BMA removal in OCTA. The framework is illustrated in Fig. 2. With the two sets of information injection, our model can learn from both the content within BMA and the context outside BMA. It is thus more comprehensive and robust. + +The imbalance of BMA sizes is another challenge for BMA removal. Most BMAs are thin stripes and are easy to remove while severe BMAs, on the contrary, are only small part of dataset but harder to remove. For previous context-guided inpainting models, the imbalanced distribution leads to performance gap between gentle and severe BMAs. These models often fail to fill in extra wide stripes due to lacking both references and hard training samples. + +Different from previously free-form inpainting frameworks [17,20,28], our CABR focuses on correcting the vasculature in the centerline areas of input image. Reflection padding is used for the stripe located near boundary. This schema reduces the learning cost and model complexity. Furthermore, we can select more hard cases to train CABR so that it works better when dealing with these broadly missing areas. + +Model Architecture. CABR has an encoder-decoder CNN backbone, which stacks gated convolution layers (GatedConv) [28] to handle the stripe with various width in a noisy OCTA. As illustrated in Fig. 2, the backbone consists of 10 GatedConv layers [28], 1 GatedConv layer with dilation [27], 2 DeConv layers and 1 regular Conv layer with sigmoid activation function for prediction. GatedConv is a kind of attention convolution that learns a dynamic feature gate for each channel and each spatial location. We choose GatedConv due to its SOTA performance in inpainting. In addition, it saves around $50\%$ trainable parameters than regular convolution with the same channel number. Considering the relatively small dataset, such light-weight module is preferred to reduce overfitting. Deconvolution used in CABR is an upsampling layer followed by a GatedConv, as illustrated in Fig. 3. + +# 3.3. Self-supervised Training + +As we mentioned before, data insufficiency is one of the main challenges in OCTA. Here, we train our model in a self-supervised way to resolve problem. We make use of the majority BMA-free areas to acquire acceptable training masks at low cost and generate as many as noisy images for training. With these easily collected masks and synthetic noisy images, we can train the BMA removal model in a self-supervised manner. + +![](images/1c6b59b600b49303c0f37177802550b93bf1684e6fcd9303d24ae7882c9e6ff2.jpg) +(a) The schema of intensity mapping used in AdBMA. + +![](images/ccd9fa5457e00def5efddb6dac0d58a88db14a27a58a18b80c8bd3c4ed8ca758.jpg) +(b) OCTA images. + +![](images/61a7796f213f033de8a1af84bfd1715b609bb52cb7f9246ed7feefdbef444393.jpg) +(c) Intensity values of the row marked by double arrows in (b). +Figure 4. In (b) (c), from left to right: clear images, synthetic images and images affected by BMA. + +Ground Truth Mask. The ground truth of vasculature mask for in vivo OCTA is either impossible or very difficult to acquire. Since OOF [12] can produce relatively accurate vessel mask for the most area $(96.4\%)$ without BMA, we resort to this defective mask with minimally additional manual annotation as the ground truth. To be specific, we only manually annotate the remaining $3.6\%$ BMA areas and combine defective mask in BMA-free areas to get the vasculature mask. This approach can produce high-recall masks at low-cost. The manually annotated part is only involved in testing and is not used in training. All these masks are verified by experts. + +BMA Synthesis. We propose the Adaptive BMA Synthesis (AdBMA) approach to generate noisy images from BMA-free areas. After inspecting the data distributions, we find that BMA has different effects on high and low intensity pixels. In other words, BMA mainly uplifts the low-intensity pixels while keeping the maximums unchanged. So we employ a remapping schema to mimic the BMA influence on clear images. Given a clear image $\pmb{I}$ and two sets of hyperparameters $(\mathcal{P}_{\mathrm{low}}, \mathcal{P}_{\mathrm{high}})$ and $(\mathcal{P}_{\mathrm{base}}, \mathcal{P}_{\mathrm{low}}, \mathcal{P}_{\mathrm{high}})$ , we synthesize BMA in four steps: (1) randomly map the intensities below $\mathcal{P}_{\mathrm{low}}$ into $[\mathcal{P}_{\mathrm{base}}, \mathcal{P}_{\mathrm{low}}]$ (half-open interval); (2) map the intensities between $\mathcal{P}_{\mathrm{low}}$ and $\mathcal{P}_{\mathrm{high}}$ into $[\mathcal{P}_{\mathrm{low}}, \mathcal{P}_{\mathrm{high}}]$ ; (3) map the intensities above $\mathcal{P}_{\mathrm{high}}$ into $[\mathcal{P}_{\mathrm{high}}, \max(\mathbf{I}))$ ; and (4) clip intensities within image maximum (usually 255) to avoid overflow. Gaussian noise is added in steps (2) and (3) to ensure uncertainty. The remapping schema is illustrated in Fig. 4a. + +The synthesized noisy images have similar distribution with the real BMA, but more importantly they have corresponding ground truth masks. The benefits of synthesizing BMA are twofold: (1) we can generate as many plausible noisy images as needed; and (2) it fits our framework and + +enables learning from noisy data. + +Fig. 4b shows a BMA-free OCTA image, an image with synthetic BMA and an image with real BMA. Moreover, Fig. 4c is the bar plot of intensity values for the row marked by double arrows in Fig. 4b. We can see that the synthetic OCTA image has not only plausible appearance but also similar intensity distribution. Thus the distribution gap between training and testing data is minimized. + +Training Scheme. The train/val splitting is area-based, which is different from the typical supervised approach. Specifically, every image is split into the BMA-free (clear) area for training and the BMA-affected (noisy) area for evaluation. During training, only the loss from the clear area with synthetic BMA is used. During testing, only the Dice score in the BMA-affected area is measured. Thus the model works in a self-supervised way and can utilize as many training samples as possible. + +# 4. Experiments + +We evaluate the proposed BMA removal framework on a mouse cortex OCTA dataset. The results are compared with the state-of-the-art motion correction model [14] and a GatedConv-based inpainting model [28]. We re-implement the GatedConv-based model for inpainting the stripe region. + +# 4.1. Dataset + +We collect 39 OCTA images of mouse cortex with vessel masks. The noise level, defined as (BMA-affected area/Total area), varies throughout the dataset. Note that, not all images have BMA noise. We validate on the BMA-affected areas from 14 OCTAs. According to the noise level, OCTAs in the validation set are further classified as the easy set (noise $< 2\%$ , 4 OCTAs), medium set $(2 \leq \text{noise} < 4\%)$ , 7 OCTAs) and hard set (noise $\geq 4\%$ , 3 OCTAs). We further collect 6 samples to extend the validation set. The BMA removal performance is measured by the Sørensen-Dice coefficient (Dice) in the rest of the paper, unless otherwise specified. + +Training Details. The hyperparameters for BMA synthesis are $(\mathcal{P}_{\mathrm{low}} = \mathcal{P}_{10\%}, \mathcal{P}_{\mathrm{high}} = \mathcal{P}_{85\%})$ and $(\mathcal{P}_{\mathrm{base}} = \mathcal{P}_{30\%}, \mathcal{P}_{\mathrm{low}'} = \mathcal{P}_{50\%}, \mathcal{P}_{\mathrm{high}'} = \mathcal{P}_{90\%})$ where $\mathcal{P}_{k\%}$ is the $k$ -th percentile of input image $\pmb{I}$ . As for the re-implemented GatedConv-based inpainting model, we randomly select $2 \sim 20\%$ rows within each patch for training. As for CABR, we select center rows in each patch with width randomly from 1 to 11 for training. Furthermore, we use data augmentation, such as random cropping, horizontal and vertical flipping, on the training set. + +Implementation. The CNN backbone used for all experiments is illustrated in Fig. 2. All convolutional layers use $3 \times 3$ kernels. The downsampling rate, stride rate and dilation rate are set to 2. The backbone has 16 feature maps in + +Table 1. Performance on the mouse cortex OCTA dataset. GatedConv* is re-implemented and trained on the OCTA dataset. "All*" is the extended validation set with "All" and 6 extra samples. + +
MethodEasyMediumHardAllAll*
OOF [12]45.7642.7043.7243.7942.93
Li et al. [14]68.8368.5160.7066.9370.21
GatedConv* [28]77.4173.4874.3774.8077.03
CABR(SynBMA)84.9981.9879.2282.2483.92
CABR(SynBMA,GE)85.7182.6779.6982.9084.54
+ +![](images/420325b810bffb4a49cb47defafce379e2574a708a86548b731f5148df51ea5d.jpg) +Figure 5. Denoising result for synthesized BMA of width $\{1,4,8\}$ . + +the first level, which increases up to 64 when the level gets deeper. All models are trained with Dice loss and Adam optimizer for 1,200 epochs. The learning rate starts from $10^{-4}$ and halves if no improvement is observed for 20 epochs. We used $256 \times 496$ input size and batch size 12 for GatedConv training. We used $64 \times 496$ input size and batch size 48 for CABR training. All models are trained on a single NVIDIA GeForce GTX Titan Xp GPU. + +# 4.2. BMA Removal Results + +To evaluate the performance of the proposed CABR framework, we compare it with the state-of-the-art OCTA motion correction model by Li et al. [14]. The result of OOF [12] is the baseline. To the best of our knowledge, there are no other publications that pertain directly to BMA removal in OCTA. So we also re-implement a GatedConv-based inpainting model [28], for inpainting the BMA-affected region. The re-implemented inpainting model has a similar amount of parameters as CABR and is trained with the same setting. + +Quantitative Result. The Dice scores on the mouse cortex OCTA dataset of different methods are in Tab. 1. The result shows a clear improvement of our method over the OOF baseline. Besides, our approach significantly outperforms the state-of-the-art model [14] by $15.97\%$ and $14.33\%$ in the validation set and the extended validation set, respectively. The proposed CABR also achieves the best performance in all subsets, which evidences the effectiveness and advantage of content-based learning. Even in the hard subset with larger and more dense BMA across OCTA, our CABR surpasses the re-implemented GatedConv by $5.32\%$ , suggest- + +ing that CABR can learn more connectivities from noise input for BMA removal. The experiment results also show that adding GS further improves the performance of CABR. + +Qualitative Result. The BMA removal results for the synthesized BMA of width 1, 4 and 8 are illustrated in Fig. 5. It shows that our method can handle severe BMA and recover vasculature while the baseline [12] fails. + +The experiment results for two validation samples are illustrated in the first and third rows of Fig. 6. We compare our method with OOF [12] (only for reference, no BMA removal effect), Li et al.'s method [14], our re-implemented GatedConv-based inpainting model [28]. We can see from the first and third rows of Fig. 6 that our method removes most of the false positive masks caused by BMA while achieving the best vasculature connectivity at the same time. Li et al.'s method [14] can also remove some BMA but the low recall is the main drawback. Specifically, thin BMA stripes can be restored while thicker ones can not. On the contrary, the re-implemented GatedConv shows better connectivity than Li et al.'s method [14] but some BMAs are remaining. The cyan and pink arrows highlight more details in the zoom-in panels of Fig. 6. + +The second OCTA is harder to handle because the stripes are relatively broader and more densely distributed. From the third and fourth rows of Fig. 6, we can see that Li et al.'s method [14] can not fill the gap in the second zoom-in area and the GatedConv-based inpainting model has more artifacts. Our method produces a complete mask with better connectivity and fewer artifacts. + +We also compare with the self-supervised StructN2V [1] and the results in Fig. 7 suggest that StructN2V is not suitable for our task: incorrect structure removal (cyan/red arrow), suffering from wide BMA (pink arrow), etc. + +OCTA Enhancement. OCTA enhancement based on vesselness mask is a regular procedure for biomedical analysis. Usually, this procedure highlights vasculature while suppressing background noise, and thus improves contrast. The enhanced OCTA is generated by multiplying the raw OCTA with corresponding vessel mask. The second and fourth rows of Fig. 6 illustrate the enhancement results of different approaches on two sets of BMA-affected OCTAs. Our method removes most of the BMA artifacts and produces an OCTA with stronger contrast, as illustrated in the zoom-in panels as the dashed rectangle areas. From the second OCTA, where BMA in the bottom area degrades image quality severely, we can see that our method still removes most of the BMAs while preserving vessel structures, thus showcasing the effectiveness of our proposed method. + +# 4.3. Ablation Study + +To study the effects of each module, we conduct the ablation experiments on the mouse cortex OCTA dataset. All experiments are based on the same training setting in + +![](images/c1b768a03f497332d9eb36cb9805fe846d7c6e47451faea766f83d28e9f2a599.jpg) + +![](images/5b68625b405ac9bd7934cddcfebca497d99ba6dce2156dd926a68ea87b0c9fec.jpg) + +![](images/843d705d49d81273268e8a2e2338e6e18a4cdbd5c554646700848e304315c8c1.jpg) + +![](images/ed81a4b667bb891c4ed1a6d594fecec7e1e0da806ee0c105848e9422af7dea78.jpg) + +![](images/f092d94652d5811de4a8ee1423e2a6a9e1a1215a02a3832a457354d30a5ce962.jpg) + +![](images/96afd51dc9de5221cdbc40db0cc35a5be5858c588fae17d4a3e899a2ae788ce8.jpg) + +![](images/0ff544219e86450e7a21b7678c3ea82730c6e42880be8ed47fb494a972e316e7.jpg) + +![](images/111962493f3333c8f891255ca8c47b7f791a9244e167af6c0ba276e878c9c980.jpg) + +![](images/dbdb62748d1de84cef68054153c2bf247e9104baacb1531ba4950248a8a42025.jpg) + +![](images/258abbc1e4cb9b57412a4a4bd136f9770a17f81666d4a316d22274b9bfc690a4.jpg) + +![](images/d7015e0e121852b239583050caa48d2016cf44993a8c821bb3dd64b5ce0bfe09.jpg) + +![](images/a61a22337abb516753812d8eff9e9eb2b6b25f161c3bccac546be91c62cc30c9.jpg) + +![](images/ab7056125fa9713bac42045c3957123ec0268bfe7cde2dbb09ff7b327d3e6b57.jpg) +0OF + +![](images/4836d0341dbd3e9a01e5b923377b9f968f67ae479b2e8acaf82a73b7b9f3039a.jpg) +Li el. al. + +![](images/0d1acd132c5f82b92c24515d2e1bb61a942742d7d565fdbfd7b18c57ad44298b.jpg) +GatedConv (re-implemented) + +![](images/b5488ddc3946e8976746fb6624bad315ea110cc361c68fb7115d1070a4a74870.jpg) +Ours +Figure 6. Two sets of OCTA masks and enhanced images of different methods. The first and third rows are the masks of OOF [12], Li's method [14], our re-implemented GatedConv-based inpainting model [28] and the proposed CABR, respectively. The corresponding enhanced images are in the second and fourth rows. The zoom-in results within the rectangles in dashed line are also illustrated for better comparison. The cyan and pink arrows highlight more details in the zoom-in panels. + +![](images/a79a5c19c5a8fac4d1027473ce75010b9b54bff9d18dad0b8acc724f1b704d17.jpg) +Figure 7. The denoising result of StructN2V [1] and our method. + +Table 2. Ablation study of CABR on the mouse cortex OCTA dataset. "Abs" means the absolute value. "Abs-BMA" means absolute GS only in BMA. "Conv" means the regular convolution. + +
Appearance +Gauss AdBMAGradient Statistics +Naive Abs Abs-BMAModule +Conv GatedDice↑(%)
✓✓81.29
✓✓82.24
✓✓✓80.08
✓✓✓82.38
✓✓✓82.57
✓✓✓82.90
+ +Sec. 4.1. For AF injection, we compare the proposed AdBMA with a naive implementation that adds Gaussian noise. Both methods generate high-intensity stripes like BMA artifacts. However, the Gaussian method does not have a blurring effect so the result is less plausible. For GS injection, the naive stands for the gradient of Sobel operator. Abs and Abs-BMA stand for the absolute value of Sobel results on the whole image and only the BMA area, respectively. To report the contribution of GatedConv module, we also conduct an ablative study and find that GatedConv does outperform regular convolution by $0.33\%$ with only about $50\%$ trainable parameters. + +Ablation of Information Injection. As shown in Tab. 2, we first investigate the effectiveness of AF injection with synthetic BMA. "Gauss" means adding Gaussian noise directly to generate training samples. Our proposed AdBMA outperforms the Gaussian-based synthetic approach by $1.66\%$ , which verifies that (1) texture information within BMA, even noisy, still benefits the recovery of vasculature; and (2) the blurring effect from AdBMA improves the performance. We also evaluate the effectiveness of GS as shown in Tab. 2. The performance of CABR is improved by $2.30\%$ for Abs and $2.82\%$ for Abs-BMA, respectively, which states the validity of GS in BMA removal. During experiments, we find that GS leads to faster convergence. CABR benefits less from GS than the synthetic BMA feature. One possible reason is that convolution layers may have learned similar or even more powerful kernels than the Sobel operator. + +Table 3. Ablation study of CABR for different model sizes on the mouse cortex OCTA dataset. # Channels is the channel number for the first layer of CNN backbone. # Parameters is the number of trainable parameters for the whole model. + +
# Channels# ParametersDice↑(%)
833.7K78.70
16133.9K82.90
32534.0K82.44
+ +Ablation of Model Size. With the same modules in the CNN backbone, we investigate how the model size influences the performance of BMA removal. Tab. 3 lists the result of CABR with different sizes. A larger channel number means more parameters and a larger model size. The 8-channel model only achieves $78.70\%$ Dice coefficient, which is less than 16-channel and 32-channel models. The results demonstrate that 8-channel is insufficient to capture all vessel information. Also, a larger model size, i.e., 32-channel in the first layer, does not boost the performance. The 16-channel model outperforms the 32-channel by $0.46\%$ with about $75\%$ less trainable parameters, suggesting that the OCTA dataset may not support training the model with over 140K parameters. + +# 5. Conclusion + +In this paper, we propose a self-supervised content-aware model to remove BMA and improve image quality in OCTA. First, the GS-based structural information and AF are extracted from the BMA area and injected into the model to capture more vasculature connectivity. Second, we train the model in a self-supervised manner with easily collected defective masks. With the rich structural and appearance information carried in the BMA stripe region as references, our model can remove BMAs and produce a better vasculature mask. Compared with other context-guided inpainting models, our content-aware model can learn guidance directly from noisy images and thus is more robust. Experiments on a mouse cortex OCTA dataset demonstrate that our model can remove most BMAs, even the huge and inconsistent ones, while existing methods fail. The current BMA synthesis approach is manually designed and still has room for improvement. Incorporating domain knowledge of BMA formulation or introducing a generative model for synthesis are potential research directions. + +Acknowledgment. This work was supported in part by NSF Grants 1814745 and 2006665, and NIH grants R01DA029718 and RF1DA048808. + +# References + +[1] Coleman Broaddus, Alexander Krull, Martin Weigert, Uwe Schmidt, and Gene Myers. Removing structured noise with self-supervised blind-spot networks. In ISBI, 2020. 3, 6, 8 +[2] Acner Camino, Miao Zhang, Simon S Gao, Thomas S Hwang, Utkarsh Sharma, David J Wilson, David Huang, and Yali Jia. Evaluation of artifact reduction in optical coherence tomography angiography with real-time tracking and motion correction technology. Biomed. Opt. Express, 7(10):3905-3915, 2016. 3 +[3] Yunjin Chen and Thomas Pock. Trainable nonlinear reaction diffusion: A flexible framework for fast and effective image restoration. TPAMI, 39(6):1256-1272, 2016. 2 +[4] Kostadin Dabov, Alessandro Foi, Vladimir Katkovnik, and Karen Egiazarian. Image denoising by sparse 3-d transform-domain collaborative filtering. 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Exemplary samples synthesized by our self-supervised person image generation framework. Our method could generate the same person images with the target poses (left image set), or generate person images with specific attributes referring to different person images (right image set). Better viewed by zooming in the electronic version. + +![](images/bbc6deffc8e2e94c2c9b31a85dd44fd338e7cc726aaef1d8880c3d73ea018f55.jpg) + +# Abstract + +Person image generation aims to perform non-rigid deformation on source images, which generally requires unaligned data pairs for training. Recently, self-supervised methods express great prospects in this task by merging the disentangled representations for self-reconstruction. However, such methods fail to exploit the spatial correlation between the disentangled features. In this paper, we propose a Self-supervised Correlation Mining Network (SCM-Net) to rearrange the source images in the feature space, in which two collaborative modules are integrated, Decomposed Style Encoder (DSE) and Correlation Mining Module (CMM). Specifically, the DSE first creates unaligned pairs at the feature level. Then, the CMM establishes the spatial correlation field for feature rearrangement. Eventually, a translation module transforms the rearranged features to realistic results. Meanwhile, for improving the fidelity of cross-scale pose transformation, we propose a graph based Body Structure Retaining Loss (BSR Loss) to preserve reasonable body structures on half body to full body generation. Extensive experiments conducted on DeepFashion dataset demonstrate the superiority of our method com + +pared with other supervised and unsupervised approaches. Furthermore, satisfactory results on face generation show the versatility of our method in other deformation tasks. + +# 1. Introduction + +Pose guided person image generation is an unaligned image to image translation problem, which aims to change the posture of a person image given target poses as condition [18,20,21,31,36,41]. Person image generation has shown great potential in many fields, such as film industry and multimedia creation. However, the difficulty of performing non-rigid deformation makes this task an active topic in the community of computer vision. + +Due to the large spatial misalignment between the source and target images, existing approaches generally need unaligned data pairs to supervise the training process [18, 21, 31, 36, 41]. For instance, [31, 41] calculate the attention map between paired poses to guide the anomalous pose deformation. [3,7,25] establish the coordinate offset flow to promote the position-level source feature sampling for person feature alignment. With such attention or flow mechanism, the generative methods could be capable to perform spatial transformations when the source images and target poses are + +provided. However, collecting paired data requires heavy workload and limits the application scenarios of these supervised approaches. Therefore, some unsupervised methods are proposed to deal with this limitation [22, 30], which utilize cycle consistent methods or create pseudo labels to promote the training procedure. However, such methods still have limitations in generation quality intuitively. + +Recently, self-supervised methods demonstrate powerful prospects to perform non-rigid spatial transformations with only source images [4, 19, 20]. They could learn disentangled representations of different image types, which are merged in the following for self-reconstruction. Early studies [4, 19] employ multi-branch network to disentangle different features and concatenate them to reconstruct the source images. Ma et al. [20] utilize AdaIN [11] for feature merging by transferring statistics from style features to pose features. However, these methods still encounter three challenges. First, the disentangled features are aligned in the feature space, which cannot provide enough supervision for spatial transformation in self-supervised methods. Second, these merging methods (e.g. concatenation or statistics transfer) are global operations, which are limited to exploiting the spatial correlation information. Third, the model lacks prior knowledge of invisible regions due to the self-supervised training process within the single pose scale, which limits the reasonable completions for invisible regions in the half body to full body transformation. + +In this paper, we propose a Self-supervised Correlation Mining Network (SCM-Net) for person image generation. The entire architecture of SCM-Net can be summarized as disentanglement, fusion and translation. In the disentanglement phase, inspired by the decomposed strategy in [21], we design a Decomposed Style Encoder (DSE) to extract the semantic-aware decoupled style features, which could form "unaligned pairs" with its counterpart pose features. Through this design, the source image itself could provide supervision for spatial feature deformation. In the fusion phase, we propose a Correlation Mining Module (CMM) to further exploit the spatial correlation between disentangled feature pairs. The CMM module computes the pairwise correlation between the corresponding positions of feature pairs to establish the dense spatial correlation field. Based on this correlation field, our model could align these disentangled features through spatially rearranging the style feature positions. In the translation phase, a translation generator with skip connections is introduced to transform the rearranged style features into realistic person images. The entire model is trained in an end-to-end manner. + +For the lack of prior information on the lower body, we design a Body Structure Retaining Loss (BSR Loss) to capture the semantic relationships among different body parts. Thus, the model could make reasonable completions based on these relationships. Specifically, we employ the graph + +representation to model the semantic relationships of human body parts. In this body graph, each node represents the perceptual features of each semantic region and each edge measures the similarity between each node pair. We match the graphs between each input person image and the corresponding generated result to establish the graph based constraint, which incorporates the body semantic relationships into our model. + +During inference, our model could introduce new target poses for human pose transfer, and perform reference based attribute editing through partial replacement of style features. Figure 1 shows some applications of our model. + +The main contributions can be summarized as follows: + +- We propose a Self-supervised Correlation Mining Network (SCM-Net) to achieve person image deformation without the supervision of unaligned data pairs. +- We design two main collaborative modules, the Decomposed Style Encoder (DSE) and the Correlation Mining Module (CMM), which could perform feature disentangling and merging for person image deformation. +- We propose a Body Structure Retaining Loss (BSR Loss) to acquire the prior knowledge of invisible regions through incorporating semantic relationships among body parts. +- Our method performs competitive results compared with the state-of-the-art methods and also obtains satisfactory results on face generation tasks, which demonstrates the migration capability of our model. + +# 2. Related Work + +# 2.1. Person Image Generation + +With the dramatic development of Generative Adversarial Networks(GANs) [6], person image generation have made great progress in recent years [4, 18-22, 25, 30, 31, 36, 37, 41]. Ma et al. [18] first introduced the pose-guide person image generation task and proposed a two stage generator to generate target person image. Zhu et al. [31, 41] proposed an attention mechanism to transfer the image information from source pose to target pose. Ren et al. [25] predicted the flow field between source person images and target poses for generating new pose images. Men et al. [21] used decomposed component encoding strategy to achieve pose transfer and person attribute editing. However, all the above methods need paired data to supervise the training process, which would take heavy workload for data collection. Several unsupervised methods have been proposed for person image generation. Pumarola et al. [22] designed a bidirectional generator and employed cycle-consistent method to supervise the training. Song et al. [30] designed a novel schema to generate pseudo semantic maps for the unsupervised generation. However, these methods still need extra target poses as input and have some artifacts in generated + +![](images/3c4da3e3ef244b093d5931571c71f938817ac54bea68f9440f3a6debf231c2be.jpg) +Figure 2. An overall workflow of our self-supervised person image generation framework. Given an input person image $I$ , we first utilize the pre-trained methods to obtain its parsing map $S$ and pose skeleton $P$ . Then, the Decomposed Style Encoder disentangles the semantic-aware decoupled style features $F_{s}$ from its pose features $F_{p}$ . Next, the Correlation Mining Module establishes the correlation field $\mathcal{C}$ to guide the feature merging. Finally, the merged features $F_{s}^{*}$ are fed into the translation generator to get the reconstruction $\hat{I}$ of the source image. The Body Structure Retaining Loss and other losses are designed to promote the training process. + +images. Recently, [4, 19, 20] proposed self-driven methods to settle these problems. However, these methods have limitations when dealing with large pose deformation problems. Inspired by the above, in this paper, we propose a novel self-supervised framework with graph representation learning for person image generation. + +# 2.2. Spatial Correlation Learning + +The purpose of spatial correlation learning is to establish dense spatial correlation fields for image translation. Liao et al. [16] proposed a coarse-to-fine strategy to compute the spatial correlation field for image analogy and style transfer. He et al. [8] measured the spatial similarity between the reference and the target to perform exemplar-based colorization. Lee et al. [14] designed a spatially correlation related module to introduce information from reference image to sketch image for sketch colorization. Zhang et al. [36] proposed a spatial-aware normalization module to preserve the spatial context relationship for human pose transfer. Zhang et al. [37] established the spatial correlation field in a shared domain to perform cross-domain image to image translation. However, the above methods can only handle the spatial correlation between unaligned data pairs. In this paper, we establish the correlation field between the disentangled features of source images, which explores more scenarios for spatial correlation learning. + +# 2.3. Graph Representation Learning + +Graph representation learning plays a significant role in the computer vision [1, 34, 39]. Due to the powerful capabilities of relationship modeling, the graph representation learning has been applied to many tasks, such as skeleton-based action recognition [34], biometrics recognition [24] and person re-identification [28, 33, 35]. Yan et al. [35] built a person-feature based graph to model the relations among images for person search. Ren et al. [24] proposed a dynamic graph for occlusion biometrics recognition. Wu et al. [33] proposed an adaptive graph representation learning scheme to promote the interactions between relevant regional features for video person Re-ID. Hou et al. [10] proposed a graph matching strategy to distill structural knowledge for road marking segmentation. Qi et al. [23] proposed an adaptive re-weighting graph to balance the contributions of different semantic nodes in face sketch synthesis. However, the above methods employ graph representation learning to enhance the ability for feature extraction or feature matching, ignoring of the characteristics of graphs for cross-scale image complication. In this paper, we apply graph representation to model the semantic relationships for person image generation, aiming to generate more reasonable body structures. + +![](images/8c9944b23f8ddceb6b14f6d2dd5ef6f7a4d0e86b13e30586420879642d4a2d09.jpg) +Figure 3. Feature map visualizations of global encoder and the DSE module. The structural information represented by the DSE module is significantly reduced compared with the global encoder. + +# 3. Method + +In this section, we present our proposed method in detail. To begin with, we introduce the overall workflow of our Self-supervised Correlation Mining Network (SCM-Net). Then we describe the whole network architecture in detail according to the three phases of disentangling, merging and translation. Finally, the total objective functions of our model are introduced. + +# 3.1. Overall Workflow + +Without requiring unaligned data pairs, our method receives a single source image as input. As shown in Figure 2, given a source person image $I$ , we leverage the pre-trained human pose estimation model [2] and human parser [5] to obtain its pose skeleton $P$ and semantic mask $S$ . For feature disentangling, we employ the pose encoder and the DSE module to extract the pose features $F_{p} \in \mathbb{R}^{C \times H \times W}$ and the semantic-aware decoupled style features $F_{s} \in \mathbb{R}^{C \times H \times W}$ , respectively. For feature merging, the CMM module is proposed to establish the dense spatial correlation field $\mathcal{C}$ . Based on this correlation field, the $F_{s}$ could perform spatial rearrangement to obtain the merged features $F_{s}^{*}$ . Eventually, the translation generator $G$ transforms the $F_{s}^{*}$ from the feature domain to realistic images. + +# 3.2. Disentangled Feature Encoding + +For feature disentangling, there are two branches (e.g., pose branch, style branch) in our framework to encode pose features and style features, respectively. + +Pose Encoding. In the pose encoding branch, we employ the down-sampling convolutional neural networks (CNNs) to extract pose feature maps $F_{p}$ from the pose skeleton $P$ . Since the $F_{p}$ is globally encoded, its structure is aligned with source image $I$ inherently. + +Decomposed Style Encoding. For style encoding, we design the DSE module to obtain the semantic-aware decoupled style features $F_{s}$ , which could form "unaligned data pairs" with their counterpart pose features. Compared with the global encoder which encodes the person image entirely, the DSE module could embed the person image $I$ from a + +![](images/a1db23b7aed9b3f4b0612f0d1d34a8858d5270c311d4838d159cfad603810402.jpg) +Figure 4. Details of the Correlation Mining Module in our model. Each position of outputs is the weighted average summation of the input. The weights are stored in the correlation field. + +complex manifold to the feature space according to different regions. + +As illustrated in Figure 2, we separate the segmentation map $S$ into 8-channel binary masks. Each channel indicates a specific body region (e.g., pants, hair). Then we employ element-wise multiplication between each binary mask and the source person image $I$ to obtain body parts. In addition, we feed each body part into an encoder whose parameters are shared for all regions to extract the partial style features $F_{s}^{i}, i \in [1,8]$ . Finally, we concatenate all $F_{s}^{i}$ along the channel dimension to construct the semantic-aware decoupled style features $F_{s}$ . Each position in style feature maps contains specific semantic information. Furthermore, for eliminating the limitation caused by the fixed concatenation order, we propose a Cross Channel Fusion (CCF) module to endow plentiful information into each position by selecting desired semantic features from different semantic regions. In structure, the CCF module has a concise design which consists of two $1 \times 1$ convolutional blocks. + +To verify the effect of DSE, we visualize the feature maps extracted by the global encoder and the DSE, respectively. As shown in Figure 3, we can observe that the signal strength distribution of the global encoder represents the structural information clearly, while the distribution of the DSE is relatively flat, which indicates the structural information degradation. + +# 3.3. Correlation based Feature Merging + +In the merging phase, we propose the CMM module, which aims to establish the dense spatial correlation field $\mathcal{C}$ for feature rearrangement. To begin with, we reshape the feature $F_{i}$ into $[F_i(1), F_i(2), \dots, F_i(hw)] \in \mathbb{R}^{C \times HW}, i \in \{p, s\}$ . Each vector $F_{i}(j) \in \mathbb{R}^{C}$ in $F_{i}$ represents the semantic information of the $j^{th}$ location in the feature map, + +$j\in [1,hw]$ + +As illustrated in Figure 4, given $F_{s}$ and $F_{p}$ , each vector $F_{s}(i)$ serves as the query to retrieve the relevant key $F_{p}(j)$ from the $F_{p}$ . Therefore, the correlation field $\mathcal{C} \in \mathbb{R}^{HW \times HW}$ is established, whose element $C_{ij}$ is the correlation of key-value pairs, followed by a softmax activation. + +$$ +C _ {i j} = \frac {\exp \left(s _ {i j}\right)}{\sum_ {i = 1} ^ {h w} \exp \left(s _ {i j}\right)} \tag {1} +$$ + +$$ +s _ {i j} = \frac {\bar {F} _ {s} (i) \bar {F} _ {p} (j)}{| | \bar {F} _ {s} (i) | | | | \bar {F} _ {p} (j) | |} \tag {2} +$$ + +where $\bar{F}_s(i)$ and $\bar{F}_p(j)$ represent the centralized feature, i.e. $\bar{F}_s(i) = F_s(i) - \mathrm{mean}(F_s(i))$ . The correlation field $\mathcal{C}$ contains the weights which could be assigned to value vectors for feature rearrangement. Specifically, the rearranged feature $F_{s}^{*} = [F_{s}^{*}(1),F_{s}^{*}(2),\dots ,F_{s}^{*}(hw)]\in \mathbb{R}^{C\times HW}$ is obtained by calculating the weighted average summation of all positions in feature $F_{s}$ . + +$$ +F _ {s} ^ {*} (i) = \sum_ {j = 1} ^ {h w} c _ {i j} F _ {s} (j), i \in [ 1, h w ] \tag {3} +$$ + +Based on the above operations, the $F_{s}^{*}$ is structurally aligned with the input pose which could be fed into the translation generator to synthesize a realistic person image. + +# 3.4. Aligned Feature Translation + +With the rearranged features $F_{s}^{*}$ as input, the translation generator could synthesize the target image $\hat{I}$ for self-reconstruction. To better preserve the structural information, we employ the U-Net architecture [26] as our translation generator, as its skip connection propagates the information directly from encoder to decoder. + +# 3.5. Objective Functions + +Adversarial Learning. Following the configuration of [41], we employ two discriminators, one is a pose discriminator $D_{p}$ to maintain the pose consistency, and the other is a style discriminator $D_{s}$ to maintain the style consistency. Both of them promote the generator $G$ to generate realistic images. The adversarial loss $L_{adv}$ is listed as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {a d v} = \mathbb {E} _ {I, P} \left[ \log \left(D _ {s} (I) \cdot D _ {p} (I, P)\right) \right] \\ + \mathbb {E} _ {I, P} [ \log ((1 - D _ {s} (G (I, P))) \\ \cdot \left. \left(1 - D _ {p} (G (I, P))\right) \right] \tag {4} \\ \end{array} +$$ + +Self-supervised Reconstruction. The reconstruction loss $L_{rec}$ can be formulated as the L1 distance between the source image $I$ and generated image $\hat{I}$ , which encourages the $\hat{I}$ to be similar with the $I$ at the pixel level. + +$$ +\mathcal {L} _ {\text {r e c}} = \left| \left| \hat {I} - I \right| \right| _ {1} \tag {5} +$$ + +![](images/b70ce6cef4ff0f73dd19d4f86279c3effe19f27b0450fa2636788d3c3125f39e.jpg) +Figure 5. Details of the graph generator in our model. Nodes represent per-region styles and the edges measure the similarities between nodes. + +Perceptual Consistency. The perceptual loss $L_{perc}$ calculates the $L_{1}$ distance between the pre-trained VGG features of $I$ and $\hat{I}$ , which measures the high-level semantic differences between images [12]. + +$$ +\mathcal {L} _ {p e r c} = \left| \left| \phi^ {l} (\hat {I}) - \phi^ {l} (I) \right| \right| _ {1} \tag {6} +$$ + +Style Consistency. The style loss $L_{style}$ calculates the statistical errors between the pre-trained VGG features of $I$ and $\hat{I}$ , which penalizes the difference in colors and textures [12]. As shown in Formula (7), $\phi^l$ is the activation at the $j$ th layer of the pre-trained VGG network, and $\mathbb{G}$ is the Gram matrix. + +$$ +\mathcal {L} _ {\text {s t y l e}} = \sum_ {l} | | \mathbb {G} (\phi^ {l} (\hat {I})) - \mathbb {G} (\phi^ {l} (I)) | | _ {1} \tag {7} +$$ + +Body Structure Retaining. The BSR Loss is proposed to endow prior knowledge of invisible regions through constraining semantic relationships among body parts. We design a graph generator to model this relationship. As illustrated in Figure 5, we employ a pre-trained VGG network and the region-wise average pooling layer [40] to obtain the body graph $\mathbb{M}$ , in which the nodes represent per-region styles and the edges measure the similarities between nodes. + +Due to the training process is self-supervised with the single pose in each iteration, the model cannot make a reasonable completion for the unknown regions when performing cross-scale pose transformation. Applying BSR Loss for training encourages the output person image to retain a reasonable structure, which is conducive for half body to + +![](images/5cf3f2eaccff30ff74989958f2d52c845e951d6eeae7d071026622acd609ad1e.jpg) +Figure 6. The results of our method in the pose guided person image generation. + +full body transformation. We calculate the BSR loss between $I$ and $\hat{I}$ as the $L_{graph}$ . + +$$ +\mathcal {L} _ {\text {g r a p h}} = \left| \left| \mathbb {M} (I, S) - \mathbb {M} (\hat {I}, S) \right| \right| _ {1} \tag {8} +$$ + +The overall objective function is shown in Formula (9), where $\alpha_{adv}$ , $\alpha_{rec}$ , $\alpha_{perc}$ , $\alpha_{style}$ , $\alpha_{garph}$ are the weights of the corresponding loss functions. + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} = \alpha_ {\text {a d v}} \mathcal {L} _ {\text {a d v}} + \alpha_ {\text {r e c}} \mathcal {L} _ {\text {r e c}} + \alpha_ {\text {p e r c}} \mathcal {L} _ {\text {p e r c}} \tag {9} \\ + \alpha_ {s t y l e} \mathcal {L} _ {s t y l e} + \alpha_ {g r a p h} \mathcal {L} _ {g r a p h} \\ \end{array} +$$ + +# 4. Experiments + +# 4.1. Implementation Details + +Dataset. We carry out our experiments on DeepFashion In-shop Clothes Retrieval Benchmark [17], which contains 52,712 high quality person images. We split the dataset following the same configurations of [20], + +Metrics. We use the common metrics such as Structural Similarity (SSIM) [32], Inception Score (IS) [27], Learned Perceptual Image Patch Similarity (LPIPS) [38], and Fréchet Inception Distance (FID) [9] to assess the quality of generated images quantitatively. SSIM indicate the similarity between paired images in raw pixel space. Meanwhile, LPIPS, IS and FID measure the realism of the generated images at the feature level. + +Network Architecture and Training Details. Both the pose encoder and style encoder employ several downsampling convolutional layers to extract features. The feature maps with resolutions $32 \times 32$ are applied for establishing the correlation field. Our method is implemented on PyTorch framework using 4 Nvidia TitanX GPUs. The weights for loss functions are set to $\alpha_{adv} = 5$ , $\alpha_{rec} = 1$ , $\alpha_{perc} = 1$ , $\alpha_{style} = 150$ , $\alpha_{graph} = 1$ , respectively. + +# 4.2. Pose Guided Person Image Generation + +Pose guided person image generation, or pose transfer, aims to change the posture of a person image given target + +![](images/a52caaceb8cc8c77abdf913907f314608c6cdadf9b89ad3ebb8c3f330d0180ed.jpg) +Figure 7. The comparisons with other state-of-the-art methods on pose guided person image generation. Zoom in for a better view. + +poses as condition. Pose transfer is an important application of person image generation. As shown in Figure 1 (left) and Figure 6 (all), given a source person image, our model could transform it to any target pose and keep the appearance details unchanged. + +Qualitative Comparison. We compare the generated images of our method with several state-of-the-art approaches, including PATN [41], XingGAN [31], ADGAN [21], MUSTGAN [20] and PISE [36]. All the results are obtained using the source code or the pre-trained model released by the authors. The results of the qualitative comparisons are shown in Figure 7. PATN and XingGAN generate blurry results since these models can not disentangle different features. The results of ADGAN and MUSTGAN have correct postures, but they fail to maintain detailed textures. This is because these models can not capture the spatial correlation well. PISE could generate desirable results. However, its results still have some unsatisfactory artifacts due to the lack of semantic relationships. Meanwhile, this model requires unaligned image pairs for training. In contrast, our model obtain competitive results only requires source images. + +![](images/51cb226a070a297ffb27cd6aa882137cae5a93b19a662770019010447954700d.jpg) +Figure 8. The results of our method in the person attribute editing. + +Quantitative Comparison. As shown in Table 1, we compare our method with several state-of-the-art supervised and unsupervised methods on the DeepFashion. As we can see, our method outperforms these methods in most metrics on both supervised and unsupervised setting, which demonstrates the superiority of our method in generating high-quality person images. + +Table 1. Quantitative comparisons with other supervised and unsupervised methods on DeepFashion. + +
MethodFID↓SSIM↑LPIPS↓IS↑
Unsupervised
VU-Net [4]23.5830.7860.32113.087
E2E [30]29.90.7360.2383.441
DPIG [19]48.20.6140.2843.228
MUST [20]15.9020.742-3.692
Supervised
Intr-Flow [15]16.1340.7980.21313.251
Def-GAN [29]18.5470.7700.29943.141
PATN [41]24.0710.7700.25203.213
ADGAN [21]18.3950.7710.22423.329
GFLA [25]14.0610.7010.22193.635
PISE [36]13.61-0.2059-
SCM-Net12.180.7510.18203.632
+ +Table 2. The evaluation results of ablation study. + +
MethodFID↓SSIM↑LPIPS↓IS↑
w/o DSE12.860.7500.1873.2456
w/o CCF17.080.7510.1753.605
w/o BSR12.610.7550.1783.441
Full12.180.7510.1823.632
+ +# 4.3. Ablation Study + +We further perform the ablation study to analyze the contribution of each module and the proposed BSR Loss in our method. Firstly, we introduce the variants implemented by alternatively removing a specific component from our full + +model. There are four settings in this module ablation. 1). W/o DSE. This model removes the DSE module and directly uses a global encoder to extract the style features. 2). W/o CCF. This model removes the Cross Channel Fusion module from the DSE. 3). W/o BSR. This model removes the BSR Loss during the training procedure. 4). Full. This model represents our full model. + +Table 2 shows the quantitative results of the ablation study. We can observe that our full model achieves the best performance on FID and IS metrics. Meanwhile, the removal of any components will degrade the performance of the model integrally. Figure 9 shows the qualitative comparisons of different ablation models. We can observe that the w/o DSE model fails to preserve the styles of source images and the w/o CCF model has limitation in preserving the detailed texture. Meanwhile, w/o BSR model can not complete the lower body well while the full model could generate reasonable results. It demonstrates that BSR Loss enhance the model's ability of capturing body structural information. Furthermore, we illustrate the comparisons on half body to full body transformation with previous self-supervised method MUST-GAN [20]. Figure 10 shows the advantages of our method when performing half body to full body transformation. We can observe that MUST-GAN [20] would generate more artifacts, while our method could complete the lower part of the body reasonably with correlation learning. + +# 4.4. Person Attribute Editing + +Our model can also achieve person attribute editing based on reference images by exchanging channel features of specific semantic areas in semantic-aware decoupled style features. As shown in Figure 1 (right) and Figure 8 (all), our method could edit the style of the upper clothes, pants and hair style respectively. + +# 4.5. Applications on Face Generation tasks + +In this section, we demonstrate the versatility of our method. Since our method could disentangle the shape and style features, it could also be applied to other image generation tasks under this self-supervised framework. Two face + +![](images/001a53a91485e622a3e9b5f1ded33ce40af943f2974b6d33ac4b6e2f9242238c.jpg) +Figure 9. The qualitative comparison of ablation study. + +![](images/c4614b8cf87c7c8925a22d5857416f4f1115e3eaedc010812d1145a966dedced.jpg) +Figure 10. Results of half body to full body transformation + +generation tasks are shown as follows. + +Reference-Based Edge Colorization. Reference-based edge colorization aims to translate an edge map to a realistic image based on a reference image. Regarding the edge map as a pose skeleton and the reference image as a person image, our self-supervised model could achieve edge colorization. We obtain the edge map following [37] and use CelebA-HQ [13] dataset for training. The results are shown in Figure 11 (top). We can observe that the results maintain a good style consistency with the reference image, and preserve a good shape consistency with input edge maps. + +Face Attribute Editing. Similar to person attribute editing, our method could also achieve face attribute editing. The results can be found in Figure 11 (bottom). We can edit specific attributes while keeping other attributes unchanged. + +# 5. Limitation + +As shown in figure 12, our self-supervised model sometimes directly transfers certain source patterns into the final + +![](images/f33f762e7613479de6200152ad59ddd54094e0701e79044b83c503f78f18acc1.jpg) +Figure 11. The results of our method in reference-based face edge colorization (top) and face attribute editing (bottom). + +results when performing pose transfer, which is a rare situation in the supervised model. This, we hypothesis, is caused by the inherent defects of self-supervised strategy that the self-reconstruction process makes the model easy to overfit. This phenomenon might be avoided by employing spatial transformation to perform data augmentation during training in the future. + +![](images/e987b34281ffa27b292faa067b5ee1514b48fbbbbc44aa9e819453a245b54103.jpg) +Figure 12. The illustrations of the model limitation. The hair and left arm are transferred directly from source image. + +# 6. Conclusion + +In this paper, we propose a Self-supervised Correlation Mining Network (SCM-Net) for person image generation. We propose two specially designed modules, the DSE module for feature disentanglement, and the CMM module for feature merging based on the spatial correlation. 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Based on the neuralization of a Bayesian estimator of the problem, this paper presents a self-supervised deep learning approach to general image restoration problems. The key ingredient of the neuralized estimator is an adaptive stochastic gradient Langevin dynamics algorithm for efficiently sampling the posterior distribution of network weights. The proposed method is applied on two image restoration problems: compressed sensing and phase retrieval. The experiments on these applications showed that the proposed method not only outperformed existing non-learning and unsupervised solutions in terms of image restoration quality, but also is more computationally efficient. + +# 1. Introduction + +Image restoration is about calculating an image $\mathbf{x}$ from a collection of its measurements, denoted by $\mathbf{y}$ , whose relationship can be described as + +$$ +\boldsymbol {y} = \Psi (\boldsymbol {x}) + \boldsymbol {n}, \tag {1} +$$ + +where $\Psi$ denotes the image formation process and $n$ denotes measurement noise. Image restoration is one fundamental problem encountered in a wide range of image-related applications. For example, image restoration in digital photography, compressed sensing, computed tomography (CT), and magnetic resonance imaging (MRI) in medical imaging, phase retrieval for scientific imaging, and many others. In general, the problem (1) is an ill-posed inverse problem, whose direct inversion is either not unique or sensitive to measurement noise. + +Over last decades, regularization method, or equivalently Bayesian estimator, has been the dominant tool for image + +restoration. These non-learning methods either impose certain prior or assume certain prior distribution on images for addressing solution ambiguity and noise sensitivity. However, it remains challenging to define an accurate image prior. In recent years, deep neural network (DNN) emerges as a prominent tool for solving inverse problems; see e.g. [11, 12, 16, 17, 20, 33, 49, 52, 58, 61, 62]. The majority of existing DNN-based solutions are supervised on an external training dataset with truth images. Such a prerequisite on truth images limits their wider applications in practice. For example, collecting truth images can be very challenging and costly in medical imaging and scientific imaging. Also, the generalization performance of a supervised learning method can be a concern in practice, if the network is trained over a biased dataset where the structures of test images are not present in training samples. + +In recent years, it is receiving an increasing interest on developing deep learning methods for imaging, which do not require truth images for training DNNs. The so-called plug-and-play prior attempts to address such an issue by adopting some pre-trained denoising network in an iterative image restoration scheme; See e.g. [35, 48, 56, 63]. While these methods do not explicitly call truth images, the pretrained networks are still supervised over the dataset with truth images related to the image for restoration. Another approach is using generative adversarial network (GAN) to synthesize training samples for training the network; see e.g. [43]. Similarly, the performance of GAN-based methods highly relies on the effectiveness of the pre-trained GAN model on simulating truth images. While GAN has been very effective on simulating the images in specific domain such as face and text, it is not so for other types of images, e.g., medical images and scientific images. + +The methods above are not completely free from the prerequisite of accessing related truth images. Recently, there has been a rapid progress on unsupervised or self-supervised learning for image denoising using un-trained DNNs; See e.g. [3, 14, 28, 40, 41, 50, 55]. However, the generalization of these denoising networks to ill-posed image restoration problems is not trivial. The existence of the non + +zero null space + +$$ +\operatorname {N u l l} (\Psi) = \left\{\boldsymbol {x}: \Psi (\boldsymbol {x}) = \mathbf {0} \right\} \neq \left\{\mathbf {0} \right\} +$$ + +in image restoration make it quite different from image denoising, as the error induced by the existence of nontrivial space $\mathrm{Null}(\Psi) \neq \{0\}$ cannot be treated as random noise. One pioneering work is the so-called deep image prior (DIP) [55] which shows that there exists certain implicit prior induced by a convolutional neural network (CNN). The DIP states that regular image structures appear before random noise when training a CNN. Such a prior has been exploited in many image restoration tasks, e.g. super-resolution [55], CT reconstruction [23], image separation [22] and blind deblurring [32, 44]. In addition to DIP, there are some other approaches to address the overfitting caused by the absence of truth images during training. For CS image reconstruction, Pang et al. [39] proposed to train a Bayesian DNN with Gaussian random weights. Heckle [24] used an underparametrized network. Metzler et al. [38] and Zhussip et al. [67] proposed to regularize the denoising network in an iterative scheme by Stein's unbiased risk estimator (SURE). + +# 1.1. Motivation and main idea + +A self-supervised deep learning method for image restoration is very attractive to the applications where collecting truth images is challenging, e.g. medical and scientific imaging. This paper is about studying an efficient and effective method for training a NN to process testing data, where neither pre-trained model nor training sample with truth image is used during training. + +The proposed method is derived from the so-called minimum mean squared error (MMSE) estimator of the problem (1) defined by + +$$ +\widehat {\boldsymbol {x}} = \int \boldsymbol {x} p (\boldsymbol {x} | \boldsymbol {y}) d \boldsymbol {x}, \tag {2} +$$ + +where $p(\boldsymbol{x}|\boldsymbol{y})$ denotes the posterior distribution. One way to calculate (2) is using the Monte Carlo (MC) method. Instead of directly sampling $p(\boldsymbol{x}|\boldsymbol{y})$ , we use a generative CNN $f(\epsilon_0; \theta)$ , parametrized by $\theta$ , to re-parametrize $\boldsymbol{x}$ : + +$$ +\boldsymbol {x} = f \left(\epsilon_ {0}; \theta\right). +$$ + +Then, $\widehat{\pmb{x}}$ in (2) can be re-expressed as + +$$ +\widehat {\boldsymbol {x}} = \int f (\epsilon_ {0}; \theta) p (\theta | \boldsymbol {y}, \epsilon_ {0}) d \theta . \tag {3} +$$ + +Such a re-parametrization allows us to utilize implicit image prior induced by CNN. Then, the remaining task is how to efficiently sample the posterior distribution + +$$ +\pi (\theta) = p (\theta | \boldsymbol {y}, \epsilon_ {0}), +$$ + +to calculate the integral (3) via the MC method: + +$$ +\widehat {\boldsymbol {x}} \approx \sum_ {k} f \left(\epsilon_ {0}; \theta_ {k}\right), \quad \text {w h e r e} \theta_ {k} \sim p (\theta | \boldsymbol {y}, \epsilon_ {0}). +$$ + +Efficient sampling restricted in feasible set. How to efficiently sample $\theta$ is critical for an accurate calculation of the integral (3). A natural treatment is, instead of sampling $\theta$ in the whole space, we only sample those parameters in a feasible set $\Omega$ , where the density function $\pi(\theta)$ concentrates. Suppose measurement noise $n$ is i.i.d. Gaussian white noise with variance $\sigma^2$ . By large number theory, we have, for image size $N \to \infty$ , + +$$ +L (\theta) = \frac {1}{N} \| \Psi (f \left(\epsilon_ {0}; \theta\right)) - \boldsymbol {y} \| _ {2} ^ {2} = \frac {1}{N} \| \Psi (\boldsymbol {x}) - \boldsymbol {y} \| _ {2} ^ {2} \rightarrow \sigma^ {2}. \tag {4} +$$ + +In other words, with sufficiently large image size, the density of $\theta$ whose $f(\epsilon_0;\theta)$ is close to $\pmb{x}$ , concentrates within the set: + +$$ +\Omega_ {\epsilon} := \left\{\theta : \sigma^ {2} - \epsilon \leq L (\theta) \leq \sigma^ {2} + \epsilon \right\}, \tag {5} +$$ + +where $\epsilon$ is a small threshold. A detailed analysis of (5) is provided in the supplementary file. To conclude, the samples from $\pi (\theta)$ within the feasible set $\Omega_{\epsilon}$ defined by (5) are sufficient for accurately calculating the integral (3). + +Adaptive SGLD for restricted MC sampling. SGLD is an Markov chain Monte Carlo (MCMC) sampling algorithm, which is proposed in [57] for efficiently sampling network weights. SGLD simulates dynamics of molecular systems with stochastic differential equation given by $d\theta_{t} = -\nabla L(\theta_{t})dt + \sqrt{2} dW_{t}$ , where $W_{t}$ is stationary Gaussian process with zero-mean and $L$ is a loss function. + +In this paper, we proposed a new type of SGLD for effectively sampling from $\pi (\theta) = p(\theta |\boldsymbol {y},\epsilon_0)$ within the feasible set $\Omega_{\epsilon}$ defined by (5). The corresponding stochastic differential equation is defined by + +$$ +d \theta_ {t} = - \nabla L (\theta_ {t}) d t + \beta \exp (c _ {0} (\frac {\sigma^ {2}}{L (\theta_ {t})} - 1)) d W _ {t}, +$$ + +where $L(\theta)$ is defined by (4), in the case where $\pmb{n} \sim \mathcal{N}(0, \sigma^2 I)$ and $\theta$ follows an uniform distribution. Then the discretization of the equation above leads to an adaptive stochastic gradient Langevin dynamics (ASGLD): + +$$ +\theta_ {k + 1} = \theta_ {k} - \gamma_ {k} \cdot \nabla L \left(\theta_ {k}\right) + \beta \exp \left(c _ {0} \left(\frac {\sigma^ {2}}{L \left(\theta_ {k}\right)} - 1\right)\right) \sqrt {\gamma_ {k}} \cdot \epsilon , \tag {6} +$$ + +where $\epsilon \sim \mathcal{N}(0,I)$ . It can be seen that in comparison to classic SGLD, ASGLD adaptively adjust the magnitude of noise perturbation based on the loss function $L(\theta)$ . The samples from ASGLD will concentrate within the feasible set $\Omega_{\epsilon}$ . See Section 3 for more details. + +# 1.2. Main contribution + +This paper proposed a self-supervised method for solving ill-posed image restoration problems, without requiring any external truth image. The method trains a CNN which approximates the MMSE estimator of the problem via MC-based integration, where the key is how to efficiently sample the posterior distribution. The answer from this paper is an adaptive SGLD method, an efficient MCMC scheme that focuses on concentrated regions of the posterior distribution. + +The proposed method is applied to solve image restoration problems in two imaging modalities: CS and phase retrieval. The experiments show that the proposed method not only provides state-of-the-art performance among all existing dataset-free solutions, but also is more computationally efficient. See below for the summary of the differences between ASGLD and most related unsupervised methods. + +- ASGLD vs. DIP [55] and its extensions: DIP utilizes the implicit prior induced by a CNN and trains the network with early-stopping. ASGLD also training a network and its algorithm is motivated by MCMC sampling based approximation to the MMSE estimator of the problem. +- ASGLD vs. BNN [39]: Both train a network to approximate the MMSE estimator of the problem. BNN approximates it via variational approximation using a Bayesian neural network (BNN) with random weights. ASGLD approximates it using MC-sampling-based integration implemented using an efficient MCMC sampler. +- ASGLD vs. plain SGLD: In comparison to classic SGLD with constant noise variance for general MCMC sampling, ASGLD proposes a new SGLD scheme with adaptive noise variance, which enables one to efficiently calculate the MC-based integration. + +See below for the summary of main contributions: + +- An MC-sampling-based MMSE estimator of image restoration with untrained deep network. +- A new adaptive SGLD scheme of MCMC sampling for efficient calculation of MC-based integration. +- Noticeable performance improvement over existing unsupervised methods in two image restoration tasks. +- A general self-supervised method with potential applications to other ill-posed inverse problems in imaging. + +# 2. Related work + +There is an abundant literature on inverse problems. Due to space limitation, we only cover the most related ones. + +Regularization methods with manually-defined prior. Regularization has been one prominent method for image restoration, which imposes a pre-defined prior on the latent image to address the ill-posedness of the problem. Most regularization methods can be viewed as an MAP estimator + +which minimizes $\min_{\pmb{x}} - \log p(\pmb{x}|\pmb{y}) = \min_{\pmb{x}} - \log p(\pmb{y}|\pmb{x}) - \log p(\pmb{x})$ , where $p(\pmb{x})$ denotes prior distribution of $\pmb{x}$ . Different priors on $\pmb{x}$ are proposed in the past, including Gaussian prior on $\pmb{x}$ , Laplacian prior on $\nabla x$ [5, 9, 10, 47] or related measurements such as wavelet coefficients [6, 18]. + +Supervised learning methods. Supervised deep learning has been used for solving a wide range of image restoration problems. One approach is to train a network on a dataset with many pairs $\{(y, x)\}$ that maps input measurements to the image for restoration; see e.g. [12, 13, 53, 64, 65]. Such an approach works well for denoising, but it does not utilize the information of the forward process $\Psi$ . To exploit the information of $\Psi$ in the network, the so-called optimization unrolling approach unrails some iteration schemes and replaces the prior-relating operations by a denoising CNN with learnable parameters; see e.g. [1, 15, 17, 42, 58, 60]. + +Deep learning methods with pre-trained network. In the optimization unrolling scheme, the embedded CNNs can be viewed as image denoisers encoding the prior of the image. The so-called deep learning with plug-and-play prior directly plug the pre-trained denoising network into the iterative scheme; see e.g. [35, 46, 48]. Instead of using pre-trained denoising network, pre-trained GAN is also used for providing the prior to regularize the prediction from the network; Ankit Raj et al. [43] used a pre-trained GAN to replace the hand-crafted prior for compressed sensing. + +Unsupervised learning specifically for image denoising. There has been a steady progress on unsupervised learning for denoising or similar tasks such as in-painting. The Noise2Noise [30] trained the network from two noisy instances of the same scene. Noise2void [28] proposed a blind-spot technique for training a denoising network on a set of noisy images. SURE-based regularization method [51] proposed a Stein's unbiased estimator of the supervised loss function from noisy images. A dropout NN is proposed in [41] to train the NN on a single noisy image. R2R [40] introduced a data augmentation scheme to provide an unbiased estimate of the loss function supervised over truth images. + +Self-supervised and unsupervised learning for image restoration. Ulyanov et al. [55] proposes the DIP which uses early stopping for avoiding overfitting, since the training favors regular structure over random patterns during early iterations. DIP has been exploited for many image restoration tasks, including blind deblurring [44] and image matting [59]. For further improving the effectiveness of DIP on addressing overfitting, Heckel et al. [25] proposed an under-parameterized deep decoder to handle the overfitting. Metzler et al. [38] and Zhussip et al. [67] proposed to regularize the denoiser by SURE in the iterative approximate message passing (AMP) scheme. Pang et al. [39] proposed a variational approximation method to the MMSE estimator by training a BNN with is weights following normal distri + +butions. Cheng et al. [14] proposed to use classic SGLD for image denoising and in-painting. Chen et al. [11] assumed equivalence in data and trained an NN in the dual space only on measurements. Li et al. [32] proposed using a dropout-based MC sampling method for blind image deblurring. + +# 3. MCMC sampling with ASGLD + +This section is devoted to a detailed discussion of the ASGLD method, with more details in supplementary file. + +Approximate MMSE estimator via MC-sampling. Consider an inverse problem expressed as + +$$ +\boldsymbol {y} = \Psi (\boldsymbol {x}) + \boldsymbol {n}, \tag {7} +$$ + +where $\pmb{y}$ denotes the measurement set, $\pmb{x}$ denotes the image, and $\pmb{n}$ denotes measurement noise. Here we consider Gaussian white noise: $\pmb{n} \sim \mathcal{N}(0, \sigma^2 I)$ . Let $f(\epsilon_0; \theta) = \pmb{x}$ denote a generative network with weights $\theta$ , which maps an initial seed $\epsilon_0$ to the image $\pmb{x}$ . Then, we have an MMSE estimator of $\pmb{x}$ , or the so-called conditional mean, given by + +$$ +\widehat {\boldsymbol {x}} = \int \boldsymbol {x} p (\boldsymbol {x} | \boldsymbol {y}) d \boldsymbol {x} = \int f \left(\epsilon_ {0}; \theta\right) p \left(\theta | \boldsymbol {y}, \epsilon_ {0}\right) d \theta . \tag {8} +$$ + +In our approach, the integral above is calculated by the MC method. Then, the remaining question is how to sample the posterior distribution defined by + +$$ +\pi (\theta) = p (\theta | \boldsymbol {y}, \epsilon_ {0}). +$$ + +As the dimension of $\theta$ is very high, to efficiently approximate the integration, the sampler should focus on the samples which make sufficient contribution to the calculation of the integral. In other words, the samples should concentrate in the subset where $\pi (\theta)$ is significant. Thus, we consider to have a restricted sampler whose samples concentrated in + +$$ +\Omega_ {\epsilon} := \left\{\theta : \sigma^ {2} - \epsilon \leq L (\theta) \leq \sigma^ {2} + \epsilon \right\}, \tag {9} +$$ + +for some small constant $\epsilon$ , where + +$$ +L (\theta) = \frac {1}{N} \| \Psi (f \left(\epsilon_ {0}; \theta\right)) - \boldsymbol {y} \| _ {2} ^ {2}. \tag {10} +$$ + +Adaptive Langevin dynamics. One popular MC sampler is the so-called MCMC sampler. For deep network, it is proposed in [57] that Langevin dynamics, an MCMC sampler, can be used for sampling the posterior distribution related to network weights. Langevin dynamic originally is for describing the dynamics of molecular systems with stochastic differential equation given by + +$$ +d \theta_ {t} = - \nabla L (\theta_ {t}) d t + \sqrt {2} d W _ {t}, \tag {11} +$$ + +where $L$ denotes a loss function. The discretization of the equation above gives the so-called SGLD: + +$$ +\theta_ {k + 1} = \theta_ {k} - \gamma_ {k} \cdot \nabla L \left(\theta_ {k}\right) + \sqrt {2 \gamma_ {k}} \cdot \epsilon , \tag {12} +$$ + +where $\epsilon \sim \mathcal{N}(0, I)$ . It can be seen that the iteration (12) can be viewed as the noisy stochastic gradient descent (SGD) method, corrupted by additional Gaussian white noise. + +To accurately calculate (8) with sufficient computational efficiency, we need to restrict the sampler such that the samples can concentrate in the feasible set $\Omega_{\epsilon}$ defined by (9). One natural idea is that, if one increases noise perturbation when $\theta$ is inside $\Omega_{\epsilon}$ and decreases the noise perturbation when $\theta$ is outside of $\Omega_{\epsilon}$ in SGLD, the resulting sampler will then be more likely to take random walk inside the feasible set $\Omega_{\epsilon}$ . Based on such an idea, we proposed a new form of Langevin dynamics for restricted MCMC sampling. + +Suppose that $\theta$ follows an uniform distribution: $\theta \sim 1_{[-T,T]}$ with sufficiently large $T$ . Then, by Bayesian rule, + +$$ +\pi (\theta) = p (\theta | \boldsymbol {y}, \epsilon_ {0}) \propto p (\boldsymbol {y} | \theta , \epsilon_ {0}) p (\theta). \tag {13} +$$ + +Taking negative logarithm on both sides, we have then + +$$ +- \log p (\theta | \boldsymbol {y}, \epsilon_ {0}) = \frac {N}{2 \sigma^ {2}} L (\theta) + \text {c o n s t .}, \tag {14} +$$ + +where $L$ is defined by (10). We propose a new form of Langevin dynamics with adaptive stochastic term, whose underlying stochastic differential equation is defined by + +$$ +d \theta_ {t} = - \nabla L (\theta_ {t}) d t + \beta \exp \left(c _ {0} \left(\frac {\sigma^ {2}}{L \left(\theta_ {t}\right)} - 1\right)\right) d W _ {t}. \tag {15} +$$ + +Then, its discretization gives + +$$ +\theta_ {k + 1} = \theta_ {k} - \gamma_ {k} \cdot \nabla L \left(\theta_ {k}\right) + \beta \exp \left(c _ {0} \left(\frac {\sigma^ {2}}{L \left(\theta_ {k}\right)} - 1\right)\right) \sqrt {\gamma_ {k}} \cdot \epsilon , \tag {16} +$$ + +where $\epsilon \sim \mathcal{N}(0,I)$ . The iteration (16) is called ASGLD. + +It can be seen that the stochastic term $\exp (c_0(\frac{\sigma^2}{L(\theta)} -1))$ is adaptive to the value of $L(\theta)$ . When one trains the DNN via SGD, the value of the loss function $L$ will decrease over the iterations. In the initial iterations with large loss, the ASGLD is close to classic SGD. When $L(\theta) > \sigma^2$ , noise level decreases with a smaller perturbation on SGD. In turn, the next sample $\theta_{t + 1}$ is likely to have a smaller $L(\theta)$ . When $L(\theta) < \sigma^2$ , noise level increases with a larger perturbation on SGD. In turn, the next sample $\theta_{t + 1}$ is likely to have a larger $L(\theta)$ as SGD is distorted by a large amount. In both cases, the iterative scheme (6) keeps the sequential samples being pulled back into the feasible set $\Omega_{\epsilon}$ when the current sample is away from $\Omega_{\epsilon}$ . The constant $c_{0}$ is chosen such that stochastic term is negligible when $L(\theta) > \frac{3}{2}\sigma^{2}$ . + +Analysis and discussion. We first showed the stationary distribution of the stochastic different equation (16). + +Theorem 3.1 (Stationary distribution). Define the density function of $\theta_t$ as $p(\theta; t)$ where $\theta_t$ is determined by (16) with random initialization. Then the stationary distribution for $\theta$ + +can be explicitly expressed as + +$$ +p _ {\infty} (\theta) \propto \exp [ - G (L (\theta)) - 2 c _ {0} \frac {\sigma^ {2}}{L (\theta)} ], +$$ + +where $G(s) \coloneqq \frac{2}{\beta^2} \int \exp(-2c_0(\frac{\sigma^2}{s} - 1)) ds$ is a function defined through indefinite integral. + +Proof. See supplementary file for the proof. + +![](images/63b44932a0704fed7ff65ec2dd24b84822d7bdda874f29d6e7e453387df7a868.jpg) + +Indeed, with suitable $\beta$ and $c_{0}$ , $p_{\infty}(\theta)$ concentrates around $L(\theta) \approx \sigma^{2}$ , i.e. the set $\Omega_{\epsilon}$ with small $\epsilon$ . Define + +$$ +E (s) = G (s) + 2 c _ {0} \frac {\sigma^ {2}}{s}, +$$ + +then the iteration (16) provides the following posterior + +$$ +p (\theta | \boldsymbol {y}, \sigma , \epsilon_ {0}) \propto \exp (- E (L (\theta))) \tag {17} +$$ + +rather than $\exp \left(-\frac{N}{2\sigma^2} L(\theta)\right)$ provided by (11). Then, + +$$ +\frac {d}{d s} E (s) = \frac {2}{\beta^ {2}} e ^ {- 2 c _ {0} \left(\frac {\sigma^ {2}}{s} - 1\right)} - 2 c _ {0} \frac {\sigma^ {2}}{s ^ {2}}. +$$ + +Let $\beta = \sqrt{\frac{\sigma^2}{c_0}}$ , we have + +$$ +\frac {d}{d s} E (\sigma^ {2}) = \frac {2}{\beta^ {2}} - 2 c _ {0} \frac {1}{\sigma^ {2}} = 0, +$$ + +$$ +\frac {d d}{(d s) ^ {2}} E (s) = \frac {2}{\beta^ {2}} e ^ {- 2 c _ {0} \left(\frac {\sigma^ {2}}{s} - 1\right)} \frac {2 c _ {0} \sigma^ {2}}{s ^ {2}} + \frac {4 c _ {0} \sigma^ {2}}{s ^ {3}} > 0, \text {f o r} s > 0. +$$ + +Clearly, $E(s)$ is convex for $s > 0$ and $s = \sigma^2$ is the global minimizer of $E(s)$ . Moreover, $E(s)$ has large curvature around the minimizer. For example, set $\beta = \sqrt{\frac{\sigma^2}{c_0}}$ , we have $\frac{dd}{(ds)^2} E(\alpha) = \frac{4c_0}{\sigma^4} (1 + c_0)$ . In the case where $\sigma^2 = 0.01$ , set $c_0 = 50$ . Then, $\frac{dd}{(ds)^2} E(\sigma^2) > 10^8$ . + +Empirical illustration in CS-MRI. The illustration is conducted by applying ASGLD on CS-MRI, configured with $10\%$ measurement noise and 1D Gaussian mask with $25\%$ sampling ratio. See Fig. 1 for the visualization of density function $\exp (-E(s))$ , and Fig. 2 for the distribution of $\{f(\epsilon_0,\theta_k)\}$ generated by ASGLD along iteration, visualized by PCA-based dimension reduction. It can be seen that the ASGLD quickly starts to sample the region close to truth after the "burn-in" iteration around 1000, and concentrate inside it afterward. In the end, the average of those samples provide an good approximation to the truth. + +Training and testing. Given a generative untrained network, the network is trained via the ASGLD (16) for total $K$ iterations. Let $K_{0}$ denotes the "burn-in" number where we assume the method starts to sample the parameters that are close to the feasible set. In other words, we generate a set of samples $\{\theta_k\}_{k = K_0}^K$ , which can be used for calculating the + +![](images/ef421d3158301943ca8818e87e8885f634a4b469159c60a860dc0a24fa3a7571.jpg) +(a) + +![](images/709a448108972c2171213812233cb189f4eae5fc0ee9ed18d1ea2d5308a3f963.jpg) +(b) + +![](images/bcddd5db81f91ed28d0ca71e7debf363b7f8a3bd4e6e0ed622f159fcfd7721a9.jpg) +Figure 1. (a) The density function $\exp(-E(s))$ (without normalization) for different $c_0$ and $\sigma^2 = 0.01$ w.r.t. pixel value range [0, 1], the maximum is obtained at $s = 0.01$ ; (b) The value of $L(\theta)$ w.r.t. iteration during the training. +First Principal Component +(a) +Figure 2. Visualization of the distribution of the samples generated from the ASGLD w.r.t. $\{f(\epsilon_0,\theta_k)\}$ . (a) The distribution of the samples from iteration 100; (b) The distribution of the samples after iteration 1100. + +![](images/6bf9965ea31ff2b7f83e6d88e65f8d0127257eb8caf9f9bdbc7b49ff35c92803.jpg) +First Principal Component +(b) + +integral of the MMSE estimator (8) by taking the average + +$$ +\hat {\boldsymbol {x}} = \int f (\epsilon_ {0}; \theta) p (\theta | \boldsymbol {y}, \epsilon_ {0}) d \theta \approx \frac {1}{K - K _ {0}} \sum_ {k = K _ {0}} ^ {K} f (\epsilon_ {0}; \theta_ {k}). +$$ + +# 4. Experiments + +The proposed method is a training algorithm for training the DNN without truth images. While it is independent of network architecture, we adopt the same U-Net as DIP [55] through all experiments to exclude the effect from network architecture for fairness. The architectures are 5-layer autoencoders with skip connections and each layer contains 128 channels. We set the fixed input $\epsilon_0$ sampling from the uniform distribution $\mathcal{U}(0,0.1)$ . All experiments are based on Pytorch on a server with NVIDIA Titan RTX GPUs. The code is publicly available at https://github.com/Wangweixi/restricted_sampling. + +In the table for quantitative comparison, the best results from all supervised methods marked as **bold**, and the best results from all traditional regularization and unsupervised learning methods are colored in blue. + +# 4.1. Image reconstruction for CS + +CS [8] is an imaging modality for faster sampling and lower energy consumption. It has a wide range of applications including medical imaging [21, 34] and computational photography [2, 19]. Image reconstruction for CS can be + +![](images/2215b7d2b473fc7472bf46e612788c70db85b7f7681a879b217985a89427888e.jpg) +DAMP [37] + +![](images/5dd95b5763d05d9321ef0b60118dbdff5ddb8607c1920535f6a2076cb6083069.jpg) +TVAL3 [31] + +![](images/de13e70c362437cd40a0351093a69b3a8af8e9e765693fb6c0e9cf521e2496e6.jpg) +ISTA [61] + +![](images/0e1805968cb2f2eba699e2752fcec3622865aacfbb8d5c58797abaff1922abfc.jpg) +DIP [55] +Figure 3. Results of CS image reconstruction using noisy input with ratio $25\%$ for "Barbara". + +![](images/2a2fb821c9302ff692a89b7024284c338e1bc993e74f0fa1ac8f135cafeda3f3.jpg) +BNN [39] + +![](images/b6e90f952d885b947a755fbec4892b8370f8f37b6d8dc652aa5cc0b4e2a512b4.jpg) +ASGLD + +![](images/7836db6fc5cbff7daeb9a8a432329da73b4496ed75835c50babf9d6a8b0fe3dd.jpg) +Truth + +Table 1. Average PSNR(dB) results of different methods for natural image reconstruction on Set11. + +
Regularized methodsSupervised methodsSelf-supervised methods
Noise σCS -ratioTVAL3 [31]D-AMP [37]ReconNet [29]ISTA [61]ISTA+ [61]DPANet [53]MACNet [12]FISTANet [58]SURE- AMP [67]DIP [55]BNN [39]ASGLD
40%30.5233.49-35.9736.0235.0435.3136.2434.1233.2835.7135.87
025%26.4428.2125.5432.5932.4431.7432.9132.6029.7631.3332.3033.06
10%21.3521.1622.6826.6426.4926.9927.6826.9422.6527.4027.4928.15
40%26.6629.25-27.9831.0930.0130.3431.0731.1428.8730.3931.11
1025%24.7526.3524.3627.2629.2029.2529.3130.3228.5027.3628.6729.35
10%21.0220.8422.0024.5524.5525.2125.5625.1122.1124.1925.2326.02
+ +formulated as solving an ill-posed linear system: + +$$ +\boldsymbol {y} = A \boldsymbol {x} + \boldsymbol {n}, +$$ + +where $A\in \mathbb{R}^{M\times N}$ ( $M\ll N$ ) denotes the sensing matrix. + +CS for natural image acquisition. Following the setting of [39, 61], we consider CS-based natural image acquisition via block-wise random Gaussian sensing matrix. The images from Set11 [61] and BSD68 [28] are cropped into non-overlapped blocks of size $33 \times 33$ to generate the measurements. The sensing matrix $A$ of size $M \times N$ ( $N = 1089$ ) is sampled from $\mathcal{N}(0, I)$ with row-wise orthogonalization. Gaussian white noise with s.t.d. 10 is added to the measurements. Three different down-sampling ratios are tested. The methods for comparison include regularization methods: TVAL3 [31] and D-AMP [37]; six supervised learning methods: ReconNet [29], ISTA and ISTA+ [61], DPANet [53], MACNet [12] and FISTANet [58]; three self-supervised methods: SURE-AMP [67], DIP [55], and BNN [39]. We set the learning rate as 0.001. For noisy data, $K = 10000$ , $K_0 = 2000$ . For noise-free data, $K = 30000$ , $K_0 = 5000$ . + +See Table 1-2 for quantitative comparison of different methods in different configurations. It showed that ASGLD not only outperformed all non-learning and unsupervised deep learning methods by a noticeable margin, but also remained very competitive against supervised learning methods. See Figure 3 for visual comparison of different methods of one example and supplementary file for more examples. + +CS-MRI. The second CS application is CS-based MRI, an important technology for rapid MRI imaging. The experi- + +ment follows the procedure of [33, 39]. The measurement matrix $A$ is implemented using random Fourier downsampling matrices and the dataset contains 21 MRI images from ADNI (Alzheimer's Disease Neuroimaging Initiative). Three down-sampling masks with $25\%$ down-sampling rate are tested: 1D Gaussian mask, 2D Gaussian masks, and radial mask; see [33, 39] for more details. ASGLD is compared to different methods, including direct zero-filling (ZF) method [4] and TV regularization method [34]; supervised ADMM-Net [60]; plug-and-play method [33] with three different networks: SCAE, SNLAE, GAN; tuning free plug-and-play deep learning TFPnP [56]; three self-supervised learning methods: DIP [55], BNN [39] and EI [11]. Both noiseless measurement and noisy measurement with noise level $\sigma = 10\%$ are tested. The learning rate is 0.002. For noisy data, $K = 7000$ , $K_{0} = 1000$ . For noise-free data, $K = 15000$ , $K_{0} = 5000$ . + +See Table 3 for quantitative comparison of different methods in different configurations. See Figure 4 for the visualization of the results from different methods. It can be seen that ASGLD is overall the top performer among the methods for comparison including supervised learning methods. See supplementary file for more experiments and visualizations. + +# 4.2. Phase retrieval + +Phase retrieval is an imaging technology used in many areas of engineering and science, e.g. diffraction imaging [26, 27], microscopy imaging [66], and holographic imaging [45]. It needs to solve a non-linear problem: + +$$ +\boldsymbol {b} = \sqrt {| \boldsymbol {A x} | ^ {2} + n}, +$$ + +Table 2. Average PSNR(dB) results of different methods for natural image reconstruction on BSD68. + +
Regularized methodsSupervised methodsSelf-supervised methods
Noise σCS -ratioTVAL3 [31]D-AMP [37]ReconNet [29]ISTA [61]ISTA+ [61]DPANet [53]MACNet [12]FISTANet [58]SURE- AMP [67]DIP [55]BNN [39]ASGLD
40%29.3928.03-32.1732.1731.3331.3932.2530.2630.1031.2831.36
025%26.4825.5725.3129.3629.2929.0029.4229.1827.0227.7828.6329.51
10%22.4921.9223.1625.3225.2925.5725.8025.0922.5324.8225.2425.51
40%26.1526.55-26.6828.9828.7828.9229.0128.1625.2428.1328.75
1025%24.8024.8724.1225.8427.2627.2427.5728.1226.1424.0726.4727.16
10%22.0321.7022.3623.8623.8624.3424.6324.3421.9322.4623.7924.56
+ +Table 3. Average PSNR (dB) results of different MRI reconstruction methods. + +
Regularized methodsSupervised methodsSelf-supervised methods
Methods NoiseZF [4]TV prior [34]ADMM -Net [60]SCAE [33]SNLAE [33]GAN [33]TFPnP [56]EI [11]DIP [55]BNN [39]ASGLD
1D Gaussian023.0625.7728.9929.3729.0627.4729.9428.9831.8031.3832.18
10%20.3722.2522.9822.7224.3723.3224.2422.9823.3825.6526.03
2D Gaussian025.332.7934.9735.6132.8532.9433.8831.7635.6336.1036.07
10%22.3824.9225.8426.0626.0626.1526.8924.6124.4127.1227.40
Radial025.4532.3233.6733.9432.5332.2633.2431.1433.8134.0834.38
10%22.3825.1625.9626.1326.3825.3327.1224.7324.5427.0727.37
+ +![](images/089524e5df24acfe6c07788b70a8718cf1adbde68e1ef164a9512c4ca03ba740.jpg) +ADMM-Net [60] + +![](images/56f656e5e49d561bd7296cdc2706de8a4d436f79b46da0e865ea37af12a6108e.jpg) +SNLAE [33] + +![](images/e946bc50533222b8f5208dd483d59a3dd9ae12983d3ea284b3fdc05122b372d4.jpg) +GAN [33] + +![](images/f0bf56ad19737cc08417ee4628360317147024ecfa6daabf26fb1fbc9a3f9e40.jpg) +TFPnP [56] +Figure 4. Reconstruction results of CS-MRI with 1D Gaussian mask of sampling ratio $25\%$ . + +![](images/9e17840e0dd4c2d7194f9dc04995b2bcfb63b80cecea04114e9c2bc2fe65bf9c.jpg) +BNN [39] + +![](images/3b7d7c8e63d49d1c472b9e1f3b5b7a15036864f6b06f2b19182bc6ce32a273bd.jpg) +ASGLD + +![](images/3df997f9f7c6c0b143e1b2496e80f57dd5e460676a90f31d264556063758437d.jpg) +Truth + +Table 4. Average PSNR(dB) results of different phase retrieval methods. + +
DatasetUnnatural-6 [35]Natural-6 [35]
Noise typeTraditionalPlug-and-playSelf-supervisedTraditionalPlug-and-playSelf-supervised
WF [7]DOLPHIn [54]prGAMP [36]prDeep [35]DIP [55]BNN [39]ASGLD WF [7]DOLPHIn [54]prGAMP [36]prDeep [35]DIP [55]BNN [39]
AWGN1020.3724.7130.0030.2028.7129.9931.5315.3323.6825.2826.1124.54
1526.1826.7032.8132.1332.4931.8934.5321.1226.7828.1928.7929.59
2031.4729.8035.8135.4432.0832.2237.3126.4230.0930.8731.3332.17
Poisson938.6730.1239.4139.0134.1632.9643.6738.8031.2138.1237.8736.21
2728.6126.8132.5333.0333.3631.8837.0929.0227.1231.2931.7130.33
8117.9522.1125.3227.1726.2529.8130.0118.6119.2823.9725.2324.40
+ +where $|\cdot|$ denotes absolute value and $\mathbf{A}$ is a sensing matrix composed by Discrete Fourier transform and bipolar (or uniform) random masks; See more details in [35]. The experiments are conducted on 2 datasets: Unnatural-6 and Natural-6 sets with 6 images each [35]. For a fair com + +parison, measurement data are obtained from three bipolar masks. We consider two types of noise: AWGN and Poisson. The noise level for AWGN is measured by SNR, while Poisson noise is measured by $\alpha$ in noise $n\sim \mathcal{N}\left(0,\alpha^2 |\pmb {A}\pmb {x}|^2\right)$ (a large $\alpha$ indicates low SNR). The compared methods include + +![](images/cb671ccf0359d26630544e5ed307bf1e6fcb4bb13ce5e1aeb6cb2d331c16ddd3.jpg) +WF [7] + +![](images/8767874f397464054da9254f1bfd4b46ea098f95635e4043f3e4764019fc46d2.jpg) +prDeep [35] + +![](images/178f57f4f37838c18995772094b376271ab77ba541dee00f21c48bf3326749b0.jpg) +prGAMP [36] + +![](images/6dbe786c6d7814e29dc97cdbba3cd45efc51020d9cb5666776fc450fcb887795.jpg) +DIP [55] +Figure 5. Results of phase retrieval with bipolar masks and sample data with $\mathrm{SNR} = 15$ + +![](images/c2a5648c05e3f162ffed2110067e7bd485fb213fcf71f6bfe6b6d017456776d3.jpg) +BNN [39] + +![](images/1c8cbeb7357d7816302bb7aa4413ac170b943575ae3abf750a7a3e0e80bc8b69.jpg) +ASGLD + +![](images/e08c364cbb69f7ef6d614fafc60f4a944ab0c98782e0996af022e9a5bb7dbb8b.jpg) +Truth + +Table 5. Comparison of ASGLD with classic SGLD on noisy measurements in terms of PSNR(dB). + +
TasksCS (σ = 10)MRI (σ = 25.5)Phase Retrieval
Set11BSD68GaussianRadialAWGN (in SNR)Poisson (α)
10%25%40%10%25%40%1D2D101520927
SGLD25.3028.5930.3124.1326.2828.0225.1126.2526.3027.6431.6633.2540.74
ASGLD26.0229.3531.1124.5627.1628.7526.0327.4027.3728.4232.4234.8242.04
+ +traditional non-learning Wirtinger flow (WF) method [7] and dictionary learning DOLPHIn [54]; two plug-and-play methods: prGAMP with BM3D denoiser [36] and supervised learned denoiser prDeep [35]; two self-supervised learning methods: DIP [55] and BNN [39]. We set the learning rate as 0.01. For both noiseless and noisy data, $K = 10000$ , $K_{0} = 2000$ . + +See Table 4 for the results. It can be seen that the ASGLD is the top performer among all compared methods. It also is the most robust to measurement noise. See Figure 5 for visual comparison of different methods of one sample. + +Table 6. Comparison of model size, no. of iterations and computing time of different methods to achieve reported results for MRI reconstruction with measurement noise ( $\sigma = 25.5$ ). + +
Methods# of params# of iterationselapsed timePSNR
BNN2M1 × 104≈520s25.70
SGLD2.2M1 × 104≈640s26.14
ASGLD2.2M0.3 × 104≈190s26.42
+ +# 4.3. Ablation study + +In this study, we would like to see how much advantage on performance and efficiency of the proposed ASGLD over plain SGLD. The experiments are conducted on both applications. See Table 5 for the ablation study on the performance, and Table 6 for the study on the efficiency. + +It can be seen from Table 5 that, thanks for our proposed effective restricted sampling strategy, in all three experiments, the proposed ASGLD outperformed the same implementation but with SGLD by a large margin. For computational efficiency, ASGLD is about 3 times faster than the one with SGLD with better result, the same for BNN. In addition, it can be seen from Figure 6 that the proposed ASGLD is also very stable during the training. + +Limitation. The proposed method aims at training an NN for + +![](images/1131ea893edb4d1deed310d5d4340c8ab34233ee3c768ec99bd141593e09f319.jpg) +Figure 6. PSNR curves of ASGLD and SGLD w and w/o average over iterations on MRI (Gaussian noise, $\sigma = 25.5$ ). + +solving inverse problem without accessing any truth images. As an unsupervised solution, it cannot have a pre-trained model to process new coming data, as supervised methods can. Such an issue limits its applicability to certain applications which require real-time processing of image data. + +# 5. Conclusion + +This paper presents a self-supervised deep learning method for general image restoration and reconstruction problems, which is built on an adaptive stochastic gradient Langevin dynamics for effective MCMC sampling used for integral calculation. The proposed method is universal and has its advantages over existing unsupervised learning methods in terms of both reconstruction quality and computational efficiency. 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This paper presents a simple but effective regularization technique for improving GAN-based image-to-image translation. To generate images with realistic local semantics and structures, we propose an auxiliary self-supervision loss that enforces point-wise consistency of the overlapping region between a pair of patches cropped from a single real image during training the discriminator of a GAN. Our experiment shows that the proposed dense consistency regularization improves performance substantially on various image-to-image translation scenarios. It also leads to extra performance gains through the combination with instance-level regularization methods. Furthermore, we verify that the proposed model captures domain-specific characteristics more effectively with only a small fraction of training data. + +# 1. Introduction + +Generative adversarial network (GAN) [8] is an innovative framework for generative modeling, i.e., generating images that follow the same distribution as training data. The performance of the state-of-the-art GAN models depends highly on the quality of discriminators, which distinguish real images from fake ones while maintaining the balance with matching generators for the joint optimization. Since discriminators are prone to overfit the training dataset and often lead to the mode collapse of generated outputs, learning robust discriminators is critical to accomplish high-performance generators. + +To this end, self-supervised learning methods have been actively used for regularizing discriminators in the GAN + +![](images/e2583797bfdaf2af6e212aaf6763a82479756e592e907c121bdb758771faa2f8.jpg) +Figure 1. Qualitative comparison of output feature maps given by three different variation of the baseline mode, CUT [26], for an example in the Horse $\rightarrow$ Zebra dataset. The activations from DCR highlight foreground accurately while suppressing background effectively, which helps the image-to-image translation task focused more on target objects. + +framework [15, 16, 32, 34]. The goal of the regularization is to obtain robust representations of images for better discrimination of real and fake images [17]. The existing methods often rely on contrastive learning in an instance-level [3, 15, 16, 32], where a pair of augmented instances from an image are encouraged to have consistent features with respect to predefined global transforms while negative images are optionally considered to achieve better representation learning in discriminators. However, the regularization based only on such global representations may be limited to imposing loose constraints on discriminators and may allow generators to deceive the discriminator despite local structural or semantic inconsistency in output images. + +To alleviate the drawback, we propose a dense consistency regularization (DCR) approach applicable to the discriminator of a GAN. DCR provides stronger constraints to the learned representations given by discriminators through their point-wise consistency between a pair of patches cropped from the same image. Our work is motivated by the hypothesis that image generation requires pixel-level prediction [14] and a dense regularization of representations is an effective way to improve the supervision quality of a discriminator. The goal of the proposed dense consistency regularization is to generate images with both semantic con + +![](images/71cbf44dd9684ec0c7a3fb42f2a44bc8cc12f59f31890fac30bedb644302d98c.jpg) +Figure 2. Illustration of the proposed DCR method. When updating a discriminator, two augmented views are randomly cropped from a single real image. The two views are then processed by the intermediate feature extraction network $D_0$ , where $D_0$ is the first part of the discriminator while the remaining part is denoted by $D_1$ . Note that $D_1$ is not used in our work. The DCR module is applied to one of the branches, and a stop-gradient operation is employed in the other one. The loss $\mathcal{L}_{\mathrm{DCR}}$ is given by the similarity between the representations of two branches over the overlapping region $\Omega$ while $\tilde{\Omega}$ denotes the binary map indicating matching pairs of pixels. + +sistency and visual harmony in spatial neighborhoods. This is achieved if the discriminator focuses on important features or regions for image-to-image translation instead of the background, as shown in Figure 1. Our main idea is illustrated in Figure 2, where the dense correspondence regularization is imposed on the intermediate layers of the discriminator. + +We evaluate the proposed approach on various image-to-image translation scenarios such as CycleGAN [37], MUNIT [13], StarGANv2 [5], CUT [26], and FSeSim [36]. According to our experiments on the Horse $\rightarrow$ Zebra, Winter $\rightarrow$ Summer, Cat $\rightarrow$ Dog, and AFHQ datasets, the models with DCR consistently improve the FID scores compared to the models without DCR, which confirms that DCR indeed captures domain-specific characteristics effectively. For example, we manage to improve the FID score of CycleGAN [37] from 78.2 to 54.4, and that of MUNIT [13] from 102.3 to 59.9 on the Horse $\rightarrow$ Zebra dataset. Moreover, we also find out that DCR is particularly powerful with a small number of training data. Specifically, StarGANv2 [5] with DCR achieves the best FID score of 17.15 even if only $10\%$ of a specific domain in the AFHQ dataset is used for training, while the best FID scores of StarGANv2 [5] are 22.63 and 17.86 with $10\%$ and $100\%$ of the examples in AFHQ. + +We summarize our contributions as follows: + +- We introduce a novel dense consistency regularization technique, referred to as DCR, for the discriminators of GANs, which facilitates high-fidelity image generation and translation. + +- We show that DCR is effective to maintain structural and semantic consistency in the spatial neighborhoods of generated images. +- We empirically demonstrate that DCR achieves outstanding performance in various image-to-image translation scenarios. + +In the rest of this paper, we first discuss closely related works to our approach in Section 2, and present our algorithm and implementation details in Section 3. Section 4 demonstrates the results from our experiments with their analysis, and Section 5 concludes this paper. + +# 2. Related Work + +This section reviews existing regularization methods imposed on the discriminator of GANs and presents generic dense representation learning techniques applicable to discriminator regularization. We also discuss existing approaches in image-to-image translation, which is the primary target task of the proposed regularizer. + +# 2.1. Regularization for Discriminator + +GAN [8] is a well-known generative model particularly effective for image generation and translation tasks. The generator is trained to produce realistic images deceiving the discriminator while the discriminator learns to distinguish between fake images obtained from the generator and real ones sampled from training data. The great advance in network architectures of GANs capacitates the generation + +of more realistic images, but GANs still suffer from inherent stability issues in training, especially high sensitivity to hyperparameters originated from the non-convexity of the min-max objective function. + +The issue has been addressed in various studies, which include integration of the normalization method [24] or regularization via gradient penalization [10, 19, 29]. The regularization for discriminators turns out to stabilize training and improve performance [15, 16, 32, 34, 35]. We hypothesize that the main reason for the improvement is good representation in the discriminator side, which is crucial to distinguish real images from fake ones and eventually increases the quality of the generator. In particular, [34] introduces a simple consistency regularization (CR) to discriminators, and obtains substantially enhanced quality of generated images with reduced computational cost compared to gradient-based regularization techniques [10, 19, 29]. + +To learn more informative representations by optimizing discriminators, self-supervised learning approaches have been employed [3, 15, 16, 32]. For instance, [3] incorporates the auxiliary rotation loss for self-supervision, by which both the real and generated images are classified into one of the relevant rotation angles, $\{0^{\circ}, 90^{\circ}, 180^{\circ}, 270^{\circ}\}$ . Contrad [15] distinguishes two independent real images as well as a pair of real and fake images to mitigate the overfitting problem in discriminators while learning more powerful representations in them. The promising results from these works imply that the learned representations in a discriminator play a crucial role in improving the performance of GANs in practice. + +# 2.2. Dense Representation Learning + +Image-level prediction tasks, e.g., image classification, often achieve significant performance improvement by incorporating self-supervised visual representation learning via instance discrimination, which maximizes the similarity between two augmented images while optionally decreasing the similarity between different ones [2, 4, 9, 11, 33]. However, such instance-level contrastive learning methods may be suboptimal as a pretext task due to the lack of their spatial sensitivity. + +To address the limitation, dense self-supervised learning approaches have been proposed, where they take into account the pixel-level similarity between two augmented images [27, 28, 30, 31]. View-Agnostic Dense Representation (VAdeR) [27] adopts the pretext task that pulls the features at the overlapping locations of two different views cropped from a single image, while making the features from the non-overlapping regions apart from each other. However, VAdeR relies heavily on a large number of negative pairs and consequently incurs high computational cost. On the other hand, [31] proposes a pixel-to-propagation consistency (PixPro) regularization without negative pairs, which + +encourages the pixels in the spatial neighborhood to have similar representations. Spatially Consistent Representation Learning (SCRL) [28] enforces the consistency of the features corresponding to the same objects that are identified in two different views of a single image. + +# 2.3. Image-to-Image Translation + +Unpaired image-to-image translation techniques are divided into two categories depending on the use of cycle consistency loss, which facilitates learning an inverse mapping from the target domain to the source domain [18, 37]. The loss is defined in either the image domain [5, 18, 21, 37] or the latent space [13, 22, 23] to preserve the key attributes between input and output images. Although the learned mapping with the cycle consistency is reliable enough to provide high-quality outputs in image-to-image translation, the translated images may contain too much information of the input images for its effective reconstruction, resulting in undesirable outputs. + +To address this issue, distance-based loss [1] and geometric consistency [7] have been adopted for the translation from the source to the target without using its inverse mapping. The contrastive learning framework is adopted to preserve the content of the original image in the translated image [26], where a patch-wise contrastive loss is proposed to maintain the correspondence between the source and target images. A structure consistency loss is employed to enforce the self-similarity between the source and target images [36]. CUT [26] and F/LSeSim [36] deliver better results than the algorithms with the cycle consistency loss by taking advantage of cross-domain similarity functions. However, these algorithms focus only on the comparison between the original and translated images with no consideration about the representations in their discriminators. Since we believe that the discriminator representation reflecting the target domain distribution accurately is a crucial component to generate high-fidelity images in imaged-to-image translation, we propose a dense consistency regularization strategy via self-supervised learning. + +# 3. Dense Consistency Regularization (DCR) + +This section presents our main algorithm, especially the technical details of dense consistency regularization module. We also discuss several implementation issues of the proposed approach. + +# 3.1. Motivation + +The role of the discriminator in GANs is to distinguish real data from fake ones created by the generator and provide the generator with the proper feedback for producing realistic images. Contrary to discriminative tasks such as image classification, image generation requires pixel-level predictions in its output. Hence, the discriminator should + +be able to capture the local context of an output image for the high-fidelity to the target domain in the image-to-image translation task. Spatial sensitivity in the representation learning has been introduced by [31], which measures the consistency of spatially overlapping pixels for more discriminative learning around object boundaries. To make the discriminator have spatial sensitivity, we design a task for the local feature similarity measure and discuss its details in the rest of this section. To obtain mid-level local features, we decompose a discriminator $D$ into two subnetworks denoted by $D_0$ and $D_{1}$ such that + +$$ +D = D _ {1} \circ D _ {0}. \tag {1} +$$ + +As in most visual representation learning, we start by sampling two augmented views $x_{1}$ and $x_{2}$ from an image $x$ . The two views are resized to a fixed resolution (e.g., $128 \times 128$ ) and passed through the shared feature extractor $D_{0}$ . + +To verify our hypothesis, we visualize the output feature map of the discriminator of CUT [26] in Figure 1, where DCR focuses on the foreground area more effectively than vanilla CUT [26] and CUT with CR [34] while suppressing the activations in the background region. This result implies that DCR is helpful to improve the quality of generated images, especially around object boundaries. + +# 3.2. DCR Module + +DCR is motivated by SimSiam [4], which utilizes only positive pairs for contrastive learning and employs the stop-gradient technique to prevent collapse to the trivial solution. Note that, since image generation task needs to learn the distribution of a target domain, sampling negative examples from the target domain dataset is not straightforward. One can introduce an additional dataset to obtain negative examples, but the selection of the negative dataset is tricky because it requires sophisticated and comprehensive supervision to check various attributes of the dataset. + +The proposed DCR module, denoted by $R(\cdot)$ , consists of two $1 \times 1$ convolutional layers and a LeakyReLU activation between the convolutions. The output feature map size of the DCR module is identical to that of its input (e.g., $W \times H \times C$ ) to maintain the spatial information. Suppose that we have the intermediate representations of two augmented images as $r_1 := R(D_0(x_1))$ and $z_2 := D_0(x_2)$ . Given the overlapping region $\Omega$ of two views $x_1$ and $x_2$ , we define the negative cosine similarity of their corresponding features, which is given by + +$$ +\operatorname {s i m} _ {\mathrm {n c}} \left(r _ {1}, z _ {2}; \tilde {\Omega}\right) \equiv \sum_ {\left\{\left(i, j\right) \mid \tilde {\Omega} (i, j) = 1 \right\}} - \frac {r _ {1} [ i ]}{\| r _ {1} [ i ] \| _ {2}} \cdot \frac {z _ {2} [ j ]}{\| z _ {2} [ j ] \| _ {2}}, \tag {2} +$$ + +where $\tilde{\Omega}$ is the binary map representing feature correspondences, $[\cdot ]$ is used to specify the index corresponding to a + +particular location in a feature map, and $\| \cdot \| _2$ indicates $\ell_2$ -norm. Following [4], the DCR loss is given by + +$$ +\mathcal {L} _ {\mathrm {D C R}} = \frac {1}{2} \operatorname {s i m} _ {\mathrm {n c}} \left(r _ {1}, F _ {\mathrm {s g}} \left(z _ {2}\right)\right) + \frac {1}{2} \operatorname {s i m} _ {\mathrm {n c}} \left(r _ {2}, F _ {\mathrm {s g}} \left(z _ {1}\right)\right), \tag {3} +$$ + +where $F_{\mathrm{sg}}(\cdot)$ is a stop-gradient layer1. + +Since we expect the discriminator to extract more useful information from images in the target domain, we apply DCR only to real images. Although the application of DCR to generated images would be helpful for learning better representations in the discriminator, we believe that this regularization is not necessarily helpful for the better simulation of the target domain distribution(Refer to Section C in the supplementary). + +# 3.3. Objective of Discriminator + +The objective of the discriminator in the standard GAN is given by + +$$ +\mathcal {L} _ {\mathrm {d i s c}} = - \mathbb {E} _ {x, y} [ \log D _ {y} (x) ] - \mathbb {E} _ {x, y} [ \log (1 - D _ {y} (G (x))) ], +$$ + +where $D_y(\cdot)$ denotes the output of the discriminator corresponding to domain $y$ . The proposed approach jointly minimizes the standard GAN loss and the DCR loss, which is given by + +$$ +\mathcal {L} _ {\mathrm {D}} = \mathcal {L} _ {\text {d i s c}} + \lambda \cdot \mathcal {L} _ {\mathrm {D C R}}, \tag {4} +$$ + +where $\lambda$ is a hyperparameter set to 1 in our experiments. + +# 3.4. Implementation Details + +This subsection discusses a couple of crucial design issues of our approach. We provide the further details about our implementation in Section A of the supplementary file. + +Location of dense representation We impose DCR to the output of the final residual block or the input of the final convolution layer in the discriminator. Since the performance gain with the proposed DCR depends heavily on the quality of dense representations, it is important to identify the proper levels of representations for the regularization. We conduct ablation studies by varying the locations for DCR within the network. More details about this issue are discussed in Section 4.5. + +DCR loss computation and positive pair selection We measure the DCR loss, $\mathcal{L}_{\mathrm{DCR}}$ , in (3) based on two local features $D_0(x_1)$ and $D_0(x_2)$ for the overlapping region. To compute $\mathrm{sim}_{\mathrm{nc}}(\cdot ,\cdot)$ , we adopt the approach described in PixPro [31]. The position and scale of each pixel in the two feature maps are first estimated and transformed to the original image space. Then, we compute the distances between all pairs of positions in the feature map and normalize the distances considering the estimated scales. + +
Method MetricHorse → ZebraWinter → SummerCat → Dog (AFHQ)AFHQ FID↓
FID↓D&C ↑FID↓D&C↑FID↓D&C↑
CycleGAN [37]-78.2±1.00.56±0.14 / 0.73±0.1280.9±4.60.88±0.03 / 0.82±0.0685.90.54 / 0.48-
DCR54.4±3.30.72±0.01 / 0.89±0.0074.6±1.70.91±0.00 / 0.82±0.0671.00.55 / 0.46-
CUT [26]-43.2±2.30.73±0.06 / 0.87±0.0277.8±0.50.56±0.12 / 0.51±0.2476.20.38 / 0.41-
DCR34.0±0.40.96±0.10 / 0.90±0.073.2±0.50.89±0.15 / 0.65±0.2468.40.54 / 0.48-
FSeSim [36]45.2±4.80.75±0.14 / 0.83±0.0486.5±4.00.66±0.05 / 0.81±0.0287.30.20 / 0.07-
DCR36.7±1.40.89±0.02 / 0.89±0.0274.5±0.20.83±0.00 / 0.86±0.0273.50.34 / 0.10-
MUNIT [13]-102.3±4.30.29±0.11 / 0.43±0.0997.0±0.50.12±0.03 / 0.16±0.06104.40.21 / 0.3261.6
DCR59.9±0.10.28±0.04 / 0.44±0.0791.2±0.40.19±0.06 / 0.31±0.0188.20.33 / 0.4256.0
StarGANv2 [5]-19.71.38 / 0.6842.20.23 / 0.3944.20.93 / 0.6918.1 (16.2*)
DCR19.41.65 / 0.7339.70.27 / 0.3833.00.98 / 0.6617.4
DRIT++ [22]-88.50.21 / 0.3593.10.24 / 0.37110.90.25 / 0.19-
DCR67.10.29 / 0.4482.60.28 / 0.44107.80.19 / 0.20-
+ +Table 1. Quantitative comparison in terms of FID scores and D&C for various image-to-image translation models on the Horse → Zebra, Winter → Summer, Cat → Dog, and AFHQ datasets. Standard deviations are calculated from two runs. For the StarGAN v2, due to the inherent uncertainty of the model using the random latent codes, we present the average performance from our reproductions while the reported score in [5] is 16.2 on the AFHQ dataset. + +PixPro [31] proposes to select positive pairs based on the fixed threshold for the distance in the whole batches. However, DCR can be applied to any locations in the dense representation map, we should consider feature map size as an additional factor. Hence, the positive pairs for the feature correspondence are identified by $\tilde{\Omega}$ , whose elements are given values as follows: + +$$ +\tilde {\Omega} (i, j) = \left\{ \begin{array}{l l} 1, & \text {i f} \operatorname {d i s t} (i, j) \leq \tau \cdot s _ {f} \\ 0, & \text {o t h e r w i s e} \end{array} , \right. \tag {5} +$$ + +where $\mathrm{dist}(\cdot, \cdot)$ denotes the normalized distance between two locations within an image, and $\tau$ and $s_f$ indicate the hyperparameters for the threshold value and the spatial resolution of the feature map, respectively. We set $\tau$ to 0.5 in our experiment and present its impact on the accuracy in Section 4.5. + +# 4. Experiments + +We verify the effectiveness of DCR in three different aspects: (a) image-to-image translation performance with one-sided and two-sided translation models, (b) benefit of the proposed regularizer with limited availability of training data, and (c) applicability to unconditional GANs. We also conduct a few ablation studies to show the robustness of the proposed approach. + +# 4.1. Experiment Setup + +We analyze our method mainly on image-to-image translation since the verification of the desired properties in an output image is more straightforward in conditional GAN models. The image-to-image translation task typically involves two distinct problems—shape deformations and texture changes, we evaluate the performance of the proposed + +approach in both aspects. Since DCR is a generic consistency regularization technique for the discriminator of a GAN, we test its applicability to unconditional GAN models. Note that an unconditional GAN model maps the predefined latent distribution to the distribution in the target domain. Hence, we consider an unconditional GAN task as a special case of a conditional GAN problem with a latent source domain while the source domain of the image-to-image translation is defined by the images in the corresponding training dataset. + +Tested models Existing unpaired image-to-image translation approaches belong to either the two-sided or one-sided framework. The two-sided framework exploits both forward and backward mappings between the source and target domains. We apply DCR to CycleGAN [37], which is one of the most representative works in the two-sided framework. We also adopt MUNIT [13] and StarGANv2 [5], which employ the cycle consistency loss at the feature level and the pixel level, respectively. In addition, we apply DCR to DRIT++ [22], which utilizes disentangled representations for image-to-image translation. As the one-sided baseline models, we employ CUT [26] based on the contrastive patch relation and FSeSim [36] based on the structure similarity. For unconditional GANs, we employ SNDCGAN [24] as the baseline and also augment ContraD [15], a recently proposed contrastive regularization method at the instance level, to achieve additional performance boosting. + +Datasets and metrics The datasets for image-to-image translation tasks need to contain images with geometric deformations or texture changes across domains. We carry out extensive experiments to verify the effectiveness of DCR on three commonly used datasets for the image-to-image translation. The tasks related to texture changes are evaluated + +![](images/1a5541da30e6cd997e86b4645f9f80de4bbb81eed9765cb0c81d3cfc8d2db175.jpg) +Figure 3. Qualitative comparison of image-to-image translation results on the Horse $\rightarrow$ Zebra, Winter $\rightarrow$ Summer, and Cat $\rightarrow$ Dog datasets. CycleGAN [37], CUT [26], and FSeSim [36] are employed as the baseline models and the proposed DCR is integrated into those models. The proposed DCR can add the appropriate patterns of the zebra on the horse and more realistic images compared to the baseline algorithms. + +on the Horse $\rightarrow$ Zebra and the Winter $\rightarrow$ Summer dataset. The Cat $\rightarrow$ Dog dataset from AFHQ is employed to test the shape deformations and geometric transformations. For the image-to-image translation with multiple domains, we also use the AFHQ dataset [5], high-quality animal faces with large intra- and inter-class variations. For unconditional GANs, we utilize CIFAR-10 [20], which contains $60K\ 32\times 32$ images with 10 labels, $50K$ for training and $10K$ for testing. We measure a Frechet Inception Distance (FID) [12] as a quantitative metric to evaluate generation quality and how accurate the target distribution is. We also report the density and coverage (D&C) [25], which simultaneously calculate diversity and fidelity of generated results. + +# 4.2. DCR for Image-to-Image Translation + +For the evaluation of DCR with various existing image-to-image translation models, we use the official implementation of each model and incorporate DCR into it. We employ Horse $\rightarrow$ Zebra, Winte $\rightarrow$ Summer, and Cat $\rightarrow$ Dog (AFHQ) to evaluate the models for a single domain. Since StarGANv2 [5] and MUNIT [13] can handle multiple domains, they are also tested on the AFHQ dataset. We trained three MUNIT [13] models for each direction and computed the average of FIDs followed by [5]. + +Table 1 presents the comprehensive results and demonstrates consistent improvements over all the baseline models on the tested datasets. For StarGANv2 [5] using AFHQ dataset, we would like to note that we reported the average of the best FID scores from 3 trials. There are some gaps + +between the reproduced results and the reported ones in the original paper [5]. This may come from the underlying randomness due to the use of random vectors for latent guided translation. Therefore, we compare the performance using the reproduced results. + +It is noteworthy that significantly improved FID scores are achieved by the proposed DCR in the same setup with the baseline models without modifying the hyperparameters. The DCR loss turns out to be effective for shape deformations, which is validated by consistently improved results on the Cat $\rightarrow$ Dog dataset in terms of FID. As described in Section 3.4, we apply DCR to the input of the last convolution layer, which is more advantageous for shape deformation tasks according to our analysis presented in Section 4.5. We also employ the recently introduced metric, D&C [25], and confirm consistently improved performance compared to the base algorithms except few exceptions. + +Figure 3 illustrates uni-modal image-to-image translation results using the baseline models, CycleGAN [37], CUT [26], and FSeSim [36], and the ones with the DCR integration into these methods. It is worth mentioning that we observe more realistic local semantics and structures in the generated images with DCR compared to the baseline models. In the case of the Horse $\rightarrow$ Zebra dataset, CUT [26] fails to provide an image with the desired zebra style while the integration of DCR into CUT [26] is effective to generate a more zebra-like image from the given horse image. Overall, DCR consistently provides better results for various datasets compared to the baseline models. Refer to + +
StarGANv2 [5]StarGANv2 [5] + DCR
10 %22.63 ± 3.7017.15 ± 0.89
30 %19.08 ± 4.8816.88 ± 1.17
100 %17.86 ± 0.5416.72 ± 0.59
+ +Section B in the supplementary document for more qualitative results from uni-modal and multi-modal image-to-image translation models. + +# 4.3. DCR with Few Target Data + +Although we achieved the FID improvement by applying DCR to various existing models, we wonder whether the proposed DCR effectively reflects the local context of target domain even under few data scenarios. To investigate this, we randomly reduce the proportion of real data from a specific domain in the training set to $30\%$ , and $10\%$ . We perform experiments with the StarGANv2 [5] and the AFHQ dataset, consisting of dog, cat, and wild domains, as a baseline. We only reduce the wild domain, which has various intra-variations (fox, cheetah, lion, and tiger). For a fair comparison, we report the average performance across three trials. Quantitative and qualitative results are shown in Table 2 and Figure 4, respectively. + +We observe that the FID score variance of StargANv2 [5] is relatively large under few data scenarios. Since data were randomly selected, the FID varied depending on the similarity of the selected data to the test data. However, the proposed DCR shows less FID variance score than baseline. This implies that the proposed method effectively captures the local context of the target domain. + +Figure 4 illustrates the reference-guided image-to-image translation results for the AFHQ dataset, where we only used $10\%$ of the data for the wild domain, while we utilized the overall data for other domains. It is worth mentioning that StarGAN v2 [5] with DCR provides significantly better translated images compared to the baseline. In particular, due to the small amount of data in the wild domain, the transformed images from the cat and dog images cannot reflect the style of the cheetah image and became lion images. However, the proposed DCR properly encoded the style from the cheetah image, and translated into the appropriate cheetah images. In addition, the proposed DCR encourages the network to generate the translated images while maintaining the geometry of the source images as well. These results clearly confirm that the DCR is a pow + +Table 2. Quantitative comparison of the best FID score for the effect of DCR with few target data. We randomly selected $10\%$ , $30\%$ , and $100\%$ of the wild domain of AFHQ dataset. The best FID score is the average of the best FID score for cat-to-wild translation and the best FID score for dog-to-wild translation. We report the mean and standard deviation of best FIDs across 3 trials. + +
MethodCIFAR-10
SNDCGAN [24]97.4
SNDCGAN+ContraD [15]10.9
SNDCGAN+Our8.6
SNDCGAN+ContraD+Our7.7
+ +Table 3. Quantitative comparison of the best FID score on unconditional image generation. + +erful regularization for efficient training of small dataset as well as for translation quality when combined with existing algorithms for image-to-image translation task. + +# 4.4. DCR with Unconditional GANs + +Since our DCR regularizes consistency of the discriminator, it is natural to study for unconditional GAN. We take SNDCGAN [24] as our baseline model and compare with a recent ContraD [15] which is instance-level contrastive learning based regularization method on CIFAR10 dataset for simplicity. + +The motivation of our work is the hypothesis that image generation requires pixel-level prediction and the dense regularization of representations is appropriate. Table 3 shows the quantitative results that DCR more improves FID than instance-level method. Indeed, the results show the possibility that dense and instance-level consistency regularization technique can boost the each others performance by fusing ContraD and DCR. However, the role of instance-level and dense-level consistency regularization is still open area and we believe it deserves further study. + +# 4.5. Ablation Study + +To better understand how the hyper-parameters of proposed method affect performance, we conduct an ablation study. We perform experiments on CycleGAN [37] model with Horse $\rightarrow$ Zebra and Cat $\rightarrow$ Dog(ImageNet [6]) dataset. + +Where to regularize One of important choices in our algorithm is where to apply the proposed regularization. We conduct experiments on two types of tasks that require shape deformation task and texture translation with preservation of the shape. We measure a FID when we integrate DCR to different representation of CycleGAN's discriminator. The results are shown in Table 4. + +The quantitative result shows proposed DCR improves the performance wherever applied to any representations. However improvement gap shows different aspect of behaviour at two types of dataset. The texture translation task shows better performance when representation is closer to pixel-level. On the other hand, shape deformation task provides better performance with the higher level representation, because it requires more semantic information compared to other tasks. In order to perform on overall tasks, + +![](images/82f06c78a1769569ca5271b88384c7d56fccdcaade8732f6847f6adee73c14eb.jpg) +Figure 4. Qualitative comparison of reference guided samples on StarGANv2 and ours. Dashed line at the right corner of the image shows that the proposed DCR synthesizes more similar structure of the source image than baseline. + +
Horse → ZebraCat → Dog*
CycleGAN [37]77.286.5
CycleGAN + DCR (layer2)49.270.5
CycleGAN + DCR (layer3)51.459.9
CycleGAN + DCR (layer4)51.157.8
+ +Table 4. Ablation study on the location of dense representation for the proposed DCR method. The layer number indicates which output of this layer is used as a dense representation. The asterisk (*) denotes the experiment using the examples in ImageNet. + +
τ00.30.50.70.9
FID77.256.751.151.457.9
+ +Table 5. Ablation study on distance threshold $\tau$ for the proposed DCR method. We conducted the ablation study on CycleGAN [37] model with Horse → Zebra dataset. $\tau = 0$ indicates the baseline model without the proposed DCR. + +we select the representation either the output of final residual block or the input of final convolution layer. + +How to identify positive pairs One of the major hyperparameters in DCR is the distance threshold $\tau$ in (5) to identify the positive pairs for the feature correspondence $\tilde{\Omega}$ . To choose the optimal threshold value $\tau$ , we experimented with various values $\tau \in \{0.3, 0.5, 0.7, 0.9\}$ on CycleGAN [37] model with Horse→Zebra dataset. Table 5 reports the quantitative comparison of the performance at the various distance threshold $\tau$ . + +The results in Table 5 show a consistent improvement + +over the baseline model $(\tau = 0)$ . This verifies the effectiveness of the proposed DCR in providing better translated images. As shown in Table. 5, we achieve the best result when we set the distance threshold $\tau$ to 0.5. Therefore, the distance threshold $\tau$ is set to 0.5 in all experiments. + +The further investigation to analyze the performance gain by the proposed DCR can be found in Supplementary Section C. We conducted the ablation studies to understand the effect of stop-gradient and the reason we apply the DCR only to the cropped regions of generated images, not to the entire images or real images. + +# 5. Conclusion + +We presented a novel regularization technique, referred to as dense consistency regularization (DCR). The proposed approach enforces the consistency between the representations of the overlapping regions in two different views from the same image. DCR is suitable for the tasks that require dense prediction and can be incorporated into various existing conditional and unconditional GAN models. According to our experiments for image-to-image translation and unconditional image generation tasks, DCR achieved outstanding performance consistently. Moreover, DCR captures a local context in the target domain effectively with only a small fraction of data and it also leads to extra performance gains through the combination with instance-level regularization methods. Refer to Section E of the supplementary document for discussions about potential negative societal impacts and limitation. + +# References + +[1] Sagie Benaim and Lior Wolf. One-sided unsupervised domain mapping. Advances in Neural Information Processing Systems, 30, 2017. 3 +[2] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. 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Existing learning-based methods for keypoint detection rely on standard translation-equivariant CNNs but often fail to detect reliable keypoints against geometric variations. To learn to detect robust oriented keypoints, we introduce a self-supervised learning framework using rotation-equivariant CNNs. We propose a dense orientation alignment loss by an image pair generated by synthetic transformations for training a histogram-based orientation map. Our method outperforms the previous methods on an image matching benchmark and a camera pose estimation benchmark. + +# 1. Introduction + +Detecting robust keypoints is an integral part of many computer vision tasks, such as image matching [21], visual localization [28, 54, 55], SLAM [13, 14, 39], and 3D reconstruction [1, 19, 57, 76]. The robust keypoints, in principle, are consistently localizable, being invariant to photometric/geometric variations of an image induced by viewpoint/illumination changes, and a keypoint is typically assigned with its characteristic orientation/scale as a geometric feature, which plays an important role for keypoint description [14, 15, 27, 37, 41, 45, 51, 62, 63, 70] or matching [6, 53, 71, 73], as shown in Fig. 1. As rotation frequently occurs for patterns of interests in real-world images, the keypoints and their geometric features are required to be consistent w.r.t rotation of the image in particular. + +The early methods have detected keypoints with their characteristic orientation/scale using a hand-crafted filter on a shallow gradient-based feature map. For example, SIFT [27] detects the keypoints by finding local extrema in difference-of-Gaussian (DoG) features on a scale space and obtains a dominant orientation from gradient histograms. While such a technique has proven effective for shallow + +![](images/a7ba5e620983f9bb509242766a4b95d45905ef4c9bf211c5a05253a64215c79b.jpg) +(a) Key.Net +Figure 1. Visualization of the predicted matches to compare the existing keypoint detector Key.Net [3] (left) with our oriented keypoint detector (right). We draw the correct matches (green) and the incorrect matches (red) using the ground-truth homography. We extract 300 keypoints and use HardNet [37] descriptor for matching. The arrows of the keypoints in the right denote the estimated orientations which are used for filtering outliers. + +![](images/b7b7167f0a433f646f1b906ed5f6edd10148c12347f2de28dfe09739938f7f5d.jpg) +(b) ours + +gradient-based feature maps, it cannot be applied to deep feature maps from standard networks, where rotation or scaling induces unpredictable variations of features. Recent methods [3, 41, 58, 70], thus, rely on learning from data. They typically train a convolutional neural network (CNN) for keypoint detection and/or description by regressing orientation and scale. Some [3,41] adopt self-supervised learning through synthetic transformation, while others [58, 70] train the networks through strong supervision by homography or SfM. All these approaches, however, often fail to detect reliable keypoints against geometric variations; they learn invariance or equivariance by relying on training with data augmentation, which does not provide a sufficient level for keypoint detection. + +In this work, we propose a self-supervised equivariant learning method for oriented keypoint detection. Recent studies [10, 11, 29, 68, 69, 75] introduce different equivariant neural networks that embed an explicit structure for equivariant learning by design. The group-equivariant CNNs + +on a cyclic group have the advantages of explicitly encoding the enriched orientation information and reducing the number of model parameters through weight sharing compared to the conventional CNNs. We propose an orientation alignment loss to estimate a characteristic orientation to the keypoint using a histogram-based representation. The histogram-based representation provides richer information than the regression methods [41, 70, 72] by predicting multiple candidates for the orientations. To train the invariant keypoint detector, we utilize a window-based loss [3] to satisfy the geometric consistency with anchor points diverse across the image. We generate the synthetic image pairs by a random in-plane rotation to create diverse examples and reduce the annotation cost. In addition, we generate a scale-space representation in the networks and use multiscale inference to consider scale-invariance approximately. + +We evaluate the rotation-invariant keypoint detection and the rotation-equivariant orientation estimation compared under synthetic rotations with the existing models [27, 41, 51]. We validate the effectiveness of our keypoint detector compared to the handcrafted methods [27, 51] and the learning-based methods [3, 14, 15, 45] in an image matching benchmark [2] using a repeatability score and matching accuracy. The estimated orientations improve the image matching accuracy with an outlier filtering in HPatches [2]. Furthermore, we show the transferability to a more complex task by evaluating 6 DoF pose estimation in IMC2021 [21]. We demonstrate ablation experiments and visualizations to verify the effectiveness of our model. + +The contributions of our paper are three-fold: + +- We propose a self-supervised framework for learning to detect rotation-invariant keypoints using a rotation-equivariant representation. +- We propose a dense orientation alignment loss by aligning a pair of histogram tensors to train the characteristic orientations. +- We demonstrate the effectiveness of our oriented keypoint detector with extensive evaluations compared to existing keypoint detection methods on standard image matching benchmarks. + +# 2. Related work + +Keypoint detection for image matching. Traditional keypoint detectors rely on carefully designed handcrafted filters. Harris [18] and Hessian [5] use first and second order image derivatives to find corners or blobs in images. Those detectors are extended by handling multi-scale and affine transformations [32, 34]. SIFT [27] detect keypoints by finding local extrema from the DoG features, and SURF [4] further boost up speed by using the Haar filters. ORB [51] propose a oriented FAST [50] detector. Recently, learning-based methods [14, 15, 40, 41, 45, 56, 58, 61, 65, 66, 70] + +use a CNN-based response map to train a keypoint detector. Key.Net [3] utilize the benefit of both representation of the handcrafted and the learning-based to improve the performance in terms of repeatability. Also, some methods [8,24,35,36,47,48,64] find correspondences in a correlation tensor using a pair of dense features without a separate keypoint detector, but constructing the correlation tensor requires high memory consumption, so it compromises the pixel accuracy of correspondences. Contrary to the learning methods that use a conventional translation-equivariant CNN, we utilize a rotation-equivariant CNN to obtain consistent 2D keypoints. Our model can significantly reduce the number of model parameters by weight sharing in group convolution. + +Local orientation estimation. SIFT [27] use a histogram of image gradients to estimate the local orientation. ORB [51] propose an efficient way to measure corner orientation using intensity centroid [49]. Learning-based methods learn the orientation implicitly through a descriptor similarity loss [16, 38, 58, 72] or explicitly through an orientation regression loss [41, 70], and they use the orientation as one of the affine parameters in patch sampling using STNs [20]. While [41, 70] learns sparse orientations of keypoints using the regression loss that minimizes the distance of angles, our model learns dense orientations of all positions using the histogram alignment loss that matches the shifted orientation histograms. Compared to regression of [41, 70], our histogram output naturally facilitates the prediction of multiple orientations and the loss of histogram alignment with the rotation-equivariant representations allows more robust learning. A previous work [23] proposes the histogram alignment loss at the local patch-level, but we extend it to all the regions of an image. The orientations are verified through an outlier filtering for image matching. + +Equivariant representation learning. [30, 31, 59] propose an equivariant representation based on restricted Boltzmann machines (RBM) through tensor factorization. Since CNNs became popular, [10] proposes group equivariant convolutional networks using discrete isometric groups. [29, 75] propose resampling filters using interpolation to encode explicit orientations. [68, 69] use harmonics as filters to extract equivariant features from more diverse groups and continuous domains. [67] extend this group to the general $E(2)$ groups, and [60] propose scale-equivariant steerable networks. From an application point of view, [17] propose rotation-equivariant networks to solve the rotated object detection on the aerial images. [44] apply the equivariant CNN for registration of multimodal images. [43] disentangle the invariance group of illumination and viewpoint for training local descriptors. The most similar work, GIFT [26], use equivariant networks to obtain dense local descriptors, but [26] constructs the group representation with augmented images, whereas we construct the representation through + +steerable kernels [67] without rotating images at runtime. + +# 3. Rotation-equivariant keypoint detection + +# 3.1. Overview + +The goal of our work is to learn to detect oriented keypoints from images. The classical keypoint detectors relying on handcrafted features satisfy the rotation/translation equivariance, but the handcrafted methods are sensitive to illumination changes or color distortions. On the contrary, recent learning-based keypoint detectors use standard CNNs to encode local geometry and high-level semantics through convolutional layers. The convolution operation is inherently translation-equivariant, not rotation-equivariant. Therefore, we use a rotation-equivariant convolution [67] without handcrafted features to take advantages of both approaches. The rotation-equivariant CNN features contribute to extract rotation-invariant keypoints with the orientations. + +Figure 2 shows the proposed method which consists of rotation-equivariant layers and is followed by two branches, the keypoint detection and the orientation estimation. The keypoint detection branch generates a rotation-invariant keypoint score map through group pooling and the orientation estimation branch generates a rotation-preserving orientation map through channel pooling. A window-based keypoint detection loss [3] and the proposed dense orientation alignment loss are used to learn the oriented keypoints in a self-supervised manner. Furthermore, the multi-scale image pyramid encourages the network to have robustness to scale changes. + +# 3.2. Preliminaries + +Equivariance. A feature extractor $\Phi$ is said to be equivariant to a geometric transformation $T_{g}$ if transforming an input $x\in X$ by the transformation $T_{g}$ and then passing it through the feature extractor $\Phi$ gives the same result as first mapping $x$ through $\Phi$ and then transforming the feature map by $T_{g}^{\prime}$ [67]. Formally, the equivariance can be expressed for transformation group $G$ and $\Phi :X\to Y$ as + +$$ +\Phi [ T _ {g} (x) ] = T _ {g} ^ {\prime} [ \Phi (x) ], \tag {1} +$$ + +where $T_{g}$ and $T_{g}^{\prime}$ represent transformations on each space as a predefined group action $g \in G$ . In this case, the function $\Phi$ operates a "structure-preserving" mapping from one representation to another. For example, convolutional operation is designed to be translation-equivariant. If $T_{t}$ is a translation group $(\mathbb{R}^{2}, + )$ , and $f$ is the $K$ -dimension feature mapping sent to $\mathbb{Z}^2 \to \mathbb{R}^K$ , the translation equivariance can be expressed as follows: + +$$ +[ T _ {t} f ] * \psi (x) = [ T _ {t} [ f * \psi ] ] (x), \tag {2} +$$ + +where $\psi$ denotes convolution filter weights $\mathbb{Z}^2\to \mathbb{R}^K$ , and $\ast$ indicates the convolution operation. + +Group-equivariant convolution. Recent studies [10-12, 67, 68] have developed convolutional neural networks that are equivariant to symmetry groups of translation, rotation and reflection. Let $H$ be a rotation group. The group $G$ can be defined by $G \cong (\mathbb{R}^2, +) \rtimes H$ as the semidirect product of the translation group $(\mathbb{R}^2, +)$ with the rotation group $H$ . Then, the rotation-equivariant convolution on group $G$ can be defined as: + +$$ +[ T _ {g} f ] * \psi (g) = [ T _ {g} [ f * \psi ] ] (g), \tag {3} +$$ + +by replacing $t \in (\mathbb{R}^2, +)$ with $g \in G$ in Eq. 2. This operation can apply to an input tensor to produce a translation and rotation-equivariant output. Note that the cyclic group $G_N$ represents an interval of $\frac{2\pi}{N}$ representing discrete rotations. + +A rotation-equivariant network can be constructed by stacking rotation-equivariant layers similar to standard CNNs. This network becomes equivariant to both translation and rotation in the same way with the translation-equivariant convolutional networks. Formally, let $\Phi = \{L_i | i \in \{1, 2, 3, \dots, M\}\}$ , which consists of $M$ rotation-equivariant layers under group $G$ . For one layer $L_i \in \Phi$ , the transformation $T_g$ is defined as + +$$ +L _ {i} \left[ T _ {g} (g) \right] = T _ {g} \left[ L _ {i} (g) \right], \tag {4} +$$ + +which indicates that the output is preserved after $L_{i}$ about $T_{g}$ . Extending this, if we apply $T_{g}$ to input $I$ and then pass it through the network $\phi$ , the transformation $T_{g}$ is preserved for the whole network. + +$$ +\left[ \Pi_ {i = 1} ^ {M} L _ {i} \right] \left(T _ {g} I\right) = T _ {g} \left[ \Pi_ {i = 1} ^ {M} L _ {i} \right] (I). \tag {5} +$$ + +# 3.3. Oriented keypoint detection networks + +In this subsection, we describe the process of creating representations for the rotation-invariant keypoint detection and the rotation-equivariant orientation estimation. + +Rotation-equivariant feature extraction. For feature extraction, we use the rotation-equivariant convolutional layers using [67]. For computational efficiency in a limited computational resource, we consider a discrete rotation group only. The layer acts on $(\mathbb{R}^2, +) \rtimes G_N$ and is equivariant for all translations and $N$ discrete rotations. At the first layer $L_1$ , the scalar field of the input image is lifted to the vector field of the group representation by defining field types in a predefined group [67]. Given an input image, $M$ stacked layers produce an output feature map via + +$$ +\mathbf {H} = \left[ \Pi_ {i = 1} ^ {M} L _ {i} \right] (I), \tag {6} +$$ + +where $\mathbf{H} \in \mathbb{R}^{|G| \times C \times H \times W}$ is a rotation-equivariant representation output, and $C$ is the number of channels assigned for each group action. In our experiments, we use 3 layers ( $M = 3$ ). The output $\mathbf{H} \in \mathbb{R}^{|G| \times C \times H \times W}$ is a group of feature maps, which represents $C$ -channel feature maps for $|G|$ + +![](images/c0ee43d6844f5acaa770184aa75bfd16b5a88bbbf883df3394af935b3cf4bc4a.jpg) +Figure 2. Overall architecture. The rotation-equivariant convolutional layer takes an input image and processes it at multiple scales. The multi-scale rotation-equivariant representation $\mathbf{H}$ s pass two separate branches that predict a keypoint map $\mathbf{K}$ and an orientation map $\mathbf{O}$ . + +orientations, and $\mathbf{H}_i$ denotes a feature map for $i$ -th orientation in $G$ . This rotation-equivariant network enables an extensive sharing of kernel weights for different orientations, i.e., rotation transformations, and thus increasing sample efficiency in learning, particularly a rotation-involving task. + +Rotation-invariant keypoint detection. Robust keypoints need to be invariant to rotation transformations; the keypointness, i.e., keypoint score, for a specific position on an image should not be affected by rotating the image. To obtain such a rotation-invariant map for keypoint scores, we collapse the group $G$ of $\mathbf{H} \in \mathbb{R}^{|G| \times C \times H \times W}$ by group pooling, reducing it to a rotation-invariant representation $\mathbf{P} \in \mathbb{R}^{C \times H \times W}$ . Specifically, we use max pooling over orientations: $\mathbf{P} = \max_{g} \mathbf{H}_{g,:,:}$ . Given multi-scale outputs $\{\mathbf{P}_s\}_{s \in S}$ , the final score map $\mathbf{K} \in \mathbb{R}^{H \times W}$ is obtained using standard convolution $\rho$ over a concatenation of $\mathbf{P}_s$ : + +$$ +\mathbf {K} = \rho (\bigcup_ {s \in S} (\zeta (\mathbf {P} _ {s}))), \tag {7} +$$ + +where $\rho$ is a convolution operation, $\bigcup$ means concatenation of the elements, and $\zeta$ denotes a bilinear interpolation function. The interpolation function resizes the input map to a target size, and the convolution transforms a rotation-invariant feature map to a rotation-invariant score map. + +Rotation-equivariant orientation estimation. To estimate a characteristic orientation for a candidate keypoint, we leverage the orientation group of rotation-equivariant tensor $\mathbf{H}$ and translate it to the orientation histogram tensor $\mathbf{Q}$ . Specifically, we collapse the channel dimension $C$ for each orientation by channel pooling and produce a $|G|$ -channel feature map $\mathbf{Q} \in \mathbb{R}^{|G| \times H \times W}$ , where each position can be seen as being assigned an orientation histogram of $|G|$ bins. We use the implementation with $1 \times 1$ group convolution with a single filter to collapse the channels of each orientation: + +$$ +\mathbf {Q} = \eta \left(\mathbf {H} _ {:, c}\right), \tag {8} +$$ + +where $\eta : \mathbb{R}^{|G| \times C} \to \mathbb{R}^{|G|}$ maps $\mathbf{H}$ to a discrete histogram distribution of $|G|$ bins. Note that the channel pooling can + +be any other operations, e.g., max pooling, average pooling, and so on. The resultant output can be interpreted as a map of characteristic orientations for corresponding positions. The output pixel-level rotation-equivariant representation $\mathbf{Q}$ is used to learn the keypoint orientation as a histogram-based dense probability map. Given multi-scale outputs $\{\mathbf{Q}_s\}_{s\in S}$ , the final orientation probability tensor $\mathbf{O}\in \mathbb{R}^{|G|\times H\times W}$ is obtained by summing the outputs over the multiple scales. + +$$ +\mathbf {O} = \sigma (\bigoplus_ {s \in S} (\zeta (\mathbf {Q} _ {s}))), \tag {9} +$$ + +where $\sigma \in \mathbb{R}^{|G|}\to [0,1]^{|G|}$ is a softmax function, and $\bigoplus$ is element-wise summation operation. + +# 3.4. Training + +In this subsection, we describe two loss functions for the keypoint detection and the orientation estimation. First, the loss for the orientation estimation will be described. + +Dense orientation alignment loss. We train the histogram tensor $\mathbf{O}$ to represent the orientations of each pixel. Our method takes both advantages of the histogram-based [27, 51] and the learning-based [41, 70, 72] approaches. The dense orientation tensor $\mathbf{O} \in \mathbb{R}^{|G| \times H \times W}$ encodes relative orientations for each feature point. We transform the histogram of the feature points in $\mathbf{O}^{\mathrm{a}}$ and the spatial dimension of $\mathbf{O}^{\mathrm{b}}$ to learn a characteristic orientation by an explicit supervision as illustrated in Figure 3. + +Image pair $I^{\mathrm{a}}$ , $I^{\mathrm{b}}$ , and the known ground-truth rotation $T_{g}$ are assumed as the input of the networks. First, we rotate $\mathbf{O}^{\mathrm{b}}$ with $T_{g}^{-1}$ for spatial alignment. Next, a histogram alignment is performed by shifting the histograms of each position in $\mathbf{O}^{\mathrm{a}}$ using $T_{g}'$ in vector space. Note that the histograms in each pixel of $\mathbf{O}$ are in a cyclic group $G$ . Finally, the aligned representations $T_{g}'(\mathbf{O}^{\mathrm{a}})$ and $T_{g}^{-1}(\mathbf{O}^{\mathrm{b}})$ are trained with the following cross-entropy loss for all pixels: + +$$ +\mathcal {L} ^ {\mathrm {o r i}} = - \sum_ {i = 1} ^ {W} \sum_ {j = 1} ^ {H} \mathbf {M} \cdot \sum_ {k = 1} ^ {| G |} T _ {g} ^ {\prime} \left(\mathbf {O} ^ {\mathrm {a}}\right) _ {k} \log \left(T _ {g} ^ {- 1} \left(\mathbf {O} ^ {\mathrm {b}}\right)\right) _ {k}, \tag {10} +$$ + +where $\mathbf{M} = \mathbf{1}\wedge T_g^{-1}(\mathbf{1})$ is a mask for removing out-ofbound regions, and $\mathbf{1}\in 1^{H\times W}$ . We omit the spatial index $i,j$ of the tensors $\mathbf{O}^{\mathrm{a}}$ , $\mathbf{O}^{\mathrm{b}}$ and $\mathbf{M}$ in Eq. 10 for simplicity. + +Window-based keypoint detection loss. We utilize a keypoint detection loss using a multi-scale index proposal [3]. In general, a good keypoint is localized in a consistent location invariant to geometric or photometric image transformations. The window-based keypoint detection loss [3] takes both advantages of selecting anchor-based keypoints [14, 66, 74] and using homography without constraining their locations [25, 41]. + +The keypoint score map $\mathbf{K} \in \mathbb{R}^{H \times W}$ is transformed by non-maximum suppression through exponential scaling based on a window. A window $m^{(i)}$ in the score map $\mathbf{K}$ is derived by the softmax over the spatial window of size $N \times N$ around an image coordinate $(u, v)$ : + +$$ +m _ {u, v} ^ {(i)} = \frac {e ^ {w _ {u , v} ^ {(i)}}}{\sum_ {j = c ^ {(i)}} ^ {c ^ {(i)} + N} \sum_ {k = c ^ {(i)}} ^ {c ^ {(i)} + N} e ^ {w _ {j , k} ^ {(i)}}}, \tag {11} +$$ + +where a window $w^{(i)}$ is a nonoverlapping $i$ -th $N \times N$ grid in the score map $\mathbf{K}$ and $c^{(i)}$ is the top-left coordinates of the window $w^{(i)}$ . Then the maximum value in $m^{(i)}$ becomes the dominant location in the window, and a weighted average by multiplying the index in the window $w^{(i)}$ is performed as follows: + +$$ +[ x ^ {(i)}, y ^ {(i)} ] ^ {\top} = [ \bar {u} ^ {(i)}, \bar {v} ^ {(i)} ] ^ {\top} = \sum_ {[ u, v ] \in w ^ {(i)}} m _ {u, v} ^ {(i)} \cdot [ u, v ] ^ {\top}, \tag {12} +$$ + +where $[x^{(i)},y^{(i)}]^{\top}$ is a soft-selected coordinate in an image. Eqs.11-12 aim to suppress noisy predictions in selecting real-value coordinates of the keypoints and to make the layer differentiable, same to the soft-argmax used in [70]. + +The index proposal loss compares the soft-selected index with a hard-selected coordinate $[\hat{x}^{(i)},\hat{y}^{(i)}]$ obtained by arg max in $w^{(i)}$ using the ground-truth geometric transformation $T_{g}$ : + +$$ +\mathcal {L} ^ {\mathrm {I P}} \left(I ^ {\mathrm {a}}, I ^ {\mathrm {b}}, T _ {g}, N\right) = +$$ + +$$ +\sum_ {i} \alpha^ {(i)} | | [ x ^ {(i)}, y ^ {(i)} ] ^ {\mathrm {a} ^ {\top}} - T _ {g} ^ {- 1} [ \hat {x} ^ {(i)}, \hat {y} ^ {(i)} ] ^ {\mathrm {b} ^ {\top}} | | ^ {2}, \tag {13} +$$ + +$$ +\text {a n d} \alpha^ {(i)} = \mathcal {R} ^ {\mathrm {a}} [ x ^ {(i)}, y ^ {(i)} ] ^ {\mathrm {a}} + \mathcal {R} ^ {\mathrm {b}} [ \hat {x} ^ {(i)}, \hat {y} ^ {(i)} ] ^ {\mathrm {b}}, +$$ + +where $\alpha^{(i)}$ is a weighting term based on the score maps, and $\mathcal{R}^{\mathrm{a}}$ and $\mathcal{R}^{\mathrm{b}}$ are the response map of $I^{\mathrm{a}}$ and $I^{\mathrm{b}}$ with coordinates related by $T_{g}^{-1}$ . Finally, the keypoint detection loss uses multiple sizes of the window and adds switching term of the input source and target: + +$$ +\begin{array}{l} \mathcal {L} ^ {\mathrm {k p t s}} \left(I ^ {\mathrm {a}}, I ^ {\mathrm {b}}, T _ {g}\right) = \sum_ {l} \lambda_ {l} \left(\mathcal {L} ^ {\mathrm {I P}} \left(I ^ {\mathrm {a}}, I ^ {\mathrm {b}}, T _ {g}, N _ {l}\right) \right. \tag {14} \\ + \mathcal {L} ^ {\mathrm {I P}} \left(I ^ {\mathrm {b}}, I ^ {\mathrm {a}}, T _ {g} ^ {- 1}, N _ {l}\right)), \\ \end{array} +$$ + +![](images/b14e0d7a45e00e7500181206eb2f31beaa2cc5e5c78546765b03a1b8ccb0c110.jpg) +Figure 3. Illustration of dense orientation alignment loss. The dense orientation histogram $\mathbf{O}^{\mathrm{b}}$ is spatially aligned using $T_{g}^{-1}$ . The equivariant histogram vectors of the feature points in $\mathbf{O}^{\mathrm{a}}$ are shifted using $T_{g}^{\prime}$ . The out-of-plane regions are excluded when computing the loss. + +where $l$ is the index of a window level, $N_{l}$ is the window size in $l$ , $\lambda_{l}$ is a balancing parameter at a window level. + +We use the final loss function $\mathcal{L}$ as follows: + +$$ +\mathcal {L} = \beta \mathcal {L} ^ {\text {o r i}} + \mathcal {L} ^ {\text {k p t s}}, \tag {15} +$$ + +where $\beta$ is a balancing parameter of the loss functions. Since image variations, in general, are not limited to discrete rotation but also include other geometric/photometric variations, e.g., continuous rotation, scaling, and illumination changes, $\mathcal{L}^{\mathrm{ori}}$ and $\mathcal{L}^{\mathrm{kpts}}$ are used to consider such variations in training. Both of the losses are thus non-zero despite our equivariant representation of the cyclic group $G_N$ . + +# 4. Experiments + +This section shows comparative experiments to demonstrate the effectiveness of our model. We describe the implementation details and the experimental benchmarks (Sec. 4.1). We experiment with the keypoints and the orientations under synthetic rotations (Sec. 4.2), and then show the results of keypoint matching on HPatches [2] and IMC2021 [21] (Sec. 4.3). We experiment the variations of our model and show the qualitative results (Sec. 4.4). + +# 4.1. Experimental setting + +Implementation details. We use the $E(2)$ -CNN framework [67] for the implementation of rotation-equivariant convolution with PyTorch [42, 46]. We use 36 for the order of cyclic group $G$ , with 2 for the channel dimension $C$ . We use 3 equivariant layers, each of which consists of a conv-bn-relu module. Each convolution layer has $5 \times 5$ kernel with padding of 2 without bias, and model parameters are randomly initialized. We use a batch size of 16. We + +train with Adam optimizer with a learning rate of 0.001. The leaning rate decay is 0.5 every 10 epochs for a total of 20 epochs. Early stopping is required to avoid overfitting, so we use the repeatability score of the validation set. The keypoint loss uses the window sizes $N_{l} \in [8,16,24,32,40]$ with $\lambda_l \in [256,64,16,4,1]$ same as [3], and the loss balancing parameter $\beta$ is 100. We use the NMS size $15 \times 15$ at test time, same to Key.Net [3]. + +Inference. For robustness to the scale change, we make eight scale pyramids by the scaling of $\sqrt{2}$ at inference time. We extract $\left\lfloor \frac{2^{2 - s} * \mathbf{p}}{\sum_{n = -2}^{5} 2^n} \right\rfloor$ keypoints at scale $s \in S = \{0,1,\dots,7\}$ when we extract a total of $\mathbf{p}$ keypoints. We assign the scale value $\sqrt{2}^{s - 2}$ for the keypoints extracted in scale $s$ . We use simple arg max to obtain an orientation value from the histogram, which performs well enough compared to a soft prediction for deriving real value. + +Training dataset. We generate a synthetic dataset for the self-supervised training. Our model needs a ground-truth relative orientation for the training. We generate random image pairs with in-plane rotation [-180, 180], which is sufficient for the planar homography [2] or the 3D viewpoint changes [21]. To improve the robustness at illumination changes, we modify the contrast, brightness, and hue value in HSV space. We exclude the images with insufficient edges through Sobel filters [22] as a pre-processing. The synthetic dataset has 9,100 image pairs of size $192 \times 192$ split into 9,000 as a training set and 100 as a validation set. We use ILSVRC2012 [52] as source data. + +Evaluation benchmark. We use two test datasets for comparative evaluation. HPatches [2] is for evaluating keypoint detection and matching. IMC2021 [21] is for evaluating the 6 DoF pose estimation accuracy. + +HPatches consists of 116 scenes with 59 viewpoint variation and 57 illumination variation [2]. Each scene consists of 5 image pairs with ground-truth planar homography, for a total of 696 image pairs. We compare our model with the existing models using 1,000 keypoints for evaluation. We use the repeatability score, the number of matches, and mean matching accuracy (MMA) as evaluation metrics proposed to [15, 33]. Repeatability1 is the ratio between the number of repeatable keypoints and the total number of detections by 3 pixel threshold. MMA is the average percentage of correct matches per image pair. We measure the correct matches by thresholding 3 and 5 pixels for MMA. + +IMC2021 is a large-scale challenge dataset of wide-baseline matching [21]. IMC2021 consists of an unconstrained urban scene with large illumination and viewpoint variations. In this experiment, we compare our method with the existing keypoint detection methods in an image match- + +![](images/5c42b0e1e5ab493912422f6569bf737629661baee62b3bf187ca181e15e97034.jpg) +Figure 4. Results of repeatability to evaluate the rotation-invariant keypoint detection under synthetic rotations with Gaussian noise. For a better view, we smooth the chart by a moving average. + +![](images/23eaba06525d4f3c5da4e1e827693850023dc72386300bc054ea5dbe1dad555f.jpg) +Figure 5. Results of orientation estimation accuracy under synthetic rotations with Gaussian noise. We use $15^{\circ}$ threshold for measuring the accuracy. + +ing pipeline [7,9,37]. We experiment on the stereo track using the validation sets of Phototourism and PragueParks. This benchmark takes the predicted matches as an input and measures the 6 DoF pose estimation accuracy. We measure the mean average accuracy (mAA) of pose estimation at $5^{\circ}$ and $10^{\circ}$ and the number of inliers. + +# 4.2. Experiments under synthetic rotations + +Inspired by Section 4.4 of [51], we conduct two experiments with synthetic images using in-plane rotation from $0^{\circ}$ to $359^{\circ}$ at $1^{\circ}$ intervals using ten images of size $224 \times 224$ that are not used for training and validation. We compare two handcrafted methods [27, 51] and two learning methods [41, 70] among the representative keypoint detectors that yield the orientations. Figure 4 shows the results of rotation-invariant keypoint detection in terms of repeatability. Our method consistently obtains better repeatability than the existing methods [27, 41, 51, 70]. Note that the learning method LF-Net [41] falls off dramatically after 10 degrees while the handcrafted, SIFT [27] and ORB [51], are robust to rotations. Figure 5 shows the results of rotation + +
Det.Desc.All variations
Rep.MMApred. match.
@3px@5px
SIFT [27]SIFT [27]41.949.452.4404.2
SIFT [27]HardNet [37]41.957.162.3437.8
SIFT [27]SOSNet [63]41.957.963.0430.8
SIFT [27]HyNet [62]41.957.362.5438.9
ORB [51]ORB [51]57.446.650.0362.0
D2-Net [15]D2-Net [15]19.835.248.6371.8
LF-Net [41]LF-Net [41]43.852.056.9330.2
R2D2 [45]R2D2 [45]45.564.674.8358.9
SPoint [14]SPoint [14]47.063.970.3466.3
SPoint [14]GIFT [26]47.068.876.0496.7
Key.Net [3]HardNet [37]55.972.579.4474.4
Key.Net [3]SOSNet [63]55.972.779.6464.7
Key.Net [3]HyNet [62]55.972.078.9475.3
oursHardNet [37]57.673.179.6505.8
oursSOSNet [63]57.673.480.0499.5
oursHyNet [62]57.672.979.5503.3
oursGIFT [26]57.675.281.5415.6
+ +Table 1. Results on HPatches. We use 1,000 keypoints in this experiment. 'Det.' denotes keypoint detection method, 'Desc.' denotes descriptor extraction method, 'Rep.' denotes the repeatability score, and 'pred. match.' is the average number of predicted matches. Numbers in bold indicate the best scores. + +equivariant orientation estimation in terms of orientation estimation accuracy. We align $\mathbf{O}^{\mathrm{b}}$ to $\mathbf{O}^{\mathrm{a}}$ using $T_{g}^{-1}$ and then measure the accuracy at the whole region of images except the boundary regions as in Figure 6. We obtain the orientation values of SIFT [27] by generating keypoints in all positions. Even though our method predicts the orientation discretely by the histogram, it is more effective than the regression-based learning methods, OriNet [72], LIFT [70], and LF-Net [41]. Especially, the accuracies of our model are consistently over $80\%$ at a threshold of 15 degrees. + +# 4.3. Keypoint matching + +Results on HPatches. Table 1 shows the results of keypoint detection and matching in HPatches [2]. We exclude our orientation in this experiment. We compare the handcrafted detectors [27, 51] and a learned detector [3] as baselines with patch-based descriptors [37, 62, 63]. We additionally compare the joint detection and description methods [14,15, 41,45] and the integration of the rotation-invariant dense descriptors [26]. We use the mutual nearest neighbor matching algorithm for all cases in this experiment. Our model achieves the best repeatability score compared to the existing keypoint detection methods [3, 14, 15, 27, 41, 45, 51], which means our detector is robust to the viewpoint and illumination changes. Our model consistently obtains more predicted matches and better MMA scores compared to the state-of-the-art keypoint detector Key.Net [3] at all cases with the patch descriptors [37,62,63]. Our model with GIFT descriptor [26] achieves better MMAs compared to the Su + +
Det.KStereo track.
Num. Inl.mAA(5°)mAA(10°)
DoG+AN [27, 38]1,02443.80.2100.277
Key.Net [3]1,024126.50.3970.512
ours1,024135.60.4410.549
DoG+AN [27, 38]2,048105.90.3850.477
Key.Net [3]2,048245.40.4730.588
ours2,048269.30.5210.632
DoG+AN [27, 38]8,000539.00.6050.718
Key.Net [3]8,000563.00.5220.635
ours8,000992.90.6010.710
+ +Table 2. Mean average accuracy (mAA; $5^{\circ}$ , $10^{\circ}$ ) of 6-DoF pose estimation and the average number of inlier matches (Num. Inl.) on IMC2021 validation set [21]. Column 'K' denotes the number of keypoints. Numbers in bold indicate the best scores. + +perPoint [14] detector of the cases with SuperPoint descriptor [14] and GIFT [26]. In particular, our model with the rotation-invariant descriptors [26] achieves the best MMAs, which shows that the rotation-invariant representation contributes to improving the accuracy of correspondences. + +Results on the IMC2021. Table 2 shows the results of 6 DoF pose estimation in IMC2021 [21] for evaluating on a complex task of general scenes2. For this experiment, we use the rest of the image matching pipeline using HardNet descriptor [37], and DEGENSAC geometric verification [9] with AdaLAM [7] for all cases. For the AdaLAM [7] stage, we use our estimated orientation values and the scale values from the scale-space inference. We compare to two baselines, DoG+AN [27, 38] and Key.Net [3]. The result shows that our model consistently improves the camera pose estimation accuracy (mAAs) and the number of inliers compared to the Key.Net [3]. Although the mAAs of our model in 8,000 keypoints are slightly lower than DoG+AN [27, 38], the number of inliers is almost double which denotes the quality of 3D reconstruction. In particular, our model with 1,024 keypoints significantly improves the mAAs and the number of inliers compared to DoG+AN [27, 38], which shows that our model estimates more accurate camera poses with less computation. Our model consistently outperforms the baseline Key.Net [3] for all metrics. + +# 4.4. Additional results + +Effect of the oriented keypoint. Table 3 shows the results in HPatches [2] by an outlier filtering algorithm $^{3}$ using the estimated orientations compared to [27, 41, 51]. Among the predicted matches, we filter the outlier matches through global consensus of the orientation values assigned in matched keypoints. We first compute the difference of estimated orientation for tentative matches and then derive + +
Det.+Des.Ori.fltr.MMAmatch.
@3px@5px
ORB [51]ORB [51]46.650.0362.0
ORB [51]ORB [51]✓42.645.8196.1
ORB [51]ours✓61.766.0228.3
SIFT [27]SIFT [27]49.452.4404.2
SIFT [27]SIFT [27]✓52.655.8251.6
SIFT [27]ours✓63.767.4236.5
LF-Net [41]LF-Net [41]52.056.9330.2
LF-Net [41]LF-Net [41]✓49.954.3197.0
LF-Net [41]ours✓63.269.2236.2
ours+HN [37]ours73.179.6505.8
ours+HN [37]ours✓76.782.3440.1
+ +Table 3. Results for the comparison using the estimated orientations by an outlier filtering in HPatches [2]. We use 1,000 keypoints. 'Det.+Des.' denotes the keypoint detector and descriptor, 'Ori.' denotes the orientation estimation method, and 'fltr.' denotes whether or not to use the outlier filtering. + +
MMA# param.
w/o out. filter.out. filter.
@3px@5px@3px@5px
G3673.179.676.782.33.3K
G1866.275.072.780.86.5K
G962.470.772.079.113.0K
G863.273.769.579.014.7K
G462.370.768.275.829.1K
-64.574.064.574.0116K
+ +Table 4. Experiment according to the order of group in HPatches [2]. The subscript of $G$ denotes the order of group. 'out. filter.' denotes the results with outlier filtering. The last row denotes the results without the group representation and using conventional CNNs. + +the most frequent difference between the pair images. We exclude matches far from the most frequent difference as the outlier. For the comparison, we replace the orientations of the comparison methods with our orientation. The results with our orientations yield higher MMAs and more predicted matches than all the results with the orientations of the baselines [27, 41, 51]. The results of our model with HardNet [37] achieve the best performance both in cases with outlier filtering and cases without filtering, so our method generates more consistent orientations to the viewpoint and illumination changes than the orientations derived by the image gradients [27, 51] and the regression [41]. + +Change the order of group. Table 4 shows the results of MMAs with the number of parameters according to the order of group $|G|$ . We make the same computation of all models by changing the number of channels $C$ . Therefore, the model size increases by $N$ times whenever the order of group decreases by $N$ times. For example, the third row in Table 4 with the order of group 9 has the number of channels 8. In the table, the results with a cyclic group $G_{36}$ are the best with the smallest model size. The last row, + +![](images/e4ecef19cc06b653c64a4ad5663290e5b09ae44d768b57b3c33a5ffb2fe7e8f2.jpg) +Figure 6. Visualization of the color-coded orientation maps. Upper is the source image, and the bottom is the target image. For the better view, we apply $T_{g}^{-1}$ to the target image as a spatial alignment. We map the orientation range from [0, 359) to [0, 255) to visualize the orientations by hue of HSV color representation. + +which replaces the rotation-equivariant layers with conventional convolutional layers, has a large number of parameters because there is no weight sharing. As the order of group increases, the number of parameters can be significantly reduced without losing performance. In addition, the model with the conventional convolutional layers fails to train the orientation, so the outlier filtering has no effect, which shows the group-equivariant CNNs are essential for the equivariant orientation learning. + +Qualitative results. Figure 6 shows qualitative comparisons of the orientation map with a handcrafted method [27] and a learning method [41] using an example of Sec. 4.2. Our model predicts the changing orientations more consistently across the images compared to [27, 41], which proves the peak of our orientation histogram for an pixel consistently changes as the region is rotated. Additional experiments and more analysis are in the supplementary material. + +# 5. Conclusion + +This paper presents a self-supervised oriented keypoint detection method using rotation-equivariant CNNs. The rotation-equivariant representation with pooling in separate dimensions generates robust features for oriented keypoint detection. The proposed dense orientation alignment loss trains the histograms consistently changing to rotation. Extensive experiments show the effectiveness of the proposed oriented keypoints compared to the existing methods in standard image matching benchmarks. 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To model the internal structures in target point clouds, we first propose to learn the global representations of unlabeled data by scaling up or down point clouds and then predicting the scales. Second, to capture the local structure in a self-supervised manner, we propose to project a 3D local area onto a 2D plane and then learn to reconstruct the squeezed region. Moreover, to effectively transfer the knowledge from source domain, we propose to vote pseudo labels for target samples based on the labels of their nearest source neighbors in the shared feature space. To avoid the noise caused by incorrect pseudo labels, we only select reliable target samples, whose voting consistencies are high enough, for enhancing adaptation. The voting method is able to adaptively select more and more target samples during training, which in return facilitates adaptation because the amount of labeled target data increases. Experiments on PointDA (ModelNet-10, ShapeNet-10 and ScanNet-10) and Sim-to-Real (ModelNet-11, ScanObjectNN-11, ShapeNet-9 and ScanObjectNN-9) demonstrate the effectiveness of our method. + +# 1. Introduction + +Large-scale learning methods based on deep neural networks [7-10, 15, 25, 26, 35, 36, 39] constitute the recent advances in 3D vision, and play an important role for visual perception in intelligent platforms such as robots, drones + +![](images/b8db4d4a803c5818ce2d01fd4d438efa14171989bbec3abc47575462a48e7b94.jpg) +Figure 1. Illustration of the self-supervised global-local structure modeling for point cloud domain adaptation. The global structure is modeled by scaling up/down the point cloud and then predicting the scale. To capture the local structure, a random 3D local area is squeezed onto a 2D plane and then reconstructed by the network. + +and self-driving cars. These intelligent platforms often employ real-time depth sensors, such as LiDAR, to capture the accurate geometric information of scenes, which are represented by 3D point clouds. However, deep neural neural networks usually requires massive amounts of labeled point clouds for representation learning, which limits the scalability to the real world. To alleviate this problem, unsupervised point cloud domain adaption is recently attracting increasing attention from the community [1, 27, 31, 43]. Domain adaptation aims to transfer the knowledge from a labeled source domain to a related but unlabeled target domain, in which the source and target domains share the same feature space. However, due to different point scales, object sizes, densities, styles, sensor perspectives, etc., point cloud representations in the target domain inevitably deviate from the corresponding representations in the source domain, result- + +![](images/21ecaca07bebf0721ea85f4f6a8bad527fc125739940d3cd734469edee74ecd5.jpg) + +![](images/18952bdc3e795783f28fd2316caed14eb3dc26acefbc1372dde99e13469c60a7.jpg) +Figure 2. Illustration of reliable voted pseudo label generation. First, target point clouds' pseudo labels are voted by a few of nearest source neighbors in the feature space. Then, the target samples whose nearest source neighbor labels are consistent enough are selected as reliable training data. + +ing in the domain shift or distributional shift problem. + +To reduce domain shift, one solution is to directly learn from the target domain via self-supervised learning, i.e., exploiting the relations or correlations between different input signals. However, most of the existing methods focus on leveraging only one of the global or local structure of unlabeled data, such as predicting global vertical rotation [24], reconstructing point clouds from randomly rearranged object local parts [29], reconstructing a collapsed local region via Chamfer Distance loss [1] or localizing a curvature-changed local area [43]. Another domain adaptation solution is to transfer the knowledge from source to target domain via adversarial training [27] and self-training [43]. + +This paper is devoted to exploiting the self-supervised and transfer learning for point cloud domain adaptation. First, as shown in Fig. 1, we propose to learn point cloud representations by scaling up or down point coordinates of one dimension and then predicting the scale based on the other two unchanged dimensions. In this way, the network is able to capture the global structure in a self-supervised manner. To model the local structure, we propose to project a 3D local area onto a 2D plane by simply setting point coordinates of a randomly selected dimension to the same value and recover the squeezed area via mean squared error loss. Second, as shown in Fig. 2, to enhance the knowledge transfer from the source domain, we propose a voting method to assign reliable pseudo labels to target samples for self-training. Specifically, pseudo labels are voted based on a few nearest source neighbors in the shared feature space. Then, only the target point clouds whose nearest source neighbor labels are consistent enough are selected as reliable training data. With networks becoming stronger + +during training, our reliable voting method adaptively selects more target data, which in return facilitates learning because the amount of labeled target data increases. + +To evaluate our method, we conduct experiments on the widely-used 3D domain adaptation benchmark PointDA [27], which consists of 10 shared classes from ModelNet40 [37], ShapeNet [2] and ScanNet [3]. Moreover, we also conduct experiments on a Sim-to-Real dataset [16], which consists of 11 shared classes from ModelNet40 and ScanObjectNN [34], and 9 shared classes from ShapeNet and ScanObjectNN, respectively. The contributions of this paper are threefold: + +- To model the structure of unlabeled target point clouds, we propose the global scaling-up-down prediction and local 3D-2D-3D projection-reconstruction methods for point cloud domain adaptation. +- To transfer the knowledge from source domain, we propose a voting method to assign reliable pseudo labels to target samples. The method is able to iteratively select more and more target data during training, which in return facilitates learning. +- Extensive experiments on two datasets show that the proposed method effectively improves the accuracy of unsupervised domain adaptation on point clouds. + +# 2. Related Work + +Point Cloud Classification. Point cloud classification is one of the fundamental tasks for point cloud processing. Recently, a number of deep neural networks have been proposed to address this problem [25, 26, 32, 35, 36]. Most of these works aim to directly manipulate point clouds without converting irregular points into regular voxel grids, to avoid the quantization errors and high computational cost of voxelization. Since a point cloud is essentially a set of unordered points and invariant to permutations of its points, the key to point cloud processing is to design effective point-based spatial modeling operations that do not rely on point orderings. Our method is independent of these works and employ them to encode point clouds. + +Self-supervised Learning. To learn from internal structures in images, self-supervised learning tries to find or exploit the relations or correlations between different input signals [5,6,13,21-23,38], e.g., modifying the input and (1) predict what changed or (2) ensure that the output representation does not change, such as learning spatial context of patches from an image [5], learning to count objects [22], predicting the missing pixels [23], recovering a plausible colored version of a grayscale image [38] and solving Jigsaw puzzles [21]. Self-supervised learning can also be applied to point clouds. Sauder and Sievers proposed to split an input point cloud into several parts and reconstruct the point cloud [29]. Poursaeed et al. proposed to rotate a + +point cloud and then predict the rotation angle [24]. Shen et al. proposed to employ geometry-aware implicit in point clouds to reduce domain biases [31]. Achituve et al. and Zou et al. proposed to first mix up two point clouds and then predict the mixed labels [1] and their angles [43], respectively. Besides, they also proposed to reconstruct and localize deformed local areas, respectively. When modeling local structure, our method is inspired by the two deformation-based methods but achieves better accuracy. + +Unsupervised Domain Adaptation. Unsupervised domain adaptation has been well developed on images [11, 19, 28, 30, 33, 40, 41]. These methods can be divided into three categories. 1) Adversarial training [19, 28, 33], which aims to directly learn unbiased representations via a discriminator to judge whether the learned features are from the target domain or the source domain, and a feature generator to confuse the discriminator. 2) Style transfer [40], which employs Generative Adversarial Networks [14] to transfer source images as the target style for training. 3) Self-training with pseudo labels [4, 11, 20, 42]. Networks trained on source domains have a certain ability to recognize target images. Therefore, target data's pseudo labels can be generated for training, in which self-paced learning [18] is usually employed to reduce noisy pseudo labels. The image-based methods can also been used for point-cloud-based domain adaptation. For example, Qin et al. [27] employed adversarial training to learn unbiased point cloud representations. Zou et al. [43] employed a self-training method, equipped with self-paced learning, for point cloud domain adaptation. Our work is also based on adversarial training and self-training but we propose a novel reliable-voting-based method for pseudo label generation. Different from the existing methods that exploit the centroid label of nearest source neighbors [42] or the prediction probabilities of nearest source neighbors [20], we use the nearest source neighbor labels in a voting manner. Moreover, we integrate voting consistency into our method, so that the unreliable pseudo labels are excluded during training. Besides, point cloud domain adaptation [1, 17] is also explored in 3D segmentation. This paper focuses on representation learning via object or shape classification. + +# 3. Proposed Method + +In this section, we first introduce and formulate the point cloud domain adaption problem in Sec. 3.1. Second, we introduce the scaling-up-down method for self-supervised global structure modeling in Sec. 3.2. Third, the 3D-2D-3D project-reconstruction method for local structure learning is described in Sec. 3.3. Fourth, in Sec. 3.4, we briefly introduce the adversarial training used in our paper. Fifth, the reliable voting method for pseudo label assignment is described in details in Sec. 3.5. Finally, the overall training procedure of our method is shown in Sec. 3.6. + +# 3.1. Problem Formulation + +The goal of unsupervised domain adaptation on point clouds is to transfer the knowledge for a labeled source domain $\mathcal{S} = \{(P_i^s, y_i^s)\}_{i=1}^{n^s}$ to an unlabeled target domain $\mathcal{T} = \{(P_i^t)\}_{i=1}^{n^t}$ , where $P \in \mathbb{R}^{m \times 3}$ , $y_i^s \in \mathcal{Y} = \{1, \dots, c\}$ , $m$ is the number of points and $c$ is the number of shared classes. The $n^s$ and $n^t$ denote the number of source and target point clouds, respectively. The key to domain adaptation is to learn a mapping function or point cloud feature generator $\Phi$ that projects point clouds from different domains into a shared feature space. The feature generator $\Phi$ can be implemented by existing deep neural networks, e.g., PointNet [25] and DGCNN [35], which encode a point cloud to a vector, i.e., $f = \Phi(P)$ . + +In this paper, we assume that point features, e.g., color, norm or other information, are not available. In this case, domain shifts can be caused by different point scales, point densities, object sizes, sensor perspectives, object styles, etc. Some of the shifts can be reduced by low-level data preprocessing and augmentation. For example, the point scale and object size problems can be addressed by normalizing object coordinates to a fixed range, e.g., $[-1,1]$ . The density problem can be addressed by sampling, e.g., Farthest Point Sampling (FPS), point clouds to the same number of points. The perspective shift problem can be mitigated by rotation-based data augmentation. However, the other shifts, e.g., object styles, have to be reduced via high-level representations, which is the goal of unsupervised point cloud domain adaption methods. + +# 3.2. Self-Supervised Global (G) Structure Modeling via Scaling-Up-Down Prediction + +To enable $\Phi$ to capture the global structure of target data without human-annotated class labels, we propose to scale up or down coordinates and then employ a regressor $\Omega$ to predict the scale based on the point cloud feature $f$ . Specifically, suppose $s_i = (s_i^x, s_i^y, s_i^z) \in \mathbb{R}^{+1 \times 3}$ is a random scale vector for the $i$ -th target point cloud. Then, the coordinates $P_i^t$ of the point cloud is scaled by $s_i \odot P_i^t$ , where $\odot$ is element-wise multiplication and $s_i$ is broadcasted for the multiplication. Finally, regressor $\Omega$ is used to predict the scale $s_i$ , + +$$ +\min _ {\Phi , \Omega} \mathcal {L} _ {g}, \quad \mathcal {L} _ {g} = \frac {1}{n ^ {t}} \sum_ {i = 1} ^ {n ^ {t}} \left| \left| \Omega \left(\Phi \left(\boldsymbol {s} _ {i} \odot \boldsymbol {P} _ {i} ^ {t}\right)\right) - \boldsymbol {s} _ {i} \right| \right| _ {2} ^ {2}. \tag {1} +$$ + +Note that, when predicting the scale, regression $\Omega$ is actually based on the relative scales of the three dimensions, instead of the absolute change. For example, when we scale up two dimensions by 2 and leave the last dimension unchanged, regressor $\Omega$ would misunderstand that the last dimension is scaled down by 0.5. To avoid this problem, we fix two of three dimensions and only scale + +![](images/18654bb932f4b3a452a243b8669b2c383cede2cbff1a702917e18fbb1c07f496.jpg) +Figure 3. Illustration of the proposed self-supervised Global-Local structure modeling and Reliable Voted pseudo label method (GLRV) for point cloud domain adaption. The framework consists of a feature generator $\Phi$ to encode point clouds, a regressor $\Omega$ to predict the scaling change for self-supervised global structure modeling, a reconstructor $\Delta$ to recover squeezed region for self-supervised local structure modeling and two classifiers $\Psi_{1}$ and $\Psi_{2}$ for supervised learning and adversarial training. Besides, a reliable voting method is employed to obtain accurate target pseudo labels for enhancing domain adaptation. + +up or down one dimension. Therefore, $s_i$ is limited to $\{(s, 1, 1), (1, s, 1), (1, 1, s)\}$ , where $s \in \mathbb{R}^+$ . Moreover, because dramatically scaling up or down point clouds will change their structures, $s$ is sampled from a small range, e.g., [0.5, 1.5] in this paper. + +# 3.3. Self-Supervised Local (L) Structure Modeling via 3D-2D-3D Projection-Reconstruction + +To enable $\Phi$ to learn the local structure without point-level human annotations, we propose a 3D-2D-3D projection-reconstruction method. Specifically, similar to [1], we first split the normalized 3D space into several regions. In this way, a point cloud is divided into multiple parts. Then, we randomly select a part that contains enough points for projection-reconstruction. Suppose $\pmb{v}_i\in \{0,1\}^{m\times 1}$ is a mask vector to indicate the selected points for the $i$ -th target point cloud. Recall that $m$ is the number of points in the cloud. When $\pmb{v}_i[j] = 1$ , it indicates the $j$ -point is selected. In this way, the selected local area can be denoted as $P_{i}^{t}[v_{i}]\in \mathbb{R}^{|||v_{i}||_{1}\times 3}$ . Third, we project the selected 3D area $P_{i}^{t}[v_{i}]$ onto a 2D panel. To do so, we randomly select a dimension $r$ . Then, the $r$ -dimensional coordinates of the selected points are squeezed to their mean. In this way, we obtain the locally projected point cloud $\hat{P_i^t}$ . Finally, a reconstructor $\Delta$ is employed to recover the projected area, + +$$ +\min _ {\Phi , \Delta} \mathcal {L} _ {l}, \quad \mathcal {L} _ {l} = \frac {1}{n ^ {t}} \sum_ {i = 1} ^ {n ^ {t}} \boldsymbol {v} _ {i} \odot | | \Delta (\Phi (\hat {\boldsymbol {P}} _ {i} ^ {t})) - \boldsymbol {P} _ {i} ^ {t} | | _ {F} ^ {2}, \tag {2} +$$ + +![](images/5cc8911c87c56601b8dce653995ed83c1a8aa61d5804a8a7f5ae68f716c05c0b.jpg) +Figure 4. Illustration of the 3D-2D-3D projection-reconstruction process for the $i$ -th target point cloud $\pmb{P}_i^t$ . The points of a selected 3D local area is indicated by a mask vector $\pmb{v}_i$ . Then, the local area is projected into 2D by squeezing the $r$ -dimensional coordinates to their mean, resulting in the locally projected point cloud $\hat{\pmb{P}}_i^t$ . Finally, the feature generator $\Phi$ and reconstructor $\Delta$ is asked to reconstruct the squeezed area based on $\hat{\pmb{P}}_i^t$ . + +where $v_{i}$ is broadcasted for the element-wise multiplication. We illustrate the 3D-2D-3D projection-reconstruction process in Fig. 4. + +# 3.4. Adversarial Training for Unbiased Representation Learning + +Like most domain adaptation works, we also employ adversarial training [14] to reduce domain shifts and learn unbiased representations. In this paper, we employ Maximum + +Classifier Discrepancy (MCD) [28] for adversarial training. MCD uses two classifiers $\Psi_{1}$ and $\Psi_{2}$ , which map the feature vector $\pmb{f}$ to two probability vectors of length $c$ , i.e., $\Psi_{1}(\pmb{f}) \in \mathbb{R}^{c}$ and $\Psi_{2}(\pmb{f}) \in \mathbb{R}^{c}$ , respectively. Recall that $c$ is the number of classes. For labeled data, MCD performs supervised-learning-based classification, + +$$ +\min _ {\Phi , \Psi_ {1}, \Psi_ {2}} \mathcal {L} _ {s}, +$$ + +$$ +\begin{array}{l} \mathcal {L} _ {s} = - \frac {1}{n ^ {s}} \sum_ {i = 1} ^ {n ^ {s}} \sum_ {j = 1} ^ {c} \mathbb {1} _ {[ j = y _ {i} ^ {s} ]} \cdot \log (\Psi_ {1} (\Phi (P _ {i} ^ {s})) [ j ]) \tag {3} \\ - \frac {1}{n ^ {s}} \sum_ {i = 1} ^ {n ^ {s}} \sum_ {j = 1} ^ {c} \mathbb {1} _ {[ j = y _ {i} ^ {s} ]} \cdot \log \left(\Psi_ {2} \left(\Phi \left(\boldsymbol {P} _ {i} ^ {s}\right)\right) [ j ]\right). \\ \end{array} +$$ + +For unlabeled data, MCD first tries to maximize the prediction discrepancy of the two classifiers with fixed $\Phi$ , + +$$ +\begin{array}{l} \min _ {\Psi_ {1}, \Psi_ {2}} \mathcal {L} _ {s} - \mathcal {L} _ {a d v}, \\ \mathcal {L} _ {a d v} = \frac {1}{n ^ {t} c} \sum_ {i = 1} ^ {n ^ {t}} | | \Psi_ {1} (\Phi (P _ {i} ^ {t})) - \Psi_ {2} (\Phi (P _ {i} ^ {t})) | | _ {1}. \tag {4} \\ \end{array} +$$ + +Then, the generator $\Phi$ is trained to minimize the discrepancy with fixed classifiers, + +$$ +\min _ {\Phi} \mathcal {L} _ {a d v}. \tag {5} +$$ + +In this way, $\Phi$ is enforced to learn unbiased representations. Note that the adversarial training method is not our contribution. + +# 3.5. Reliable Voted (RV) Target Pseudo Label Generation for Enhancing Domain Adaptation + +Although adversarial training provides a way to reduce domain shifts, its effectiveness is usually limited. In this paper, we propose a self-training method to directly transfer the knowledge from source to target domain via target pseudo labels. Specifically, our method employs a voting strategy to assign pseudo labels to target samples. The pseudo labels of target point clouds are voted based on the labels of a few of their nearest source neighbors in the shared feature space. Suppose $\pmb{f}_i^t$ and $\pmb{f}_j^s$ are the features of the $i$ -th target and the $j$ -th source point clouds, respectively. Their similarity is calculated as + +$$ +e _ {i j} ^ {t s} = \frac {\boldsymbol {f} _ {i} ^ {t} \cdot \boldsymbol {f} _ {j} ^ {s}}{\left\| \boldsymbol {f} _ {i} ^ {t} \right\| _ {2} \times \left\| \boldsymbol {f} _ {j} ^ {s} \right\| _ {2}}. \tag {6} +$$ + +Then, the $k$ -nearest source neighbors are selected as follows, + +$$ +\mathcal {N} \left(\boldsymbol {P} _ {i} ^ {t}, k\right) = \left\{j \mid e _ {i j} ^ {t s} \in \operatorname {t o p} - k \left(\left\{e _ {i 1} ^ {t s}, \dots , e _ {i n s} ^ {t s} \right\}\right) \right\}. \tag {7} +$$ + +Third, the pseudo label of the $i$ -th target point cloud is assigned with a voting mechanism, + +$$ +\tilde {y} _ {i} ^ {t} = \operatorname {v o t e} \left(\left\{y _ {j} ^ {s} \mid j \in \mathcal {N} \left(\boldsymbol {P} _ {i} ^ {t}, k\right) \right\}\right), \tag {8} +$$ + +where the vote function simply selects the majority as the output. + +Although we employ a $k$ -NN based voting method, the pseudo labels can be still unreliable, which may add noise into training data and lead to accuracy drop. To address this problem, we propose to only exploit reliable target point clouds, of which nearest source neighbor labels are consistent enough, to train the model with their voted pseudo labels, + +$$ +h _ {i} = \left\{ \begin{array}{l l} 0, & \frac {\sum_ {j \in \mathcal {N} \left(\boldsymbol {P} _ {i} ^ {t} , k\right)} \mathbb {1} _ {[ y _ {j} ^ {s} = \tilde {y} _ {i} ^ {t} ]}}{k} < \lambda , \\ 1, & \frac {\sum_ {j \in \mathcal {N} \left(\boldsymbol {P} _ {i} ^ {t} , k\right)} \mathbb {1} _ {[ y _ {j} ^ {s} = \tilde {y} _ {i} ^ {t} ]}}{k} \geq \lambda , \end{array} \right. \tag {9} +$$ + +where $\lambda \in (0,1]$ is the consistency threshold and $h_i$ indicates where the $i$ -th target point cloud is selected as a reliable training sample. Finally, the selected reliable target data is used to train the feature generator in a supervised manner, + +$$ +\min _ {\Phi , \Psi_ {1}, \Psi_ {2}} \mathcal {L} _ {t}, +$$ + +$$ +\begin{array}{l} \mathcal {L} _ {t} = - \frac {1}{| | \boldsymbol {h} | | _ {1}} \sum_ {i = 1} ^ {n ^ {t}} h _ {i} \sum_ {j = 1} ^ {c} \mathbb {1} _ {[ j = \tilde {\boldsymbol {y}} _ {i} ^ {t} ]} \cdot \log \left(\Psi_ {1} \left(\Phi \left(\boldsymbol {P} _ {i} ^ {t}\right)\right) [ j ]\right) \\ - \frac {1}{\left| \left| \boldsymbol {h} \right| \right| _ {1}} \sum_ {i = 1} ^ {n ^ {t}} h _ {i} \sum_ {j = 1} ^ {c} \mathbb {1} _ {[ j = \tilde {y} _ {i} ^ {t} ]} \cdot \log (\Psi_ {2} (\Phi (\boldsymbol {P} _ {i} ^ {t})) [ j ]), \tag {10} \\ \end{array} +$$ + +where $\pmb{h} = (h_1, \dots, h_{n^t})$ is the selection indicator vector. + +Note that, $k$ and $\lambda$ are the only two hyper-parameters of our reliable voting method. Moreover, as shown in the following experiments, we can further simplify this method by fixing $\lambda$ to 1.0. In this case, $k$ is the only hyper-parameter of this method and a bigger $k$ indicates a higher reliability threshold. + +Even though with fixed $k$ and $\lambda$ , our reliable voting method has the ability to automatically and adaptively select an increasing amount of target data during training. At the early stage of training, because the feature generator $\Phi$ is weak and the domain shift is large, only a few target point clouds, which are similar to source samples and easy to be recognized, reach the consistency threshold and are selected as reliable training data. When $\Phi$ becomes stronger and domain shift reduces, target representations become more discriminative and the consistency of nearest source neighbors' labels increases. Consequently, more target point clouds are added into the training set. In return, the increasing of labeled target data facilitates training. In this way, the feature generator $\Phi$ is improved progressively. + +# 3.6. Overall Training + +In summary, our approach includes two self-supervised learning methods, i.e., scaling-up-down prediction and 3D-2D-3D projection-reconstruction, and two transfer learning + +ALGORITHM 1: GLRV Training Procedure +Input : labeled source dataset $\mathcal{S} = \{(P_i^s,y_i^s)\}_{i = 1}^{n^s}$ unlabeled target dataset $\mathcal{T} = \{(P_i^t)\}_{i = 1}^{n^t}$ number of source neighbors for voting $k$ reliability or consistency threshold $\lambda$ feature generator $\Phi$ , classifiers $\Psi_{1}$ and $\Psi_{2}$ regression $\Omega$ , reconstructor $\Delta$ number of training rounds $R$ number of epochs $E$ for each round. +Output: $\Phi ,\Psi_1,\Psi_2,\Omega$ and $\Delta$ +Initialization: randomly initialize $\Phi ,\Psi_1,\Psi_2,\Omega$ and $\Delta$ randomly initialize pseudo labels $\{\tilde{y}_i^t\}_{i = 1}^n$ zero-initialize selection indicator $h = 0$ +for 1 to $R$ do for 1 to $E$ do for $(P_i^s,y_i^s),(P_i^t,\tilde{y}_i^t)$ in $(S,T)$ do min $\mathcal{L}_s$ with $(P_i^s,y_i^s)$ . min $\mathcal{L}_g$ with $P_{i}^{t}$ . min $\mathcal{L}_l$ with $P_{i}^{t}$ . if $h_i = 1$ then min $\mathcal{L}_t$ with $(P_i^t,\tilde{y}_i^t)$ else min $\mathcal{L}_s - \mathcal{L}_{adv}$ with $(P_i^s,y_i^s)$ and $P_{i}^{t}$ min Ladv with $P_{i}^{t}$ end end end update pseudo labels $\{\tilde{y}_i^t\}_{i = 1}^{n^t}$ and selection indicator h based on $\Phi ,k$ and $\lambda$ + +methods, i.e., adversarial training and our reliable voted self-training method. The framework of our approach is illustrated in Fig. 3. The overall training process is shown in Alg. 1. The training contains multiple rounds. After each round, we perform reliable voted pseudo label generation. Each round contains several epochs. In each epoch, we perform supervised learning, scaling-up-down prediction, 3D-2D-3D projection-reconstruction and adversarial training. + +# 4. Experiments + +# 4.1. Datasets + +PointDA. The PointDA [27] dataset is a widely-used benchmark for point cloud domain adaptation evaluation, which extracts the samples in 10 shared classes from ModelNet40 [37], ShapeNet [2] and ScanNet [3], respectively. In this way, PointDA consists of three subsets: ModelNet-10 (M10), ShapeNet-10 (S10) and ScanNet-10 (S*10). Given the three subsets, we can conduct six types of adaptation scenarios: M10 → S10, M10 → S*10, S10 → M10, S10 → + +
Self-SupervisedTransferAccuracy
Scale3D-2D-3DAdversarialPseudo Label
VoteReliable
XXXXX64.2
✓69.8
✓67.9
✓✓71.2
✓66.7
✓67.4
✓✓73.8
✓✓✓74.2
✓✓✓✓✓76.2
+ +Table 1. Ablation study on each component of our method. Experiments are conducted on PointDA with the $\mathrm{S} * {10} \rightarrow \mathrm{S}{10}$ scenario. When none of the components is employed,the model is directly transferred to the target domain without adaptation. + +
MethodM→SM→S*S→MS→S*S*→MS*→S
Rotation [24]82.841.774.049.064.768.7
Scale (ours)84.046.076.448.366.269.8
+ +Table 2. Comparison of vertical rotation and our scaling-up-down method for self-supervised global structure modeling on PointDA. + +
AdaptationDef-Rec [1]Def-Loc [43]3D-2D-3D (ours)
M10 → S1083.378.683.5
M10 → S*1046.652.353.4
S10 → M1079.875.075.7
S10 → S*1049.951.448.7
S*10 → M1070.769.368.2
S*10 → S1064.463.667.9
+ +Table 3. Comparison of deformation-reconstruction (Def-Rec), deformation-localization (Def-Loc) and our 3D-2D-3D method for self-supervised local structure modeling on PointDA. + +$\mathrm{S}^{*}10$ $\mathrm{S}^{*}10\to \mathrm{M}10$ and $\mathrm{S}^{*}10\rightarrow \mathrm{S}10$ + +Sim-to-Real. The Sim-to-Real [16] dataset is a fairly new benchmark, which consists of 11 shared classes from ModelNet40 and ScanObjectNN [34], and 9 shared classes from ShapeNet and ScanObjectNN, respectively. The dataset is built to evaluate meta-learning on point clouds. In this paper, we also employ the dataset for evaluating point cloud domain adaptation. The dataset consists of four subsets: ModelNet-11 (M11), ScanObjectNN-11 (S\*O11), ShapeNet-9 (S9) and ScanObjectNN-9 (S\*O9). Different from PointDA, Sim-to-Real asks models to transfer knowledge from simulated ModelNet or ShapeNet to real-world ScanObjectNN. Therefore, there are two types of adaptation scenarios Sim-to-Real: M11 $\rightarrow$ S\*O11 and S9 $\rightarrow$ S\*O9. + +
MethodM10 → S10M10 → S*10S10 → M10S10 → S*10S*10 → M10S*10 → S10
w/o Adaptation83.3 ± 0.743.8 ± 2.375.5 ± 1.842.5 ± 1.463.8 ± 3.964.2 ± 0.8
DANN [12]74.8 ± 2.842.1 ± 0.657.5 ± 0.450.9 ± 1.043.7 ± 2.971.6 ± 1.0
PointDAN [27]83.9 ± 0.344.8 ± 1.463.3 ± 1.145.7 ± 0.743.6 ± 2.056.4 ± 1.5
RS [29]79.9 ± 0.846.7 ± 4.875.2 ± 2.051.4 ± 3.971.8 ± 2.371.2 ± 2.8
DefRec + PCM [1]81.7 ± 0.651.8 ± 0.378.6 ± 0.754.5 ± 0.373.7 ± 1.671.1 ± 1.4
GAST [43]84.8 ± 0.159.8 ± 0.280.8 ± 0.656.7 ± 0.281.1 ± 0.874.9 ± 0.5
GLRV (ours)85.4 ± 0.460.4 ± 0.478.8 ± 0.657.7 ± 0.477.8 ± 1.176.2 ± 0.6
+ +Table 4. Accuracy on the PointDA dataset. Our GLRV method achieves four best accuracies among the six adaptation scenarios. + +
MethodM11 → S*O11S9 → S*O9
w/o Adaptation61.68 ± 1.2657.42 ± 1.01
PointDAN [27]63.32 ± 0.8554.95 ± 0.87
MetaSets [16]72.42 ± 0.2160.92 ± 0.76
GLRV (ours)75.16 ± 0.3462.46 ± 0.55
+ +Table 5. Accuracy on the Sim-to-Real dataset. Our GLRV method achieves the best accuracies on the four adaptation scenarios. + +The background of ScanObjectNN objects is not used. + +# 4.2. Implementation + +Following existing works [1, 16, 43], we employ DGCNN [35] as feature generator. For PointDA, we use the setting of [1,43]. For Sim-to-Real, we follow the setting of [16]. The training contains 20 rounds, with 50 epochs in each round. Batch size is set to 32 and learning rate is set to 0.001. By default, the $k$ and $\lambda$ of reliable voting is set to 10 and 1.0, respectively. + +# 4.3. Comparison to the State-of-the-art + +For PointDA, we compare our method with the state-of-the-art point-based domain adaptation methods, including Domain Adversarial Neural Network (DANN) [12], Point Domain Adaptation Network (PointDAN) [27], Reconstruction Space Network (RS) [29], Deformation Reconstruction Network with Point Cloud Mixup (DefRec + PCM) [1] and Geometry-Aware Self-Training (GAST) [43]. We report the mean accuracy and standard error with three seeds in Table 4. Our GLRV method achieves four best accuracies on the six adaptation scenarios. + +We also compare our scaling-up-down and 3D-2D-3D approaches with existing global (vertical rotation classification [24]) and local (deformation-reconstruction [1] and deformation-localization [43]) modeling methods, respectively. Results in Table 2 and Table 3 show the effectiveness of our method. + +For Sim-to-Real, we compared our method with a point cloud domain adaptation method, i.e., PointDAN [27], and + +a meta-learning method, i.e., MetaSets [16]. We perform each adaptation scenarios three times and report the average and the standard deviation of the results in Table 5. Our method outperforms both the domain adaptation and meta-learning methods. + +# 4.4. Ablation Study + +A) Influence of scaling-up-down prediction, 3D-2D-3D projection-reconstruction, adversarial training and reliable voted pseudo label. + +To investigate the influence of each component in our method, we conduct an ablation study on PointDA with the $\mathrm{S}^{*}10\rightarrow \mathrm{S}10$ scenario. The results are show in Table 1. All the four components effectively improve domain adaption. Among them, the reliable voted pseudo label method (Vote $^+$ Reliable) is the most effective, which increases the baseline $(64.2\%)$ by $9.6\%$ . Note that, without the consistency-based reliable target sample section, the improvement drops significantly. This is because the single voting method fails to obtain accurate pseudo labels and inevitably adds noise into training data. + +B) Progressively selecting more and more target data and gradually improving accuracy. + +To verify the ability of the reliable voting method to iteratively and adaptively select more and more target data during training, we show the number of selected reliable target samples, the accuracy of their pseudo labels and the accuracy on the test dataset in Fig. 5a $\sim$ Fig. 5f. Under the premise of fixed or slightly varying accuracy of pseudo labels, more and more target training data is selected, which means that the number of correctly labeled target point clouds increases. With the correct labeled target data increasing, the feature generator is gradually improved on the target domain. + +C) Impact of $k$ and $\lambda$ on voted pseudo label generation and adaptation performance. + +Our reliable voting method contains two hyperparameters, i.e., $k$ and $\lambda$ . To investigate the impact of the two hyper-parameters, we conduct the $S^{*}10 \to S10$ adaption with different $k$ and $\lambda$ . The results are shown in Fig. 5j $\sim$ Fig. 5l. To investigate $k$ , we fix $\lambda$ to 1.0. When $k = 5$ , a + +![](images/bfe91b0352bff3411bdc4730062032dc575134466474c18c856ca7f1917a2e5a.jpg) +(a) $\mathrm{M10}\rightarrow \mathrm{S10}$ + +![](images/882894b60f839dbed70b1e311ed9e4bd1811a1316b186bd88fa9122bb6928e8e.jpg) +(b) M10 $\rightarrow$ S10 + +![](images/1d7815b23a33a927ce9a40dfa7785eab50f93b990e93893af02209d1ffda677f.jpg) +(c) $\mathrm{M}10\to \mathrm{S}^{*}10$ + +![](images/b3821cfc15d1e93ee57340ecc4e1967b031b3117c3c5c5b856afddddc1d63ae6.jpg) +(d) S10 $\rightarrow$ M10 + +![](images/523371238bac98a020f8997a808a6f3a8ecfa394000b2c3dba46286e349d263b.jpg) + +![](images/25a8ab93c31432a434a066ea9347c3c02ceb7f5d1cbafd3932794dc39bd42de0.jpg) + +![](images/bdc8f5118a0e6bd7ce252a7633a752b7dc25fd6a46b15ed993a548646b3fe75c.jpg) + +![](images/7121b0d2ea78f5a64d5c6092d0b76d7c9c6215ae05de70eca8c208f0b3557af8.jpg) + +![](images/15e21e01b5d6f8a56318d682622a2563ad4c1f9fe9da436c0e863feb7b661572.jpg) +(e) $\mathrm{S}^* 10\to \mathrm{M}10$ +(i) $k$ on test accuracy +Figure 5. Influence of reliable voted pseudo labels. Experiments are conducted on PointDA. (a)~(f): With training, the proposed method adaptively selects more and more target data and test accuracies increase gradually. (g)~(l): Impact of $k$ and $\lambda$ on voted pseudo label generation and adaptation performance ( $S^*10 \rightarrow S10$ ). To show the real trend, test accuracies are evaluated without source validation. + +![](images/e075e3257520bd5a2127e861bd062fbd8606025623649be0b5101ba946dc0ad9.jpg) +(f) $\mathrm{S}^{*}\mathrm{10}\rightarrow \mathrm{S10}$ +(j) $\lambda$ on proportion of reliable data + +![](images/39f9a2328edc9d896523fe887adbc2cabecd6d0c31ee8d2e74f6339664667a6d.jpg) +(g) $k$ on proportion of reliable data +(k) $\lambda$ on accuracy of pseudo labels + +![](images/5622d2acf544cea768a05ee39eb54936c61acea4a9c308d1ba617649e013b18f.jpg) +(h) $k$ on accuracy of pseudo labels +(1) $\lambda$ on test accuracy + +large number of target samples with noisy pseudo labels are selected. In this case, the method plays a negative role to adapting. When $k$ increases, the reliability increases, leading to the accuracy improvement. When $k$ is too large, although the pseudo label accuracy increases, too few target data is selected. Consequently, the advantage of pseudo labels diminishes and the corresponding improvement weakens. To investigate $\lambda$ , $k$ is fixed to 10. When $\lambda$ decreases from 1.0 to 0.6, the selected target data becomes less reliable. Because noise is added, the accuracy decreases. + +# 5. Conclusion + +In this paper, we propose two self-supervised learning methods, i.e., scaling-up-down prediction and 3D-2D-3D + +projection-reconstruction, and one reliable voted pseudo label method for point cloud domain adaptation. Experiments on two datasets demonstrate the effectiveness of our approach. However, when selecting target data, our reliable voting method does not take the class balance problem into consideration. 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Our intuition is that 3D geometric consistency priors such as smooth regions and surface discontinuities may imply consistent semantics or object boundaries, and can act as strong cues to guide the learning of 2D image representations without semantic labels. Specifically, we introduce 3D geometric consistency into a contrastive learning framework to enforce the feature consistency within image views. We propose to use geometric consistency sets as constraints and adapt the InfoNCE loss accordingly. We show that our learned image representations are general. By fine-tuning our pre-trained representations for various 2D image-based downstream tasks, including semantic segmentation, object detection, and instance segmentation on real-world indoor scene datasets, we achieve superior performance compared with state-of-the-art methods. + +# 1. Introduction + +Self-supervised image representation learning is an important problem in the field of computer vision and has been rapidly developed in recent years. Existing works in this area mainly focus on designing various pretext tasks to learn general and intrinsic image features in self-supervised manners [14, 18, 37]. Those pretext tasks are usually low-level and can capture general image properties that favor many downstream tasks, like image classification, semantic segmentation, object detection, instance segmentation, etc. Due to its ability to learn from a large amount of unlabeled data, self-supervised representation learning has already become a standard training regime in many real-world applications [2, 3, 15, 55]. + +Recently, researchers have started to use 3D data, usually + +![](images/cdd274265630426a5c3464ef316ef5de5ada17da0a3f92db6542151f0136e90b.jpg) +Pre-training with Geometric Set Consistency + +![](images/5b72c057ba75a5b2feedc2fda6cb016740bfb8133c130201b5cf4518aa999943.jpg) + +![](images/83bdcb72d3ef072b464bf1e4d25675c7bf6c9e85f3496245c7f4e9760e3bc47a.jpg) +Object Detection +Figure 1. We introduce geometric consistency set to enforce the consistency within images for self-supervised image representation learning. We show that, the image representations pre-trained in this way can improve the performance of some 2D downstream tasks including semantic segmentation, object detection and instance segmentation. + +![](images/3fb6fa79658368381d2c5e91501b79aa3f515a67dec61fb02d32b060fbfc4ce1.jpg) +Instance Segmentation + +![](images/be7c693f87515be51dbbd6f295688867da575115c7e33192d71c12f123db8da0.jpg) +Semantic Segmentation + +represented by point clouds, meshes, or voxel grids, as guidance for learning image representations [18, 30]. Compared with 2D images, 3D data has complementary advantages for learning discriminative image features. Since 3D data is usually acquired by real-world scanning and reconstruction, and has the same dimension as the real-world scenes, learning geometric structures from 3D data is much easier than 2D images. Moreover, complex occlusions, as well as the texture of objects will also affect the performance of image perception methods. Meanwhile, 3D data is occlusion-free, and geometric cues like smooth regions and sharp edges can be strong priors for semantic understanding. Thus it is natural to use 3D geometric cues to favor the learning of image + +representations. + +Pioneering works, like Pri3D [18], mainly rely on multiview pixel-level consistency or 2D-3D pixel to point consistency for learning image representations in a self-supervised manner. The image representations learned in this way are proven to have significantly better performance than learning purely from 2D images for downstream tasks. Despite these great successes, the geometric consistency priors in 3D data (i.e. smooth regions or depth gaps) are not directly employed, which we demonstrate are strong cues and can significantly enhance the learning of image semantics. + +In this paper, we propose to use geometric consistency to promote the learning of image representations. Our intuition is that 3D points within the same smooth or even planar regions may share similar semantics, while the discontinuities or depth gaps in 3D space may imply semantic changes. Such geometric cues are directly observable in unlabeled 3D data. However, due to complex textures, these cues can be hardly learned from purely unlabeled 2D images. Based on the above intuition, we design a simple yet effective method to learn the geometric consistency priors described above. Specifically, we leverage the continuities and discontinuities of 3D data, and use the clustering method to cluster the 3D data into many local small segments, termed geometric consistency sets, to guide the learning of image representations in a self-supervised contrastive way. Our method is simple and can be easily implemented. We show that by exploring geometric consistency in the self-supervised pre-training stage, the performance of downstream tasks can be significantly improved. + +In the following, we summarize our main contributions: + +1) We introduce geometric consistency into a contrastive learning framework for self-supervised image representation learning. +2) We propose a simple yet effective multi-view contrastive loss with geometric consistency sets to leverage the consistency within images. +3) We demonstrate superior performance on several downstream tasks compared with SOTA methods. + +# 2. Related Works + +# 2.1. Scene Understanding + +Learning based scene understanding tasks, including semantic scene segmentation [19, 28, 32, 40], object detection [20, 38, 39] and instance segmentation [17, 24, 54], are fundamental tasks in computer vision and have been rapidly developed in recent years. Due to the available of large scale, real scanned 2D and 3D datasets [1, 8, 12, 47], these tasks have been widely explored. + +View-based methods [9, 23] mainly rely on 2D images for scene understanding tasks, and the results produced with 2D networks can be further fused to 3D space based on + +multi-view consistency. In recent years, with the development of 3D deep learning networks [7, 13, 40, 49, 51], the performance of scene understanding tasks has been further promoted. The architectures of 3D networks can be roughly classified into two categories including point-based [40, 51], and sparse-voxel based [7, 13, 49]. These architectures are mainly designed for extracting features from sparse and unordered 3D data and have achieved great success in 3D scene understanding. Besides, since 2D images have clearer textures while 3D data is occlusion free from which extracting structure information is much easier, it is also an important research topic to study the joint training of 2D and 3D data [18, 30, 31, 48] for scene understanding tasks. + +In this paper, we propose to use 3D geometric consistency as guidance to promote the learning of 2D image representations and improve the performance of 2D scene understanding tasks. + +# 2.2. Self-Supervised Image Pre-training + +Self-supervised image pre-training as a fundamental way for learning representations from a large amount of data has shown significant impact in the field of computer vision and has been proved to be useful for various applications. Researchers in this field mainly aim at designing pretext tasks [25, 35-37] to learn intrinsic and general image representations that may favor various downstream tasks. Contrastive learning [4, 6, 14, 37], due to its effectiveness and simplicity, has attracted great attention in recent years. The key idea of contrastive learning is to enforce the consistency between positive pairs while pushing away negative samples. Mainstream works mainly use various data augmentation strategies to get the positive pairs, including cropping, rotating, Gaussian blurring, etc. Besides, region-wise contrastive learning methods [29, 53] performance contrasting at region level to learn the region level similarities. Recently, researchers start to involve 3D data into contrastive pre-training [18, 30, 31], and the positive samples can be directly induced via multi-view consistency. + +In our work, we also explore using 3D data to promote the learning of image representations. In addition to multi-view consistency, we further leverage geometric consistency to enhance the consistency within image views. + +# 2.3. Multimodal Representation Learning + +Multimodal representation learning aims at learning joint representations by interacting between the data from different modalities. By incorporating the advantages from different modalities, the representations learned in this way are usually much better than those learned with a single modality only. Vision language pre-training [27, 34, 41] is a successful example. The availability of a large amount of image and language pairs makes the learned representations generalizable to various downstream tasks. Recently, + +![](images/9f19ad21682db945908aa187dbc12760f061d30c609a67f56a9559ff92a2012e.jpg) + +![](images/3f9d1d7e394a4540826fc2f2b2a9a1ee909e9f1fa1067310234a29e1ab62a157.jpg) +RGB Image +Figure 2. Pipeline of our pre-training method. Given a collection of multi-view unlabeled images together with the corresponding 3D geometry, we propose to use geometric consistency sets (illustrated with different colors), acquired via 3D clustering, to guide the learning of image representations. Specifically, the multi-view feature maps extracted with a 2D encoder will be first aggregated according to the corresponding geometric consistency sets, and then set-level InfoNCE loss will be used on the aggregated features to leverage the consistency within images. + +![](images/d28c8cd0479d2444247ef6d0d25cdb0b4a6ed42f3110a310cd86c34827f61e59.jpg) +2D Encoder + +![](images/d9733e36e8252fde85802ce566396c8b7b5046f4e2d82f85a7c19c60a45de10a.jpg) + +![](images/5ba0ca8c0c09dfce19919fe3d0bfcaaefcf1429ac510af105f3c6a5abd02bcb0.jpg) +Feature Map + +![](images/de256a20df6579db5d40315722bc6afe9e91bb27c8a9ea5cb1fa76ad5276eb20.jpg) +Geometric Guidance +3D Geometry + +![](images/225175675e45c9809101cba1236e218b2558d43ed0780348a3487d2cd3b7acbe.jpg) + +![](images/f271600f5d8e3d60c524129e9082e7165a59fa6835617cf1238062baa116256c.jpg) +Geometric Consistency Set + +![](images/0edba63373455a8e60face46679a34b377d25294c2dc804c4e52c6d8da37b402.jpg) + +with the availability of large scale RGB-D datasets, learning representations jointly from 2D and 3D data has attracted great attention in the research community [18, 30, 31, 48]. In particular, Pri3D [18] proposed to use 3D data as guidance for learning 2D to 2D and 2D to 3D pixel-level consistency. P4Contrast [31] proposes to use point-pixel pairs for contrastive learning, and constructs negative samples artificially based on disturbed RGB-D points. TupleInfoNCE [30] compose new negative tuples for contrastive learning using modalities from different scenes to ensure that the weak modalities are not being ignored. + +Existing works mainly use pixel-level multi-view consistency of single or multiply modalities. In our work, we use geometric consistency sets as guidance to explore intraview consistency for 2D representation learning. + +# 2.4. Pseudo Labeling + +Pseudo labeling [21, 26, 33, 42, 46], as an effective way for learning with unlabeled data, has been widely studied in various applications. The key to the success of pseudo labeling methods is to generate high-quality pseudo labels for the unlabeled data. Researchers in this field have explored various ways for acquiring pseudo labels, including predicting directly with trained networks [26, 33], neighborhood graph propagation [21] or confidence based selection [42, 46] etc. + +The mainstream works mainly use pseudo labels in semi-supervised or weakly supervised learning scenarios. In our work, the geometric consistency sets we used serve as pseudo consistency labels to guide the learning of 2D image representations in a self-supervised manner. + +# 3. Method + +Given a large collection of unlabeled images $\{I_i\}$ together with the corresponding 3D scenes $\{S_i\}$ represented as 3D points, the goal of our method is to pre-train an image encoder $f_{\theta}$ that can extract general and representative features from the input images with the guidance of geometric consistency in a self-supervised manner. And the pre-trained encoder $f_{\theta}$ can improve the performance of various downstream tasks after fine-tuning on relatively small labeled datasets. Note that 3D data is only used for pretraining and is not available in the fine-tuning stage. + +Figure 2 illustrates our overall framework. In order to learn the image representations given a set of multi-view unlabeled images together with the corresponding 3D data, our observation is that the consistency or inconsistency of the geometric features in 3D space can serve as strong prior that may imply consistent semantics or object boundaries. For example, points that lie in the same smooth or even planar region may share the same semantics, while those separated by geometry dis-continuities or depth gaps may infer semantic changes. Based on the above observation, we propose to incorporate geometric consistency sets, for example clustering the 3D data with similar geometry features into local smooth segments, into a contrastive learning framework to leverage the geometric consistency in learning image representations, and adapt the InfoNCE loss accordingly. In the following, we will first describe the formulation of the set-InfoNCE loss that generalizes the InfoNCE loss to enforce the consistency within image views. And then, we will provide the detailed implementation of our proposed contrastive training framework under the guidance of geometric consistency set. + +# 3.1. Set-InfoNCE Loss + +![](images/7546188c454769f0a20725647e17162fd65af370bdd8f96355d622fb27301bfa.jpg) + +![](images/b40c53b8c8e9624e7ed3dd2768057b79ec0d3c80cee51109479d47486a834d07.jpg) +2D Projection + +![](images/dc3dd2ada34ccb5bae678eee9826ded03ed5b958db68cf31f165240816b44966.jpg) +Image $I_{m}$ Projected Geo-sets $\{P_i^m\}_i$ + +![](images/7e6c160c818d2ecaeda0b06670ef89930b0a4182e2326ae7ee1f9724d8025de6.jpg) +Geometric Consistency Set +Figure 3. Geometric consistency set. We visualize the geometric consistency sets (with different colors) as well as the corresponding 2D projections on two corresponding image views. + +![](images/b0d0437f75ae9ee67c527c6588e87333c2ebbd0eae5c35bc42ad468210c18656.jpg) +Image $I_{n}$ Projected Geo-sets $\{P_i^n\}_i$ + +2D contrastive image representation learning mainly aims at learning consistent representations by contrasting multi-view images on either image level or pixel level. The multi-view images can be acquired via different data augmentation strategies or from real-world scanned sequences. Contrastive learning then enforces the feature consistency between different views that correspond to the same content while pushing away the others. For the pixel level contrastive representation learning, current works use pixel-level InfoNCE loss [18], which is defined as: + +$$ +\mathcal {L} _ {\text {p i x e l}} = - \sum_ {(i, j) \in M _ {p}} \log \frac {\exp \left(\mathbf {f} _ {i} \cdot \mathbf {f} _ {j} / \tau\right)}{\sum_ {(\cdot , k) \in M _ {p}} \exp \left(\mathbf {f} _ {i} \cdot \mathbf {f} _ {k} / \tau\right)} \tag {1} +$$ + +where $M_{p}$ denotes the set of pixel-to-pixel matching pairs from one view to another, $\mathbf{f}_i$ is the normalized feature vector of the pixel at the $i$ th position, and $\tau$ is the temperature parameter for controlling the concentration of the features in the representation space. + +Though the representations learned with pixel-level InfoNCE loss [18] has been proven to be beneficial for many downstream tasks, additional aggregated correspondences among the pixels like the geometric consistency prior could further improve the representation learning. In the following, we give the formulation of the set level InfoNCE loss that generalizes the pixel level InfoNCE to leverage such aggregated correspondences: + +$$ +\mathcal {L} _ {s e t} = - \sum_ {(i, j) \in M _ {s}} \log \frac {\exp \left(\mathcal {F} \left(P _ {i}\right) \cdot \mathcal {F} \left(P _ {j}\right) / \tau\right)}{\sum_ {(\cdot , k) \in M _ {s}} \exp \left(\mathcal {F} \left(P _ {i}\right) \cdot \mathcal {F} \left(P _ {k}\right) / \tau\right)}, \tag {2} +$$ + +where $P_{i}$ is a set of feature points that are likely to have the same semantics, $\mathcal{F}$ is a mapping from a set to a feature vector in $\mathbb{R}^c$ , and $M_{s}$ denotes the correspondence pairs among + +sets. Obviously Eqn. 1 is a special case to Eqn. 2 when the sets $P_{i} = \{\mathbf{f}_{\mathbf{i}}\}$ degenerate to one-element only. In our implementation, we set $\mathcal{F}(P_i) = \frac{1}{|P_i|}\sum_{s_j\in P_i}\mathbf{f}_{\mathbf{s}_j}$ for aggregating the features from all the points within sets, and we will also discuss different variations of $\mathcal{F}$ in Section 5.2. + +Note that the set level InfoNCE loss defined in Eqn. 2 is general, and the strategies for acquiring the set $P_{i}$ might be different for different scenarios [29, 50, 53]. In this paper, we define our geometric consistency set under the guidance of 3D geometry, and will give the detailed description in Section 3.2. + +# 3.2. Learning with Geometric Set Consistency + +Intuitively, the geometric consistency can be a strong prior that can guide the learning of within image consistency. The geometric cues like smooth regions and depth gaps may imply the same semantics or object boundaries respectively. In the following, we give the formal definition of the proposed set-InfoNCE loss with geometric consistency sets under projection. + +Formally, for a given equivalence relation $\sim$ among the points in all the scenes $\cup S_{i}$ , we call the quotient set $\{P_j\} = \cup S_i / \sim$ as the collection of geometric consistency sets. For example, when we have some pre-defined geometric labels among the 3D points and define the equivalence relation as points that share the same label, then the geometric consistency set $P_{i}$ would contain all the points that have the $i$ th label. Besides, for each image $I_{m}$ , we call $P_{j}^{m} = \{\text{proj}(s)\in I_{m}|s\in P_{j}\}$ as the projection of $P_{j}$ from 3D onto 2D image view $I_{m}$ . By adapting Eqn. 2, we could define our set-InfoNCE loss with geometric consistency set as: + +$$ +\mathcal {L} _ {\text {g e o \_ s e t}} = - \sum_ {(i, m, n) \in M _ {s}} \log \frac {\exp \left(\mathcal {F} \left(P _ {i} ^ {m}\right) \cdot \mathcal {F} \left(P _ {i} ^ {n}\right) / \tau\right)}{\sum_ {(k , l , \cdot) \in M _ {s}} \exp \left(\mathcal {F} \left(P _ {i} ^ {m}\right) \cdot \mathcal {F} \left(P _ {k} ^ {l}\right) / \tau\right)}, \tag {3} +$$ + +where $i$ is the index of the geometric consistency set and $m, n$ are the view indices. $M_{s} = \{(i, m, n)\}$ maintains the matching pairs of projections $P_{i}^{m}, P_{i}^{n}$ from one view to another for each geometric consistency set $P_{i}$ . + +In general, any proper notion of spatial equivalence induces its corresponding geometric consistency sets; in this work, we use a simple 3D clustering method and find it already works well in our case. We leave the exploration of more sophisticated spatial partitioning methods as future work. Specifically, for a sequence of 2D images acquired by scanning around a specific scene, we first have the corresponding 3D surface $S$ via 3D reconstruction. To obtain geometric consistency sets, we use the surface over-segmentation results produced by a normal-based graph cut method [11, 22]. As shown in Figure 3, the 3D points that are likely to have the same semantics can be clustered into the same geometric consistency set. + +# 3.3. Training Strategy + +We use a two-stage training strategy to pre-train with our method. Besides our geometric guided set-InfoNCE loss that mainly considers set-level consistency and involves some high-level semantics such as smooth regions and surface discontinuities, we also include the pixel-level multiview consistency to enforce the low-level distinction beneficial for the downstream tasks. Thus we propose to pretrain the network from low-level to high-level progressively with two stages. Specifically, in the first stage, we train the network with pixel to pixel and pixel to point multi-view contrastive loss termed as View and Geo loss in Pri3D [18]. And then, in the second stage, we continue to train the network with our geometric guided set-InfoNCE loss alone. In this way, we can achieve better performance on downstream tasks than training solely with our set-InfoNCE loss or with Pri3D losses. + +# 4. Experimental Setup + +In this section, we will provide a detailed description of our experimental setup, including the backbone architectures, datasets for pre-training and evaluation, and the implementation details. More experiment details are given in the supplementary materials. + +# 4.1. Backbone Architecture + +We use a UNet-style [44] architecture with residual connections as our network backbone since it has been widely used in various deep learning tasks. Specifically, it uses ResNet [16] as encoder, and the decoder part contains standard convolution blocks together with bi-linear interpolation layers for upsampling. In most of our experiments, we use ResNet50 as our encoder for its efficiency and effectiveness. In addition, we also use ResNet18 as the encoder to see the effectiveness of our method with a more lightweight architecture. + +# 4.2. Dataset + +We conduct our experiments on two widely used datasets ScanNet [8] and NYUv2 [47], where ScanNet is used for both pre-training and downstream task fine-tuning, and NYUv2 is used for demonstrating the transferability of the representations learned with our method on ScanNet. In the following, we give more details about the two datasets. + +ScanNet ScanNet [8] contains large amount of RGB-D sequences together with the corresponding 3D scene reconstructions. It has 1513 scenes for training, which contains around 2.5M images in total. Following Pri3D [18], we regularly sample every 25th frame from the original ScanNet sequence for pre-training. And the frame pairs with more + +than $30\%$ pixel overlap will be used for contrastive training. Totally, we have around 804k frame pairs in the pretraining stage. Note that we do not use any semantic labels for pre-training. For fine-tuning on downstream tasks, we use the standard labeled training and validation set of ScanNet benchmark [8], and the 2D images are sampled every 100th frame from the original sequence. Thus, in the fine-tuning stage, we have around 20k images for training and 5k images for validation. + +NYUv2 NYUv2 [47] is a dataset consisting of 2D images scanned from various indoor scenes, and in this paper, it is used for fine-tuning downstream tasks. Totally it has 1449 labeled images, in which 795 images are used for training and 654 images for testing. + +# 4.3. Comparison Methods + +Supervised ImageNet Pre-training [10] The network is pre-trained with the supervised classification task on the ImageNet dataset. + +MoCoV2 [5] For MoCoV2, there are various strategies for feeding the data, we only list the best performing result (i.e. MoCoV2-supIN $\rightarrow$ SN) from Pri3D [18]. To be specific, MoCoV2 is initialized with supervised ImageNet pretraining and then trained on ScanNet with randomly shuffled images. + +Pri3D [18] Pri3D is the method most related to ours, in which 3D data and contrastive pre-training are used. Specifically, it comprises 2D to 2D and 2D to 3D point InfoNCE loss, termed View and Geo loss, respectively, and is also initialized with supervised ImageNet pre-training. + +Depth Prediction The network is pre-trained with a single view depth prediction task, and is also initialized with supervised ImageNet pre-training. We obtain the results directly from Pri3D [18] where the method is implemented as a baseline. + +# 4.4. Implementation Details + +We use the following setting in our experiments unless explicitly specified. For pre-training with our method, Stochastic gradient descent(SGD) [43] with Polynomial Learning Rate Policy (PolyLR) [45] is used for optimization. The initial learning rate is 0.1 and the batch size is 64. Following Pri3D [18], we initialize the network with ImageNet pre-trained weights. In the first stage of pre-training, we train the network with View and Geo loss from Pri3D for 5 epochs. And then in the second stage, the network is trained with our proposed methods for 2 epochs. We use 8 NVIDIA V100 GPUs for training our network, and all the experiments are implemented with PyTorch. + +![](images/3fdc1f2371d195eb813e86c2c3511578fe697224fe3fdb8abd45f213e423c958.jpg) +Figure 4. Qualitative results of semantic segmentation task on ScanNet and NYUv2 datasets. All the methods are pre-trained on ScanNet with ResNet50 as the backbone. For Pri3d we reproduce the results with their released code. + +![](images/ab974ab8d46bbe9c558fb66e70219d95bc9e6ce8abf746254655e7eac066a093.jpg) + +
MethodResNet50ResNet18
From Scratch39.137.5
ImageNet Pre-training55.751.0
MoCoV256.652.9
Depth Prediction58.4-
Pri3D(View)61.354.4
Pri3D(Geo)61.155.3
Pri3D(View + Geo)61.755.7
Ours63.157.2
+ +# 5. Experimental Results + +# 5.1. Fine-tuning for 2D Downstream Tasks + +In the following, we demonstrate the effectiveness of our method by fine-tuning the pre-trained network on several 2D downstream tasks, including semantic segmentation, instance segmentation, and object detection. + +Semantic Segmentation on ScanNet We demonstrate the effectiveness of our pre-trained representation by fine-tuning it with the ScanNet standard labeled training set, and mean IoU is used as the evaluation metric. ResNet50 + +Table 1. 2D semantic segmentation results on ScanNet. We use ResNet50 and ResNet18 as the backbone, mIoU for evaluation. + +
Method20%40%60%80%100%
Pri3d(View + Geo)51.556.258.960.361.7
Ours54.158.360.461.563.1
+ +Table 2. Data efficient learning results on ScanNet. We fine-tune our pre-trained representations with a limited amount of training data (from $20\%$ to $100\%$ ). ResNet50 is used as the backbone, and mIoU is used for evaluation. + +or ResNet18 is used as the backbone encoder for all pre-training methods. In Table 1, we compare our results with other state-of-the-art pre-training methods. Our method outperforms all the state-of-the-art methods for both ResNet50 and ResNet18 backbones, which confirms the effectiveness of our proposed self-supervised pre-training strategy with geometry-guided set consistency. Figure 4 demonstrates some qualitative results, as we can see that the segmentation results of our method are less noisy and have clearer details. + +We further test our method with different amounts of data for fine-tuning to study the performance under limited data scenarios. ResNet50 is used as the backbone. As shown in Table 2, by comparing our method with the best performing SOTA method, we can achieve superior performance consistently under different ratios of training data. + +Moreover, we also test our pre-trained representations + +
MethodResNet50
DeepLabV3(ImageNet)57.0
DeepLabV3(Pri3D)61.3
DeepLabV3(Ours)62.2
DeepLabV3+(ImageNet)57.8
DeepLabV3+(Pri3D)61.6
DeepLabV3+(Ours)62.7
PSPNet(ImageNet)59.7
PSPNet(Pri3D)62.8
PSPNet(Ours)63.7
+ +Table 3. 2D semantic segmentation results on ScanNet with different network architectures. ResNet50 is used as the backbone for all architectures, and mIoU is used for evaluation. + +
MethodAP@0.5AP@0.75AP
From Scratch32.717.716.9
ImageNet Pre-training41.725.925.1
MoCoV243.526.825.8
Pri3D(View)43.727.026.3
Pri3D(Geo)44.227.626.6
Pri3D(View + Geo)44.527.426.6
Ours45.127.626.9
+ +with more advanced 2D semantic segmentation architectures including DeepLabV3 [2], DeepLabV3+ [3] and PSPNet [55]. As shown in Table 3, our method consistently outperforms the state-of-the-art methods by a large margin. Which further validate the effectiveness of considering geometric consistency set for self-supervised image representation learning. + +Instance Segmentation and Detection on ScanNet We fine-tune our pre-trained representations on 2D ScanNet object detection and instance segmentation tasks to see the generalizability of the learned representations. Specifically, ResNet50 is used as the backbone encoder for all the pretraining methods. Mask-RCNN [15] implemented by Detectron2 [52] is used for object detection and instance segmentation tasks. As shown in Table 4 and 5, we can achieve comparable or superior performance compared with the other state-of-the-arts on different evaluation metrics. + +Transfer to NYUv2 We demonstrate the transferability of our pre-trained representations to other datasets. Specifically, we use ResNet50 as the backbone encoder for all pretraining methods. The network is pre-trained on ScanNet + +Table 4. 2D object detection results on ScanNet. We use ResNet50 as the backbone and average precision for evaluation. + +
MethodAP@0.5AP@0.75AP
From Scratch25.813.112.2
ImageNet Pre-training32.617.817.6
MoCoV233.918.118.3
Pri3D(View)34.318.718.3
Pri3D(Geo)34.418.718.3
Pri3D(View + Geo)35.819.318.7
Ours36.019.319.5
+ +Table 5. 2D instance segmentation results on ScanNet. We use ResNet50 as the backbone and average precision for evaluation. + +
MethodResNet50
From Scratch24.8
ImageNet Pre-training50.0
MoCoV247.6
Pri3D(View)54.2
Pri3D(Geo)54.8
Pri3D(View + Geo)54.7
Ours55.4
+ +Table 6. 2D semantic segmentation results on NYUv2. mIoU is used as the evaluation metric. + +
MethodAP@0.5AP@0.75AP
From Scratch21.310.39.0
ImageNet Pre-training29.917.316.8
MoCoV230.118.117.3
Pri3D(View)33.019.818.9
Pri3D(Geo)33.820.219.1
Pri3D(View + Geo)34.020.419.4
Ours34.620.519.7
+ +Table 7. 2D object detection results on NYUv2. We use ResNet50 as the backbone, and average precision for evaluation. + +[8] dataset, and fine-tuned for downstream tasks on NYUv2 [47] dataset. Following Pri3D [18], we use the learning rate 0.01 instead of 0.1 for semantic segmentation task. As demonstrated in Table 6, 7 and 8, our pre-trained representations achieve superior performance compared with SOTA methods on most evaluation metrics, which further confirms that our pre-trained image representations are general and transferable across different datasets. + +# 5.2. Ablation Study + +Different Implementation of Set Feature Aggregation We study a different choice of the set feature aggregation function $\mathcal{F}$ in Eqn. 3 to see whether it will influence the performance. Instead of using the average function to aggre + +
MethodAP@0.5AP@0.75AP
From Scratch17.29.28.8
ImageNet Pre-training25.113.913.4
MoCoV227.214.714.8
Pri3D(View)28.115.715.7
Pri3D(Geo)29.015.915.2
Pri3D(View + Geo)29.516.315.8
Ours29.716.316.5
+ +gate set-level features for both positive and negative pairs, here we test an asymmetric implementation. To be specific, for $\mathcal{F}(P_i^m)$ and $\mathcal{F}(P_k^l)$ in Eqn. 3 we select the feature of an arbitrary point from each set, and for $\mathcal{F}(P_i^n)$ average function is used. We pre-train the network with the newly defined loss on ScanNet and fine-tune it for ScanNet semantic segmentation. ResNet50 is used as the backbone. In this way, we get the performance of $63.1\mathrm{mIoU}$ on the validation set, which is comparable with our result in Table 1. + +Ablation of Geometric Consistency Set We study the stability of our method by varying the parameters of the over-segmentation method [11, 22] used for generating geometric consistency sets. To be specific, we generate geometric consistency sets on ScanNet under different clustering edge weight thresholds, and pre-train our network accordingly. As shown in Table 9, our method yields robustness to the clustering parameters. + +Table 8. 2D instance segmentation results on NYUv2. We use ResNet50 as the backbone, and average precision for evaluation. + +
Threshold0.010.020.030.040.05
mIoU63.262.962.963.263.1
+ +Pre-training with GT Semantic Label Instead of using a geometry-guided consistency set, we also study the performance of the set-InfoNCE loss under the guidance of the ground truth semantic labels. Specifically, we use ground truth semantic labels to obtain the ground truth consistency sets and pre-train our network with ResNet50 as encoder on ScanNet [8]. Note that ground truth category id is not used in pre-training. By fine-tuning the pre-trained representations for the ScanNet 2D semantic segmentation task, it could achieve the performance of $66.4\mathrm{mIoU}$ , which implies that a more sophisticated consistency set generation strategy may help to improve the result further. + +Table 9. Ablation of geometric consistency set. 2D semantic segmentation results on ScanNet with different over-segmentation parameters used for pre-train. ResNet50 is used as the backbone. + +
MethodResNet50
Pri3D Original61.7
Pri3D Continue(View)61.4
Pri3D Continue(Geo)61.6
Pri3D Continue(View + Geo)61.5
Ours63.1
+ +Table 10. Ablation of Pri3D. Continuous training of different configurations of Pri3D can not lead to better results. Pri3D Continue means continuous training of Pri3D. + +Ablation of Pri3D Since in the first stage of our method we use View and Geo loss in Pri3D [18] to train the initial representations, one may wonder whether training Pri3D for more epochs will lead to better performance compared with the results listed in their original paper. To address this concern, we test thoroughly by continuing training from the Pri3D checkpoint with different combinations of their losses for two more epochs. And then fine-tune the network on ScanNet semantic segmentation task [8]. Totally, in this experiment, Pri3D is pre-trained for 7 epochs. As shown in Table 10, continuous training of different configurations of Pri3D can not lead to better results. + +# 6. Limitations & Future Work + +While our proposed pre-training method demonstrates superior performance compared with the state-of-the-art methods, there still exist several limitations. Since our approach relies on 3D geometric consistency to guide the learning of image representations, it can hardly be applied directly on the datasets such as ImageNet [10], where 3D reconstructions are not applicable. Besides, in this work, we use a simple 3D clustering method for computing geometric consistency sets; one may consider using more advanced clustering techniques to further improve the performance. + +# 7. Conclusion + +We propose a method that uses 3D geometric consistency as guidance for self-supervised image representation learning. We leverage the continuities and discontinuities of 3D data and use the 3D clustering results to produce geometric consistency sets for 2D image views. 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Existing methods often rely on Class Activation Mapping (CAM) that measures the correlation between image pixels and classifier weight. However, the classifier focuses only on the discriminative regions while ignoring other useful information in each image, resulting in incomplete localization maps. To address this issue, we propose a Self-supervised Image-specific Prototype Exploration (SIPE) that consists of an Image-specific Prototype Exploration (IPE) and a General-Specific Consistency (GSC) loss. Specifically, IPE tailors prototypes for every image to capture complete regions, formed our Image-Specific CAM (IS-CAM), which is realized by two sequential steps. In addition, GSC is proposed to construct the consistency of general CAM and our specific IS-CAM, which further optimizes the feature representation and empowers a self-correction ability of prototype exploration. Extensive experiments are conducted on PASCAL VOC 2012 and MS COCO 2014 segmentation benchmark and results show our SIPE achieves new state-of-the-art performance using only image-level labels. The code is available at https://github.com/chenqi1126/SIPE. + +# 1. Introduction + +Semantic segmentation aims to assign a semantic category label to each pixel in an image, which has been widely applied in autonomous driving [14], medical imaging [38] and remote sensing image interpretation [17]. Benefiting from Convolutional Neural Networks (CNNs), semantic segmentation has achieved remarkable progress in fully supervised manner. However, training a fully supervised segmentation model requires a large number of + +![](images/aaff5e320e569892fe7c3314b555a18d040b2cad414d28d4318d5666624587c7.jpg) + +![](images/f02a04be8775dafcdc2e083cb0b3c143c04e52811567579d3d2303eaa6b3a426.jpg) + +![](images/54d611afb1c7997a68123ec065edf14e832513ffa05fa570d685c009a0589f86.jpg) +Figure 1. Main motivation. We visualize the pixel-level feature distribution of four cat images by t-SNE [39]. The original CAM activates each pixel using class center (green star). Our method extracts image-specific prototypes (pink star) to generate Image-Specific CAM (IS-CAM) that captures more complete regions. + +pixel-level annotations, which is notoriously expensive and time-consuming to collect. An alternative approach is to learn from weak labels, e.g., image-level labels [2], bounding boxes [26, 49], scribbles [29, 34, 46] and points [3, 5]. Among these works, image-level labels based Weakly Supervised Semantic Segmentation (WSSS) has enjoyed great popularity within the community. + +Most of existing methods leverage Class Activation Mapping (CAM) [53] technology to provide localization cues of target object. Specifically, these methods train a classifier and regard its learned weights as a general representation of each class, i.e., class center. Then, this class center is used to correlate with image pixels to obtain localization maps as shown in Fig. 1. However, CAM tends to + +focus on a few primary regions (cat's head) while ignoring other useful cues (cat's body). To explain the problem, we visualize pixel-level features of foreground extracted from a trained classification network. Those features are shown with four different colors and their transparency degree indicate the activation of CAM. We find that the class center always gives high activations to the close pixels (correspond to some primary regions) and ignores the distant pixels. The imbalanced activations lead to the incomplete localization map as demonstrated in Fig. 1. In addition, activating features on each image by the centroid of that features (pink star) can be beneficial to explore more complete regions (see Image-Specific CAM (IS-CAM) shown in Fig. 1). Therefore, this paper aims to tailor image-specific prototypes to adaptively describe the image itself. + +To this end, we propose a novel weakly supervised semantic segmentation framework, called Self-supervised Image-specific Prototype Exploration (SIPE). The proposed SIPE consists of an Image-specific Prototype Exploration (IPE) and a General-Specific Consistency (GSC) loss, which is illustrated in Fig. 2. Specifically, IPE is realized as two sequential steps to characterize prototypes, allowing to capture more complete localization maps. In the first step, we utilize inter-pixel semantics to explore spatial structure cues, locating robust seed regions of each class. Given the seed regions, we extract image-specific prototypes and then produce our IS-CAM by prototypical correlation. In addition, GSC is proposed to construct the consistency of general CAM and our specific IS-CAM. This self-supervised signal further optimizes the feature representation and empowers a self-correction ability of prototype exploration. Extensive experiments are conducted on Pascal VOC 2012 [11] and MS COCO 2014 [30] and results show that our SIPE achieves new state-of-the-art performance when only image-level labels are available. + +Our main contributions are summarized as: + +- We propose Self-supervised Image-specific Prototype Exploration (SIPE) to learn image-specific knowledge for weakly supervised semantic segmentation. +- We propose Image Prototype Exploration (IPE) that tailors image-specific prototypes for each image, which is achieved by structure-aware seed locating and background-aware prototype modeling. It enables the model to capture more complete localization maps. +- We propose a General-Specific Consistency (GSC) loss to effectively regularize the original CAM and IS-CAM, empowering the feature representation. + +# 2. Related Work + +Due to the low annotation costs, image-level labels based weakly supervised semantic segmentation has attracted in- + +creasing attention. Most existing methods adopt Class Activation Mapping (CAM) to generate localization maps and then refine them as pseudo labels to train a fully supervised segmentation model. To achieve a high performance segmentation model, many strategies have been investigated to improve the quality of localization maps. + +Erasure and accumulation. Erasure methods explore more object regions by intentionally removing the discriminative regions from the images [23, 37, 43] or feature maps [8, 18]. However, erasing most of the discriminative regions may confuse the classifier and result in false positives. To avoid this problem, some works accumulate multiple activations by applying well-designed sampling on dilated convolution rate [44], image scales [50], spatial location [24] and training process [20]. + +Cross-image mining. Considering the sharing semantics between images, some works design cross-image relation mining modules, such as cross-image affinity [13], max bipartite matching [31] and co-attention classifier [36] to excavate semantic context of weak labels. Furthermore, the collaborative information of multi-images is explored to capture the potential knowledge by graph convolution network [28] and self-attention mechanism [45]. + +Background Modeling. Many methods [21, 27, 47, 48] obtain precise background by using auxiliary saliency maps, which is laborious. Without auxiliary maps, Fan et al. [12] propose intra-class discriminator to separate the foreground and the background for each class. However, due to the object and scene diversity of images, it is quite tricky to learn a general intra-class discriminator for each class. + +Self-supervised Learning. More recent, self-supervised methods mine potential information and build supervisory signals, which has been demonstrated a promising solution to narrow the supervision gap between fully and weakly supervised semantic segmentation. Wang et al. [42] apply consistency regularization on CAM from various transformed images to accomplish self-supervision learning. Chang et al. [4] introduce a self-supervised task that discovers sub-categories, which provides additional supervision to enhance feature representations. + +In contrast to existing methods, we fully consider the distinctiveness of images, and introduce image-specific prototypes to discover complete regions and construct a self-supervised manner to empower feature representation. + +# 3. Approach + +This section elaborates the proposed SIPE framework for weakly supervised semantic segmentation as shown in Fig. 2. Firstly, we briefly review the preliminary of CAM. Then we describe the pipeline of exploring image-specific prototypes and Image-Specific CAM (IS-CAM). Finally, a self-supervised learning with General-Specific Consistency (GSC) is introduced to empower feature representation. + +![](images/8d4aa5d95dec37e8f087e0600b10627d884ca842b1b92a47ced4f75c034797b8.jpg) +Figure 2. Overview of the proposed SIPE for weakly supervised semantic segmentation. It mainly consists of two proposed methods: an Image-specific Prototype (IPE) Exploration and a General-Specific Consistency (GSC) loss. Specifically, in our IPE, a structure-aware seed locating method is proposed to achieve more robust seed regions and a background-aware prototype modeling is developed to extract hierarchical features. In addition, we add consistent regularization between two types of CAM (i.e., general CAM and our IS-CAM). This self-supervised signal effectively does correction in both CAM and IS-CAM. + +# 3.1. Class Activation Mapping + +Given an input image and a pretrained classification network, the class activation map $M_{f} = \{M_{k}\}_{k = 1}^{K}$ over $K$ foreground classes can be represented as follows: + +$$ +\boldsymbol {M} _ {k} = \operatorname {R e L U} \left(\boldsymbol {\theta} _ {k} ^ {T} \boldsymbol {F} _ {s}\right), \quad \forall k \in K, \tag {1} +$$ + +where $F_{s}$ is the semantic feature from the last layer of the network, $\theta_{k}$ denotes the $k$ -th classifier weight, and thus $M_{k}$ is the $k$ -th class-specific activation map. Following previous works, CAM is further normalized to [0, 1] by the maximum value along the spatial axes so that it could be regarded as the probability for each class. + +Considering the importance of background in segmentation task, we follow [42] to estimate the background activation map $M_{b}$ based on $M_{f}$ . Since CAM tends to cover object regions partially, the estimated background often contains high responses in foreground regions, which will bring considerable noise. To reduce such confusion, we weaken the background probability by introducing an attenuation coefficient $\alpha = 0.5$ : + +$$ +\boldsymbol {M} _ {\boldsymbol {b}} = \alpha \left(1 - \max _ {1 \leq k \leq K} \boldsymbol {M} _ {k}\right). \tag {2} +$$ + +We combine the processed background activation map with the foreground activation map as a whole, i.e. $M = M_{f} \cup M_{b}$ , to help model background knowledge. + +# 3.2. Image-specific Prototype Exploration + +Image-specific prototype is proposed to represent the feature distribution of each class, allowing to capture more complete regions. Different from the prototype representation in few-shot segmentation [33, 40, 52], there is no + +ground truth pixel-level mask in WSSS. To explore image-specific prototypes for characterizing a feature distribution, we design an efficient two-step pipeline. The first step provides robust class-wise seed regions and the second step aggregates these seeds on a comprehensive feature space to achieve accurate image-specific representation. + +Structure-aware Seed Locating. A straightforward approach to obtain seeds is empirically selecting thresholds for CAM [19], but it is difficult to use a fixed threshold on different images due to the diversity of objects and scenarios. Although CAM pays more attention to discriminative regions, it also produces weak activations on the remaining regions. It means that CAM has the potential to provide the spatial structure of semantic objects. Besides, a pixel's spatial structure can be constituted by clustering high correlation pixels. For an image, we can determine each pixel's category by comparing its spatial structure with CAMs. Based on above analysis, we propose a structure-aware seed locating method by exploring inter-pixel semantics to capture the spatial structure and employing CAMs as the templates to match the optimal category. + +Fig. 3 illustrates the proposed method with selected foreground and background examples. Firstly, for an arbitrary pixel $i$ , we take its semantic feature vector $\pmb{f}^i$ as the query to compute semantic correlation with all pixels in that feature map. Since pixels with high correlation scores are more likely to belong to the same class, these high correlation pixels can highlight the spatial structure. Therefore, we define the spatial structure of a pixel by inter-pixel semantic correlation: + +$$ +\boldsymbol {S} ^ {i} (j) = \operatorname {R e L U} \left(\frac {\boldsymbol {f} ^ {i} \cdot \boldsymbol {F} _ {s} (j)}{\| \boldsymbol {f} ^ {i} \| \cdot \| \boldsymbol {F} _ {s} (j) \|}\right), \tag {3} +$$ + +![](images/f2d4d7a03eab8916384d9cc5097a339d365f05122903c8b94f4cd76e95086d2d.jpg) +Figure 3. Illustration of structure-aware seed locating of selected foreground (green) and background pixels (red). The structure map are obtained by semantic correlation. Then the class-wise structure similarity can be evaluated by IoU and the maximal one is selected as the final class. + +where $\cdot$ is dot product and $j$ is spatial index over the feature map as well as the structure map. $S^i (j)$ denotes the semantic correlation between pixel $i$ and $j$ , and $S^i$ is the structure map of pixel $i$ . We suppress negative correlations by ReLU function to eliminate the influence of irrelevant pixels. + +Secondly, we evaluate the class-wise IoU between the structure map of pixel $i$ and CAM as the structure similarity: + +$$ +C _ {k} ^ {i} = \frac {\sum_ {j} M _ {k} (j) \boldsymbol {S} ^ {i} (j)}{\sum_ {j} \left[ M _ {k} (j) + \boldsymbol {S} ^ {i} (j) - M _ {k} (j) \boldsymbol {S} ^ {i} (j) \right]}. \tag {4} +$$ + +Here, $C_k^i$ denotes the structure similarity for pixel $i$ with respect to $k$ -th class. $j$ is spatial index over the activation map as well as the structure map. From Fig. 3, we can see that the foreground pixel (green star) correlates with the cat's body and achieves the highest IoU with CAM of the cat category. Additionally, the background pixel (red star) is not associated with foreground pixels, so it is more likely to belong to the background class. + +Finally, pixel $i$ is assigned to the category with maximal similarity: + +$$ +\boldsymbol {R} _ {k} ^ {i} = \left\{ \begin{array}{l l} 1, & \text {i f} k = \arg \max _ {k ^ {\prime}} C _ {k ^ {\prime}} ^ {i}, \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {5} +$$ + +By repeating this process for all pixels of the image in parallel, the seed regions $\mathbf{R}$ of both foreground and background classes are located as shown in Fig. 2. + +Background-aware Prototype Modeling. In this section, we simultaneously model foreground and background prototypes. Considering that background does not have specific semantics, it is difficult to explore representative + +![](images/fc12f97a4584b6c19e43e8fd5b3212866e6b74eb689d8e840da0ed6da12b7fe0.jpg) +Figure 4. Illustration of the modified backbone for extracting hierarchical feature representations. The semantic feature is extracted from the last layer and the hierarchical feature is the fusion of four stages of the backbone. + +background prototypes on semantic feature space. Instead, features from shallow layers contain rich low-level visual information (e.g. color, texture), which is more suitable to model background-related information. Therefore, we modify the architecture of the backbone to capture hierarchical features for effective prototype representation. + +Fig. 4 illustrates the architecture of modified backbone. Specifically, we add four convolution layers to extract multi-scale outputs. Then the multi-scale outputs are resized to the same size and concatenated to form the hierarchical feature $F_{h}$ . Thus image-specific prototypes $P_{k}$ of foreground and background can be formulated as the centroid of seed regions in hierarchical feature space: + +$$ +\boldsymbol {P} _ {k} = \frac {\sum_ {i} \boldsymbol {F} _ {h} ^ {i} * \mathbb {1} \left(\boldsymbol {R} _ {k} ^ {i} = 1\right)}{\sum_ {i} \mathbb {1} \left(\boldsymbol {R} _ {k} ^ {i} = 1\right)}, \tag {6} +$$ + +where $i$ indexes the spatial locations and $\mathbb{1}(\cdot)$ outputs 1 if the argument is true or 0 otherwise. This process performs class-wise compression on the seed pixels, achieving $K$ foreground prototypes and one background prototype. + +With these image-specific prototypes, the Image-Specific CAM (IS-CAM) is computed as follows: + +$$ +\tilde {\boldsymbol {M}} _ {k} (j) = \operatorname {R e L U} \left(\frac {\boldsymbol {F} _ {\boldsymbol {h}} (j) \cdot \boldsymbol {P} _ {k}}{\| \boldsymbol {F} _ {\boldsymbol {h}} (j) \| \cdot \| \boldsymbol {P} _ {k} \|}\right), \tag {7} +$$ + +where $\tilde{M}_k(j)$ is the $k$ -th IS-CAM at pixel $j$ . The correlation is bounded in $[-1, 1]$ , and followed by ReLU to remove negative correlations. + +Compared to the original CAM that takes classifier weight as the class center to compute the correlation of each pixel, the proposed IS-CAM utilizes prototypes tailored for every image to achieve more complete object regions. Besides, background prototype modeling provides high-quality background localization cues, which in turn help determine accurate foreground regions. + +# 3.3. Self-supervised Learning with GSC + +To further take advantage of image-specific knowledge, we introduce a self-supervised learning paradigm. The + +overall training loss consists of multi-label classification loss and the General-Specific Consistency (GSC) loss, + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {g s c}}. \tag {8} +$$ + +The classification loss is computed by a multi-label soft margin loss between the image-level category label $y$ and the prediction $\hat{y}$ , which is obtained by averaging over foreground maps generated by CAM. + +$$ +\mathcal {L} _ {c l s} = \frac {1}{K} \sum_ {i = 1} ^ {K} y _ {i} \log \sigma \left(\hat {y} _ {i}\right) + \left(1 - y _ {i}\right) \log \left(1 - \sigma \left(\hat {y} _ {i}\right)\right), \tag {9} +$$ + +where $\sigma$ is the sigmoid activation function. + +The GSC is employed to minimize the difference between original CAM activated by classifier weight and IS-CAM activated by image-specific prototypes. The mathematical definition of this consistency regularization is formulated as the L1 normalization of the two kinds of CAM: + +$$ +\mathcal {L} _ {g s c} = \frac {1}{K + 1} | | \boldsymbol {M} - \tilde {\boldsymbol {M}} | | _ {1}, \tag {10} +$$ + +where $M, \tilde{M}$ denotes the original CAM and IS-CAM respectively. The loss is averaged over $K$ foreground classes and one background class. + +With this consistency, the image-specific knowledge is injected into the feature representation, and the collaborative optimization is accomplished in the training cycles. IS-CAM forces the original CAM to pay attention to the absent object regions, which implicitly narrows the feature distance between the discriminative and missing pixels. Besides, the enhanced semantic and hierarchical features are favorable to capture more comprehensive and accurate image-specific prototypes and improve the quality of localization maps. + +# 4. Experiments + +In this section, we first elaborate the experimental settings including dataset, evaluation metric and implementation details. Second, we compare our method with state-of-the-art approaches on the PASCAL VOC 2012 dataset [11] and MS COCO 2014 dataset [30]. Third, we conduct a series of ablation studies to verify the effectiveness of the proposed method. + +# 4.1. Experimental Settings + +Dataset and Evaluated Metric. We evaluate our proposed method on PASCAL VOC 2012 segmentation benchmark [11] with 20 foreground classes and one background class. The official dataset split contains 1,464 images for training, 1,449 for validation and 1,456 for testing. Following the common experimental protocol in semantic segmentation, we take additional annotations from SBD [15] + +to build an augmented training set with 10,582 images. Another MS COCO 2014 dataset has totally 81 classes and contains 80k train and 40k validation images, which is challenging for weakly supervised semantic segmentation. Note that only image-level classification labels are available during network training for both datasets. Mean intersection over union (mIoU) is used as a metric to evaluate segmentation results. The results for the PASCAL VOC test set are obtained from the official evaluation server. + +Implementation Details. In our experiments, the ImageNet [9] pretrained ResNet50 [16] is adopted as backbone with output stride of 16, where fully connected layer is replaced by a classifier with output channels of 20. The augmentation strategy is the same to [25], including random flipping, random scaling and crop. The model is trained with a batch size of 16 on 2 Nvidia A100 GPUs. SGD optimizer is adopted to train our model for 5 epochs, with a momentum of 0.9 and a weight decay of 1e-4. The learning rates for the backbone and the newly added layers are set as 0.1 and 1, respectively. We use poly learning scheduler decayed with a power of 0.9 for the learning rate. + +Inference At the inference stage, the network generates foreground and background seeds by hierarchical features and activates to localization maps. Instead of checking various mIoU scores over the training set to obtain pseudo labels as other works [25, 42], we directly compute pseudo labels with the background localization maps. + +# 4.2. Comparison with State-of-the-arts + +Improvements on localization maps. We first evaluate mIoU on localization maps, where those maps are generated by the proposed IS-CAM. Tab. 1 presents the comparison with other advanced methods on PASCAL VOC 2012 train set. Among these compared methods, ECS [37] provides the best results with a mIoU of $56.6\%$ . Our proposed SIPE achieves the state-of-the-art performance of $58.6\%$ . Furthermore, we report the performance with denseCRF post-processing. The results show that our SIPE with denseCRF improves the mIoU to $64.7\%$ and outperforms all other methods, which may be benefited from our high-quality localization maps. We interpret this performance gain comes from the capability of SIPE to generate complete localization maps for foreground and background. As the localization maps can capture satisfying boundaries of semantic objects, the denseCRF is less confusing while refining the CAMs. Fig. 5 shows the visual comparison of foreground localization maps on PASCAL VOC 2012 train set. It can be observed that our SIPE is effective in capturing the whole semantic regions under various scenes, such as different object scales, crowded objects, and multiple categories. The + +![](images/00e2ce05bb075485b3e4d5ac9d0a193bb15129679f5f1c1023e364a12155cd70.jpg) +Figure 5. Visual comparison of localization maps generated by different methods on PASCAL VOC 2012 train set. From top to down: original image, Baseline, SCE [4], SEAM [42], AdvCAM [25] and our SIPE. + +Table 1. mIoU (%) of localization maps on PASCAL VOC 2012 train set. The best results are shown in bold. + +
MethodPub.Local. Maps+denseCRF
Baseline-50.154.3
SCE [4]CVPR2050.955.3
SEAM [42]CVPR2055.456.8
EDAM [45]CVPR2152.858.2
AdvCAM [25]CVPR2155.662.1
ECS [37]ICCV2156.658.6
CSE [23]ICCV2156.062.8
SIPE (Ours)58.664.7
+ +obtained high-quality localization maps will further benefit our segmentation results. + +Improvements on segmentation results. To further evaluate the performance of our methods, we train fully supervised models using generated pseudo labels and compare the segmentation results with the state-of-the-arts. Following the common practice [25], the pseudo labels are refined by IRN [1] and used to train DeepLabV2 [7]. Tab. 2 presents the comparison with state-of-the-art methods on PASCAL VOC 2012 val and test sets. Using only image-level labels, our SIPE outperforms previous methods with $68.8\%$ mIoU on val set and $69.7\%$ mIoU on test set. In addition, our method performs favorably against NSROM [48] and EPS [27], which introduce saliency maps as auxiliary + +Table 2. Comparison with other state-of-the-arts on PASCAL VOC 2012 val and test sets. The best results among methods only using image-level labels are shown in bold. + +
ModelPub.Sup.BackboneValTest
DSRG [19]CVPR18I + SResNet10161.463.2
SeeNet [18]NIPS18I + SResNet10163.162.8
FickleNet [24]CVPR19I + SResNet10164.965.3
OAA+ [20]ICCV19I + SResNet10165.266.4
G-WSSS [28]AAAI21I + SResNet10168.268.5
NSROM [48]CVPR21I + SResNet10170.470.2
EPS [27]CVPR21I + SResNet10171.071.8
AuxSegNet [47]ICCV21I + SResNet3869.068.6
IRN [1]CVPR19IResNet5063.564.8
ICD [12]CVPR20IResNet10164.164.3
SCE [4]CVPR20IResNet10166.165.9
SEAM [42]CVPR20IResNet3864.565.7
BES [6]ECCV20IResNet10165.766.6
MCIS [36]ECCV20IResNet10166.266.9
CONTA [10]NIPS20IResNet10166.166.7
LIID [32]TPAMI20IResNet10166.567.5
A2GNN [49]TPAMI21IResNet10166.867.4
AdvCAM [25]CVPR21IResNet10168.168.0
CDA [35]ICCV21IResNet3866.166.8
ECS [37]ICCV21IResNet3866.667.6
CSE [23]ICCV21IResNet3868.468.2
CPN [51]ICCV21IResNet3867.868.5
SIPE (Ours)IResNet3868.269.51
SIPE (Ours)IResNet10168.869.72
+ +![](images/d48e4c60d3594b7cb48b191f4d55ca88e45a365d79c21637c661ae146bc72275.jpg) +Figure 6. Qualitative segmentation results on the validation set of PASCAL VOC 2012 and MS COCO 2014. + +![](images/b1764a088c5d0a18d66a7aa408e45b3e99f96c210b0433313d7d2d5e0edb0b47.jpg) + +Table 3. Comparison with other state-of-the-arts on MS COCO 2014 val set. The best results are shown in bold. + +
ModelPub.Sup.BackboneVal
DSRG [19]CVPR18I + SVGG1626.0
G-WSSS [28]AAAI21I + SResNet10128.4
EPS [27]CVPR21I + SResNet10135.7
AuxSegNet [47]ICCV21I + SResNet3833.9
SEC [22]ECCV16IVGG1622.4
IRN [1]CVPR19IResNet5032.6
IAL [41]IJCV20IVGG1627.7
SEAM [42]CVPR20IResNet3831.9
CONTA [10]NIPS20IResNet10133.4
CSE [23]ICCV21IResNet3836.4
SIPE (Ours)IResNet3843.6
SIPE (Ours)IResNet10140.6
+ +labels for this task. For a fair comparison, we also train the model with ResNet38 following the default setting as [42]. Our SIPE achieves $69.5\%$ mIoU on test set, exceeding the existing methods that use ResNet38 backbone. The qualitative segmentation results on val set are shown in Fig. 6. Based on our SIPE, DeepLabV2 shows more robustness to various challenging scenarios, such as different object scales, multiple objects and multiple categories. + +In Tab. 3, we also evaluate our method in MS COCO 2014 dataset [30]. The same training script with the experiment on PASCAL VOC 2012 is employed, but no refinement with IRN due to the large computation cost. Our method achieves $43.6\%$ mIoU with ResNet38 backbone on the validation set, which is $7.2\%$ higher than previous SOTA CSE [23]. Using ResNet101 backbone, we also outper + +Table 4. Effect of the main contributions. CAM: orginal CAM, IPE: image-specific prototype exploration, GSC: general-specific consistency. + +
CAMIPEGSCmIoU (%)
✓50.1
✓✓53.2
✓✓✓58.6
+ +forms EPS [27] by $4.9\%$ . These outstanding performances over existing state-of-the-arts on both datasets confirm the effectiveness of our SIPE, which well explores image-specific prototypes via self-supervised learning paradigm. + +# 4.3. Ablation Studies + +Effect of the main contributions. We conduct an ablation study to verify the effect of the proposed two key contributions, i.e., Image-specific Prototype Exploration (IPE) and General-Specific Consistency (GSC). As shown in Tab. 4, with image-specific prototypes, our IS-CAM can improve the original CAM by $2.1\%$ on mIoU score. To enhance the feature representation, GSC is introduced for self-supervised training. The proposed GSC improves the quality of IS-CAM $(5.4\%)$ by a clear margin. By combining these two methods, our full method performs significantly better than the original CAM. Fig. 7 visualizes CAM and IS-CAM with different settings. From the first two rows, we can observe that image-specific prototypes can activate more useful regions. Additionally, our IS-CAM shows that the proposed method produces more clear background activations than that from CAM. When training our model with GSC, the quality of localization maps is obviously improved, especially for background. + +![](images/9bd9796671a22305e709dae87836d92760122ff5b6d91a47bf79b1dd092b849f.jpg) +Figure 7. Visualization of CAM and IS-CAM with different settings. Our IS-CAM shows more complete regions of person. Moreover, the proposed GSC further refines the background activations. The boundary is well captured as the white box. + +![](images/43dbca1a3f49476a6f180d04158256ec065b603f4d9290657077922b27c17977.jpg) +Figure 8. Ablation study of structure-aware seed locating. The proposed structural-aware seed locating method is consistently better than CAM with fixed threshold, as well as CAM with adaptive threshold. + +Effect of structure-aware seed locating. To verify the effectiveness of the proposed structure-aware seed locating, we compare the mIoU with other seed generation approaches including applying threshold or argmax operations on CAM. As shown in Fig. 8, applying different thresholds on CAM exhibits fluctuations and can only achieve maximal mIoU of $53.3\%$ . In addition, simply applying argmax results in slightly performance gains $(+0.4\%)$ . These methods are still hard to find compete regions because both of them only depend on the single pixel's probability. In contrast, the proposed structure-aware seed locating largely outperforms the above methods owing to the proposed structure information. + +Effect of prototype modeling. We conduct ablation study of prototype modeling on localization maps. The IoUs of four options concerning feature and Background + +Table 5. Ablation study of combinations of feature selection and Background Prototype Modeling (BPM) via GSC. Each item reports mIoUs for two pseudo labels where the former are generated by searching the best background threshold [42] and the latter are generated by estimated background map. The best results are shown in bold. + +
Featurew/o BPMw/ BPM
ThresholdEstimatedThresholdEstimated
Semantic56.054.655.954.3
Hierarchical53.951.257.658.6
+ +Prototype Modeling (BPM) are presented in Tab. 5: (1) Semantic feature without BPM, (2) Semantic feature with BPM, (3) Hierarchical feature without BPM, and (4) Hierarchical feature with BPM. We report threshold-based and estimated-based pseudo labels for each type of option. Our SIPE adopts option (4) where hierarchical feature is learned for image-specific background modeling. It shows that our method achieves the highest performance in both values among all options. From (1) to (2), the mIoU is basically unchanged because the background often does not have specific semantics. From (1) to (3), the mIoU drops over $2\%$ since the low-level information brings confusion to foreground localization. It is worth noting that only when hierarchical feature and background modeling are employed at the same time, the mIoU of the estimated-based pseudo labels exceed that bases on threshold, which strongly proves the effectiveness of estimating background cues. + +# 5. Conclusion + +In this paper, we propose Self-supervised Image-specific Prototype Exploration (SIPE) for weakly supervised semantic segmentation. In our framework, an Image-specific Prototype Exploration (IPE) is proposed to achieve more favorable localization maps. It is achieved by structure-aware seed locating and background-aware prototype modeling. In addition, a General-Specific Consistency (GSC) loss is developed to efficiently regularize the general CAM and Image-Specific CAM (IS-CAM), empowering the feature representation. Extensive experiments show that our SIPE sets new state-of-the-art performance on two well-known benchmarks using image-level labels. + +Acknowledgments. This project is supported by the KeyArea Research and Development Program of Guangdong Province (2019B010155003), and the National Natural Science Foundation of China (62072482). 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Sun $^{1*}$ Serim Ryou $^{1*†}$ Roni H. Goldshmid $^{1}$ Brandon Weissboud $^{1}$ John O. Dabiri $^{1}$ David J. Anderson $^{1}$ Ann Kennedy $^{2}$ Yisong Yue $^{1,3}$ Pietro Perona $^{1}$ + +$^{1}$ Caltech $^{2}$ Northwestern University $^{3}$ Argo AI + +Code & Project Website: https://sites.google.com/view/b-kind + +![](images/0e681f09067c76a9f5cb9b3eb555ee0f78c5a5d90048791d4988cf2407489247.jpg) +Figure 1. Self-supervised Behavioral Keypoint Discovery. Intermediate representations in the form of keypoints are frequently used for behavior analysis. We propose a method to discover keypoints from behavioral videos without the need for manual keypoint or bounding box annotations. Our method works across a range of organisms (including mice, humans, flies, jellyfish and tree), works with multiple agents simultaneously (see flies and mice above), does not require bounding boxes (boxes visualized above purely for identifying the enlarged regions of interest) and achieves state-of-the-art performance on downstream tasks. + +# Abstract + +We propose a method for learning the posture and structure of agents from unlabelled behavioral videos. Starting from the observation that behaving agents are generally the main sources of movement in behavioral videos, our method, Behavioral Keypoint Discovery (B-KinD), uses an encoder-decoder architecture with a geometric bottleneck to reconstruct the spatiotemporal difference between video frames. By focusing only on regions of movement, our approach works directly on input videos without requiring manual annotations. Experiments on a variety of agent types (mouse, fly, human, jellyfish, and trees) demonstrate the generality of our approach and reveal that our discovered keypoints represent semantically meaningful body parts, which achieve state-of-the-art performance on keypoint regression among self-supervised methods. Additionally, B-KinD achieve comparable performance to super + +vised keypoints on downstream tasks, such as behavior classification, suggesting that our method can dramatically reduce model training costs vis-a-vis supervised methods. + +# 1. Introduction + +Automatic recognition of object structure, for example in the form of keypoints and skeletons, enables models to capture the essence of the geometry and movements of objects. Such structural representations are more invariant to background, lighting, and other nuisance variables and are much lower-dimensional than raw pixel values, making them good intermediates for downstream tasks, such as behavior classification [4, 11, 15, 39, 43], video alignment [26, 44], and physics-based modeling [7, 12]. + +However, obtaining annotations to train supervised pose detectors can be expensive, especially for applications in behavior analysis. For example, in behavioral neuroscience [34], datasets are typically small and lab-specific, and the training of a custom supervised keypoint detector + +presents a significant bottleneck in terms of cost and effort. Additionally, once trained, supervised detectors often do not generalize well to new agents with different structures without new supervision. The goal of our work is to enable keypoint discovery on new videos without manual supervision, in order to facilitate behavior analysis on novel settings and different agents. + +Recent unsupervised/self-supervised methods have made great progress in keypoint discovery [20, 21, 51] (see also Section 2), but these methods are generally not designed for behavioral videos. In particular, existing methods do not address the case of multiple and/or non-centered agents, and often require inputs as cropped bounding boxes around the object of interest, which would require an additional detector module to run on real-world videos. Furthermore, these methods do not exploit relevant structural properties in behavioral videos (e.g., the camera and the background are typically stationary, as observed in many real-world behavioral datasets [5, 15, 22, 29, 34, 39]). + +To address these challenges, the key to our approach is to discover keypoints based on reconstructing the spatiotemporal difference between video frames. Inspired by previous works based on image reconstruction [20, 37], we use an encoder-decoder setup to encode input frames into a geometric bottleneck, and train the model for reconstruction. We then use spatiotemporal difference as a novel reconstruction target for keypoint discovery, instead of single image reconstruction. Our method enables the model to focus on discovering keypoints on the behaving agents, which are generally the only source of motion in behavioral videos. + +Our self-supervised approach, Behavioral Keypoint Discovery (B-KinD), works without manual supervision across diverse organisms (Figure 1). Results show that our discovered keypoints achieve state-of-the-art performance on downstream tasks among other self-supervised keypoint discovery methods. We demonstrate the performance of our keypoints on behavior classification [42], keypoint regression [20], and physics-based modeling [7]. Thus, our method has the potential for transformative impact in behavior analysis: first, one may discover keypoints from behavioral videos for new settings and organisms; second, unlike methods that predict behavior directly from video, our low-dimensional keypoints are semantically meaningful so that users can directly compute behavioral features; finally, our method can be applied to videos without the need for manual annotations. + +To summarize, our main contributions are: + +1. Self-supervised method for discovering keypoints from real-world behavioral videos, based on spatiotemporal difference reconstruction. +2. Experiments across a range of organisms (mice, flies, human, jellyfish, and tree) demonstrating the generality of the method and showing that the discovered keypoints are + +semantically meaningful. + +3. Quantitative benchmarking on downstream behavior analysis tasks showing performance that is comparable to supervised keypoints. + +# 2. Related work + +Analyzing Behavioral Videos. Video data collected for behavioral experiments often consists of moving agents recorded from stationary cameras [1,4,5,11,15,22,33,39]. These behavioral videos contain different model organisms studied by researchers, such as fruit flies [4, 11, 15, 24] and mice [5, 17, 22, 39]. From these recorded video data, there has been an increasing effort to automatically estimate poses of agents and classify behavior [13, 14, 17, 24, 30, 39]. + +Pose estimation models that were developed for behavioral videos [16, 30, 35, 39] require human annotations of anatomically defined keypoints, which are expensive and time-consuming to obtain. In addition to the cost, not all data can be crowd-sourced due to the sensitive nature of some experiments. Furthermore, organisms that are translucent (jellyfish) or with complex shapes (tree) can be difficult for non-expert humans to annotate. Our goal is to enable keypoint discovery on videos for behavior analysis, without the need for manual annotations. + +After pose estimation, behavior analysis models generally compute trajectory features and train behavior classifiers in a fully supervised fashion [5, 15, 17, 39, 43]. Some works have also explored using unsupervised methods to discover new motifs and behaviors [3, 18, 28, 50]. Here, we apply our discovered keypoints to supervised behavior classification and compare against baseline models using supervised keypoints for this task. + +Keypoint Estimation. Keypoint estimation models aim to localize a predefined set of keypoints from visual data, and many works in this area focus on human pose. With the success of fully convolutional neural networks [40], recent methods [8,32,45,49] employ encoder-decoder networks by predicting high-resolution outputs encoded with 2D Gaussian heatmaps representing each part. To improve model performance, [32,45,49] propose an iterative refinement approach, [8,36] design efficient learning signals, and [9,47] exploit multi-resolution information. Beyond human pose, there are also works that focus on animal pose estimation, notably [16,30,35]. Similar to these works, we also use 2D Gaussian heatmaps to represent parts as keypoints, but instead of using human-defined keypoints, we aim to discover keypoints from video data without manual supervision. + +Unsupervised Part Discovery. Though keypoints provide a useful tool for behavior analysis, collecting annotations is time-consuming and labor-intensive especially for new domains that have not been previously studied. Unsupervised keypoint discovery [20, 21, 51] has been proposed to reduce keypoint annotation effort and there have been + +![](images/8ab33c659cb5c03498caa1db7cdde53b045b9b267794306209c5095a6c1837b4.jpg) +Figure 2. B-KinD, an approach for keypoint discovery from spatiotemporal difference reconstruction. $I_{t}$ and $I_{t + T}$ are video frames at time $t$ and $t + T$ . Both frame $I_{t}$ and frame $I_{t + T}$ are fed to an appearance encoder $\Phi$ and a pose decoder $\Psi$ . Given the appearance feature from $I_{t}$ and geometry features from both $I_{t}$ and $I_{t + T}$ (Sec 3.1), our model reconstructs the spatiotemporal difference (Sec 3.2.1) computed from two frames using the reconstruction decoder $\psi$ . + +many promising results on centered and/or aligned objects, such as facial images and humans with an upright pose. These methods train and evaluate on images where the object of interest is centered in an input bounding box. Most of the approaches [20, 27, 51] use an autoencoder-based architecture to disentangle the appearance and geometry representation for the image reconstruction task. Our setup is similar in that we also use an encoder-decoder architecture, but crucially, we reconstruct spatiotemporal difference between video frames, instead of the full image as in previous works. We found that this enables our discovered keypoints to track semantically-consistent parts without manual supervision, requiring neither keypoints nor bounding boxes. + +There are also works for parts discovery that employ other types of supervision [21, 37, 38]. For example, [37] proposed a weakly-supervised approach using class label to discriminate parts to handle viewpoint changes, [21] incorporated pose prior obtained from unpaired data from different datasets in the same domain, and [38] proposed a template-based geometry bottleneck based on a pre-defined 2D Gaussian-shaped template. Different from these approaches, our method does not require any supervision beyond the behavioral videos. We chose to focus on this setting since other supervisory sources are not readily available for emerging domains (ex: jellyfish, trees). + +In previous works, keypoint discovery has been applied to downstream tasks, such as image and video generation [21, 31], keypoint regression to human-annotated poses [20, 51], and video-level action recognition [25, 31]. While we also apply keypoint discovery to downstream tasks, we note that our work differs in approach (we discover keypoints directly on behavioral videos using spatiotemporal difference reconstruction), focus (behavioral videos of diverse organisms), and application (real-world + +behavior analysis tasks [7, 42]). + +# 3. Method + +The goal of B-KinD (Figure 2) is to discover semantically meaningful keypoints in behavioral videos of diverse organisms without manual supervision. We use an encoder-decoder setup similar to previous methods [20, 37], but instead of image reconstruction, here we study a novel reconstruction target based on spatiotemporal difference. In behavioral videos, the camera is generally fixed with respect to the world, such that the background is largely stationary and the agents (e.g. mice moving in an enclosure) are the only source of motion. Thus spatiotemporal differences provide a strong cue to infer location and movements of agents. + +# 3.1. Self-supervised keypoint discovery + +Given a behavioral video, our work aims to reconstruct regions of motion between a reference frame $I_{t}$ (the video frame at time $t$ ) and a future frame $I_{t + T}$ (the video frame $T$ timesteps later, for some set value of $T$ .) We accomplish this by extracting appearance features from frame $I_{t}$ and keypoint locations ("geometry features") from both frames $I_{t}$ and $I_{t + T}$ (Figure 2). In contrast, previous works [20, 21, 27, 37, 38] use appearance features from $I_{t}$ and geometry features from $I_{t + T}$ to reconstruct the full image $I_{t + T}$ (instead of difference between $I_{t}$ and $I_{t + T}$ ). + +We use an encoder-decoder architecture, with shared appearance encoder $\Phi$ , geometry decoder $\Psi$ , and reconstruction decoder $\psi$ . During training, the pair of frames $I_{t}$ and $I_{t + T}$ are fed to the appearance encoder $\Phi$ to generate appearance features, and those features are then fed into the geometry decoder $\Psi$ to generate geometry features. In our approach, the reference frame $I_{t}$ is used to generate both appearance and geometry representations, and the future + +frame $I_{t + T}$ is only used to generate a geometry representation. The appearance feature $h_a^t$ for frame $I_{t}$ are defined simply as the output of $\Phi$ : $h_a^t = \Phi (I_t)$ . + +The pose decoder $\Psi$ outputs $K$ raw heatmaps $\mathbf{X}_i\in \mathbb{R}^2$ then applies a spatial softmax operation on each heatmap channel. Given the extracted $p_i = (u_i,v_i)$ locations for $i = \{1,\dots ,K\}$ keypoints from the spatial softmax, we define the geometry features $h_g^t$ to be a concatenation of 2D Gaussians centered at $(u_{i},v_{i})$ with variance $\sigma$ + +Finally, the concatenation of the appearance feature $h_a^t$ and the geometry features $h_g^t$ and $h_g^{t + T}$ is fed to the decoder $\psi$ to reconstruct the learning objective $\hat{S}$ discussed in the next section: $\hat{S} = \psi (h_a^t,h_g^t,h_g^{t + T})$ . + +# 3.2. Learning formulation + +# 3.2.1 Spatiotemporal difference + +Our method works with different types of spatiotemporal differences as reconstruction targets. For example: + +Structural Similarity Index Measure (SSIM) [48]. This is a method for measuring the perceived quality of the two images based on luminance, contrast, and structure features. To compute our reconstruction target based on SSIM, we apply the SSIM measure locally on corresponding patches between $I_{t}$ and $I_{t + T}$ to build a similarity map between frames. Then we compute dissimilarity by taking the negation of the similarity map. + +Frame differences. When the video background is static with little noise, simple frame differences, such as absolute difference $(S_{|d|} = |I_{t + T} - I_t|)$ or raw difference $(S_d = I_{t + T} - I_t)$ , can also be directly applied as a reconstruction target. + +# 3.2.2 Reconstruction loss + +We apply perceptual loss [23] for reconstructing the spatiotemporal difference $S$ . Perceptual loss compares the L2 distance between the features computed from VGG network $\phi$ [41]. The reconstruction $\hat{S}$ and the target $S$ are fed to VGG network, and mean squared error is applied to the features from the intermediate convolutional blocks: + +$$ +\left. \mathcal {L} _ {\text {r e c o n}} = \left\| \phi \left(S \left(I _ {t}, I _ {t + T}\right)\right) - \phi (\hat {S} \left(I _ {t}, I _ {t + T}\right)) \right\| _ {2}. \right. \tag {1} +$$ + +# 3.2.3 Rotation equivariance loss + +In cases where agents can move in many directions (e.g. mice filmed from above can translate and rotate freely), we would like our keypoints to remain semantically consistent. We enforce rotation-equivariance in the discovered keypoints by rotating the image with different angles and imposing that the predicted keypoints should move correspondingly. We apply the rotation equivariance loss (simi + +![](images/717ee8fab3429ff6ab8543a8b422ce534b91d502787bb937d065a2980bc19f1a.jpg) +Figure 3. Behavior Classification Features. Extracting information from the raw heatmap (Section 3.3): the confidence scores and the covariance matrices are computed from normalized heatmaps. Note that the features are computed for all $x, y$ coordinates. We visualize the zoomed area around the target instance for illustrative purposes. + +lar to the deformation equivariance in [46]) on the generated heatmap. + +Given reference image $I$ and the corresponding geometry bottleneck $h_g$ , we rotate the geometry bottleneck to generate pseudo labels $h_g^{R^\circ}$ for rotated input images $I^{R^\circ}$ with degree $R = \{90^\circ, 180^\circ, 270^\circ\}$ . We apply mean squared error between the predicted geometry bottlenecks $\hat{h}_g$ from the rotated images and the generated pseudo labels $h_g$ : + +$$ +\mathcal {L} _ {r} = \left\| h _ {g} ^ {R ^ {\circ}} - \hat {h} _ {g} \left(I ^ {R ^ {\circ}}\right) \right\| _ {2}. \tag {2} +$$ + +# 3.2.4 Separation loss + +Empirical results show that rotation equivariance encourages the discovered keypoints to converge at the center of the image. We apply separation loss to encourage the keypoints to encode unique coordinates, and prevent the discovered keypoints from being centered at the image coordinates [51]. The separation loss is defined as follows: + +$$ +\mathcal {L} _ {s} = \sum_ {i \neq j} \exp \left(\frac {- \left(p _ {i} - p _ {j}\right) ^ {2}}{2 \sigma_ {s} ^ {2}}\right). \tag {3} +$$ + +# 3.2.5 Final objective + +Our final loss function is composed of three parts: reconstruction loss $\mathcal{L}_{\text{recon}}$ , rotation equivariance loss $\mathcal{L}_r$ , and separation loss $\mathcal{L}_s$ : + +$$ +\mathcal {L} = \mathcal {L} _ {\text {r e c o n}} + \mathbb {1} _ {\text {e p o c h} > n} \left(w _ {r} \mathcal {L} _ {r} + w _ {s} \mathcal {L} _ {s}\right). \tag {4} +$$ + +We adopt curriculum learning [2] and apply $\mathcal{L}_r$ and $\mathcal{L}_s$ once the keypoints are consistently discovered from the semantic parts of the target instance. + +# 3.3. Feature extraction for behavior analysis + +Following standard approaches [5, 17, 39], we use the discovered keypoints from B-KinD as input to a behavior quantification module: either supervised behavior classifiers or a physics-based model. Note that this is a separate process from keypoint discovery; we feed discovered geometry information into a downstream model. + +In addition to discovered keypoints, we extracted additional features from the raw heatmap (Figure 3) to be used as input to our downstream modules. For instance, we found that the confidence and the shape information from the of the network prediction of keypoint location was informative. When a target part is well localized, our keypoint discovery network produces a heatmap with a single high peak with low variance; conversely, when a target part is occluded, the raw heatmap contains a blurred shape with lower peak value. This "confidence" score (heatmap peak value) is also a good indicator for whether keypoints are discovered on the background (blurred over the background with low confidence) or tracking anatomical body parts (peaked with high confidence), visualized in Supplementary materials. The shape of a computed heatmap can also reflect shape information of the target (e.g. stretching). + +Given a raw heatmap $\mathbf{X}_k$ for part $k$ , the confidence score is obtained by choosing the maximum value from the heatmap, and the shape information is obtained by computing the covariance matrix from the heatmap. Figure 3 visualizes the features we extract from the raw heatmaps. Using the normalized heatmap as the probability distribution, additional geometric features are computed: + +$$ +\sigma_ {x} ^ {2} (\mathbf {X} _ {k}) = \sum_ {i j} (x _ {i} - u _ {k}) ^ {2} \mathbf {X} _ {k} (i, j), +$$ + +$$ +\sigma_ {y} ^ {2} \left(\mathbf {X} _ {k}\right) = \sum_ {i j} \left(y _ {j} - v _ {k}\right) ^ {2} \mathbf {X} _ {k} (i, j), \tag {5} +$$ + +$$ +\sigma_ {x y} ^ {2} (\mathbf {X} _ {k}) = \sum_ {i j} (x _ {i} - u _ {k}) (y _ {j} - v _ {k}) \mathbf {X} _ {k} (i, j). +$$ + +# 4. Experiments + +We demonstrate that B-KinD is able to discover consistent keypoints in real-world behavioral videos across a range of organisms (Section 4.1.1). We evaluate our keypoints on downstream tasks for behavior classification (Section 4.2) and pose regression (Section 4.3), then illustrate additional applications of our keypoints (Section 4.4). + +# 4.1. Experimental setting + +# 4.1.1 Datasets + +CalMS21. CalMS21 [42] is a large-scale dataset for behavior analysis consisting of videos and trajectory data from a pair of interacting mice. Every frame is annotated by an + +expert for three behaviors: sniff, attack, mount. There are $507\mathrm{k}$ frames in the train split, and $262\mathrm{k}$ frames in the test split (video frame: $1024 \times 570$ , mouse: approx $150 \times 50$ ). We use only the train split on videos without miniscope cable to train B-KinD. Following [42], the downstream behavior classifier is trained on the entire training split, and performance is evaluated on the test split. + +MARS-Pose. This dataset consists of a set of videos with similar recording conditions to the CalMS21 dataset. We use a subset of the MARS pose dataset [39] with keypoints from manual annotations to evaluate the ability of our model to predict human-annotated keypoints, with $\{10, 50, 100, 500\}$ images for train and $1.5\mathrm{k}$ images for test. + +Fly vs. Fly. These videos consist of interactions between a pair of flies, annotated per frame by domain experts. We use the Aggression videos from the Fly vs. Fly dataset [15], with the train and test split having $1229\mathrm{k}$ and $322\mathrm{k}$ frames respectively (video frame: $144 \times 144$ , fly: approx $30 \times 10$ ). Similar to [43], we evaluate on behaviors of interest with more than 1000 frames in the training set (lunge, wing threat, tussle). + +Human 3.6M. Human 3.6M [19] is a large-scale motion capture dataset, which consists of 3.6 million human poses and images from 4 viewpoints. To quantitatively measure the pose regression performance against baselines, we use the Simplified Human 3.6M dataset, which consists of 800k training and 90k testing images with 6 activities in which the human body is mostly upright. We follow the same evaluation protocol from [51] to use subjects 1, 5, 6, 7, and 8 for training and 9 and 11 for testing. We note that each subject has different appearance and clothing. + +Jellyfish. The jellyfish data is an in-house video dataset containing 30k frames of recorded swimming jellyfish (video frame: $928 \times 1158$ , jellyfish: approx 50 pix in diameter). We use this dataset to qualitatively test the performance of B-KinD on a new organism, and apply our keypoints to detect the pulsing motion of the jellyfish. + +Vegetation. This is an in-house dataset acquired over several weeks using a drone to record the motion of swaying trees. The dataset consists of videos of an oak tree and corresponding wind speeds recorded using an anemometer, with a total of 2.41M video frames (video frame: $512 \times 512$ , oak tree: varies, approx $\frac{1}{4}$ of the frame). We evaluate this dataset using a physics-based model [7] that relates the visually observed oscillations to the average wind speeds. + +# 4.1.2 Training and evaluation procedure + +We train B-KinD using the full objective in Section 3.2.5. During training, we rescale images to $256 \times 256$ and use $T$ of around 0.2 seconds, except Human3.6M, where we use $128 \times 128$ . Unless otherwise specified, all experiments are ran with all keypoints discovered from B-KinD with SSIM reconstruction and with 10 keypoints for mouse, fly, and jel + +![](images/66dc46dfb148aba43d3252d75c60b7892ba4389461139b4f9440a034a1ce1ee5.jpg) +Figure 4. Comparison with existing methods [20], full image, bounding box, and SSIM reconstruction (ours). "Jakab et al." and "full image" results are based on full image reconstruction. "White mouse bounding box" and "black mouse bounding box" show the results when the cropped bounding boxes were fed to the network for image reconstruction. + +![](images/ea01d3b7b191982ce306e5e386f2588fe5aa9d08b3a61e543ff2e2bf3de9240f.jpg) + +![](images/5a9ec0a77df1a697ae733eff8c70ae54ff9e00b0e3a3b992ab87df419286db17.jpg) + +![](images/234b0de40b366c8556768603403860ae6a25ab21fb5f2c90b38e0bdb2f7799ef.jpg) + +![](images/a43528080fc4ad60e4a128279d5a8d75622438211a8ac8a59f369f4e26bb30e0.jpg) + +lyfish, 16 keypoints for Human3.6M, 15 keypoints for Vegetation. We train on the train split of each dataset as specified, except for jellyfish and vegetation, where we use the entire dataset. Additional details are in the Supplementary materials. + +After training the keypoint discovery model, we extract the keypoints and use it for different evaluations based on the labels available in the dataset: behavior classification (CalMS21, Fly), keypoint regression (MARS-Pose, Human), and physics-based modeling (Vegetation). + +For keypoint regression, similar to previous works [20, 21], we compare our regression with a fully supervised 1-stack hourglass network [32]. We evaluate keypoint regression on Simplified Human 3.6M by using a linear regressor without a bias term, following the same evaluation setup from previous works [27,51]. On MARS-Pose, we train our model in a semi-supervised fashion with 10, 50, 100, 500 supervised keypoints to test data efficiency. For behavior classification, we evaluate on CalMS21 and Fly, using available frame-level behavior annotations. To train behavior classifiers, we use the specified train split of each dataset. For CalMS21 and Fly, we train the 1D Convolutional Network benchmark model provided by [42] using B-KinD keypoints. We evaluate using mean average precision (MAP) weighted equally over all behaviors of interest. + +# 4.2. Behavior classification results + +CalMS21 Behavior Classification. We evaluate the effectiveness of B-KinD for behavior classification (Table 1). Compared to supervised keypoints trained for this task, our keypoints (without manual supervision) is comparable when using both pose and confidence as input. Compared to other self-supervised methods, even those that use bounding boxes, our discovered keypoints on the full image generally achieve better performance. + +Keypoints discovered with image reconstruction, similar to baselines [20,37] cannot track the agents well without using bounding box information (Figure 4) and does not per + +
CalMS21PoseConfCovMAP
Fully supervised
MARS † [39]✓.856 ± .010
✓✓.874 ± .003
✓✓✓.880 ± .005
Self-supervised
Jakab et al. [20]✓.186 ± .008
Image Recon.✓.182 ± .007
✓✓.184 ± .006
✓✓✓.165 ± .012
Image Recon. bbox†✓.819 ± .008
✓✓.812 ± .006
✓✓✓.812 ± .010
Ours✓.814 ± .007
✓✓.857 ± .005
✓✓✓.852 ± .013
+ +Table 1. Behavior Classification Results on CalMS21. "Ours" represents classifiers using input keypoints from our discovered keypoints. "conf" represents using the confidence score, and "cov" represents values from the covariance matrix of the heatmap. † refers to models that require bounding box inputs before keypoint estimation. Mean and std dev from 5 classifier runs are shown. + +
FlyMAP
Hand-crafted features
FlyTracker [15].809 ± .013
Self-supervised + generic features
Image Recon..500 ± .024
Image Recon. bbox†.750 ± .020
Ours.727 ± .022
+ +Table 2. Behavior Classification Results on Fly. "FlyTracker" represents classifiers using hand-crafted inputs from [15]. The self-supervised keypoints all use the same "generic features" computed on all keypoints: speed, acceleration, distance, and angle. † refers to models that require bounding box inputs before keypoint estimation. Mean and std dev from 5 classifier runs are shown. + +form well for behavior classification (Table 1). When we provide bounding box information to the model based on image reconstruction, the performance is significantly improved, but this model does not perform as well as B-KinD keypoints from spatiotemporal difference reconstruction. + +For the per-class performance (see the Supplementary materials), the biggest gap exists between B-KinD and MARS on the "attack" behavior. This is likely because during attack, the mice are moving quickly, and there exists a lot of motion blur and occlusion which is difficult to track without supervision. However, once we extract more information from the heatmap, through computing keypoint confidence, our keypoints perform comparably to MARS. + +Fly Behavior Classification. The FlyTracker [15] uses hand-crafted features computed from the image, such as contrast, as well as features from tracked fly body parts, + +![](images/4e6f5993ce54f0ec79be3adaae44521a7857b7240e9a84e727ced7cd2dc8cebd.jpg) +Figure 5. Keypoint data efficiency on MARS-Pose. The supervised model is based on [39] using stacked hourglass [32], while the semi-supervised model uses both our self-supervised loss and supervision. PCK is computed at $0.5cm$ threshold, averaged across nose, ears, and tail keypoints, over 3 runs. "b" and "w" indicates the black and white mouse respectively. + +such as wing angle or distance between flies. Using discovered keypoints, we compute comparable features without assuming keypoint identity, by computing speed and acceleration of every keypoint, distance between every pair, and angle between every triplet. For all self-supervised methods, we use keypoints, confidence, and covariance for behavior classification. Results demonstrate that while there is a small gap in performance to the supervised estimator, our discovered keypoints perform much better than image reconstruction, and is comparable to models that require bounding box inputs (Table 2). + +# 4.3. Pose regression results + +MARS Pose Regression. We evaluate the pose estimation performance of our method in the setting where some human annotated keypoints exist (Figure 5). For this experiment, we train B-KinD in a semi-supervised fashion, where the loss is a sum of both our keypoint discovery objective (Section 3.2.5) as well as standard keypoint estimation objectives based on MSE [39]. For both black and white mouse, when using our keypoint discovery objective in a semi-supervised way during training, we are able to track keypoints more accurately compared to the supervised method [39] alone. We note that the performance of both methods converge at around 500 annotated examples. + +Simplified Human 3.6M Pose Regression. To compare with existing keypoint discovery methods, we evaluate our discovered keypoints on Simplified Human3.6M (a standard benchmarking dataset) by regressing to annotated keypoints (Table 3). Though our method is directly applicable to full images, we train the discovery model using cropped bounding box for a fair comparison with baselines, which all use cropped bounding boxes centered on the subject. Compared to both self-supervised + prior information and self-supervised + regression, our method shows state- + +
Simplified H36Mallwaitposegreetdirectdiscusswalk
Fully supervised:
Newell [32]2.161.881.922.151.621.882.21
Self-supervised + unpaired labels
Jakab [21]‡2.732.662.272.732.352.354.00
Self-supervised + template
Schmidtke [38]3.313.513.283.503.032.973.55
Self-supervised + regression
Thewlis [46]7.517.548.567.266.477.935.40
Zhang [51]4.145.014.614.764.454.914.61
Lorenz [27]2.79------
Ours (best)2.442.502.222.472.222.772.50
Ours (mean)2.532.582.312.562.342.832.58
Ours (std).056.047.062.048.066.048.063
+ +Table 3. Comparison with state-of-the-art methods for landmark prediction on Simplified Human 3.6M. The error is in $\%$ -MSE normalized by image size. All methods predict 16 keypoints except for [21]‡, which uses 32 keypoints for training a prior model from the Human 3.6M dataset. B-Kind results are computed from 5 runs. + +
Learning Objective%-MSE
Image Recon.2.918 ± 0.139
Abs. Difference2.642 ± 0.174
Difference2.770 ± 0.158
SSIM2.534 ± 0.056
Self-supervised + extracted features
SSIM2.494 ± 0.047
+ +Table 4. Learning objective ablation on Simplified Human3.6M. $\%$ -MSE error is reported by changing the reconstruction target. Extracted features correspond to keypoint locations, confidence, and covariance. Results are from 5 B-KinD runs. + +of-the-art performance on the keypoint regression task, suggesting spatiotemporal difference is an effective reconstruction target for keypoint discovery. + +Learning Objective Ablation Study We report the pose regression performance on Simplified Human3.6M (Table 4) by varying the spatiotemporal difference reconstruction target for training B-KinD. Here, image reconstruction also performs well since cropped bounding box is used as an input to the network. Overall, spatiotemporal difference reconstruction yield better performance over image reconstruction, and performance can be further improved by extracting additional confidence and covariance information from the discovered heatmaps. + +# 4.4. Additional applications + +We show qualitative performance and demonstrate additional downstream tasks using our discovered keypoints, on pulse detection for Jellyfish and on wind speed regression for Vegetation. + +Qualitative Results. Qualitative results (Figure 6) demonstrates that B-KinD is able to track some body parts consistently, such as the nose of both mice and keypoints + +![](images/27c5f5efae5fe15917ec296393254dfc05d28d8d5775af4899c034c1c4e2d24d.jpg) + +![](images/cf43d8e2dfc893d6b06234c8d0d47ba33b2719275f82291a4fc45c2044cf862a.jpg) +Figure 6. Qualitative Results of B-KinD. Qualitative results for B-KinD trained on CalMS21 (mouse), Fly vs. Fly (fly), Human3.6M (human), jellyfish and Vegetation (tree). Additional visualizations are in the Supplementary materials. + +![](images/b92173d7ef666f5547797c8459307dee57aa7eb197fd1473f5035dc192aefd5b.jpg) + +![](images/34abee4058b550c96260ebaa47b3a7a21bce0338f4138b69e449f051f31ee5fb.jpg) + +![](images/653ae78370eb79a675b2cfcd605d4ffa5f15e1b03a3826ec5845d447b13e47c9.jpg) + +![](images/5603ce34ad8f92f643915dc0cc6b4d0c4d865d446e98838d363b934e31cf8e2d.jpg) + +![](images/f7110214a8e6ed22b39acd3ab5f75f12e072cd3a6490f5a8b3eb6c41b302b338.jpg) + +![](images/60220268f997dd2967625fe217a1ce82d428fe0478d4a57b46ad211008dec86c.jpg) + +![](images/a5f6a96bf0c9647c0e854cbc49deddaeced67531d44235d23a38c4401662664d.jpg) + +![](images/9b3b38411f9665abd74ec8d9626173573a457e55838207765d33756fa50be8f5.jpg) + +![](images/70e35448d1269cf9f12383d72935c4ab8a994e9bb5a4dbb7f9d07ef1aa5adc1c.jpg) + +![](images/573605d9e154ec8fd401ca1a3e24fe1d931e2fb944f22cf436989a7a0a351ba9.jpg) + +along the spine; the body and wings of the flies; the mouth and gonads of the jellyfish; and points on the arms and legs of the human. For visualization only, we show only keypoints discovered with high confidence values (Section 3.3); for all other experiments, we use all discovered keypoints. + +Pulse Detection. Jellyfish swimming is among the most energetically efficient forms of transport, and its control and mechanics are studied in hydrodynamics research [10]. Of key interest is the relationship between body plan and swim pulse frequency across diverse jellyfish species. By computing distance between B-KinD keypoints, we are able to extract a frequency spectrogram to study jellyfish pulsing, with a visible band at the swimming frequency (Supplementary materials). This provides a way to automatically annotate swimming behavior, which could be quickly applied to video from multiple species to characterize the relationship between swimming dynamics and body plan. + +Wind Speed Modeling. Measuring local wind speed is useful for tasks such as tracking air pollution and weather forecasting [6]. Oscillations of trees encode information on wind conditions, and as such, videos of moving trees could function as wind speed sensors [6, 7]. Using the Vegetation dataset, we evaluate the ability of our keypoints to predict wind speed using a physics-based model [7]. This model defines the relationship between the mean wind speed and the structural oscillations of the tree, and requires tracking these oscillations from video, which was previously done manually. We show that B-KinD can accomplish this task automatically. Using our keypoints, we are able to regress the measured ground truth wind speed with an $R^2 = 0.79$ , suggesting there is a good agreement between the proportionality assumption from [7] and the experimental results using the keypoint discovery model. + +Limitations. One issue we did not explore in detail, and which will require further work, is keypoint discovery for agents that may be partially or completely occluded at some point during observation, including self + +occlusion. Additionally, similar to other keypoint discovery models [27, 38, 51], we observe left/right swapping of some body parts, such as the legs in a walking human. One approach that might overcome these issues would be to extend our model to discover the 3D structure of the organism, for instance by using data from multiple cameras. Despite these challenges, our model performs comparably to supervised keypoints for behavior classification. + +# 5. Discussion and conclusion + +We propose B-KinD, a self-supervised method to discover meaningful keypoints from unlabeled videos for behavior analysis. We observe that in many settings, behavioral videos have fixed cameras recording agents moving against a (quasi) stationary background. Our proposed method is based on reconstructing spatiotemporal difference between video frames, which enables B-KinD to focus on keypoints on the moving agents. Our approach is general, and is applicable to behavior analysis across a range of organisms without requiring manual annotations. + +Results show that our discovered keypoints are semantically meaningful, informative, and enable performance comparable to supervised keypoints on the downstream task of behavior classification. Our method will reduce the time and cost dramatically for video-based behavior analysis, thus accelerating scientific progress in fields such as ethology and neuroscience. + +# 6. Acknowledgements + +This work was generously supported by the Simons Collaboration on the Global Brain grant 543025 (to PP and DJA), NIH Award #R00MH117264 (to AK), NSF Award #1918839 (to YY), NSF Award #2019712 (to JOD and RHG), NINDS Award #K99NS119749 (to BW), NIH Award #R01MH123612 (to DJA and PP), NSERC Award #PGSD3-532647-2019 (to JJS), as well as a gift from Charles and Lily Trimble (to PP). + +# References + +[1] David J Anderson and Pietro Perona. Toward a science of computational ethology. Neuron, 84(1):18-31, 2014. 2 +[2] Yoshua Bengio, Jérôme Louradour, Ronan Collobert, and Jason Weston. Curriculum learning. In ICML, 2009. 4 +[3] Gordon J Berman, Daniel M Choi, William Bialek, and Joshua W Shaevitz. Mapping the stereotyped behaviour of freely moving fruit flies. Journal of The Royal Society Interface, 11(99):20140672, 2014. 2 +[4] Kristin Branson, Alice A Robie, John Bender, Pietro Perona, and Michael H Dickinson. High-throughput ethomics in large groups of drosophila. 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However, the problem remains challenging when one tries to generalize the detector to forgeries created by unseen methods in the training dataset. This work addresses the generalizable deepfake detection from a simple principle: a generalizable representation should be sensitive to diverse types of forgeries. Following this principle, we propose to enrich the "diversity" of forgeries by synthesizing augmented forgeries with a pool of forgery configurations and strengthen the "sensitivity" to the forgeries by enforcing the model to predict the forgery configurations. To effectively explore the large forgery augmentation space, we further propose to use the adversarial training strategy to dynamically synthesize the most challenging forgeries to the current model. Through extensive experiments, we show that the proposed strategies are surprisingly effective (see Figure 1), and they could achieve superior performance than the current state-of-the-art methods. Code is available at https://github.com/liangchen527/SLADD. + +# 1. Introduction + +The realistic image generation brought by the generative adversarial network (GAN) raises a security issue that human portraits can be easily substituted to provide malicious bioinformatics [11, 45, 15, 44, 51, 56, 40, 54, 48]. This forgery becomes a threat to subject identifications which have been extensively utilized in digital payment, video surveillance, and social media. To reduce these risks, there is an emerging investigation on deepfake detectors to identify face forgeries. Formulated as a binary classification problem, current detectors [26, 3, 2, 32, 39] perform well + +![](images/003a85c8f8fa9395adb48223433e3b62346a0d3033aa7877ba0d8008816bdcfb.jpg) +Figure 1. Performance improvements of the proposed strategies for the baseline model (i.e. Xception [41]). The models are trained on the four types of data from Faceforensics++ dataset [41] and tested on CelebDF [28], DFDC [12], and DF1.0 [20] datasets. + +when training and testing forgeries are synthesized from the same dataset and same forgery methods. However, in practice the testing forgeries are usually from unseen datasets and synthesized by unseen methods. Discrepancies between training and testing data lead to inferior performance of detectors. There is a performance drop when detectors recognize forgeries outside the training dataset, which brings challenges to deepfake detectors for practical usage. + +Attempts have been made in recent arts to improve the generalizations. For example, to overcome dataset bias, some studies [24, 58] suggest data augmentation is an effective tool against poor generalization. These methods augment training data by synthesizing new face forgeries with their empirically designed augmentations. However, their augmentations are with a limited choice of strategy. The lacking of variety may jeopardize the generalization. Meanwhile, intrinsic forgery attributes shared between forgeries, such as detail discrepancies [30], and frequency features [39, 29], are also mined broadly with hand-crafted representations to distinct forgeries. But these attributes mainly rely on imperceptible image patterns, which are sensitive to post-processing steps, such as compression. They vary significantly in different datasets, thus leading to large detection bias and limiting their generalization [60]. + +In this paper, we address the deepfake detection from a simple heuristic principle: a generalizable representation should be sensitive to the various types of forgeries. Training a model by following this principle could potentially avoid the "blind spot" of the model or avoid relying on patterns specific to a dataset, since otherwise the model may not be capable of identifying a variety of forgeries. Pushing this idea to the limit, we propose to enrich the "diversity of forgeries" by synthesizing forgery images from a large pool of configurations1. Specifically, given a pristine, we randomly choose a reference image2 from training data, our synthesizer network (i.e. generator) produces forgery configurations that specify the forgery region, the blending type, and the blending ratio. Then based on these configurations, a synthesized forgery is generated (some examples are shown in Figure 2). To enhance the "sensitivity to the forgeries", our detector network (i.e. discriminator) is required to predict the configurations of an input in addition to judging if it is a forgery or not. Further, to effectively explore the large space of forgery augmentation, we adopt an adversarial training strategy to dynamically construct the augment that is most challenging to the current detector network. Different from the empirically designed augmentations [24, 58, 6], our adversarial augmentation strategy enjoys a large variety, and it can be dynamically constructed by the performance of the discriminator. + +Through our experimental studies, we demonstrate the effectiveness of employing both adversarial augmentation and self-supervised tasks. A significant improvement over the baseline approach is observed, and our method also performs favorably against other state-of-the-art detectors. + +# 2. Related Works + +Deepfake detection. Recent studies have made various attempts for deepfake detection and achieve remarkable success [26, 41, 3, 2, 32, 39, 14, 24, 30, 29, 19, 47, 23, 36, 5]. Several arts discuss low-level differences between pristines and forgeries and suggest using them as classification clues. Li et al. [24] assume blending artifacts exist in all pristines and suggest finding the blending boundary beside the detection task; Qian et al. [39] and Luo et al. [30] use high-frequency details as additional inputs for their models; Liu et al. [29] adopt phase spectrums to capture the up-sampling artifacts of face forgery for the task. Despite their effectiveness in many cases, the low-level artifacts are sensitive to post-processing steps which vary in different datasets, thus limiting their generalization [60]. Some works suggest borrowing features from other tasks for deepfake detection. + +![](images/1e475054a290539cbc26d6880c7d973dc420ffbb6efcfcfa169b6e819253a88a.jpg) + +![](images/8a56303e9e5c182dcf8fed1ba2969d10ec1fd12e594344012fb3a5b4693e50d2.jpg) + +![](images/0f36e6d4b3cc1e289227902c2bfb7fac4927896bfbfbb8215b81e2f9e4be9be5.jpg) + +![](images/cb65f1384d452b9ed0320fe3df0944d76bc0cbdb5f47233f645eab0131074513.jpg) + +![](images/145e6344198459c3c55a14b263a4aaf8c40b0e288805fe9e49fc31a1429c9d9f.jpg) + +![](images/a7adfae428da9aa5b327e5fa7cefe8ee94336bc4d08760740cc5c5d2a6ab998d.jpg) + +![](images/1ae2085adfff3225571c7243b723e0bbee344bd8f1ddba600a896716b9f5c90b.jpg) +(a) Pristine + +![](images/96a1bd6dd4dbedf1bf589c48bb7a1266e15bf1cb128f000c3f136dcef7258769.jpg) +(b) Reference + +![](images/bbbc1e057da21f75f6577d9338e799fff83b7588e6e3383bc52b6ea092ea7e7b.jpg) +(c) Forgery (adv) +Figure 2. Examples of the input pristine, reference images, and their corresponding synthesized adversarial forgeries. + +Such as the features from lips reading [19], facial image decomposition [60], and landmark geometric features [43]. Although these features can bring promising improvements, their generalization performance to the deepfake data are questionable. While annotating the deepfake data for these tasks is rather expensive, incorporating these tasks often lead to limited improvements. + +Adversarial learning. Adversarial training aims to use adversarial examples for augmenting the training samples, which often contains a generator and a discriminator, and they are trained on the principle of defending against adversarial attacks [17, 22, 31, 55]. Goodfellow et al. [17] first use the fast gradient sign method to improve the adversarial robustness. Madry et al. [22] further propose a multi-step scheme termed as projected gradient descent to enable powerful robustness compared to other works. Moreover, different from previous works that use adversarial training to enlarge datasets through directly synthesizing new images [46, 37, 4, 18, 16], Zhang et al. [55] suggest automatically choosing augmentation policies in an adversarial manner, which shows a great reduction in computing cost than the previous method [10]. However, most of these adversarial training strategies are designed for general tasks, such as classification. In contrast, our adversarial example synthesizing process is similar to the deepfake generation procedure, thus is more suitable for the deepfake detection task. + +# 3. Proposed Method + +We propose to improve the generalizability of deepfake detector with the help of adversarial data augmentation, + +![](images/ece9206c7d4a71ac17b8c7db5a829f2a248a0610a304101182cdb5ee0b657633.jpg) +Figure 3. Overview of our model. The synthesizer network (i.e. generator) outputs three forgery configurations that are further used to synthesize a new forgery, and these forgery configurations are also used as labels to guide the detector network (i.e. discriminator). We train the generator and discriminator in an adversarial manner. Please refer to the text for details. + +which enriches the types of forgeries, and self-supervised tasks that enforce sensitivity to forgery configurations. The pipeline of our model is shown in Figure 3. During training, we randomly select a reference image if the input is pristine. These two images are sent to a synthesizer network to produce configurations that specify the facial forgery region, the blending type, and the mixup blending ratio (if mixup blending is selected). Then a new forgery is synthesized based on these two images and the selected configurations. The synthesized forgery is passed to our detector for the real or fake and configurations predictions. Note the input will skip the forgery synthesizing process if it is an original forgery from the training data. We adopt an adversarial training strategy to train the system, in which the synthesizer is regarded as the generator, and the detector is regarded as the discriminator. The training process will train the forgery synthesizer to produce new forgeries to challenge the detector. Once trained, only the detector is used for deepfake detection. + +# 3.1. Selecting Space and Synthesizing Forgery + +Our synthesizer network $G(\cdot, \theta)$ takes a pristine $\mathbf{I}_p \in \mathbb{R}^{H \times W \times 3}$ and a reference image $\mathbf{I}_f \in \mathbb{R}^{H \times W \times 3}$ as inputs and output three configurations: the forgery region reference index $R_g$ , the blending type index $T_g$ (a discrete number), and the mix-up blending ratio $A_g$ (a continuous value). For $A_g$ , we directly generate a scalar from the input $\mathbf{I}_p$ and $\mathbf{I}_f$ . For $R_g$ , $T_g$ , we first generate two probability distributions $p(R_g)$ and $p(T_g)$ , indicating the chance of selecting a particular index of $R_g$ and $T_g$ , and then randomly sample a index according to the probability. For the simplicity of discussion, we use $p_m$ to denote those two probabilities. These configurations, $R_g$ , $T_g$ and $A_g$ , control how a forgery image is generated. Their definitions are as follows: + +$R_{g}$ : The index $R_{g} \in \{0, \dots, 9\}$ determines a specific facial + +region. We divide the facial image into 10 regions based on its landmark, including the left eye, right eye, nose, mouth, and their combinations. Examples of different regions are shown in Figure 4 (c) - (l). We only consider the facial features because most deepfake arts focus on them, and they convey the most information in a facial image; + +$T_{g}$ : The reference number $T_{g} \in \{0, \dots, 3\}$ determines the blending type. We use three blending techniques, including alpha, Poisson [38], and mixup blending. Without the loss of generality, we include a do-nothing choice among the blending type pool, so that we can use the original pristine from the dataset for further classification. + +$A_{g}$ : The continuous value $A_{g} \in [0,1]$ is the blending ratio which is only effective when mixup blending is selected. + +We adopt a random shape deformation operation and apply Gaussian blur with random kernel size to the selected forgery region before the synthesizing step. An example of the final mask is shown in Figure 4 (m). Then, to synthesize the adversarial forgery $\mathbf{I}_a$ , we crop the facial parts determined by $R_g$ from $\mathbf{I}_f$ , and blend it into $\mathbf{I}_p$ using the configurations indicated by the synthesizer network. Specifically, we use the official implementations from OpenCV for alpha and Poisson blendings to synthesize $\mathbf{I}_a$ , and for mixup blending, $\mathbf{I}_a$ can be obtained by: + +$$ +\mathbf {I} _ {a} = A _ {g} \times \mathbf {M} _ {d} * \left(\mathbf {I} _ {f} - \mathbf {I} _ {p}\right) + \mathbf {I} _ {p}, \tag {1} +$$ + +where $\mathbf{M}_d$ is the deformed final mask, and $*$ is the Hadamard product. + +Like existing deepfake methods, the cropped facial parts are applied with color transfer (aligning the mean of the RGB channels, respectively) and face alignment before the alpha and Poisson blending steps, which can avoid obvious artifacts in the newly synthesized forgery. Examples of newly synthesized forgeries with different blending types are shown in Figure 4 (n) - (p). + +![](images/0381a873000315ab4322b0d3f87f0401b39a42dc9f5b4ef378f24194bed81165.jpg) +(a) Pristine + +![](images/7277f8647a729868bf88be4069d270eb981e838d61d77c4fa94ced78740e7062.jpg) + +![](images/a09b072a9c86e196fa4f1b6530f544ca57321b2b180ce68cd08acf4970560abe.jpg) + +![](images/b265bc150f98236c3ebc7deff018f8f32e13f9cf4f3467168821ae96c601972a.jpg) + +![](images/979fd1b94289dd165de4b15e550a1f8300f99c166223d6d0a9f9affaa6905c23.jpg) + +![](images/7a806a67c2a9040cfa8413344757de1b3dbabbb2854a953485a5538a4a3c1062.jpg) + +![](images/a7d2d2483c540505f820ee1ca2c868d6950bd31a9bd251e808a13db354ce94d8.jpg) + +![](images/c7b2f772524842143e08b4b71d600cb2c8df140fa7e40b08acab14d3e1dc248f.jpg) + +![](images/f62d78421e9f5505ab50ec2e53cd318d5d3ceb00c8fdb941b1319b63f57d176d.jpg) +(b) Random reference +Figure 4. An example of the pristine and randomly chosen reference images (i.e. (a) and (b)), the corresponding selecting space of the manipulate regions (i.e. (c) - (m)), and the adversarial forgeries synthesized by different blending types (i.e. (n) - (p)) under the instruction of the deformed manipulate region map (i.e. (m)). The selected region number is 7. in this example, and the blending ratio for (o) is 0.5. + +![](images/1287d54d44906abe713d1b7849ebd4fc8046c31b459dabf26749618779519c58.jpg) +(c) No. 0. left eye +(d) No. 1. right eye + +![](images/f0d720eb654b99b4066efc2de75a5bbd88c57b85231e7ca926da364d0ce58e1e.jpg) +(e) No. 2. nose +(f) No. 3. mouth + +![](images/c510efc145c6f144bcdad366471698e94041198da0148904dc3bf49606564fc9.jpg) +(g) No. 4. +nb. No. 0 & 1 +(h) No. 5. Comb. No. 0 & 2 + +![](images/974f5e8ab3cad481088ae4ce4856c79f9b547ac560ac64348dd92e678800193c.jpg) +(i) No. 6. Comb. No. 1 & 2 +(j) No. 7. Comb. No. 2 & 3 + +![](images/4d37f8266cef14ecebca5605e6ae22f0c8856292b6bfdc41dea00f24c97a0645.jpg) +(k) No. 8. +ab. No. 0, 1 & 2 +(1) No. 9. + +![](images/dd99720e6940d9facef4da7c00918b1882c74208d912f9d9faa35bd9aa624117.jpg) +(m) deformed final mask +(n)Forgery by alpha blending + +![](images/a94d8af326f83588ebc09f61d2f4155ba6d1f22d3f6818d21c56368d4d155df9.jpg) +(o) Forgery by mixup blending +(p) Forgery by Poisson blending + +# 3.2. Joint Training with Self-Supervised Tasks + +Self-supervised tasks have been shown effective for improving generalization in previous works [7, 50]. However, those attempts often consider self-supervised learning tasks proven effective for image classification tasks. In contrast to them, this paper employs an auxiliary self-supervised task specifically designed for the deepfake detection problem. By doing so, we expect that the auxiliary task aligns better with the target task and thus could lead to better performance. Our idea follows a multi-task scheme that allows the model to simultaneously learn from two tasks, the main task and a set of auxiliary self-supervised task. Specifically, for the auxiliary tasks, we consider forgery region estimation, blending type estimation and blending ratio estimation. We elaborate on each task and the loss in the following. + +Main task loss $\mathcal{L}_{\text{Main}}$ . The main task is a binary classification task that predicts whether a given input image is pristine or forgery. Similar to previous work [30], we adopt the AM-Softmax Loss [49] to compute $\mathcal{L}_{\text{Main}}$ since it allows for smaller intra-class variations and larger inter-class differences than the regular cross-entropy loss. + +Forgery region estimation loss $\mathcal{L}_R$ . We also create a forgery region estimation task. Specifically, a forgery region prediction head is attached to the detector network and generates forgery region mask with the size of $[H / 16 \times W / 16]$ . The ground-truth forgery mask $\mathbf{M}_{gt}$ is created depending on categories of the input images, which is divided into three categories. Specifically, if the input image is the adversarial forgery, the corresponding $\mathbf{M}_{gt}$ is the resized deformed final mask (i.e. $\mathbf{M}_{gt} = \mathbf{M}_d$ ); As most datasets provide the ground truth forgery region, we can directly use them as $\mathbf{M}_{gt}$ if the input image is an original forgery from the training dataset; If the input image is an original pristine from the training dataset, the $\mathbf{M}_{gt}$ is an all-zero matrix (i.e. $\mathbf{M}_{gt} = \mathbf{0}$ ), indicating there is no forgery region in the input + +image. An $L_{1}$ loss is applied for the task: + +$$ +\mathcal {L} _ {R} = \frac {\left\| \mathbf {M} _ {g t} - \mathbf {M} _ {e} \right\| _ {1}}{H / 1 6 \times W / 1 6}, \tag {2} +$$ + +where $\mathbf{M}_e$ is the estimated region map from our detector network, and $\| \cdot \| _1$ denotes the $L_{1}$ norm. + +Blending type estimation loss $\mathcal{L}_T$ . We then introduce a blending type estimation task that aims to estimate the blending type of input images. Similar to the forgery region estimation task, the ground-truth of the prediction target, i.e., ground-truth blending type $T_{gt}$ , for this task varies accordingly to the category of the input data. When the input is a synthesized adversarial forgery, $T_{gt}$ can be directly borrowed from the output of the generator (i.e. $T_{gt} = T_g$ , where $T_{g} \in \{0,1,2\}$ according to the selected blending type); If the input is the original pristine, we set $T_{gt} = 3$ , implying there is no blending operation in the image; As the blending types are often unavailable in the existing datasets, we thus set $T_{gt} = 4$ if the input image is the original forgeries from the training dataset, indicating a blending type outside of our selecting space. Similarly, we adopt the AM-Softmax Loss [49] to compute $\mathcal{L}_T$ . + +Blending ratio estimation loss $\mathcal{L}_A$ . To take full advantage of the blending information provided in the forgery synthesizing process, we further construct a task to estimate the blending ratio output by the synthesizer network. Because the blending ratio is only effective when the synthesizer network selects the mixup blending, we can set the prediction ground-truth $A_{gt} = A_g$ when the input image is a synthesized adversarial forgery using mixup blending. Correspondingly, this loss is not computed when the input image is either the original images in the training dataset or adversarial forgery synthesized with other blending types. An $L_1$ loss is adopted to compute $\mathcal{L}_A$ : + +$$ +\mathcal {L} _ {A} = \tau \times \| A _ {g t} - A _ {e} \| _ {1}, \tag {3} +$$ + +where $A_{e}$ is the estimated blending ratio from the detector network, and $\tau$ is a binary value, which s.t. $\tau = 1$ if $T_{gt} = 2$ (i.e. the blending type is mixup blending) and $\tau = 0$ otherwise, thus ensuring $\mathcal{L}_A$ is only effective when adopting the mixup blending in the forgery synthesizing process. + +# 3.3. Adversarial Training + +To better leveraging the forgery augmentation space, we adopt adversarial training to dynamically construct the most challenging auxiliary task. Specifically, we use the synthesizer network $G(\cdot ,\theta)$ as the generator, which maximizes the training loss of the target discriminator (i.e. the detector network $D(\cdot ,w)$ ) through adversarial learning. The optimization process can be presented as, + +$$ +\min _ {w} \max _ {\theta} \mathcal {L}, \text {s . t .} \mathcal {L} (\theta , w) = \mathcal {L} _ {\text {M a i n}} + \alpha \mathcal {L} _ {R} + \mu \mathcal {L} _ {T} + \gamma \mathcal {L} _ {A}, \tag {4} +$$ + +where $\alpha$ , $\mu$ , and $\gamma$ are weight hyper-parameters. Recall that $\theta$ denotes all the parameters in the generation process. Following the common practice of adversarial training, the above optimization problem can be approximately solved by iteratively updating the discriminator and the generator. + +We first present the learning process of the discriminator. Eq. (4) is a minimization problem regarding $w$ . By fixing the current generator parameter $\theta$ , with the learning rate of $\eta$ and batch size of $N$ , we perform gradient descent update: + +$$ +w ^ {t + 1} = w ^ {t} - \eta \frac {1}{N} \sum_ {n = 1} ^ {N} \nabla_ {w ^ {t}} \mathcal {L} _ {n} \left(\theta^ {t}, w ^ {t}\right), \tag {5} +$$ + +where $\mathcal{L}_n$ is the loss for the $n$ -th sample in a mini-batch. + +The generator is designed to increase the training loss of the target discriminator by synthesizing more challenging samples than the original benign examples, thus encouraging the discriminator to learn more generalizable features. It plays a zero-sum game in an adversarial framework with the discriminator. Mathematically, we can formulate the object as a maximizing problem according to Eq. (4), + +$$ +\theta^ {t + 1} = \arg \max _ {\theta^ {t}} \mathcal {L} \left(w ^ {t + 1}, \theta^ {t}\right). \tag {6} +$$ + +However, directly updating $\theta$ by solving Eq. (6) could be problematic because there exist non-differentiable sampling operations that will break gradient flow from $D(\cdot ,w)$ to $G(\cdot ,\theta)$ . To handle that, we apply REINFORCE algorithm [52] to approximate the gradient calculation for $\theta$ : + +$$ +\begin{array}{l} \theta^ {t + 1} = \theta^ {t} + \epsilon \nabla_ {\theta^ {t}} \mathcal {L} _ {b} \\ \approx \theta^ {t} + \epsilon \frac {1}{M} \sum_ {m = 1} ^ {M} \mathcal {L} _ {b} \nabla_ {\theta^ {t}} \log p _ {m}, \tag {7} \\ \end{array} +$$ + +where $\mathcal{L}_b = \frac{1}{N}\sum_{n = 1}^N\mathcal{L}_n(w^{t + 1},\theta^t)$ , $M$ denotes the number of selected configuration series in a batch. $p_m$ represents the probabilities of generating $R_{g}$ and $T_{g}$ , which is + +estimated from the synthesizer network $G(\cdot ,\theta)$ + +# 4. Experiments + +# 4.1. Settings + +Training datasets. Following recent deepfake detection methods [39, 24, 30, 29, 47, 23], we train our model in the Faceforencis++ (FF++) dataset [41]. It contains 1,000 original videos, where 720 videos are used for training, 140 videos are reserved for testing and the rest for validation. All videos undergo four state-of-the-art deepfake methods, which includes Deepfakes (DF) [11], Face2Face (F2F) [45], FaceSwap (FS) [15], and NeuralTextures (NT) [44]. Final outputs are generated with different compression levels including RAW, High Quality (HQ) and Low Quality (LQ), respectively. We use the HQ and LQ versions in our experiments, and the HQ version is adopted by default unless otherwise stated. + +Testing datasets. To evaluate the generalizability of our method, we use the following benchmark datasets: CelebDF [28], which contains 408 real videos and 795 synthesized videos that are generated by the improved deepfake technology; Deepfake Detection Challenge (DFDC) [12], which includes over 1,000 real and over 4,000 fake videos manipulated by multiple Deepfake, GANbased, and nonlearned methods; DeeperForensics-1.0 (DF1.0) [20], which consists of over 11,000 fake videos generated by their DFVAE [20] method. + +We use DLIB [42] for face extraction and alignment, and we resize the aligned faces to $256 \times 256$ for all the samples in training and test datasets. + +Implementation details. We modify Xception [8] as the backbones for our synthesizer and detector networks, and their parameters are initialized by Xception pre-trained on ImageNet. The hyper-parameter used in (4) are $\alpha = 0.1$ , $\mu = 0.05$ , and $\gamma = 0.1$ . We use the Adam optimizer [21] for both the two networks with $\beta_{1} = 0.9$ and $\beta_{2} = 0.999$ and the batch size is fixed as 32. The learning rates are set to $2 \times 10^{-4}$ and $5 \times 10^{-5}$ for the detector and synthesizer networks, respectively. + +# 4.2. Generalizability Comparisons + +To comprehensively evaluate the generalizability of our method, we compare several state-of-the-art methods including Xception [41], Face X-ray [24], F3Net [39], RFM [47], and SRM [30]. To ensure fair comparisons, we use the provided codes of Xception [41], RFM [47], and SRM [30] from the authors, and we reimplement Face X-ray [24] and F3Net [39] rigorously following the companion paper's instructions and train these models under the same settings. + +Generalizations under different datasets. In these experiments, we train the compared models on each of the + +
MethodDFF2FFSNTAvg.
DFDCCelebDFDF1.0DFDCCelebDFDF1.0DFDCCelebDFDF1.0DFDCCelebDFDF1.0
Xception [41]0.6540.6810.6170.7080.5980.7450.7080.6010.6050.6460.6250.8380.669
Face X-ray [24]0.6090.5540.6680.6330.6840.7660.6460.6970.7950.6130.7030.8660.686
F3Net [39]0.6820.6640.6580.6790.6540.7610.6790.6360.6510.6720.6890.9320.696
RFM [47]0.7580.7230.7170.7360.6630.7320.7140.5910.7140.7260.6000.8460.710
SRM [30]0.6790.6500.7200.6870.6930.7750.6710.6430.7710.6560.6510.9360.711
Ours0.7720.7300.7420.7870.7810.7860.7420.8000.6950.7410.7590.8890.769
+ +Table 1. Generalizability comparisons with state-of-the-art methods in the term of AUC. The best results are in bold. The first row denotes the training data, and the second row shows the corresponding test dataset. Our method performs favorably among the models compared. + +
Training setMethodTest set
LQHQ
DFFSDFFS
NTXception [41]0.5870.5170.7700.718
Face X-ray [24]0.5710.5100.5850.779
F3Net [39]0.5830.5190.8050.612
RFM [47]0.5580.5160.7980.639
SRM [30]0.5550.5290.8380.795
Ours0.6280.5680.8460.721
+ +four methods in $\mathrm{FF}++$ [41], and evaluate it on the benchmark datasets including CelebDF [28], DFDC [12], and DF1.0 [20]. This setting is rather challenging because both pristines and forgeries in the test dataset are unseen in the training dataset. + +We compare different methods by using the Area Under Curve (AUC) metric and present the results in Table 1. As seen, our method outperforms other models in most cases and achieves the overall best performance. This clearly demonstrates the advantage of the proposed adversarial augmentation and self-supervised tasks. SRM [30] and F3Net [39] both rely on high-frequency components of a image to distinguish forgeries from pristine. Our experiment suggests that they attain worse generalization performance than our approach. This may be because the high-frequency cue identified effective on the $\mathrm{FF}++$ dataset [41] may not necessarily generalize to other datasets that adopt different post-processing steps. RFM [47] encourages the use of multiple facial regions for forgery detection and thus leads to improved generalization performance. However, their method still cannot avoid some data source biases, such as all the whole facial parts in a training sample are from the same source. This limitation may explain why their performance is inferior to ours. Face X-ray [24] uses the blended artifacts in the forgery for generalization. Compared to our method, Their generalizability will degrade when these artifacts share different patterns in the training and test dataset. As a baseline, Xception [41] does not in- + +Table 2. Generalizability comparisons across different compression levels in the term of AUC. Our method achieves comparable performance against existing methods. + +
Training setMethodTest set
F2FFS
F2FLAE [14]0.9090.632
ClassNSeg [34]0.9280.541
Forensic-Trans [9]0.9450.726
Ours0.9600.848
+ +Table 3. Comparisons with models adopt multi-task learning in the term of ACC. Our model performs favorably against these arts. + +
MethodFF++CelebDF
Two-stream [59]0.7010.538
Meso4 [1]0.8470.548
MesoInception4 [1]0.8300.536
FWA [27]0.8010.569
DSP-FWA [27]0.9300.646
Xception [41]0.9970.653
VA-MLP [33]0.6640.550
Headpose [53]0.4730.546
Capsule [35]0.9660.575
SMIL [25]0.9680.563
Two-branch [32]0.9320.734
SPSL [29]0.9690.724
MADD [57]0.9980.674
Ours0.9840.797
+ +Table 4. Extensive evaluations with other state-of-the-art methods in the term of AUC. The models are trained on FF++ dataset. Our method performs favorably when tested on FF++, and it outperforms others when tested on CelebDF. + +corporate any augmentation or feature engineering. Its performance drops drastically in unseen forgeries. + +Generalizations under different compression levels. Given that real world forgeries may be post-processed by different methods, such as compression. It is crucial that deployed deepfake detectors are not easily subverted by unseen post-processing processes. To evaluate the generalizability of the compared models regarding the varying post-processing methods, we separately train them on NT data, while testing them on DF and FS with different compression levels. + +
MethodDFF2FFSNTAvg.
DFDCCelebDFDF1.0DFDCCelebDFDF1.0DFDCCelebDFDF1.0DFDCCelebDFDF1.0
Xception [41]0.6540.6810.6170.7080.5980.7450.7080.6010.6050.6460.6250.8380.669
Xception w/ adv0.7170.7030.6740.7390.7780.7350.7370.6440.6020.6620.7220.7940.709
Ours w/ ran0.7630.6630.6900.7630.7450.6960.7380.7000.6500.7050.6660.8100.716
Ours0.7720.7300.7420.7870.7810.7860.7420.8000.6950.7410.7590.8890.769
+ +Table 5. Ablation studies regarding the effectiveness of the adversarial training. The metric is AUC. Please see Sec. 4.4 for detailed experiment settings. + +
MethodDFF2FFSNTAvg.
DFDCCelebDFDF1.0DFDCCelebDFDF1.0DFDCCelebDFDF1.0DFDCCelebDFDF1.0
Ours w/ ran ops0.7350.6660.7820.6940.6470.8270.7370.6010.6460.6910.6850.8120.710
Ours w/ ops [55]0.7210.7260.7770.6860.6470.8400.7370.5340.7200.6780.6420.8290.711
Ours w/ aug [24]0.7220.6920.7120.7220.7100.7390.7190.7260.6400.7140.6690.8410.717
Ours w/ aug [58]0.7540.6790.6870.7460.6040.7530.7260.6970.6740.7700.7130.8630.722
Ours0.7720.7300.7420.7870.7810.7860.7420.8000.6950.7410.7590.8890.769
+ +Table 6. Ablation studies regarding the effectiveness of the data augmentation strategies. The metric is AUC. Please see Sec. 4.4 for detailed experiment settings. + +The evaluated AUC values are presented in Table 2. We can observe that almost all models generalize competitively when trained and tested on data with the same compression levels. However, models that based on imperceptible image patterns [41, 24, 39, 30] suffer from large performance drop when test on unseen LQ data. The results are not surprising since the low-level clues are largely destroyed when the images are highly compressed. The same results are reported for RFM [47]. Because all facial parts in a face sample usually share the same compression level, exploring more facial regions cannot guarantee well generalizability across different compression levels. On the other hand, the proposed method is substantially less affected by the compression levels, outperforming all other methods, as it uses more generalizable forgery configurations instead of just the low-level artifacts. We believe the improvements over Xception [41], which is with a similar network setting, are due to the adopted adversarial self-supervised framework. + +# 4.3. State-of-the-art Comparisons + +Comparison to multi-task learning detectors. Using multi-task learning strategies to boost deepfake detection has been explored in previous works, including LAE [14], ClassNSeg [34], and Forensic-Trans [9]. All these works suggest simultaneously classifying and localizing forgery regions. Unlike their localization task, the self-supervised task involved in our self-supervised framework aims to recognize the forgery configurations selected by the synthesizer network, which not only avoids the tedious annotation work, but also considers more configurations that are prevalent in forgeries. + +To ensure fair comparisons, we use the same evaluation settings in our experiments with that from the compared arts. We train our model on the F2F data and test it on F2F + +and FS. The comparison results are presented in Table 3, where our model outperforms other algorithms in test samples with both seen and unseen deepfake techniques. Note the results are directly cited from the reported statistics in their original papers. + +Comparison to other state-of-the-art detectors. We further evaluate our method against several state-of-the-art models, including the Two-stream [59], MesoNet [1], Headpose [53], FWA [27], VA-MLP [33], Capsule [35], SMIL [25], Two-branch [32], SPSL [29], MADD [57]. We train our model on the FF++ dataset and test it on FF++ and CelebDF. Results of some methods are directly cited from [29]. As shown in Table 4, our method performs competitively with other models when tested on the FF++ dataset, and it achieves the best performance when tested on CelebDF, which further validates the effectiveness and superior generalizability of our method. + +# 4.4. Ablation Study + +This section analyzes the effectiveness of adversarial learning, data augmentation, and self-supervised tasks. We provide more analyses in our supplementary material. + +Adversarial Learning. To validate whether the adversarial training strategy can improve the generalizability, we conduct an ablation study by comparing our methods with the following variant. (1) Xception [41]: the baseline approach without using both adversarial learning and self-supervised learning (2) Xception w/ adv: we add adversarial augmentation (but not self-supervised learning) to the Xception baseline. (3) Ours w/ ran: we replace adversarial augmentation with random augmentation. That is, instead of relying on the forgery synthesizer to generate configurations, we randomly select configurations to perform augmentation. This + +
DFF2FFSNTAvg.
\( \mathcal{L}_R \)\( \mathcal{L}_T \)\( \mathcal{L}_A \)DFDCCelebDFDF1.0DFDCCelebDFDF1.0DFDCCelebDFDF1.0DFDCCelebDFDF1.0
✓✓-0.7700.6860.6870.7680.7140.7790.7220.7090.6530.7350.7200.8560.733
✓-✓0.7630.7160.7090.7600.7340.8000.7760.6360.7070.7240.6830.8350.737
-✓✓0.7220.6850.6560.7650.7330.7710.7130.6980.6590.7350.7090.8380.724
---0.7170.7030.6740.7390.7780.7350.7370.6440.6020.6620.7220.7940.709
✓✓✓0.7720.7300.7420.7870.7810.7860.7420.8000.6950.7410.7590.8890.769
+ +Table 7. Effectiveness of the proposed self-supervised auxiliary tasks. The metric is AUC. We disable the self-supervised task by assigning a zero weight to the corresponding loss. + +variant is used to test if the improvement brought by the adversarial augmentation is from the "adversarial training" or the "augmentation" or both. + +The experimental comparison is shown in Table 5. We can see that using adversarial augmentation alone (Xception w/ adv) can lead to significant (around $4\%$ ) improvement over the baseline approach (Xception). This shows the effectiveness of our adversarial augmentation. We also observe that if replacing the adversarial augmentation with random augmentation, the performance of our method leads to a significant drop. This suggests that adversarial training is essential for our system. + +Data augmentations. We first replace our augmentation step with general augmentation strategies in [10, 55], which includes 16 image operations, such as rotation and cutout [13], and 10 magnitudes. Two augmentation forms are compared. The first one imposes random image operations on the training dataset (i.e. Ours w/ ran ops); the second uses a same synthesizer network to select different operations and magnitudes for different samples, which is similar to the setting in [55] (i.e. Ours w/ ops [55]). Note the goals of the detector are to estimate the types of image operation and their magnitudes in these two settings. We further compare our augmentation strategy with that from [24] and [58] (i.e. Ours w/ aug [24] and [58]). Both these two methods suggest synthesizing new forgeries to augment the training data, where the forgery regions are fixed in the inner faces, and alpha blending is adopted for all samples in [24] while Poisson blending is mainly used in [58]. + +Evaluation results are shown in Table 6. We observe that strategies with commonly used image operations perform less effectively than our method, and the improvements gained from the adversarial training are also subtle compared to ours. The main reason is that the commonly used image operations are used for general tasks. They may be ineffective in our task. In contrast, our augmentation method is specially designed for deepfake detection, which is more related to the forgery synthesizing process. Thus, it is not surprising that our augmentation strategy outperforms general image operations. Meanwhile, different from the empirically designed augmentations [24, 58], our augmentation is with multiple forms. With the help of adversarial training, more diverse samples can be created to improve + +the generalization. These advantages explain why our augmentation strategy performs better than [24, 58]. + +Self-supervised tasks. We seamlessly integrate three auxiliary self-supervised tasks to boost the generalizability of our model. To evaluate the effectiveness of these tasks, we conduct ablation studies by assigning zero weight to the loss corresponds to each of these tasks (i.e. $\mathcal{L}_R$ , $\mathcal{L}_T$ , and $\mathcal{L}_A$ correspond to the forgery region estimation mask, blending type estimation task, and the blending ratio estimation task, respectively). All models are trained on the four methods of $\mathrm{FF}++$ and evaluated on benchmark datasets using the same settings. Results are shown in Table 7. We can observe that each auxiliary task plays a vital role in our framework, where our method performs the best when all three self-supervised tasks are incorporated. On the other hand, excluding any of these tasks will decrease the overall performance, and using only the main classification loss lead to significantly worse performance than others. This validates the effectiveness of the proposed self-supervised tasks. + +# 5. Conclusions and Discussions + +In this paper, we propose a deepfake detection method that can generalize well in unseen scenarios. Our design is based on the intuition that a generalizable deepfake detector should be sensitive to different types of forgeries. We thus leverage a synthesizer and adversarial training framework to dynamically generate forgeries. Training to identify those generated forgeries, the network can learn more robust feature representation and lead to a more generalizable deepfake detector. Through extensive experiments, we demonstrate the effectiveness of the proposed method. + +The major limitation of the current method is that the augmentation type in the synthesizer is still limited. 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Asano +QUVA Lab +University of Amsterdam +y.m.asano@uva.nl + +# Abstract + +Progress in self-supervised learning has brought strong image representation learning methods. Yet so far, it has mostly focused on image-level learning. In turn, tasks such as unsupervised image segmentation have not benefited from this trend as they require spatially-diverse representations. However, learning dense representations is challenging, as in the unsupervised context it is not clear how to guide the model to learn representations that correspond to various potential object categories. In this paper, we argue that self-supervised learning of object parts is a solution to this issue. Object parts are generalizable: they are a priori independent of an object definition, but can be grouped to form objects a posteriori. To this end, we leverage the recently proposed Vision Transformer's capability of attending to objects and combine it with a spatially dense clustering task for fine-tuning the spatial tokens. Our method surpasses the state-of-the-art on three semantic segmentation benchmarks by $17\% - 3\%$ , showing that our representations are versatile under various object definitions. Finally, we extend this to fully unsupervised segmentation – which refrains completely from using label information even at test-time – and demonstrate that a simple method for automatically merging discovered object parts based on community detection yields substantial gains. + +# 1. Introduction + +Defining what makes an object an object is hard. In philosophy, Peirce defines an object as anything we can think and talk about [40]. In computer vision, object definitions for semantic segmentation are more pragmatic and feature various notions of objectness as well as different levels of granularity. For instance, the COCO-Stuff benchmark distinguishes between stuff (objects without a clear shape) and things (objects with a "well-defined" shape) [3, 35] and features coarse and fine object categories. Others, like + +![](images/0aa3f42277331fb58780f6a2a03a946ab6a0ce9bc7ed1e66bbcb56d6834ca65a.jpg) +Figure 1. ViTs and Resnets compared under foreground extraction and semantic segmentation. We use Jaccard distance as a measure for foreground extraction. Starting from a DINO initialization, our method, Leopart, closes the performance gap between self-supervised ViTs and their supervised counterparts as well as Resnets. Leopart (CBFE+CD) further improves a ViT's object extraction capabilities and sets new state-of-the-art for fully unsupervised semantic segmentation. + +Cityscapes [12], choose a segmentation that is most informative for a specific application like autonomous driving and therefore also include sky and road as object classes. + +This variedness of object definitions is challenging for self-supervised or unsupervised semantic segmentation as human annotations that carry the object definitions are, at most, used at test time. However, the ability to learn self-supervised dense representations is desirable as this would allow scaling beyond object-centric images and allow effective learning on billions more generic images. Furthermore, unsupervised segmentation can be highly useful as a starting point for more efficient data labeling, as segmen + +tation annotations are even more expensive than image labelling [35]. To tackle the lack of a principled object definition during training, many methods resort to defining object priors such as saliency and contour detectors to induce a notion of objectness into their pretext tasks [9, 28, 30, 49, 56], effectively rendering such methods semi-supervised and potentially not generalizable. In this paper, we instead stay in the fully unsupervised domain and explore a novel yet simple alternative for training densely. We learn object parts (Leopart) through a dense image patch clustering pretext task. Object part learning promises a principled formulation for self-supervised dense representation learning as object parts can be composed to form objects as defined in each benchmark, after generic pretraining. + +In this paper, we explore the use of a Vision Transformer (ViT) with our new loss and excavate its unique aptness for self-supervised segmentation. While vision transformers have shown great potential unifying architectures and scaling well with data into billions, they have mostly been shown to work for image-level tasks [6,8,16] or dense tasks [11,37,50,52] but in a supervised manner. Our work aims to close this gap by self-supervisedly learning dense ViT models. We combine the recently discovered property of self-supervised ViTs to localise objects [6] with our dense loss to train spatial tokens for unsupervised segmentation. + +We validate our method from two different angles: First, we conduct a transferability study and show that our representations perform well on downstream semantic segmentation tasks. Second, we tackle the more challenging fully unsupervised setup proposed in [49] based on directly clustering the pixel or patch embeddings. For that, two model characteristics are important: unsupervised foreground extraction and a semantically-structured embedding space, see Figure 1. To our surprise, even though self-supervised ViTs excel at extracting objects, they do not learn a spatial token embedding space that is discriminative for different object categories. On the other hand, ViTs trained under supervision achieve better semantic segmentation performance, but the attention heads perform poorly at localizing objects. In contrast, our method outperforms self-supervised ViTs and Resnets in fully unsupervised semantic segmentation as well as in learning transferable dense representations. + +Thus, our contributions are as follows: + +- We propose a dense clustering pretext task to learn semantically-rich spatial tokens closing the gap between supervised ViTs and self-supervised ViTs. +We show that a ViT trained with our pretext task learns transferable representations that surpass the state-of-the-art on Pascal VOC, COCO-Thing and COCO-Stuff semantic segmentation at the same time by $17\% - 3\%$ . +- We develop a novel cluster-based foreground extraction and overclustering technique based on community + +detection to tackle fully unsupervised semantic segmentation and surpass the state-of-the-art by $>3\%$ . + +# 2. Related Work + +Our work takes inspiration from standard image-level self-supervised pretraining while extending this to the domain of dense representation learning using Vision Transformers. + +Image-level self-supervised learning. Self-supervised learning aims to learn powerful representations by replacing human annotation with proxy tasks derived from data alone. Current methods can be roughly categorized into instance-level and group-level objectives. Instance-level objectives include predicting augmentations applied to an image [15, 22, 31, 38, 39, 54, 55] or learning to discriminate between images [2, 7, 17, 25, 53], often done by the use of contrastive losses [24]. + +On the other hand, group-level objectives explicitly allow learning shared concepts between images by leveraging clustering losses [1,4,5,48]. [4] proposes k-means clustering in feature space to produce pseudo labels for training a neural network. [1] casts the problem of finding pseudo labels as an optimal transport problem unifying the clustering and representation learning objectives. This formulation was adapted to an online setting in SwAV [5] together with a new multi-crop augmentation strategy, a random cropping method that distinguishes between global and local crops of an image. The IIC method [32], also conducts clustering, however using a mutual information objective. While it can also be used densely, it has been found to focus on lower-level features specific to each dataset [49]. Another recent line of works completely refrains from group level clustering or instance-based discrimination by predicting targets from a slowly moving teacher network [6,23]. + +Our work adapts this teacher-student setup and shows its benefits beyond image-level tasks. To this effect, we build on the clustering pretext task from [5] and reformulate it such that it can be used on an image patch level with teacher-student setups. We also use the multi-crop augmentation strategy and provide an interpretation from the perspective of dense prediction tasks. + +Dense self-supervised learning. Based on the observation that image-level learning does not imply expressive dense representations [26, 41], dedicated self-supervised dense representation learning has attracted a lot of attention [10,20,21,28-30,32,34,36,44,46,49,51,57]. DenseCL reformulates the contrastive objective used in MoCo [25] to work on spatial features by establishing dense correspondences across views and is currently the state-of-the-art in transfer learning for semantic segmentation on PVOC [34]. Other methods resort to defining an unsupervised object prior such as region proposals [9], contour de + +![](images/701b8a4f46bca2700632c90ba59dde60d91d50aef0dd0b1371a2f33e88a42a34.jpg) +Figure 2. Leopart training pipeline. We start from a DINO initialization. We feed different crops to the student and teacher network to produce patch-level cluster predictions and optimal cluster assignments targets. This requires an alignment step of cluster targets and assignments. We further focus clustering on foreground patches by leveraging the ViT's attention map. + +tectors [30, 57], saliency [49] or object masks [28]. For instance, the current state-of-the-art for unsupervised semantic segmentation, MaskContrast [49], uses a pretrained saliency estimator to mine positive and negative pixels for contrastive learning. + +Concurrent to our work, [34] proposes an intra-image clustering step of pixel embeddings before applying a contrastive loss on the identified pixel groups to segment images. However, as they are reliant on combining the former with an image-level loss, it is not well-suited for more generic images with multiple objects where image-level and pixel-level semantics do not match. In contrast, our method uses a single clustering objective that is generalized for the dense setting, but that also works on object-centric images. Furthermore, by leveraging ViT's natural ability to direct its attention to objects, we do not require any external saliency generator like [49]. + +There are also works that have explored unsupervised object parts segmentation [10, 29], with the explicit goal to determine parts given object masks. However, our goal is different as we use part representations as an intermediary for semantic segmentation on classic, object-level settings. + +Superficially similar to our work is also another concurrent work [46], which tackles object detection by using the similarity between DINO's frozen last layer self-attention patch keys as a metric for merging image patches to objects. In contrast, we use DINO's spatial tokens and propose to fine-tune them for semantic segmentation. + +# 3. Method + +Our goal is to learn an embedding space that groups image patches containing the same part of an object. + +This is motivated by the hypothesis that object part representations are more general than object representations, as parts can be recombined in multiple ways to different objects. As an example, a wheel representation can be com- + +bined to a car representation but also a bus representation. Therefore, object part representations should transfer better across datasets. For that, we aim to design a pretext task that allows for intra-image category learning on an image-patch-level. Thus, a clustering pretext task is a natural choice. As shown in Figure 2, we retrieve patch-level optimal cluster assignments from a teacher network and predict them from the student network. The choice of a clustering pretext task is further supported by empirical evidence showing that clustering pretext outperforms contrastive pretext for dense prediction tasks [20,34]. Instead of pretraining models from scratch which requires substantial GPU budgets, we use our loss to fine-tune pretrained neural networks. Further, this circumvents known cluster stability issues and clusters capturing low-level image features when applied to a patch-level as reported in [48]. + +# 3.1. Fine-tuning loss for spatial tokens + +Image Encoder. Given an image $x \in \mathbb{R}^{3 \times H \times W}$ , we flatten the image into $N = \left\lfloor \frac{H}{P} \right\rfloor \cdot \left\lfloor \frac{W}{P} \right\rfloor$ separate patches $x_{i}, i \in 1, \ldots, N$ of size $P \times P$ each. The vision encoder we use is a ViT [16], which at the maps the image patches $x_{i}$ to a vector of $N$ spatial tokens $f(x) = [f(x_{1}), \ldots, f(x_{N})]$ . + +Leopart fine-tuning loss. To train the ViT's spatial tokens, we first randomly crop the image $V$ -times into $v_{g}$ global views and $v_{l}$ local views. When sampling the views we compute their pairwise intersection in bounding box format and store it in a matrix $B$ . We denote the transformed version of the image as $x_{t_j}, j \in \{1, \dots, V\}$ . Then, we forward the spatial tokens through a MLP projection head $g$ with a L2-normalization bottleneck to get spatial features for each crop: $g(f(x_{t_j})) = Z_{t_j} \in \mathbb{R}^{D \times N}$ . To create prediction targets, we next find an optimal soft cluster assignment $Q_{t_j}$ of all spatial token's feature vector $Z_{t_j}$ to $K$ prototype vectors $[c_1, \ldots, c_K] = C \in \mathbb{R}^{D \times K}$ . For that, we follow the online optimization objective of SwAV [5] that works on the whole image batch $b$ . $Q$ is optimized such that the similarity between all feature vectors in the batch and the prototypes is maximized, while at the same time being regularized towards assigning equal probability mass to each prototype vector. This can be cast to an optimal transport problem and is solved efficiently with the Sinkhorn-Knopp algorithm [14]. Instead of optimizing over $|b|$ feature vectors, we instead optimize over $N \cdot |b|$ spatial feature vectors as we have $N$ spatial tokens for each image. As our batchesizes are small, we utilize a small queue that keeps the past 8192 features, as is done in SwAV. + +With the optimal cluster assignment of all image crops' spatial tokens $Q_{t_k} \in \mathbb{R}^{N \times K}$ , we formulate a swapped prediction task: + +$$ +L \left(x _ {t _ {1}}, \dots , x _ {t _ {V}}\right) = \sum_ {j = 0} ^ {v _ {g}} \sum_ {i = 0} ^ {V} \mathbb {1} _ {k \neq j} l \left(x _ {t _ {i}}, x _ {t _ {j}}\right) \tag {1} +$$ + +Here, $l$ is the 2D cross entropy between the softmax and aligned cluster assignment predictions and the aligned optimal cluster assignments: + +$$ +l \left(x _ {t _ {i}}, x _ {t _ {j}}\right) = H \left[ \left(s _ {\tau} \left(\alpha_ {B _ {j, i}} \left(g (\Phi \left(x _ {t _ {i}}\right)\right) ^ {T} C\right), \alpha_ {B _ {i j}} \left(Q _ {t _ {j}}\right) \right], \right. \tag {2} +$$ + +where $H$ is cross-entropy and $s_{\tau}$ a softmax scaled by temperature $\tau$ . We use $L$ to jointly minimize the prototypes $C$ as well as the neural networks $f$ and $g$ . $C$ is further L2-normalized after each gradient step such that $Z^T C$ directly computes the cosine similarity between spatial features and prototypes. + +Since global crops capture the majority of an image, we solely use these to compute $Q_{t_j}$ , as the spatial tokens can attend to global scene information such that the overall prediction target quality improves. Further, using local crops to produce cluster assignment predictions effectively enables, as local crops just cover parts of images and thus also parts of objects, object parts to object category reasoning, an important ability for scene understanding. + +Alignment. In Equation 2 we introduce the alignment operator $\alpha_{B_{ij}}(\cdot)$ . This is necessary, because $x_{t_j}$ and $x_{t_i}$ cover different parts of the input image and thus $Q_{t_j}$ and the cluster assignment prediction $Z_{t_i}^T C$ correspond to different image areas. To tackle this, $\alpha(\cdot)$ restores the spatial dimensions $\left\lfloor \frac{H}{P} \right\rfloor \times \left\lfloor \frac{W}{P} \right\rfloor$ and aligns the tensor using the crop intersection bounding boxes $B_{ji}$ and $B_{ij}$ respectively. In our experiments we use RoI-Align [27] as operator, producing features with a fixed and compatible output size. + +Foreground-focused clustering. To focus the clustering on the foreground tokens, we further leverage the ViT's CLS token attention maps $A_{i} \in [0,1]^{N}$ of each of its attention heads. To create a foreground clustering mask that can be used during training, we first average the attention heads to one map and apply a Gaussian filter for smoothing. We then obtain a binary mask $A_{b}$ by thresholding the map to keep 60% of the mass following [6]. We use $\alpha_{B_{ji}}$ to align the global crop's attention to the intersection with crop $j$ . The resulting mask is then applied as 0-1 weighting to the 2D cross entropy loss, $l \odot A_{b}$ . Note that we extract the attention maps and spatial tokens with the same forward pass, thus not impacting training speed. + +# 3.2. Fully unsupervised semantic segmentation + +In this section we describe our method that enables us to do fully unsupervised semantic segmentation. All of them work directly in the learned spatial token embedding space and are based on simple K-means clustering. + +# 3.2.1 Cluster-based Foreground Extraction (CBFE) + +Under the hypothesis that clusters in our learned embedding space correspond to object parts, we should be able to ex + +tract foreground objects by assigning each cluster id to foreground object (fg) or background (bg): $\Theta : \{1, \ldots, K\} \to \{\mathrm{fg}, \mathrm{bg}\}$ . Thus, at evaluation time, we construct $\Theta$ without supervision, by using ViT's merged attention maps $A_{b}$ as a noisy foreground hint. Similar to how we process the attention maps to focus our clustering pretext on foreground, we average the attention heads, apply Gaussian filtering with a 7x7 kernel size and keep $60\%$ of the mass to obtain a binary mask. Using train data, we rank all clusters by pixel-wise precision with $A_{b}$ and find a good threshold $c$ for classifying a cluster as foreground. This gives us $\Theta$ that we apply to the patch-level clustering to get a foreground mask. + +# 3.2.2 Overclustering with community detection (CD) + +As we will see from Table 1, the segmentation results improve substantially with higher clustering granularities. However, this is mainly because overclustering draws on label information to group clusters to ground-truth objects and in the limit of providing one cluster for each pixel, it would be equivalent to providing full supervision signals. Here, we propose a novel overclustering method that requires no supervision at all. + +Assuming that our clusters correspond to object parts, we interpret objects as a set of object parts that co-occur together. Thus, local co-occurrence of clusters in an image should provide a hint about such objects. Using co-occurrence statistics to categorize objects has been proposed before in [19, 42]. However, we are the first to work with object parts and no labels and employ a novel network science method to discover objects. To group the clusters, we construct an undirected and weighted network $G = (V, E, w)$ , with $v_{i}, i \in \{1, \dots, K\}$ corresponding to each cluster. Then, we calculate the conditional co-occurrence probability $P(v_{j} | v_{i})$ for clusters $i$ and $j$ over all images $D$ . We use a localized co-occurrence variant that regards the 8-neighborhood up to a pixel distance $d$ . With the co-occurrence probabilities at hand, we define $w(e_{i,j}) = \min(P(v_{j} | v_{i}), P(v_{j} | v_{i}))$ . This asymmetric edge weight definition is motivated by the fact that parts need not be mutually predictive: For instance, a car windshield might co-occur significantly with sky but presence of a sky is not predictive for a car windshield. + +To find communities in $G$ , we use the common Infomap algorithm [45] as it works with weighted graphs and scales linearly with $|E|$ . It works by leveraging an information-theoretic definition of network communities: Random walks sample information flow in networks and inform the construction a map $\Theta_K$ from nodes to $M$ communities minimizing the expected description length of a random walk. With the discrete many-to-one mapping $\Theta_K: V \to \{1, \ldots, M\}$ obtained from Infomap and computed on train data, we merge the clusters of the validation data to + +the desired number of ground-truth classes and do Hungarian matching [33]. Note that Hungarian matching does not extract any meaningful label information; it merely makes the evaluation metric permutation-invariant [32]. + +# 4. Experiments + +In this section, we evaluate the image patch representations learned by Leopart. We first ablate design decisions of our method to find an optimal configuration. To evaluate whether some datasets are more information-rich for object parts learning than others, we also ablate training on different datasets. We further test the performance of our dense representations under a transfer learning setup for semantic segmentation. Furthermore, we show that Leopart can also be used for fully unsupervised segmentation requiring no label information at all for evaluation. + +# 4.1. Setup + +Evaluation protocols. For all experiments, we discard the projection head used during training. Instead we directly evaluate the ViT's spatial tokens. We use two main techniques for evaluation: linear classifier and overclustering. For linear classifier (LC), we fine-tune a 1x1 convolutional layer on top of the frozen spatial token or the preGAP layer4 features, following [49]. For overclustering, we run K-Means on all spatial tokens of a given dataset. We then group cluster to ground-truth classes by greedily matching by pixel-wise precision and run Hungarian matching [33] on the merged cluster maps to make our evaluation metric permutation-invariant following [32]. We always report overclustering results averaged over five different seeds. Overclustering is of special interest as it works directly in the learned embedding space and therefore requires less supervision than training a linear classifier. For completeness we also report results fine-tuning a deeper fullyconvolutional net (FCN) following [51]. Generally, we follow the fine-tuning procedures of prior works [49, 51, 57]. We report results in mean Intersection over Union (mIoU) unless specified otherwise. + +Model training. We train a ViT-Small with patch size 16 and start training from DINO weights [6]. All models were trained for 50 epochs using batches of size 32 on 2 GPUs. Further training details are provided in the Appendix. + +Datasets. We train our model on ImageNet-100, comprising 100 randomly sampled ImageNet classes [47], COCO [35] and Pascal VOC (PVOC) [18]. When finetuning on COCO-Stuff and COCO-Thing, we use a $10\%$ split of the training sets. Evaluation results are computed on the full COCO validation data for COCO-Stuff and COCO-Thing and PVOC12 val. This setup up makes sure that our representations are assessed under varying object definitions (e.g. stuff vs. thing) and granularities. Further details are provided in the Appendix. + +
maskLCNum. clusters
100300500
all67.437.944.647.8
bg64.728.139.041.4
fg67.838.247.250.7
+ +(a) Focusing clustering on foreground (fg) helps. + +
cropsLCNum. clusters
100300500
[2]66.133.042.545.0
[2,2]67.737.845.449.3
[2,4]67.838.247.250.7
+ +(b) Local crops boost performance. + +
tchrLCNum. clusters
100300500
X67.634.644.347.9
✓67.838.247.250.7
+ +(c) Using an EMA teacher helps. + +
protosLCNum. clusters
100300500
10067.736.845.449.2
30067.838.247.250.7
50067.435.844.849.1
+ +(d) 300 prototypes work well. + +Table 1. Ablations of different design decisions for Leopart. + +
DatasetsizeLCK=500K=300K=100
IN-100126k67.850.747.238.2
COCO118k69.153.049.944.3
PASCAL10k64.550.747.838.2
+ +Table 2. Training data study for Leopard. We use the best performing model config from Table 1 and train on different datasets. + +# 4.2. Fine-Tuning Loss Ablations + +In this section, we ablate the most important design decisions and hyperparameters of our fine-tuning loss as well as the aptness of different datasets for learning object parts. We evaluate on PVOC val and report three different over-clustering granularities next to LC results. + +Model Ablation. In Table 1 we report the model ablation results. As described in Section 3, we propose to leverage attention maps to guide our clustering algorithm. Note that the attention maps are just a noisy approximation of foreground objects. Thus, it only focuses spatial token clustering on foreground but does not neglect objects in the background. We find that foreground clustering gives substantial performance gains over our two ablated versions: clustering of all spatial tokens (up to $3\%$ ) and clustering mostly background tokens (up to $10\%$ ), as shown in Table 1a. + +In Table 1b we ablate the multi-crop augmentation strategy. More specifically, we compare using four local crops against using only two or no local crops. The usage of local crops (last vs. second to last row) gives a much larger performance gain than using just more local crops (second to last vs. first row). This shows that predicting cluster assignments from constrained local image information is an important aspect for learning expressive dense representations. Interestingly, the overclustering results are effected more by this ablation, showing that local crops are important for learning a semantically-structured embedding space. + +We also ablate the number of prototypes used for Sinkhorn-Knopp clustering in Table 1d. We find that the best performance is achieved with a moderate overcluster + +
MethodTrainPVOC12COCO-ThingsCOCO-Stuff
LCK=500LCK=500LCK=500
Sup. ViTIN + IN2168.155.165.250.949.035.1
Sup. ResNetIN53.836.557.844.244.430.8
instance-level:
MoCo-v2 [25]IN45.0†39.147.536.232.628.3
DINO [6]IN50.617.450.623.547.732.1
SwAV [5]IN50.7†35.756.737.346.033.1
pixel/patch-level:
IIC [32]PVOC28.0†-----
MaskContrast [49]IN+PVOC49.245.447.537.032.025.6
DenseCL [51]IN49.043.653.041.040.930.3
LeopardIN68.050.562.549.251.243.8
LeopartIN+CC69.353.367.655.953.543.6
+ +ing of 300 prototypes. Note however, that the number of prototypes we use for training is not equivalent to the number of clusters used for evaluation, which we denote for instance by $\mathrm{K} = 500$ . Lastly, even though we fine-tune a pretrained model, we find that an EMA teacher still helps with learning more expressive representations as can be seen in Table 1c. + +Training Data. In Table 2 we report results under varying training data: ImageNet-100, COCO and PVOC. ImageNet-100 usually features object-centric images with few objects. In comparison, COCO and PVOC contain images with more complex scenes. For comparability, we adapt the number of epochs for PVOC to 500 such that all models are trained for the same number of iterations. We find that our method's performance improves by up to $6\%$ when trained on COCO instead of ImageNet-100. This shows the potential of our dense clustering loss when applied to less object-centric images and is in stark contrast to other methods reporting that their results get worse when training on COCO instead of ImageNet [34, 51, 57]. Finally, we see the worse results on PVOC as a confirmation of the fact that even for fine-tuning, larger data sets perform better for ViTs. + +# 4.3. Transfer learning + +Next, we study how well our dense representations, once learned, generalize to other datasets. We train our model on ImageNet-100 or COCO and report LC and overclustering results on PVOC12, COCO-Things and COCO-Stuff. As shown in Table 3, we outperform self-supervised prior works by large margins on all three datasets even though some use further datasets and supervision. On PVOC12 we surpass the state-of-the-art by more than $17\%$ for lin + +Table 3. Transfer learning for semantic segmentation results. Best results are in bold and second best are underlined. 'IN', 'IN21', 'CC' and 'PVOC' indicate training on ImageNet, ImageNet21k, CoCo and Pascal trainaug respectively. $\dagger$ indicates result taken from [49]. + +
MethodmIoU
Sup. ResNet18.5
Sup. ViT21.1
DINO [6]4.6
SwAV [25]13.7
MoCo-v2 [25]18.5
MaskContrast [49]35.0†
Leopart (CBFE+CD)41.7
+ +Table 4. Unsupervised semantic segmentation results. We outperform other state-of-the-art methods by a large margin. $\dagger$ indicates result taken from [49]. + +
mIoU
K=15048.8
DINO4.6
+ Leopart18.9 (+14.3%)
+ CBFE36.6 (+17.7%)
+ CD41.7 (+5.1%)
+ +Table 5. Component contributions. We show the gains that each individual component brings for PVOC segmentation and $\mathrm{K} = {21}$ . + +
MethodTrainPVOC12 FCN
SegSort [30]CC+PVOC36.2†
Hier. Grouping [56]CC+PVOC48.8†
DINO [6]IN60.6
Hier. Grouping [56]IN64.7†
MoCo-v2 [25]CC64.5†
MoCo-v2 [25]IN67.5†
DenseCL [51]CC67.5†
DenseCL [51]IN69.4†
LeopardIN70.1
LeopardIN+CC71.4
Leopard (ViT-B/8)IN+CC76.3
+ +Table 6. FCN transfer learning results. We follow the same notation as in Table 3. Note that Hierarchical Grouping and Seg-sort fine-tune a larger ASPP decoder. $\dagger$ indicates result taken from [51, 56] + +ear evaluation and by more than $5\%$ for overclustering. On COCO-Things and COCO-Stuff we improve linear classifier by $>5\%$ and $>3\%$ and overclustering by $>8\%$ and $>10\%$ respectively. Note that these gains are not due to the DINO initialisation nor due to ViTs per-se as the starting DINO model performs on par with other instance-level self-supervised methods that use ResNets like SwAV. In fact, DINO's embedding space exhibits inferior semantic structure in comparison to MoCo-v2 and SwAV as can be seen from the overclustering results on PVOC12 $(-18\%)$ and COCO-Things $(-12\%)$ . Our method is also on par with the performance of a supervised ViT even though it was trained on a $>10x$ times larger full ImageNet (IN-21k) dataset [43]. When fine-tuning on COCO instead of IN-100, we see further improvements on all datasets. The results confirm that + +![](images/27fb909db4727a2a94549ffb453d67512049ce08b797b18fc35ac35966fecd20.jpg) +(a) DINO + +![](images/007e2701f62c7df7e1b85bd9153370f866049564da9daaef1863f9cfc2e732d2.jpg) +(b) + Leopart +Figure 3. Qualitative Segmentations by DINO and our gradual improvements. We cluster the spatial tokens and visualize the resulting clusters obtained after each step of our method. + +![](images/a251540e79cc15af3680b33685f738237854bf13deab725a9345e4b3db2f484b.jpg) +(c) + CBFE + +![](images/75c36b556bd373b114dfce0a46246e605cf93f8d7d5e3a16e44025473c7e4c38.jpg) +(d) + CD + +it is desirable to learn object parts representations, as they work well under different object definitions, as evidenced by strong performances across datasets. + +In Table 6, we evaluate Leopart by fine-tuning a full FCN on top of frozen features. Again, we outperform all prior works, including DenseCL, the current state-of-the-art. Interestingly, while DenseCL shows a performance gain of more than $20\%$ when fine-tuning a FCN instead of a linear layer, our performance gain from fine-tuning is relatively low at around $2\%$ . We hypothesize that this behaviour is because our learned embedding space is already close to maximally informative for semantic segmentation under linear transformations. In contrast, DenseCL's embedding space alone is less informative in itself and requires a more powerful non-linear transformation. We push state-of-the-art even further by fine-tuning a larger ViT-Base with patch size 8 (ViT-B/8) improving FCN performance by around $5\%$ . We report further details and experiments in the Appendix. + +# 4.4. Fully unsupervised semantic segmentation + +Encouraged by our strong $\mathrm{K} = 500$ overclustering results in Table 3, we next evaluate fully unsupervised semantic segmentation. This relies only on the learned embedding space's structure and refrains from using any test-time label information, i.e. the number of final clusters needs to be equivalent to the ground-truth. To that extent, we start with a simple K-means clustering of the spatial tokens to get cluster assignments for each token. As prior works, we base our evaluation on PVOC12 val and train self-supervised on an arbitrary dataset [49], in this case COCO. In Table 4 we compare our method to prior state-of-the-art. We outperform our closest competitor, MaskContrast, by $>4\%$ . While like MaskConstraint, we cluster only foreground tokens, we use our embedding space clustering instead of a pretrained unsupervised saliency estimator to do cluster-based foreground extraction (CBFE). Also, instead of averaging the feature representations per image, we use our novel unsupervised overclustering method with community detection (CD), allowing us to detect multiple object categories in one image. + +
MethodJacc. (%)B-F1 [13] (%)
DINO attention [6]48.736.5
Unsup. saliency [49]55.940.8
Leopart IN CBFE58.642.1
Leopart CC CBFE59.640.7
+ +Table 7. Foreground extraction results on PVOC val. Our method improves over DINO attentions with respect to Jaccard distance and Boundary F1 score and shows performance on par with a dedicated unsupervised saliency estimator. + +![](images/7d6fc17b34b83b007a4f7672ccf140e253522fece1fd6e2262454dce5b68b012.jpg) +(a) Attention Masks +Figure 4. DINO Attention masks vs. Leopart Cluster masks. + +![](images/2906406b0607966afd69f6eda678994be1a91172d98c521db30c036ef51d42a3.jpg) +(b) Cluster masks + +# 4.4.1 Performance gain study + +In Figure 3, we show the gradual visual improvement of the segmentations. By using Leopart we substantially improve the DINO baseline by more than $14\%$ , as shown quantitatively in Table 5. This is also apparent when comparing Figure 3a to Figure 3b. The DINO segmentations show no correspondence to object categories, whereas the segmentations obtained by Leopart assign the same colors to the bus in the first and third image of the top row as an example. However, our segmentations do not correspond well with PVOC's object definitions, as we oversegment background. To further improve this, we extract foreground resulting in the segmentation maps shown in Figure 3c. The segmentation focuses on the foreground and object categories start to emerge more visibly. However, some objects are still oversegmented such as busses and cats. Thus, we run our proposed community detection algorithm to do fully unsupervised overclustering, resulting in the segmentations shown in Figure 3d. + +CBFE. For foreground extraction, we follow the method proposed in Section 3.2.1. As shown in Table 7, our foreground masks obtained through CBFE outperform DINO's + +![](images/a11ae367f904c258f0768279f9bfa03c28559696a4feb2836d5551dfe9a73b26.jpg) +Figure 5. Communities found in our cluster co-occurrence network constructed through self-supervision. Each node corresponds to a cluster in our learnt embedding space. The nodes are colored by community membership. + +attention maps by more than $9\%$ . This is remarkable as we can only improve the attention map if the foreground clusters also segment the foreground correctly where the noisy foreground hint from DINO's attention is wrong. In Figure 4, we show mask visualizations to provide a qualitative idea of this phenomenon. While the attention masks only mark the most discriminative regions they fail to capture the foreground object's shape (Fig. 4(a)). Our cluster masks, however, alleviate this providing a crisp foreground object segmentation (Fig. 4(b)). With the foreground masks extracted, we can specify K-Means to run only on foreground spatial tokens. This further improves our fully unsupervised segmentation performance by $>17\%$ , as shown in Table 5. + +CD. We have seen that overclustering yields benefits in terms of performance but requires additional supervision for merging clusters during evaluation. To reap the benefits of this process whilst staying unsupervised, we construct a network based on cluster co-occurrences and run community detection (CD) following the method proposed in Section 3.2.2. We find that CD can further improve our performance by $>5\%$ and brings our fully unsupervised semantic segmentation results closer to the upper bound of supervised overclustering at test-time with $K = 150$ , as shown in Table 5. + +Finally, in Figure 5 we show a visualization of the constructed network, the discovered communities as well as + +some exemplary parts clusters. For instance, Leopart discovers bicycle wheels and car wheels separately. This demonstrates that we can learn high-level semantic clusters that do not latch on low-level information such as shape. Furthermore, we can observe that clusters that are semantically similar, such as human hair and human faces, are also part of the same community and close in the resulting network. Also, a gradual semantic transition within connected components can be observed as shown for dog snout and cat ears being part of different communities that are interconnected. + +# 5. Discussion + +Limitations. Since we do not learn on a pixel but on a patch level, our segmentation maps are limited in their resolution and detection capabilities. Thus, our method will fail when fine-grained pixel-level segmentation is required or very small objects covering less than an image patch are supposed to be segmented. Further, our unsupervised overclustering method does a hard assignment of clusters to communities. This has the limitation that object parts which occur in several objects are assigned to the wrong object category when they appear in a specific context. We show an example of this phenomenon in the Appendix, but leave a solution to this to future work. + +Potential negative societal impact. Self-supervised semantic segmentation can scale to large datasets with little to no human labelling effort and extract information from it. However, as human input is kept to a minimum, rigorous monitoring of the segmentation results is mandatory, as objects might not be segmented in a way that we are used to or problematic biases in the data might become apparent. Lack of monitoring, could have potential negative impacts in areas such as autonomous driving and virtual reality. + +Conclusion. In this paper, we propose a dense clustering pretext task for the spatial tokens of a ViT learning a semantically-rich embedding space in contrast to other self-supervised ViTs. We motivate our pretext task by observing that object definitions are brittle and object parts learning promises a principled alternative. Our experiments show that this formulation is favorable as we improve state-of-the-art on PVOC, COCO-Stuff and COCO-Thing semantic segmentation benchmarks featuring different object definitions and granularities. Our semantically-rich embedding space can also be directly used for fully unsupervised segmentation, showing that objects can be defined as co-occurring object parts. + +# Acknowledgements + +A.Z. is thankful for using compute while interning at Pina Earth. Y.M.A is thankful for MLRA funding from AWS. + +# References + +[1] Yuki M Asano, Christian Rupprecht, and Andrea Vedaldi. Self-labelling via simultaneous clustering and representation learning. In ICLR, 2020. 2 +[2] Piotr Bojanowski and Armand Joulin. Unsupervised learning by predicting noise, 2017. 2 +[3] Holger Caesar, Jasper Uijlings, and Vittorio Ferrari. Cocostuff: Thing and stuff classes in context. 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It is often used as a precursor step to obtain useful initial network weights which contribute to faster convergence and superior performance of downstream tasks. While self-supervision allows one to reduce the domain gap between supervised and unsupervised learning without the usage of labels, the self-supervised objective still requires a strong inductive bias to downstream tasks for effective transfer learning. In this work, we present our material and texture based self-supervision method named MATTER (MATerial and Texture Representation Learning), which is inspired by classical material and texture methods. Material and texture can effectively describe any surface, including its tactile properties, color, and specularity. By extension, effective representation of material and texture can describe other semantic classes strongly associated with said material and texture. MATTER leverages multi-temporal, spatially aligned remote sensing imagery over unchanged regions to learn invariance to illumination and viewing angle as a mechanism to achieve consistency of material and texture representation. We show that our self-supervision pretraining method allows for up to $24.22\%$ and $6.33\%$ performance increase in unsupervised and fine-tuned setups, and up to $76\%$ faster convergence on change detection, land cover classification, and semantic segmentation tasks. Code and dataset: https://github.com/periakiva/MATTER. + +# 1. Introduction + +Automated understanding of remote sensing imagery has been a long standing goal of the computer vision community. Its broad applicability has driven research and development in construction phase detection [23], infrastructure mapping [36, 55, 71, 100], land use monitoring [41], post natural disaster damage assessment [42, 89, 97], urban 3D reconstruction [39, 57], population migration prediction [19], and climate change tracking [79]. Most of those methods require some degree of annotation effort, which is often expensive and/or time consuming. Satellite imagery + +is increasingly plentiful and accessible, with hundreds of satellites collecting images on a daily basis [1, 35, 81, 94]. However, annotating land cover, change, or similar labels often requires domain knowledge and/or extreme attention to detail, as labels in remote sensing imagery cover more numerous and smaller objects seen from unfamiliar view points. As a result, annotators require more domain expertise compared to standard benchmark datasets such as Pascal VOC [38], COCO [61], or similar. + +Recent work in self-supervised learning aims to alleviate the requirement of labeled data by either detecting self-applied transformations, such as color or rotation change, or implicit metadata information, such as temporal order or geographical location. Those objectives are often achieved using contrastive learning methods [17, 45, 53], in which the distance between feature representations of original and transformed images is minimized. More advanced contrastive methods use triplet loss [10, 84] or quadruplet loss [18] which also include negative examples with which the distance between feature representations is maximized. Despite filling a significant need in the remote sensing domain, these approaches have been yet to be thoroughly investigated. Even methods that utilize contrastive approaches, such as SeCo [68] and the work of Ayush et al. [4], which learn seasonal change invariance or geographic-location consistency, still show weaker transfer-ability to downstream task learning, as demonstrated by inferior performance and convergence speeds shown in Tab. 1, 3. + +Instead, we hypothesize that material and texture have a strong inductive bias to most downstream remote sensing tasks, with pre-training of surface representation to improve performance and convergence speeds (measured in epochs) for those tasks. Consider the task of change detection in remote sensing imagery: when semantic class changes (i.e., soil to building, or forest to soil), change can also be expected in materials and texture, demonstrating the high correlation between material and texture and the change detection task. We show the effectiveness of our self-supervised pre-trained features in both raw and fine-tuned forms, obtaining state-of-the-art (SOTA) performance in change detection (unsupervised and fine-tuned), land cover segmentation (fine-tuned), and land cover classification (fine-tuned). + +Here, we propose a novel self-supervised material and texture representation learning method which is inspired by classical and modern texton filter banks [58, 87, 113]. Textons [52, 58, 66] refer to the description of micro-structures in images often used to describe material and texture consistency [25, 27, 58, 101, 108]. Note that literature has only loosely defined what material, structures, texture, and surface refer to. Here, we define material as any single or combination of elements (soil, concrete, vegetation, etc.) corresponding to some multi-spectral signature, structures as gradients in intensity, texture as spatial distribution of structures, and surface as the combination of material and texture. Note that here we define the physical surface, rather than the geometric or algebraic surface, as described by its material and textural properties. By extension, we aim to jointly describe combinations of materials and textures in a single objective. For example, within a given image patch, a mixture of grass and concrete should be represented differently than patches with grass or concrete separately. In this example, the grass-concrete mixture may be associated to both grass and concrete material classes. To that end, we learn surface representations that describe the affinity, represented as residuals [48], to all pre-defined surface classes, represented as clusters. We achieve this by contrastively learning the similarity between the residuals of multi-temporal, spatially aligned imagery of unchanged regions to obtain consistent material and texture representations, regardless of illumination or viewing angle. This framework acts as a pre-training stage for downstream remote sensing tasks. + +Overall, our contributions are: 1) We present a novel material and texture based approach for self-supervised pretraining to generate features with high inductive bias for downstream remote sensing tasks. We propose a texture refinement network to amplify low level features and adapt residual cluster learning to characterize mixed materials and texture patches in a self-supervised, contrastive learning framework. 2) We achieve SOTA performance on unsupervised and supervised change detection, semantic segmentation, and land cover classification using our pre-trained network. 3) We provide our curated multi-temporal, spatially aligned, and atmospherically corrected remote sensing imagery dataset, collected over unchanged regions used for self-supervised learning. + +# 2. Related Work + +# 2.1. Downstream Remote Sensing Tasks + +The main downstream tasks we investigate in this work are change detection, land cover segmentation, and land cover classification. The problem of change detection in satellite imagery has been thoroughly investigated over time [12, 13, 15, 24, 49, 77, 78, 83]. Notable examples include Daudt et al. [29], which predicts change by minimizing + +feature differences at every layer of the network from a given image pair input, and Chen et al. [13], which utilizes a spatial-temporal attention mechanism to detect anomalies in sequences of images. Land cover segmentation and classification have also seen a surge in interest, with growing repositories of annotated datasets [3, 32, 47, 91, 96] and methods [2,5,44,82,93,96]. H20-Net [2] synthesizes multispectral bands and uses self-sampled points to generate pseudo-ground truth for flood and permanent water segmentation. VecRoad [93] sets the problem of road segmentation as iterative graph exploration. Multi3Net [82] learns fusion of multi-temporal, multi-spectral features from high resolution imagery to jointly predict pixels of floods and building. + +# 2.2. Self-Supervision + +In order to effectively utilize large amounts of unlabeled data, recent methods have focused on obtaining good feature representations without explicit annotation efforts. This is done by deriving information from the data itself or learning sub-tasks within data instances without changing the overall objective. The first is often used when high confidence labels can be obtained and trained on, similar to [2, 4], where the method infers weak supervision about input images through provided meta-data or classical methods. The second, and more common approach, leverages metric learning objectives to learn generalizable features for the same data instance or class. Recent methods involve learning invariance to color and geometric transformations [9, 50, 70], temporal ordering [6, 40], sub-patch relative location prediction [34], frame interpolation [73], colorization [33, 56, 110], patch and background filling [102], and point cloud reconstruction [105]. + +More relevant to the remote sensing domain, SeCo [68] has taken a step toward utilizing the potential in the abundance of satellite imagery by contrastively learning seasonal invariance as a pre-text self-supervision task. It then fine-tunes the pre-trained network on downstream tasks such as change detection and land cover classification. Ayush et al. [4] also proposes a self-supervised approach enforcing geographical-location consistency as a pre-training objective used for downstream tasks such as land-cover segmentation and classification. While both methods show improved results on benchmark datasets when compared to random weights initialization, we show that their inductive bias is still significantly weaker than that of our material and texture consistency based pre-trained weights, which learn an illumination and viewing angle invariance to achieve consistency of material and texture representation. + +# 2.3. Material and Texture Identification + +Early material and texture recognition methods relied on hand crafted filter banks, whose combinatorial output are also referred to as textons [58], to encode statistical representations of image patches [7, 8, 26, 28, 58, 95, 114]. + +![](images/a3219b7a33e4373a1722aef2f5d12781b82bd25cd3ec8464708b03cb513f02c5.jpg) +Figure 1. (Left) MATTER: anchor, positive, and negative images $x_{a}$ , $x_{p}$ , and $x_{n}$ are densely windowed to $P$ crops which are fed to encoder $E$ , and correspond to output features $z_{a}$ , $z_{p}$ , and $z_{n}$ . Crops are also fed to the Texture Refinement Network (shown in blue) which amplifies activation of low-level features to increase their impact in deeper layers. The encoder's output is then fed to the Surface Residual Encoder to generate patch-wise cumulative residuals, which represents affinity between input data and all learned clusters. A residual vector between feature output $z_{a}$ and cluster $v$ is denoted as $r_{a,v}$ . Output learned residuals, cluster weights, and number of clusters are noted as $r$ , $\theta$ , and $\Upsilon$ respectively. (Right) Simplified example of the contrastive objective with $\Upsilon = 3$ . Residuals from learned clusters are extracted and averaged for all crops as representations of correlation between inputs and all clusters. Best viewed in zoom and color. + +Later works investigated the use of clustering and interpatch statistics as replacement for pre-defined filter banks [98, 99], at the cost of defining the feature space it operates in. Most notable feature spaces include color intensity [14], texture homogeneity [43, 58, 69], multi-resolution features [74, 88], and feature curvature [63, 86]. More recent, deep learning approaches have translated the problem of texture representation to focus on explicit identification of materials through texture encoding [20, 109, 112], differential angular imaging [106], 3D surface variation estimation [31], auxiliary tactile property [85], and radiometric properties estimation such as the bidirectional reflectance distribution function (BRDF) [11, 62, 103] and the bidirectional texture function (BTF) [104]. Those methods seek to learn low-level features that are key to material classification and segmentation. Some methods choose to add skip connections [60, 107, 115] to supply low-level features in deep layers, and others choose explicit concatenation of texture related information [59, 85]. Many of these elements are meant to reduce the receptive field or increase impact of low-level features of the network while keeping it sufficiently deep. FV-CNN [22] aims to generate texture descriptions of densely sampled windows. Since the features describe regions removed from global spatial information, it explicitly constrains the receptive field of the network to the size of the window. DeepTEN [109] learns residual representations of material images in an end-to-end pipeline using material labels. Our approach combines elements from FV-CNN and DeepTEN in two ways. First, we densely sample windows and refine low level features as receptive field constraints. Then, we contrastively learn implicit surface residual representations without the usage of material labels or auxiliary information. To our knowledge, we are the first to employ self-supervised material and texture based objectives for pre-training steps. + +# 3. Methodology + +The goal of MATerial and TTexture Representation Learning (MATTER) is to learn a feature extractor that generates illumination and viewing angle invariant material and texture representations from given multi-temporal satellite imagery sampled over unchanged regions. To this end, to train our model, we utilize our self-collected dataset described in Sec. 4.1, which samples multi-temporal imagery of rural and remote regions, in which little to no change is assumed between every consecutive pair of sampled images. See Fig. 2 for an overview of our approach. + +Given an anchor reference image $x_{a} \in \mathcal{R}^{B \times H \times W}$ sampled over an unchanged region, we obtain a positive, temporally succeeding image $x_{p} \in \mathcal{R}^{B \times H \times W}$ over the same region, and a negative image $x_{n} \in \mathcal{R}^{B \times H \times W}$ sampled over a different region. $B, H,$ and $W$ correspond to number of channel bands, height, and width of input images. We tile all images into $P$ equally sized, corresponding patches of size $h \times w$ , with spatially aligned reference and positive patches, $c_{a}$ and $c_{p}$ , and negative patches, $c_{n}$ , randomly sampled from regions other than the reference region. The usage of densely sampled crops aims to restrict the receptive field by removing features from the global spatial context, and to prevent the model from learning higher level features ineffective in describing surfaces. We study the effects of receptive field variation in Sec. 5.1. + +To learn material and texture centric features, we present the Texture Refinement Network (TeRN) (Sec. 3.1), and patch-wise Surface Residual Encoder (Sec. 3.2). TeRN aims to amplify the activation of lower level features essential for texture representation (as seen in Fig. 3), and Surface Residual Encoder is our patch-wise adaptation of Deep-TEN [109] to learn surface-based residual representations. We train our network to minimize the feature dis + +![](images/8e3d4a9c3857b8ca63feb408ce4a5776713567dde4ce3418fc7199e71b8c883d.jpg) +Figure 2. Texture Refinement Network (TeRN) assigns convolution weights based on the cosine similarity of the kernel's center pixel and its neighbors, divided by the standard deviation of that kernel. We then convolve features $z^{(1)}$ to refine low-level features essential for texture and material centric learning. The symbols $\circledast$ and $\odot$ correspond to convolution and element-wise multiplication operations. Best viewed in zoom. + +tance of positive patch pairs, $c_{a}$ and $c_{p}$ , and maximize the feature distance of negative patch pairs, $c_{a}$ and $c_{n}$ , where the features are the learned residual representations. For our learning objective, we use the Noise Contrastive Estimation loss [75]: + +$$ +\mathcal {L} _ {N C E} = - \mathbb {E} _ {C} \left[ \log \frac {\exp \left(f \left(c _ {a}\right) \cdot f \left(c _ {p}\right)\right)}{\sum_ {c _ {j} \in C} \exp \left(f \left(c _ {a}\right) \cdot f \left(c _ {j}\right)\right)} \right], \tag {1} +$$ + +where $f(c_{j})$ is the output features of input patch $c_{j}$ , and $C$ is the set of positive and negative patches. + +# 3.1. Texture Refinement Network + +Capturing texture details is difficult in low resolution images, and is especially challenging when considering satellite images that have low contrast. As a result, texture will be less visible and have less impact on the final extracted features. We address this challenge by using our Texture Refinement Network (TeRN) to refine lower level texture features to increase their impact in deeper layers. TeRN utilizes the recently introduced pixel adaptive convolution layer [90], in which the convolution kernel weights are a function of the features locally confined by the kernel. Here, our kernel considers the corresponding local pixels in the original image as follows: given kernel $k^{i,j}$ centered at location $(i,j)$ , we calculate the cosine similarity between pixel $x_{i,j}$ and all of its neighboring pixels $\mathcal{N}(i,j)$ . We note that while this can be achieved with any similarity metric, we observe that orientation based functions (such as cosine similarity) produce better results than magnitude based functions (such as Euclidean distance). The output + +![](images/def7ef83426fb7d9208e36f744e1133560f2582602c17bc6d037cc3a7585b5de.jpg) + +![](images/f78b04f749a9f2e6e98319fe08cfbd4ec691e7645e73625a0fd4f8eb8b5a9417.jpg) +Input Image + +![](images/354e3003ce36386dba5561ff9dda52a3aff9feb2437a9ffb366db1df55d1e4b1.jpg) + +![](images/3d16a5221ecc471c3bdec1f66d2c21ec41bf1f597d8600ba8114274aa196f7f4.jpg) +Raw Features + +![](images/c6d825674f8e5531df9c467ecc9656a199c902b9847208ac4c6f036066f07c5c.jpg) + +![](images/5ea604f2459eaba23329e46e32256dc294c4aea8dbf65bd201bca73bc2e7b734.jpg) +Refined Features +Figure 3. Qualitative results of our Texture Refinement Network (TeRN). It can be seen that similar textured pixels obtain similar feature activation intensity in the refined output. Notice how the building in the second row obtains similar activation throughout the concrete building pixel locations compared to the raw features output. Best viewed in zoom and color. + +matrix is then divided by the squared standard deviation of all pixels within $\mathcal{N}(i,j)$ , noted as $\sigma_{\mathcal{N}(i,j)}$ . + +$$ +k ^ {i, j} = - \frac {1}{\sigma_ {\mathcal {N} (i , j)} ^ {2}} \frac {x _ {i , j} \cdot x _ {p , q}}{\left| \left| x _ {i , j} \right| \right| _ {2} \cdot \left| \left| x _ {p , q} \right| \right| _ {2}}, \forall p, q \in \mathcal {N} (i, j). \tag {2} +$$ + +The output matrix of those operations describes both the similarity of the center pixel to its surroundings, and the intensity gradients within the kernel. As previously defined, texture is the spatial distribution of structures, which are represented as intensity gradients. Since we want to emphasize texture, we explicitly polarize the feature activation in regions with high variance or low similarity, with kernel weights decreasing with high variance and/or low cosine similarity. When convolved over our low level features, it highlights edges, and encourages representation consistency for pixels with similar material signatures, as seen in figure 3. The described operation constitutes a single kernel location of a single refinement layer. We define a single refinement layer, $K$ , when the operation is repeated for all image locations. We construct an $L$ -layer refinement network, where each layer is able to utilize different kernel sizes, dilations, and strides. Since the network has deterministically defined weights, it does not have learned parameters. A base TeRN kernel, and its integration in the overall network, are visually depicted in Fig. 2, and sample refined features in Fig. 3. + +# 3.2. Learning Consistency of Surface Residuals + +The task of residual encoding is tightly related to classical k-means clustering [64] and bag-of-words [51], in which some hard cluster assignment is learned based on the data instance proximity to cluster centers. Given the cluster centers, the residual is calculated as the distance of any data instance from its corresponding cluster center. In practice, we can use the residual to measure how similar a given data instance is to its assigned cluster, and all other clusters. Our + +method adapts the work presented in Deep-TEN [109] to learn patch-wise residual encodings without explicit handcrafted clustering through a differentiable pipeline. Traditionally, in Deep-TEN [109] and other classical and deep clustering methods [9,17,21,45,65], the objective is to cluster image-wise inputs to corresponding class-wise cluster centers. In contrast, as we employ a patch-wise approach. A given patch containing some material and texture may be associated with multiple clusters (i.e. if a patch captures multiple material elements), so it requires a soft representation depicting an affinity to all learned clusters, and not only to its closest cluster. + +Consequently, we learn residuals of small patches and enforce multi-temporal consistency between corresponding patch residuals, imposing similarity of cluster affinity. Given an output feature vector $z_{i}^{1 \times D}$ for some crop $c_{i}$ , and a set of $\Upsilon$ learned cluster centers $Q = \{q_{0}, q_{2}, \dots, q_{\Upsilon - 1}\}$ , each of shape $1 \times D$ , we can find the residual corresponding to the feature vector $z_{i}$ and learned cluster center $q_{v}$ using $r_{i,v}^{1 \times D} = z_{i} - q_{v}$ . We repeat this for all cluster centers and take the weighted average of residuals from each cluster to obtain the cumulative residual vector, + +$$ +r _ {i} = \frac {1}{\Upsilon} \sum_ {v = 0} ^ {\Upsilon - 1} \theta_ {i, v} r _ {i, v}, \tag {3} +$$ + +with learned cluster weight $\theta_v$ . By combining the residuals of a given crop, we represent its affinity with all learned clusters. When maximizing or minimizing similarity between residuals, we effectively enforce a consistent cluster affinity between input crops. + +# 4. Experiments + +# 4.1. Self-Supervised Pre-Training + +Pre-Training Dataset. To train our self-supervised task, we collect a large amount of freely available, orthorectified, atmospherically corrected Sentinel-2 imagery of regions with limited human development. Regions of interest were manually selected to cover a variety of climates. Given spatial and temporal ranges, we use the PyStac library [37] to fetch imagery from the AWS Sentinel-2 catalog closest to our points of interest. Imagery within the spatial-temporal constraints containing over $20\%$ cloud cover and less than $80\%$ data coverage were removed. A maximum of 100 images meeting these constraints were collected per region. The collected images were divided into 14,857, $1096\times 1096$ $px^2$ sized tiles for training. The resultant dataset contains 27 regions of interest spanning $1217km^2$ over three years. We provide all points of interest (Lat., Long.) in the supplementary material, and will release the dataset upon publication. + +Implementation Details. We adopt a standard ResNet-34 backbone, with TeRN inserted after the first layer, and the Surface Residual Encoder as the output layer. TeRN is constructed with 10 blocks, each containing three layers of + +
DatasetOSCD [30]
MethodSup.Precision (%)Recall (%)F-1 (%)
Full Supervision
U-Net [80] (random)\(\mathcal{F}\)70.5319.1729.44
U-Net [80] (ImageNet)\(\mathcal{F}\)70.4225.1236.20
MoCo-v2 [45]\(\mathcal{S}+\mathcal{F}\)64.4930.9440.71
SeCo [68]\(\mathcal{S}+\mathcal{F}\)65.4738.0646.94
DeepLab-v3 [16] (ImageNet)\(\mathcal{F}\)51.6351.0653.04
Ours (fine-tuned)\(\mathcal{S}+\mathcal{F}\)61.8057.1359.37
Self-Supervision only
VCA [67]\(\mathcal{S}\)9.9220.7713.43
MoCo-v2 [45]\(\mathcal{S}\)29.2111.9216.93
SeCo [68]\(\mathcal{S}\)74.7015.2025.26
Ours\(\mathcal{S}\)37.5272.6549.48
+ +Table 1. Precision, recall, and F-1 (\%) accuracies (higher is better) of the "change" class on Onera Satellite Change Detection (OSCD) dataset validation set [30]. $\mathcal{F}$ , and $S$ represent full and self-supervision respectively. $S + \mathcal{F}$ refer to self-supervised pretraining followed by fully supervised fine-tuning. Random and ImageNet denote the type of backbone weight initialization that method uses. + +kernel size $3 \times 3$ and dilations of 1-1-2. For the Surface Residual Encoder, we use $\Upsilon = 64$ . We use training patch size of $7 \times 7$ , batch size of 32, learning rate of 0.01, momentum of 0.6, and weight decay of 0.001 for training. For the Noise Contrastive Estimation loss, we use a temperature scaling of 0.05. We pre-train the network for 110,000 iterations or until convergence. Note that the self-supervised baselines SeCo [68] and Ayush et al. [4] use 1 million and 543,435 images respectively for pre-training, while we use only 14,857 images. + +# 4.2. Change Detection + +Implementation Details. This task is evaluated on the Onera Satellite Change Detection (OSCD) dataset [30], and performed in two ways: self-supervised, and supervised fine-tuning. The self-supervised approach utilizes only the pre-trained backbone to extract patch-wise residual features from both images, with each $9 \times 9$ patch representing its center pixel. We calculate the euclidean distance as a change metric between corresponding residual features, which are thresholded using Otsu thresholding [76] to predict change pixels when residual distance is large. For the fine-tuned approach, we use image-wise inputs to a DeepLab-v3 [16] with skip-connections network with our pre-trained backbone, fine-tuning the decoder for 30 epochs while freezing the backbone's weights. We use channel-wise concatenations of image pairs as input to the network, with the output features optimized using the cross entropy loss and ground truth change masks. For evaluation, we report precision, recall, and F-1 score of the "change" class in Tab. 1. We use batch-size of 32, learning rate of 0.001, momentum of 0.6, and weight decay of 0.001. For the self-supervised baseline methods, we use the publicly available model weights and follow the same previously described self-supervised change prediction pipeline. The fully-supervised baselines + +
DatasetBigEarthNet [91]
MethodSup.Fine-Tune EpochsmAP (%)
Inception-v2 [92]F-48.23
InDomain [72]S + F9069.70
S-CNN [91]F-69.93
ResNet-50 [46] (random)F-78.98
ResNet-50 [46] (ImageNet)F-86.74
MoCo-v2 [45]S + F10086.05
SeCo [68]S + F10087.81
Ours (fine-tuned)S + F2487.98
+ +Table 2. Mean average precision accuracy (higher is better) on BigEarthNet land cover multi-label classification dataset validation set [91]. $\mathcal{F}$ , and $S$ represent full and self-supervision respectively. $S + \mathcal{F}$ refer to self-supervised pre-training followed by fully supervised fine-tuning. + +follow the same steps as our fine-tuned approach, without the pre-trained weight initialization. + +Results Discussion. In Tab. 1 and Fig. 6 we compare our method to SOTA baselines for both self-supervised and fine-tuned approaches. We present common semantic segmentation networks initialized with weights that are random, or pre-trained with ImageNet [54], MoCo-v2 [45], and SeCo [68]. We hypothesized that change in material and texture corresponds to actual change in the scene. Hence by learning good material and texture representation and comparing representations of image pairs, we can reliably locate regions of change. As evident by Tab. 1, our self-supervised approach learns sufficiently good material and texture representation to outperform other fine-tuned methods, surpassing self-supervised SeCo by $24.22\%$ , and fine-tuned SeCo by $2.08\%$ . When considering our fine-tuned method, we outperform our baselines even further, with $12.43\%$ performance increase compared to our self-supervision based baseline, and $6.33\%$ performance increase compared to the fully supervised baseline. Additionally, we show that the inductive bias of material and texture representation to the task of change detection is significant as evidenced by the quicker convergence speed (measured in epochs), with our method converging within only 30 epochs, compared to 100 epochs reported by SeCo. + +# 4.3. Land Cover Classification + +Implementation Details. We evaluate our pre-trained backbone on the BigEarthNet [91] dataset for the task of multi-label land cover classification. The dataset provides 590,326 multi-spectral images of size $120 \times 120$ annotated with multiple land-cover labels, split into train and validation sets (95%/5%). We fine-tune a classifier head added to our frozen pre-trained backbone network for 24 epochs using given ground truth labels. We use SGD optimizer, batch-size of 128, learning rate of 0.0005, momentum of 0.6, and weight decay of 0.001. For performance, we report the mean average precision of all classes (19). + +
DatasetSpaceNet [96]
MethodSup.Fine-Tune EpochsmIoU (%)
DeepLab-v3 [16] (random)F-69.44
DeepLab-v3 [16] (ImageNet)F-72.22
MoCo-v2 [45]S + F10078.05
Ayush et al. [4]S + F10078.51
Ours (fine-tuned)S + F2481.12
+ +Table 3. Mean intersection over union (higher is better) on SpaceNet building segmentation dataset validation set [96]. $\mathcal{F}$ , and $\mathcal{S}$ represent full and self-supervision respectively. $\mathcal{S} + \mathcal{F}$ refer to self-supervised pre-training followed by fully supervised fine-tuning. Random and ImageNet denote the type of backbone weight initialization that method uses. + +![](images/c58143e90f38084a9ca83a6e4d9254f3fff73c4f5033d0101b501b18df9a8340.jpg) +Figure 4. Qualitative results of our method on SpaceNet dataset [96]. Cyan, magenta, gray, and red colors represent true positive, false positive, true negative, and false negative respectively. Best viewed in zoom and color. + +Results Discussion. Tab. 2 reports the mean average precision performance of baseline and our methods after fine-tuning. While our method only outperforms our baseline by $0.18\%$ , we note that our method converges within 24 epochs, which is significantly faster than our best-performing baseline which reports convergence within 100 epochs. + +# 4.4. Semantic Segmentation + +Implementation Details. We use the SpaceNet building segmentation dataset for this task. The dataset provides 10,593 multi-spectral images of size $163 \times 163$ labeled with pixel-wise building/no-building masks, split into train and validation sets (90%/10%). We use a DeepLab-v3 [16] with skip-connections network with our frozen pre-trained backbone and fine-tune it for 24 epochs with batch-size of 32, learning rate of 0.0085, momentum of 0.6, and weight decay of 0.001. We report mean intersection over union (mIoU) of the best performing epoch in Tab. 3. The fully-supervised baselines follow the same steps as our fine-tuned approach, without the pre-trained weight initialization. + +Results Discussion. Tab. 3 and Fig 4 compare the quantitative and qualitative results of baselines and our method. For our baselines, we report Ayush et al. [4] and MoCo-v2 [45], which use PSANet [111] with backbones pre-trained on geography consistency objective. We also report the performance of DeepLab-v3 initialized with random and ImageNet [54] pre-trained weights. As shown in Tab. 3, our method requires significantly less epochs to obtain superior performance on the SpaceNet building segmentation dataset. We outperform our self-supervised based baseline by $2.61\%$ , and fully supervised based baseline by $8.90\%$ with $76\%$ convergence speed reduction. + +# 5. Results + +Evident by our qualitative and quantitative results, our method provides both superior performance and convergence time (measured in epochs) for the evaluated downstream tasks. It is shown that material and texture are strongly associated with common remote sensing downstream tasks, and the ability to represent material and texture effectively improves performances on those tasks. Since quantitatively measuring the ability to represent material without material labels is difficult, we analyze and showcase qualitative texture and material results in the form of visual word maps (pixel-wise cluster assignments). We also discuss limitations, running time, pseudo-code, and additional qualitative results in the supplementary material. + +Visual Word Maps Generation. In order to measure the effectiveness of our approach to describe materials and textures, we qualitatively evaluate the visual word maps (pixel-wise cluster assignments) generated by our method. Ideally, we expect similar material and textures to be mapped to the same clusters, without over or under grouping of pixels. We visually compare classical textons, a patch-wise backbone, and our method in Fig. 5. The patch-wise backbone has the same base architecture as MATTER, but without TeRN and surface residual encoding modules. Both methods were trained on the same dataset, with the same hyperparameters, and number of iterations, as described in Sec. 4.1. It can be seen that the textons and patch-wise backbone approaches generate two extreme cases of over-sensitivity and undersensitivity to changes in material and texture. Since textons operate on raw intensity values, the inter-material variance is small, making it highly sensitive to small texture changes. This can be seen in the textons-generated visual word map, in which small irregularities on the road results in mapping to different visual words. On the other hand, the patch-wise backbone, even with the receptive field constraints through patched inputs, still loses crucial low-level details essential for texture representation. This is indicated by the grouping of obviously different textures to a single visual word. In contrast, as demonstrated in Fig. 5, our Texture Refinement Network and Surface Residual Encoder boost the im + +![](images/7769ea0dc9d967a97d1e55a10b4275b8f84eabb0a26ef4ab2b3a90c7d3fc408b.jpg) + +![](images/f7f1509de83a1c8aee4d0820e179b16762fd74fb6deaa92c21d724f776216010.jpg) +Image + +![](images/c668d5c2f32eb37485daa87f3aa025828c87ee5dd1fceca3ca07ee66835d4713.jpg) + +![](images/423c3d72f1a7147601cd3a410685ab7767eaf007ccb1abb647163442babbad57.jpg) +Textons + +![](images/faa1450fe26f1da8f0c9d3739522a72838da891fdf026b936a5731f758538482.jpg) + +![](images/57ea8f976fbd964692bc6d0a44ae8debddf619de5e0824ab47bb7a3e4e1849fe.jpg) +Patch-wise Backbone + +![](images/e1f6c1af6ea5dd015179e9b244e80c9ef0e787558002db84bd3eacfae1474199.jpg) + +![](images/5fcab2ef7a4e859f78810271759d489e7e87d5b46800173df53d934a0f9eb7bf.jpg) +Ours +Figure 5. Qualitative evaluation of our generated material and texture based visual word maps. It can be seen that our method provides more descriptive surface-based features that are not highly sensitive to small texture irregularities like textons, or under-sensitive to structure changes like the patch-wise backbone. Best viewed in zoom and color. Colors are random. + +
Train Crop SizeInference Crop Size
-791113151719
546.6847.3846.9446.9445.7444.5143.74
748.5249.4849.0149.0247.7646.6445.92
948.5847.6048.0247.8346.5145.5745.45
1148.9847.8347.3246.6545.6444.5144.16
1347.4647.1446.3546.9944.6543.7943.09
1547.6347.1547.3046.1045.5544.6844.10
1746.7446.8146.4945.9244.6943.6043.19
+ +Table 4. Receptive Field Constraint Analysis. F-1 score $(\%)$ performance for the unsupervised change detection task. Reported values are of the "change" class with respect to training and inference crop sizes (without fine-tuning). It can be seen that the method benefits from smaller receptive field, achieving superior performance when using smaller train and inference crop sizes. + +pact of low-level features, generating surface-based visual word maps. Our method is able to retain texture-essential features, and generalize surface representation which translates to superior surface-based visual word maps. + +# 5.1. Ablation Study + +Constraining Receptive Field. In Tab. 4 we study the effects of varying receptive field constraints on our method. As mentioned before, as the receptive field increases, the impact of low-level features diminishes, along with the quality of material and texture representation. Unlike traditional methods, which resort to the usage of smaller networks to reduce receptive field, we explicitly constrain the method by feeding crops to the network, removing them from any global context. Recall that the objective of our method is to learn representation of material and spatial distribution of micro-structures, which are largely affected by low level features which are diminished in larger receptive field methods. In practice, the largest possible receptive field of our network during training is $7 \times 7 = 49$ pixels, which is significantly smaller than the receptive fields of ResNet-50, and ResNet-101, and ResNet-152 with sizes of 483, 1027, and 1507 pixels respectively. It can be seen in + +![](images/d70bba899cd35ecf41a74c40181865f5f3a0a3d44c9fdd64a00f159c68846651.jpg) + +![](images/4caafa594234405b9927d2abbef26f3025a68b3e1cffd6307efe3d30d972e77c.jpg) + +![](images/f8639d79eec5c161279c23596ec7c93e91facd21e5c26257d107c093909009f8.jpg) +Image 1 + +![](images/de599453a4028b53e8397c92d68da25490658da42b94bf8d0a4591dde965e852.jpg) + +![](images/e8e6435704e23a620ab83226f163c5a3284d3592b5bac933f759bac26dec6dd6.jpg) + +![](images/9342a89ffafa4142ec7c421c960eed14cbf9765fc59dc3cfc9deb09b0d479000.jpg) +Image 2 + +![](images/354bb17a7d161af153058014386451fe0d748c5b77ff6fe6cb7cd2486a3e59ac.jpg) + +![](images/daaeb2fb8a2ea442b78aa0b07354c4b0b936507758a37df2cc4a451cf2e5bc21.jpg) + +![](images/9c406e212c5c95ff4ef1d346d054cdf66ca5acbd60f323c240e105b06b798add.jpg) +Ground Truth + +![](images/b82e5e5311c06682e29a04997c352afed4927fad8fe13dd0628c51f5cd73f655.jpg) + +![](images/50d505b7f04962651bfcaa511e9515db8bf66a476db9b112e6076bd57d8637cd.jpg) + +![](images/4e54cdb18bb2f366adeba7824d2cee134cfbf22d36679bfa9cbd5806c1560e4a.jpg) +DeepLab [16] +Figure 6. Qualitative results of our method on Onera Satellite Change Detection (OSCD) dataset [30]. It can be seen that our self-supervised alone is capable of detecting change only by inferring on the change of material and texture. The fine-tuned model is able to utilize the pre-trained material and texture based weights and achieve significantly better results than models with ImageNet weight initialization. Cyan, magenta, gray, and red colors represent true positive, false positive, true negative, and false negative respectively. Best viewed in zoom and color. + +![](images/0b4b511cb011d7c77b7eb6c1449cec9508d5f1f168a6aa1206ed0f9b7acd1658.jpg) + +![](images/1434a9d7614a0beb246bef9ea485696cfc2b78035d80e65c8e27d2562a34f72d.jpg) + +![](images/181239a47c8f067ee5eaeb04b51a5d34c0eead5c5105857d373200b28cc1758a.jpg) +Difference of Residuals + +![](images/04ea675888b54a0c75553bd7457d56829e4969774f6d3c3b4c2f4dac6725347e.jpg) + +![](images/958ae691748599a993c19f99cda722d4997dbdc38cf89b48129529e45cae5ad0.jpg) + +![](images/77102980be9824e5d8bd1d30a5a1b6ddb0a32da044fc42bb13940dad5a7a1290.jpg) +Ours $(S)$ + +![](images/c1c6a0f5b5f1cbc7f00b0f68fb71b3212148b001350d9c7e457d151174df61ee.jpg) + +![](images/4c1ffb538e3ef9c4660ca6a894b846f26aaceadee38d44ffe6fb86eea338f0d8.jpg) + +![](images/ffdb2d9a2d1960342ad7830144a727fffe5dd98352f845b31cba441a6d14b64b.jpg) +Ours $(S + \mathcal{F})$ + +Tab. 4 that in fact, the method benefits from removal from global spatial context and smaller receptive fields, helping it learn better representation for material and texture and achieve better performance on the unsupervised change detection task. Our best results are achieved with train crop size of $7 \times 7$ , and inference crop size of $9 \times 9$ , while worst performance is achieved with largest training and inference receptive fields. + +Impact of Modules. In Tab. 5 we study the impact of each module in our proposed method. We evaluate performance of the self-supervised change detection task (F-1 score of "change" class) as an ablation metric since it has strong transferability to material and texture representation learning. We consider all possible network combinations with patch-wise backbone, TeRN, and Surface Residual encoder. The patch-wise backbone corresponds to the network fed by patch-wise inputs, without TeRN or Surface Residual encoder. We then selectively add TeRN and Surface Residual Encoder to the network and record its performance. Every network combination was trained and evaluated with the same hyperparameters and procedure described in Sec. 4.1 and 4.2. It can be seen that each module provides incremental performance boost, with best performance achieved when both modules are implemented in the network. + +# 6. Conclusion + +In this work, we present MATTER, a novel self-supervised method that learns material and texture based representation for multi-temporal, spatially aligned satellite imagery. By utilizing patch-wise inputs and our refine + +
Patch-wise BackboneTexture RefinementSurface ResidualF-1 Score (%)
✓37.42
✓✓41.84
✓✓43.23
✓✓✓49.48
+ +Table 5. Ablation study. F-1 score of the "change" class of the Onera Satellite Change Detection dataset using the self-supervised approach with respect to modules used. + +ment network, we constrain the receptive field and enhance texture-essential features. Those are then mapped to residuals of learned clusters as an affinity measurement, which represents the material and texture composition of the sampled patch. Through our self-supervision pipeline, MATTER learns discriminative features for various material and texture surfaces, which are shown to have strong correlation to change (change of surface infers actual change), or can be used as pre-trained weights for other remote sensing tasks. + +Acknowledgement This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2021-2011000005. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. + +# References + +[1] World meteorological organization (wmo) observing systems capability analysis and review (oscar) tool, https://space.oscar.wmo.int/satellites. 1 +[2] Peri Akiva, Matthew Purri, Kristin Dana, Beth Tellman, and Tyler Anderson. H2o-net: Self-supervised flood segmentation via adversarial domain adaptation and label refinement. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 111-122, 2021. 2 +[3] Hamed Alemohammad and Kevin Booth. 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Turrisi da Costa $^{*1}$ Xavier Alameda-Pineda $^{2}$ Elisa Ricci $^{1,3}$ Karteek Alahari $^{2}$ Julien Mairal $^{2}$ + +1 University of Trento 2 Inria† 3 Fondazione Bruno Kessler + +# Abstract + +Self-supervised models have been shown to produce comparable or better visual representations than their supervised counterparts when trained offline on unlabeled data at scale. However, their efficacy is catastrophically reduced in a Continual Learning (CL) scenario where data is presented to the model sequentially. In this paper, we show that self-supervised loss functions can be seamlessly converted into distillation mechanisms for CL by adding a predictor network that maps the current state of the representations to their past state. This enables us to devise a framework for Continual self-supervised visual representation Learning that (i) significantly improves the quality of the learned representations, (ii) is compatible with several state-of-the-art self-supervised objectives, and (iii) needs little to no hyperparameter tuning. We demonstrate the effectiveness of our approach empirically by training six popular self-supervised models in various CL settings. Code: github.com/DonkeyShot21/cassle. + +# 1. Introduction + +During the last few years, self-supervised learning (SSL) has become the most popular paradigm for unsupervised visual representation learning [3, 7, 8, 13, 14, 25, 27, 54]. Indeed, under certain assumptions (e.g., offline training with large amounts of data and resources), SSL methods are able to extract representations that match the quality of representations obtained with supervised learning, without requiring annotations. However, these assumptions do not always hold in real-world scenarios, e.g., when new unlabeled data are made available progressively over time. In fact, in order to integrate new knowledge into the model, training needs to be repeated on the whole dataset, which is impractical, expensive, and sometimes even impossible when old data is not available. This issue is exacerbated by the fact that SSL models are notoriously computationally expensive to train. + +![](images/02e523ade0f062e62a8f68edae8344318090168faa41b4840144e51f1c5c9453.jpg) + +![](images/1c87794a3ebcf75f1c1fed4355e80550d03b4e81775cfb5a23df22d2d2f50231.jpg) +Figure 1. Linear evaluation accuracy of representations learned with different self-supervised methods on class-incremental CIFAR100 and ImageNet100. In blue the accuracy of SSL fine-tuning, in green the improvement brought by CaSSLe. The red dashed line is the accuracy attained by supervised fine-tuning. + +Continual learning (CL) studies the ability of neural networks to learn tasks sequentially. Prior art in the field focuses on mitigating catastrophic forgetting [17, 22, 24, 37]. Common benchmarks in the CL literature evaluate the discriminative performance of classifiers learned with supervision from non-stationary distributions. In this paper, we tackle the same forgetting phenomenon in the context of SSL. Unsupervised representation learning is indeed appealing for sequential learning since it does not require human annotations, which are particularly hard to obtain when new data is generated on-the-fly. This setup, called Continual Self-Supervised Learning (CSSL), is surprisingly underinvestigated in the literature. + +In this work, we propose CaSSLe, a simple and effective framework for CSSL of visual representations based on the intuition that SSL models are intrinsically capable of learning continually, and that SSL losses can be seamlessly converted into distillation losses. Our key idea is to train the + +current model to predict past representations with a prediction head, thus encouraging it to remember past knowledge. CaSSLe has several favourable features: (i) it is compatible with popular state-of-the-art SSL loss functions and architectures, (ii) it is simple to implement, and (iii) it does not require any additional hyperparameter tuning with respect to the original SSL method. Our experiments demonstrate that SSL methods trained continually with CaSSLe significantly outperform all the related methods (CSSL baselines and several methods adapted from supervised CL). + +We also perform a comprehensive analysis of the behavior of six popular SSL methods in diverse CL settings (i.e., class, data, and domain incremental). We provide empirical results on small (CIFAR100), medium (ImageNet100), and large (DomainNet) scale datasets. Our study sheds new light on interesting properties of SSL methods that emerge when learning continually. Among other findings, we discover that, in the class-incremental setting, SSL methods typically approach or outperform supervised learning (see Fig.1), while this is not generally true for other settings (data-incremental and domain-incremental) where supervised learning still shows a sizeable advantage. + +# 2. Related Work + +Self-Supervised Learning. Recent SSL approaches have shown performance comparable to their supervised learning equivalents [3, 7, 8, 13, 14, 25, 27, 54]. In a nutshell, most of these methods use image augmentation techniques to generate correlated views (positives) from a sample, and then learn a model that is invariant to these augmentations by enforcing the network to output similar representations for the positives. Initially, contrastive learning, based on instance discrimination [52] using noise-contrastive estimation [26, 38], was a popular strategy [13, 27]. However, this learning paradigm requires large batch sizes or memory banks. A few methods that use a negative-free cosine similarity loss [15, 25] have addressed such issues. + +Concurrently, clustering-based methods (SwAV [7], DeepCluster v2 [6, 7] and DINO [8]) have also been proposed. They do not operate on the features directly, and instead compare positives through a cross-entropy loss using cluster prototypes as a proxy. Redundancy reduction-based methods have also been popular [3, 20, 54]. Among them, BarlowTwins [54] considers an objective function measuring the cross-correlation matrix between the features, and VicReg [3] uses a mix of variance, invariance and covariance regularizations. Methods such as [19] have explored the use of nearest-neighbour retrieval and divide and conquer [49]. However, none of these works studied the ability of SSL methods to learn continually and adaptively. + +Continual Learning. A plethora of methods have been developed to counteract catastrophic forgetting [2, 4, 9-12, 18, 21, 30, 31, 33, 35, 39, 41, 43-47, 51, 55]. Following [17], + +these works can be organized into three macro-categories: replay-based [4, 12, 35, 39, 43, 44], regularization-based [2, 9-11, 18, 21, 30, 31, 33, 47, 51, 55], and parameter isolation methods [45, 46]. All these works evaluate the effectiveness of CL methods using a linear classifier learned sequentially over time. However, this evaluation does not reflect an important aspect, i.e., the internal dynamics of the hidden representations. Moreover, most CL methods tend to rely on supervision in order to mitigate catastrophic forgetting. A few of them can be adapted for the unsupervised setting, although their effectiveness is greatly reduced (see discussion in Sec. 5, Sec. 6 and the supplementary material). + +Works such as [1, 42, 48] laid the foundations of unsupervised CL, but their studies are severely limited to digit-like datasets, e.g., MNIST and Omniglot, and the proposed methods are unfit for large-scale scenarios. Recently, [5,23] explored self-supervised pretraining for supervised continual learning with online and few-shot tasks, and [10] presented a supervised contrastive CL approach. Two concurrent works [34, 36] have also attempted to address CSSL recently. The former [34] extends [10] to the unsupervised setting, but is specifically designed for contrastive SSL, such as [13, 27], and lacks generalizability to other popular SSL paradigms. The latter [36] is also limited as it only shows small-scale experiments in the class-incremental setting and considers just two SSL methods. In contrast, we present a general framework for CSSL with superior performance, conduct large-scale experiments on three challenging settings, thereby presenting a deeper analysis of CSSL. + +# 3. Preliminaries + +Self-Supervised Learning. The training procedure of several state-of-the-art SSL methods [3, 7, 8, 13, 19, 25, 27, 54] can be summarized as follows. Given an image $\pmb{x}$ in a batch sampled from a distribution $\mathcal{D}$ , two correlated views $\pmb{x}^A$ and $\pmb{x}^B$ are extracted by applying stochastic image augmentations, such as random cropping, color jittering and horizontal flipping. View $\pmb{x}^A$ is fed to an encoder $f_{\theta} = f_{p} \circ f_{b}$ which is parametrized by $\theta$ and has a backbone $f_{b}$ and a projection head $f_{p}$ , that extracts feature representations $\pmb{z}^A = f_{\theta}(\pmb{x}^A)$ . Similarly, $\pmb{x}^B$ is forwarded into the same networks, or possibly copies thereof, updated with exponential moving average (EMA), to obtain the representation $\pmb{z}^B$ . A loss function $\mathcal{L}_{SSL}$ is applied to these representations to learn the parameters $\theta$ as follows: + +$$ +\underset {\theta} {\operatorname {a r g m i n}} \mathbb {E} _ {\boldsymbol {x} \sim \mathcal {D}} \left[ \mathcal {L} _ {S S L} \left(\boldsymbol {z} ^ {A}, \boldsymbol {z} ^ {B}\right) \right]. \tag {1} +$$ + +More details on the implementation of $\mathcal{L}_{SSL}$ are provided in Sec. 5.1 and Tab. 1. This procedure turns out to be extremely powerful at extracting visual representations from large unlabeled datasets. The intuition behind the success of these models is that they learn to be invariant to augmentations. Importantly, augmentations are hand-crafted in a way + +that the two views $\boldsymbol{x}^A$ and $\boldsymbol{x}^B$ contain roughly the same semantics as $\boldsymbol{x}$ , but their overall appearance (geometry, colors, resolution, etc.) is different. This forces the model map images with the same semantics to similar regions of the feature space. Interestingly, these augmentations are much stronger, i.e., they distort the image more, than augmentations commonly used to train supervised models. + +Continual Learning. The CL problem focuses on training models such as deep neural networks from non-stationary data distributions. More formally, this involves a network $f_{\theta'}' = f_c' \circ f_b'$ with parameters $\theta'$ , backbone $f_b'$ and a classifier $f_c'$ , that learns from an ordered set of tasks $\{1, \dots, T\}$ , each exhibiting a different data distribution $\mathcal{D}_t$ . Usually, an image $x$ sampled i.i.d. from $\mathcal{D}_t$ is processed by $f'$ that predicts a probability distribution $p$ over the set of classes $\mathcal{V}_t$ . The objective is to find parameters $\theta'$ such as: + +$$ +\underset {\theta^ {\prime}} {\operatorname {a r g m i n}} \sum_ {t = 1} ^ {T} \mathbb {E} _ {(\boldsymbol {x}, \boldsymbol {y}) \sim \mathcal {D} _ {t}} \left[ \mathcal {L} _ {C L} (\boldsymbol {p}, \boldsymbol {y}) \right], \tag {2} +$$ + +where, in most cases, $\mathcal{L}_{CL}$ is the cross-entropy loss. However, during task $t$ , the previous data distribution $\mathcal{D}_{t - 1}$ is not available and therefore Eq. (2) cannot be minimized directly. Current research focuses on approximating $\theta^{\prime}$ using indirect approaches. Some of them [18, 33] are based on knowledge distillation [29], i.e., transferring knowledge from one network to another by forcing them to produce the same outputs. We will discuss the applicability of distillation methods in CSSL in Sec. 5. + +# 4. Continual Self-Supervised Learning + +In this paper, we tackle the problem of Continual Self-Supervised Learning as an extension of both SSL and CL. In practice, a CSSL experiment starts with the first task, where the model is trained as per the specific self-supervised method that it implements, with no difference from offline training. Subsequent tasks are then presented to the model sequentially, and the data from the previous tasks are discarded. No labels are provided during this training phase. For the sake of simplicity and since we are exploring a new, challenging setting, we assume task boundaries to be provided to the model. More formally, the CSSL objective is to learn a strong feature extractor that is invariant to augmentations on all tasks. Following the notation introduced in Sec. 3, we define: + +$$ +\underset {\theta} {\operatorname {a r g m i n}} \sum_ {t = 1} ^ {T} \mathbb {E} _ {\boldsymbol {x} \sim \mathcal {D} _ {t}} \left[ \mathcal {L} _ {S S L} \left(\boldsymbol {z} ^ {A}, \boldsymbol {z} ^ {B}\right) \right]. \tag {3} +$$ + +Note the absence of labels $\mathbf{y}$ when sampling from $\mathcal{D}_t$ , the summation over the set of tasks inherited from Eq. (2) and the SSL loss function in Eq. (1). The expectation is approximated using stochastic gradient descent on minibatches. + +Evaluation. After each task, it is possible (for evaluation purposes) to train a linear classifier on top of the obtained backbone $f_{b}$ . With this linear classifier we report accuracy on the test set. This protocol is compatible with standard CL metrics, as shown in Sec. 6.1. We explore three CSSL settings in our work. + +- Class-incremental: each task $t$ is represented by a dataset $D_{t} \sim \mathcal{D}_{t}$ containing images that belong to a set of classes $\mathcal{Y}_{t}$ such that $\mathcal{Y}_{t} \cap \mathcal{Y}_{s} = \emptyset$ for each other task $s \neq t$ . Note that the class labels are only used for splitting the dataset and they are unknown to the model. In practice, the set of classes in the dataset are shuffled and then partitioned into $T$ tasks. Each task contains the same number of classes. +- Data-incremental: each task $t$ contains a set of images $D_{t}$ such that $D_{t} \cap D_{s} = \emptyset$ for each other task $s \neq t$ . No additional constraints are imposed on the classes. In practice, the whole dataset is shuffled and then partitioned into $T$ tasks. Each task can potentially contain all the classes. +- **Domain-incremental:** each task $t$ contains a set of images $D_{t}$ drawn from a different domain. We assume that the set of classes $\mathcal{V}_{t}$ in each dataset remains the same for all tasks but the data distribution changes, as if the data were collected from different sources. + +# 5. The CaSSLe Framework + +We now introduce "CaSSLe", our framework for continual self-supervised learning of visual representations and detail its compatibility with several SSL methods. + +Distillation in CSSL. From a supervised CL perspective, the concept of invariance is interesting. Here, we would like to learn representations of previously-learned semantic concepts that are invariant to the state of the model's parameters. Indeed, this idea was investigated in prior works [18, 30] that leverage knowledge distillation for CL. However, such approaches are only mildly effective in a CSSL scenario, as we show in Sec. 6. We believe this is due to CSSL being fundamentally different from supervised CL. In CSSL, we aim to extract the best possible representations that can be subsequently reused in a variety of tasks, and maximize the linear separability of features at the end of the CL phase. Thus, the linear classifier does not benefit much from the stability of the representations. Also, forcing the representations not to change may prevent the model from learning new concepts. This is especially critical for SSL methods for two reasons: (i) the performance of the models improve substantially with longer training, implying that the representations continue to get refined, and (ii) they exhibit different losses and feature normalizations that might interfere with distillation and vice-versa (e.g., BarlowTwins uses standardization while [18, 30] use $l2$ -normalization). Nonetheless, the features still need to be informative of previous tasks to maximize the separability of the old distribution but the current state might be too different from the pre + +![](images/3971423daed08f0a66acd6ba2936891ad28ae00636440ee8170a27cd15881ef6.jpg) +Figure 2. Overview of the CaSSLe framework. + +vious one making comparing representations complicated. + +Distillation through SSL losses. Our framework, shown in Fig. 2, is based on the following ideas: (i) a predictor network that maps the current state of the representations to their past state, by leveraging a distillation through time strategy that satisfies both stability and plasticity principles, and (ii) a family of adaptable distillation losses inherited from the SSL literature that solves the issue of having different objectives interfering with each other. + +When a new task is received, we start by making a copy of the current model. This copy does not require gradient computation and will not be updated. We call this the frozen encoder $f^{t-1}$ . As soon as an image $\boldsymbol{x} \in D_t$ is available we apply our stochastic image augmentations and extract its features $\boldsymbol{z} = f^t(\boldsymbol{x})$ . In addition, we also use the frozen encoder to extract another feature vector $\bar{z} = f^{t-1}(\boldsymbol{x})$ . Now, our goal is to ensure that $\boldsymbol{z}$ contains at least as much information as (and ideally more than) $\bar{z}$ . Instead of enforcing the two feature vectors to be similar, and hence discouraging the new model from learning new concepts, we propose to use a predictor network $g$ to project the representations from the new feature space to the old one. If the predictor is able to perfectly map from one space to the other, then it implies that $\boldsymbol{z}$ is at least as powerful as $\bar{z}$ . + +We are now ready to perform distillation, but which is the most appropriate distillation loss? Since we want the representations produced by $g$ to be invariant to the state of the model, we propose to use the same SSL loss used to simulate invariance to augmentations. Empirically, we verify that this choice reduces interference and minimizes the need for hyperparameter tuning. We can hence write a generic distillation loss by reusing the definition of $\mathcal{L}_{SSL}$ : + +$$ +\mathcal {L} _ {D} (\boldsymbol {z}, \bar {\boldsymbol {z}}) = \mathcal {L} _ {S S L} (g (\boldsymbol {z}), \bar {\boldsymbol {z}}). \tag {4} +$$ + +Note that $\bar{z}$ is always detached from the computational graph, such that the frozen encoder does not receive any gradient, and the gradient only flows through the predictor $g$ , as prescribed in [15]. On the one hand, if training converges and $\mathcal{L}_D$ is minimized, the features predicted by $g$ will likely be quasi-invariant to the state of the model, which satisfies the stability principle. On the other hand, the current encoder is less bound to its previous state, hence representations $\pmb{z}$ can be more plastic. The loss can be extended to multiple views by applying it to both representations, i.e., $\mathcal{L}_D(z^A,\bar{z}^A) + \mathcal{L}_D(z^B,\bar{z}^B)$ , and also swapped distillation, e.g., $\mathcal{L}_D(z^A,\bar{z}^B)$ and vice-versa (see ablation in Tab. 6). + +The final loss of an SSL method trained continually with the CaSSLe framework is given by: + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {S S L} \left(\boldsymbol {z} ^ {A}, \boldsymbol {z} ^ {B}\right) + \mathcal {L} _ {D} \left(\boldsymbol {z} ^ {A}, \bar {\boldsymbol {z}} ^ {A}\right) \tag {5} \\ = \mathcal {L} _ {S S L} (\boldsymbol {z} ^ {A}, \boldsymbol {z} ^ {B}) + \mathcal {L} _ {S S L} (g (\boldsymbol {z} ^ {A}), \bar {\boldsymbol {z}} ^ {A}). \\ \end{array} +$$ + +This loss can be made symmetric by applying it to both the views (swapping $A$ and $B$ in Eq. (5)) and it can also be easily adapted for multi-crop [7]. Note that we do not use any hyperparameter to weight the importance of the distillation loss with respect to the SSL loss. + +# 5.1. Compatibility of SSL methods with CaSSLe + +The main difference among SSL methods is the loss function that they use. Following the notation defined in Sec. 3, and the loss functions in Tab. 1, we now detail if and how SSL losses can be used in our CaSSLe framework. Full derivation of distillation losses is deferred to the supplementary material. + +InfoNCE-based methods [13, 27] perform instance discrimination, where positive samples help to build invariance to augmentations. The negatives prevent the model from falling into degenerate solutions. The InfoNCE (a.k.a. contrastive) loss can be written as in Eq. (6), where subscript $i$ is the index of a generic sample in the batch, sim is the cosine similarity and $\eta(i)$ is the set of negatives for sample $i$ in the current batch. Distilling knowledge with this loss is equivalent to performing instance discrimination of current task samples but in the feature space learnt in the past. Thus, the predictor $g$ learns to project samples from the present to the past space to maximize the distance with the negative samples, and the similarity with itself in the past. + +MSE-based approaches [15,25] enforce consistency among positive samples and ignore the negatives. BYOL [25] uses a momentum encoder and SimSiam [15] performs a stop gradient operation to avoid degenerate solutions. Since the representations are $l2$ -normalized, their loss (Eq. 7) can be rewritten as the negative cosine similarity: $-\mathrm{sim}(\pmb{q}^A,\pmb{z}^B) = -\frac{\pmb{q}^A}{||\pmb{q}^A||_2}\cdot \frac{\pmb{z}^B}{||\pmb{z}^B||_2}$ , where $\pmb{q}^{A} = h(\pmb{z}^{A})$ and $h$ is a prediction head. The gradient is backpropagated only + +Table 1. Overview of state-of-the-art SSL methods and losses. In all tables, highlight colors are coded according to the type of loss. + +
MethodsLossEquation
SimCLR [13]InfoNCE- log exp(sim(zA i, zB i) / τ) / ∑zj ∈η(i) exp(sim(zA i, zj) / τ)(6)
MoCo [27]
NNCLR [19]
BYOL [25]MSE- ||qA - zB||2/2(7)
SimSiam [15]
VICReg [3]
SwAV [7]Cross-entropy- ∑d aD log exp(sim(zA, cD) / τ) / ∑k exp(sim(zA, ck) / τ)(8)
DCV2 [7]
DINO [8]
BarlowCross-correlation∑u (1 - Cuv)2 + λ ∑u ∑v ≠ u Cuv2(9)
Twins [54]
VICReg [3]
+ +through the representations of the first argumentation. A special case of this family of methods is VICReg [3], which uses a combination of multiple losses, where MSE acts as invariance term. Features are not $l2$ -normalized in VICReg and its predictor is the identity function. In our framework, this loss encourages the model to predict the past state of representations without additional regularization. + +Cross-entropy-based. Instead of simply enforcing invariance of the representations to augmentations, cluster prototypes $\mathbf{C} = \{\mathbf{c}_1,\dots ,\mathbf{c}_K\}$ are used as a proxy in these approaches, so that the model learns to predict invariant cluster assignments. Slight variations of this idea result in different methods: SwAV [7], DeepClusterV2 [7] and DINO [8]. Once a probability distribution over the prototypes is predicted, the cross-entropy loss (Eq. 8) is used to compare the two views. Features and cluster prototypes $c$ are l2-normalized. The assignments $\pmb{a}^{B}$ can be calculated in several ways, e.g., k-means in DeepCluster, Sinkhorn-Knopp in SwAV and EMA in DINO. When employed as a distillation loss, cross-entropy encourages $g$ to predict the assignments generated by the frozen encoder with a set of frozen prototypes: $\pmb{a}^{B} = \frac{\exp\left(\sin\left(\bar{z}^{B},c_{d}^{t - 1}\right) / \tau\right)}{\sum_{k}\exp\left(\sin\left(\bar{z}^{B},c_{k}^{t - 1}\right) / \tau\right)}$ , where $\mathbf{C}^{t - 1} = \{\mathbf{c}_1^{t - 1},\ldots ,\mathbf{c}_K^{t - 1}\}$ . + +Cross-correlation-based. These methods use a different approach based on decorrelating the components of the feature space, e.g., Barlow Twins [54], VICReg [3] and W-MSE [20]. For our analysis, we will mainly focus on Barlow Twins' implementation of this objective. Extensions to VICReg are left for future work. The cross-correlation based objective function is shown in Eq. 9, where $\lambda$ is an hyperparameter to control the importance of the first and the second terms of the loss, and $\mathcal{C}_{uv} = \frac{\sum_{i}z_{i,u}^{A}z_{i,v}^{B}}{\sqrt{\sum_{i}(z_{i,u}^{A})^{2}}\cdot\sqrt{\sum_{i}(z_{i,v}^{B})^{2}}}$ is the value of position $(u,v)$ of the cross-correlation matrix computed between the representations of the views along the batch dimension. Note that the representations here are mean centered along the batch dimension, such that each unit has mean output zero over the batch. Performing distillation with this loss has the addi + +tional effect of decorrelating the dimensions of the predicted features $g(z^A)$ + +# 6. Experiments + +# 6.1. Experimental Protocol + +Evaluation Metrics. Following previous work [35], we propose the following metrics to evaluate the quality of the representations extracted by our CSSL model: + +$\triangleright$ Linear Evaluation Accuracy: accuracy of a classifier trained on top of the backbone $f_{b}$ on all tasks (or a subset, e.g., $10\%$ of the data) or a downstream task. For class incremental and data-incremental, we use the task-agnostic setting, meaning that at evaluation time we do not assume to know the task ID. For the domain-incremental setting, we perform both task-aware and task-agnostic evaluations (the latter is discussed in the supplementary material). To calculate the average accuracy we compute $A = \frac{1}{T}\sum_{i=1}^{T} A_{T,i}$ , where $A_{j,k}$ is the linear evaluation accuracy of the model on task $k$ after observing the last sample from task $j$ . +- Forgetting: a common metric in the CL literature, it quantifies how much information the model has forgotten about previous tasks. It is formally defined as: $F = \frac{1}{T - 1}\sum_{i = 1}^{T - 1}\max_{t\in \{1,\dots,T\}}(A_{t,i} - A_{T,i})$ . +$\triangleright$ Forward Transfer: measures how much the representations that we learned so far are helpful in learning new tasks, namely: $FT = \frac{1}{T - 1}\sum_{i = 2}^{T}A_{i - 1,i} - R_i$ where $R_{i}$ is the linear evaluation accuracy of a random network on task $i$ . + +Datasets. We perform experiments on 3 datasets: CIFAR100 [32] (class-incremental), a 100-class dataset with 60k 32x32 colour images; ImageNet100 [50] (class- and data-incremental), 100-class subset of the ILSVRC2012 dataset with $\approx 130\mathrm{k}$ images in high resolution (resized to 224x224); DomainNet [40] (domain-incremental), a 345-class dataset containing roughly 600k high-resolution images (resized to 224x224) divided into 6 domains. We experiment with 5 tasks for the class- and data-incremental settings and with 6 tasks (one for each domain in DomainNet) in the case of domain-incremental. The supplementary material presents additional results with different number of tasks. For the domain-incremental setting, we order the domains in decreasing number of images. + +Implementation details. The SSL methods are adapted from solo-learn [16], an established SSL library, which is the main code base for all our experiments. The number of epochs per task is as follows: 500 for CIFAR100, 400 for ImageNet100, 200 for DomainNet. The backbone $f_{b}$ is a ResNet18 [28], with batch size 256. We use LARS [53] for all our experiments. The offline version of each method, that serves as an upper bound, is trained for the same number of epochs as the continual counterpart for a fair comparison. All the results for offline upper bounds are ob + +Table 2. Comparison with state-of-the-art CL methods on CIFAR100 (5 tasks, class-incremental) using linear evaluation top-1 accuracy, forgetting and forward transfer. + +
StrategySimCLRBarlow TwinsBYOL
A (↑)F (↓)T (↑)A (↑)F (↓)T (↑)A (↑)F (↓)T (↑)
Fine-tuning48.91.033.554.30.439.252.70.135.9
EWC [31]53.60.033.356.70.239.156.40.039.9
ER [44]50.30.132.754.63.039.454.70.436.3
DER [4]50.70.433.255.32.539.654.81.136.7
LUMP [36]52.30.334.557.80.341.056.40.237.9
Less-Forget [30]52.50.233.856.40.240.158.60.241.1
POD [18]51.30.133.855.90.340.357.90.041.1
CaSSLe58.30.236.460.40.442.262.20.043.6
Offline65.8--70.9--70.5--
+ +Table 3. Comparison with Lin et al. [34] on CIFAR100 (2 and 5 tasks, class-incremental setting). MoCoV2+ is an updated version of MoCoV2 that uses a symmetric loss. The difference between the two is $\approx 1\%$ at convergence [15]. + +
StrategyMethod2 Tasks5 Tasks
Lin et al. [34]SimCLR55.7-
MoCoV256.153.8
CaSSLeSimCLR61.858.3
MoCoV2+63.359.5
+ +tained using the checkpoints provided in [16]. For some SSL methods, it was necessary to slightly increase the learning rate over the values provided by [16] in order for the methods to fully convergence in the CSSL setting. Although tuning the hyperparameters might be beneficial in some settings, we do not perform any hyperparameter tuning for CaSSLe. We also neither change the parameters of the SSL methods, nor use a weight for the distillation loss (as per Eq. (5)). + +Baselines. Most of the CL methods require labels which makes them unsuitable for CSSL. However, a few works can be adapted for our setting with minimal changes. We choose baselines from three categories [17]: prior-focused regularization (EWC [31]), data-focused regularization (POD [18], Less-Forget [30]), and rehearsal-based replay (ER [44], DER [4]) methods. We also compare with two concurrent works that propose approaches for CSSL (LUMP [36], Lin et al. [34]). Finally, we do not consider methods based on VAEs [1,42], since they have been shown to yield poor performance on large scale. Details on how the baselines are selected, implemented and tuned for CSSL can be found in the supplementary material. + +# 6.2. Results + +Comparison with the state of the art. In Tab. 2 we report comparison with CL baselines and fine-tuning in composition with three SSL methods: SimCLR, Barlow Twins and BYOL. We select these three methods for the following reasons: (i) they feature different losses (InfoNCE, Cross-correlation and MSE), (ii) they exhibit different feature normalizations ( $l2$ , standardization and mean centering), and (iii) they use different techniques to avoid collapse (neg + +![](images/cca05e142b151e9c15fa860386bcafd409d66b51f00a48a00bd7d96c713c0af4.jpg) +Figure 3. Evolution of top-1 linear evaluation accuracy over tasks on CIFAR100 (5 tasks, class-incremental). + +![](images/fe3e9aeb7bd91996e98ce5afd321619d3343cb3362f9079d1c058c4a45504537.jpg) + +![](images/cd1bb95eddfdd88060c4c7e5ece60b63d148bf8cf5fb9473c995b6b61cc65ef2.jpg) + +atives, redundancy reduction, momentum encoder). The comparison is performed on class-incremental CIFAR100 with 5 tasks. Offline learning results are reported as upper bound. + +First, we notice that CaSSLe produces better representations than all the other strategies, outperforming them by large margins with all SSL methods in terms of top-1 accuracy. Moreover, our framework also shows better forward transfer, meaning that its features are easier to generalize to other tasks (also evident in Tab. 8). CaSSLe appears to reduce catastrophic forgetting with respect to fine-tuning, and is comparable to other methods. In general, SSL methods already have low forgetting with respect to supervised learning on CIFAR100 (see Tab. 4) and therefore there is little margin for improvement. However, on higher resolution images (ImageNet100) CaSSLe actually achieves remarkable results in the mitigation of catastrophic forgetting. + +Replay-based methods (ER, DER) clearly do not help against forgetting in CSSL. We found two reasons for this failure. First, in supervised CL, replay-based methods benefit from storing labels, which contain a lot of information about previous tasks and enable the retraining of the linear classifier on old classes. This is not the case in CSSL, where labels are unavailable. Second, SSL models need more training epochs to converge, which means that samples in the buffer are also replayed many more times. This causes severe overfitting on these exemplars, defeating the purpose of the replay buffer. LUMP mitigates this effect by augmenting the buffer using mixup but does not reach too far, surpassing other baselines only with Barlow Twins. EWC holds up surprisingly well, outperforming more recent methods, meaning that the importance of the weights can be calculated accurately with the self-supervised loss. Distillation methods (POD, Less-Forget) show good performance. However, they use $l2$ -normalization in their loss, causing loss of information when coupled with Barlow Twins, which decreases accuracy. + +Fig. 3 shows the evolution of top-1 linear evaluation accuracy over the whole training trajectory on class incremental CIFAR100 with 5 tasks. CaSSLe outperforms the other methods, and keeps improving throughout the sequence. We found BYOL to be unstable when simply finetuning the model. CaSSLe, EWC and Less-Forget mitigate this instability completely. On the other hand, LUMP first + +Table 4. Linear evaluation top-1 accuracy on class-incremental CIFAR100 and ImageNet100 with 5 tasks. CaSSLe is compared to fine-tuning, offline and supervised learning. + +
MethodStrategyCIFAR100ImageNet100
A (↑)F (↓)T (↑)A (↑)F (↓)T (↑)
Barlow TwinsFine-tuning54.30.439.263.110.744.4
CaSSLe60.40.442.268.21.347.9
Offline70.9--80.4--
SwAVFine-tuning55.50.032.864.44.342.8
CaSSLe57.80.034.566.00.243.6
Offline64.9--74.3--
BYOLFine-tuning52.70.135.966.02.943.2
CaSSLe62.20.042.266.41.146.6
Offline70.5--80.3--
VICRegFine-tuning51.50.936.461.37.942.0
CaSSLe53.60.241.164.84.345.3
Offline68.5--79.4--
MoCoV2+Fine-tuning47.30.233.462.08.441.6
CaSSLe59.50.039.668.81.546.8
Offline69.9--79.3--
SimCLRFine-tuning48.91.033.561.58.140.3
CaSSLe58.30.236.468.02.245.8
Offline65.8--77.5--
SupervisedFine-tuning54.16.836.563.15.642.5
Offline75.6--81.9--
+ +drops slightly and then recovers. We believe this is due to some instability introduced by the mixup regularization, to which the model takes time to adapt. + +In Tab. 3 we also compare with Lin et al. [34] on class incremental CIFAR100. Although our method is not specifically designed for contrastive learning, it substantially outperforms Lin et al. with 2 and 5 tasks. It is worth noting that MoCoV2+ is slightly better than MoCoV2 ( $\approx 1\%$ difference), whereas our gains are much larger ( $\approx 7\%$ ). + +Ablation study. We ablate the most critical design choices we adopt in CaSSLe: (i) distillation without swapped views, and (ii) the presence of a prediction head $g$ . These results are reported in Tab. 6. Our full framework clearly outperforms its variants with swapped views and without predictor. This validates our hypothesis that a predictor to map new features to the old feature space is crucial. The result that swapping views does not help is likely due to the frozen encoder not being invariant to the current task. + +Class-incremental. In Tab. 4 we report a study of CSSL with 6 SSL methods in composition with the CaSSLe framework on class-incremental CIFAR100 and ImageNet100. Fine-tuning and Offline SSL results are reported as lower and upper bounds. The accuracy of supervised learning is also reported. CaSSLe always improves with respect to fine-tuning. In particular, our framework produces higher forward transfer and lower forgetting, especially on ImageNet100, where methods tend to forget more. Notably, CaSSLe outperforms supervised fine-tuning, ex + +Table 5. Training 5 times longer on 1/5 of the data vs. training continually w/ and w/o CaSSLe on ImageNet100 (5 tasks, class- and data-incremental). Bold is best, underlined is second best. + +
SettingMethodFine-tuneOffline 1/5CaSSLe
Class-inc.SimCLR61.563.168.0
Barlow Twins63.163.568.2
BYOL66.060.666.4
Data-inc.SimCLR68.967.272.1
Barlow Twins71.370.274.9
BYOL74.066.773.3
+ +Table 6. Ablation study of design choices in CaSSLe. + +
StrategyMethodSwapNo pred.Ours
CaSSLeSimCLR49.352.658.3
Barlow Twins57.457.360.4
BYOL52.058.662.2
+ +cept when coupled with VICReg on CIFAR100. On average, SSL methods trained continually with CaSSLe improve by $6.8\%$ on CIFAR100 and $4\%$ on ImageNet100. + +Data-incremental. Tab. 7 presents results for linear evaluation top-1 accuracy on ImageNet100 with 5 tasks in a data-incremental scenario. While no SSL method is better than supervised fine-tuning, Barlow Twins coupled with CaSSLe is competitive. CaSSLe improves performance in all cases by $2\%$ on average, except for BYOL. This is likely due to the fact that in the data-incremental scenario remembering past knowledge is less important than in other scenarios, and BYOL already has a momentum encoder that provides some information about the past. This hypothesis is validated by the fact that MoCoV2+ (that uses a momentum encoder) improves less than SimCLR when coupled with CaSSLe. We believe that, by tuning the EMA schedule, improvement could also be achieved for BYOL. In addition, BYOL already shows impressive performance with fine-tuning, outperforming all the other methods by more than $2\%$ . Interestingly, SwAV comes closest to its offline upper bound, with only a $3\%$ decrease in performance when coupled with CaSSLe. + +Domain-incremental. We also examine the capability of CaSSLe to learn continually when the domain from which the data is drawn changes. Tab. 7 shows the average top-1 accuracy of a linear classifier trained on top of the frozen feature extractor on all domains separately (domain-aware). Domain-agnostic evaluation and results for each domain are presented in the supplementary material. Again, CaSSLe improves every method by $4.4\%$ on average, showing that our distillation strategy is robust to domain shift, and although the data distribution is really different, information transfer is still performed. Interestingly, most of the methods, when trained with CaSSLe get very close to their offline accuracy. + +Long training vs continual training. We also analyze the following question: is it worth training continually or is it better to train for longer on a small dataset? This + +Table 7. Linear evaluation accuracy on ImageNet100 (5 tasks, data-incremental) and DomainNet (6 tasks, domain-incremental). + +
MethodStrategyImageNet100 (Data-inc.)DomainNet (Domain-inc.)
Barlow TwinsFine-tuning71.350.3
CaSSLe74.955.5
Offline80.457.2
SwAVFine-tuning70.849.6
Knowledge71.354.3
Offline74.354.6
BYOLFine-tuning74.050.6
CaSSLe73.355.1
Offline80.356.6
VICRegFine-tuning70.249.3
CaSSLe72.352.9
Offline79.456.7
MoCoV2+Fine-tuning69.543.2
CaSSLe71.946.7
Offline78.253.7
SimCLRFine-tuning68.945.1
CaSSLe72.150.0
Offline77.552.6
SupervisedFine-tuning75.955.9
Offline81.966.4
+ +depends on two factors: (i) the SSL method, and (ii) the CSSL setting. For SimCLR and Barlow Twins in the class incremental setting it seems to be better to train offline on 1/5 of the classes instead of training continually with 5 tasks. In this setting, offline BYOL seems to suffer from instability, ending up lower than fine-tuning. On the other hand, on the data-incremental setting, fine-tuning outperforms longer training, especially for BYOL, which also outperforms CaSSLe (as explained previously). Apart from this exception, CaSSLe always produces better representations than other strategies, making it the go-to option. + +Downstream and semi-supervised. In Tab. 8, we present the downstream performance of CaSSLe compared with fine-tuning when trained on ImageNet100 and evaluated on DomainNet (Real). Barlow Twins, SwAV and BYOL show higher performance than the supervised model, even when considering a fine-tuning strategy. This is probably due to the fact that SSL methods tend to learn more general features than their supervised counterparts. CaSSLe improves performance on all the SSL methods, making them surpass the supervised baseline. Lastly, when compared with fine-tuning, CaSSLe improves the performance of SSL methods by $3.4\%$ on average. Tab. 9 contains the top-1 accuracy on ImageNet100 when training a linear classifier on a frozen backbone with limited amount of labels ( $10\%$ and $1\%$ ). First, we can observe that no SSL method with fine-tune surpasses the performance of supervised learning. When using CaSSLe, MoCoV2+ outperforms supervised with $10\%$ labels and, in general, Barlow Twins and MoCoV2+ work best in both semi-supervised settings. CaSSLe + +Table 8. Downstream performance with different SSL methods trained onImagenet-100 and evaluated on DomainNet (Real). + +
StrategyBarlow TwinsSwAVBYOLVICRegMoCoV2+SimCLRSupervised
Fine-tune56.255.955.054.052.451.654.3
CaSSLe60.356.956.956.358.756.5
+ +Table 9. Top-1 linear accuracy on Imagenet-100 with different SSL methods, semi-supervised setting with ${10}\%$ and $1\%$ of labels. + +
PercentageStrategyBarlow TwinsSwAVBYOLVICRegMoCoV2+SimCLRSupervised
10%Fine-tune56.657.655.753.654.952.560.8
CaSSLe60.358.256.556.561.758.9
1%Fine-tune42.642.542.340.440.939.748.1
CaSSLe47.043.143.443.247.846.8
+ +improves all SSL methods when compared with fine-tuning. + +# 7. Conclusion + +In this work, we study Continual Self-Supervised Learning (CSSL), the problem of learning a set of tasks without labels continually. We make two important contributions for the SSL and CL communities: (i) we present CaSSLe, a simple and effective framework for CSSL that shows how SSL methods and losses can be seamlessly reused to learn continually, and (ii) we perform a comprehensive analysis of CSSL, leading to the emergence of interesting properties of SSL methods. + +Limitations. Although CaSSLe shows exciting performance, it has some limitations. First, it is applicable in settings where task boundaries are provided. Second, our framework increases the amount of computational resources needed for training by roughly $30\%$ , both in terms of memory and time. Finally, CaSSLe does not perform clustering, meaning that it is unable to directly learn a mapping from data to latent classes, and thus needs either a linear classifier trained with supervision, or some clustering algorithm. + +Broader impact. The capabilities of supervised CL agents are bounded by the need for human-produced annotations. CSSL models can potentially improve without the need for human supervision. This facilitates the creation of powerful AIs that may be used for malicious purposes such as discrimination and surveillance. Also, since in CSSL the data is supposed to come from a non-curated stream, the model may be affected by biases in the data. This is problematic because biases are then transferred to downstream tasks. + +Acknowledgements. This work was supported by the European Institute of Innovation & Technology (EIT) and the H2020 EU project SPRING, funded by the European Comission under GA 871245. It was carried out under the "Vision and Learning joint Laboratory" between FBK and UNITN. Karteek Alahari was funded by the ANR grant AVENUE (ANR-18-CE23-0011). Julien Mairal was funded by the ERC grant number 714381 (SOLARIS project) and by ANR 3IA MIAI@Grenoble Alpes (ANR-19-P3IA-0003). Xavier Alameda-Pineda was funded by the ARN grant ML3RI (ANR-19-CE33-0008-01). This project was granted access to the HPC resources of IDRIS under the allocation 2021-[AD011013084] made by GENCI. + +# References + +[1] Alessandro Achille, Tom Eccles, Loic Matthey, Christopher P Burgess, Nick Watters, Alexander Lerchner, and Irina Higgins. Life-long disentangled representation learning with cross-domain latent homologies. NeurIPS, 2018. 2, 6 +[2] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In ECCV, 2018. 2 +[3] Adrien Bardes, Jean Ponce, and Yann LeCun. 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In ICML, 2017. 2 \ No newline at end of file diff --git a/selfsupervisedmodelsarecontinuallearners/images.zip b/selfsupervisedmodelsarecontinuallearners/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a02f0467acdccab815b8331df15887f508ef448f --- /dev/null +++ b/selfsupervisedmodelsarecontinuallearners/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:829561901e490fc826fc2ff9931f218b71b6a157e698556a61a13466fb58891d +size 375028 diff --git a/selfsupervisedmodelsarecontinuallearners/layout.json b/selfsupervisedmodelsarecontinuallearners/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..54606a7abcf84e7e615a65489f9089bc05671f01 --- /dev/null +++ b/selfsupervisedmodelsarecontinuallearners/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cf97d38dc2faa346c8b95198c13add9e33f40ecfb37817b2b1bd001ba094a0e2 +size 416121 diff --git a/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_content_list.json b/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..13917e1781b28382ebe6f62439adc3d8848d9cca --- /dev/null +++ b/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e6e34021b479ad4aa1d6df2dfc9c040e2c238485a32fb7aa094abffee64b9a83 +size 90395 diff --git a/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_model.json b/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b94d1c5ca035b79fff9561222686faf2f28ca127 --- /dev/null +++ b/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7a3fb6d5fd91f63dba4c2e41fde3f2b919d4f4d36ffbfa49984388d5c9497a78 +size 111588 diff --git a/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_origin.pdf b/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e37eea78d26a3ce4a73f74b47ce6fc0818279920 --- /dev/null +++ b/selfsupervisedneuralarticulatedshapeandappearancemodels/4053f341-cd9e-4477-9f7c-ea2c6460fd9a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:03acc7f81be141e02aa09dc2baf5fbbdac11eac8c3523785db0b0408ef4a293b +size 8306809 diff --git a/selfsupervisedneuralarticulatedshapeandappearancemodels/full.md b/selfsupervisedneuralarticulatedshapeandappearancemodels/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8ade28cd680e453b3cce5a14e4733ea5d149ffc5 --- /dev/null +++ b/selfsupervisedneuralarticulatedshapeandappearancemodels/full.md @@ -0,0 +1,364 @@ +# Self-supervised Neural Articulated Shape and Appearance Models + +Fangyin Wei $^{1*}$ + +Szymon Rusinkiewicz1 + +Rohan Chabra + +$\mathbf{ra}^2$ Lingni $\mathbf{Ma}^2$ + +Chris Sweeney + +Christoph Lassner + +Richard Newcombe + +Michael Zollhoefer + +Mira Slavcheva2 + +$^{1}$ Princeton University + +$^{2}$ Reality Labs Research + +![](images/7846e7ca06b0d6af5552cb7261817d9054d489f4b024cfb81395c8d69a13ab64.jpg) + +![](images/1484432d69cad053f155a304828d6d94c98978839150a2758bcf9674a079e71a.jpg) +Figure 1. Our self-supervised method learns the shape and appearance of articulated object classes. After training from multi-view synthetic images of different states of object instances, our model can reconstruct and animate objects from static real-world images. Left: input real views of a static object. Middle: 3D reconstruction with shape and color. Right: animation driven by the learned articulation codes. + +![](images/90cc94edd1c0433263b83bb50f4be222d58382d870788dd8297e7e029727971c.jpg) + +![](images/0dcfeadddaa98bcf23f46430a142d2b29da0afe480f36aa5ab6331f8d0898861.jpg) + +![](images/d7586e71ebf6284468305072e5a91da25d508b5b086d3956c75b6eff61ff7953.jpg) + +![](images/2abdf44f641c3969ded806f5dd2cd7c836df1c7f47b24a2f667f9d137df0d6fe.jpg) + +![](images/f8fd8ced7a6e179ff9d83a158e357c1248879e9b9cd4836e3bf061b0d85dd2a0.jpg) + +![](images/b9e72bbbe8797157c503b3077e5f8019f03b90aef1b24f3763c62b0ebd5042e3.jpg) + +![](images/8c5bae9b2cf70f72a33794b9117ecb41ff63a494fbba0969d1fe54b2c0d20a17.jpg) + +![](images/161806750021e29eb3975d1ab75e6b4c61a330a14548cec8a1b8081d4373a97d.jpg) + +![](images/c53e163ded7c0fb43c236e5b586e8d68192f4d7f730008431d6a8e8dc4f0e958.jpg) + +![](images/8a9b0bd0edf7438ca50d88acaaa78c4c814ce26b22759e7d1292abf0720ab8dc.jpg) + +![](images/8728a520716cd64717f4174f9cedab7cd0657ed34eafe29be519391603589c30.jpg) + +![](images/ac84fd4b09809066be689cff8d667df611653b0cd6687f13903d217e4e6706fa.jpg) + +![](images/8d7a965f1f2d186bf27dc9712dc2e151756aad78575f0860811b9a74808d0d27.jpg) + +![](images/237fb25cfc29a707e5c67c90b0464acefc0d324be6ee2c6089a386d3752f91d1.jpg) + +![](images/fd2bb6811e7986376c50ff237d4a7ba8cc12667a27701684f1c5401d60e8d050.jpg) + +![](images/9f0da5a29288355d3a4bddf931ea64d0b0fb8d22787c1ee388ea421169da5fce.jpg) + +# Abstract + +Learning geometry, motion, and appearance priors of object classes is important for the solution of a large variety of computer vision problems. While the majority of approaches has focused on static objects, dynamic objects, especially with controllable articulation, are less explored. We propose a novel approach for learning a representation of the geometry, appearance, and motion of a class of articulated objects given only a set of color images as input. In a self-supervised manner, our novel representation learns shape, appearance, and articulation codes that enable independent control of these semantic dimensions. Our model is trained end-to-end without requiring any articulation annotations. Experiments show that our approach performs well for different joint types, such as revolute and prismatic joints, as well as different combinations of these joints. Compared to state of the art that uses direct 3D supervision and does not output appearance, we recover more faithful geometry and appearance from 2D observations only. In addition, our representation enables a large variety of applications, such as few-shot reconstruction, the generation of novel articulations, and novel view-synthesis. Project page: https://weify627.github.io/nasam/. + +# 1. Introduction + +Reconstructing articulated 3D objects from image observations in terms of their underlying geometry, kinemat- + +ics, and appearance is one of the fundamental problems of computer vision with many important applications, e.g. in robotics and augmented/virtual reality. This inverse graphics problem is highly challenging and of underconstrained nature, since image formation, i.e., mapping from the 3D world to discrete 2D pixel measurements, tightly entangles all visible properties of an object—and finding non-visible properties, such as kinematics, requires additional information such as information over time. + +Most approaches that tackle this inverse problem rely on object/class-specific priors learned from large datasets with available 3D ground truth, which are challenging and expensive to collect. The learned manifold of shape, appearance, and motion is often encoded via a low-dimensional latent space. In the devised approaches, this learned low-dimensional prior is then used to better constrain the inverse reconstruction problem. + +The majority of previous techniques in the literature has focused on reconstructing classes of static objects; dynamic objects, especially with controllable articulation, are less explored. For example, occupancy networks condition the decision boundary of a neural classifier on a shape code to represent a class of static objects [32]. Approaches such as DeepSDF follow a similar principle, but employ a learned continuous signed distance field (SDF) [41] to model the object's surface implicitly as the zero level-set of a coordinate-based neural network. DISN [59] further improves this technique and can recover more details. All the mentioned approaches require dense 3D ground truth geometry for training and do not model object appearance. One exception is IDR [70] which employs inverse differ + +entiable rendering to reconstruct the shape (using an SDF) and view-dependent appearance of a single object, but this approach does not generalize to an entire object class. + +Prior work on articulated deformations heavily focuses on humans and animals [9,22,31,34,39,49,67,72] due to the availability of large datasets and readily available (learned) priors. One exception is the A-SDF [36] technique which is focused on general articulated objects. It learns separate codes for shape and articulation and employs an SDF for representing the objects. This approach learns a geometry prior across a class of articulated objects but does not jointly learn an appearance prior. Additionally, it requires dense 3D ground truth for training. We provide comparisons with A-SDF in our experiments. + +Looking at these related works in context raises the question: Is it possible to jointly learn a prior over the 3D geometry, kinematics, and appearance over an entire class of articulated objects from only photometric 2D observations without requiring access to 3D ground truth? + +We propose a novel approach for learning the geometry, kinematics, and appearance manifold of a class of articulated objects given only a set of color images as input. Our novel 3D representation of articulated objects is learned in a self-supervised manner from only color observations without the need for explicit geometry supervision. It enables independent control of the learned semantic dimensions. Our model is trained end-to-end without requiring any articulation annotations. Experiments show that our approach performs well on both of the most widespread joint types: revolute and prismatic joints, as well as combinations thereof. We outperform the state of the art, even though these related approaches require access to ground truth geometry for explicit geometry supervision. In addition, our approach handles a larger variety of joint types than A-SDF [36]. Furthermore, our representation enables various applications, such as few-shot reconstruction, the generation of novel articulations, and novel view-synthesis. In summary, our contributions are: + +- A novel approach that learns a representation of the geometry, appearance, and kinematics of a class of articulated objects with only a set of color images as input. +- We introduce an embedding space for geometry, kinematics, and view-dependent appearance that enables a large variety of applications, such as the generation of new articulations and novel view synthesis. +- Our model, trained only on synthetic data, enables few-shot reconstruction of real-world articulated objects via fine-tuning, as shown in Fig. 1. + +# 2. Related Work + +Articulated Object Modeling. In robotics, research on articulated objects focuses on kinematic models [1, 21, 47]. + +In the vision community, prior work on articulated deformations heavily focuses on humans and animals [9, 22, 31, 34, 39, 49, 67, 72]. Less explored is how to represent general objects with piece-wise rigidity. Following the success of neural implicit representations, A-SDF [36] extends DeepSDF [41] with separate shape and articulation codes to model category-level articulation. By adding joint angles to the shape code, A-SDF learns a mapping to the corresponding deformed shape. Instead of using known joint angles and dense 3D supervision as in A-SDF, we learn the articulation codes without the ground-truth labeling and only from images. Li et al., [25] propose the normalized articulated object coordinate space (NAOCS) as a canonical representation for category-level articulated objects. This idea is further explored by CAPTRA [61] to track object articulation from point clouds, and adopted by StrobeNet [71] to reconstruct articulated objects by first aggregating NAOCS predictions from multi-view color observations. However, the reconstruction only provides geometry. Recently, LASR [68] proposes a template-free approach to reconstructing articulated shapes from monocular video. The algorithm jointly estimates the rest pose, skinning, articulation, and camera intrinsics by solving an inverse graphics problem resulting in coarse animatable meshes. + +Deformation Fields for Shape Reconstruction. Shape deformation deals with deforming a shape to best fit a set of observations. DynamicFusion [37] relied on local depth correspondences, follow-up methods used sparse SIFT features [20], dense color tracking [16] or dense SDF alignment [53,54]. Such methods are subject to failure under fast motion due to the use of handcrafted functions for maintaining correspondences. Recently, the performance of non-rigid tracking has been improved by data-driven approaches with learned correspondences [4, 5, 26]. Lately, there has been an exploration of neural generative models for shape deformation. DIF [10] represents shapes by a template implicit field shared across the category, together with a 3D deformation field and a correction field dedicated to each shape instance. FiG-NeRF [65] approximates neural radiance fields of objects and simultaneously performs foreground/background separation. NPMs [40] is a neural parametric model that learns latent shape and pose spaces to model 3D deformable shapes. Unlike most of the above methods, we approximate geometry and view-dependent appearance of the shape. without any 3D supervision. + +Neural Representations for Geometry. Neural scene representations have been found compact and powerful to model the geometry and motion of objects [24, 42]. Implicit fields [7] use an implicit coordinate-based function and a latent code to model multiple object classes. Local Deep Implicit Functions [14] decompose space into a structured set of learned implicit functions to represent deformable shapes. Occupancy networks [32] use a local neural classi- + +fer to represent objects. Approaches such as DeepSDF [41] follow a similar idea, but employ an SDF. DISN [59] further improves this technique and can recover more details. Local implicit grid representations [6, 8] decompose a scene into local parts for which it learns implicit representations. All of these methods only model the geometry of rigid objects. + +Neural Representations for Appearance. Neural Radiance Fields (NeRF) model the appearance of static scenes via a coordinate-based scene representation [35]. Scene Representation Networks [52] map world coordinates to a feature representation that can be translated to a rendering. Differentiable Volumetric Rendering [38] predicts a texture field. Proxy-geometry, such as spheres or points can be used to speed up the rendering process [50,58]. Point-based representations have been explored independently for view synthesis as well [2, 23, 62]. Neural Volumes breaks down the space into separate volumes with their own neural representations [29] and can model dynamic scenes. For an in-depth discussion of recent neural rendering approaches, we refer to a recent survey [56]. + +Neural Representations for Motion. A hallmark feature of dynamic scenes is that they can be analyzed using flow fields, and these in turn can be used to represent them [11, 27]. There are several works that build on top of neural radiance fields to capture scenes in motion [3, 13, 24, 43, 44, 46, 48, 63]. However, they do not allow to control the scene rendering. Tretschk et al. [57] allow to strengthen or weaken foreground motion. All of the aforementioned works in this paragraph do not allow to control the resulting reconstruction. Most prior work on controllable representations is around humans, for facial avatars [12, 17, 30, 60] or human bodies [19, 28, 39, 45, 55, 66]. LASR [68] is a very general method that creates meshes for arbitrary objects. It then provides a rigged model with an estimated skeleton to animate the object, however with very coarse results. D-NeRF [48] approximates the radiance field of a deforming shape by using time as an input to the system but only works for a single scene. + +# 3. Method + +Our goal is to build a representation that models the geometry and appearance of a class of articulated objects from RGB images without geometry priors. This representation must enable reconstructing unseen shapes and generating new articulations. To this end, we utilize a differentiable rendering system with implicit neural representations and learn a category-level embedding space with disentangled shape, appearance, and articulation representations. To enforce the disentanglement, different articulations of the same instance share the same shape code. The geometry is predicted by deforming a canonical shape conditioned on a learned articulation code. Without any joint annotations, + +the model is able to learn a continuous space for articulation that allows for generating new articulations. + +We define an 'articulated object' as an object which consists of several rigid parts connected by joints. We define further an articulation of an articulated object as a specific state of its joints (e.g., a laptop with joint angles $40^{\circ}$ and $90^{\circ}$ are two distinct articulations). An object with a specific articulation is modeled by a representation set $(\theta, \phi, \psi)$ where $\theta \in \mathbb{R}^m, \phi \in \mathbb{R}^n, \psi \in \mathbb{R}^q$ are the code for geometry, appearance, and articulation, respectively. In this section, we first review our backbone differentiable renderer and introduce a category-level embedding space (Sec. 3.1). Then we describe how to enforce disentanglement and the deformation field prediction (Sec. 3.2). In Sec. 3.3, we summarize the entire framework for training and inference. + +# 3.1. Differentiable Renderer with Category Priors + +We opt for Implicit Differentiable Renderer (IDR) [70] as the backbone differentiable renderer. While it originally works for a single object, we extend it to learn category-level geometry and appearance embedding. IDR is an end-to-end neural system that can learns 3D geometry, appearance, and camera extrinsics from masked 2D images and noisy camera pose initializations. There are three unknowns in IDR [70]: geometry with learnable parameters $\Theta \in \mathbb{R}^r$ , appearance with learnable parameters $\Phi \in \mathbb{R}^s$ , and camera extrinsics $\tau \in \mathbb{R}^k$ . The geometry is represented as + +$$ +\mathcal {S} _ {\Theta} = \{x \in \mathbb {R} ^ {3} | f (x; \Theta) = 0 \}, \tag {1} +$$ + +where $f$ models the signed distance function (SDF) to its zero level set $S_{\Theta}$ (i.e. the object's surface) [70]. Given a pixel indexed by $p$ , the rendered color of the pixel is + +$$ +L _ {p} (\Theta , \Phi , \tau) = M \left(\hat {x} _ {p}, \hat {n} _ {p}, v _ {p}; \Phi\right), \tag {2} +$$ + +where $L_{p}$ is the surface light field radiance and $\hat{x}_p = \hat{x}_p(\Theta, \tau)$ denotes the first intersection of the ray $R_p$ and the surface $S_\Theta$ with the corresponding surface normal $\hat{n}_p = \hat{n}_p(\Theta)$ and the viewing direction $v_p$ . Both $f$ and $M$ are approximated by MLPs. + +In the original IDR [70], each trained model only works for a single scene or object instance. We extend it to work across an entire class of objects by introducing additional embedding space. For each object instance $i$ from a class, we learn a geometry code $\theta_{i} \in \mathbb{R}^{m}$ and an appearance code $\phi_{i} \in \mathbb{R}^{n}$ . During the learning process, all objects from the same category share the same geometry ( $\Theta$ ) and appearance ( $\Phi$ ) parameters. The new geometry and light field functions for object $i$ become: + +$$ +\mathcal {S} _ {\Theta} = \{x \in \mathbb {R} ^ {3} | f (x, \theta_ {i}; \Theta) = 0 \}, \tag {3} +$$ + +$$ +L _ {p} (\Theta , \Phi , \tau , \theta_ {i}, \phi_ {i}) = M (\hat {x} _ {p}, \hat {n} _ {p}, v _ {p}, \phi_ {i}; \Phi). \tag {4} +$$ + +![](images/5f35d2e111cf8bf329aa391e877d9290c7f01daedc02b03cbdb465e86b8d61d4.jpg) +Figure 2. Framework overview. Each object $i$ with articulation state $j$ is represented as $(\theta_i, \phi_i, \psi_j)$ , where each parameter encodes geometry, appearance, and articulation, respectively. A deformation network takes in the shape and articulation code in addition to query 3D locations (computed given camera parameters) to predict the displacement of the location. The displaced locations and the shape code pass through a geometry network to predict the geometry of the canonical pose shape. In the case of no deformation MLP, the geometry network directly takes in the 3D location, shape code and articulation code. For the predicted geometry and given appearance code, an appearance network outputs an image according to input camera parameters. + +Leveraging the category-level prior embedded in $\Theta$ and $\Phi$ allows to reconstruct unseen objects from the same category by recovering only their geometry and appearance codes. + +# 3.2. Code Sharing and Deformation Field + +To encode the articulation, we further introduce an articulation code. For a category with $M$ training objects and $N$ sampled articulation states for each object, let shape $\mathcal{X}_{ij}$ denote an articulated object $i$ from a specific category with articulation state $j$ . We jointly learn the representation $(\theta_{ij},\phi_{ij},\psi_{ij})$ . Note that when articulations across different objects are aligned, we can further enforce disentanglement by having all objects from the same category share the same set of articulation codes and all articulation states of the same object share the same object code. Therefore, the representation for shape $\mathcal{X}_{ij}$ becomes $(\theta_i,\phi_i,\psi_j)$ , as illustrated in Fig. 2. + +One observation is that geometry change happens both when articulating the same object and between different object identities. Learning to generate shapes by simultaneously processing the object identity and articulation state information may cause unwanted interference. Therefore, we split the shape prediction module into two parts: a geometry network $S$ with parameters $\Theta \in \mathbb{R}^r$ and an (optional) deformation network $\mathcal{D}$ with parameters $\Psi \in \mathbb{R}^t$ . The former predicts the geometry of a canonical shape for each object given its shape code and is articulation-invariant. Conditional on a shape and articulation code that describes an articulated shape, the deformation network predicts a displacement of the query point to transform the query into the canonical space [43, 44, 57]. So the new geometry prediction flow is + +$$ +x ^ {\prime} = x + \mathcal {D} _ {\Psi} (x, \theta_ {i}, \psi_ {j}; \Psi), \tag {5} +$$ + +$$ +\mathcal {S} _ {\Theta} = \left\{x ^ {\prime} \in \mathbb {R} ^ {3} \mid f \left(x ^ {\prime}, \theta_ {i}; \Theta\right) = 0 \right\}. \tag {6} +$$ + +This separation of articulation prediction from the canonical shape helps further disentangle object identity and articulation state. + +# 3.3. Training and Inference + +During training, given camera intrinsic and extrinsic parameters and masked multi-view images, the model is trained to optimize both the latent embeddings $(\theta_{i},\phi_{i},\psi_{j})$ and network weights $(\Theta ,\Phi)$ . As shown in Fig. 2, each object $i$ with articulation state $j$ is represented as $(\theta_{i},\phi_{i},\psi_{j})$ where each parameter encodes geometry, appearance, and articulation, respectively. A deformation network takes in the shape and articulation code in addition to query 3D locations (computed given camera parameters) to predict the displacement of the location. The displaced locations and the shape code pass through a geometry network to predict the geometry of the canonical pose shape. For the predicted geometry and given appearance code, an appearance network outputs an image according to input camera parameters. Let $I_{p}\in [0,1]^{3},O_{p}\in \{0,1\}$ be the RGB and mask values respectively for a pixel $p$ in an image taken with camera $c_{p}(\tau)$ and direction $v_{p}(\tau)$ $(p\in \bar{P}$ indexes all pixels in the input collection of images), and $\tau$ represents the parameters of all the cameras in scene. The overall loss function has the form: + +$$ +\mathcal {L} (\Theta , \Phi , \tau , \left\{\theta_ {i} \right\}, \left\{\phi_ {i} \right\}, \left\{\psi_ {j} \right\}) = +$$ + +$$ +L _ {R G B} + \rho L _ {\text {m a s k}} + \lambda L _ {E} + \beta L _ {\text {c o d e}}. \tag {7} +$$ + +We train on mini-batches of $P \subset \bar{P}$ pixels sampled from one view of shape $\mathcal{X}_{ij}$ following IDR [70]. The RGB loss is computed over regions where intersection has been found between the surface $S_{\times}$ and Ray $R_{p}$ (i.e., $c_{p} + t_{p,0}v_{p}$ for $O_{p} = 1$ ): + +$$ +L _ {R G B} = \frac {1}{| P |} \sum_ {O _ {p} = 1} \left| I _ {p} - L _ {p} \left(\Theta , \Phi , \tau , \theta_ {i}, \phi_ {i}, \psi_ {j}\right) \right|, \tag {8} +$$ + +where $|\cdot|$ is $L_{1}$ norm and $L_{p}$ is defined in Eq. 4. The mask loss is + +$$ +L _ {\text {m a s k}} = \frac {1}{\alpha | P |} \sum_ {O _ {p} = 0} C E \left(O _ {p}, S _ {p, \alpha} (\Theta , \tau , \theta_ {i}, \psi_ {j}), \quad (9) \right. +$$ + +where $CE$ is the cross-entropy loss and $S_{p,\alpha} = \mathrm{sigmoid}(-\alpha \min_{t\leq 0}f(c + tv,\theta_i;\Theta))$ is an almost-everywheredifferentiable approximation to an indicator function for an object-occupied pixel $p$ [70]. We enforce $f$ to be approximately a signed distance function with the Eikonal regularization following Implicit Geometric Regularization (IGR) [15]: + +$$ +L _ {E} (\Theta) = \mathbb {E} _ {x} \left(\| \nabla_ {x} f (x, \theta_ {i}, \psi_ {j}; \Theta) \| - 1\right) ^ {2}, \tag {10} +$$ + +where $x$ is distributed uniformly in a bounding box of the scene. Lastly, following [42], we include a zero-mean multivariate Gaussian prior per latent code to facilitate learning a continuous shape manifold: + +$$ +L _ {c o d e} \left(\theta_ {i}, \phi_ {i}, \psi_ {j}\right) = \| \theta_ {i} \| _ {2} ^ {2} + \| \phi \| _ {2} ^ {2} + \| \psi_ {j} \| _ {2} ^ {2}. \tag {11} +$$ + +The goal during inference is to recover the representation $(\theta_{i},\phi_{i},\psi_{j})$ given the RGB images of an unseen object. The three codes are randomly initialized, and then optimized through backpropagation with the following objective: + +$$ +\hat {\theta} _ {i}, \hat {\phi} _ {i}, \hat {\psi} _ {j} = \underset {\theta_ {i}, \phi_ {i}, \psi_ {j}} {\arg \min } \mathcal {L} (\Theta , \Phi , \tau , \theta_ {i}, \phi_ {i}, \psi_ {j}). \tag {12} +$$ + +During optimization we can either fix the network weights (for in-distribution testing) or jointly optimize the network weights (for out-of-distribution testing). + +# 4. Experiments + +# 4.1. Experiment Setup + +Dataset All experiments use SAPIEN [64], a large-scale, public domain data set containing 2346 articulated objects across 46 categories. We select six categories with representative articulation types and a sufficient number of instances: laptop, stapler, dishwasher, two-door fridge (LR for left and right, UD for up and down), eyeglasses, and storage furniture with drawer(s) (and door). We use the SAPIEN simulation environment [64] to render RGB images and corresponding masks. During training and testing, we sample every $10^{\circ}$ for rotational joints and 10 states in total for sliding joints. For multiple joints, we take all combinations of each single joint sampling. For each articulation, 60 views are sampled for training and 6 views for inference. Please refer to supplementary materials for further details. + +Evaluation Metrics We evaluate both the geometry and appearance of the predicted shape. For geometry, we sample 30,000 points per shape [36, 42] and evaluate the Chamfer-L1 distance, which is the mean of the accuracy and the completeness score [33]. For evaluating the rendered appearance, we report the Peak Signal-to-noise Ratio (PSNR). All visualizations in this paper are rendered from unseen views. Training and Inference For training, latent codes are randomly initialized with $\mathcal{N}(0,\frac{1}{l})$ , where $l$ is the code length. + +Table 1. Methods used in experiments. We specify whether they: handle static or articulated objects; share articulation code; use deformation field; output appearance or only geometry. We list the necessary input at train and test time. SDFs means SDF samples. + +
Method nameart./ staticshare art.deform. fieldtrain inputtest inputappear ance
A-SDFart.✓×SDFsSDFs×
IDR 6 viewsstatic××6 RGBs6 RGBs✓
IDR 60 viewsstatic××60 RGBs6 RGBs✓
Ours-baseart.××60 RGBs6 RGBs✓
Ours-Artart.✓×60 RGBs6 RGBs✓
Ours-Defart.×✓60 RGBs6 RGBs✓
Ours-ArtDefart.✓✓60 RGBs6 RGBs✓
+ +We set $\rho = 100, \lambda = 0.1, \beta = 0.0001$ for the loss in Eq. 7. We start with $\alpha = 50$ and multiply it by a factor of 2 every 50,000 iterations (up to a total of 5 multiplications). During inference, articulation codes are initialized to the mean of all learned articulation codes, while other codes are initialized as in training. We run 600 iterations to recover the latent codes; if we do test-time adaptation [36], we fine-tune both, model weights and codes, for another 600 iterations. + +Baseline Methods The method variants that we compare are listed in Tab. 1. For A-SDF [36], we sample SDF values from SAPIEN data as described in [36] and run the author-provided code. For IDR [70], we use our own implementation in PyTorch which follows the original work, but without the global lighting feature: the SAPIEN dataset does not provide such effects and we empirically found this does not influence the result. Each method may additionally use test-time adaptation (TTA), as described in [36], which in addition to optimizing the latent codes, optimizes the network weights during inference. + +# 4.2. Reconstruction + +To reconstruct unseen testing objects, we first optimize the codes (optionally with network weights) through backpropagation. Then we run another forward pass to extract the mesh and render images. In Tab. 2 and Tab. 3, we compare both geometry and appearance with previous methods for 9 object categories, respectively. We report the scores of our full model with articulation code sharing and using deformation field, with and without TTA. Please refer to the supplementary materials for a full list of results of each variant of our method. For reference, we also compare with two IDR models. Note that IDR does not have an embedding space to encode categorical priors and can only reconstruct a single static object or scene that it has been trained on, i.e. for IDR we train and test on the same object instances, one model per articulation state. Since this is too computationally expensive, we randomly choose two objects with two articulations in each category and report the average PSNR as the PSNR on each category for IDR. Our model is trained on 60 views per articulation and tested on 6 views per artic + +Table 2. Comparison for reconstructing unseen synthetic shapes (Chamfer-L1). We compare our method with A-SDF [36] and IDR [70]. As training IDR for each object is too computationally expensive, we present the average across 2 articulation states for 2 objects from each category. IDR is tested on the same objects it is trained on. Please note that our method uses 60 views for training and 6 views for inference. A-SDF* indicates A-SDF results compared to the geometry it trains on, while all other results use a sampling of the original geometry as ground truth. Lower score is better. + +
MethodLaptopStaplerDishwasherEyeglassesFridgeLRFridgeUDDrawerDrawerUDDrawer+Door
A-SDF*0.1261.5100.54315.9720.5990.8371.3624.7912.282
A-SDF TTA*0.1030.9780.2097.7921.6824.6231.1422.8320.476
A-SDF0.5806.0584.18017.2981.5271.4271.9716.0482.945
A-SDF TTA0.5425.3583.7569.0521.3510.8421.6894.1391.082
IDR 6 views1.6561.1134.1391.3867.9151.8264.202fails12.672
IDR 60 views0.2590.9943.1061.17112.3682.1193.0477.87113.491
Ours-ArtDef0.3821.1253.9459.7902.7383.6482.6275.9793.264
Ours-ArtDef TTA0.3550.9363.9367.8942.0633.6492.7455.9123.243
+ +Table 3. Comparison with IDR [70] for reconstructing unseen synthetic shapes (PSNR). The training and inference procedures of IDR and our methods are the same as in Tab. 2. Note that IDR trains a separate model for each articulation state of each object instance, it is trained on 60 views and then tested on 6 novel views of the same object, i.e. it trains and tests on the same instances, while our method is trained per category and is tested on unseen objects. IDR 60 views is trained on 60 views and tested on 6 novel views, offering an upper bound for the quality we can expect from our method. Higher score is better. + +
MethodLaptopStaplerDishwasherEyeglassesFridgeLRFridgeUDDrawerDrawerUDDrawer+Door
IDR 6 views13.329.7517.6411.4910.8113.4715.26fails15.80
IDR 60 views20.7022.4024.1026.5920.0123.4924.3221.1922.71
Ours-ArtDef18.3317.1820.7920.6918.7923.7224.6522.2523.34
Ours-ArtDef TTA17.8418.1520.8720.8918.9423.5224.2722.2023.96
+ +ulation for unseen objects, while IDR is trained on 60 or 6 views for one static object and tested on novel views of the same object with the same articulation. Therefore, IDR trained on 60 views gives us a sense of the upper bound performance of our differentiable rendering system. + +Note that meshes in the dataset are not watertight, so A-SDF processes them with the Manifold [18] software in order to be able to sample SDF values, which does a resampling that leads to a thickening of the original meshes. In A-SDF [36] output geometry is evaluated against those thickened meshes that were used for training, rather than the original geometry, so we follow the same evaluation protocol and report it as A-SDF* in Tab. 2, achieving comparable numbers to the original paper. All other method variants are evaluated with respect to a sampling of the original geometry, which may sometimes contain points sampled from hidden, internal structures, such as the bottom of a laptop's trackpad, but the fraction of these points is small. + +We can see that despite being used on a harder task, our model performs on par with 60-view IDR on many categories such as furniture. On other categories, our PSNR is significantly lower. This is, because these categories tend to have higher frequency texture. To show the benefit of the learned categorical prior introduced in our model, we further compare with an IDR model trained on 6 views. Eventually, we would like to have a model that works nicely on unseen objects with only very limited observations. This brings up the question: should we model the object by over + +fitting an IDR model with very few views or leveraging categorical priors—which is better? The comparison between our method and 6-view IDR in Tab. 3 and Tab. 2 clearly shows that by introducing a shape, articulation, and appearance prior, our model during inference significantly improves over an overfitted IDR with same number of views. We observe through visualization that our variants with deformation field performs better than without it when articulations involve topology change (e.g., a closed laptop being opened). And sometimes TTA may result in overfitting to appearance and makes the geometry prediction worse. + +We visualize the testing results from unseen views in Fig. 3 and compare with A-SDF (with TTA). All models are trained with shared articulations and after testing time optimization. The first two rows are single rotational joints followed by three rows of multi-joint categories with various joint type combinations. We can see that for classes with small intra-class geometry variation such as laptop and dishwasher, A-SDF works well, which is also consistent with observations from Tab. 2. However, for classes with larger intra-class shape variations such as staplers and eyeglasses, A-SDF fails to capture the geometry details. For example, for A-SDF, the geometry of the bottom part of both staplers are not correct, despite being directly optimized with 3D geometry during inference. While A-SDF originally only shows results on rotational joints, we further test both methods on other joint types. We can see that the performance of A-SDF on sliding joints is much worse + +![](images/e0685b38497f0444f65902f929832459ac9bf8011af6a4dde770f2c3bc09abfa.jpg) +Figure 3. Reconstruction results from unseen data. We compare to A-SDF on various joint types and combinations, including revolute, prismatic and multiple ones. While A-SDF trains using both geometry and articulation ground truth and only predicts geometry, our method also faithfully recovers appearance in addition to producing better geometry and more accurate articulations from only RGB supervision. + +![](images/98f0961914c42638266c80dc118b2fff408f311d0ae39a1b20a37c2919b0be56.jpg) + +than on rotational joints. We reckon one reason is that A-SDF requires articulation ground truth input during training. However, for drawers with different lengths, it is hard to define a single value shared across all objects. In contrast, our method does not require articulation annotation and learns the articulation code through training. Please refer to the supplementary material for more results. + +# 4.3. Analysis + +Interpolation and Extrapolation One application of the proposed method is to generate new articulations of an object through interpolation and extrapolation, given only a few training articulations. To do so, we render a few images for two articulations, and optimize their shape, articulation, and appearance codes jointly with the images. After the two sets of codes are estimated, we interpolate/extrapolate a set of shape, articulation and appearance codes. This procedure follows what is done in A-SDF [36], to which we compare in Fig. 4 for different joint types and combinations. We run the two fastest variants of our method for this, i.e. those without deformation field. Note that there is no TTA for either method as the two estimated code sets which are being interpolated need to share the same network weights. We see that A-SDF may fail on extrapolations more than $6^{\circ}$ out of the training range for laptop and extrapolations for other classes, while our method is able to recover plau + +sible shapes. The quantitative results in Tab. 4 demonstrate that our interpolated models are geometrically more accurate than those of A-SDF for the majority of object categories. + +Disentangling Geometry and Appearance. The separate geometry and appearance networks strongly enforce disentanglement, as inherited from IDR [70]. One application of our method is to switch the geometry and appearance codes between different objects. As shown in Fig. 5, by replacing the appearance code with one from another pair of eyeglasses, we can faithfully create a new pair of eyeglasses that has a new appearance but the same geometry. Note how the colors from the thin frame correctly map onto the frame of the new eyeglasses, despite the large geometry difference between the shapes. Our learned embedding space that encodes categorical prior also helps with the correct mapping. + +# 4.4. Testing on Real-world RGB Images + +Since our method only uses images for supervision and does not require any 3D annotations that may be expensive, it can be easily set up to test on real data. In this section, we directly test our proposed method (trained from synthetic data) on images captured in the real world. We use a personal cell phone to record a static opened laptop or drawer with fixed focal length and exposure. We then run Structure-from-Motion (SfM) algorithm [51] on + +Table 4. Interpolation Chamfer-L1 error. Evaluation details are the same as in Tab. 2. Lower score is better. + +
MethodLaptopStaplerDishwasherEyeglassesFridgeLRFridgeUDDrawerDrawerUDDrawer+Door
A-SDF*0.3594.9892.10145.3261.4451.6771.6346.0674.454
A-SDF0.6105.9184.74443.7081.7081.8811.9587.1055.032
Ours-base0.3471.4863.0292.6323.0684.7232.9525.1953.226
Ours-Art0.3091.7162.8072.5883.8603.3573.0864.1513.845
+ +![](images/bca2da5730bb25448da6b655196c5b9d101339765f5b3c70d1166e2fbf18938a.jpg) +Figure 4. Interpolation and extrapolation comparison. For these unseen objects, we first infer the geometry, appearance and articulation codes for multiple testing states, then we interpolate / extrapolate the inferred codes to generate new articulations. The proposed method successfully generates shapes with articulations beyond the range seen during training for various joint types. + +![](images/addb3960a3434f1c12be949ceb9186b39c40cbc187be32faf3dd5922f15b8288.jpg) +Figure 5. Disentangling shape and appearance for shape synthesis. + +the captured frames to estimate the camera calibration parameters and their poses. For each view, we then run https://remove.bg to estimate a segmentation mask for the foreground object. The views shown in Fig. 1 are the input images to our model. We test our model trained on synthetic data from SAPIEN with deformation field and shared articulation code on these real-world images. The shape, articulation, and appearance codes are initialized as described earlier, we then jointly fine-tune both network weights and + +codes on these images for 2000 iterations. At this point, we are able to reconstruct the static real objects. Then by replacing the inferred articulation code with the articulation codes learned during training, we are able to articulate the static reconstruction realistically. + +# 4.5. Limitations + +While we push the boundaries for articulated shape reconstruction by removing limitations on required data and supervision compared to previous methods, remaining limitations exist. Even though we are able to fine-tune our object models on real data, the domain gap from synthetic to real remains large, and the appearance prior we learn from the limited synthetic data is not powerful enough to explain general object appearance. As a consequence, we make use of foreground masks to alleviate this problem. A more elegant direction for future work could be to follow the example of VolSDF [69] and extend the method towards unsupervised disentanglement of shape and appearance. Another limitation is the current scaling behavior w.r.t. the number of joints: for modeling objects with $n$ joints with $m$ states, we need $m^n$ combinations. This is only feasible for objects with a low number of joints. Better joint priors and decoupling are interesting directions for future research. + +# 5. Conclusion + +In this paper, we set out to answer the research question whether it is possible to jointly learn a prior over the 3D geometry, articulation, and appearance of an entire class of objects, solely from photometric 2D observations, with no articulation annotations. Our results show that this is not only possible but, given enough computational power, can be achieved with high fidelity and with remarkably little data. In our experiments, we successfully fine-tune our model to real-world data using only 6 views and create animatable objects that closely resemble the real-world objects under articulations, interpolated, and extrapolated. At the same time, our method is the first that not only handles revolute, but also prismatic joints and combinations thereof. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5524-5532, Los Alamitos, CA, USA, Jul 2017. 2 \ No newline at end of file diff --git a/selfsupervisedneuralarticulatedshapeandappearancemodels/images.zip b/selfsupervisedneuralarticulatedshapeandappearancemodels/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..6b5e69e30b481d1cc62765b4c48299ad55ee59d6 --- /dev/null +++ b/selfsupervisedneuralarticulatedshapeandappearancemodels/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:eb1a7427396d4170fc65e1a3529726a8c060b4eb9d9ac4ee655843d34eb21f4c +size 522707 diff --git a/selfsupervisedneuralarticulatedshapeandappearancemodels/layout.json b/selfsupervisedneuralarticulatedshapeandappearancemodels/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7e654d7e49a390d6adc374f6180d4b24d3dbd4b1 --- /dev/null +++ b/selfsupervisedneuralarticulatedshapeandappearancemodels/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:866fbb03a46b2ac23fde2db34373d7bb39418e6c82f0de6042c59e54e9527397 +size 425689 diff --git a/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_content_list.json b/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..574bb76308c3a5c707b2e03fd360b1e2d4b8c38c --- /dev/null +++ b/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3722315cec883c3f7b980cb269041bf5aa5de384f8e1075b83836e44d4de71b8 +size 92267 diff --git a/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_model.json b/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_model.json new file mode 100644 index 0000000000000000000000000000000000000000..eac9ae67ad9be94a4fada8d48ccaabb75a22cfcf --- /dev/null +++ b/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:60ffe60b4bf43c029fbe1adb70a38b7f341407f32d24e65f0ee29d73ada57f5a +size 122035 diff --git a/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_origin.pdf b/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2972ad6b850fe8c3fc207a607adc0e664828bc51 --- /dev/null +++ b/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/6dde2183-85f5-43f4-aeaa-c473dcd8cdcf_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1b295f924d0650cb2821601fb4a59becebac589ac8b3744133aa2b9239a7a6ff +size 3178446 diff --git a/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/full.md b/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4d689919f3c5ded2e478230ca005bb641113d96b --- /dev/null +++ b/selfsupervisedobjectdetectionfromaudiovisualcorrespondence/full.md @@ -0,0 +1,413 @@ +# Self-supervised object detection from audio-visual correspondence + +Triantafyllos Afouras $^{1*†}$ Yuki M. Asano $^{2*}$ Francois Fagan $^{3}$ Andrea Vedaldi $^{3}$ Florian Metze $^{3}$ $^{1}$ University of Oxford $^{2}$ University of Amsterdam $^{3}$ Meta AI afourast@robots.ox.ac.uk + +# Abstract + +We tackle the problem of learning object detectors without supervision. Differently from weakly-supervised object detection, we do not assume image-level class labels. Instead, we extract a supervisory signal from audio-visual data, using the audio component to "teach" the object detector. While this problem is related to sound source localisation, it is considerably harder because the detector must classify the objects by type, enumerate each instance of the object, and do so even when the object is silent. We tackle this problem by first designing a self-supervised framework with a contrastive objective that jointly learns to classify and localise objects. Then, without using any supervision, we simply use these self-supervised labels and boxes to train an image-based object detector. With this, we outperform previous unsupervised and weakly-supervised detectors for the task of object detection and sound source localization. We also show that we can align this detector to ground-truth classes with as little as one label per pseudo-class, and show how our method can learn to detect generic objects that go beyond instruments, such as airplanes and cats. + +# 1. Introduction + +While recent progress in learning image and video representations has been substantial [22, 33, 38, 93], this has not yet translated into an ability to learn interpretable and actionable concepts automatically. By that, we mean that some manual labels are still required in order to map unsupervised representations to useful concepts such as image classes or object detections. In this paper, we thus consider the problem of learning interpretable concepts without any manual supervision. In particular, we focus on a problem that has not been explored extensively in the literature: learning to simultaneously detect and classify objects with no manual labels at all. + +![](images/1eba7b740f177ad24326314af08469a630f6fb42716c53e90d418c60c444b594.jpg) +Figure 1. We train an object detector simply by watching videos. Without using any manual annotations, we learn to detect different objects in images, by first self-labelling boxes and object categories and then using those as targets to teach a detector. The detection results shown are outputs from our trained model; for visualisation purposes we show Hungarian-matched labels. + +This problem is related to weakly supervised object detection (WSOD [16, 61]), with the difference that, in WSOD, the learning algorithm is given image-level labels telling it whether the image contains an occurrence of a given object type or not. Inspired by recent work in self-supervised learning, we seek to replace this source of external supervision with an internal supervisory signal extracted from the observation of video data. Videos are far richer than images, for example because they contain motion. Here, we focus on the multi-modal aspect of videos and use sound as a weak and noisy cue to learn about objects in the visual component of the data. + +The power of multi-modal self-supervision has been demonstrated before in self-supervised representation learning, and, closely related, in video clustering [9]. However, while video clustering can provide an interpretation of the data in terms of discrete classes, it does not provide any information about the location of the relevant ob + +jects in images. On the other hand, sound source localisation [7, 11, 49, 65] has considered precisely the problem of localizing the source of sounds in images. It is therefore tempting to trivially combine image classification and sound source localisation in the hope of learning the type and location of objects automatically. + +Unfortunately, such an approach does not lead to a satisfactory object detector. To understand why, it is important to note that the goal of sound source localisation is to localize the sound while it is being heard. This is insufficient for a detector because many objects emit sounds only occasionally and they become invisible to source localisation when they are silent. Instead, a detector that works in the visual domain should be responsive even when the object cannot be heard. Furthermore, source localisation methods generally only extract a heatmap giving the distribution of possible object locations; in contrast, a detector solves the much harder problem of enumerating all individual object instance that occur in an image by outputting instances-specific bounding boxes. + +In order to solve these issues, we should treat the sound component as a useful cue to learn an object detector, but not as a cue which is necessary for detection. Instead, we consider the problem of taking as input a collection of raw videos and producing a list of object classes and locations, in order to train an image-based detector. + +On a high level, our method is based on the following observation: we can use a sound source localisation network to learn about possible locations of sounding objects in videos. From this, we can extract a collection of bounding box pseudo-annotations for the objects and use those to learn a standard object detector. Because the latter only uses the visual modality, it immediately transfers to the detection of objects even when no relevant sound is present. + +However, one challenge is that sound source localisation does not provide the necessary class information to train class-specific detectors, effectively resulting in only learning a region proposal network for generic objects, with high rates of false positives. To this end, we note that most sound source localizers are based on noise-contrastive formulations that, together with clustering-based approaches, are currently state-of-the-art in self-supervised representation learning. From this, we derive a joint formulation that can simultaneously benefit from and learn to localize sound sources and classify them without any supervision. The resulting output can then be used to train any off-the-shelf object detector such as a Faster-RCNN [72] to learn an object detector without any supervision, as shown in Fig. 1. + +Empirically, we test our method by training and testing on VGGSound [21] and AudioSet [31], as well as testing only on a subset of OpenImages [52]. + +# 2. Related Work + +Audio-Visual Sound Source Localisation. Early work in sound-source localisation includes probabilistic models for localisation [26, 39, 49] and segmentation [45], but more recently the focus has shifted to dual-stream neural networks. For example, [7, 37, 77] propose a contrastive learning approach that matches the visual and audio components of the data. The work of [40, 44] instead clusters visual and audio features, associating to them centroids by means of a contrastive loss. Other works [2, 63] learn heatmaps by exploiting audio-visual synchronization in the same video, used previously for lip-to-mouth synchronization and active-speaker detection [23, 56], or by leveraging explicit attention modules [48]. Zhao et al. [102, 103] learn to associate pixels with audio sources by training with a mix-and-separate objective. Others [69] combine activation maps learned from class labels [19, 76] with a contrastive objective, use different levels of supervision and fusion techniques [70], or improve heatmaps by mining hard negative locations [20]. + +The work most similar to ours is [42], who first train a source localisation model with a contrastive objective and then use the learned heatmaps to extract object representations that are clustered using K-means. The cluster assignments are then used to train classifiers on top of the audio and video encoders. The paper proceeds to use these learned representations to discriminatively localize sound sources while suppressing quiet objects in 'cocktail party' scenarios. + +Compared to our work, none of the above can detect and thus enumerate individual object occurrences because they produce heatmaps. Furthermore, they all require audio during inference, and therefore cannot be used on individual images or to detect silent objects. + +Audio-visual category discovery. Learning visual categories is usually cast as image clustering, for which there is abundant prior work, such as recent 'deep clustering' methods [10, 18, 46, 89, 94, 97], or clustering with segmentation [90]. However, there is less work for clustering audio-visual data. In [5] the authors extend Deep Cluster [18] to the video domain by constructing two sets of labels from opposing modalities, which are used for cross-modal representation learning. The work of [75] combines clustering with audio-visual co-segmentation achieving combined audio-visual source separation. In [9], the authors extend the self-labelling method of [10] to multi-modal data by learning a shared set of labels between the two modalities. This work builds on the latter to complement and boost sound source localisation in a joint learning framework. + +Weakly Supervised Object Detection (WSOD). Weakly supervised detection uses (manual) image-level category labels without bounding box annotations. Many approaches + +![](images/f90ff3ba6b2bf9959686fa9b467f3a48c716c57cd58f57c286ca070e928457ed.jpg) + +![](images/0fb841b67a404e1f385fa66d67112704cbb2db2fabe26f091d781c919179618b.jpg) +Figure 2. Self-supervised object detection from audio-visual correspondence: We combine noise-constractive and clustering-based self-supervised learning to generate self-detections (boxes and labels) and use those as targets to train a detector. The trained detector can be used to detect objects from many categories on images without requiring audio. + +are based on a form of multiple-instance learning [17, 32, 57, 85, 91, 95, 96, 98, 99, 101], or proposal clustering [84]. Recent works in the area [47, 73] combine a variety of ideas, such as self-training [106] and spatial dropout [92] or explore the use of mixed annotations [74]. Other works obtain improvements by adding curriculum learning [100], using motion cues in videos [81], adversarial training [79], combining segmentation and detection [30, 54, 78], or modelling the uncertainty of object locations [8]. Other methods use technique such as CAM or analogous techniques [15, 19, 27, 76, 80, 105] as a form of weakly supervised saliency or localisation maps. Recent works have suggested that saliency methods can also be applied to self-supervised networks [13, 34], e.g. for object colocalisation [13]. + +Self-supervised multi-modal learning. Our work is also related to methods that use multiple modalities for representation learning [5, 6, 10, 12, 59, 66, 67] and synchronization [24, 50, 64]. A number of recent papers have leveraged speech as a weak supervisory signal to train video representations [53, 58, 60, 82, 83] whereas [3] uses speech, audio and video. Some works distil knowledge learned from one modality into another [1, 4, 28, 104]. Other works incorporate optical flow and other modalities [35, 36, 68, 102] to learn representations. For instance, the work of [87] learns to temporally localize audio events through audio-visual attention. CMC [86] learns representations that are invariant to multiple views of the data such as different color channels. Multi-modal self-supervision is also used to learn + +sound source separation in [29], albeit they assume to have pre-trained detectors. + +# 3. Method + +Our goal is to learn object detectors using only unlabeled videos, simultaneously learning to enumerate, localize and classify objects. Our approach consists of three stages summarized in Fig. 2: first, we learn useful representations using clustering and contrastive learning; second, we extract bounding boxes and class categories by combining the trained localisation and classification networks; third, we train an off-the-shelf object detector by using these self-extracted labels and boxes as targets. Next, we explain each stage and refer the reader to the arXiv version for further architecture and training details. + +# 3.1. Representation Learning + +Sound source spatial localisation. Our method starts by training a sound source localisation network (SSLN) using a contrastive learning formulation inspired by [7]. The SSLN is learned from pairs $(v, a)$ , where $v \in \mathbb{R}^{3 \times H \times W}$ is a video frame (i.e., a still image) and $a \in \mathbb{R}^{T \times F}$ is the spectrogram of the audio captured in a temporal window centered at that particular video frame. + +We consider a pair of deep neural networks. The first network $f^v (v)\in \mathbb{R}^{C\times h\times w}$ extracts from the video frame a field of $C$ -dimensional feature vectors, one per spatial location. We use the symbol $f_{u}^{v}(v)\in \mathbb{R}^{C}$ to denote the feature vector associated to location $u\in \psi = \{1,\dots ,h\} \times$ + +$\{1, \ldots, w\}$ . Here $h \times w$ is the resolution at which the spatial features are computed and is generally a fraction of the video frame resolution $H \times W$ . The second network $f^a(a) \in \mathbb{R}^C$ extracts instead a feature vector for the audio signal. + +Importantly, the spatial and audio features share the same $C$ -dimensional embedding space and can thus be contrasted. We further assume that the vectors $f_{u}^{v}(v)$ and $f^{a}(a)$ are $L^2$ normalized (this is obtained by adding a normalization layer at the end of the corresponding networks). The cosine similarity of the two feature vectors is then used to compute a heatmap of spatial locations, with the expectation that objects that are correlated with the sounds would respond more strongly. This heatmap is given by: + +$$ +h _ {u} (v, a) = \left\langle f _ {u} ^ {v} (v), f ^ {v} (a) \right\rangle / \rho , \quad u \in \psi , +$$ + +where $\rho$ , is a learnable temperature parameter. + +For the multi-modal contrastive learning formulation [25, 62, 67], the heatmap is converted in an overall score that the video $v$ and audio $a$ are in correspondence. This is done by taking the maximum of the response: + +$$ +S(v,a) = \max_{u\in \psi}h_{u}(v,a). +$$ + +The contrastive learning objective is defined by considering videos $(v,a)\in \mathcal{B}$ in a batch $\mathcal{B}$ . This comprises two terms. The first tests how well a video frame matches with its specific audio among the ones available in the batch: + +$$ +\mathcal {L} _ {a \rightarrow v} (\mathcal {B}) = - \frac {1}{| \mathcal {B} |} \sum_ {(v, a) \in \mathcal {B}} \log \frac {\exp S (v , a)}{\sum_ {(v ^ {\prime} , a ^ {\prime}) \in \mathcal {B}} \exp S (v , a ^ {\prime})}. +$$ + +The second is analogous, testing how well an audio matches with its specific video frame: + +$$ +\mathcal {L} _ {v \rightarrow a} (\mathcal {B}) = - \frac {1}{| \mathcal {B} |} \sum_ {(v, a) \in \mathcal {B}} \log \frac {\exp S (v , a)}{\sum_ {(v ^ {\prime} , a ^ {\prime}) \in \mathcal {B}} \exp S (v ^ {\prime} , a)}. +$$ + +These two losses are averaged in the noise-contrastive loss: + +$$ +\mathcal {L} _ {\mathrm {N C}} (\mathcal {B}) = \left(\mathcal {L} _ {a \rightarrow v} (\mathcal {B}) + \mathcal {L} _ {v \rightarrow a} (\mathcal {B})\right) / 2 \tag {1} +$$ + +Category self-labeling. Spatial localisation does not provide any class information, whereas our goal is to also associate 'names' to the different objects in the dataset. To this end, we consider the self-labelling approach of [9]. To briefly explain the formulation, let $y(v,a) \in \mathcal{V} = \{1,\dots ,K\}$ be a label associated to the training pair $(v,a)$ . We also consider two classification networks. The first maps a video $v$ to class scores $g^{v}(v) \in \mathbb{R}^{K}$ and is optimized by minimizing the standard cross-entropy loss: + +$$ +\mathcal {L} _ {v} (\mathcal {B} | y) = - \frac {1}{| \mathcal {B} |} \sum_ {(v, a) \in \mathcal {B}} \log \operatorname {s o f t m a x} (y (v, a) \mid g ^ {v} (v)). +$$ + +Note that this classification loss is equivalent to a contrastive loss on the cluster indices (as opposed to image indices) without normalization: As the last classification layer can be viewed as computing dot-products with each corresponding cluster's feature, it pushes the representation towards the feature of the corresponding cluster and away from the other clusters. The other network $g^{a}(a)$ is analogous, but uses the audio signal: + +$$ +\mathcal {L} _ {a} (\mathcal {B} | y) = - \frac {1}{| \mathcal {B} |} \sum_ {(v, a) \in \mathcal {B}} \log \operatorname {s o f t m a x} (y (v, a) \mid g ^ {a} (a)). +$$ + +As noted in [9], the crucial link between the two losses is that the labels $y$ are shared between modalities. This is obtained by averaging the two losses: + +$$ +\mathcal {L} _ {\mathrm {c l u s t}} (\mathcal {B} | y) = \left(\mathcal {L} _ {v} (\mathcal {B} | y) + \mathcal {L} _ {a} (\mathcal {B} | y)\right) / 2. \tag {2} +$$ + +Note that the labels $y$ are unknown; following [9] these are learned in an alternate fashion with the classification networks, minimizing the same loss (2). In order to avoid degenerate solutions, the labels' marginal distribution must be specified, e.g. using a simple equipartitioning constraint: + +$$ +\frac {1}{| \mathcal {D} |} \sum_ {(v, a) \in \mathcal {D}} 1 _ {\{y (v, a) = k \}} = \frac {1}{K} \quad \text {f o r a l l} k = 1, \dots , K \tag {3} +$$ + +where $\mathcal{D}$ denotes the entire dataset (union of all batches). Optimizing $y$ can be done efficiently by using the SK algorithm as in [9]. + +Joint training. To summarize, given the dataset $\mathcal{D}$ , we optimize stochastically w.r.t. random batches $\mathcal{B}$ the loss: + +$$ +\mathcal {L} (\mathcal {B} | y) = \lambda \mathcal {L} _ {\mathrm {N C}} (\mathcal {B}) + (1 - \lambda) \mathcal {L} _ {\text {c l u s t}} (\mathcal {B} | y) \tag {4} +$$ + +where $\lambda$ is a balancing hyperparameter. + +The loss is optimized with respect to the localisation networks $f^v$ and $f^a$ and the classification networks $g^v$ and $g^a$ . These networks share common backbones $q^v$ and $q^a$ and differ only in their heads, so they can be written as $f^v = \hat{f}^v \circ q^v$ , $g^v = \hat{g}^v \circ q^v$ , $f^a = \hat{f}^a \circ q^a$ and $g^a = \hat{g}^a \circ q^a$ . + +The model is trained by alternating between updating the labels $y$ with eq. (2) under constraint (3) and updating the networks by optimizing eq. (4). + +# 3.2. Extraction of Self-labels for Detection + +Once the localisation and classification networks have been trained, they can be used to extract self-annotations for training a detector. This is done in two steps: extracting object bounding boxes and finding their class labels. + +Box extraction. To obtain "self-bounding boxes" for the objects, we use the simple heuristic suggested by [105]: the heatmap $h(v, a)$ is thresholded at a value $\epsilon(h)$ , the largest connected component is identified, and a tight bounding + +box $t^*(v, a) \in \Omega^2$ around that component is extracted (the notation means that the box is specified by the location of the top-left and bottom-right corners). + +The threshold is determined dynamically as a convex combination of the maximum and average responses of the heatmap, controlled by hyperparameter $\beta$ : + +$$ +\epsilon (h) = \beta \max _ {u \in \psi} h _ {u} + (1 - \beta) \frac {1}{| \psi |} \sum_ {u \in \psi} h _ {u}. \tag {5} +$$ + +Class labelling. As noted above, we only extract a single object from each frame for the purpose of training the detector. Likewise, we only need to extract a single class label for the frame. This is done by taking the maximum response of the visual and audio-based classification networks: + +$$ +y ^ {*} (v, a) = \underset {y \in \mathcal {Y}} {\arg \max } \left[ g _ {y} ^ {v} (v) + g _ {y} ^ {a} (a) \right]. \tag {6} +$$ + +Filtering the annotations. The assumption that frames contain a dominant object introduces noise but simplifies the problem and gives us the ability to use the audio to obtain purer clusters. Notably, we do not require the method above to work for all frames but instead rely on our detector to smooth over the specific and noisy self-annotations to learn a holistic detection. + +# 3.3. Training the Object Detector + +The process described above results in a shortlist of training triplets $(v, t^{*}, y^{*}) \in \mathcal{D}_{\mathrm{det}}$ , where $v$ is a video frame (an image), $t^{*}$ is the extracted bounding box and $y^{*}$ is its class label. We use this dataset to train an off-the-shelf detector, in particular Faster R-CNN [71] for its good compromise between speed and quality. + +Recall that, given an image $v$ , Faster R-CNN detector considers a set of bounding box proposals $m \in M(v) \subset \Omega^2$ . It then trains networks $y(m) = f_{\mathrm{det}}^{\mathrm{cls}}(m|v) \in \{1, \dots, K, \mathrm{bkg}\}$ and $t(m) = f_{\mathrm{det}}^{\mathrm{loc}}(m|v) \in \mathbb{R}^4$ inferring, respectively, the class label $y(m)$ and a refined full-resolution bounding box $t(m)$ for the box proposal $m$ . The label space is extended to also include a background class bkg, which is required as most proposals do not land on any object. + +The detector is trained by finding an association between proposals and annotations. To this end, if $m^{*} = \arg \max_{m\in M(v)}\mathrm{IoU}(m,t^{*})$ is the proposal that matches the pseudo-ground truth bounding box $t^{*}$ the best, one optimizes: + +$$ +\begin{array}{l} \mathcal {L} _ {\det } (v, t ^ {*}, y ^ {*}) = \mathcal {L} _ {\operatorname {r e g}} (t \left(m ^ {*}\right), t ^ {*}) + \mathcal {L} _ {\operatorname {c l s}} \left(y \left(m ^ {*}\right), y ^ {*}\right) \\ + \sum_ {m \in M (v): \operatorname {I o U} (m, t ^ {*}) < \tau} \mathcal {L} _ {\mathrm {c l s}} (y (m), \mathrm {b k g}). \\ \end{array} +$$ + +Here $\mathcal{L}_{\mathrm{reg}}$ is the $L^1$ loss for the bounding box corner coordinates and $\mathcal{L}_{\mathrm{cls}}$ the standard cross-entropy loss. Intuitively, + +this loss requires the best proposal $m^{*}$ to match the pseudoground truth class $y^{*}$ and bounding box $t^{*}$ of, while mapping proposal $m$ that are a bad match $(\tau \leq 0.7)$ to class bkg. Further details, including how the region-proposal network that generates the proposals is trained, are given in the the arXiv version + +Discussion. Training a detector is obviously necessary to solve the problem we set out to address. However, it can also be seen as a way of extracting 'clean' information from the noisy self-annotations. Specifically: (i) the noise in individual annotations is smoothed over the entire dataset; (ii) because of the built-in NMS step, the detector still learns to extract multiple objects per image even though a single self-annotation is given for each training image; (iii) by learning to reject a large number of false bounding box proposals, the detector learns to be more precise than the self-annotations. + +# 4. Experiments + +We first introduce the datasets, experimental setup and relevant baselines; we then test our method against those, analyse it further via ablations and its capacity to generalize. + +# 4.1. Datasets + +AudioSet-Instrument. AudioSet [31] is a large scale audio-visual dataset consisting of 10-second video clips originally from YouTube. For training we use the AudioSet-Instruments [7] subset of the "unbalanced" split, containing 110 sound source classes as well as its more constrained subset used by [43] spanning 13 instrument classes. Following previous work we use the "balanced" subset for evaluation on the annotations provided by [43]. + +VGGSound. VGGSound contains over 200K 10-second clips from YouTube spanning 309 categories of objects where there is some degree of correlation between the audio and the video. We create one subset by keeping only the 50 musical instrument categories yielding around 54K training videos, and one other subset, by keeping from those only the 39 categories that can be roughly mapped to the test-set annotations (details in the arXiv version). For VGGSound pseudo-ground truth test-set annotations are obtained using a supervised detector from [29], following [43]. + +OpenImages. For evaluation, we also use the subset of the OpenImages [52] dataset containing musical instruments, which spans 15 classes. + +# 4.2. Baselines + +There is currently no prior work on learning an object detector for multiple object classes without any supervision. Instead, we compare against weakly-supervised detectors (hence using image-level labels) and unsupervised localisation methods that only produce heatmaps (not detections). + +![](images/46855256d54f8398fac89eb22afa720b8caf8641c1fa5787c334a6584ea103e9.jpg) +Figure 3. Qualitative results and comparison with a weakly supervised object detection method, PCL [84], on the OpenImages test set. Our method accurately detects objects, capturing their boundaries, even though it has been trained without any supervision. For visualisation purposes, we show the labels obtained from matching with the Hungarian method. More qualitative results provided in the arXiv version. + +For weakly-supervised detection, we consider PCL [84], the strongest such baseline for which we could find an implementation. + +For our second baseline, we consider heatmap-based localisation methods that, similarly to us, use cross-modal self-supervised learning. Here we compare against the state-of-the-art DSOL method of [43] that produces a heatmap roughly localizing the objects and producing class pseudolabels. + +Finally, we also compare against other baselines such as simply predicting a large centered box and class-agnostic region proposal methods such as selective search, and using a RPN obtained from supervised training on COCO [55]. Further details are provided in the the arXiv version. + +# 4.3. Implementation Details. + +Assessing class pseudolabels. Since class pseudolabels do not come with the name of the class (they are just cluster indices), they must be put in correspondence with human-labelled classes for evaluation. Following prior work in unsupervised image clustering [10, 14, 46, 89], we apply Hungarian matching [51] to the learned clusters and the ground truth classes. Importantly, the matching is done after the detector is trained and only done for assessment; meaning that the detector does not use any manual label. + +Detector training. If not stated otherwise, the localizer and detector are trained on VGGSound and AudioSet whereas OpenImages are only used for evaluation. We do not have any information on the number of instruments in VGGSound and use all videos with no single/multi-object curation. For a fair comparison with DSOL, and only for the relevant experiment in Table 2, we train on AudioSet using the single-instrument subset for learning the localizer. + +Number of clusters. For VGGSound training we use $K = 39$ if not stated otherwise, matching the 39 object types in the training set. Since the dataset is roughly balanced, uniform margins are used as described in [9]. For + +AudioSet training we use $K = 30$ and Gaussian marginals. Further implementation details can be found in the arXiv version + +# 4.4. Results + +Self-supervised object detection. We summarise the results of our evaluations on the three test sets that we consider in Table 1. Following the image object detection literature, we use mAP at different IoU thresholds as the evaluation metric. Our method clearly outperforms the PCL baseline even though it uses no manual annotations at all during training. PCL outperforms our approach in some of the datasets only if the IoU threshold used for mAP computation is relaxed substantially (0.3 IoU). However, for stricter thresholds our approach works better, which suggests that our detections have a relatively high spatial accuracy. + +To understand the impact of the noisy class self-labels, we also train and test a detector (Ours - weak sup.) with the bounding box labels from our localisation network, but utilising the ground truth video categories. The resulting performance difference is modest, resulting in a $3\%$ AP50 drop in VGGSound and AudioSet. This further demonstrates the accuracy of our class self-labels, but also shows the potential of our model to leverage weak supervision if available. + +Per-class performance breakdown. To better understand the strengths and weaknesses of our method, we report a performance breakdown by object class in Table 3. We observe that the model obtains good results consistently for classes of large objects with a distinctive appearance (e.g. accordions and harps), while it is weaker for smaller objects such as oboes, or for objects that appear closely in numbers, like drums. + +Comparison to audio-visual heatmaps. In Table 2 we compare the performance of our method trained on AudioSet to state-of-the-art sound source localisation methods. For a fair comparison to these methods, we convert the union of our predicted bounding boxes with confidence + +
MethodNo labels?VGGSoundAudiosetOpenImages
mAP30mAP50mAPmAP30mAP50mAPmAP30mAP50mAP
PCL (WSOD) [84]X54.927.77.639.017.54.437.914.53.5
Ours - weak sup.X67.642.914.250.630.910.348.933.79.5
Center Box*✓29.65.61.515.13.50.720.74.20.8
Selective Search* [88]✓5.21.10.42.80.40.17.42.10.7
COCO-trained RPN*X33.47.51.619.04.10.824.411.12.6
Ours - self-boxes*✓48.129.610.027.814.14.8NANANA
Ours - full✓52.339.414.744.328.09.639.928.57.6
+ +Table 1. Self-supervised object detection. We report object detection metrics across three test datasets and find our method is far superior to other unsupervised approaches and outperforms even the weakly supervised baseline in most metrics. For methods denoted by *, we report class-agnostic evaluation numbers. The class-agnostic performance of the self-boxes that are used to train the detector reveals that the latter greatly outperforms them, which highlights the benefit of our approach. + +
Methodsingle-instr.multi-instr.
IoU-0.5AUCcIoU-0.3
Sound of pixels [103]38.240.639.8
Object t. Sound [7]32.739.527.1
Attention [77]36.539.529.9
DMC [41]32.838.232.0
DSOL [43]38.940.948.7
Ours50.647.552.4
+ +Table 2. Comparison to sound localisation methods. Since our detector does not require audio, we obtain detections on the video frames directly. Our model outperforms the baselines. Baselines numbers taken from [42]. + +
Dataset\( \mathbf{mAP}_{50} \)AccordionCelloDrumFluteHornGuitarHarpPianoSaxophoneViolinBanjoTromboneTrumpetOboe
OpenImages28.575.330.26.66.515.014.580.428.822.528.857.09.718.16.3
Audioset28.041.344.90.95.521.739.582.652.72.517.446.78.0--
VGGSound39.488.639.41.850.03.434.995.650.214.456.3100.02.211.03.8
+ +Table 3. Per-class mAP breakdown For entries with $\underline{ - }$ ’ the test set does not contain any samples for that class. + +
#GT-cls.KmAP50
VGGSO.Images
392034.424.4
393035.125.1
393939.428.5
395041.027.5
+ +Table 4. Number of clusters K. Our method is relatively robust $(< 5\%$ decrease in AP) to the number of self-labelling clusters. + +
Matching\( \mathbf{{mAP}}_{50} \)
VGGSO.Images
Hung.39.428.5
Argmax39.630.1
Manual41.029.5
1-shot36.425.1
10-shot37.125.8
+ +Table 5. Matching strategies. Even with 39 labels, our method performs accurately. + +above a set threshold into a binary map, and use the latter as a pseudo-heatmap to use the same evaluation code. Our approach outperforms others for both class-agnostic single object localisation and for class-aware multi-object localisation, without using audio signals during inference. + +We note however that cIOU is not a very reliable metric for evaluating a detector (or even sound localizer) as it favours high recall over precision: by averaging this metric over all classes the most frequent ones (e.g. drums, guitars, pianos) dominate the metric. We therefore propose to the research community – and report in this paper – mean average precision (mAP) values as a more indicative metric. + +Ablation: Number of clusters K. In Table 4, we perform an experiment varying the number of clusters $K$ , and as a consequence the number of object categories that the detector learns, while keeping the test-set (containing 15 classes) fixed. We observe that out method achieves reasonable performance for a wide range of $K$ . The performance is fairly stable when $K$ is more than the ground truth classes, and gradually decreases when fewer clusters are used. + +Data-efficient detector alignment. In Table 5 we conduct an investigation into the matching of the clusters to + +the ground truth labels. Recall that, for evaluation, we assign clusters to ground truth labels using the Hungarian algorithm. We can improve the computational efficiency of this step by using majority voting instead, which results in the same accuracy on VGGSound and a gain of $1.6\%$ on OpenImages. Using a manual grouping strategy (see the arXiv version for details) yields another small boost. We can also improve the statistical efficiency as follows. While the evaluation protocol computes the optimal assignments assuming that all videos are labelled, in a real-world application we are interested in naming clusters with as little labelled data as possible. To do this, we still use majority voting, but we assume that only the top $m$ videos per cluster (based on the strength of association) are labelled. We find that even by just using $m = 1$ (i.e., a total number of 39 annotations), our method still achieves $37.1\%$ and $25.3\%$ on VGGSound and OpenImages. This is a $3\%$ drop compared to the Hungarian algorithm and can be further reduced to $2.3\%$ by using $m = 10$ (i.e., 390 annotations). + +Qualitative analysis. We show examples of successfully detected objects in challenging images in Fig. 3, where we also include the outputs of the PCL baseline. Although our model has not been manually shown any objects boundaries during training we see that it can learn very accurate boxes around them and that it can successfully identify multiple objects in complicated scenes. We provide further examples in the arXiv version. + +Towards general object detection. The results presented thus far have focused on subsets of common datasets with instruments solely to ensure comparability with prior works. Since one main goal of self-supervised learning is to leverage the vast amount of unlabelled data, we wish to + +![](images/0049fc05247661ff2b06f19b9ae146af96612601bfa7f356cc1e702050c4a2fd.jpg) + +![](images/d6ccac3a2605423a203e6d14c9b8c9b723106ef7d8e432643ee3bfc341c8f55a.jpg) + +![](images/f8c4835a3e0a15b07cbbf072c7b7a3cadb1da6a5c4232e7e5a2829e40bd969f0.jpg) + +![](images/bcdabb3d47b08049456535b4cb6d42ade506d42bbf3c36548206695cd265b61f.jpg) + +![](images/3d1bd646865738eae54df44345a4f35a6f89cc24c35b1d71cabcf8ecbb559bfb.jpg) + +![](images/7dd3fab5b579cdb0ca7c8d31eaddcdc29a957e90c0513437d7f90e35dd72bb6c.jpg) +Figure 4. Object detection beyond musical instruments. Our proposed method can learn to accurately detect objects from more general categories, as long as they can be associated with a characteristic sound. The results shown here are from a model trained without labels directly on the full VGGSound dataset which includes 309 different video classes. Our method successfully learns to detect non-instrument objects, even in difficult multi-instance cases. + +![](images/2e1560d130dbe29dd9271f31d64f822f241ab6e53b00b8b35efcc173fb9ce6bd.jpg) + +![](images/83ce046be71f2da1a9c2b830eda20b232d1d6f5631cc052019c6184a18d5f16c.jpg) + +![](images/adc1e070971c95682b1bfbbea14b4b65bfd4e7419f6839cf726530f93f836c12.jpg) + +![](images/bb7114902334534296e64374347e4123813da251e1763f239d7caae4e15b8477.jpg) + +
ClassAP30AP50AP[50:95:5]
Mean45.624.46.5
Airplane62.727.06,5
Ambulance56.930.97.1
Bird26.515.83.7
Car29.818.45.1
Cat67.728.07.7
Comp. Keyboard.53.342.612.9
Comp. Mouse35.925.48.8
Frog43.519.54.7
Lion34.122.24.9
Snowmobile64.314.33.5
+ +Table 6. Results on general object categories. + +investigate how general and robust our proposed method when applied on a far larger scale. For this, we increase our pretraining dataset by approximately $10\times$ , simply by taking the whole of the VGGSound dataset, without any filtering. We set $K$ to 300 and keep all training parameters the same; the result is an unsupervisedly trained object detector that can classify 300 pseudo-classes. As before, we match these to the VGGSound labels with the Hungarian algorithm and select ten categories for which we have annotations in the OpenImages dataset (details in the arXiv version). + +In Fig. 4 we show qualitative results of some detections on OpenImages. The numerical results are given in Table 6. We find that even for objects that are deformable, such as cats, we get high $\mathrm{AP}_{30}$ values of $67.7\%$ and that even objects that vary in shape, such as airplanes (see Fig. 4, bottom-right), we achieve a good performances $62.7\%$ . While the results for the $\mathrm{AP}_{50:95:5}$ metric indicate that there is still room for improvement, these initial results show that leveraging larger and more diverse video datasets for self-supervisedly learning object detectors is a promising avenue. We note that, since minimal curation is performed on the training data, and we use a large number of different object categories in a noisy dataset, this training setting is very challenging. These results further highlight the potential of our proposed method. + +# 5. Discussion + +Limitations & societal impact. We refer the reader to the arXiv version for an extensive examination of failure cases. Detection failures manifest as multiple instance grouping, missing instances or part-of-object detection, all well documented in the WSOD literature [73]. Another error is detecting wrong objects that often appear together with the objects of interest due to biases in the data (e.g. mouth regions as wind instruments). Wrong classification occurs often because i) visually similar classes are confused - e.g. Horn and Trumpet; ii) of incorrect semantic matching; iii) confusion due to the object's orientation - e.g. a vertical violin confused for a cello. Regarding training, there are likely further optimizations possible, such as a more end-to-end design. As for most unsupervised methods, a downside of our approach compared to supervised detection is the reduced human control on the learned concepts, which may warrant additional manual validation before deployment. + +Conclusion. We have presented a method for training strong object detectors purely with self-supervision by watching unlabelled videos. We demonstrated that our best models perform better than a heatmap-based methods while not requiring and audio and better than weakly supervised baselines, even after curating the dataset to filter out noisy samples for training the latter. We have also addressed one shortcoming of using the Hungarian algorithm for evaluation by showing that data-efficient alignment of self-supervised detectors is possible with as little as one image per pseudo-label. Finally, we applied our method to domains beyond musical instruments and found that it can learn reasonable detectors in this much less curated setting, paving the way to general self-supervised object detection. + +# Acknowledgements + +Y.M.A is thankful for MLRA funding from AWS. + +# References + +[1] Triantafyllos Afouras, Joon Son Chung, and Andrew Zisserman. 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Moeslund $^{3}$ , Mubarak Shah $^{8}$ + +1University Politehnica of Bucharest, Romania, 2MBZ University of Artificial Intelligence, UAE, 3Aalborg University, Denmark, 4University of Bucharest, Romania, 5SecurifAI, Romania, 6Milestone Systems, Denmark, 7Linköping University, Sweden, 8University of Central Florida, US + +# Abstract + +Anomaly detection is commonly pursued as a one-class classification problem, where models can only learn from normal training samples, while being evaluated on both normal and abnormal test samples. Among the successful approaches for anomaly detection, a distinguished category of methods relies on predicting masked information (e.g. patches, future frames, etc.) and leveraging the reconstruction error with respect to the masked information as an abnormality score. Different from related methods, we propose to integrate the reconstruction-based functionality into a novel self-supervised predictive architectural building block. The proposed self-supervised block is generic and can easily be incorporated into various state-of-the-art anomaly detection methods. Our block starts with a convolutional layer with dilated filters, where the center area of the receptive field is masked. The resulting activation maps are passed through a channel attention module. Our block is equipped with a loss that minimizes the reconstruction error with respect to the masked area in the receptive field. We demonstrate the generality of our block by integrating it into several state-of-the-art frameworks for anomaly detection on image and video, providing empirical evidence that shows considerable performance improvements on MVTec AD, Avenue, and ShanghaiTech. We release our code as open source at: https://github.com/ristea/sspcab. + +# 1. Introduction + +Anomaly detection is an important task with a broad set of applications ranging from industrial inspection (finding defects of objects or materials on industrial production lines) [5, 7, 10, 15, 36, 56, 62, 76] to public security (detecting abnormal events such as traffic accidents, fights, explosions, etc.) [12, 13, 17-19, 27, 28, 33, 39, 41, 47-50, 52, 67, 72, 73, 77, 78]. The task is typically framed as a one-class classification (outlier detection) problem, where methods [2, 8, 12, 21, 25, 27, 29, 33, 35, 37, 40, 43-45, 49- + +51, 53, 54, 57, 69, 73, 75, 81, 82] learn a familiarity model from normal training samples, labeling unfamiliar examples (outliers) as anomalies, at inference time. Since abnormal samples are available only at test time, supervised learning methods are not directly applicable to anomaly detection. To this end, researchers turned their attention to other directions such as reconstruction-based approaches [15, 19, 21, 36, 37, 43, 47, 49, 54, 62, 69, 71], dictionary learning methods [7-9, 14, 40, 55], distance-based models [6, 10, 25, 27, 50, 51, 53, 57, 58, 63, 65, 68, 70], change detection frameworks [11, 26, 38, 48], and probabilistic models [1, 2, 16, 23, 29, 44, 45, 56, 61, 74]. + +A distinguished subcategory of reconstruction methods relies on predicting masked information, leveraging the reconstruction error with respect to the masked information as an abnormality score. The masked information can come in different forms, e.g. superpixels [36], future frames [37], middle bounding boxes [17], among others. Methods in this subcategory mask some part of the input and employ a deep neural network to predict the missing input information. Different from such methods, we propose to integrate the capability of reconstructing the masked information into a neural block. Introducing the reconstruction task at a core architectural level has two important advantages: (i) it allows us to mask information at any layer in a neural network (not only at the input), and (ii) it can be integrated into a wide range of neural architectures, thus being very general. + +We design our reconstruction block as a self-supervised predictive block formed of a dilated convolutional layer and a channel attention mechanism. The dilated filters are based on a custom receptive field, where the center area of the kernel is masked. The resulting convolutional activation maps are then passed through a channel attention module [24]. The attention module ensures the block does not simply learn to reconstruct the masked region based on linearly interpolating contextual information. Our block is equipped with a loss that minimizes the reconstruction error between the final activation maps and the masked information. In other words, our block is trained to predict the masked information in a self-supervised manner. Our self-supervised + +![](images/553adcd95d31c94fd6a466a5428f9c6e8fef65e673e9e57704054936e2eb39eb.jpg) +Figure 1. Our self-supervised predictive convolutional attentive block (SSPCAB). For each location where the dilated convolutional filter is applied, the block learns to reconstruct the masked area using contextual information. A channel attention module performs feature recalibration by using global information to selectively emphasize or suppress reconstruction maps. Best viewed in color. + +predictive convolutional attentive block (SSPCAB) is illustrated in Figure 1. For each location where the dilated convolutional filter is applied, the block learns to reconstruct the masked area using contextual information. Meanwhile, the dilation rate becomes a natural way to control the context level (from local to global), as required for the specific application. + +We integrate SSPCAB into various state-of-the-art anomaly detection frameworks [18, 34, 37, 39, 49, 79] and conduct comprehensive experiments on the MVtec AD [5], Avenue [40] and ShanghaiTech [43] data sets. Our empirical results show that SSPCAB can bring significant performance improvements, e.g. the region-based detection criterion (RBDC) of Liu et al. [39] on Avenue increases from $41\%$ to $62\%$ by adding SSPCAB. Moreover, with the help of SSPCAB, we are able to report new state-of-the-art performance levels on Avenue and ShanghaiTech. Additionally, we show extra results on the Avenue data set, indicating that the masked convolutional layer can also increase performance levels, all by itself. + +In summary, our contribution is twofold: + +- We introduce a novel self-supervised predictive convolutional attentive block that is inherently capable of performing anomaly detection. +- We integrate the block into several state-of-the-art neural models [18,34,37,39,49,79] for anomaly detection, showing significant performance improvements across multiple models and benchmarks. + +# 2. Related Work + +As anomalies are difficult to anticipate, methods are typically trained only on normal data, while being tested on both normal and abnormal data [21, 49]. Therefore, outlier detection [25, 27, 50, 51, 53] and self-supervised learning [17-19, 34, 39, 41, 49, 79] approaches are extensively + +used to address the anomaly detection task. Anomaly detection methods can be classified into: dictionary learning methods [7-9, 14, 40, 55], change detection frameworks [11, 26, 38, 48], probability-based methods [1, 2, 16, 23, 29, 44, 45, 56, 61, 74], distance-based models [6, 10, 25, 27, 50, 51, 53, 57, 58, 63, 65, 68, 70], and reconstruction-based methods [15, 19, 21, 36, 37, 43, 47, 49, 54, 62, 69, 71, 79]. + +Dictionary-based methods learn the normal behavior by constructing a dictionary, where each entry in the dictionary represents a normal pattern. Ren et al. [55] extended dictionary learning methods by considering the relation among different entries. Change-detection frameworks detect anomalies by quantifying changes across the video frames, i.e. a significant deviation from the immediately preceding event marks the beginning of an abnormal event. After quantifying the change, approaches such as unmasking [26] or ordinal regression [48] can be used to segregate anomalies. Probability-based methods build upon the assumption that anomalies occur in a low probability region. These methods estimate the probability density function (PDF) of the normal data and evaluate the test samples based on the PDF. For example, Mahadevan et al. [44] used a Mixture of Dynamic Textures (MDTs) to model the distribution of the spatio-temporal domain, while Rudolph et al. [56] employed normalizing flow to represent the normal distribution. Distance-based methods learn a distance function based on the assumption that normal events occur in the close vicinity of the learned feature space, while the abnormal events are far apart from the normal data. For instance, Ramachandra et al. [51] employed a Siamese network to learn the distance function. Reconstruction-based methods rely on the assumption that the normal examples can be reconstructed more faithfully from the latent manifold. Our new block belongs to the category of reconstruction-based anomaly detection methods, particularly siding with meth + +ods that predict or reconstruct missing (or masked) information [17, 36, 37]. + +Reconstruction-based methods. In the past few years, reconstruction-based methods became prevalent in anomaly detection. Such methods typically use auto-encoders [21] and generative adversarial networks (GANs) [37], as these neural models enable the learning of powerful reconstruction manifolds via using normal data only. However, the generalization capability of neural networks sometimes leads to reconstructing abnormal frames with low error [12, 18], affecting the discrimination between abnormal and normal frames. To address this issue, researchers have tried to improve the latent manifold by diversifying the architecture and training methodologies. Some works focusing on transforming the architectures include memory-based auto-encoders [12, 39, 49], which memorize the normal prototypes in the training data, thus increasing the discrimination between normal and abnormal samples. Other works remodeled the reconstruction manifold via training the models with pseudo-abnormal samples [4, 18, 79]. The adversarial training proposed in [17] applies gradient ascent for out-of-domain pseudo-abnormal samples and gradient descent for normal data, thus learning a more powerful discriminative manifold for video anomaly detection. Zavrtanik et al. [79] created pseudo-abnormal samples by adding random noise patches on normal images for image anomaly detection. Some variants of auto-encoders, such as Variational Auto-Encoders (VAEs), have been proposed in [39, 83] for the anomaly detection task. These works are based on the assumption that VAEs can only reconstruct the normal images. Liu et al. [39] used a conditional VAE, conditioning the image prediction on optical flow reconstruction, thus accumulating the error from the optical flow reconstruction task with the image prediction. However, this approach can only be applied to video anomaly detection, due to the presence of motion information in the form of optical flow. + +Reconstruction of masked information. A surrogate task for many anomaly detection approaches [15,22,37,42,77] is to erase some information from the input, while making neural networks predict the erased information. Haselmann et al. [22] framed anomaly detection as an inpainting problem, where patches from images are masked randomly, using the pixel-wise reconstruction error of the masked patches for surface anomaly detection. Fei et al. [15] proposed the Attribute Restoration Network (ARNet), which includes an attribute erasing module (AEM) to disorient the model by erasing certain attributes from an image, such as color and orientation. In turn, ARNet learns to restore the original image and detect anomalies based on the assumption that normal images can be restored properly. The Cloze task [42] is about learning to complete a video when certain frames are removed, being recently employed by Yu et al. [77] for anomaly detection. In a similar direc + +tion, Georgescu et al. [17] proposed middle frame masking as one of the auxiliary tasks for video anomaly detection. Both approaches are based on the assumption that an erased frame can be reconstructed more accurately for regular motion. Future frame prediction [34] utilizes past frames to predict the next frame in the video. The anomaly, in this case, is detected through the prediction error. Another approach based on GANs [59] learns to erase patches from an image, while the discriminator identifies if patches are normal or irregular. + +Unlike existing approaches, we are the first to introduce the reconstruction-based functionality as a basic building block for neural architectures. More specifically, we design a novel block based on masked convolution and channel attention to reconstruct a masked part of the convolutional receptive field. As shown in the experiments, our block can be integrated into a multitude of existing anomaly detection frameworks [18, 34, 37, 39, 49, 79], almost always bringing significant performance improvements. + +# 3. Method + +Convolutional neural networks (CNNs) [30, 31] are widely used across a broad spectrum of computer vision tasks, also being prevalent in anomaly detection [18, 20, 34, 39, 49]. CNNs are formed of convolutional layers equipped with kernels which learn to activate on discriminative local patterns, in order to solve a desired task. The local features extracted by a convolutional layer are combined into more complex features by the subsequent convolutional layers. From this learning process, a hierarchy of features emerges, ranging from low-level features (corners, edges, etc.) to high-level features (car wheels, bird heads, etc.) [80]. While this hierarchy of features is extremely powerful, CNNs lack the ability to comprehend the global arrangement of such local features, as noted by Sabour et al. [60]. + +In this paper, we introduce a novel self-supervised predictive convolutional attentive block (SSPCAB) that is proposed at learning to predict (or reconstruct) masked information using contextual information. To achieve highly accurate reconstruction results, our block is forced to learn the global structure of the discovered local patterns. Thus, it addresses the issue pointed out in [60], namely the fact that CNNs do not grasp the global arrangement of local features, as they do not generalize to novel viewpoints or affine transformations. To implement this behavior, we design our block as a convolutional layer with dilated masked filters, followed by a channel attention module. The block is equipped with its own loss function, which is aimed at minimizing the reconstruction error between the masked input and the predicted output. + +We underline that our design is generic, as SSPCAB can be integrated into just about any CNN architecture, being able to learn to reconstruct masked information, while offer + +![](images/bf40cd0b07c7c328418eeefcf83d0f261ee50803e83ed2d7d1d37eb3f1410a2c.jpg) +Figure 2. Our masked convolutional kernel. The visible area of the receptive field is denoted by the regions $K_{i}, \forall i \in \{1, 2, 3, 4\}$ , while the masked area is denoted by $M$ . A dilation factor $d$ controls the local or global nature of the visible information with respect to $M$ . Best viewed in color. + +ing useful features for subsequent neural layers. Although the capability of learning and using global structure might make SSPCAB useful for a wide range of tasks, we conjecture that our block has a natural and direct applicability in anomaly detection, as explained next. When integrated into a CNN trained on normal training data, SSPCAB will learn the global structure of normal examples only. When presented with an abnormal data sample at inference time, our block will likely provide a poor reconstruction. We can thus measure the quality of the reconstruction and employ the result as a way to differentiate between normal and abnormal examples. In Section 4, we provide empirical evidence to support our claims. + +SSPCAB is composed of a masked convolutional layer activated by Rectified Linear Units (ReLU) [46], followed by a Squeeze-and-Excitation (SE) module [24]. We next present its components in more details. + +Masked convolution. The receptive field of our convolutional filter is depicted in Figure 2. The learnable parameters of our masked convolution are located in the corners of the receptive field, being denoted by the sub-kernels $\pmb{K}_i \in \mathbb{R}^{k' \times k' \times c}, \forall i \in \{1, 2, 3, 4\}$ , where $k' \in \mathbb{N}^+$ is a hyperparameter defining the sub-kernel size and $c$ is the number of input channels. Each kernel $\pmb{K}_i$ is located at a distance (dilation rate) $d \in \mathbb{N}^+$ from the masked region in the center of our receptive field, which is denoted by $M \in \mathbb{R}^{1 \times 1 \times c}$ . Consequently, the spatial size $k$ of our receptive field can be computed as follows: $k = 2k' + 2d + 1$ . + +Let $X \in \mathbb{R}^{h \times w \times c}$ be the input tensor of our masked convolutional layer, where $c$ is the number of channels, and $h$ and $w$ are the height and width, respectively. The convolutional operation performed with our custom kernel in a certain location of the input $X$ only considers the input values from the positions where the sub-kernels $K_{i}$ are located, the other information being ignored. The results of the convolution operations between each $K_{i}$ and the corresponding inputs are summed into a single number, as if the sub-kernels $K_{i}$ belong to a single convolutional ker + +nel. The resulting value denotes a prediction located at the same position as $M$ . Naturally, applying the convolution with one filter produces a single activation map. Hence, we would only be able to predict one value from the masked vector $M$ , at the current location. To predict a value for every channel in $M$ , we introduce a number of $c$ masked convolutional filters, each predicting the masked information from a distinct channel. As we aim to learn and predict the reconstruction for every spatial location of the input, we add zero-padding of $k' + d$ pixels around the input and set the stride to 1, such that every pixel in the input is used as masked information. Therefore, the spatial dimension of the output tensor $Z$ is identical to that of the input tensor $X$ . Finally, the output tensor is passed through a ReLU activation. We underline that the only configurable hyperparameters of our custom convolutional layer are $k'$ and $d$ . + +Channel attention module. Next, the output of the masked convolution is processed by a channel attention module, which computes an attention score for each channel. Knowing that each activation map in $Z$ is predicted by a separate filter in the presence of masked information, we infer that the masked convolution might end up producing activation maps containing disproportionate (uncalibrated) values across channels. Therefore, we aim to exploit the relationships between channels, with the goal of scaling each channel in $Z$ in accordance with the quality of the representations produced by the masked convolutional layer. To this end, we employ the channel attention module proposed by Hu et al. [24]. The SE module [24] provides a mechanism that performs adaptive recalibration of channel-wise feature responses. Through this mechanism, it can learn to use global information to selectively emphasize or suppress reconstruction maps, as necessary. Another motivation to use attention is to increase the modeling capacity of SSP-CAB and enable a non-linear processing between the input and output of our block. + +Formally, the channel attention block reduces $Z$ to a vector $z \in \mathbb{R}^c$ through a global pooling performed on each channel. Subsequently, the vector of scale factors $s \in \mathbb{R}^c$ is computed as follows: + +$$ +\boldsymbol {s} = \sigma \left(\boldsymbol {W} _ {2} \cdot \delta \left(\boldsymbol {W} _ {1} \cdot \boldsymbol {z}\right)\right), \tag {1} +$$ + +where $\sigma$ is the sigmoid activation, $\delta$ is the ReLU activation, and $W_{1} \in \mathbb{R}^{\frac{c}{r} \times c}$ and $W_{2} \in \mathbb{R}^{c \times \frac{c}{r}}$ represent the weight matrices of two consecutive fully connected (FC) layers, respectively. The first FC layer consists of $\frac{c}{r}$ neurons, squeezing the information by a reduction ratio of $r$ . + +Next, the vector $s$ is replicated in the spatial dimension, generating a tensor $S$ of the same size as $Z$ . Our last step is the element-wise multiplication between $S$ and $Z$ , producing the final tensor $\hat{X} \in \mathbb{R}^{h \times w \times c}$ containing recalibrated features maps. + +Reconstruction loss. We add a self-supervised task consist + +ing of reconstructing the masked region inside our convolutional receptive field, for every location where the masked filters are applied. To this end, our block should learn to provide the corresponding reconstructions as the output $\hat{\pmb{X}}$ . Let $G$ denote the SSPCAB function. We define the self-supervised reconstruction loss as the mean squared error (MSE) between the input and the output, as follows: + +$$ +\mathcal {L} _ {\mathrm {S S P C A B}} (G, \boldsymbol {X}) = (G (\boldsymbol {X}) - \boldsymbol {X}) ^ {2} = \left(\hat {\boldsymbol {X}} - \boldsymbol {X}\right) ^ {2}. \tag {2} +$$ + +When integrating SSPCAB into a neural model $F$ having its own loss function $\mathcal{L}_F$ , our loss can simply be added to the respective loss, resulting in a new loss function that comprises both terms: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {F} + \lambda \cdot \mathcal {L} _ {\text {S S P C A B}}, \tag {3} +$$ + +where $\lambda \in \mathbb{R}^{+}$ is a hyperparameter that controls the importance of our loss with respect to $\mathcal{L}_F$ . We adopt this procedure when incorporating SSPCAB into various neural architectures during our experiments. + +# 4. Experiments and Results + +# 4.1. Data Sets + +MVTec AD. The MVTec AD [5] data set is a standard benchmark for evaluating anomaly detection methods on industrial inspection images. It contains images from 10 object categories and 5 texture categories, having 15 categories in total. There are 3629 defect-free training images and 1725 test images with or without anomalies. + +Avenue. The CHUK Avenue [40] data set is a popular benchmark for video anomaly detection. It contains 16 training and 21 test videos. The anomalies are present only at inference time and include people throwing papers, running, dancing, loitering, and walking in the wrong direction. + +ShanghaiTech. The ShanghaiTech [43] benchmark is one of the largest data sets for video anomaly detection. It is formed of 330 training and 107 test videos. As for Avenue, the training videos contain only normal samples, but the test videos can contain both normal and abnormal events. Some examples of anomalies are: people fighting, stealing, chasing, jumping, and riding bike or skating in pedestrian zones. + +# 4.2. Evaluation Metrics + +Image anomaly detection. On MVTec AD, we evaluate methods in terms of the average precision (AP) and the area under the receiver operating characteristic curve (AUROC). The ROC curve is obtained by plotting the true positive rate (TPR) versus the false positive rate (FPR). We consider both localization and detection performance rates. For the detection task, the TPR and FPR values are computed at the image level, i.e. TPR is the percentage of anomalous images that are correctly classified, while FPR is the percentage of normal images mistakenly classified as anomalous. + +For the localization (segmentation) task, TPR is the percentage of abnormal pixels that are correctly classified, whereas FPR is the percentage of normal pixels wrongly classified as anomalous. To determine the segmentation threshold for each method, we follow the approach described in [5]. + +Video anomaly detection. We evaluate abnormal event detection methods in terms of the area under the curve (AUC), which is computed by marking a frame as abnormal if at least one pixel inside the frame is abnormal. Following [18], we report both the macro and micro AUC scores. The micro AUC is computed after concatenating all frames from the entire test set, while the macro AUC is the average of the AUC scores on individual videos. The frame-level AUC can be an unreliable evaluation measure, as it may fail to evaluate the localization of anomalies [50]. Therefore, we also evaluate models in terms of the region-based detection criterion (RBDC) and track-based detection criterion (TBDC), as proposed by Ramachandra et al. [50]. RBDC takes each detected region into consideration, marking a detected region as true positive if the Intersection-over-Union with the ground-truth region is greater than a threshold $\alpha$ . TBDC measures whether abnormal regions are accurately tracked across time. It considers a detected track as true positive if the number of detections in a track is greater than a threshold $\beta$ . Following [18, 50], we set $\alpha = 0.1$ and $\beta = 0.1$ . + +# 4.3. Implementation Choices and Tuning + +For the methods [18,34,37,39,49,79] chosen to serve as underlying models for SSPCAB, we use the official code from the repositories provided by the corresponding authors, inheriting the hyperparameters, e.g. the number of epochs and learning rate, from each method. Unless specified otherwise, we replace the penultimate convolutional layer with SSPCAB in all underlying models. + +In a set of preliminary trials with a basic auto-encoder on Avenue, we tuned the hyperparameter $\lambda$ from Eq. (3), representing the weight of the SSPCAB reconstruction error, considering values between 0.1 and 1, at a step of 0.1. Based on these preliminary trials, we decided to use $\lambda = 0.1$ across all models and data sets. However, we observed that $\lambda = 0.1$ gives a higher than necessary magnitude to our loss for the framework of Liu et al. [39]. Hence, for Liu et al. [39], we reduced $\lambda$ to 0.01. + +# 4.4. Preliminary Results + +We performed preliminary experiments on Avenue to decide the hyperparameters of our masked convolution, i.e. the kernel size $k'$ and dilation rate $d$ . We consider values in $\{1,2,3\}$ for $k'$ , and values in $\{0,1,2\}$ for $d$ . In addition, we consider two alternative loss functions, namely the Mean Absolute Error (MAE) and Mean Squared Error (MSE), and several types of attention to be added after the masked convolution, namely channel attention (CA), spatial + +
MethodLoss typedk'rAttention typeAUCRBDCTBDC
MicroMacro
Plain auto-encoder-----80.083.449.9851.69
MAE01--83.384.147.4652.11
11--83.984.649.0552.21
21--83.284.348.5652.03
MSE01--83.684.247.8652.21
11--84.284.949.2252.29
21--83.684.348.4451.98
MSE02--83.784.047.4153.02
12--84.085.148.2251.84
22--82.783.146.9450.22
MSE03--82.683.748.2851.91
13--82.984.748.1352.07
23--83.183.847.1349.96
MSE118CA85.985.653.8156.33
11-SA84.384.453.3153.41
118CA+SA85.785.653.9854.11
MSE114CA85.685.353.8355.99
1116CA84.484.953.2854.37
+ +Table 1. Micro AUC, macro AUC, RBDC and TBDC scores (in %) obtained on the Avenue data set with different hyperparameter configurations, i.e. kernel size $(k^{\prime})$ , dilation rate $(d)$ , reduction ratio $(r)$ , loss type, and attention type, for our SSPCAB. Results are obtained by introducing SSPCAB into a plain auto-encoder that follows the basic architecture designed by Georgescu et al. [18]. Best results are highlighted in bold. + +# attention (SA), and both $(\mathrm{CA} + \mathrm{SA})$ + +For the preliminary experiments, we take the appearance convolutional auto-encoder from [18] as our baseline, stripping out the additional components such as optical flow, skip connections, adversarial training, mask reconstruction and binary classifiers. Our aim is to test various SSPCAB configurations on top of a basic architecture, without trying to overfit the configuration to a specific framework, such as that of Georgescu et al. [18]. To this end, we decided to remove the aforementioned components, thus using only a plain auto-encoder in our preliminary experiments. + +The preliminary results are presented in Table 1. Upon adding the masked convolutional layer based on the MAE loss on top of the basic architecture, we observe significant performance gains, especially for $k' = 1$ and $d = 1$ . The performance further increases when we replace the MAE loss function with MSE. We performed extensive experiments with different combinations of $k'$ and $d$ , obtaining better results with $k' = 1$ and $d = 1$ . We therefore decided to fix the loss to MSE, the sub-kernel size $k'$ to 1, and the dilation rate $d$ to 1, for all subsequent experiments. Next, we introduced various attention modules after our masked convolution. Among the considered attention modules, we observe that channel attention is the one that better complements our masked convolutional layer, providing the highest performance gains for three of the metrics: $5.9\%$ for the + +![](images/cc1438d543a3dc43cecd37a753344347e31ecee4f88ea3eef44b4fc75d34a4a4.jpg) +Figure 3. Anomaly localization examples of DRAEM [79] (blue) versus DRAEM+SSPCAB (green) on MVTec AD. The groundtruth anomalies are marked with a red mask. Best viewed in color. + +![](images/c8beaddf3fac72e66444d56c6403cbd1922f944d73b4b1fd78335fa868d4efe1.jpg) + +![](images/5c6cbcb05b486a48082d822b47a38c0a8e6521c461bc61d99a9cf58b26ea461b.jpg) + +micro AUC, $2.2\%$ for the macro AUC, and $4.6\%$ for TBDC. Accordingly, we selected the channel attention module for the remaining experiments. Upon choosing to use channel attention, we test additional reduction rates $(r = 4$ and $r = 16)$ , without observing any improvements. As such, we keep the reduction rate of the SE module to $r = 8$ , whenever we integrate SSPCAB into a neural model. + +# 4.5. Anomaly Detection in Images + +Baselines. We choose two recent models for image anomaly detection, i.e. CutPaste [34] and DRAEM [79]. + +Li et al. [34] proposed CutPaste, a simple data augmentation technique that cuts a patch from an image and pastes it to a random location. The CutPaste architecture is built on top of GradCAM [64]. The model is based on a self-supervised 3-way classification task, learning to classify samples into normal, CutPaste and CutPaste-Scar, where a scar is a long and thin mark of a random color. Li et al. [34] also used an ensemble of five 3-way CutPaste models trained with different random seeds to improve results. + +Zavrtanik et al. [79] introduced $DRAEM$ , a method based on a dual auto-encoder for anomaly detection and localization on MVTec AD. We introduce SSPCAB into both the localization and detection networks. + +Results. We present the results on MVTec AD in Table 2. Considering the detection results, we observe that SSPCAB brings consistent performance improvements on most categories for both CutPaste [34] and DRAEM [79]. Moreover, the overall performance gains in terms of detection AUROC are close to $1\%$ , regardless of the underlying model. Given that the baselines are already very good, we consider the improvements brought by SSPCAB as noteworthy. + +Considering the localization results, it seems that SSP-CAB is not able to improve the overall AUROC score of DRAEM [79]. However, the more challenging AP metric tells a different story. Indeed, SSPCAB increases the overall AP of DRAEM [79] by $1.5\%$ , from $68.4\%$ to $69.9\%$ . + +In Figure 3, we illustrate a few anomaly localization examples where SSPCAB introduces significant changes to the anomaly localization contours of DRAEM [79], showing a higher overlap with the ground-truth anomalies. We believe that these improvements are a direct effect induced + +
ClassLocalizationDetection
DRAEM [79]DRAEM [79]CutPaste [34]
3-wayEnsemble
+SSPCAB+SSPCAB+SSPCAB+SSPCAB+SSPCAB
AUROCAUROCAPAPAUROCAUROCAUROCAUROCAUROCAUROC
TextureCarpet95.595.053.559.497.098.293.190.793.996.8
Grid99.799.565.761.199.9100.099.999.9100.099.9
Leather98.699.575.376.0100.0100.0100.0100.0100.0100.0
Tile99.299.392.395.099.6100.093.494.094.695.0
Wood96.496.877.777.199.199.598.699.299.199.1
ObjectBottle99.198.886.587.999.298.498.398.698.299.1
Cable94.796.052.457.291.896.980.682.981.283.6
Capsule94.393.149.450.298.599.396.298.198.297.6
Hazelnut99.799.892.992.6100.0100.097.398.398.398.4
Metal Nut99.598.996.398.198.7100.099.399.699.999.9
Pill97.697.548.552.498.999.892.495.394.996.6
Screw97.699.858.272.093.997.986.390.888.790.8
Toothbrush98.198.144.751.0100.0100.098.398.899.499.6
Transistor90.987.050.748.093.192.995.596.596.197.3
Zipper98.899.081.577.1100.0100.099.499.199.999.9
Overall97.397.268.469.998.098.995.296.196.196.9
+ +Table 2. Localization AUROC/AP and detection AUROC (in %) of state-of-the-art methods on MVTec AD, before and after adding SSPCAB. The best result for each before-versus-after pair is highlighted in bold. + +![](images/9bb5fcb844900d1796454cb1e3b769d51d7bddc7f61c8a79516e8c3cfe70c1bb.jpg) +Figure 4. Frame-level anomaly scores for Liu et al. [37] before (baseline) and after (ours) integrating SSPCAB, for test video 18 from Avenue. Anomaly localization results correspond to the model based on SSPCAB. Best viewed in color. + +by the reconstruction errors produced by our novel block. We provide more anomaly detection examples in the supplementary. + +# 4.6. Abnormal Event Detection in Video + +Baselines. We choose four recently introduced methods [18, 37, 39, 49] attaining state-of-the-art performance levels in video anomaly detection, as candidates for integrating SSPCAB. We first reproduce the results using the official implementations provided by the corresponding authors [18, 37, 39, 49]. We refrain from making any modifi + +cation to the hyperparameters of the chosen baselines. Despite using the unmodified code from the official repositories, we were not able to exactly reproduce the results of Liu et al. [39] and Park et al. [49], but our numbers are very close. As we add SSPCAB into the reproduced models, we consider the reproduced results as reference. We underline that, for Georgescu et al. [18], we integrate SSPCAB into the auto-encoders, not in the binary classifiers. We report RBDC and TBDC results whenever possible, computing the scores using the implementation provided by Georgescu et al. [18]. + +Results. We report the results on Avenue and ShanghaiTech in Table 3. First, we observe that the inclusion of SSPCAB in the framework of Liu et al. [37] brings consistent improvements over all metrics on both benchmarks. Similarly, we observe consistent performance gains when integrating SSPCAB into the model of Park et al. [49]. We note that the method of Park et al. [49] does not produce anomaly localization results, preventing us from computing the RBDC and TBDC scores for their method. SSPCAB also brings consistent improvements for Liu et al. [39], the only exception being the macro AUC on Avenue. For this baseline [39], we observe a remarkable increase of $21.22\%$ in terms of the RBDC score on Avenue. Finally, we notice that SSPCAB also improves the performance of the approach proposed by Georgescu et al. [18] for almost all metrics, the exceptions being the TBDC on Avenue and RBDC on ShanghaiTech. In summary, we conclude that integrating SSPCAB is beneficial, regardless of the underlying model. Moreover, due to the integration of SSPCAB, we are able + +
VenueMethodAvenueShanghaiTech
AUCRBDCTBDCAUCRBDCTBDC
MicroMacroMicroMacro
BMVC 2018Liu et al. [38]84.4-------
CVPR 2018Sultani et al. [66]-----76.5--
ICASSP 2018Lee et al. [32]87.2--76.2--
WACV 2019Ionescu et al. [27]88.9-------
ICCV 2019Nguyen et al. [47]86.9-------
CVPR 2019Ionescu et al. [25]87.490.415.7727.0178.784.920.6544.54
TNNLS 2019Wu et al. [73]86.6------
TIP 2019Lee et al. [33]90.0------
ACMMM 2020Yu et al. [77]89.6---74.8---
WACV 2020Ramachandra et al. [50]72.035.8080.90----
WACV 2020Ramachandra et al. [51]87.241.2078.60----
PRL 2020Tang et al. [69]85.1--73.0--
Access 2020Dong et al. [12]84.9--73.7--
CVPRW 2020Doshi et al. [13]86.4--71.6--
ACMMM 2020Sun et al. [67]89.6--74.7--
ACMMM 2020Wang et al. [72]87.0--79.3--
ICCVW 2021Astrid et al. [4]84.7---73.7---
BMVC 2021Astrid et al. [3]87.1---75.9---
CVPR 2021Georgescu et al. [17]91.592.857.0058.3082.490.242.8083.90
CVPR 2018Liu et al. [37]85.181.719.5956.0172.880.617.0354.23
CVPR 2022Liu et al. [37] + SSPCAB87.384.520.1362.3074.582.918.5160.22
CVPR 2020Park et al. [49]82.886.8--68.379.7--
CVPR 2022Park et al. [49] + SSPCAB84.888.6--69.880.2--
ICCV 2021Liu et al. [39]89.993.541.0586.1874.283.244.4183.86
CVPR 2022Liu et al. [39] + SSPCAB90.992.262.2789.2875.583.745.4584.50
TPAMI 2021Georgescu et al. [18]92.390.465.0566.8582.789.341.3478.79
CVPR 2022Georgescu et al. [18] + SSPCAB92.991.965.9964.9183.689.540.5583.46
+ +Table 3. Micro-averaged frame-level AUC, macro-averaged frame-level AUC, RBDC, and TBDC scores (in %) of various state-of-the-art methods on Avenue and ShanghaiTech. Among the existing models, we select four models [18, 37, 39, 49] to show results before and after including SSPCAB. The best result for each before-versus-after pair is highlighted in bold. The top score for each metric is shown in red. + +to report new state-of-the-art results on Avenue and ShanghaiTech, for several metrics. + +In Figure 4, we compare the frame-level anomaly scores on test video 18 from Avenue, before and after integrating SSPCAB into the method of Liu et al. [37]. On this video, SSPCAB increases the AUC by more than $5\%$ . We observe that the approach based on SSPCAB can precisely localize and detect the abnormal event (person walking in the wrong direction). We provide more anomaly detection examples in the supplementary. + +# 5. Conclusion + +In this paper, we introduced SSPCAB, a novel neural block composed of a masked convolutional layer and a channel attention module, which predicts a masked region in the convolutional receptive field. Our neural block is trained in a self-supervised manner, via a reconstruction loss of its own. To show the benefit of using SSP-CAB in anomaly detection, we integrated our block into a series of image and video anomaly detection methods + +[18, 34, 37, 39, 49, 79]. Our empirical results indicate that SSPCAB brings performance improvements in almost all cases. The preliminary results show that both the masked convolution and the channel attention contribute to the performance gains. Furthermore, with the help of SSPCAB, we are able to obtain new state-of-the-art levels on Avenue and ShanghaiTech. We consider this as a major achievement. + +In future work, we aim to extend SSPCAB by replacing the masked convolution with a masked 3D convolution. In addition, we aim to consider other application domains besides anomaly detection. + +# Acknowledgments + +The research leading to these results has received funding from the EEA Grants 2014-2021, under Project contract no. EEA-RO-NO-2018-0496. This work has also been funded by the Milestone Research Programme at AAU, SecurifAI, and the Romanian Young Academy, which is funded by Stiftung Mercator and the Alexander von Humboldt Foundation for the period 2020-2022. + +# References + +[1] Amit Adam, Ehud Rivlin, Ilan Shimshoni, and Daviv Reinitz. Robust Real-Time Unusual Event Detection Using Multiple Fixed-Location Monitors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30(3):555-560, 2008. 1, 2 +[2] Borislav Antic and Bjorn Ommer. Video parsing for abnormality detection. In Proceedings of ICCV, pages 2415-2422, 2011. 1, 2 +[3] Marcella Astrid, Muhammad Zaigham Zaheer, Jae-Yeong Lee, and Seung-Ik Lee. Learning not to reconstruct anomalies. 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Roth +NVIDIA + +Bennett Landman Vanderbilt University + +Daguang Xu +NVIDIA + +Vishwesh Nath\nNVIDIA + +Ali Hatamizadeh†‡ NVIDIA + +# Abstract + +Vision Transformers (ViT)s have shown great performance in self-supervised learning of global and local representations that can be transferred to downstream applications. Inspired by these results, we introduce a novel self-supervised learning framework with tailored proxy tasks for medical image analysis. Specifically, we propose: (i) a new 3D transformer-based model, dubbed Swin UNet Transformers (Swin UNETR), with a hierarchical encoder for self-supervised pre-training; (ii) tailored proxy tasks for learning the underlying pattern of human anatomy. We demonstrate successful pre-training of the proposed model on 5,050 publicly available computed tomography (CT) images from various body organs. The effectiveness of our approach is validated by fine-tuning the pre-trained models on the Beyond the Cranial Vault (BTCV) Segmentation Challenge with 13 abdominal organs and segmentation tasks from the Medical Segmentation Decathlon (MSD) dataset. Our model is currently the state-of-the-art on the public test leaderboards of both $\mathsf{MSD}^1$ and BTCV $^2$ datasets. Code: https://monai.io/research/swin-unetr. + +# 1. Introduction + +Vision Transformers (ViT)s [16] have started a revolutionary trend in computer vision [12, 54] and medical image analysis [6, 19]. Transformers demonstrate exceptional capability in learning pre-text tasks, are effective in learning of global and local information across layers, and provide + +![](images/1ce04aaaf2c06188462a4bfd46974c03aaada23967d458f177cd76c89822de2b.jpg) +Figure 1. Overview of our proposed pre-training framework. Input CT images are randomly cropped into sub-volumes and augmented with random inner cutout and rotation, then fed to the Swin UNETR encoder as input. We use masked volume inpainting, contrastive learning and rotation prediction as proxy tasks for learning contextual representations of input images. + +scalability for large-scale training [38, 52]. As opposed to convolutional neural networks (CNNs) with limited receptive fields, ViTs encode visual representations from a sequence of patches and leverage self-attention blocks for modeling long-range global information [38]. Recently, Shifted windows (Swin) Transformers [30] proposed a hierarchical ViT that allows for local computing of self-attention with + +non-overlapping windows. This architecture achieves linear complexity as opposed to quadratic complexity of self-attention layers in ViT, hence making it more efficient. In addition, due to the hierarchical nature of Swin Transformers, they are well-suited for tasks requiring multi-scale modeling. + +In comparison to CNN-based counterparts, transformer-based models learn stronger features representations during pre-training, and as a result perform favorably on fine-tuning downstream tasks [38]. Several recent efforts on ViTs [5, 48] have achieved new state-of-the-art results by self-supervised pre-training on large-scale datasets such as ImageNet [15]. + +In addition, medical image analysis has not benefited from these advances in general computer vision due to: (1) large domain gap between natural images and medical imaging modalities, like computed tomography (CT) and magnetic resonance imaging (MRI); (2) lack of cross-plane contextual information when applied to volumetric (3D) images (such as CT or MRI). The latter is a limitation of 2D transformer models for various medical imaging tasks such as segmentation. Prior studies have demonstrated the effectiveness of supervised pre-training in medical imaging for different applications [9, 39]. But creating expert-annotated 3D medical datasets at scale is a non-trivial and time-consuming effort. + +To tackle these limitations, we propose a novel self-supervised learning framework for 3D medical image analysis. First, we propose a new architecture dubbed Swin UNet TR transformers (Swin UNETR) with a Swin Transformer encoder that directly utilizes 3D input patches. Subsequently, the transformer encoder is pre-trained with tailored, self-supervised tasks by leveraging various proxy tasks such as image inpainting, 3D rotation prediction, and contrastive learning (See Fig. 1 for an overview). Specifically, the human body presents naturally consistent contextual information in radiographic images such as CT due to its depicted anatomical structure [43,50]. Hence, proxy tasks are utilized for learning the underlying patterns of the human anatomy. For this purpose, we extracted numerous patch queries from different body compositions such as head, neck, lung, abdomen, and pelvis to learn robust feature representations from various anatomical contexts, organs, tissues, and shapes. + +Our framework utilizes contrastive learning [35], masked volume inpainting [37], and 3D rotation prediction [17] as pre-training proxy tasks. The contrastive learning is used to differentiate various ROIs of different body compositions, whereas the inpainting allows for learning the texture, structure and correspondence of masked regions to their surrounding context. The rotation task serves as a mechanism to learn the structural content of images and generates various sub-volumes that can be used for contrastive learning. We utilize these proxy tasks to pre-train our proposed framework on a collection of 5,050 CT images that are acquired from various publicly available datasets. + +Furthermore, to validate the effectiveness of pre-training, + +we use 3D medical image segmentation as a downstream application and reformulate it as a 1D sequence-to-sequence prediction task. For this purpose, we leverage the Swin UNETR encoder with hierarchical feature encoding and shifted windows to extract feature representations at four different resolutions. The extracted representations are then connected to a CNN-based decoder. A segmentation head is attached at the end of the decoder for computing the final segmentation output. We fine-tune Swin UNETR with pre-trained weights on two publicly available benchmarks of Medical Segmentation Decathlon (MSD) and the Beyond the Cranial Vault (BTCV). Our model is currently the state-of-the-art on their respective public test leaderboards. + +Our main contributions in this work are summarized as follows: + +- We introduce a novel self-supervised learning framework with tailored proxy tasks for pre-training on CT image datasets. To this end, we propose a novel 3D transformer-based architecture, dubbed as Swin UNETR, consisting of an encoder that extracts feature representations at multiple resolutions and is utilized for pre-training. +- We demonstrate successful pre-training on a cohort of 5,050 publicly available CT images from various applications using the proposed encoder and proxy tasks. This results in a powerful pre-trained model with robust feature representation that could be utilized for various medical image analysis downstream tasks. +- We validate the effectiveness of proposed framework by fine-tuning the pre-trained Swin UNETR on two public benchmarks of MSD and BTCV and achieve state-of-the-art on the test leaderboards of both datasets. + +# 2. Related Works + +Medical Segmentation with Transformers Vision transformers are first used in classification tasks and are adopted from sequence-to-sequence modeling in natural language processing. Self-attention mechanisms that aggregate information from the entire input sequence are first achieving comparable, then better performance against prior arts of convolutional architectures such as ResNet [21] or U-Net [13]. Recently, transformer-based networks [24, 47, 49, 55] are proposed for medical image segmentation. In these pioneering works, the transformer blocks are used either as a bottleneck feature encoder or as additional modules after convolutional layers, resulting in limited exploitation of the spatial context advantages of transformers. Comparing to prior works [6, 47], which are using transformers as secondary encoder, we propose to utilize transformers to embed high-dimensional volumetric medical images, which allow for a more direct encoding of 3D patches and positional embeddings. + +![](images/83019d3583efe5856be9f6a92c65d8392a12c552f0809c1111c31b3d5a6f68bf.jpg) +Figure 2. Overview of the Swin UNETR architecture. + +Most medical image analysis tasks such as segmentation requires dense inference from multi-scale features. Skip connection-based architectures such as UNet [13] and pyramid networks [40] are widely adopted to leverage hierarchical features. However, vision transformers with a single patch size, while successful in natural image applications, are intractable for high-resolution and high-dimensional volumetric images. To avoid quadratic overflow of computing self-attention at scales [29, 41], Swin Transformer [30, 31] is proposed to construct hierarchical encoding by a shifted-window mechanism. Recent works such as Swin UNet [4] and DS-TransUNet [28] utilize the merits of Swin Transformers for 2D segmentation and achieve promising performance. Augmenting the above-mentioned methods, we learn from 3D anatomy in broader medical image segmentation scenarios by incorporating hierarchically volumetric context. + +Pre-training in Medical Image Analysis In medical image analysis, previous studies of pre-training on labeled data demonstrate improved performance by transfer learning [9, 39]. However, generating annotation for medical images is expensive and time-consuming. Recent advances in self-supervised learning offer the promise of utilizing unlabeled data. Self-supervised representation learning [2, 14, 27] constructs feature embedding spaces by designing pre-text tasks, such as solving jigsaw puzzles [34]. Another commonly used pre-text task is to memorize spatial context from medical images, which is motivated by image restoration. This idea is generalized to inpainting tasks [18, 37, 57] to learn visual representations [3, 7, 46] by predicting the original image patches. Similar efforts for reconstructing spatial context have been formulated as solving Rubik's cube problem [58], random rotation prediction [17, 42] and contrastive coding [11, 35]. Different from these efforts, our pre-training framework is simulta + +neously trained with a combination of pre-text tasks, tailored for 3D medical imaging data, and leverages a transformer-based encoder as a powerful feature extractor. + +# 3. Swin UNETR + +Swin UNETR comprises a Swin Transformer [30] encoder that directly utilizes 3D patches and is connected to a CNN-based decoder via skip connections at different resolutions. Fig. 2 illustrates the overall architecture of Swin UNETR. We describe the details of encoder and decoder in this section. + +# 3.1. Swin Transformer Encoder + +Assuming that the input to the encoder is a sub-volume $\mathcal{X} \in \mathbb{R}^{H \times W \times D \times S}$ , a 3D token with a patch resolution of $(H', W', D')$ has a dimension of $H' \times W' \times D' \times S$ . The patch partitioning layer creates a sequence of 3D tokens with size $\frac{H}{H'} \times \frac{W}{W'} \times \frac{D}{D'}$ that are projected into a $C$ -dimensional space via an embedding layer. Following [30], for efficient modeling of token interactions, we partition the input volumes into non-overlapping windows and compute local self-attention within each region. Specifically, at layer $l$ , we use a window of size $M \times M \times M$ to evenly divide a 3D token into $\left\lfloor \frac{H'}{M} \right\rfloor \times \left\lfloor \frac{W'}{M} \right\rfloor \times \left\lfloor \frac{D'}{M} \right\rfloor$ windows. In the subsequent layer $l + 1$ , we shift the partitioned windows by $\left( \left\lfloor \frac{M}{2} \right\rfloor, \left\lfloor \frac{M}{2} \right\rfloor, \left\lfloor \frac{M}{2} \right\rfloor \right)$ voxels. The shifted windowing mechanism is illustrated in Fig. 3. The outputs of encoder blocks in layers $l$ and $l + 1$ are computed as in + +$$ +\begin{array}{l} \hat {z} ^ {l} = \mathrm {W - M S A} (\mathrm {L N} (z ^ {l - 1})) + z ^ {l - 1} \\ z ^ {l} = \operatorname {M L P} (\operatorname {L N} (\hat {z} ^ {l})) + \hat {z} ^ {l} \\ \hat {z} ^ {l + 1} = \overline {{\mathrm {S W - M S A}}} \left(\mathrm {L N} \left(z ^ {l}\right)\right) + z ^ {l} \tag {I} \\ z ^ {l + 1} = \operatorname {M L P} \left(\operatorname {L N} \left(\hat {z} ^ {l + 1}\right)\right) + \hat {z} ^ {l + 1}, \\ \end{array} +$$ + +where W-MSA and SW-MSA denote regular and window partitioning multi-head self-attention modules, respectively, + +$\hat{z}^l$ and $\hat{z}^l$ are the outputs of W-MSA and SW-MSA; LN and MLP denote layer normalization and Multi-Layer Perceptron (see Fig. 2). Following [30], we adopt a 3D cyclic-shifting for efficient batch computation of shifted windowing. Furthermore, we calculate the self-attention according to + +$$ +\operatorname {A t t e n t i o n} (Q, K, V) = \operatorname {S o f t m a x} \left(\frac {Q K ^ {\top}}{\sqrt {d}}\right) V. \tag {2} +$$ + +where $Q, K, V$ represent queries, keys and values respectively, $d$ is the size of the query and key. + +Our encoder uses a patch size of $2 \times 2 \times 2$ with a feature dimension of $2 \times 2 \times 2 \times 1 = 8$ (i.e. single input channel CT images) and a $C = 48$ -dimensional embedding space. Furthermore, the overall architecture of the encoder consists of 4 stages comprising of 2 transformer blocks at each stage (i.e. $L = 8$ total layers). In between every stage, a patch merging layer is used to reduce the resolution by a factor of 2. Stage 1 consists of a linear embedding layer and transformer blocks that maintain the number of tokens as $\frac{H}{2} \times \frac{W}{2} \times \frac{D}{2}$ . Furthermore, a patch merging layer groups patches with resolution $2 \times 2 \times 2$ and concatenates them, resulting in a $4C$ -dimensional feature embedding. A linear layer is then used to downsample the resolution by reducing the dimension to $2C$ . The same procedure continues in stage 2, stage 3 and stage 4 with resolutions of $\frac{H}{4} \times \frac{W}{4} \times \frac{D}{4}$ , $\frac{H}{8} \times \frac{W}{8} \times \frac{D}{8}$ and $\frac{H}{16} \times \frac{W}{16} \times \frac{D}{16}$ respectively. The hierarchical representations of the encoder at different stages are used in downstream applications such as segmentation for multi-scale feature extraction. + +# 3.2.Decoder + +The encoder of Swin UNETR is connected to a CNN-based decoder at each resolution via skip connections to create a "U-shaped" network for downstream applications such as segmentation. Specifically, we extract the output sequence representations of each stage $i$ ( $i \in \{0,1,2,3,4\}$ ) in the encoder as well as the bottleneck ( $i = 5$ ) and reshape them into features with size $\frac{H}{2^i} \times \frac{W}{2^i} \times \frac{D}{2^i}$ . The extracted representations at each stage are then fed into a residual block consisting of two post-normalized $3 \times 3 \times 3$ convolutional layers with instance normalization [45]. The processed features from each stage are then upsampled by using a deconvolutional layer and concatenated with processed features of the preceding stage. The concatenated features are fed into a residual block with aforementioned descriptions. For segmentation, we concatenate the output of the encoder (i.e. Swin Transformer) with processed features of the input volume and feed them into a residual block followed by a final $1 \times 1 \times 1$ convolutional layer with a proper activation function (i.e. softmax) for computing the segmentation probabilities (see Fig. 2 for details of the architecture). + +# 4. Pre-training + +We pre-train the Swin UNETR encoder with multiple proxy tasks and formulate it with a multi-objective loss func + +![](images/ce101eb367ee939b9016936c7e63edffa9b13b61f9d4eee0f74d5052986f2c53.jpg) +3D Tokens: $8 \times 8 \times 8$ Window size: $4 \times 4 \times 4$ + +![](images/694310dc08fa811db930f0a366b7a7c978e210a3143473d23847a20aff7671cf.jpg) +Number of windows: 8 + +![](images/06392e8fcfd84a4261f80cc457c30f8774a567aba4f361f13c8092fbe3dbb891.jpg) +Layer $l + 1$ Self-attention Unit +Figure 3. Shifted windowing mechanism for efficient self-attention computation of 3D tokens with $8 \times 8 \times 8$ tokens and $4 \times 4 \times 4$ window size. + +tion (Fig. 1). The objective of self-supervised representation learning is to encode region of interests (ROI)-aware information of the human body. Inspired by previous works on context reconstruction [18, 57] and contrastive encoding [20], we exploit three proxy tasks for medical image representation learning. Three additional projection heads are attached to the encoder during pre-training. Furthermore, the downstream task, e.g. segmentation, fine-tunes the full Swin UNETR model with the projection heads removed. In training, sub-volumes are cropped random regions of the volumetric data. Then, stochastic data augmentations with random rotation and cutout are applied twice to each sub-volume within a mini-batch, resulting in two views of each data. + +# 4.1. Masked Volume Inpainting + +The cutout augmentation masks out ROIs in the subvolume $\mathcal{X} \in \mathbb{R}^{H \times W \times D \times C}$ randomly with volume ratio of $s$ . We attach a transpose convolution layer to the encoder as the reconstruction head and denote its output as $\hat{\mathcal{X}}^{\mathcal{M}}$ . The reconstruction objective is defined by an $L1$ loss between $\mathcal{X}$ and $\hat{\mathcal{X}}^{\mathcal{M}}$ + +$$ +\mathcal {L} _ {\text {i n p a i n t}} = \left\| \mathcal {X} - \hat {\mathcal {X}} ^ {\mathcal {M}} \right\| _ {1}, \tag {3} +$$ + +The masked volume inpainting is motivated by prior work which focused on 2D images [37]. We extend it to 3D domain to showcase its effectiveness on representation learning of volumetric medical images. + +# 4.2. Image Rotation + +The rotation prediction task predicts the angle categories by which the input sub-volume is rotated. For simplicity, we employ $R$ classes of $0^{\circ}, 90^{\circ}, 180^{\circ}, 270^{\circ}$ rotations along the $z$ -axis. An MLP classification head is used for predicting the softmax probabilities $\hat{y}_r$ of rotation categories. Given the ground truth $y_r$ , a cross-entropy loss is used for rotation prediction task: + +$$ +\mathcal {L} _ {\text {r o t}} = - \sum_ {r = 1} ^ {R} y _ {r} \log \left(\hat {y} _ {r}\right), \tag {4} +$$ + +The 3D rotation and cutout also serves simultaneously as an augmentation transformation for contrastive learning. + +# 4.3. Contrastive Coding + +The self-supervised contrastive coding presents promising performance on visual representation learning when transferred to downstream tasks [10, 36]. Given a batch of augmented sub-volumes, the contrastive coding allows for a better representation learning by maximizing the mutual information between positive pairs (augmented samples from same sub-volume), while minimizing that between negative pairs (views from different sub-volumes). The contrastive coding is obtained by attaching a linear layer to the Swin UNETR encoder, which maps each augmented sub-volume to a latent representation $v$ . We use cosine similarity as the distance measurement of the encoded representations as defined in [10]. Formally, the 3D contrastive coding loss between a pair $v_{i}$ and $v_{j}$ is defined as: + +$$ +\mathcal {L} _ {\text {c o n t r a s t}} = - \log \frac {\exp \left(\operatorname {s i m} \left(v _ {i} , v _ {j}\right) / t\right)}{\sum_ {k} ^ {2 N} 1 _ {k \neq i} \exp \left(\operatorname {s i m} \left(v _ {i} , v _ {k}\right) / t\right)}, \tag {5} +$$ + +where $t$ is the measurement of normalized temperature scale. 1 is the indicator function evaluating to 1 iff $k \neq i$ . sim denotes the dot product between normalized embeddings. The contrastive learning loss function strengthens the intra-class compactness as well as the inter-class separability. + +# 4.4. Loss Function + +Formally, we minimize the total loss function by training Swin UNETR's encoder with multiple pre-training objectives of masked volume inpainting, 3D image rotation & contrastive coding as follows: + +$$ +\mathcal {L} _ {t o t} = \lambda_ {1} \mathcal {L} _ {\text {i n p a i n t}} + \lambda_ {2} \mathcal {L} _ {\text {c o n t r a s t}} + \lambda_ {3} \mathcal {L} _ {\text {r o t}}. \tag {6} +$$ + +A grid-search hyper-parameter optimization was performed which estimated the optimal values of $\lambda_1 = \lambda_2 = \lambda_3 = 1$ . + +# 5. Experiments + +# 5.1. Datasets + +Pre-training Datasets: A total of 5 public CT datasets, consisting of 5,050 subjects, are used to construct our pre-training dataset. The corresponding number of 3D volumes for chest, abdomen and head/neck are 2,018, 1,520 and 1,223 respectively. The collection and source details are presented in the supplementary materials. Existing annotations or labels are not utilized from these datasets during the pre-training stage. + +BTCV: The Beyond the Cranial Vault (BTCV) abdomen challenge dataset [26] contains 30 subjects with abdominal + +CT scans where 13 organs are annotated by interpreters under supervision of radiologists at Vanderbilt University Medical Center. Each CT scan is acquired with contrast enhancement phase at portal venous consists of 80 to 225 slices with $512 \times 512$ pixels and slice thickness ranging from 1 to $6 \, \text{mm}$ . The multi-organ segmentation problem is formulated as a 13 classes segmentation task (see Table 1 for details). The preprocessing pipeline is detailed in supplementary materials. + +MSD: Medical Segmentation Decathlon (MSD) dataset [1] comprises of 10 segmentation tasks from different organs and image modalities. These tasks are designed to feature difficulties across medical images, such as small training sets, unbalanced classes, multi-modality data and small objects. Therefore, the MSD challenge can serve as a comprehensive benchmark to evaluate the generalizability of medical image segmentation methods. The pre-processing pipeline for this dataset is outlined in supplementary materials. + +# 5.2. Implementation Details + +For pre-training tasks, (1) masked volume inpainting: the ROI dropping rate is set to $30\%$ (as also used in [2]); the dropped regions are randomly generated and they sum up to reach overall number of voxels; (2) 3D contrastive coding: a feature size of 512 is used as the embedding size; (3) rotation prediction: the rotation degree is configured to $0^{\circ}$ , $90^{\circ}$ , $180^{\circ}$ , and $270^{\circ}$ . We train the model using the AdamW [32] optimizer with a warm-up cosine scheduler of 500 iterations. The pre-training experiments use a batch-size of 4 per GPU (with $96 \times 96 \times 96$ patch), and initial learning rate of $4e^{-4}$ , momentum of 0.9 and decay of $1e^{-5}$ for 450K iterations. Our model is implemented in PyTorch and MONAI4. A five-fold cross validation strategy is used to train models for all BTCV and MSD experiments. We select the best model in each fold and ensemble their outputs for final segmentation predictions. Detailed training hyperparameters for fine-tuning BTCV and MSD tasks can be found in the supplementary materials. All models are trained on a NVIDIA DGX-1 server. + +# 5.3. Evaluation Metrics + +The Dice similarity coefficient (Dice) and Hausdorff Distance $95\%$ (HD95) are used as measurements for experiment results. HD95 calculates $95^{th}$ percentile of surface distances between ground truth and prediction point sets. Metric formulations are as follows: + +$$ +\mathrm {D i c e} = \frac {2 \sum_ {i = 1} ^ {I} Y _ {i} \hat {Y} _ {i}}{\sum_ {i = 1} ^ {I} Y _ {i} + \sum_ {i = 1} ^ {I} \hat {Y} _ {i}}, \tag {7} +$$ + +$$ +\mathrm {H D} = \max \left\{\max _ {y ^ {\prime} \in Y ^ {\prime}} \min _ {\bar {y} ^ {\prime} \in \bar {Y} ^ {\prime}} \| y ^ {\prime} - \bar {y} ^ {\prime} \|, \max _ {\bar {y} ^ {\prime} \in \bar {Y} ^ {\prime}} \min _ {y ^ {\prime} \in Y ^ {\prime}} \| \bar {y} ^ {\prime} - y ^ {\prime} \| \right\}. \tag {8} +$$ + +where $Y$ and $\bar{Y}$ denote the ground truth and prediction of voxel values. $Y'$ and $\hat{Y}'$ denote ground truth and prediction + +
MethodsSplRKidLKidGallEsoLivStoAorIVCVeinsPanAGAvg.
SETR NUP [53]0.9310.8900.8970.6520.7600.9520.8090.8670.7450.7170.7190.6200.796
SETR PUP [53]0.9290.8930.8920.6490.7640.9540.8220.8690.7420.7150.7140.6180.797
SETR MLA [54]0.9300.8890.8940.6500.7620.9530.8190.8720.7390.7200.7160.6140.796
ASPP [8]0.9350.8920.9140.6890.7600.9530.8120.9180.8070.6950.7200.6290.811
TransUNet [6]0.9520.9270.9290.6620.7570.9690.8890.9200.8330.7910.7750.6370.838
CoTr* [47]0.9430.9240.9290.6870.7620.9620.8940.9140.8380.7960.7830.6470.841
CoTr [47]0.9580.9210.9360.7000.7640.9630.8540.9200.8380.7870.7750.6940.844
RandomPatch [44]0.9630.9120.9210.7490.7600.9620.8700.8890.8460.7860.7620.7120.844
PaNN [56]0.9660.9270.9520.7320.7910.9730.8910.9140.8500.8050.8020.6520.854
nnUNet [23]0.9670.9240.9570.8140.8320.9750.9250.9280.8700.8320.8490.7840.888
UNETR [19]0.9720.9420.9540.8250.8640.9830.9450.9480.8900.8580.8520.8120.891
Swin UNETR0.9760.9580.9560.8930.8750.9850.9530.9480.9040.8990.8970.8460.918
+ +![](images/2343be79d7ce2856bb4b0fb087244a79610c9b6976a88a0be1c0861664e98778.jpg) +Figure 4. Qualitative visualizations of the proposed Swin UNETR and baseline methods. Three representative subjects are demonstrated. Regions of evident improvements are enlarged to show better details of pancreas (blue), portal vein (light green), and adrenal gland (red). + +Table 1. Leaderboard Dice results of BTCV challenge on multi-organ segmentation. The proposed method achieves state-of-the-art performance in both free and standard competitions. Note: Spl: spleen, RKid: right kidney, LKid: left kidney, Gall: gallbladder, Eso: esophagus, Liv: liver, Sto: stomach, Aor: aorta, IVC: inferior vena cava, Veins: portal and splenic veins, Pan: pancreas, AG: left and right adrenal glands. + +
MethodRankAverage Accuracy
Dice ↑NSD ↑
Swin UNET178.6889.28
DiNTS [22]277.9388.68
nnUNet [23]377.8988.09
Models Gen. [57]476.9787.19
Trans VW [18]576.9687.64
+ +Table 2. Overall performance of top-ranking methods on all 10 segmentation tasks in the MSD public test leaderboard. NSD denotes Normalized Surface Distance. + +surface point sets. Surface Dice [33] is also used, which is referred as Normalized Surface Distance (NSD) in MSD challenge evaluation. The metric measures the overlap of ground truth and prediction surfaces (with a fixed tolerance) instead of the overlap of two volumes. This provides a measure of agreement between the surfaces of two structures. + +# 5.4. Results + +# 5.4.1 BTCV Multi-organ Segmentation Challenge + +We extensively compare the benchmarks of our model with baselines. The published leaderboard evaluation is shown in Table 1. Compared with other top submissions, the proposed Swin UNETR achieves the best performance. We obtain the state-of-the-art Dice of 0.908, outperforming the second, third and fourth top-ranked baselines by $1.6\%$ , $2.0\%$ and $2.4\%$ on average of 13 organs, respectively. Distinct improvements can be specifically observed for organs that are smaller in size, such as splenic and portal veins of $3.6\%$ against prior state-of-the-art method, pancreas of $1.6\%$ , and adrenal glands of $3.8\%$ . Moderate improvements are observed in other organs. The representative samples in Fig. 4 demonstrate the success of identifying organ details by Swin UNETR. Our method detects the pancreas tail (row 1), and branches in the portal vein (row 2) in Fig. 4, where other methods under segment parts of each tissue. In addition, our method demonstrates distinct improvement in segmentation of adrenal glands (row 3). + +
OrganTask01 Brain TumourTask03 LiverTask06 Lung
MetricDice1Dice2Dice3Avg.NSD1NSD2NSD3Avg.Dice1Dice2Avg.NSD1NSD2Avg.Dice1NSD1
Kim et al [25]67.4045.7568.2660.4786.6572.0390.2882.9994.2572.9683.6196.7688.5892.6763.1062.51
Trans VW [18]68.0346.9868.4061.1487.5272.4290.9183.6295.1876.9086.0497.8692.0394.9574.5476.22
C2FNAS [51]67.6248.6069.7261.9887.6172.8791.1683.8894.9872.8983.9498.3889.1593.7770.4472.22
Models Gen. [57]68.0346.9868.4061.1487.5272.4290.9183.6295.7277.5086.6198.4891.9295.2074.5476.22
nnUNet [23]68.0446.8168.4661.1087.5172.4790.7883.5995.7575.9785.8698.5590.6594.6073.9776.02
DiNTS [22]69.2848.6569.7562.5689.3373.1691.6984.7395.3574.6284.9998.6991.0294.8674.7577.02
Swin UNETR70.0252.5270.5164.3589.0780.3093.4687.6195.3575.6885.5298.3491.5994.9776.6077.40
+ +
OrganTask07 PancreasTask08 Hepatic VesselTask09 SpleenTask10 Colon
MetricDice1Dice2Avg.NSD1NSD2Avg.Dice1Dice2Avg.NSD1NSD2Avg.Dice1NSD1Dice1NSD1
Kim et al [25]80.6151.7566.1895.8373.0984.4662.3468.6365.4983.2278.4380.8391.9294.8349.3262.21
Trans VW [18]81.4251.0866.2596.0770.1383.1065.8071.4468.6284.0180.1582.0897.3599.8751.4760.53
C2FNAS [51]80.7654.4167.5996.1675.5885.8764.3071.0067.6583.7880.6682.2296.2897.6658.9072.56
Models Gen. [57]81.3650.3665.8696.1670.0283.0965.8071.4468.6284.0180.1582.0897.3599.8751.4760.53
nnUNet [23]81.6452.7867.2196.1471.4783.8166.4671.7869.1284.4380.7282.5897.4399.8958.3368.43
DiNTS [22]81.0255.3568.1996.2675.9086.0864.5071.7668.1383.9881.0382.5196.9899.8359.2170.34
Swin UNETR81.8558.2170.7196.5779.1087.8465.6972.2068.9584.8381.6283.2396.9999.8459.4570.89
+ +# 5.4.2 Segmentation Results on MSD + +The overall MSD results per task and ranking from the challenge leaderboard are shown in Table. 2. The proposed Swin UNETR achieves state-of-the-art performance in Task01 BrainTumour, Task06 Lung, Task07 Pancreas, and Task10 Colon. The results are comparable for Task02 Heart, Task03 Liver, Task04 Hippocampus, Task05 Prostate, Task08 HepaticVessel and Task09 Spleen. Overall, Swin UNETR presents the best average Dice of $78.68\%$ across all ten tasks and achieves the top ranking in the MSD leaderboard. The detail number of multiple tasks are shown in Table 3. Qualitative visualization can be observed in Fig. 5. Swin UNETR with self-supervised pre-training demonstrates visually better segmentation results in the CT tasks. The pre-trained weights are only used for fine-tuning CT tasks including Liver, Lung, Pancreas, HepaticVessel, Spleen, and Colon. For MRI tasks: Brain Tumour, Heart, Hippocampus, Prostate, experiments are trained from scratch because of the domain gap between CT and MRI images. Due to space limitations, we present the MSD test benchmarks for the remaining three MRI tasks in the supplementary materials. + +# 5.5. Ablation Study + +# 5.5.1 Efficacy of Pre-training + +A comparison of all MSD CT tasks using pre-trained model against training from scratch can be observed in Fig. 6. Distinct improvement can be observed for Task03 Liver, Dice of $77.77\%$ comparing to $75.27\%$ . Task08 Hepatic Vessel achieves $68.52\%$ against $64.63\%$ . Task10 Colon shows the largest improvement, from $34.83\%$ to $43.38\%$ . Task07 Pancreas and Task09 Spleen both achieve significant improvement from $67.12\%$ to $67.82\%$ , and $96.05\%$ to $97.32\%$ respectively. + +![](images/66b78dc8538629c5a123030ba83c1f3bd032917dca748870fcdfffbc3818daab.jpg) + +![](images/a3660885af8f2cec43daf22bc0f4166f6464450ca59f2bf1621db81d30254299.jpg) +Lung + +![](images/baae1c8cd8bd3382218f7a5fcf2d67e45edcf48f13d122f75c86681af940270e.jpg) + +![](images/52cc0445be017010d6553a2db9aa8912fbf8868b68f01446a11de00bac90bb5e.jpg) +Pancreas + +![](images/43f9d8804e244c615a3fa0e58a93c8391983c11516550a19297797185460b322.jpg) + +![](images/0b634d2da346bb383d36fd0a5ceef1aa62259cc95aeaa486872368ffc3e515b6.jpg) +Hepatic Vessel +Figure 5. Qualitative results of representative MSD CT tasks. Average Dice values are illustrated on top of each image. Our model demonstrates more accurate performance in comparison to DiNTS for both organ and tumor segmentation across different tasks. + +Table 3. MSD test dataset performance comparison of Dice and NSD. Benchmarks obtained from MSD test leaderboard ${}^{5}$ . + +
Loss FunctionAverage Accuracy
Dice ↑HD ↓
Scratch83.4342.36
Lrot83.5636.19
Lcontrast83.6738.81
Linpaint83.8528.94
Linpaint + Lrot84.0126.06
Linpaint + Lcontrast84.4524.37
Linpaint + Lcontrast + Lrot84.7220.03
+ +Table 4. Ablation study of the effectiveness of each objective function in the proposed pre-training loss. HD denotes Hausdorff Distance. Experiments on fine-tuning the BTCV dataset. + +# 5.5.2 Reduce Manual Labeling Efforts + +Fig. 7 demonstrates the comparison results of fine-tuning using a subset of BTCV dataset. We show using $10\%$ of + +![](images/44fc2ddfb50dc0ffafcf317cc2f4815cb0b747c7edfe0fe609b13d0813ca36db.jpg) +Figure 6. The indication of Dice gap between using pre-training (Green) and scratch model (Blue) on MSD CT tasks validation set. + +![](images/f1274e71ba766fe464820487b97d9cdbc1ddaa10ec1cad7093495e786c5d1177.jpg) +Figure 7. Data-efficient performance on BTCV test dataset. Significance under Wilcoxon Signed Rank test, $* : p < 0.001$ . + +labeled data, experiments with pre-training weights achieve approximately $10\%$ improvement comparing to training from scratch. On employing all labeled data, the self-supervised pre-training shows $1.3\%$ higher average Dice. The Dice number 83.13 of learning from scratch with entire dataset can be achieved by using pre-trained Swin UNETR with $60\%$ data. Fig. 7 indicates that our approach can reduce the annotation effort by at least $40\%$ for BTCV task. + +# 5.5.3 Size of Pre-training Dataset + +We perform organ-wise study on BTCV dataset by using pre-trained weights of smaller unlabeled data. In Fig. 8, the fine-tuning results are obtained from pre-training 100, 3,000, and 5,000 scans. We observe that Swin UNETR is robust with respect to the total number of CT scans trained. Fig. 8 demonstrates the proposed model can benefit from larger pre-training datasets with increasing size of unlabeled data. + +# 5.5.4 Efficacy of Self-Supervised Objectives + +We perform empirical study on pre-training with different combinations of self-supervised objectives. As shown in Table 4, on BTCV test set, using pre-trained weights by inpainting achieves the highest improvement at single task modeling. On pairing tasks, inpainting and contrastive learning show Dice of $84.45\%$ and Hausdorff Distance (HD) of 24.37. Overall, employing all proxy tasks achieves best Dice of $84.72\%$ . + +![](images/f4b262232d1e65a6fad9ea4b6f0a2b82c5c5dd720f25d872cb8b44a64bdcf0d3.jpg) +Figure 8. Pre-trained weights using 100, 3000 and 5000 scans are compared for fine-tuning on the BTCV dataset for each organ. + +# 6. Discussion and Limitations + +Our state-of-the-art results on the test leaderboards of MSD and BTCV datasets validate the effectiveness of the proposed self-supervised learning framework in taking the advantage of large number of available medical images without the need of annotation effort. Subsequently, fine-tuning the pretrained Swin UNETR model achieves higher accuracy, improves the convergence speed, and reduces the annotation effort in comparison to training with randomly initialized weights from scratch. Our framework is scalable and can be easily extended with more proxy tasks and augmentation transformations. Meanwhile, the pre-trained encoder can benefit the transfer learning of various medical imaging analysis tasks, such as classification and detection. In MSD pancreas segmentation task, Swin UNETR with pre-trained weights outperforms AutoML algorithms such as DiNTS [22] and C2FNAS [51] that are specifically designed for searching the optimal network architectures on the same segmentation task. Currently, Swin UNETR has only been pre-trained using CT images, and our experiments have not demonstrated enough transferability when applied directly to other medical imaging modalities such as MRI. This is mainly due to obvious domain gaps and different number of input channels that are specific to each modality. As a result, this is a potential direction that should be studied in future efforts. + +# 7. Conclusions + +In this work, we present a novel framework for self-supervised pre-training of 3D medical images. Inspired by merging feature maps at scales, we built the Swin UNETR by exploiting transformer-encoded spatial representations into convolution-based decoders. By proposing the first transformer-based 3D medical image pre-training, we leverage the power of Swin Transformer encoder for fine-tuning segmentation tasks. Swin UNETR with self-supervised pre-training achieves the state-of-the-art performance on the BTCV multi-organ segmentation challenge and MSD challenge. Particularly, we presented the large-scale CT pre-training with 5,050 volumes, by combining multiple publicly available datasets and diversities of anatomical ROIs. + +# References + +[1] Michela Antonelli, Annika Reinke, Spyridon Bakas, Keyvan Farahani, Bennett A Landman, Geert Litjens, Bjoern Menze, Olaf Ronneberger, Ronald M Summers, Bram van Ginneken, et al. 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Based on the fact that self-supervised learning is helpful when a large number of data are available, we propose two self-supervised learning approaches to improve the baseline performance for view consistency reasoning and camera pose reasoning tasks on the SPARE3D dataset. For the first task, we use a self-supervised binary classification network to contrast the line drawing differences between various views of any two similar 3D objects, enabling the trained networks to effectively learn detail-sensitive yet view-invariant line drawing representations of 3D objects. For the second type of task, we propose a self-supervised multi-class classification framework to train a model to select the correct corresponding view from which a line drawing is rendered. Our method is even helpful for the downstream tasks with unseen camera poses. Experiments show that our method could significantly increase the baseline performance in SPARE3D, while some popular self-supervised learning methods cannot. + +# 1. Introduction + +Human visual reasoning, especially spatial reasoning, has been widely studied from psychological and educational perspectives [17, 19]. Researches show that trained humans can achieve good performance on spatial reasoning tasks [32] because they can solve these tasks using spatial memory, logic, and imagination. However, the spatial reasoning of deep networks is yet to be explored and improved. In other visual learning tasks such as image classification, object detection, and segmentation, state-of-the-art deep networks have shown their superior performance to humans by memorizing indicative visual patterns from enormous image instances for prediction. However, it seems difficult for deep networks to reason using the same mechanism about the spatial information such as the view consistency + +![](images/0cd96d033a86122db9b818af945163d5372edebab9107d16fbcb7eb3405f7f8f.jpg) +Figure 1. We significantly improve SPARE3D baselines using self-supervised learning approaches. Note that in this figure, all the networks are trained using the same amount of data (data generated from 5,000 CAD models) as used on the SPARE3D dataset. + +and camera poses from 2D images [14]. + +To our best knowledge, we are the first to investigate spatial reasoning tasks in the SPARE3D $^1$ dataset [14], that provides several challenging spatial reasoning tasks in line drawings (Figure 1). The dataset is unique in that: (1) it uses line drawings as inputs, (2) it is a non-categorical dataset, meaning there is no class label information for each object, (3) it defines spatial reasoning instead of recognition tasks. Specifically, we focus on the view-consistency reasoning task (the Three-view to Isometric or $T2I$ ) and the two camera-pose reasoning tasks (the Isometric to Pose or $I2P$ , and the Pose to Isometric or $P2I$ ). The task examples are illustrated in Figure 1 and for more details of the task + +settings, we refer the readers to the SPARE3D paper [14]. + +To improve the DNN's performance, our first effort is to explore the supervised learning network's ability in three aspects: (1) the quantity of data used for learning, (2) the network's capacity (width and depth), and (3) the network's structure. However, we find changing these factors could not bring significant improvement (all these results are shown in the supplementary), while it might cost more time and computational resources to generate data for supervised learning. + +Compared with supervised learning, self-supervised learning is helpful when a large number of unlabeled data are available. Moreover, in many visual learning tasks, self-supervised learning as a pre-training task can learn better visual representations that can be further fine-tuned via supervision for downstream tasks, achieving similar or even better results than supervised learning [6]. Based on these findings, we design two self-supervised learning methods for both view consistency reasoning task and camera pose reasoning task on the SPARE3D dataset. + +For the view consistency reasoning task, we design a contrastive spatial reasoning method to tackle the challenges in SPARE3D tasks (Figure 2). This is necessary because most of the existing contrastive learning methods do not explicitly consider the relationship between different views, nor do they force deep networks to focus on detailed differences between images. We demonstrate both qualitative and quantitative results that show our method helps deep networks capture these small details while being view invariant, which is crucial for the view consistency task. + +For the camera pose reasoning task, we propose a self-supervised learning network for improving the deep network's ability to find the correlation between the pose and the image rendered from the pose (see Figure 3). Our experiment results show that our self-supervised learning network is not only helpful for the downstream tasks with seen views but also helpful for the tasks with unseen views. This shows a potential to even improve pose estimation by transferring the learned representations from a camera pose reasoning pretext task to related downstream tasks. + +In sum, our major contributions are: + +- A novel contrastive learning method by self-supervised binary classifications, which enables deep networks to effectively learn detail-sensitive yet view-invariant multi-view line drawing representations for view consistency reasoning task; +- A self-supervised multi-class classification method to learn pose-aware representations from multi-view line drawing images; +Significantly improved spatial reasoning performance of deep networks on line drawings based on the above, some of which surpass human performance. + +# 2. Related Work + +Self-supervised learning has achieved great success due to the performance improvement on many visual learning tasks [11, 12, 18, 21, 23, 26, 28, 36, 39, 43]. Successful self-supervised learning frameworks use different tricks to create artificial labels based solely on the inputs. One way is to use spatial information or spatial relationships between image patches in a single image. For example, Gidaris et al. [10] designed the pretext task by asking the network to predict image rotations. Another way is to ask the network to recover the positions of shuffled image patches [20, 29, 37], or predict the relative position [8]. In addition, the color signal contained in an RGB image could also be used. By recovering the color for grayscale images generated from RGB images, networks can learn the semantic information of each pixel [24, 46]. Despite the success of the spatial reasoning tasks in the SPARE3D dataset, these methods are ineffective since they only use visual information from a single image. Our method aims to consider the common information between different images and, thus, is more suitable to solve those reasoning problems. + +One way of grouping various self-supervised learning methods is to divide them into generative vs. contrastive ones [27]. On the one hand, generative ones learn visual representations via pixel-wise loss computation and thus forcing a network to focus on pixel-based details; on the other hand, contrastive ones learn visual representations by contrasting the positive and negative pairs [1, 38, 40, 41]. Many researchers explored contrastive learning by comparing shared information between multiple positive or negative image pairs. These methods often attempt to minimize the distance of the features extracted from the same data source and maximize the distance between features from different data sources in the feature space. Hjelm et al. [16] propose Deep InfoMax based on the idea that the global feature extracted from an image should be similar to the same image's local feature and should be different from a different image's local feature. Based on this method, Bachman et al. [3] further use image features extracted from different layers to compose more negative or positive image pairs. SimCLR [5] differs from the previous two methods in that it only considers the global features of the augmented image pairs to compose positive and negative pairs. SimCLRv2 [6] make further improvements on Imagenet [7] by conducting contrastive learning with a large network, finetuning using labeled data, and finally distilling the network to a smaller network. Compared to SimCLR, MoCo [15] stores all generated samples to a dictionary and uses them as negative pairs instead of generating negative pairs in each step. These tactics could help reduce the batch size requirement while still achieving good performance. Differently, SwaV [4] trains two networks that can interact and learn from each other, with one network's input being the + +![](images/2443a838cd52fb29bdb204ff180e582d9fbe0c29afd1390437bcdb708b229e99.jpg) +Figure 2. Contrastive spatial reasoning architecture for task T2I. We train a contrastive learning network, then use the learned representations to the downstream task T2I. Front (F), Right (R), Top (T) represent line drawings and an isometric (I) line drawing. $a_1, b_1, a_2, b_2$ are the encoded feature vectors; $C, K$ are the dimension of the latent vectors. The $f_{\theta_1}, f_{\theta_2}, f_{\theta_3}$ , and $f_{\theta_4}$ are CNN networks; $g_{\phi_1}, g_{\phi_2}$ , and $h_{\psi}$ are MLP networks. $\oplus$ is a concatenation operation. BCE represents binary cross-entropy loss. + +augmented pair of another network's input. Besides, researchers also theoretically analyze why these contrastive learning methods work well [2, 25, 34, 35]. + +However, it is difficult to apply the aforementioned contrastive learning methods directly to tasks which requires consideration of the relationships between multi-view images. Contrastive multiview coding [33] has a misleading name in our context because that "multiview" in fact, means different input representations instead of views from different camera poses. Therefore it is not suitable for SPARE3D tasks. Kim et al. [22] propose a method to solve a few-shot visual reasoning problem on RAVEN dataset [44], which is perhaps more relevant to us due to the use of contrastive learning in visual reasoning. Yet because it is designed for analogical instead of spatial reasoning, it is not directly applicable to SPARE3D tasks either. + +# 3. Self-supervised Spatial Reasoning + +In this section, we explore a self-supervised learning method to learn the representations for all three tasks in SPARE3D: a contrastive spatial reasoning network for view consistency reasoning task $T2I$ , a self-supervised learning network for camera pose reasoning task $I2P$ and $P2I$ . For the camera pose reasoning task, we extend the downstream task settings to show our method is helpful when the cam + +era poses in the downstream task are not seen in the pretext task. + +# 3.1. Contrastive learning network for task T2I + +According to the discussion in the Introduction 1, we believe contrastive learning can help the network learn better line drawing representations. Because it is not difficult to obtain a large number of unlabeled CAD models, we design our specialized contrastive spatial reasoning method as illustrated in Figure 2. Our method can be divided into three steps: 3D model augmentation, line-drawing feature extraction, contrastive loss computation. + +Step 1: 3D data augmentation. Our data augmentation happens in 3D instead of 2D because the visual differences between different views are caused by 3D boolean operation. We generate two sets of images: a branch 1 set and a branch 2 set for each augmented CAD model. Each image set contains the three-view drawings and the isometric view drawing. We denote the branch 1 set by $\{F_1, R_1, T_1, I_1\}$ , and the branch 2 set by $\{F_2, R_2, T_2, I_2\}$ , where $F, R, T$ and $I$ stand for front, right, top views and the isometric view separately. The branch 1 and branch 2 image sets are generated from two different modifications to the original CAD model. Each modification is a random Boolean op + +eration (intersection, union, or difference) on the original CAD model with a random primitive (sphere, cube, cone, or cylinder.) Figure 2 gives an example of generating the two image sets. + +Step 2: line-drawing feature extraction. In this paper, $f, g, h$ represent neural networks; $\theta, \phi, \psi$ are the network weights in the three networks respectively. $F_{i}, R_{i}, T_{i}$ , and $I_{i}$ ( $i \in \{1, 2\}$ ) are fed into four convolutional neural networks (CNN) individually. The four networks are denoted by $f_{\theta_1}, f_{\theta_2}, f_{\theta_3}$ , and $f_{\theta_4}$ , where $f_{\theta_j}: \mathbb{R}^{3 \times H \times W} \to \mathbb{R}^C$ , $j \in \{1, 2, 3, 4\}$ ; $H$ and $W$ are the height and width of the images. Note that the four networks share the same architecture but with different parameters. Then, the outputs from $f_{\theta_1}, f_{\theta_2}$ , and $f_{\theta_3}$ are concatenated and fed into a one-layer MLP $g_{\phi_1}: \mathbb{R}^{3C} \to \mathbb{R}^K$ , and the output from $f_{\theta_4}$ is fed into another one-layer MLP $g_{\phi_2}: \mathbb{R}^C \to \mathbb{R}^K$ . $g_{\phi_1}, g_{\phi_2}$ also share the same architecture but with different parameters. The outputs from $g_{\phi_1}$ and $g_{\phi_2}$ are noted as a $a_i$ and $b_i$ ( $i \in \{1, 2\}$ ), which encode the information from the 3-view images and the isometric image respectively. + +Step 3: Contrastive loss computation. After having the four latent codes $(a_{1}, a_{2}, b_{1},$ and $b_{2})$ , we concatenate each $a$ and each $b$ , which gives four combinations $a_{1} \oplus b_{1}$ , $a_{1} \oplus b_{2}$ , $a_{2} \oplus b_{1}$ , and $a_{2} \oplus b_{2}$ (see Figure 2). Then we send the four concatenated latent codes to a binary classifier $h_{\psi}: \mathbb{R}^{2K} \to (0,1)$ , where the $h_{\psi}$ is a two-layer MLP. The outputs from $h_{\psi}$ are $\hat{p}_{1}, \hat{p}_{2}, \hat{p}_{3}$ , and $\hat{p}_{4}$ respectively, and are used to compute the binary cross entropy (BCE) loss with the ground truth. We define the ground truth to be 1 if the original two latent codes used to concatenate are from the same image pairs, and the ground truth to be 0 from different image pairs. Therefore, $p_{1} = p_{4} = 1$ , $p_{2} = p_{3} = 0$ . The final loss is $\frac{1}{4}\sum_{k=1}^{4} BCE(\hat{p}_{k}, p_{k})$ , $(k \in \{1,2,3,4\})$ . + +Difference with SimCLR. Unlike existing contrastive learning methods such as SimCLR, the representation from our method is designed to be both multi-view-consistent and detail-sensitive. Technically, our method differs from them in that: 1) our data augmentation operates on 3D CAD models with Boolean operations (intersection, union, or difference), instead of single-image operations like random cropping, color distortion, and Gaussian blur; 2) our positive pairs are two sets of multi-view line drawings (three-view line drawings and isometric line drawing) that are rendered in the same data branch, and our negative pairs are image sets from different data branches, unlike being sampled from other data instances; 3) we use binary cross-entropy loss to optimize the network, unlike the NT-Xent loss [13, 45] which has the temperature parameter to tune. Our experimental results also show the advantage of using BCE loss over the NT-Xent loss. + +Representation adaption for task $T2I$ . We notice that all the learned parameters $\theta, \phi, \psi$ can be loaded to the neural network for further supervised fine-tuning because the con + +trastive spatial reasoning method is just a pre-training step, and it uses exactly the same network architecture as the network for the supervised learning (see Figure 2 downstream tasks: $T2I$ ). + +# 3.2. Self-supervised learning network for task $I2P$ and $P2I$ + +We propose a self-supervised learning pretext task, as can be seen in Figure 3. As mentioned in Introduction 1, the learned representations from the pretext task can be helpful to both $I2P$ and $P2I$ tasks, even when the camera poses in the downstream tasks are not seen in the pretext task. The network design can be divided into two steps: line-drawing feature extraction; loss computation. + +Step 1: line-drawing feature extraction. For the three view images, similar as the network design for contrastive spatial reasoning for task $T2I$ , $\{F,R,T\}$ are sent to the share-weight neural network (CNN) $f_{\eta_1}, f_{\eta_2}, f_{\eta_3}$ separately to obtain three features, where $f_{\eta_j}: \mathbb{R}^{3 \times H \times W} \to \mathbb{R}^C$ , $j \in \{1,2,3\}$ . Then the three vectors are concatenated and fed into a one-layer MLP $g_{\omega_1}: \mathbb{R}^{3C} \to \mathbb{R}^K$ , generating $c_1$ which encodes the information from the 3-view images. + +For the eight isometric view images, each of the images goes through the same network. For the sake of simplicity, we use $I_{1}$ (isometric view image rendered from camera pose 1) as an example. $I_{1}$ is sent to a neural network (CNN) $f_{\eta_4}$ followed by a one-layer MLP $g_{\omega_2}: \mathbb{R}^C \to \mathbb{R}^K$ , and the output latent vector is noted as $d_{1}$ . + +After having $c_{1}$ and $d_{1}$ for three view feature and isometric view feature separately, we concatenate them and send the concatenated vector to a two-layer MLP $g_{\omega_3}:\mathbb{R}^K\to \mathbb{R}^8$ . The obtained 8-dimensional vector $e_1$ can represent the camera-pose probability logits of the eight candidate isometric views. Therefore, for all the eight isometric view images $I_{1},I_{2},\ldots ,I_{8}$ , we will have eight $1\times 8$ vectors, $e_1,e_2,\dots ,e_8$ separately. We concatenate the eight vectors to obtain a $8\times 8$ matrix, forming the output of the self-supervised learning pretext task. + +Step 2: loss computation. This matrix is used to calculate the BCE loss with the ground truth matrix. The ground truth matrix is a $8 \times 8$ identity matrix, and each row is the logits for the corresponding isometric view. For example, the logit value of the first value in the first row is 1, while other values are 0, since the logits in the first row represents the isometric view pose 1. The BCE loss is: $\frac{1}{64} \sum_{i=1}^{8} \sum_{j=1}^{8} BCE(\hat{p}_{ij}, p_{ij})$ , $(i,j \in \{1,2,\dots,8\})$ , the ground truth $p_{ij} = 1$ when $i = j$ , otherwise $p_{ij} = 0$ . + +Representation adaption for task $I2P$ and $P2I$ . In task $I2P$ , three view images and one isometric view image (rendered from one of the poses in view 1, 2, 5, 6, pose defined in SPARE3D dataset) are given, and the network is asked to select the correct viewpoint from view 1, 2, 5, 6. Therefore, for each question, we send the three-view image $F$ , $R$ , + +![](images/9a384291661df4dc4c814df6a271e13904b11c7fd9cffbd0b5ad89adb96816df.jpg) +Figure 3. Self-supervised learning network architecture for task $I2P$ and $P2I$ . We train a self-supervised learning network (left subfigure), then use the learned representations to the downstream tasks $I2P$ and $P2I$ (right subfigure). The $f_{\eta_1}$ , $f_{\eta_2}$ , $f_{\eta_3}$ , and $f_{\eta_4}$ are CNN networks; $g_{\omega_1}$ , $g_{\omega_2}$ , and $g_{\omega_3}$ are MLP networks; $c_1, d_1, e_1$ are the encoded feature vectors. + +![](images/392ac9f73e92f935fda3ba27338a8e95318457830378c7e265114bc02ea16b28.jpg) + +$T$ , and the isometric image $I$ to the trained self-supervised network and obtain a eight-digit vector. Then we select the first, second, fifth, and sixth values in the vector as the prediction pose of the network, which can represent the potential view that is used in this task. Then, the max value in the prediction pose vector is considered as the predicted pose, and we give value 1 to the corresponding pose and 0 to other poses to form a one hot encoder. Finally, the BCE loss is computed using the predicted one hot encoder and the ground truth one hot encoder. + +In task $P2I$ , the three-view images and a selected pose from 8 potential poses are sent to the network. The network then selects the isometric view image corresponding to the pose from four potential answers (four rendered isometric view images). For representation adaption, we send the three-view image $F$ , $R$ , $T$ and one potential answer image $A_{i}$ , $i \in \{1,2,3,4\}$ to the trained self-supervised network and obtain four 8 dimensional vectors. For each vector, the value represents the probability of the pose that the answer image is rendered from. Finally, we extract the value from the column that corresponds to the given pose for each vector, forming a four-dimensional vector. For example, the four vectors in the first column will be extracted if the given pose is 1. Then we use the extracted vector to compute the BCE loss with the ground truth one hot encoder. + +Extension experiment for camera pose reasoning task. Besides testing the self-supervised network's learned representations on $I2P$ and $P2I$ tasks in the SPARE3D dataset, we are also curious on whether this self-supervised learning could help camera pose reasoning that contains poses unseen during training? Therefore, we design two extension downstream task of $I2P$ and $P2I$ by increasing the potential camera pose number from 4, 8 to 20, 20 respectively. The 20 camera poses are viewed in the supplementary. + +# 4. Experiments and Discussions + +In this section, we introduce the experiment details for training two of our self-supervised learning networks and the baseline methods. Then, we compare the classification accuracy of our method with baseline methods on all three tasks, including the extension $I2P$ and $P2I$ tasks. Additionally, for $T2I$ task, we also visualize the attention maps obtained from our methods and supervised baseline methods, demonstrating that our method can better localize the differences between the candidate answers. All experiments are implemented with PyTorch [30], using NVIDIA GeForce GTX 1080 Ti GPU. + +Data for training and testing. For all the tasks, we + +Table 1. Comparison of performance on T2I for SL method vs. SSL method. SL and SSL represent supervised learning and self-supervised learning, respectively. 5K and 14K are the training data amount. Fine-tuning means we further use the 5K training data in SPARE3D to fine-tune the parameters. For supervised learning, we evaluate the network performance for: (1) using early fusion or late fusion structure (details in the supplementary), (2) whether or not using ImageNet pre-trained parameters. + +
SLearly-fusion(5K)early-fusion(pretrained, 5K)late-fusion(pretrained, 5K)early-fusion(14K)early-fusion(pretrained, 14K)late-fusion(pretrained, 14K)
55.030.625.263.651.427.4
SSLJigsaw puzzle[29]Colorization[46]SimCLR[5]RotNet[10]Ours (NT-Xent loss)Ours (BCE loss)
27.423.431.030.648.474.9
+ +use the same test data in SPARE3D dataset for testing (except the extension I2P and extension P2I tasks). To prevent the network from "memorize" the data, we avoid using the same models for self-supervised training, supervised finetuning, and testing for all the tasks. Next, we will discuss how we generate training data for different tasks. + +In our contrastive learning approach for $T2I$ task, we first generate image sets for two branches. In practice, we download 14,051 models from the ABC dataset for training and 737 models for testing. Then we use PythonOCC [31] to apply different random Boolean operations on each model, generating four images for branch 1 and branch 2, respectively. Therefore, we have $14,051 \times 8$ rendered images. + +All $14,051 \times 8$ images are used for three self-supervised baselines that we compare with, namely Jigsaw Puzzle, Colorization, SimCLR, and RotNet. For supervised learning with 5K dataset, we use the original data from SPARE3D paper, with 5,000 questions for training. For supervised learning with 14K dataset, we use the 14,051 CAD models to generate new questions for training. + +For the self-supervised network for $I2P$ and $P2I$ , we generate different training sets with CAD model amount ranging from 5,000 to 40,000, with 5,000 as a step. For each CAD model, it generates three-view images $(F,R,T)$ and eight isometric view images $(I_1,I_2,\dots ,I_8)$ . For a fair comparison, we also generate different scale datasets for supervised learning, ranging from 5,000 to 40,000, and all the implementation settings are the same as in SPARE3D. + +For both the extension I2P and extension P2I tasks, we need to: 1) create supervised training dataset with different size, ranging from 5,000 to 40,000, and 2) create a test set with 1,000 questions, which is the same number as in the original I2P and P2I settings. We follow the implementation settings as in SPARE3D, and the only change is we increase the potential view number to 20. + +Hyperparameter settings. We tune the learning rate and batch size for each self-supervised learning method and supervised learning method for all tasks. + +For $T2I$ , our contrastive learning network, with either NT-Xent loss or BCE loss, uses a learning rate of 0.00005, batch size 4. Jigsaw puzzle, Colorization, SimCLR, and RotNet all use learning rate 0.00001 and batch + +size 10, 30, 70, 16, respectively. For supervised learning, we follow the hyperparameter settings as in SPARE3D. + +For the $I2P$ and $P2I$ tasks, the learning rate and batch size for our self-supervised network are 0.00005 and 4. For the extension $I2P$ and extension $P2I$ tasks, the learning rate is 0.00001, and the batch size are 70 and 20 respectively. For supervised learning, we follow the hyperparameter settings as in SPARE3D. + +Details of the two proposed self-supervised networks. For both our contrastive learning method and self-supervised method, we use the VGG-16 network as the backbone for image feature extraction, and parameters keep the same. Note that for the contrastive learning network using NT-Xent loss, we use $a_1, b_1, a_2, b_2$ as the latent vectors. $a_1, b_1$ and $a_2, b_2$ are considered as positive pairs, while other remaining pairs, including the pairs within the batch, are negative. The value of $C$ is set to be 18, 432 (by flattening the $6 \times 6 \times 512$ feature map). The value of $K$ is set to be 4096, the same as in the SPARE3D paper. The size of input line drawings is $200 \times 200 \times 3$ . The output of the last convolutional layer is a $6 \times 6 \times 512$ feature map. + +Self-supervised learning baseline network adaptation for $T2I$ . For task $T2I$ , we use Jigsaw puzzle [29], Colorization [46], SimCLR [5], and RotNet [10] as four self-supervised learning baseline methods to compare with our method, see Table 1. For the network structures of the Jigsaw puzzle, Colorization, and RotNet, we follow these papers' original design, only replacing the backbone networks with VGG-16 to ensure that the learned parameters can be loaded to the networks of the downstream tasks. For SimCLR, we define the positive "image pairs" in our case as the $\{F,R,T\}$ and $I$ images, which are generated from the same CAD model. We then use the same contrastive network as in Figure 2 to extract the features for $\{F,R,T\}$ and $I$ images separately, and the learned parameters can be loaded to the downstream tasks. + +Extension I2P and extension P2I task implementation. For these two tasks that use 20 views as potential camera pose, we compare our self-supervised learning pre-trained networks with the supervised learning baseline methods. For supervised learning baseline methods of extension I2P and extension P2I, we follow the network de + +sign as $I2P$ and $P2I$ respectively. The only difference is that, for each task, the output of the last MLP layer $g_{\omega_3}$ changes to a 20 dimensional latent vector. Therefore, when loading the learned parameters from the self-supervised network, we discard the last layer MLP of the trained model and train the parameters using the extension supervised learning training data for 20 views. + +# 4.1. T2I task result analysis + +Classification accuracy for task $T2I$ . As can be seen in Table 1, our methods (both with or without fine-tuning) outperform other methods, including self-supervised baseline methods and supervised methods. Our fine-tuned result can achieve $74.9\%$ accuracy on $T2I$ task, approaching the average untrained human performance of $80.5\%$ . Here direct evaluation means we use the learned parameters from the trained contrastive learning network, and fine-tuning means we further use the 5,000 training data for supervised learning to fine-tune the learned parameters. + +Although we use more data in the contrastive pretraining, the higher accuracy of our method is not only due to increased data volume. As aforementioned, we use 14,051 CAD models to generate image sets for contrastive learning. We also use these models to generate 14,051 questions for purely supervised learning. This ensures the number of CAD models used for our method is the same as for purely supervised learning. With the same number of CAD models for training (14K dataset), we find the best performance that supervised learning can achieve is $63.6\%$ . Although increasing the data volume can help improve the baseline performance for supervised learning, from $55.0\%$ to $63.6\%$ , the result is still significantly lower than our method, which is $74.9\%$ . + +We believe the good performance of our method is because contrastive learning helps the network learn the detail-sensitive yet view-invariant visual representations in the line drawings. This reason could also explain an interesting phenomenon that we observe, which is that the direct evaluation (without fine-tuning) using the learned parameters from contrastive spatial reasoning can achieve $71.4\%$ accuracy (see Table 1). Thus, a good visual representation should be able to transfer to the downstream tasks with little further training. + +Qualitatively, we show that our contrastive learning method can help the network learn the detail-sensitive yet view-invariant visual representations. We visualize the attention map for our contrastive learning method and supervised learning method using the schemes in [42]. For supervised learning, we generate attention maps on both early fusion and late fusion method with no pre-trained parameters. For early fusion, the input line drawings, including front, right, top, and one isometric line drawing, are concatenated before being sent to the CNN. Therefore, each composite + +Table 2. Comparison of performance on $I2P$ and $P2I$ tasks for SL method vs. SSL method. + +
Data amount (K)510152025303540
I2P(SL)83.686.487.788.588.790.490.691.1
I2P SSL)88.793.295.196.496.797.797.598.0
P2I(SL)65.467.168.567.869.869.668.570.4
P2I SSL)72.480.881.982.182.883.18383.4
+ +Table 3. Comparison of performance on extension I2P and extension P2I tasks for SL method vs. SSL method. Note that for SSL methods, we fine-tune the network for the downstream tasks. + +
Data amount(K)510152025303540
I2P(SL)15.114.515.914.817.717.816.317.5
I2P SSL)42.945.548.450.151.351.754.856.5
P2I(SL)51.447.233.752.944.343.352.744.8
P2I SSL)67.473.566.276.275.068.175.777.9
+ +image will have one attention map. We put the attention map with the corresponding candidate isometric line drawing, leaving the attention map for the front, right, and top as empty. For late fusion and our method, after having the attention map for each input image, we put it together with the corresponding input line drawing. All the results are shown in Figure 4 (more results in the supplementary). The comparison between the three rows of attention maps generated from the three methods shows that our method can help the CNN better capture the tiny detailed differences between the candidate answer drawings, which is the key to selecting the correct answer from four similar options. + +# 4.2. $I2P$ and $P2I$ task result analysis + +Classification accuracy for task $I2P$ and $P2I$ . For a fair comparison, we change the supervised learning network's structure to match the structure of our self-supervised learning method. More details will be discussed in the supplementary. The results can be seen in Table 2. With the increase of data amount for training, both supervised learning, and our self-supervised learning-based method achieve higher accuracy. For task $I2P$ , the best accuracy achieves $98.0\%$ , and for task $P2I$ , the best accuracy is $83.4\%$ . The best performance happens when using the 40,000 scale dataset with our self-supervised learning method. + +Therefore, we claim that the increased data amount can help both supervised and self-supervised learning methods. However, our self-supervised learning method has the advantages that: 1) more efficient to improve the accuracy, compared with using the same amount of data as supervised learning methods, and 2) more helpful when the supervised learning method does not perform well. For the second advantage, since the number of potential cameras poses in task $I2P$ and $P2I$ are 4 and 8 respectively, it is natural to expect that it will be more difficult for the neural network to solve the $P2I$ task. In $P2I$ task, we find that even after increas + +![](images/4c0df517bd95f71e432de33b867b5f427ea7bba5a975a7309aca9f91c1f64214.jpg) +Figure 4. Attention maps for SL vs. SSL method in T2I task. For each CAD model, the first row are the line drawings. The second and third row are the attention maps generated from supervised learning using early fusion and late fusion, respectively. The fourth row are the attention maps generated from our method. N/A indicates no attention map for the corresponding view. Best viewed in color. + +![](images/55554b3f3abbf0d5b0368c5019f63c083ab778953972ac4d2ff4c672a3f09e9c.jpg) + +ing the training data amount for supervised learning, the performance improvement is limited. However, our self-supervised learning method can achieve around $10\%$ higher accuracy than the supervised learning method, revealing its advantage over the supervised learning method. + +Classification accuracy for task extension I2P and extension P2I. We also show that our self-supervised learning methods can help extension I2P and extension P2I. Table 3 shows our self-supervised learning-based method outperforms the supervised learning method for different data amounts on both tasks. We believe it is because the "rough" pose reasoning in the pretext task can help the "fine" pose reasoning in the downstream task. "rough" is because the network only needs to reason about 8 poses; "fine" means in the downstream tasks, the network is required to reason about more views, and these views are located in between the 8 poses. Once the network has the ability to determine the "rough" pose and use it as prior information, it will be easier for the network to reason about the "fine" pose. + +# 4.3. Limitations and discussion + +One limitation is that our methods are designed for the tasks in the SPARE3D dataset. Therefore, they are beneficial for object level spatial reasoning, yet not directly for scene level spatial reasoning. One main difference between these two settings is whether the views are "outside-in" for 3D shapes or "inside-out" for scenes [9]. To make spatial reasoning helpful in robot manipulation, navigation or other scenarios, scene level spatial reasoning is necessary. + +Besides, our methods are tested on a specific dataset and solve some basic spatial reasoning tasks. More effort is required to explore how our methods can be applied to more general spatial reasoning tasks, which can help the community better utilize the power of spatial reasoning to solve real-world problems. + +# 5. Conclusion + +In this paper, we focus on enhancing the deep networks' performance on multi-view line drawing spatial reasoning tasks on the SPARE3D dataset. Specifically, we focus on two types of tasks: 1) view consistency task, which contains task $T2I$ , 2) camera pose reasoning task, which contains task $I2P$ and $P2I$ . We quantitatively and qualitatively show the advantage of using our self-supervised learning methods for all three tasks. + +In the future, We plan to explore how our network design for reasoning about 2D and 3D information could benefit the more general vision-related tasks like AI-assisted design, localization, and navigation. + +# Acknowledgment + +The research is supported by NSF FM Program under EEC-2036870. Siyuan Xiang gratefully thanks the IDC Foundation for its scholarship. The authors gratefully acknowledge the constructive comments and suggestions from the anonymous reviewers and area chairs. + +# References + +[1] Ankesh Anand. 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In this work, we propose a super-resolution method for such multi-exposure sequences, a problem that has received very little attention in the literature. The proposed method can handle the signal-dependent noise in the inputs, process sequences of any length, and be robust to inaccuracies in the exposure times. Furthermore, it can be trained end-to-end with self-supervision, without requiring ground truth high resolution frames, which makes it especially suited to handle real data. Central to our method are three key contributions: i) a base-detail decomposition for handling errors in the exposure times, ii) a noise-level-aware feature encoding for improved fusion of frames with varying signal-to-noise ratio and iii) a permutation invariant fusion strategy by temporal pooling operators. We evaluate the proposed method on synthetic and real data and show that it outperforms by a significant margin existing single-exposure approaches that we adapted to the multi-exposure case. + +# 1. Introduction + +High resolution (HR) satellite imagery is a key element in a broad range of tasks, including human activity monitoring and disaster relief. Super-resolution by computational methods has recently been adopted [7, 41] by the remote sensing industry (Planet SkySat, Satellogic Aleph-1). By leveraging high frame rate low-resolution (LR) acquisitions, low-cost constellations can be effective competitors to more traditional high-cost satellites. In order to capture the full dynamic range of the scene, some satellites use exposure bracketing, resulting in sequences with varying exposures. While several works have addressed multi-image super-resolution (MISR) of single-exposure sequences, almost no previous work considers the multi-exposure case. + +MISR techniques exploit the aliasing in several LR acquisitions to reconstruct a HR image. The maximum attainable resolution is capped by the spectral decay of the blur + +kernel resulting from the sensor's pixel integration and the camera optics, which imposes a frequency cutoff beyond which there is no usable high frequency information. + +Aggregating many frames is also interesting as it allows significant noise reduction. If the LR frames are acquired with bracketed exposures, it is possible to integrate them in a super-resolved high dynamic range (HDR) image. Long exposures have higher signal-to-noise ratio (SNR) which helps reduce the noise in dark regions, whereas short exposures provide information in bright regions which can cause saturation with longer exposure times. + +In this work, our goal is to perform joint super-resolution and denoising from a time series of bracketed satellite images. We focus on push-frame satellite sensors such as the SkySat constellation from Planet. We increase the resolution by a factor of two, which is the frequency cutoff of the combined optical and sensor's imaging system. The SkySat satellites [41] contain a full-frame sensor capable of capturing bursts of overlapping frames: a given point on the ground is seen in several consecutive images. However, our technique is general and can be applied to other satellites, or beyond satellite imagery to consumer cameras capable of multi-exposure burst or video acquisition. + +Several methods have addressed either MISR or HDR imaging from multiple exposures, but their combination has received little attention. Existing works consider an ideal setup in which frames can be aligned with an affinity [7,53] or a homography [55], and the number of acquisitions is large enough to render the problem an overdetermined system of equations. Such motion models are good approximations for satellite bursts, but ignore parallax [8], which can be noticeable for mountains and tall buildings. + +In the case of satellite imaging, push-frame cameras capable of capturing multi-exposure bursts are relatively recent, which explains why all previous works on MISR focus on the single-exposure case [7, 17, 40, 43], except for SkySat's proprietary method [41] producing the L1B product, whose details are not public. Deep learning methods currently outperform traditional model-based approaches [47]. In general, learning-based methods require large realistic datasets with ground truth to be trained, as + +![](images/e38f1a776c8c2851201500503d9a4d9b73e23c25b593f8c3bfe22e33e358a12f.jpg) + +![](images/0e1cf5928100d14fe1fa6a7914c37f17802beefba52fdb5aeeba12003b8e9725.jpg) + +![](images/f6b1afc626bf2edf7f062ebeef9620543a09dd4eb9abb1e157c4dac7d40b832b.jpg) + +![](images/e8b52cf85f0d5cd2ee55da3857c892df0e9b33831b6cea1daaa56f122f7c859d.jpg) + +![](images/629c913861dc5d1bffe26974fe281f133dfc41b394d34d723ad92c2a9289b136.jpg) + +![](images/79eaaa95b0ac57ff029b6b5489174d3d7b52191a5bbdc86fbbdf0e18c54cb941.jpg) + +![](images/70d7b0a3c885ae8ea048367db6be324eb78f1c5e45f064f47a29642dd8156a7e.jpg) + +![](images/35a35c2a2673bd9b1a3eb80e687e4f80c9c9b542629fe82234153de616086e9f.jpg) + +![](images/fb3770a164e01a43a6f01a5fc638a675e9b9318d0ada9eabf0eef50f5b7d14eb.jpg) + +![](images/a78d8f0b472728c0e5ab4d4df3b2740092d0699bed33a66cbd4713a7712ddf74.jpg) + +![](images/d49c923cee2e7460258e4c97b66a56e92c1c4470d86813a2f34e68dfb6279927.jpg) +$LR_{1}$ +$LR_{2}$ +ME S&A +Figure 1. Super-resolution from a real multi-exposure sequence of 10 SkySat images. Top row: Original low resolution images with different exposures. Bottom row: Reconstructions from five methods, including ours trained with self-supervision (right). + +![](images/f5c286c3b1b97300f99575ad04c4ecc0106573c1c60e733b65f3bf39f35bd2ae.jpg) +$LR_{3}$ +$LR_{4}$ +Planet L1B [41] + +![](images/53cf13211ddf6312862e2cbbd5213810ef7b6228b6f6e5c4010ed1b8ccb7ae0a.jpg) +$LR_{5}$ +$LR_{6}$ +BD-ACT [7] + +![](images/7f0e7d488a42915eac1ecd08f521451307cbebc260bac06f867a53ae33badbc5.jpg) +$LR_{7}$ +$LR_{8}$ +DSA [43] + +![](images/013b74cfa7c97bc70e4d70c8687c9b2de9c4e20dd91019d14c4f02beaf4fef50.jpg) +$LR_{9}$ +$LR_{10}$ +Our HDR-DSP + +methods trained on synthetic data [4] fail to generalize to real images [14]. One of such datasets is the PROBA-V dataset [37], acquired with a satellite equipped with two cameras of different resolutions. This dataset has fostered the publication of several deep learning approaches to satellite MISR [9, 17, 39]. However, the PROBA-V dataset is not appropriate for MISR of LR image bursts acquired at a high frame rate, as the PROBA-V sequences are multi-date and present significant content and illumination changes. + +A promising direction is to use self-supervised learning techniques, which have been applied to video restoration tasks such as denoising and demosaicing [18-20, 51, 58], and recently to MISR [43]. These techniques benefit from the temporal redundancy in videos. Instead of using ground truth labels, one of the degraded frames in the input sequence is withheld from the network and used as label. + +Our work builds upon Deep Shift-and-Add (DSA) [43], a self-supervised deep learning method for MISR of single-exposure bursts of satellite images. The model is trained without supervision by exploiting the frame redundancy. + +Contributions. In this work, we propose High Dynamic Range Deep Shift-and-Pool, HDR-DSP a self-supervised method for joint super-resolution and denoising of bracketed satellite imagery. The method is able to handle time-series with a variable number of frames and is robust to errors in the exposure times, as the ones provided in the metadata are often inaccurate. This makes our method directly applicable to real image data (see Figure 1). This is, to the best of our knowledge, the first multi-exposure MISR method for satellite imaging, and beyond satellite imagery, it is the first approach based on deep-learning. + +Our contributions are the following: + +Feature Shift-and-Pool. We propose a shift-and-pool module that merges features (computed by an encoder network on each input LR frame) into a HR feature map by temporal pooling using permutation invariant statistics: average, + +maximum, and standard deviation. This gives a rich fused representation which yields a substantial improvement over the average [43], in both single and multiple exposure cases. + +Robustness to inaccurate exposure times via base-detail decomposition. We propose normalizing the input frames and decomposing them into base and detail. The errors caused by the inaccurate exposure times affect mainly the base, whereas the detail containing the aliasing required for super-resolution can be safely processed by the network. Note that vignetting and stray light can also cause exposure issues that affect single and multi-exposure MISR alike. + +Noise-level-aware detail encodings. The noise present in the LR images is signal-dependent, its variance being an affine function of the intensity. To deal with such noise, we provide the un-normalized LR images to the encoder in addition to the normalized detail components. This gives the encoder information about the noise level of each pixel, necessary for an optimal fusion. + +Self-supervised loss with grid shifting. Using random shifts of the high-resolution grid, we make the self-supervised loss of [43] translation equivariant, leading to improved results. + +We validate our contributions with an ablation study on a synthetic dataset ( $\S 5.2$ ), designed to model the main characteristics of real bracketed SkySat sequences. Since there are no previous works on multi-exposure MISR, we compare against state-of-the-art single-exposure MISR methods which we adapt and retrain to multi-exposure inputs ( $\S 5.3$ ). + +We also introduce a dataset of 2500 multi-exposure real SkySat bursts (§5.4). The dataset only consists of noisy LR images, but we can nevertheless train our network on it, since it is self-supervised. Both on synthetic and real data, the proposed HDR-DSP method attains the best results by a significant margin even though it is trained without high resolution ground truth data. The dataset is available for download on the project website. + +# 2. Related work + +Most works on video and burst super-resolution focus on the single-exposure case [7, 12, 17, 34, 39, 43, 49, 52]. The problem of super-resolution from multi-exposure sequences has received much less attention. In [53] it is modeled as an overdetermined system and solved via a non regularized least-squares approach. An affine motion model and exact knowledge of the exposure times are assumed. The authors in [55] address the case in which the images have motion blur due to the camera shake. They also consider a static scene and do not consider noise. A related method for HDR imaging uses dual exposure sensors, which interlace two exposures in even and odd columns of the image [15, 26]. This can be seen as horizontally super-resolving the video. + +Other works perform a related task: joint superresolution and reverse tone-mapping [30-32]. The difference with our problem is that the input video is a single-exposure LR video, and the goal is to artificially increase its dynamic range to adapt it to HDR screens. + +Methods for HDR imaging from multiple exposures need to deal with the noise. Granados et al. [23] address the case of signal-dependent noise and propose a fixed point iteration of the MLE estimator which is close to the Cramer-Rao bound [3]. In these works, the denoising comes only from the temporal fusion. In [1, 2], this is incorporated in into spatio-temporal patch-based denoisers. + +Our work can also be related to burst and video joint denoising and demosaicing [19, 25, 56], as demosaicing can be regarded as a super-resolution problem. + +# 3. Observation model + +We denote by $\mathfrak{I}_t$ a dynamic infinite-resolution ideal scene. The camera on the satellite captures a sequence of $m$ low resolution images $\bar{I}_i^{LR}$ with different exposures. For the $i$ -th acquisition, the dynamic scene $\mathfrak{I}_t$ is integrated during an exposure time $e_i$ centered at $t_i$ . Even if satellites travel at a very high speed relative to the ground, precise electro-optical image stabilization systems (with piezo-electric actuators [29, 33] or steering mirrors [46]) assure that the observed scene $\mathfrak{I}_t$ is mostly constant during the exposure time ( $\sim 2\mathrm{ms}$ ), which allows us to approximate the temporal integration with a product in our observation model + +$$ +\bar {I} _ {i} ^ {L R} = e _ {i} \Pi_ {1} \left(\mathfrak {I} _ {t _ {i}} * k\right) + n _ {i} = e _ {i} \mathcal {I} _ {i} ^ {L R} + n _ {i}. \qquad (1) +$$ + +Here $k$ is the Point Spread Function (PSF) modeling jointly optical blur and pixel integration, $\Pi_1$ is the bi-dimensional sampling operator due to the sensor array, $\mathcal{I}_i^{LR}$ is the clean low-resolution image corresponding to an exposure of 1 unit of time and $n_i$ denotes the noise. Throughout the text, calligraphic fonts $\mathcal{I}_i$ denote noise-free images and regular fonts $I_i$ noisy ones. A bar $\bar{I}_i = e_i I_i$ indicates that the image is multiplied by its exposure time (i.e. as it is acquired by the + +sensor), while its absence denotes images normalized to an exposure time of 1. We consider the $r$ -th image $\bar{I}_r^{LR}$ in the time series as the reference, and without loss of generality we assume its exposure time to be one, $e_r = 1$ . + +We model the noise as spatially independent, additive Gaussian noise with zero mean and signal-dependent variance $n_i(x) \sim \mathcal{N}(0, \sigma^2 (\bar{\mathcal{I}}_i^{LR}(x)))$ , where + +$$ +\sigma^ {2} \left(\bar {\mathcal {I}} _ {i} ^ {L R} (x)\right) = a e _ {i} \mathcal {I} _ {i} ^ {L R} (x) + b, \tag {2} +$$ + +is an approximation of the Poisson shot noise plus Gaussian readout noise [21,45], with parameters $a$ and $b$ . + +Because of the spectral decay imposed by the pixel integration and optical blur $(k)$ , the images $\mathfrak{I}_{t_i} * k$ are band limited with a cutoff at about twice the sampling rate of the LR images for SkySat. Our goal is to increase the resolution by a factor 2 by estimating $\widehat{\mathcal{I}}_r^{HR}$ , a non-aliased sampling of $\mathfrak{I}_{t_r} * k$ from several LR observations $\{\bar{I}_i^{LR}\}_{i=1}^m$ with varying exposures $\{e_i\}_{i=1}^m$ . A sharp super-resolved image can then be recovered by partially deconvolving $k$ . + +In order for the method to be applicable in practice, it needs to handle time series with a variable number of frames $m$ , and to be robust to inaccuracies in the exposure times $e_i$ , as the exposure times in the image metadata are only a coarse approximation of the real ones. + +# 4. Proposed method + +Our method builds upon the DSA method for MISR introduced in [43], which can be regarded as a trainable generalization of the traditional shift-and-add (S&A) algorithms [6, 22, 24, 28, 38]. A feature S&A is used to fuse feature representations produced from the LR images by an encoder network. A motion estimation network computes the optical flows between each input LR frame and the reference frame. The output of the feature S&A is a high-resolution aggregated feature map, which is then decoded by another network to produce the output image. + +The DSA method could be extended to multi-exposure sequences by applying it to the normalized images $\bar{I}_i^{LR} = \bar{I}_i^{LR} / e_i$ . This approach however is sub-optimal because it neglects the fact that the normalization alters the noise variance model, and fails if the reported exposure times are inaccurate, which is the case in practice. + +To better exploit multiple exposures, we propose two modifications: (1) A base-detail decomposition, which provides robustness to errors in the exposure times; (2) An encoding of the images that is made dependent on the noise variance, which allows the encoder to weight different contributions according to their signal-to-noise ratio. In addition, we also propose a new feature pooling fusion intended to capture a richer picture of the encoded features, leading to a substantial improvement in reconstruction quality, both for single and multiple exposure cases. The resulting net + +![](images/9b33316d72047a12ac314b2f5285cc51b73aabd94c7e848f164bc5e5d61c1413.jpg) +Figure 2. Overview of our proposed multi-exposure super-resolution network architecture HDR-DSP at inference time. + +work can be trained end-to-end with self-supervision, i.e. without requiring ground truth. + +# 4.1. Architecture + +Figure 2 shows a diagram of our proposed architecture which takes as input a sequence of multi-exposed LR images $\{\bar{I}_i^{LR}\}_{i = 1}^m$ along with the corresponding exposure times $e_i$ and produces one super-resolved image $\widehat{\mathcal{I}}_r^{HR}$ . The input LR images are first normalized to unit exposure time. The normalized LR images $\{I_i^{LR}\}_{i = 1}^m$ are then decomposed into base $\{B_i^{LR}\}$ and detail $\{D_i^{LR}\}$ components. The bases contain the low frequencies. We align and average them to reduce the low frequency noise and upsample the result using bilinear zooming to produce the HR base component. The LR detail images are fed to a shared convolutional Encoder network that outputs a feature representation of each LR image. The features are then merged into a HR feature map by our shift-and-pool block (FSP), which aligns the LR features into the HR grid of the reference frame, and applies different pooling operations. The pooled features are then concatenated and fed to a Decoder CNN module that produces the HR detail image. The final HR image is obtained by adding the HR base and detail $\widehat{\mathcal{I}}_r^{HR} = \widehat{\mathcal{B}}_r^{HR} + \widehat{\mathcal{D}}_r^{HR}$ . + +The trainable modules of the proposed architecture (shown in red in Figure 2) include the Motion Estimator, the Encoder, and the Decoder. + +Base-Detail decomposition. As mentioned above, normalizing a sequence of the frames $\bar{I}_i^{LR}$ by their reported exposures $e_i$ does not result in stable intensity levels across the sequence. This can be due to small errors in $e_i$ . However, uncorrected vignetting or stray light also contribute the same effect, even in single-exposure imagery. + +The nature of the super-resolution task makes it very sensitive to these exposure fluctuations. The shift-and-add operation would merge the LR features into an incoherent high-resolution feature map, making the task of the decoder more difficult, resulting in loss of details or high-frequency + +artifacts (see Figure 3). Refining the initial $e_i$ could limit this problem. But this entails its own challenges, especially if one also considers vignetting and stray light sources. + +Instead, in this paper we propose a more robust and simple alternative, which is based on a base-detail decomposition [44] of the normalized LR images defined as follows + +$$ +B _ {i} ^ {L R} = I _ {i} ^ {L R} * G, \quad D _ {i} ^ {L R} = I _ {i} ^ {L R} - B _ {i} ^ {L R}, \tag {3} +$$ + +for $i = 1,\ldots ,m$ . Here $G$ is a Gaussian kernel of standard deviation 1. We then process independently the details $\{D_i^{LR}\}$ and the bases $\{B_i^{LR}\}$ to produce the corresponding high resolution estimates $\widehat{\mathcal{D}}_r^{HR}$ and $\widehat{\mathcal{B}}_r^{HR}$ . This decomposition is linear and does not affect the super-resolution since the alias is preserved in the detail components $\{D_i^{LR}\}$ . + +As the detail images span a smaller intensity range than the complete image $I_{i}^{LR}$ , an error $\delta$ in the exposure time results in a small deviation in the detail and a large one in the base: $\delta B_{i}^{LR} + \delta D_{i}^{LR} = \delta I_{i}^{LR}$ . The small error in the detail can be handled by a super-resolution method. + +On the other hand, the base images do not need to be super-resolved, but still need to be denoised. In this work we propose a simple processing that aligns and averages the bases and upsamples the result. To fully exploit the high signal-to-noise ratio of longer exposures, the average is weighted by the exposure times $e_i$ + +$$ +B ^ {H R} = \operatorname {Z o o m} \left(\frac {\sum_ {i} e _ {i} \operatorname {W a r p} \left(B _ {i} ^ {L R}\right)}{\sum_ {i} e _ {i}}\right). \tag {4} +$$ + +This weighting is an approximation of the ML estimator of Granados et al. [23] (details in the supplementary material). + +Base and detail decompositions have been used in superresolution networks [27, 31] to focus the network capacity on the details. In our case, the decomposition also provides robustness to errors in the radiometric normalization. + +Motion Estimator. We follow the works of [43,49] to build a network (with the same hourglass architecture) that esti- + +![](images/5626bca50f840ba59fbea002e6780b31fa49eb695eca7babed25cb09bfa00951.jpg) +DSA [43] (without BD) + +![](images/5bf412ca1aaddfb9a65aef7861cafd38000c9458a20140b3de97c514ca039f1e.jpg) +Our HDR-DSP (with BD) +Figure 3. High frequency artifacts in a reconstruction from a real SkySat sequence (using DSA [43]) with exposure time errors (left). HDR-DSP with the proposed base-detail (BD) decomposition does not present artifacts (right). + +mates the optical flows between the normalized LR frames $\{I_i^{LR}\}_{i = 1}^m$ and the normalized reference frame $I_r^{LR}$ + +$$ +F _ {i \rightarrow r} = \mathbf {M o t i o n E s t} \left(I _ {i} ^ {L R}, I _ {r} ^ {L R}; \Theta_ {\mathbf {M}}\right) \in [ - R, R ] ^ {H \times W \times 2}, \tag {5} +$$ + +where $\Theta_{\mathbf{M}}$ denotes the network parameters. A small Gaussian filter $(\sigma = 1)$ is applied to the input images to reduce the alias [43,54]. The network is trained with a maximum motion range of $[-R,R]^2$ (with $R = 5$ pixels). The training was adapted to better handle the noise difference due to the multi-exposure setting (see §4.2). + +Noise-level-aware detail encodings. The Encoder module generates relevant features $J_{i}^{LR}$ for each normalized LR detail image $D_{i}^{LR}$ in the sequence + +$$ +J _ {i} ^ {L R} = \operatorname {E n c o d e r} \left(D _ {i} ^ {L R}, \bar {I} _ {i} ^ {L R}; \Theta_ {\mathbf {E}}\right) \in \mathbb {R} ^ {H \times W \times N}, \tag {6} +$$ + +where $\Theta_{\mathbf{E}}$ is the set of parameters of the encoder and $N = 64$ is the number of produced features. The network architecture is detailed in the supplementary material. + +The un-normalized low resolution frames $\tilde{I}_i^{LR}$ are also fed to the encoder. This is motivated by the fact that the maximum likelihood fusion of noisy acquisitions into a (HDR) image is a weighted average, where the weights are the inverse of the noise variances [3,23]. In the proposed architecture, the normalized details $D_i^{LR}$ are fused to produce a high resolution detail $\hat{\mathcal{D}}_r^{HR}$ . The noisy un-normalized images are unbiased estimators of an affine function of the noise variances $\sigma^2 (\tilde{I}_i^{LR}) / a - b / a$ , thus they provide to the encoder the information required to compute the optimal fusion weights. The resulting features $J_{i}^{LR}$ are then aggregated via a set of pooling operations, without any particular handling related to different source exposures. + +Feature Pooling. We propose the Feature Shift-and-Pool block (FSP) which maps the LR features into their positions on the reference HR grid and pools them. First the features are "splatted" bilinearly onto the HR grid by the SPMC module [52]. Each LR frame is upscaled by introducing zeros between samples and motion compensated following the flows $F_{i\rightarrow r}$ . This is differentiable with respect to + +the intensities and the optical flows. Each splatted pixel is assigned a bilinear weight depending on the fractional part of its position in the HR grid. See [43, 52] for details. + +This results in a set of aligned sparse HR feature maps + +$$ +J _ {i} ^ {H R} = \operatorname {S P M C} \left(J _ {i} ^ {L R}, \left\{F _ {i \rightarrow r} \right\}\right) \in \mathbb {R} ^ {s H \times s W \times N}, \tag {7} +$$ + +and the corresponding bilinear splattering weights $W_{i}^{HR} = \mathrm{SPMC}(1, \{F_{i \to r}\})$ . The upscaling factor $s$ is set to 2. + +As in [43], we use a weighted average pooling in the temporal direction (8). In addition, we propose computing the standard deviation and the max (9): + +$$ +J _ {A} ^ {H R} = \left(\sum_ {i} J _ {i} ^ {H R}\right) \left(\sum_ {i} W _ {i} ^ {H R}\right) ^ {- 1}, \tag {8} +$$ + +$$ +J _ {M} ^ {H R} = \max _ {i} J _ {i} ^ {H R}, \quad J _ {S} ^ {H R} = \operatorname {s t d} _ {i} J _ {i} ^ {H R}. \tag {9} +$$ + +Note that this block does not have any trainable parameters, a trainable layer may attain a similar performance at a much higher computational cost (see the supplementary material). + +These feature pooling operations render the architecture invariant to permutations of the input frames [5]. The key idea is that through end-to-end training, the encoder network will learn to output features for which the pooling is meaningful. Therefore, it is essential that the pooling operation is capable of passing all the necessary information to the decoder. Indeed, average pooling captures a consensus of the features, which amounts to a temporal denoising. But in aliased image sequences, it is common to come across features that are only visible in a single frame. Thus, the idea of the max-pooling operation is to preserve these unique features that would otherwise be lost in the average. The standard deviation pooling completes the picture by measuring the point-wise variability of the features. + +The pooled features are independent of the number of processed frames. But this information is important as the decoder may interpret features resulting from aggregating many images differently than those resulting from just a few. For this reason, the aggregation weights $W^{HR} = \sum_{i} W_{i}^{HR}$ are also concatenated with the pooled features. As we will see in §5.2, incorporating $W^{HR}$ improves the network ability to handle a variable number of input frames. + +Decoder. The Decoder network reconstructs the HR detail image $\widehat{\mathcal{D}}_r^{HR}$ from the pooled features + +$$ +\widehat {\mathcal {D}} _ {r} ^ {H R} = \operatorname {D e c o d e r} \left(J _ {A} ^ {H R}, J _ {M} ^ {H R}, J _ {S} ^ {H R}, W ^ {H R}; \Theta_ {\mathbf {D}}\right) \in \mathbb {R} ^ {s H \times s W}, \tag {10} +$$ + +where $\Theta_{\mathbf{D}}$ denotes the set of parameters of the decoder. The architecture is detailed in the supplementary material. + +# 4.2. Self-supervised learning + +To train the HDR-DSP detail fusion network, we adapt the fully self-supervised framework of [43], which requires no ground truth HR images. During training, the LR frames + +are randomly selected and for every sequence, one frame is set apart as the reference $I_r^{LR}$ . Then, all the other LR images in each sequence are registered against the reference using the MotionEst network yielding the flows $F_{i\rightarrow r}$ . The reference frame serves as the target for the self-supervised training similarly to noise-to-noise [20, 35]. The procedure relies on the minimization of a reconstruction loss in the LR domain plus a motion estimation loss to ensure accurate alignment of the frames. The losses and the proposed adaptations are detailed in the following paragraphs. + +Self-supervised SR loss. The self-supervised loss forces the network to produce an HR detail $\hat{\mathcal{D}}_r^{HR}$ such that when subsampled, it coincides (modulo the noise) with the withheld target detail $D_r^{LR}$ + +$$ +\ell_ {s e l f} \left(\widehat {\mathcal {D}} _ {r} ^ {H R}, D _ {r} ^ {L R}\right) = \left\| \Pi_ {2} \left(\widehat {\mathcal {D}} _ {r} ^ {H R} * k\right) - D _ {r} ^ {L R} \right\| _ {1}, \tag {11} +$$ + +where $\widehat{\mathcal{D}}_r^{HR} = \mathbf{Net}(\{D_i^{LR}\}_{i\neq r},\{\bar{I}_i^{LR}\}_{i = 1}^m)$ is the SR output, and $\Pi_{2}$ is the subsampling operator that takes one pixel over two in each direction. As in [43] we include the convolution kernel $k$ in the loss. This forces the network to produce a deconvolved HR image that once convolved with $k$ and subsampled matches the optical blur present in $D_r^{LR}$ . + +During training, the LR reference is only used in the motion estimator to compute the optical flows, but it is not fused into the HR result to avoid unwanted trivial solutions [11, 18, 43]. At inference time we use the reference as this leads to improved results [43]. + +Grid shifting. The self-supervised loss (11) downsamples the super-resolved detail to compare it with the reference LR detail. But since the downsampling is fixed, only the sampled positions intervene in the loss, which breaks the translation equivariance of the method. To avoid this issue, during training we augment the data by adding to the estimated optical flows a random shift of $0.5\epsilon$ in each dimension $(\epsilon \in \{0,1\})$ . As a result, the super-resolved image is shifted by $\epsilon$ , which is easily compensated before computing the loss. This yields an improvement in PSNR of 0.2dB. + +Motion estimation loss. The motion estimator is trained with unsupervised learning as in [57]. The loss consists of a warping term and a regularization term. We observed that the optical flow is very sensitive to the intensity fluctuations between frames (as in our normalized LR frames $I_{i}^{LR}$ ), which result in imprecise alignments. To prevent this issue we compute the warping loss on the details rather than on the images, which is common in traditional optical flow [36, 49]. The loss is computed for each flow $F_{i\rightarrow r}$ estimated by the MotionEst module + +$$ +\begin{array}{l} \ell_ {m e} \left(\left\{F _ {i \rightarrow r} \right\} _ {i = 1} ^ {m}\right) = \lambda_ {1} T V \left(F _ {i \rightarrow r}\right) + \\ \sum_ {i} \left\| \text {D e t a i l} \left(I _ {i} ^ {L R} - \text {P u l l b a c k} \left(I _ {r} ^ {L R}, F _ {i \rightarrow r}\right)\right)\right\| _ {1}, \tag {12} \\ \end{array} +$$ + +where Pullback computes a bicubic warping of $I_r^{LR}$ according to a flow, Detail applies a high-pass filter, TV is the finite difference discretization of the classic Total Variation regularizer [48], and $\lambda_1 = 0.003$ is a hyperparameter controlling the regularization strength. + +Training. The self-supervised training of HDR-DSP is done in two stages. We first pretrain the motion estimator on the simulated data to ensure that it produces accurate flows. Then, we train the entire system end-to-end with the pretrained MotionEst using the self-supervised loss $(\lambda_{2} = 3)$ + +$$ +\operatorname {l o s s} = \ell_ {\text {s e l f}} + \lambda_ {2} \ell_ {\text {m e}}. \tag {13} +$$ + +Other training details are in the supplementary material. + +# 5. Experiments + +For our experiments, we use real multi-exposure pushframe images (L1A) acquired by SkySat satellites [41]. For the quantitative evaluations we also simulated a multi-exposure and a single-exposure datasets from L1B products (super-resolved products by Planet with a factor of 1.25). + +# 5.1. Simulated multi-exposure dataset + +The two simulated datasets were generated from 1371 crops of L1B products (1096 train, 200 test, 75 val). First, we generate the noise-free LR images normalized to an exposure time of 1. Random subpixel translations of $\{\Delta_i\}_{i=1}^m$ are applied to the ground truth followed by $\times 2$ subsampling + +$$ +\begin{array}{l} \mathcal {I} _ {r} ^ {L R} = \Pi_ {2} (\mathcal {I} ^ {H R}), \\ \mathcal {I} _ {i} ^ {L R} = \Pi_ {2} \left(\operatorname {S h i f t} _ {\Delta_ {i}} \left(\mathcal {I} ^ {H R}\right)\right), \quad i \neq r \tag {14} \\ \end{array} +$$ + +where $\Pi_2$ is the subsampling operator. The exposure times are simulated as $e_i = \alpha^{c_i}$ , where $c_{i} \in \{-5,..,5\}$ , and $\alpha = \mathrm{uniform}(1.2,1.4)$ . The noises $n_i = \sqrt{ae_i\mathcal{I}_i^{LR} + b\mathcal{N}(0,1)}$ are then added to all the un-normalized frames to produce the noisy multi-exposure sequence $\bar{I}_i^{LR} = e_i\mathcal{I}_i^{LR} + n_i$ . The constants $a = 0.119$ , $b = 12.050$ were estimated from real SkySat images with the Ponomarenko noise curve estimation method [16,45]. The single-exposure dataset is generated in the same manner but with all $e_i = 1$ . To simulate the exposure inaccuracies, during training and testing the $e_i$ values are contaminated with noise within a range of $5\%$ . + +We use a PSNR score in our evaluation. The SkySat L1A images have a dynamic range of 12 bits, but we observed that the peak signal is at about 3400 DN. Therefore, our PSNR is normalized with a peak of 3400. We denote PSNR ME (resp. PSNR SE) as the average PSNRs computed on all the multi-exposure (resp. single-exposure) test sequences. + +# 5.2. Ablation study + +We study in Table 1 the importance of the base-detail decomposition. We consider simulated multi-exposure (ME) + +Table 1. Handling of multi-exposure sequences with base-detail decomposition (BD) and using the un-normalized LR frames $I_{i}^{LR}$ as an additional encoder input. + +
Methods (all HDR-DSP)fullw/o BDw/o BD (trained SE)w/o LR
PSNR(dB) ME54.7053.7652.9153.94
PSNR(dB) SE54.7254.1654.5454.16
+ +Table 2. Feature pooling choice. Using average (A), maximum (M), and standard deviation (S) pooling improves the results. + +
FeaturesAMS (HDR-DSP)ASAMA
PSNR(dB) ME54.7054.4654.4454.17
PSNR(dB) SE54.7254.4754.4854.20
+ +Table 3. Handling variable number of frames (PSNR ME (dB)). + +
Methods (all HDR-DSP)fullw/o WHRHDR-DSP 4HDR-DSP 14
4 frames52.8152.6052.6951.31
14 frames55.8555.5954.2655.53
variable n frames54.7054.4553.8554.07
+ +and single-exposure (SE) sequences presenting small exposure errors that match the ones observed in real sequences. If we train HDR-DSP without the proposed base-detail (w/o BD), the performance drops noticeably, which is also visible on real sequences (Figure 3). Even when training specifically for a single-exposure setting, as with DSA [43], the performance with base-detail is superior. In addition, we can see that removing the un-normalized LR frame from the encoder inputs (w/o LR) leads to a large performance drop for both single- and multi-exposure. + +The experiment shown in Table 2 studies the impact of using multiple feature pooling strategies: average, maximum, and standard deviation. It shows that using the three greatly improves the results: about $0.5\mathrm{dB}$ with respect to just using average. We observed that not including the average among the pooling strategies yields much worse results. + +The aggregation weight feature $W^{HR}$ was added to improve the handling by the decoder of sequences with variable number of input frames. The results in Table 3 confirm the importance of providing these weights. We also compare with networks trained for a fixed number of frames (HDR-DSP 4 and 14) and observe that in this case the performance drops even when testing for those specific configurations. We conclude that the weights become useless if the training does not consider a variable number of frames. + +Lastly, removing the grid shifting (§4.2) from the training also reduces the PSNR ME: from 54.70 to 54.49dB. + +# 5.3. Comparison with the state-of-the-art + +We compare our self-supervised network on the simulated dataset against state-of-the-art MISR methods for + +Table 4. PSNR ME (dB) over the synthetic test set with 15 images in the case of $0\%$ , $5\%$ and $20\%$ exposure time errors. + +
MethodsRAMSME S&AHR-netBD-ACTDSAHDR-DSP
0% exp. error52.0553.3354.3054.2455.5556.00
5% exp. error51.8452.4354.2254.2354.9955.99
20% exp. error49.9549.1953.8254.2054.3055.90
+ +satellite images: DSA [43], HighRes-net (HR-net) [17], RAMS [50], and ACT [7]. A weighted Shift-and-add [38] with bicubic splatting adapted to multi-exposure sequences (ME S&A) serves as the baseline. HR-net and RAMS are two supervised networks designed to perform superresolution of multi-temporal PROBA-V satellite images. In the context of push-frame satellites, we use the reference-aware version [42] of HR-net and RAMS rather than the original approaches, as they achieve higher quality results. DSA and ACT are two state-of-the-art super-resolution methods for SkySat imagery. ACT also serves as a proxy for comparison with other interpolation-based methods from the literature [56]. + +We adapt these methods to multi-exposure sequences. The deep learning approaches are fed with the normalized input images, whereas for ACT method we apply the same base-detail decomposition described in §4.1 and use ACT to restore the details (denoted BD-ACT). The registration step of ME S&A, BD-ACT, and RAMS are done with the inverse compositional algorithm [10, 13], which is robust to noise and brightness changes. The motion estimator of DSA is also trained with the loss on the details (§4.2). + +Table 4 shows a quantitative comparison of the methods over the test set in the case of adding exposure time errors of $5\%$ (as during training) and $20\%$ . These errors are estimated from SkySat data (exposures ranging from 0.5 to $4.5~\mathrm{ms}$ ); see the supplementary material for details. Note that even with exact exposure times (row $0\%$ ), vignetting or stray light effects still justify the use of the proposed base-detail decomposition. Our self-supervised network ranks first in all cases with a significant gain of more than 1dB over all others (see Figure 4). Interestingly, the performance of most methods degrades quickly for large inaccuracy in exposure times. Only the methods using the base-detail decomposition (BD-ACT and ours) are robust to these inaccuracies. Note that HDR-DSP has never seen errors of $20\%$ during training. + +# 5.4. Results on real data + +The proposed self-supervised training allows to train HDR-DSP on real multi-exposure sequences taken from SkySat satellites. From the L1A product of Planet SkySat, we extracted 2500 sequences ( $128 \times 128$ pixels) preregistered up-to an integer translation. Out of 2500 sequences, 300 are used for testing. Each sequence contains + +![](images/4a9b836565ba8117b39ed9133b17f42c5db78c0bd5453c2f6d0aa2839dfc4752.jpg) +LR + +![](images/56e293f50f0f219facc908603660c7a743746428cadabdd8c4d7ca7d5aaf3103.jpg) +ME S&A 43.16dB + +![](images/a70326d54722159c8bc5f782bda6bfd10b5bdfc95c2b95da8e48393191dbca3e.jpg) +RAMS 42.99dB + +![](images/ac81fe4f9c3dfd7cb60369b3c3260f45d691346800de7148a5a14250db8a1158.jpg) +HR-net 43.58dB + +![](images/1b757576b613779ed137c860c44ac4e425b5936aa51c2a5a7f08e5ad5b22c46f.jpg) +BD-ACT 43.59dB + +![](images/4062ee889e748e5842f483f4fd65629cfc4d8355a32adbed25f5b5bae34ff555.jpg) +DSA 45.95dB + +![](images/566cba4511242ac2889e52d1659a0a1b11973a02e792f45e349bdb6b4cc96caa.jpg) +HDR-DSP 49.32dB + +![](images/c60ae10f307dc829549335b5668106a894bc52aedfec88125ef052e9ae8f086b.jpg) +HR + +![](images/63f3fd31e246920ae0915e2ceb0de4bc93dda840965f9771ffa70e6264f4e42d.jpg) +Figure 4. Super-resolution from a synthetic multi-exposure sequence (5% exp. error) of 15 aliased LR images. Methods are trained on a synthetic dataset and receive as inputs the normalized ME images except BD-ACT and HDR-DSP, which use the base-detail decomposition. + +![](images/6126c553d96faac18fcf020ea6518b521613cd2dea006d70365e73de5c5a0a31.jpg) +LR $e = 1.1$ + +![](images/fd4a367d8bc142433e593f730e8375b9c97acfc75874fc6cbfd0536f2ed11389.jpg) +LR $e = 0.7$ + +![](images/783ea3a69c28fcbcf55d8e4bdd6743fbb4919d2ccbfc2e445c0d19bed83ab484.jpg) +LR $e = 0.5$ + +![](images/302aafe687098fc239c48c1971b770eb862b96880df3aa3ac663610fc484b1da.jpg) +LR $e = 1.5$ +Planet L1B +Figure 5. Super-resolution from a real multi-exposure sequence of 9 SkySat images. The first line corresponds to 4 normalized LR images in that sequence with different exposure times. The second line shows the reconstructions by Planet (L1B), DSA, BD-ACT and our method HDR-DSP. + +![](images/3aee3baff1c3ce38f676db3020903cb1a5df53e7245c4604ecacf9ef7d8db3de.jpg) +DSA + +![](images/7209b405ffbc3b336fdfc6b755af7a61440c0b8abd5d539a4818f54666f3730a.jpg) +BD-ACT + +![](images/a36e867b9825ff1ec0273e04cc0613b2e5e9b67be07d4b79d5b63cfd0a463f07.jpg) +Our HDR-DSP + +from 4 to 15 frames. In about $75\%$ of the sequences the exposure time varies within each sequence and we used the exposure time information provided in the metadata. + +Figure 5 compares HDR-DSP against Planet L1B, DSA, and BD-ACT. The top row shows four normalized frames of the sequence, where we can notice the dependence of the noise level on the exposure time. The method used in the Planet L1B product is unknown. It super-resolves by a factor of 1.25 but contains noticeable artifacts and lacks fine details. The result from DSA exhibits a high-frequency pattern due to the imprecise exposure times. BD-ACT is able to cope with the exposure changes thanks to the base-detail decomposition, but the result is still very noisy. In contrast, HDR-DSP shows a clean and detailed reconstruction. + +Figure 1 also shows a multi-exposure LR sequence along with the results from ME S&A, Planet L1B, ACT, DSA and HDR-DSP. Comparing HDR-DSP with DSA, we see that the former provides a cleaner result thanks to the base-detail decomposition and the proposed improvements over + +the DSA architecture and training procedure, which is also observed in the synthetic experiments. + +# 6. Conclusion and limitations + +The proposed HDR-DSP method is able to reconstruct high-quality results from multi-exposure bursts, providing fine details, low-noise, and high dynamic range. The proposed base-detail processing allows robustness to errors in the exposure time that are common in practice. In addition, a significant performance improvement is obtained by making the image encoding dependent on the noise variance, and using a new feature pooling designed to capture richer representations. Thanks to its fully self-supervised training, the method requires no ground truth and can thus be applied on real data. We show its effectiveness by training a model that super-resolves multi-exposure SkySat L1A acquisitions, leading to a substantial resolution gain with respect to the state-of-the-art. + +Limitations. The context of remote sensing allows one to make additional assumptions that do not hold in more general settings: 1. The considered noise levels are away from the challenging photon-limited regime; 2. Motion and occlusions are much easier to handle. In particular, the latter point should be improved to apply this method to video or burst super-resolution. Besides, the proposed method does not handle saturation. This will be studied in future work. + +Acknowledgments. Work supported by a grant from Région Île-de-France. This work was performed using HPC resources from GENCI-IDRIS (grants 2022-AD011012453R1 and 2022-AD011012458R1) and from the "Mésocentre" computing center of CentraleSupélec and ENS Paris-Saclay supported by CNRS and Région Île-de-France (http://mesocentre.centralesupelec.fr/). We thank Planet for providing the L1A SkySat images. + +# References + +[1] Cecilia Aguerrebere, Andres Almansa, Julie Delon, Yann Gousseau, and Pablo Musé. A bayesian hyperprior approach for joint image denoising and interpolation, with an application to hdr imaging. IEEE Transactions on Computational Imaging, 3(4):633-646, 2017. 3 +[2] Cecilia Aguerrebere, Julie Delon, Yann Gousseau, and Pablo Muse. Simultaneous hdr image reconstruction and denoising for dynamic scenes. In IEEE International Conference on Computational Photography (ICCP), pages 1-11. IEEE, 2013. 3 +[3] Cecilia Aguerrebere, Julie Delon, Yann Gousseau, and Pablo Musé. 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Crowley $^{1}$ , Dominique Vaufreydaz $^{1}$ $^{1}$ Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG, 38000 Grenoble, France + $^{2}$ Tencent AI Lab $^{3}$ LIGM (UMR 8049) - Ecole des Ponts, UPE + $^{4}$ Samsung AI Center, Cambridge $^{5}$ MIT CSAIL + +# Abstract + +Transformers trained with self-supervision using self-distillation loss (DINO) have been shown to produce attention maps that highlight salient foreground objects. In this paper, we show a graph-based method that uses the self-supervised transformer features to discover an object from an image. Visual tokens are viewed as nodes in a weighted graph with edges representing a connectivity score based on the similarity of tokens. Foreground objects can then be segmented using a normalized graph-cut to group self-similar regions. We solve the graph-cut problem using spectral clustering with generalized eigen-decomposition and show that the second smallest eigenvector provides a cutting solution since its absolute value indicates the likelihood that a token belongs to a foreground object. + +Despite its simplicity, this approach significantly boosts the performance of unsupervised object discovery: we improve over the recent state-of-the-art LOST by a margin of $6.9\%$ , $8.1\%$ , and $8.1\%$ respectively on the VOC07, VOC12, and COCO20K. The performance can be further improved by adding a second stage class-agnostic detector (CAD). Our proposed method can be easily extended to unsupervised saliency detection and weakly supervised object detection. For unsupervised saliency detection, we improve IoU for $4.9\%$ , $5.2\%$ , $12.9\%$ on ECSSD, DUTS, DUTOMRON respectively compared to state-of-the-art. For weakly supervised object detection, we achieve competitive performance on CUB and ImageNet. Our code is available at: https://www.m-psi.fr/Papers/TokenCut2022/ + +# 1. Introduction + +Object detection is a key enabling technology for real-world vision systems for tasks such as robotics, autonomous driving, traffic monitoring, manufacturing, and embodied artificial intelligence [21, 63, 64]. However, the perfor + +![](images/90ead898494d7fc0bd8037cc7c9d1015c912d74485f87729647185594fe34f35.jpg) +(a) DINO [6] + +![](images/b7a49a1fb06089c84b5d3dd649f71c82809782b3d8d83220f9e935f4d60d9a8b.jpg) +(b) LOST [45]. + +![](images/5de538279fe55d77f31265354ee99fc845138b4a92daa40dc3bbf7d4d73406a7.jpg) + +![](images/f20f966f8482a62c637be365ea3fd4c126f855b451d08d9a2f69636b45764643.jpg) + +![](images/5b2278e1cad68f7a816950e8366360bababccbea6c3673f36c002139d3ce2bad.jpg) +(d) Attention maps associated to different patches + +![](images/e3967d5a6eae0f9677ecbb220547cffbd19a874186e194f2e8d20d25a3a758da.jpg) +(c) TokenCut (ours) + +![](images/45d353a22edaaccb373b6ead2dcc29d897b56358db97b5a207b7d778e1e2e627.jpg) + +![](images/e447177e5f279da8c98310e2713f4d8cd38d64207691998fb3a82ac81b6816ad.jpg) +Figure 1. The attention map of the class token used in DINO [6] (a) and the map of the inverse degrees used in LOST [45] (b) are noisy for foreground / background separation. Our proposed method provides a clean attention map that can be used to segment salient objects (c). Considering the attention map associated to different patches highlight different regions of the object (d), it is reasonable to build a graph computing attention maps from multiple patches. + +mance of current state-of-the-art object detectors is limited by the high cost of annotating sufficient training data [33] for supervised learning. This limitation becomes even more apparent when using transfer learning to adapt a pre-trained object detector to a new application domain. Approaches such as active learning [1], semi-supervised learning [34], and weakly-supervised learning [39] have attempted to overcome this barrier by providing more efficient learning, but with only limited success. + +In this work, we focus on object discovery in natural images with no human annotations. This is an important + +problem and a critical step for many downstream applications [56]. Poor object discovery can lead to poor overall system performance. Current approaches for this problem adopt some forms of bounding box proposal mechanism [11, 55, 56, 61] and formulate object discovery as an optimization problem. However, this approach can be computationally expensive [55] as each pair of bounding box proposals across different images needs to be compared, and the optimization may fail to scale to larger datasets due to the quadratic computation overhead [57]. + +Transformers have recently been shown to outperform convolutional neural networks for visual recognition. Vision Transformers, such as ViT [18] accept image patches as input tokens and use stacked layers of encoders with self-attention to map tokens to image-level class labels. Recent results with DINO [6] have shown that when trained with self-distillation loss [25], the attention maps associated to the class token from the last layer indicate salient foreground regions. However, as illustrated in Fig. 1a, such attention maps are noisy and it is not clear that they can be used for unsupervised object discovery. + +With LOST [45], the authors propose construction of a graph and use the inverse degrees of nodes to segment objects. A heuristic seed expansion strategy is used to overcome noise (Fig. 1b) and detect a single bounding box for a foreground object. The attention maps associated with different nodes often contain meaningful information, as illustrated in Fig. 1d. We have investigated whether it is possible to use the information in the entire graph by projecting the graph into a low dimensional subspace using eigendecomposition. We have discovered that such a projection can be used with Normalized Cut [43] (Ncut) to significantly improve foreground / background segmentation (Fig. 1c). + +In this paper, we propose TokenCut, a simple but effective graph-based approach for unsupervised object discovery. We build on the self-supervised vision transformer trained with DINO [6] as our backbone feature encoder and locate objects with the resulting features. Instead of using only the class token, we use all token features. We construct an undirected graph based on the token features in the last self-attention layer, where the visual tokens are viewed as graph nodes with edges representing a connectivity score based on similarity of the features. We then use a normalized graph-cut to group self-similar regions and delimit the foreground objects. We solve the graph-cut problem using spectral clustering with generalized eigendecomposition and show that the second smallest eigenvector provides a cutting solution indicating the likelihood that a token belongs to a foreground object. Our approach can be considered as a run-time adaptation, which means that the model is able to adapt to each specific test image despite the shared training model. + +Despite its simplicity, our approach significantly im + +proves unsupervised object discovery. The method achieves $68.8\%$ , $72.1\%$ and $58.8\%$ on VOC07 [19], VOC12 [20], COCO20K [33] respectively, thus outperforming LOST [45] by a margin of $6.9\%$ , $8.1\%$ and $8.1\%$ respectively. TokenCut with second stage CAD further improves the performance to $71.4\%$ , $75.3\%$ and $62.6\%$ on VOC07, VOC12, COCO20k respectively, which outperforms LOST + CAD by $5.7\%$ , $4.9\%$ and $5.1\%$ respectively. + +In addition, we show that TokenCut can be easily extended to weakly supervised object detection and unsupervised saliency detection. For weakly supervised object detection, the goal is to detect objects using only image-level annotations. We freeze the encoder and fine-tune a linear classifier with weakly-supervised image labels. We then apply TokenCut on the features extracted from the fine-tuned encoder. Our approach produces clearly improved results on the CUB dataset [59] and competitive performance on ImageNet-1K [14]. For unsupervised saliency detection, we use the foreground region discovered by the proposed approach and apply Bilateral Solver [5] as a post-processing step to refine edges of the foreground region. In terms of results, our approach significantly improves previous state-of-the-art methods on ECSSD [44], DUTS [60] and DUTOMRON [66]. + +In summary, our main contributions are as follows: + +- We propose a simple and effective method to discover objects in images without supervision based on the self-supervised vision transformers. This method significantly outperforms previous state-of-the-art methods for unsupervised object discovery when tested on multiple datasets; +- We extend the proposed method to weakly-supervised object detection and show that the simple approach can achieve competitive performance; +- We also show that this method can be used for unsupervised saliency detection. The results demonstrate that TokenCut significantly improves the previous state-of-the-art performance on multiple datasets. + +# 2. Related Work + +Self-supervised vision transformers. ViT [18] has shown that a transformer architecture [53] can be used as an effective encoder for images and provide useful features for supervised vision tasks. MoCo-v3 [8] demonstrated that ViT can provide self-supervised representation learning and achieve strong results using contrastive learning. Recently, DINO [6] proposed to train transformers with self-distillation loss [25], showing that ViT contains explicit information that can be used for semantic segmentation of an image. Inspired by BERT [16], [32] proposed MST, which dynamically masks some tokens and learns to recover missing tokens using a global image decoder. Also motivated by + +![](images/e795016cf7c46d64a8362c1a7e1e040fd91e653d9488049d394130f2ccdfe04c.jpg) +Figure 2. An overview of the TokenCut approach. We construct a graph where the nodes are tokens and the edges are similarities between the tokens using transformer features. The foreground and background segmentation can be solved by Ncut [43]. Performing bi-partition on the second smallest eigenvector allows to detect foreground object. + +BERT [16], BEIT [4] first tokenizes the original image into visual tokens then randomly mask some tokens and learn to recover them using a transformer. Recently, MAE [23] masks a high proportion of images and reconstructs the missing pixels with an asymmetric encoder-decoder. + +Unsupervised object discovery. Given a group of images, unsupervised object discovery seeks to discover and delimit similar objects that appear in multiple images. Some methods [9, 26, 28, 29, 54] are designed to segment common repeated objects in an image collection, but rely on strong assumptions about the frequency of appearance of an object. Other approaches [11, 50, 55, 56] use bounding box proposals and formulate the object discovery as an optimization problem. [57] proposed a novel formulation of unsupervised object discovery as a ranking problem and showed that discovery could be scaled to datasets with more than 10K images. Recently, LOST [45] significantly improved over state-of-the-art for unsupervised object discovery. LOST extracts features using a self-supervised transformer based on DINO [6] and designs a heuristic seed expansion strategy to obtain a single object region. Our work is closely related to LOST [45], as we also use self-supervised transformer features. However, rather than relying on the attention map of some specific nodes, we propose a graph-based method that employs the attention scores of all the nodes and can be used with Ncut [43] to obtain a more precise segmentation of the image object. + +Weakly supervised object detection. Weakly supervised object detection [22, 67, 68, 71] can be used to locate image objects using only image-level annotation. Early approaches [7, 41, 76] mainly relied on a Class Activation Map (CAM) which is introduced in [76] to generate class-specific localization maps and find discriminant regions. Several methods [12, 13, 36, 46, 68, 74] have been proposed to improve CAM by erasing the discriminant regions and forcing the networks to capture additional object regions. Data augmentation techniques such as Cutout [17] and CutMix [69] have been shown to provide improvement for both classification and localization performance. Some methods + +achieve both classification and localization using two separate networks [22, 35, 70]. [70] trained the localization network using pseudo bounding boxes generated by [61]. [70] first learns a classifier, then freeze its weights and train another detector. [22] learns a regressor and a classifier using the consistency of CAM between two transformations. Unlike these approaches, which are specifically designed for weakly supervised object detection, we propose an unified solution to both unsupervised object discovery and weakly supervised object detection based on transformer. + +Unsupervised saliency detection. Unsupervised saliency detection seeks to segment a salient objects within an image. Earlier work on this problem [27, 31, 65, 77] used classical techniques such as color contrast [10], certain background priors [62], or super-pixels [31, 66]. More recently, unsupervised deep models [37, 60, 72] have incorporated heuristic saliency methods as pseudo ground truth to train deep CNN models. However, these methods rely on a CNN model pretrained with supervised training. [58] has proposed an unsupervised Large-Scale GAN that does not make use of labels during training. In the following, we show that incorporating a simple post-processing step into our unsupervised object discovery can provide a strong baseline method for unsupervised saliency detection. + +# 3. Approach: TokenCut + +The TokenCut algorithm can be used to predict bounding boxes that locate a salient object in an image. Our approach, illustrated in Fig. 2, is based on a graph where the nodes are tokens and the edges are similarities between the tokens using features based on the latent variables of the transformer. In the following, we first briefly present vision transformers in Section 3.1.1 and Normalized Cut in Section 3.1.2. We then introduce our solution and the implementation details in Section 3.2. + +# 3.1. Background + +# 3.1.1 Vision Transformers + +Given an image of size $H \times W$ , vision transformers (ViT) [18] take non-overlapping 2D image patches of res + +olutions $K \times K$ as inputs, with the number of patches $N = HW / K^2$ . Each patch is represented as a token, described by a vector of numerical features, referred to as an embedding. An extra learnable token, denoted as a class token $CLS$ , is used to represent the aggregated information of the entire set of patches. This $CLS$ token and the set of patch tokens are fed to a standard transformer network with a "pre-norm" layer normalization [2]. + +The vision transformer is composed of a multiple layers of encoders, each with feed-forward networks and multiple attention heads for self-attention, paralleled with skip connections. For the unsupervised object discovery task, we use a vision transformer trained with self-supervised learning using DINO [6] and extract latent variables from the final layer as the input features for our proposed method. + +# 3.1.2 Normalized Cut (Ncut) + +Graph partitioning. Ncut [43] can be used to partition a graph into two disjoint sets A and B. The method partitions the graph so as to minimizing the Ncut energy [43]: + +$$ +N c u t (A, B) = \frac {C (A , B)}{C (A , \mathcal {V})} + \frac {C (A , B)}{C (B , \mathcal {V})} \tag {1} +$$ + +where $C$ measures the degree of similarity between two sets. $C(A,B) = \sum_{v_i\in A,v_j\in B}\mathcal{E}_{i,j}$ and $C(A,\mathcal{V})$ is the total connection from nodes in A to all nodes in the graph. + +As shown by Shi and Malik [43], the optimization problem in Eqn 1 is equivalent to: + +$$ +\operatorname {m i n} _ {\mathbf {x}} N \operatorname {c u t} (\mathbf {x}) = \operatorname {m i n} _ {\mathbf {y}} \frac {\mathbf {y} ^ {T} (\mathcal {D} - \mathcal {E}) \mathbf {y}}{\mathbf {y} ^ {T} \mathcal {D} \mathbf {y}}. \tag {2} +$$ + +With the condition $\mathbf{y} \in \{1, -b\}^N$ , $\mathbf{b}$ satisfies $\mathbf{y}^T \mathcal{D} \mathbf{1} = 0$ . $\mathcal{D}$ is a diagonal matrix with $\mathbf{d}_i = \sum_j \mathcal{E}_{i,j}$ on its diagonal. + +Ncut solution with the relaxed constraint. Taking $\mathbf{z} = \mathcal{D}^{\frac{1}{2}}\mathbf{y}$ . Eqn 2 can be rewrite as: + +$$ +\min _ {\mathbf {z}} \frac {\mathbf {z} ^ {T} \mathcal {D} ^ {- \frac {1}{2}} (\mathcal {D} - \mathcal {E}) \mathcal {D} ^ {- \frac {1}{2}} \mathbf {z}}{\mathbf {z} ^ {T} \mathbf {z}}. \tag {3} +$$ + +Indicating in [43], the formulation in Eqn 3 is equivalent to the Rayleigh quotient [52], which is equivalent to solve $\mathcal{D}^{-\frac{1}{2}}(\mathcal{D} - \mathcal{E})\mathcal{D}^{-\frac{1}{2}}\mathbf{z} = \lambda \mathbf{z}$ , where $\mathcal{D} - \mathcal{E}$ is the Laplacian matrix and known to be positive semidefinite [38]. Therefore $\mathbf{z}_0 = \mathcal{D}^{\frac{1}{2}}\mathbf{1}$ is an eigenvector associated to the smallest eigenvalue $\lambda = 0$ . According to Rayleigh quotient [52], the second smallest eigenvector $\mathbf{z}_1$ is perpendicular to the smallest one $(\mathbf{z}_0)$ and can be used to minimize the energy in Eqn 3, + +$$ +\mathbf {z} _ {1} = a r g m i n _ {\mathbf {z} ^ {T} \mathbf {z} _ {0}} \frac {\mathbf {z} ^ {T} \mathcal {D} ^ {- \frac {1}{2}} (\mathcal {D} - \mathcal {E}) \mathcal {D} ^ {- \frac {1}{2}} \mathbf {z}}{\mathbf {z} ^ {T} \mathbf {z}}. +$$ + +Taking $\mathbf{z} = \mathcal{D}^{\frac{1}{2}}\mathbf{y}$ + +$$ +\mathbf {y} _ {1} = \operatorname {a r g m i n} _ {\mathbf {y} ^ {T} \mathcal {D} \mathbf {1} = 0} \frac {\mathbf {y} ^ {T} (\mathcal {D} - \mathcal {E}) \mathbf {y}}{\mathbf {y} ^ {T} \mathcal {D} \mathbf {y}}. +$$ + +Thus, the second smallest eigenvector of the generalized eigensystem $(\mathcal{D} - \mathcal{E})\mathbf{y} = \lambda \mathcal{D}\mathbf{y}$ is the real valued solution to the Ncut [43] problem. + +# 3.2. TokenCut Algorithm + +Graph construction. Our method uses the vision transformers as described in Section 3.1.1 to produce a vector of features for each $K \times K$ image patch. A fully connected undirected graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ of patches is constructed where each $\mathcal{V}$ represents a patch with a feature vector $\{v_i\}_{i=1}^N$ , and each patch is linked to adjacent patches by labeled edges, $\mathcal{E}$ . Edge labels represent a similarity score $S$ based on the cosine similarity of the feature vectors of the two patches. + +$$ +\mathcal {E} _ {i, j} = \left\{ \begin{array}{l l} 1, & \text {i f} S \left(v _ {i}, v _ {j}\right) \geq \tau \\ \epsilon , & \text {e l s e} \end{array} , \right. \tag {4} +$$ + +where $\tau$ is a hyper-parameter and $\epsilon$ equals a small value $1e - 5$ to assure that the graph is fully connected and $S$ is the cosine similarity between features. Note that the spatial information has been implicitly included in the features via positional encoding in transformer. + +$$ +S \left(v _ {i}, v _ {j}\right) = \frac {v _ {i} v _ {j}}{\left\| v _ {i} \right\| _ {2} \left\| v _ {j} \right\| _ {2}}. \tag {5} +$$ + +We apply Ncut algorithm, as described in Section 3.1.2, on constructed graph $\mathcal{G}$ and obtain the second smallest eigenvector of the generalized eigensystem, which can be seen as an attention map of the potential objects. We provide visualization of this attention map in Section 4. + +Discovering Salient Object with TokenCut. We assume that there is at least one object in the image and the object occupies the foreground region. To successfully segment the foreground objects from the image, we must solve three problems: i) We must determine a means to partition the graph into two subgraphs and ii) given a bi-partition of the graph, we must determine which partition represents the foreground. iii) In case of detecting multiple connected components in the foreground, we must identify the most salient object. + +For the first problem, in our initial experiments we have used a simple average value of the projection onto the second smallest eigenvector to determine the similarity value for cutting the graph $\overline{\mathbf{y}_1} = \frac{1}{N}\sum_i\mathbf{y}_1^i$ . Formally, $A = \{v_{i}|\mathbf{y}_{1}^{i}\leq \overline{\mathbf{y}_{1}}\}$ and $B = \{v_{i}|\mathbf{y}_{1}^{i} > \overline{\mathbf{y}_{1}}\}$ . We have compared this to using the classical clustering algorithms of K-means + +![](images/efaae3d6f549463a85d9ac383cdc7622bbc4b22d7f74dccfcf3b9f096ace5810.jpg) + +![](images/24f2309ac89f9055f3af1125ae65106a026d863c7f0ad2e5f9806ab26ee12f9f.jpg) + +![](images/debcf6175fa7b2c033a07d523de2f80bfc61df24d23c6bbe08f0c9ff3858aadd.jpg) + +![](images/a1c2f53e317600933bc150a96321346cfea65852f3e8b92a1d91c0d5cbba075f.jpg) + +![](images/eee0222241fdca4c87aa371a970c7902b6f0f682840e2e307214dae1ed9a7960.jpg) + +![](images/75142a050af5f7c993a7ffd5d238860b13f3dab50e1573e9642eba79a2e34d83.jpg) + +![](images/5c7b5e7957b4b0a84dca3716fc909c1229675b831a06eaa62007d574f2e7d264.jpg) + +![](images/b53d02f99e12443d14e3090a7062d511837cdefa9beedffe25ef5fcb59d98c37.jpg) + +![](images/6714f5cd9e4025f72af0bf20ea9df377ceaf0b3e8a57859bf89d663e0837d7eb.jpg) + +![](images/89751d89af85de0eae09400eb5181fdce79adff3d23f813f4d220bf445daf02a.jpg) + +![](images/b6f76439fed56182d6aff7808fc89c1746d9635b7082bd0dba08a4353adca27d.jpg) + +![](images/341afa840a71970b86fb95feb72de5cc5f6874a1216e7a310b954c132239ff95.jpg) + +![](images/7e97c5f03928a6e6a1d3cef9ecd346990182fb761a8309c9e6cce1ac229c8144.jpg) + +![](images/8a280ece06deeb43a6974955b909df5f8db24620cc0e4a95b615329f359a3224.jpg) + +![](images/43e9e920045f29ec6d0ede71756cb1465acf935992893fb4acc449ae8d0d31a5.jpg) + +![](images/ed3f60cf5eab77c0043012a55770cd59b2a2f5e1ee2c4935c9d651f5ec9edf51.jpg) + +![](images/9286838d2f19f09b544dcb84199b810740e903c1d398496030303081fad0ffb6.jpg) +(a) DINO CLS +Token Attention +Figure 3. Visual results of unsupervised single object discovery on VOC12. In (a), we show the attention of the CLS token in DINO [6] which is used for detection (b). LOST [45] is mainly relied on the map of inverse degrees (c) to perform detection (d). For our approach, we illustrate the eigenvector in (e) and our detection in (f). Blue and Red bounding boxes indicate the ground-truth and the predicted bounding boxes respectively. + +![](images/d453e8faae552c35f328a340f25a7973b17b4dc92bdfce58d6ac9dc43e546711.jpg) +(b) DINO +Detection + +![](images/56916dfbe0b7c415746b8b77fcfef1b2fd1a6426e05b2106add9a53808954500.jpg) +(c) LOST Inverse +Degree Attention + +![](images/ade7cc92b1dac445ea351f7a7404e82a91a619a5d7118fb569e2ee6e3edf0e4a.jpg) +(d) LOST +Detection + +![](images/df3a206a8eea7fceb147c1eb2adffa3d3637360f7dcd736b68ae9185784ebf9a.jpg) +(e) Our Eigen +Attention + +![](images/002d3d9277000e77a2a5c18d3d64763a4ca236170c279953c7b0d2967b067db1.jpg) +(f) Our +Detection + +and EM to cluster the second smallest eigen vector into 2 partitions. The comparison is available in the supplementary material, indicating that the mean generally provides better results. + +For the second problem, the foreground contains the salient object and is assumed to be less connected to the entire graph. Intuitively, $\mathbf{d}_i < \mathbf{d}_j$ if $v_{i}$ belongs to the foreground while $v_{j}$ is the background token. Therefore, the eigenvector of the foreground object should have a larger absolute value than the one of the background. We use the maximum absolute value $v_{max}$ to select the foreground partition and the most salient object. The partition that contains $v_{max}$ is taken as foreground. As our graph has no explicit spatial constraint, the foreground might contain more than one connected regions. We simply select the largest connected component existing in the foreground containing the maximum absolute value $v_{max}$ as our final object region. + +In summary, the TokenCut algorithm consists of the following steps: + +1. Given an image, build a graph $\mathcal{G} = (\mathcal{V},\mathcal{E})$ according to Equation 4 and 5. +2. Solve the generalized eigensystem $(\mathcal{D} - \mathcal{E})\mathbf{y} = \lambda \mathcal{D}\mathbf{y}$ + +for the eigenvector associated to the second smallest eigenvalue $\mathbf{y}_1$ . + +3. Compute bi-partition using the average over $\mathbf{y}_1$ : $\overline{\mathbf{y}_1} = \sum_i \frac{\mathbf{y}_1^i}{N}$ . $A = \{v_i | \mathbf{y}_1^i \leq \overline{\mathbf{y}_1}\}$ and $B = \{v_i | \mathbf{y}_1^i > \overline{\mathbf{y}_1}\}$ +4. Find the largest connected component associated to the maximum absolute value of $\mathbf{y}_1$ . + +Implementation details. For our experiments, we use the ViT-S/16 model [18] trained with self-distillation loss (DINO) [6] to extract features of patches. We employ the keys features of the last layer as the input features $v$ . Ablations on different features as well as transformers trained with self-supervised learning are provided in the supplementary material. We set $\tau = 0.2$ for all datasets, the dependency on $\tau$ is provided in Section 4.4. In terms of running time, our un-optimised implementation takes approximately 0.32 seconds to detect a bounding box of a single image with resolution $480 \times 480$ on a single GPU QUADRO RTX 8000. + +Table 1. Comparisons for unsupervised single object discovery. We compare TokenCut to state-of-the-art object discovery methods on VOC07 [19], VOC12 [20] and COCO20K [33, 56] datasets. Model performances are evaluated with CorLoc metric. "Inter-image Simi." means the model leverages information from the entire dataset and explores inter-image similarities to localize objects. + +
MethodInter-image Simi.DINO [6] Feat.VOC07 [19]VOC12 [20]COCO20K [33, 56]
Selective Search [45, 51]X-18.820.916.0
EdgeBoxes [45, 78]X-31.131.628.8
Kim et al. [30, 45]✓-43.946.435.1
Zhang et al. [45, 73]✓-46.250.534.8
DDT+ [45, 61]✓-50.253.138.2
rOSD [45, 56]✓-54.555.348.5
LOD [45, 57]✓-53.655.148.5
DINO-seg [6, 45]XViT-S/16 [18]45.846.242.1
LOST [45]XViT-S/16 [18]61.964.050.7
TokenCutXViT-S/16 [18]68.8 (↑ 6.9)72.1 (↑ 8.1)58.8 (↑ 8.1)
LOD + CAD* [45]✓-56.361.652.7
rOSD + CAD* [45]✓-58.362.353.0
LOST + CAD* [45]XViT-S/16 [18]65.770.457.5
TokenCut + CAD* [45]XViT-S/16 [18]71.4 (↑ 5.7)75.3 (↑ 4.9)62.6 (↑ 5.1)
+ +* +CAD indicates to train a second stage class-agnostic detector with "pseudo-boxes" labels. + +# 4. Experiments + +We evaluate our approach on three tasks: unsupervised single object discovery, weakly supervised object detection and unsupervised saliency detection. We present results of unsupervised single object discovery in Section 4.1. The results of weakly supervised object detection are in Section 4.2. The results of unsupervised saliency detection in Section 4.3. We provide analysis of $\tau$ in Section 4.4, other ablation studies will be presented in supplementary material. + +# 4.1. Unsupervised Single Object Discovery + +Evaluation metric. We report performance using the CorLoc metric for precise localisation, as used by [11, 15, 47, 55, 56, 57, 61]. CorLoc counts a predicted bounding box as correct if the intersection over union (IoU) score between the predicted bounding box and one of the ground truth bounding boxes is superior to 0.5. + +Quantitative Results. We evaluate our approach on three commonly used benchmarks for unsupervised single object discovery: VOC07 [19], VOC12 [20] and COCO20K [33, 56]. The qualitative results are provided in Tab. 1. We evaluate the CorLoc scores in comparison with previous state-of-the-art single object discovery methods [30, 45, 51, 56, 57, 61, 73, 78] on VOC07, VOC12, and COCO20K datasets. These methods can be roughly divided into two groups based on whether the model leverages information from the entire dataset and explores inter-image similarities or not. Because of quadratic complexity of region comparison among images, models with inter-image similarities are generally difficult to scale to larger datasets. The selective search [51], edge boxes [78], LOST [45] and TokenCut do not require inter-image similarities and are thus much more efficient. As shown in the table, TokenCut consistently outperforms all previous methods on all datasets by a large margin. Specifically, TokenCut improves the state- + +of-the-art by $6.9\%$ , $8.1\%$ and $8.1\%$ in VOC07, VOC12 and COCO20K respectively using the same ViT-S/16 features. + +We also list a set of results that including a second stage unsupervised training strategy to boost the performance. This is referred to as class-agnostic detection (CAD). A CAD is trained by assigning the same "foreground" category to all the boxes produced by the first stage single object discovery model. As shown in Tab. 1, TokenCut + CAD outperforms the state-of-the-art by $5.7\%$ , $4.9\%$ and $5.1\%$ on VOC07, VOC12 and COCO20k respectively. + +Qualitative Results. In Fig. 3, we provide visualization for DINO-seg [6], LOST [45] and Tokencut. For each method, we visualize the heatmap that is used to perform object detection. For DINO-seg, the heatmap is the attention map associated to the CLS token. For LOST, the detection is mainly based on the map of inverse degree $\left(\frac{1}{\mathrm{d}_i}\right)$ . For TokenCut, we display the second smallest eigenvector. The visual result demonstrates that Tokencut can extract a high quality segmentation of the salient object. Comparing with DINO-seg and LOST, TokenCut is able to extract a more complete segmentation as can be seen in the first and the third samples in Fig. 3. In some other cases, when all the methods have a high quality map, TokenCut has the strongest intensity on the object, this phenomenon can be viewed in the last sample in Fig. 3. More visual results can be found in the supplementary material. + +# 4.2. Weakly Supervised Object Localization + +Evaluation metrics. We report three standard metrics: Top-1 Cls, GT Loc and Top-1 Loc. Top-1 Cls represents the top-1 accuracy of image classification. GT Loc is similar to CorLoc in which a predicted box is counted as correct if the IoU score is superior to 0.5 between the predicted bounding box and one of the ground-truth bounding boxes. Top-1 Loc is the most important metric as it considers measuring both the classification and the detection: a predicted bounding box is counted as a true positive if the class of the image is + +Table 2. Comparisons for weakly supervised object localization. We report Top-1 Cls, GT Loc and Top-1 Loc on CUB [59] and ImageNet-1K [14] datasets. Compared state-of-the-art methods are divided into two groups: with ImageNet-1K supervised pretraining and with ImageNet-1K self-supervised pretraining. + +
Pretrained DatasetMethodBackboneCUB [59], Acc. (%)ImageNet-1K [14], Acc. (%)
Top-1 ClsGT LocTop-1 LocTop-1 ClsGT LocTop-1 Loc
ImageNet-1K [14] supervised pretrainCAM [76]GoogLeNet [48]73.8-41.165-43.6
HaS-32 [46] + [3]GoogLeNet [48]75.461.147.468.960.644.6
ADL [13] + [3]ResNet50 [24]75.077.659.575.862.249.4
ADL [13]InceptionV3 [49]74.6-53.072.8-48.7
I2C [75]InceptionV3 [49]-72.65673.368.553.1
PSOL [70]‡InceptionV3 [49]--65.5-65.254.8
SLT-Net [22]*InceptionV3 [49]76.486.566.178.167.655.7
ImageNet-1K [14] self-supervised pretrainLOST [45]ViT-S/16 [18]79.589.771.377.060.049
TokenCutViT-S/16 [18]79.591.8 (↑ 2.1)72.9 (↑ 1.6)77.065.4 (↑ 5.4)52.3 (↑ 3.3)
+ +$\star$ uses ten crop augmentations to get final classification results. $\star$ and $\ddagger$ learn a classifier and a detector separately. + +Table 3. Comparisons for unsupervised saliency detection We compare TokenCut to state-of-the-art unsupervised saliency detection methods on ECSSD [44], DUTS [60] and DUT-OMRON [66]. TokenCut achieves better results comparing with other competitive approaches. + +
MethodECSSD [44]DUTS [60]DUT-OMRON [66]
maxFβ(%)IoU(%)Acc.(%)maxFβ(%)IoU(%)Acc.(%)maxFβ(%)IoU(%)Acc.(%)
HS [65]67.350.884.750.436.982.656.143.384.3
wCtr [77]68.451.786.252.239.283.554.141.683.8
WSC [31]68.349.885.252.838.486.252.338.786.5
DeepUSPS [37]58.444.079.542.530.577.341.430.577.9
BigBiGAN [58]78.267.289.960.849.887.854.945.385.6
E-BigBiGAN [58]79.768.490.662.451.188.256.346.486.0
LOST [42, 45]75.865.489.561.151.887.147.341.079.7
LOST [42, 45]+Bilateral Solver [5]83.772.391.669.757.288.757.848.981.8
TokenCut80.371.291.867.257.690.360.053.388.0
TokenCut + Bilateral Solver [5]87.4 (↑ 3.7)77.2 (↑ 4.9)93.4 (↑ 1.8)75.5 (↑ 5.8)62.4 (↑ 5.2)91.4 (↑ 2.7)69.7 (↑ 11.9)61.8 (↑ 12.9)89.7 (↑ 7.9)
+ +correctly predicted and the IoU is superior to 0.5 between the predicted bounding box and the ground-truth bounding box. + +Results. We use two datasets to evaluate model performances on weakly supervised object localization: CUB-200-2011 [59] (CUB) and ImageNet-1k [40]. The fine-tuning details can be found in supplementary material. In Tab. 2, we compare TokenCut to the state-of-the-art weakly-supervised object localization approaches on CUB and ImageNet-1K datasets. The methods can be divided into two groups: models initialized with ImageNet-1K supervised pre-training [3, 13, 22, 46, 70, 75, 76] and models initialized with ImageNet-1K self-supervised pre-training [45]. + +On the CUB dataset, TokenCut achieves the best performance over all methods, and outperforms the state-of-the-art LOST method by $2.1\%$ and $1.6\%$ on GT Loc and Top-1 Loc. Interestingly, all the ImageNet-1K self-supervised pretraining models are better than the supervised pretrained models. We believe that this is because supervised pretraining learns a more discriminative representation of the pretrained dataset than self-supervised pretraining, leading to a reduction in transferability to downstream datasets such as CUB. In comparison, self-supervised pretraining can learn a more general representation and thus provides better transferability. + +On the ImageNet-1K dataset, TokenCut outperforms LOST by $5.4\%$ and $4.4\%$ on GT Loc and Top-1 Loc, and achieves a comparable performance with the ImageNet-1K supervised pretrain model. If the downstream task + +is ImageNet-1K, then the supervised pretraining with ImageNet-1K can provide discriminative features that improve the localization task as they are tuned to the dataset. + +Table 4. Analysis of $\tau$ . We report CorLoc for unsupervised single object discovery on VOC07, VOC12, COCO20K, and Top-1 Loc for weakly supervised object detection on CUB and ImageNet-1K. + +
τCorLocTop-1 Loc
VOC07VOC12COCO20KCUBImageNet-1K
067.471.356.173.053.8
0.168.672.158.273.253.4
0.268.872.158.872.952.3
0.367.772.158.270.850.4
+ +# 4.3. Unsupervised Saliency detection + +Evaluation Metrics We report three standard metrics: F-measure, IoU and Accuracy. $F$ -measure is a standard measure in saliency detection. It is computed as $F_{\beta} = \frac{(1 + \beta^{2})Precision \times Recall}{\beta^{2}Precision + Recall}$ , where the Precision and Recall are defined based on the binarized predicted mask and ground truth mask. The max $F_{\beta}$ is the maximum value of 255 uniformly distributed binarization thresholds. Following previous works [42, 58], we set $\beta = 0.3$ for consistency. IoU(Intersection over Union) score is computed based on the binary predicted mask and the ground-truth, the threshold is set to 0.5. Accuracy measures the proportion of pixels that have been correctly assigned to the object/background. The binarization threshold is set to 0.5 for masks. + +![](images/deb4bcdf33b8066472d0cd1269d3f33972cc7cb08e94412751303ff57c6d52d1.jpg) +(a) Input + +![](images/20ff5fbcc1b306f7685043533fefbfd432503b726107c186c7d5dd6f6fc40ced.jpg) +(b) Ours + +![](images/3ddb02ada10d566081f67663e0a9766f03d53be59c5e97e859f240b07d9e5d8b.jpg) +(c) Ours + BS + +![](images/0effe1f15cbea6c0945e3c67972e9c98b330a755750bc41453620291558386e6.jpg) +(d) GT + +![](images/f57bdba8d63131a43dbdea4a462587d2efcc67f9013f8f6e4c610380d16f1d5c.jpg) +Figure 4. Visual results of unsupervised segments on ECSSD [44]. In (a), we show the input image. TokenCut detection result is presented in (b). TokenCut + Bilateral Solver results is shown in (c). (d) is the ground truth. + +![](images/bba3edfd221c59e5138e71af50ddc617a7415070342144704328db5a37567bd2.jpg) +(a) Input +Figure 5. Visual results of images taken from the Internet. We show the input images, our eigen attention and final detection in (a) (b) (c) respectively. + +![](images/4bf266616d76e7fe61d215086e5998687ebd5074b62c49f3efc84f8c6f97e19f.jpg) + +![](images/92ac7ea36989920f37f2368530fe1bc955d83c7767a119f0f8116f941fd3b1f9.jpg) +(b) Eigen Attention + +![](images/59d956dabd34f4b67d91318fbe8175119115710b3eb297c4df96ca3fccd76db1.jpg) +Figure 6. Failure cases on VOC12 (1st and 2nd row) and COCO (3rd row). LOST [45] mainly relies on the map of inverse degrees (a) to perform detection (b). For our approach, we illustrate the eigenvector in (c) and our detection in (d). Blue and Red bounding boxes indicate the ground-truth and the predicted bounding boxes respectively. + +![](images/a7f8395678533d4648676b94ea847e21dc4de2fc5949091795a085362b9c3304.jpg) +(c) Detection + +Results We further evaluate TokenCut on three commonly datasets for unsupervised saliency detection: ECSSD [44], DUTS [60] and DUT-OMRON [66]. The qualitative results are in Tab. 3. TokenCut significantly outperforms previous state-of-the-art. Adding Bilateral Solver [5] refines the boundary of an object and further boosts the performance over TokenCut, which can also be seen from the visual results presented in Fig. 4. + +# 4.4. Analysis and Discussion + +Analysis of $\tau$ . In Tab. 4, we provide an analysis on $\tau$ defined in Equation 4. The results indicate that the effects of variations in $\tau$ value are not significant and that a suitable threshold is $\tau = 0.2$ . + +Internet Images We further test TokenCut on Internet images. The results are in Figure 5. We can see even the inputs images are with noisy background, our algorithm can still provide precise attention map cover the object leading to accurate bounding box prediction, which demonstrates again the robustness of our approach. + +![](images/71d79aa8afc3e35f1b3de4e6074deac5bb1d6c0f868b4ac59cad3e13eb94ebdb.jpg) + +![](images/75a61fbfde0dd65f14e39c285871eb44b9ad73aa57cfbda7b61ed5536e6df65c.jpg) + +![](images/e237bc4cf8d71ea489a1fbd1c59d3060fc789a3856cd3531905b6fffc4500042.jpg) + +![](images/286c134eef2e79e95b2dc919b3fa9c25a40d363f510f319fec6914a249601077.jpg) + +![](images/32c8de510242336b7466426a0d2240f0f31dafe00108f145709930d5fb4ab66a.jpg) + +![](images/6bd535ed56c859775375c3f3084ebadd904bf6dd6869535bd0a343d6d9dd268e.jpg) + +![](images/9d11083c26969e3b28355f58e40cd24016c45daacea7c4aecdbe6db1a595d1ac.jpg) + +![](images/57bf6094445d550f17dc8716f0a1a4710ad1cf005b571efa2288101d7afb0691.jpg) + +![](images/b0044ddf64b078b2f5c087e7eacb32728c0cd757c610eb3f22c8d34965b0466f.jpg) +(a) LOST + +![](images/cfb86541035f2416290fc8857a6cdb400cb15dd3c716a04274574046a6fd5645.jpg) +(b) LOST +Inverse Attn. +Detection + +![](images/45ff8f5aca562e88541fc3890264e9ee90d481f7c7abd54d0c8762daefdd0e21.jpg) +(c) Our Eigen +Attention + +![](images/66693f0a30af5216da3e0a759cd3b9bdfd0c8cb1357a00020ad5432c0db1ba19.jpg) +(d) Our +Detection + +Limitations Despite the good performance of TokenCut, it has several limitations. Examples of failure cases are shown in Fig. 6: i) TokenCut focuses on the largest salient part in the image, which may not be the desired object (Fig. 6, 1st row). ii) Similar to LOST [45], TokenCut assumes that a single salient object occupies the foreground. If multiple overlapping objects are present in an image, both LOST and our approach will fail to detect one of the objects (Fig. 6, 2nd row). iii) Neither LOST nor our approach can handle occlusion (Fig. 6, 3rd row). + +# 5. Conclusion + +We have introduced TokenCut, a simple but effective approach for unsupervised object discovery. TokenCut uses self-supervised learning with transformers to constructs a graph where nodes are patches and edges represent similarities between patches. We showed that salient objects can be directly detected and delimited using Ncut. We evaluated this approach on unsupervised single object discovery, weakly supervised object detection and unsupervised saliency detection, and showed that it provides a significant improvement over previous approaches. Our results indicate that self-supervised transformers can provide a rich and general set of features that may likely be used for a variety of computer vision problems. + +Acknowledgements This work has been partially supported by the MIAI Multidisciplinary AI Institute at the Univ. Grenoble Alpes (MIAI@Grenoble Alpes - ANR-19-P3IA-0003), and by the EU H2020 ICT48 project Humane AI Net under contract EU #952026. + +# References + +[1] Hamed H Aghdam, Abel Gonzalez-Garcia, Joost van de Weijer, and Antonio M López. Active learning for deep detection neural networks. In ICCV, 2019. 1 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv, 2016. 4 +[3] Wonho Bae, Junhyug Noh, and Gunhee Kim. 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Ryoo $^{1}$ + +$^{1}$ Stony Brook University $^{2}$ Mohamed bin Zayed University of AI $^{3}$ Australian National University $^{4}$ Linköping University + +kranasinghe@cs.stonybrook.edu + +# Abstract + +In this paper, we propose self-supervised training for video transformers using unlabeled video data. From a given video, we create local and global spatiotemporal views with varying spatial sizes and frame rates. Our self-supervised objective seeks to match the features of these different views representing the same video, to be invariant to spatiotemporal variations in actions. To the best of our knowledge, the proposed approach is the first to alleviate the dependency on negative samples or dedicated memory banks in Self-supervised Video Transformer (SVT). Further, owing to the flexibility of Transformer models, SVT supports slow-fast video processing within a single architecture using dynamically adjusted positional encoding and supports long-term relationship modeling along spatiotemporal dimensions. Our approach performs well on four action recognition benchmarks (Kinetics-400, UCF-101, HMDB-51, and SSv2) and converges faster with small batch sizes. Code is available at: https://git.io/J1juJ + +# 1. Introduction + +Self-supervised learning enables extraction of meaningful representations from unlabeled data, alleviating the need for expensive annotations. Recent self-supervised methods perform on-par with supervised learning for certain vision tasks [11, 12, 16, 37]. The necessity of self-supervised learning is even greater in domains such as video analysis where annotations are more expensive [40, 44, 63, 65]. + +At the same time, the emergence of vision transformers (ViTs) [26] and their successful adoption to different computer vision tasks including video understanding [4,9,29,53,67,68] within the supervised setting shows their promise in the video domain. In fact, recent works using simple ViT backbones [9] surpass convolutional neural networks (CNN) for supervised video analysis with reduced compute. Motivated by the ability of self-attention to model + +![](images/479ef67e11e25501a14c1057e82cf1a851b6abef58442a54b9173ce9edc9c404.jpg) +Figure 1. Our Self-supervised Video Transformer (SVT) learns cross-view and motion correspondences by jointly matching video clips sampled with varying field of view and temporal resolutions. Specifically, Global views (top and bottom right) with different temporal resolutions as well as Local views (bottom left) from different spatiotemporal windows are sampled. The representations of these multiple views are matched in a student-teacher framework to learn cross-view and motion correspondences (middle block). The proposed self-supervised framework can learn high-quality spatiotemporal features while converging faster. + +long-range dependencies, we propose a simple yet effective method to train video transformers [9] in a self-supervised manner. This process uses spatial and temporal context as a supervisory signal (from unlabelled videos) to learn motion, scale, and viewpoint invariant features. + +Many existing self-supervised representation learning methods on videos [64, 65, 88] use contrastive learning objectives which can require larger batch sizes, longer training regimes, careful negative mining and dedicated memory banks. Further, the contrastive objectives require careful temporal sampling [64] and multiple networks looking at similar/different clips to develop attract/repel loss formulations [65]. In contrast, we propose to learn self-supervised features from unlabelled videos via self-distillation [72] by a twin network strategy (student-teacher models) [13, 34]. + +Our proposed approach, Self-supervised Video Transformer (SVT), trains student and teacher models with a similarity objective [13] that matches the representations along spatial and temporal dimensions by space and time attention [9]. We achieve this by creating spatiotemporal positive views that differ in spatial sizes and are sampled at different time frames from a single video (Fig. 1). During training, teacher video transformer parameters are updated as an exponential moving average of the student video transformer. Both of these networks process different spatiotemporal views of the same video and our objective function is designed to predict one view from the other in the feature space. This allows SVT to learn robust features that are invariant to spatiotemporal changes in videos while generating discriminative features across videos [34]. SVT does not depend on negative mining or large batch sizes and remains computationally efficient as it converges within only a few epochs ( $\approx$ 20 on Kinetics-400 [14]). + +In addition to the above advantages, our design allows the flexibility to model varying time-resolutions and spatial scales within a unified architecture. This is a much desired feature for video processing since real-world actions can occur with varying temporal and spatial details. Remarkably, current self-supervision based video frameworks [64, 87] operate on fixed spatial and temporal scales which can pose difficulties in modeling the expressivity and dynamic nature of actions. We note that convolutional backbones used in these approaches lack the adaptability to varying temporal resolutions (due to fixed number of channels) and thus require dedicated networks for each resolution [30, 45]. To address this challenge, the proposed SVT uses dynamically adjusted positional encodings to handle varying temporal resolutions within the same architecture. Further, the self-attention mechanism in SVT can capture both local and global long-range dependencies across both space and time, offering much larger receptive fields as compared to traditional convolutional kernels [57]. + +The main contributions in this work are as follows: + +- We introduce a novel mechanism for self-supervised training of video transformers by exploiting spatiotemporal correspondences between varying fields of view (global and local) across space and time (Sec. 3.2). +- Self-supervision in SVT is performed via a joint motion and crossview correspondence learning objective. Specifically, global and local spatiotemporal views with varying frame rates and spatial characteristics (Sec. 3.2.1 Sec. 3.2.2) are matched by our motion and crossview correspondences in the latent space. +- A unique property of our architecture is that it allows slow-fast training and inference using a single video transformer. To this end, we propose to use dynamic positional encoding within SVT to handle variable frame rate inputs generated from our sampling strategy (Sec. 3.2.3). + +Our extensive experiments and results on various video datasets including Kinetics-400 [14], UCF-101 [69], HMDB-51 [49], and SSv2 [33] show state-of-the-art transfer of our self-supervised features using only RGB data. Further, our method shows a rapid convergence rate. + +# 2. Related Work + +Transformers in Vision. Since the initial success of transformers in natural language processing (NLP) tasks [21,77], they have emerged as a competitive architecture for various other domains [46]. Among vision tasks, the initial works focused on a combination of convolutional and self-attention based architectures [10,83,85,90]. A convolution free variant, vision transformer (ViT) [26], achieved competitive performance on image classification tasks. While earlier works proposing ViT [26] depended on large-scale datasets, more recent efforts achieve similar results with medium-scale datasets using various augmentation strategies [71, 76]. Later architectures also explore improving computational efficiency of ViTs focusing on transformer blocks [52, 67, 89]. ViTs have also been adopted for video classification tasks [4,9,29,67,68]. Our work builds on the TimeSformer backbone [9], a direct adaptation of standard ViTs using separate attention across dimensions. + +Self-supervised Learning in Images. Early image-based self-supervised learning work focused on pretext tasks that require useful representations to solve [24, 25, 48, 58, 61, 78, 91]. However, recently contrastive methods have dominated self-supervised learning [6, 13, 16, 17, 19, 27, 37, 38, 50, 55, 74, 75]. These approaches generally consider two views of a single sample (transformed through augmentations) and pull them (positives) together while pushing away from all other (negative) samples in representation space [6, 59]. Key drawbacks of these methods are the necessity for careful mining of positive / negative samples [75] and reliance on large numbers of negative samples (leading to large batch sizes [16] or memory banks [37]). While clustering methods improve on this using cluster targets [3, 5, 7, 11, 12, 41, 73, 88], recent regression based methods that predict alternate representations [13, 34] eliminate the need for sample mining and negative samples. In particular, Caron et al. [13] explore predicting spatially local-global correspondences with ViT backbones within the image domain, which we extend in our work to the video domain with suitable improvements. + +Self-supervised Learning in Videos. While self-supervised learning in videos were initially dominated by approaches based on pretext tasks unique to the video domain [2, 32, 43, 54, 56, 62, 70, 79-81, 84], recent work focuses more on contrastive losses similar to the image domain [22, 31, 35, 36, 64, 65]. A combination of previous pretext tasks over multiple modalities with cross-modality distillation is presented in [63]; SVT differs in how our + +![](images/fb0980388e135137dbb808e72143f4e4bb37960cc96c487c57b688e40aea825b.jpg) +Figure 2. Our spatiotemporal sampling generates global and local views from a given input video. Global views contain different frame rates and spatial characteristics controlled by sampling strategy and combinations of augmentations. Local views have varying frame rates as well as limited fields of view due to random cropping. One global view is randomly selected and passed through the teacher model to generate a target while other global and local views are passed through the student model. Network weights are then updated by matching the online student local (cross-view correspondences) and global (motion correspondences) views to the target teacher global view. We use a standard ViT backbone with separate space-time attention [9] followed by an MLP for predicting target features from online features. + +self-distillation operates within a single modality and network. The idea of varying resolution along temporal dimension is explored in [15,40]. They use contrastive losses between different videos at same resolution for speed consistency or the same video at different resolutions for appearance consistency. Unlike these works, we jointly vary spatial and temporal resolutions and use a predictive objective as self-supervision. The idea of views with limited locality is also explored in [8,20,65]. While [8] uses views of varying locality for disentangling the representation space into temporally local and global features using contrastive objectives, our approach uses view locality to learn correspondences along and across dimensions with our predictive objective. A similar predictive objective with temporal locality constrained views is used in [65] and contrastive losses with spatial local-global crops is used in [20]; however our approach focuses on spatio-temporal constraints extending correspondences across dimensions, uses a single shared network for processing alternate views, and additionally combines varying resolutions to generate our alternate views exploiting unique ViT architectural features. + +# 3. Self-supervised Video Transformer + +In this section, we discuss our Self-supervised Video Transformer (SVT) approach. Unlike contrastive methods, we process two clips from the same video with varying spatial-temporal characteristics (Sec. 3.2) avoiding the need + +for negative mining or memory banks. Our loss formulation matches the representations from both dissimilar clips to enforce invariance to motion and spatial changes for the same action sequence. A naive objective enforcing invariance would collapse all representations to be the same, however we use a teacher-student network pair where the former acts as a more stable target for the later, enabling convergence of the online student network to learn discriminative representations [34]. This approach simultaneously incorporates rich spatiotemporal context in the representations while keeping them discriminative. In the following, we first introduce the overall architecture of SVT in Sec. 3.1 followed by the self-supervised learning process in Sec. 3.2, our objective functions in Sec. 3.3 and inference in Sec. 3.4. + +# 3.1. SVT: Architecture + +We apply separate attention along temporal and spatial dimensions of input video clips using a video transformer [9]. Consider a video $\mathbf{X} = \{\pmb{x}_t\}_{t=1}^N$ , where $N$ represents the number of frames. We define a clip (also termed view interchangeably) as a subset of these $N$ frames selected through a sampling strategy. We define $H, W, T$ to be the height, width, and number of frames respectively for the sampled clip. Our sampling methodology (Fig. 2) generates two types of clips, global $(\pmb{g})$ and local $(l)$ spatiotemporal views. Both $\pmb{g}$ and $l$ are subsets of the video frame set $\mathbf{X}$ , with views $\pmb{g} = \{\pmb{x}_t'\}_{t=1}^{K_g}$ , $l = \{\pmb{x}_t''\}_{t=1}^{K_l}$ , and $|K_l| \leq |K_g|$ . + +Global views are generated by uniformly sampling a variable number of frames from a randomly selected $90\%$ portion of a video's time axis. We generate two such global spatiotemporal views $(g_{1}, g_{2})$ at low $(T = 8)$ and high $(T = 16)$ frame rates and spatial resolution $H = W = 224$ . Local views are generated by uniformly sampling frames from a randomly selected video region covering $1/8^{th}$ of the time axis and $\approx 40\%$ area along spatial axes. We generate eight such local spatiotemporal views with $T \in \{2, 4, 8, 16\}$ and spatial resolution fixed at $H = W = 96$ . Specifically, we randomly sample two global $(g_{1}, g_{2})$ and eight local $(l_{1}, \ldots, l_{8})$ spatiotemporal views. Note that both spatial and temporal dimensions within our sampled views differ from those of the original video. We introduce the channel dimension, $C$ , which is fixed at 3 for RGB inputs considered in our case. Our SVT, comprising of 12 encoder blocks, processes each sampled clip of shape $(C \times T \times W \times H)$ , where $W \leq 224$ , $H \leq 224$ and $T \leq 16$ (different for each clip). Our network architecture (Fig. 2) is designed to process such varied resolution clips during both training and inference stages within a single architecture (Sec. 3.2.3). + +During training, we divide each frame within a view into patches [26]. Thus, for a given view of maximum size $H = W = 224$ and $T = 16$ , each SVT encoder block processes a maximum of 196 spatial and 16 temporal tokens, and the embedding dimension of each token is $\mathbb{R}^{768}$ [26]. Since the maximum number of spatial and temporal tokens vary due to variable dimensions in our views, we deploy dynamic positional encoding (Sec. 3.2.3) to account for any missing tokens for views of size $W < 224$ , $H < 224$ and $T < 16$ . Note the minimum spatial and temporal sizes in our proposed views are $H = W = 96$ and $T = 2$ , respectively. In addition to these input spatial and temporal tokens, we use a single classification token as the feature vector within the architecture [21,26]. This classification token represents the common features learned by the SVT along spatial and temporal dimensions of a given video. Finally, we use a multi-layer perceptron (MLP) as a projection head over the classification token from the final encoder block [13, 34]. We define the output of our projection head as $f$ . + +As illustrated in Fig. 2, our overall approach uses a teacher-student setup inspired from [13, 34] for self-distillation [72]. Our teacher model is an exact architectural replica of the student model. + +# 3.2. SVT: Self-supervised Training + +We train SVT in a self-supervised manner by predicting the different views (video clips) with varying spatiotemporal characteristics from each other in the feature space of student and teacher models. To this end, we adopt a simple routing strategy that randomly selects and passes different views through the teacher and student models. The + +teacher SVT processes a given global spatiotemporal view to produce a feature vector, $\pmb{f}_{g_t}$ , which is used as the target label, while the student SVT processes local and global spatiotemporal views to produce feature vectors, $\pmb{f}_{g_s}$ , and $\pmb{f}_{l_s}^{(1)},\dots,\pmb{f}_{l_s}^{(8)}$ , which are matched to the target feature $\pmb{f}_{g_t}$ through our proposed loss (Eq. 1). During each training step, we update the student model weights via backpropagation while teacher weights are updated as an exponential moving average (EMA) of the student weights [13]. + +Our motivation for predicting such varying views of a video is that it leads to modeling the contextual information defining the underlying distribution of videos by learning motion correspondences (global to global spatiotemporal view matching) and cross-view correspondences (local to global spatiotemporal view matching) (Fig. I). This makes the model invariant to motion, scale and viewpoint variations. Thus, our self-supervised video representation learning approach depends on closing the gap between feature representations of different spatiotemporal views from the same video using a self-distillation mechanism. Next, we explain how motion correspondences and cross-view correspondences are learned, followed by our loss formulation. + +# 3.2.1 Motion Correspondences + +A defining characteristic of a video is the frame rate. Varying the frame rate can change motion context of a video (e.g., walking slow vs walking fast) while controlling nuanced actions (e.g., subtle body-movements of walking action). In general, clips are sampled from videos at a fixed frame rate [64, 87]. However, given two clips of varying frame rate (different number of total frames for each clip), predicting one from the other in feature space explicitly involves modeling the motion correspondences (MC) of objects across frames. Further, predicting subtle movements captured at high frame rates will force a model to learn motion related contextual information from a low frame rate input. We model this desired property into our training by matching global to global spatiotemporal views. Refer to Appendix A for further details. + +# 3.2.2 Cross-View Correspondences + +In addition to learning motion correspondences, our training strategy aims to model relationships across spatiotemporal variations as well by learning cross-view correspondences (CVC). The cross-view correspondences are learned by matching the local spatiotemporal views processed by our student SVT $(\pmb{f}_{l_s}^{(i)}: i \in [1,8])$ with a global spatiotemporal view representation processed by our teacher SVT model $(\pmb{f}_{g_t})$ . Our local views cover a limited portion of videos along both spatial and temporal dimensions. + +Our intuition is that predicting a global spatiotemporal view of a video from a local spatiotemporal view in the latent space forces the model to learn high-level context + +tual information by modeling, a) spatial context in the form of possible neighbourhoods of a given spatial crop, and b) temporal context in the form of possible previous or future frames from a given temporal crop. Note that in the cross-view correspondences, we predict a global view frame using all frames of a local view by our similarity objective (Eq. 3). + +# 3.2.3 Dynamic Positional Embedding + +Vision transformers [26] require inputs to be converted to sequences of tokens, which allows efficient parallel processing. Positional encoding is used to model ordering of these sequences [57]. Interestingly, positional encoding also allows ViT to process variable input resolution by interpolating the positional embedding for the missing tokens. As mentioned earlier, our motion and cross-view correspondences involve varying spatial and temporal resolutions which results in variable spatial and temporal input tokens during training (Sec. 3.1). We use this property of positional encoding to our advantage by accommodating varying spatial and temporal tokens in our proposed training mechanism. In implementing this, during training we use a separate positional encoding vector for spatial and temporal dimensions and fix these vectors to the highest resolution across each dimension. Similar to [26], our positional encoding is a learned vector. We vary the positional encoding vectors through interpolation during training to account for the missing spatial or temporal tokens at lower frame rate or spatial size. This allows our single SVT model to process inputs of varying resolution while also giving the positional embedding a dynamic nature which is more suited for different sized inputs in the downstream tasks. During slow-fast inference (Sec. 3.4) on downstream tasks, the positional encoding is interpolated to the maximum frame count and spatial resolution used across all views. + +We note that our learned positional encoding is implicitly tied to frame number to cue the relative ordering of the sampled frames. Given the varying frame rates of views, it does not encode the exact time stamp (frame rate information). We hypothesize that despite not differentiating frame rates, cuing frame order is sufficient for SVT training. + +# 3.2.4 Augmentations + +In addition to our sampling strategy (temporal dimension augmentations), we also apply standard image augmentations to the spatial dimension, i.e., augmentations are applied to the individual frames sampled for each view. We follow temporally consistent spatial augmentations [64] where the same randomly selected augmentation is applied equally to all frames belonging to a single view. The standard augmentations used include random color jitter, gray scaling, Gaussian blur, and solarization. We also apply random horizontal flips to datasets not containing flip equivariant classes (e.g., walking left to right). + +# 3.3. SVT Loss + +We enforce motion and cross-view correspondences by matching our proposed spatiotemporal views within the feature space. Specifically, we match global to global views to learn motion and local to global views to learn cross-view correspondences by minimizing the following objective: + +$$ +\mathcal {L} = \mathcal {L} _ {l g} + \mathcal {L} _ {g g}. \tag {1} +$$ + +The global and local spatiotemporal views are passed though the student and teacher models to get the corresponding feature outputs $\pmb{f}_g$ and $\pmb{f}_l$ . These feature vectors are normalized to obtain $\tilde{\pmb{f}}$ as follows: + +$$ +\tilde {\boldsymbol {f}} [ i ] = \frac {\exp (\boldsymbol {f} [ i ]) / \tau}{\sum_ {i = 1} ^ {n} \exp (\boldsymbol {f} [ i ]) / \tau}, +$$ + +where $\tau$ is a temperature parameter used to control sharpness of the exponential function [13] and $\tilde{f}[i]$ is each element of $\tilde{f} \in \mathbb{R}^n$ . + +Motion Correspondence Loss: We forward pass a global view through the teacher SVT serving as the target feature which is compared with an alternate global view processed by the student SVT to obtain a loss term (Eq. 2). This loss measures the difference in motion correspondences between these two global views. + +$$ +\mathcal {L} _ {g g} = - \tilde {\boldsymbol {f}} _ {g _ {t}} \cdot \log \left(\tilde {\boldsymbol {f}} _ {g _ {s}}\right), \tag {2} +$$ + +where, $\tilde{f}_{g_s}$ and $\tilde{f}_{g_t}$ are the feature outputs of different global spatiotemporal views from the student and teacher network respectively and $[\cdot ]$ is dot product operator. + +Cross-view Correspondence Loss: All local spatiotemporal views are passed through the student SVT model and mapped to a global spatiotemporal view from the teacher SVT model to reduce the difference in feature representation, learning cross-view correspondences (Eq. 3). + +$$ +\mathcal {L} _ {l g} = \sum_ {i = 1} ^ {k} - \tilde {\boldsymbol {f}} _ {g _ {t}} \cdot \log \left(\tilde {\boldsymbol {f}} _ {l _ {s}} ^ {(i)}\right), \tag {3} +$$ + +where the sum is performed over $k$ different local spatiotemporal views ( $k = 8$ used consistently across all experiments) and $\tilde{f}_{ls}^{(i)}$ are the feature outputs for $i^{th}$ local view. + +Convergence: Given our two separate student $(\theta)$ and teacher $(\xi)$ networks, let us view our overall loss, $L$ as a function of their learnable parameters, $L_{\theta ,\xi}$ . There exists a concern of collapse to a trivial solution (teacher and student outputs always equal a constant) during training. However, we note that SVT parameters do not converge to such a minimum over $L_{\theta ,\xi}$ because: a) The SVT teacher parameter updates are not in the direction of $\nabla_{\xi}L_{\theta ,\xi}$ since $\xi_{t + 1}\gets \tau \xi_t + (1 - \tau)\theta_t$ for $\tau \in [0,1]$ (EMA update). b) + +![](images/e8c8a2464672db4b7c8647f34919a7150e7f111d4af578b48829379678db5c5f.jpg) +Figure 3. Slow-Fast Inference: we uniformly sample two clips of the same video at resolutions (8, 224, 244) and (64, 96, 96), pass through a shared network, and generate two different feature vectors (class tokens). These vectors are combined in a deterministic manner (with no learnable parameters), e.g. summation, to obtain a joint vector that is fed to the downstream task classifier. + +SVT's gradient descent on $L_{\theta, \xi}$ does not act jointly over $(\theta, \xi)$ . This is similar to BYOL [34] where such a loss acts on the outputs of student and teacher networks. Additionally, as suggested in [13], we also use centering and sharpening of teacher outputs to further facilitate convergence. + +# 3.4. SVT: Slow-Fast Inference + +Slow-Fast inference refers to using two different video clips with high spatial but low temporal and low spatial but high temporal resolutions. This allows capturing finer information across each dimension with minimal increase in computation. Recent methods [30, 45] deploy such inference but use multiple network architectures for processing videos at different resolutions. However, our dynamic positional encodings allow Slow-Fast inference within our single SVT model (Sec. 3.2.3) as illustrated in Fig. 3. We use this on downstream tasks for improved performance. + +# 4. Experiments + +# 4.1. Experimental Setup and Protocols + +Datasets: We use the Kinetics-400 data [14] (train set) for the self-supervised training phase of SVT. We use its validation set for evaluation. Additionally, we evaluate on three downstream datasets, UCF-101 [69], HMBD-51 [49], and Something-Something v2 (SSv2) [33]. + +Self-supervised Training: We train our models for 20 epochs on the train set of Kinetics-400 dataset [14] without any labels using a batch size of 32 across 4 NVIDIA-A100 GPUs. This batch size refers to the number of unique videos present within a given batch. We randomly initialize weights relevant to temporal attention while spatial attention weights are initialized using a ViT model trained in a self-supervised manner over the ImageNet-1k dataset [66]. We follow this initialization setup to obtain faster space-time ViT convergence similar to the supervised setting [9]. We use an Adam optimizer [47] with a learning rate of $5e - 4$ + +scaled using a cosine schedule with linear warmup for 5 epochs [18,71]. We also use weight decay scaled from 0.04 to 0.1 during training. Our code builds over the training frameworks from [9,13,28,86]. + +Downstream Tasks: We perform two types of evaluations on our downstream task of action recognition for each dataset, a) Linear: We train a linear classifier over our pretrained SVT backbone (which is frozen during training) for 20 epochs with a batch size of 32 on a single NVIDIA-V100 GPU. We use SGD with an initial learning rate of $8e - 3$ , a cosine decay schedule and momentum of 0.9 similar to recent work [13, 64]; b) Fine-tuning: We replace the projection head over the SVT with a randomly initialized linear layer, initialize the SVT backbone with our pre-trained weights, and train the network end-to-end for 15 epochs with a batch size of 32 across 4 NVIDIA-V100 GPUs. We use SGD with a learning rate of $5e - 3$ decayed by a factor of 10 at epochs 11 and 14, momentum of 0.9, and weight decay of $1e - 4$ following [9]. + +During both training of linear classifier and fine-tuning of SVT, we sample two clips of varying spatiotemporal resolution from each video. During evaluation, we follow our proposed slow-fast inference strategy (Sec. 3.4). We use two clips per video sampled at different spatiotemporal resolutions $(T,W,H) \in \{(8,224,224),(64,96,96)\}$ with 3 spatial crops each for testing (6 clips in total). This is computationally more efficient in comparison to recent works [64, 65] that uniformly sample 10 clips at similar or high resolutions from full-length videos with 3 crops each for testing (total of 30 clips per video). + +# 4.2. Results + +We compare SVT with state-of-the-art approaches (trained on RGB input modality for fair comparison) for the downstream task of action recognition. + +UCF-101 & HMDB-51: Our method out-performs state-of-the-art for UCF-101 and is on-par for HMDB-51 (Tab. 1). While CORP [39] exhibits higher performance on HMDB-51, we highlight how SVT: a) is pretrained for a much shorter duration (20 epochs) with smaller batch-sizes (32); b) uses a single architectural design across all tasks. CORP [39] models are pre-trained for 800 epochs with a batch-size of 1024 using 64 NVIDIA-V100 GPUs and uses different variants $(\mathrm{CORP}_f$ and $\mathrm{CORP}_m)$ to obtain optimal performance on different datasets. + +Kinetics-400: We present our results on Kinetics-400 [14] in Tab. 2 where our approach obtains state-of-the-art for both linear evaluation and fine-tuning settings. Performance on Kinetics-400 is heavily dependent on appearance attributes, i.e. a large proportion of its videos can be recognized by a single frame [92]. Strong performance of SVT on this dataset exhibits how well our proposed approach learns appearance related contextual information. + +Table 1. UCF-101 [69] & HMBD-51 [49]: Top-1 (\%) accuracy for both linear evaluation and fine-tuning. All models are pre-trained on Kinetics-400 [14] except ELo [63] which uses YouTube8M dataset [1]. Gray shaded methods use additional optical flow inputs. S-Res and T-Res represent spatial and temporal input resolution, respectively. Our approach shows state-of-the-art or on par performance. + +
MethodBackboneTFLOPsS-ResT-ResEpochsUCF-101 [69]HMDB-51 [49]
LinearFine-tuneLinearFine-tune
MemDPC [35] (ECCV '20)R2D3D-34-22464-54.186.130.554.5
CoCLR [36] (Neurips '20)S3D0.071283210077.887.952.454.6
ELo [63] (CVPR '20)R(2+1)D17.5224-100-84.2-53.7
RSPNet [15] (AAAI '21)S3D-G0.0711216200-89.9-59.6
VideoMoCo [60] (CVPR '21)R(2+1)D17.51123220078.7-49.2-
BE [82] (CVPR '21)I3D2.222241650-87.1-56.2
CMD [42] (CVPR '21)R(2+1)D-26-11216120-85.7-54.0
CVRL [64] (CVPR '21)R3D-503.192243280089.292.257.366.7
TCLR [20] (Arxiv '21)R(2+1)D-18-11216100-84.3-54.2
MoDist [87] (Arxiv '21)R3D-503.19224810091.594.063.067.4
BraVe [65] (ICCV '21)R3D-503.1922416-92.595.168.374.6
Vi²CLR [23] (ICCV '21)S3D0.071283230075.489.147.355.7
ASCNet [40] (ICCV '21)S3D-G0.0722464200-90.8-60.5
TEC [44] (ICCV '21)S3D-G0.0712832200-88.2-63.5
LSFD [8] (ICCV '21)C3D-22416--79.8-52.1
MCN [51] (ICCV '21)R3D3.19128325073.189.742.959.3
CORP [39] (ICCV '21)R3D-503.192241680090.293.558.768.0
SVT (Ours)ViT-B [9]0.59224162090.893.757.867.2
+ +Table 2. Kinetics-400 [14]: Top-1 (\%) accuracy is reported for both linear evaluation and fine-tuning on the Kinetics-400 validation set. All models are pre-trained on the training set of Kinetics-400 dataset. Our approach shows state-of-the-art performance. + +
MethodBackboneFine-tuneLinear
CVRL [64] (CVPR'21)R3D-10170.467.6
Vi²CLR [23] (ICCV'21)S3D71.263.4
CORP [39] (ICCV'21)R3D-50-66.6
SVT (Ours)ViT-B [9]78.168.1
+ +Table 3. SSv2 [33]: Top-1 (\%) for both linear evaluation and finetuning on the SSv2 validation set. All models are pre-trained on Kinetics-400. Our approach produces best results. + +
MethodBackboneFine-tuneLinear
MoDist [87] (Arxiv'21)R3D-5054.916.6
CORP [39] (ICCV '21)R3D-5048.8-
SVT (Ours)ViT-B [9]59.218.3
+ +SSv2: Similarly, we obtain state-of-the-art results on SSv2 dataset [33] for both linear evaluation and fine-tune settings as presented in Tab. 3. Multiple classes in SSv2 share similar backgrounds and object appearance, with complex movements differentiating them [39]. Performance on this dataset indicates how SVT feature representations capture strong motion related contextual cues as well. + +# 4.3. Ablative Analysis + +We systematically dissect the contribution of each component of our method. We study the effect of five individual elements: a) different combinations of local and global view correspondences; b) varying field of view along temporal vs spatial dimensions; c) temporal sampling strategy; d) spatial augmentations; e) slow-fast inference. In all our ablative experiments, SVT self-supervised training uses a subset of the Kinetics-400 train set containing 60K videos. Evaluation is carried out over alternate train-set splits of UCF-101 and HMDB-51. We train SVT for 20 epochs and evaluate using the same setup as described in Sec. 4.1. + +View Correspondences. Learning correspondences between local and global views is the key motivation behind our proposed cross-view correspondences. Since multiple local-global view combinations can be considered for matching and prediction between views, we explore the effect of predicting each type of view from the other in Tab. 4. We observe that jointly predicting local to global and global to global view correspondences results in the optimal performance, while predicting global to local or local to local views leads to reduced performance. We believe this trend exists due to the emphasis on learning rich context in the case of joint prediction, which is absent for individual cases. Further, the performance drop for local to local correspondences (non-overlapping views) conforms with previous findings on the effectiveness of temporally closer positive views for contrastive self-supervised losses [31, 64]. + +Table 4. View Correspondences. Predicting local to global and global to global views remains optimal over any other combination. + +
l→gg→gl→lg→lUCF-101HMDB-51
✓XXX84.1150.72
X✓XX81.9549.04
✓✓XX84.6452.17
✓✓✓X83.1151.23
✓✓X✓84.7151.88
✓✓✓✓83.6951.71
+ +Table 5. Spatial vs Temporal variations. Cross-view correspondences with varying field of view along both spatial and temporal dimensions lead to optimal results. Temporal variations between views has more effect than applying only spatial variation. + +
SpatialTemporalUCF-101HMDB-51
✓✗73.8142.91
✗✓82.9042.59
✓✓84.6452.17
+ +Table 6. Temporal Sampling Strategy. We compare our proposed temporal sampling strategy, motion correspondences (MC) (Sec. 3.2.1), against the alternate approach of temporal interval sampler (TIS) [64] used with CNNs under contrastive settings. + +
UCF-101HMDB-51
Ours + TIS [64]82.2450.10
Ours + MC84.6452.17
+ +Table 7. Augmentations: Using temporally consistent augmentations (TCA) [64] applied randomly over the spatial dimensions for different views result in consistent improvements on UCF-101 and HMDB-51 datasets. + +
UCF-101HMDB-51
w/o TCA [64]84.2052.10
w TCA [64]84.6452.17
+ +Table 8. Slow-Fast Inference: Feeding multiple views of varying spatiotemporal resolutions to a single shared network (multi-view) results in clear performance gains over feeding single-views across both UCF-101 and HMDB-51 datasets. + +
Slow-FastUCF-101HMDB-51
X84.6452.17
✓84.8053.22
+ +Spatial vs Temporal Field of View. The optimal combination of spatiotemporal views in Tab. 4 involves varying the field of view (crops) along both spatial and temporal dimensions (Sec. 3.2.2). We study the effects of these variations (spatial or temporal) in Tab. 5. No variation along the spatial dimension denotes that all frames are of fixed spatial resolution $224 \times 224$ with no spatial cropping, and no temporal variation denotes that all frames in our views are sampled from a fixed time-axis region of a video. We observe that temporal variations have a significant effect on UCF-101, while variations in the field of view along both spatial and temporal dimension perform the best (Tab. 5). + +Temporal Sampling Strategy. We study how our proposed temporal sampling strategy for motion correspondences (MC) could be replaced with alternate sampling approaches. To verify the effectiveness of MC, we replace it within SVT with an alternate approach. The temporal interval sampling (TIS) strategy in [64] obtains state-of-the-art performance under their contrastive video self-supervised setting with CNN backbones. Our experiments incorporating TIS in SVT (Tab. 6) highlight the advantage of our proposed MC sampling strategy over TIS. + +Augmentations: We next explore standard spatial augmentations used on videos. Temporally consistent augmentations (TCA) proposed in [64] lead to improvements in their CNN based video self-supervision approach. We evaluate its effect on our approach in Tab. 7 which shows slight improvements. Given these performance gains, we adopt TCA in our SVT training process as well. + +Slow-Fast Inference: Finally, we study the effect of our + +proposed Slow-Fast inference (Sec. 3.4) in Tab. 8. We observe higher gains on HMDB-51 [49], where the classes are easier to separate with motion information [36]. + +# 5. Conclusion + +We present a video transformer based model trained using self-supervised objectives named SVT. Given an input video sequence, our approach first creates a set of spatiotemporally varying views sampled at different scales and frame rates from the same video. We then define two sets of correspondence learning tasks which seek to model the motion properties and cross-view relationships between the sampled clips. Specifically, our self-supervised objective reconstructs one view from the other in the latent space of student and teacher networks. Our approach is fast to train (converges within fewer iterations), does not require negative samples or large batch sizes, models long-range temporal dependencies, and performs dynamic slow-fast inference leading to better downstream performance. 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It is a challenging task since representation optimization and feature retention can only be achieved under supervision from new classes. To address this problem, we propose a novel self-sustaining representation expansion scheme. Our scheme consists of a structure reorganization strategy that fuses main-branch expansion and side-branch updating to maintain the old features, and a main-branch distillation scheme to transfer the invariant knowledge. Furthermore, a prototype selection mechanism is proposed to enhance the discrimination between the old and new classes by selectively incorporating new samples into the distillation process. Extensive experiments on three benchmarks demonstrate significant incremental performance, outperforming the state-of-the-art methods by a margin of $3\%$ , $3\%$ and $6\%$ , respectively. + +# 1. Introduction + +Since deep neural networks have made great advances in fully supervised conditions, research attention is increasingly turning to other aspects of learning. An important aspect is the ability to continuously learn new tasks as the input stream is updated, which is often the case in real applications. In recent years, class-incremental learning (CIL) [11, 27], a difficult type in continual learning, has attracted much attention, which aims to recognize new classes without forgetting the old ones that have been learned. + +In this case, re-training the old and new class samples jointly in each phase is time-consuming and laborious, not to mention that the old class samples may not be fully available. A simple alternative is to fine-tune the network using the new class, however, it will cause the catastrophic forgetting problem [8]. That is, during the optimization process, + +![](images/c8015708d7f0b72b6a210f7f22d8b1a2a9337f47683127ae31ee4972a0d0bee7.jpg) +Figure 1. The t-SNE visualization. Compared to the baseline in Section 4.1, (1) the representations of the old classes in our method are better maintained (circular area), (2) and the novel class is more discriminating from the old classes (rectangular area). + +the entire representation and the classifier become biased toward the new class, resulting in a sharp drop in the performance for the old class. To deal with it, recent CIL methods maintain the past knowledge by preserving some representative samples (i.e., exemplars [27]) and introducing various distillation losses [7], and correct the bias caused by number imbalance by calibrating the classifier [11]. + +However, most of the existing methods [21, 30] assume that a certain number (e.g., 2000) of exemplars can be stored in memory, which is usually difficult to satisfy in practice due to user privacy or device limitations. This fact poses great difficulties to incremental learning, because the optimization of the representation and the correction of the classifier will degenerate directly from the imbalance between the old and new classes. To this end, this paper focuses on this ability of incrementally learning new classes where old class samples cannot be preserved, which is called non- + +![](images/66deed07c1e3417dc5c6b87ab8e0cc30a889c42f0803188a91ebd5d337265f09.jpg) +Figure 2. Motivation of our method. In NECIL, the rehearsal-based and structure-based methods suffer from the unreliability of distillation in the absence of exemplars and continuously expanding structure, respectively. DSR is proposed to drive network to expand from a structurally recoverable direction, thus maintaining the discrimination during the new optimization process. On this foundation, we utilize MBD to exploit the ability of distillation-based methods to balance old and new class knowledge. + +exemplar class-incremental learning (NECIL [44]). + +A natural idea for this problem is to directly transfer the existing CIL framework (i.e., rehearsal-based and structure-based methods in Section 2.1) to NECIL, but the experimental results show that this way leads to performance degradation and parameter explosion. On one hand, in rehearsal-based methods, due to the lack of old class samples, the distillation that the new class samples participate in is the only one that can help maintain the representation of old classes. However, for new samples, it is impractical to provide the same complete old class distribution as the exemplars, so it is difficult to effectively promote the knowledge transfer in the distillation process. Consequently, representative features learned in the old phase are lost phase by phase with the decrease of relevance to the new class. + +On the other hand, the idea of structure-based methods is to leave the old model for inference and expand a new model for training at each new phase [28,35]. Although this strategy maintains the performance of the old class completely, demonstrating strong performance [35], the network parameters that increase linearly with phase (i.e., 5, 10 and 20 in this paper) during training are discouraging. Besides, although a large amount of data can be used to learn the discriminative features among new classes, it is easy to confuse with similar ones from the old distribution. The augmentation of prototypes [44] can only improve the selection of the optimal boundary for the classifier, but cannot essentially improve the discrimination of the old and new classes in the feature representation. As shown in Fig. 1, the representations of old classes obtained by the standard CIL method are more confused compared to the initial phase, because they may gradually overlap with similar classes due to the lack of effective supervision. At the same time, the new + +class may directly overlap with the old cluster, resulting in serious confusion to the subsequent optimization process. + +To address this problem, we propose a self-sustaining representation expansion scheme to learn a structure-cyclic representation, promoting the optimization from the expanded direction while integrating the overall structure at the end of each phase. As shown in Fig. 2, the preservation of the old classes is reflected in both the structure and feature aspects. First, we adopt a dynamic structure reorganization (DSR) strategy, which leaves structured space for the learning of new class while stably preserving the old class space through maintaining heritage at the main-branch and fusing update at the side-branch. Second, on the basis of the expandable structure, we employ a main-branch distillation (MBD) to maintain the discrimination of the new network with respect to the old features by aligning the invariant distribution knowledge on the old classes. + +Specifically, we insert a residual adapter in each block of the old feature extractor to map the old representation to a high-dimensional embedding space, forcing the optimization flow to only pass through the expanding branches unrelated to the old class. After the optimization, we adopt the structural re-parameterization technique to fuse the old and new features and map them back to the initial space losslessly. Furthermore, to reduce the confusion between the newly incremental classes and the original classes, we add a prototype selection mechanism (PSM) during the distillation process. The normalized cosine is first used to measure the similarity between the new representation and the old prototype. Then samples similar to the old classes are used for distillation, maintaining the old knowledge with a soft label that retains the old class statistical information, while those samples dissimilar to the old classes are used for new + +class training. This mechanism improves the performance of forward transfer and mitigates the lack of joint optimization to some extent. Our main contributions are as follows: + +1) A self-sustaining representation expansion scheme is proposed for non-exemplar incremental learning, in which a cyclically expanding optimization is accomplished by a dynamic structure reorganization strategy, resulting in a structure-invariant representation. +2) A prototype selection mechanism is proposed, which combinatorially co-uses the preserved invariant knowledge and the incoming new supervision to reduce the feature confusion among the similar classes. +3) Extensive experiments are performed on benchmarks including CIFAR-100, TinyImageNet and ImageNet-Subset, and the results demonstrate the superiority of our method over the state of the art. + +# 2. Related Work + +# 2.1. Incremental Learning + +As deep learning research advances [34, 41], there is a growing demand for continual learning of neural networks, which requires the network to learn new tasks without forgetting the old knowledge to achieve the stability-plasticity trade-off. CIL [32, 45] is the most difficult scenery in continual learning and has received more attention recently. Current methods can broadly divided into the following three classes. Regularization-based methods [15, 39] estimate the importance of the network parameters learned in the past tasks and constrain their optimization accordingly. Rehearsal-based methods [1, 7, 12, 22, 33] preserve exemplars of fixed memory size to maintain the distribution of old classes in the incremental phases, and adopt the distillation skills to retain the discriminative features of the old task. [11] incorporates three components, cosine normalization, less-forget constraint, and inter-class separation, to address the imbalance between previous and new data. The techniques on exemplar and distillation in rehearsal-based methods are widely used in class-incremental learning. Structure-based methods [13, 29] select and expand different sub-network structures involved in the optimization process of the incremental tasks. [24] progressively chooses optimal paths for the new tasks while encouraging parameter sharing, which promotes the forward knowledge transfer. [35] freezes the previously learned representation and augment it with additional feature dimensions from a new mask-based feature extractor. The structure-based methods are often mixed with other techniques such as exemplar and distillation, and have achieved good results. + +Recently, some works [36, 38, 44] focus on a challenging but practical non-exemplar class-incremental learning problem, where no past data can be stored due to equipment limits or privacy security. [38] estimates the seman + +tic drift of incremental features and compensates the prototypes in each test phase. [44] adopts prototype augmentation to maintain the decision boundary of previous tasks, and employ self-supervised learning to learn more transferable features for future tasks. We follow their NECIL settings. However, different from their work considering generalizable features and augmented prototypes, we mainly consider the adjustment for joint representation learning and distillation process in the absence of exemplars. + +# 2.2. Residual Block + +Residual block has been widely used in convolutional neural network as the basic structure of ResNet [10], which improves the network depth and prevents vanishing gradient. Further improvements have been investigated for superior dynamic performance [19] and inference efficiency [5, 6, 9] recently. In domain adaptation [20, 43], residual adapter [18, 25, 26] is proposed to learn style information related to new domains, thus improving the overall generalization performance of the network. In these efforts, residual block is used to improve joint optimization performance or statistical domain information. Instead, we consider dynamically incremental residual blocks to learn new knowledge efficiently while maintaining old features. + +# 3. Problem Description + +The NECIL problem is defined as follows. Here we denote $X, Y$ and $Z$ as the training set, the label set and the test set, respectively. Our task is to train the model from a continuous data stream, i.e., training sets $X^1, X^2, \dots, X^n$ , where samples of a set $X^i$ ( $1 \leq i \leq n$ ) are from the label set $Y^i$ , and $n$ represents the incremental phase. It should be mentioned that all the incremental classes are disjoint, that is, $Y^i \cap Y^j = \emptyset (i \neq j)$ . Except that there are sufficient samples in the current phase $X^i$ , no old samples are available in memory for old classes. To measure the performance of models in NECIL task, we calculate the classification accuracy on the test set $Z^i$ at each phase $i$ . Different from the training set, the classes of the test set $Z^i$ are from all the seen label sets $Y^1 \cup Y^1 \dots \cup Y^i$ . + +# 4. Methodology + +First of all, we demonstrate the paradigms of standard CIL and how we adapt it to the NECIL setting as the baseline. Then we analyze the optimization flow of the overall pipeline and explain why it doesn't work well. Finally, two proposed core components dynamic structure reorganization and prototype selection are introduced. + +# 4.1. Standard NECIL Paradigm + +[27] first proposed a practical strategy for decoupling representation and classifiers learning in the CIL setting, + +![](images/894c965dcb89964ba5f8c86c677f3c7893730a5fbcd6b3edb964a2b92bccbc3c.jpg) + +![](images/d9eacba2bdce4908ae32ed013a712232535b7b24a6e1a239223ee399fb4c3a92.jpg) +Figure 3. Our proposed self-sustaining representation expansion scheme for NECIL: (a) overview of our scheme, (b) dynamic structure reorganization, and (c) main-branch distillation and prototype balance. The source code will be made available to the public. + +![](images/e726389134ccd710f69c1c0861e64dfa4bd23aac1162741fda69210242d1cf3e.jpg) + +which is followed by most subsequent work. The three main components are representation learning using knowledge distillation and prototype rehearsal, prioritized exemplar selection, and classification by a balance calibration. + +Incremental Representation Learning. As the exemplar cannot be saved in the NECIL setting, the representation learning will be slightly different, mainly in terms of cross-entropy loss and distillation loss. At the first phase, a standard classification model $f_{\theta}^{1}$ consisting of the feature extractor $f_{e}^{1}$ and classifier $g_{c}^{1}$ is optimized under the full supervision, i.e., $X^{1}$ and $Y^{1}$ . At the incremental phase $(n > 1)$ , the input of the current model is only the predicted images $Q$ from $X^{n}$ without old samples. A base feature extractor $f_{e}^{n}$ such as VGG [31] or ResNet [10] parameterized by $\theta_{e}^{n}$ is utilized to learn the corresponding representation: + +$$ +r _ {q} ^ {n} = f _ {e} ^ {n} (Q; \theta_ {e} ^ {n}). \tag {1} +$$ + +Then, to learn the discriminative features among the novel classes, the obtained representation is optimized under the supervision of the class label $\mathbf{y}_q^n$ from $Y^{n}$ . We adopt the fully connected layer as the classifier $g_{c}^{n}$ to map the repre + +sentation to the label space, + +$$ +s _ {q} ^ {n} = g _ {c} ^ {n} \left(r _ {q} ^ {n}; \theta_ {c} ^ {n}\right), L _ {c e} = F _ {c e} \left(s _ {q} ^ {n}, y _ {q} ^ {n}\right), \tag {2} +$$ + +$F_{ce}$ represents the standard cross-entropy loss. Finally, to maintain the useful information learned with the old classes, the knowledge distillation is used to measure the similarity between the obtained representation and that of the previous model $f_{e}^{n - 1}$ , + +$$ +r _ {q} ^ {n - 1} = f _ {e} ^ {n - 1} \left(Q; \theta_ {e} ^ {n - 1}\right), L _ {k d} = F _ {k d} \left(r _ {q} ^ {n}, r _ {q} ^ {n - 1}\right), \tag {3} +$$ + +$F_{kd}$ represents Euclidean distance the same as [44]. + +Incremental Classifier Calibration. A common way to overcome the imbalance between the exemplars and new samples in CIL is to under-sample a balanced subset for fine-tuning. As there is no exemplars in NECIL, we memorize one prototype in the deep feature space for each class, which is consistent with PASS [44]. Different from PASS augmenting the prototypes via Gaussian noise, we choose to over-sample (i.e., $U_{p_B}$ ) prototypes to the batch size (i.e., B), achieving the calibration of the classifier, which is the simplest way adopted in the long-tail recognition [2], + +$$ +p _ {B} = U p _ {B} (\text {P r o t o t y p e}), L _ {\text {p r o t o}} = F _ {c e} \left(p _ {B}, y _ {B}\right), \tag {4} +$$ + +$y_{B}$ is the over-sampled label set of the initial prototypes. The final loss for current model is their addition: + +$$ +L = L _ {c e} + \lambda L _ {k d} + \gamma L _ {p r o t o}, \tag {5} +$$ + +$\lambda$ and $\gamma$ are loss weights, and we set them to 10. + +# 4.2. Optimization + +Different from the previous work focusing on the effect on the classifier, this paper tries to analyze the representation. In the CIL, Equation 2 can be turned into two parts: + +$$ +L _ {c e} = F _ {c e} \left(s _ {q} ^ {n}, y _ {q} ^ {n}\right) + F _ {c e} \left(s _ {e} ^ {n}, y _ {e} ^ {n}\right), \tag {6} +$$ + +$s_e^n$ represents the saved exemplars, whose number is much lower than that of $s_q^n$ . While this imbalance can bias the optimization process towards features that are more discriminative for the new class, the added distillation in Equation 3 can alleviate this problem, + +$$ +L _ {k d} = F _ {k d} \left(r _ {q} ^ {n}, r _ {q} ^ {n - 1}\right) + F _ {k d} \left(r _ {e} ^ {n}, r _ {e} ^ {n - 1}\right). \tag {7} +$$ + +$r_e^n$ represents the representation of exemplars. In this case, the features that are significant for the old and new classes will be maintained. However, note that there is no exemplars involved in the above NECIL setting. It means that the joint optimization on the old and new class representations completely collapses into feature optimization that is relevant only to incremental classes. What is reflected in the first part is that the cross-entropy loss will only focus on the features that facilitate the recognition of the new class, while in the second part, it will focus on the maintenance of the features related to the new class, which both accelerate the forgetting of the representative features of the old class. Suppose the forgetting rate (Fr) of distillation part in the initial phase is $\alpha$ . Note that the distillation loss is based on the overall representation of the previous phase, and the error will accumulate exponentially with the phase, that is, $F r_n \geq \alpha^{n-1}$ . Therefore, it is necessary to correct this error from the representational level. + +# 4.3. Self-Sustaining Representation Expansion + +Dynamic Structure Reorganization. To retain the representation [42] of the old class and guarantee the unbiased training of the new class, we propose a dynamic structure reorganization strategy. In general, as shown in Fig. 3, we firstly adopt the structural expansion to add the side branch to the current model by block for the optimization of new classes. Specifically, we insert a residual adapter to each convolution block of the fixed feature extractor from previous phase. The optimized flow propagates only through the adapter, updating the most discriminating position while maintaining the old features, + +$$ +\begin{array}{l} f _ {e} ^ {n} (Q; \theta_ {e} ^ {n}) = F _ {t r a n s f o r m} (f _ {e} ^ {n - 1} (Q; \theta_ {e} ^ {n - 1})) \\ = f _ {e} ^ {n - 1} \left(Q; \hat {\theta} _ {e} ^ {n - 1} \oplus \Delta \theta_ {e} ^ {n}\right), \tag {8} \\ \end{array} +$$ + +where $\hat{\cdot}$ represents the fixed parameters, and $\oplus$ represents the structural expansion operation. After training, we use the structural re-parameterization [6] to integrate the side-branch information into the main branch losslessly, ensuring that the number of network parameters does not increase at the end of each phase. Specifically, the parameters in the residual structures are fused with the parameters of the original convolution kernel and BatchNorm [14] through the zero-padding operation and linear transformation, and finally the adapters are removed to keep the network structure unchanged for the next update, + +$$ +\begin{array}{l} f _ {e} ^ {n - 1} (Q; \hat {\theta} _ {e} ^ {n - 1} \oplus \Delta \theta_ {e} ^ {n}) \\ = f _ {e} ^ {n} \left(Q; \theta_ {e} ^ {n \prime} \oplus 0\right) = f _ {e} ^ {n} \left(Q; \theta_ {e} ^ {n \prime}\right). \tag {9} \\ \end{array} +$$ + +Prototype Selection. While new features are learned based on the old structure, the old class features are maintained in coordination with the main-branch distillation. To reduce the feature confusion in the distillation part, we adopt a prototype selection mechanism based on the expandable embedding space. In general, based on the similarity between the representation of new samples and the old prototypes, dissimilar samples are involved in the update of residual adapter to learn new features, and similar samples are involved in the distillation to retain the old discriminative features maintained in the main branch at previous phase. Specifically, after mapping all new samples to the learned embedding space [3, 40], we compute the normalized cosine scores $S_i$ between them and all prototypes, + +$$ +S i = \operatorname {C o s i n e} \left(N \left(r _ {q} ^ {n}\right), \operatorname {N o r} (\text {P r o t o t y p e})\right), \tag {10} +$$ + +Nor represents the normalization operation. We then set a threshold value, and attach a mask to the corresponding position of its distillation loss $(Mask_{kd})$ if greater than the threshold $\sigma$ , and add a mask to the corresponding part of its cross-entropy loss $(Mask_{ce})$ if less than the threshold. Finally, the two losses are summed with the prototype balance loss as the final optimization function for the new phase. + +$$ +L = \operatorname {M a s k} _ {c e} \left(L _ {c e}\right) + \lambda \operatorname {M a s k} _ {k d} \left(L _ {k d}\right) + \gamma L _ {\text {p r o t o}}. \tag {11} +$$ + +# 5. Experiments + +# 5.1. Dataset and Settings + +Dataset. To evaluate the performance of our proposed method, we conduct comprehensive experiments on three datasets CIFAR-100 [16], TinyImageNet [17] and ImageNet-Subset. CIFAR-100 contains 60000 images of $32 \times 32$ size from 100 classes, and each class includes 500 training images and 100 test images. TinyImageNet contains 200 classes, and each class contains 500 training images, 50 validation images and 50 test images. It provides more phases and incremental classes to compare the sensitivity of different methods. ImageNet-Subset is a 100-class + +
DSRMBDPSMCIFAR-100
5 phases10 phases20 phases
61.1157.0851.04
✓64.8663.2554.09
✓62.7062.6058.57
✓✓65.1063.8760.60
✓✓✓65.8864.6961.61
+ +Table 1. Ablation study of our method on CIFAR-100. + +
CIFAR-100
Method5 phases10 phases20 phases
3×3 conv64.2863.4760.81
1×1 conv + bn65.8864.8460.72
1×1 conv65.8765.1261.60
+ +Table 2. Performance under different expanding structures. + +subset of ImageNet-1k [4], which is much larger. For the order and division of all dataset classes in our experiments, we followed exactly the settings in [44]. + +Setting. As adopted in [44], we use ResNet-18 as the backbone network. The difference is that we use standard supervised training for the whole optimization process instead of involving self-supervised learning. For a fair comparison, we achieve the same accuracy as [44] at the first phase for all datasets. We use an Adam optimizer, in which the initial learning rate is set to 0.001 and the attenuation rate is set to 0.0005. The model stops training after 100 epochs, and batch size is set to 128. + +Evaluation Metrics. Following [44], we report average incremental accuracy and average forgetting, and our performance is evaluated on three different runs. Average incremental accuracy is computed as the average accuracy of all the incremental phases (including the first phase), which compares the overall incremental performance of different methods fairly. Average forgetting is computed as the average forgetting of different tasks throughout the incremental process, which directly measures the ability of different methods to resist catastrophic forgetting. + +# 5.2. Ablation Study + +To prove the effectiveness of our proposed method, we conduct several ablation experiments on CIFAR-100. The performance of our scheme is mainly attributed to two prominent components: the dynamic structure reorganization strategy (DSR) and the main-branch distillation (MBD). To clarify the function of DSR, we replace the dynamic representation with the structurally invariant representation, which is adopted in most CIL methods [7, 44]. To clarify the function of MBD, we replace the distillation process with the one that interacts with the continuously optimized representation. As can be seen in Table 1, the + +![](images/511c8fb28622f99abc5f3fcaa846ae677eeb1881ced5be71bcb248e98b5c53e9.jpg) +Figure 4. Illustration of the role of the selection mechanism. + +![](images/8d4856d093dd55f88142f7d6ab9769bc6b775b73db0ed35140189442405aae76.jpg) +(a) Finetuning + +![](images/624924c00ce732f418a7d56eb71df0f90224eca1937c752f522f249b3038fc90.jpg) +(b) iCaRL + +![](images/4225ea7d83351d24fcb4295ff126f62b96bd66c306f7daf8e1258efe2744eef1.jpg) +(c) Ours +Figure 5. Confusion matrices of different methods on CIFAR-100. + +dynamic representation and main-branch distillation separately bring a $4.3\%$ and $4.8\%$ improvement in overall performance. It demonstrates that the two parts are far more useful than standard representation and common distillation respectively in NECIL. It is worth noting that the former plays a greater role when there are fewer incremental phases (i.e., 5 and 10 phases), while the latter shines more brightly when there are more incremental phases (i.e., 20 phases). It demonstrates that keeping the old class features helps to improve the overall performance of incremental learning in the short term. However, as analyzed in the introduction, if the distilled network keeps decaying or fixed, the errors will accumulate as the incremental phase increases. At this point, how to reasonably correct the distillation loss is the key to ensure the long-term effect. + +# 5.3. Analysis + +The impact of the adapter structure. To explore the impact of the structure of residual adapter on expandable representation during training, we design the following experiments. We adopt three different convolution blocks to the residual part: $1 \times 1$ convolution only, $3 \times 3$ convolution only and the combination of $1 \times 1$ convolution and BatchNorm. As shown in Table 2, the results of $1 \times 1$ convolution and the combination are similar, and that of $3 \times 3$ convolution is one point lower. It suggests that the $1 \times 1$ convolution structure is good enough to learn the representation of the new class without needing more parameters. + +The impact of the threshold in prototype selection. To verify the role of the PSM, we conduct data statistics on the incremental samples. As shown in Fig. 8, the new classes have a large difference in similarity. And the intra-class + +![](images/49b4f675ffb4077d3b0890b93e5809af6c051ccf91776b2f8ffa1e0adf5338b7.jpg) +(a) + +![](images/3b0cd0d6dec7459d1d1a2ad53da2de14c5b44450e80ecc141426dc4d159d5398.jpg) +(b) +Figure 6. Effect of our scheme on the representation. (a) DSR maintains the discriminative features and inter-relations of old classes, thus enhancing the clustering and separation of the distribution of old classes. (b) MBD results in a better distinction between similar classes. + +
MethodsCIFAR-100TinyImageNetImageNet-Subset
P=5P=10P=20P=5P=10P=20P=10
(1)E=20iCaRL-CNN*51.0748.6644.4334.6431.1527.9050.53
iCaRL-NCM* [27]58.5654.1950.5145.8643.2938.0460.79
EEIL* [1]60.3756.0552.3447.1245.0140.5063.34
UCIR* [11]63.7862.3959.0749.1548.5242.8366.16
(2)E=0EWC* [15]24.4821.2015.8918.8015.7712.3920.40
LwF_MC* [27]45.9327.4320.0729.1223.1017.4331.18
MUC* [37]49.4230.1921.2732.5826.6121.9535.07
SDC [38]56.7757.0058.90---61.12
PASS [44]63.4761.8458.0949.5547.2942.0761.80
Ours65.88+2.4165.04+3.2061.70+2.8050.39+0.8448.93+1.6448.17+6.1067.69+5.89
+ +Table 3. Comparisons of the average incremental accuracy (%) with other methods on CIFAR-100, TinyImageNet, and ImageNet-Subset. P represents the number of phases and E represents the number of exemplars. Models with an asterisk * represent the reproduced results in [44]. The red footnotes in the last row represent the relative improvement compared with the results of SOTA. + +fluctuations are also large, so different classes and samples involved in the optimization process will bring different changes. Therefore it is important to reasonably place them in the two potentially conflicting processes of old feature distillation and new feature learning. To demonstrate the sensitivity of the threshold on the distillation effect, we plot its fluctuation curve. As shown in Fig. 4, all curves rise to a peak at a threshold of 0.8, then gradually fall and lose distillation effect. It suggests that in the absence of the exemplars, fine-grained optimization of the new samples can better maintain the old features and learn the new features. + +Classification accuracy of old and novel classes. To evaluate performance of both old and new classes during training, we compare their accuracy at each phase. As shown in Fig. 5, our method achieves similar performance + +between the old and new classes without favoring one side due to overfitting, which is a prerequisite for a good incremental learning system. + +# 5.4. Visualization + +To better demonstrate the role of DSR and MBD during optimization, we show the visualization results with t-SNE [23]. As shown in Fig. 6 (a), although the old classes have slightly changed in the representation after multi-phase optimization, their discrimination and relative relationship almost do not decline with our DSR. As shown in Fig. 6 (b), newly incremental classes are easily confused with some of the old classes. Owing to our MBD, the optimized features are promoted to differentiate from the old class, thus improving the seperation of novel clusters. + +![](images/ae291c2c55f2bc31d4178032c96427fd873f38f064026eb6ccc8968b244ea7b2.jpg) +(a) 5 phases CIFAR-100 + +![](images/edec7dcec07807387a1ecb35d38febd06dd3d4b48ac29deb0b281d7e80e6923b.jpg) +(b) 10 phases CIFAR-100 + +![](images/cd8a54d0ecd458624399953ff52f50e632b362d17f6a4c6ac920df9b08c44ac3.jpg) +c) 20 phases CIFAR-100 + +![](images/b713f6fb8eeeea386c009752b601a4fbb7c67fb7c8fafc752b0e82bcb8e092ec.jpg) + +![](images/57f08a951ae61edecdd9319335a24b36d2bc2f05fbbd727a546cd5174433fdec.jpg) +(d) 5 phases TinyImagNet +Figure 7. Classification accuracy on CIFAR-100, TinyImageNet and ImageNet-Subset, which contains the complete curves. + +![](images/0097509da7fe659e37e68f000da64801de84061b351bc2ef99c6504e9ba262be.jpg) +(e) 10 phases TinyImagNet + +![](images/3c4465a177f407ee62a6bf101658b4c2ca3a39a018fd940bda6f93c3908c4757.jpg) +(f) 20 phases TinyImagNet + +![](images/e7798513d454281858485982b661bd0a6d6bd684a1e3e302c6d98fe00dee8656.jpg) +(g) 10 phases ImagNet-Subset + +![](images/11808d0c60e6390a082be51f4a13421b33c38840579fc9068a4c6b8ccb97fa9a.jpg) +Figure 8. Statistics of similarity on the incremental samples. + +
CIFAR-100TinyImageNet
Method5102051020
iCaRL-CNN42.1345.6943.5436.8936.7045.12
iCaRL-NCM24.9028.3235.5327.1528.8937.40
EEIL23.3626.6532.4025.5625.9135.04
UCIR21.0025.1228.6520.6122.2533.74
LwF.mc44.2350.4755.4654.2654.3763.54
MUC40.2847.5652.6551.4650.2158.00
PASS25.2030.2530.6118.0423.1130.55
Ours18.3719.4819.009.1714.0614.20
+ +Table 4. Results of average forgetting on 5, 10 and 20 phases. + +# 5.5. Comparison with SOTA + +To better assess the overall performance of our scheme, we compare it to the SOTA of NECIL (EWC*, LwF_MC*, MUC*, SDC and PASS) and some classical methods of exemplar-based CIL (iCARL*, EEIL* and UCIR*). + +Average accuracy and average forgetting. As shown in Table 3, compared to the SOTA of non-exemplar methods $(\mathrm{E} = 0)$ , our method achieves average improvement of 3, 3 and 6 points on CIFAR-100, TinyImageNet and ImageNet-Subset, respectively. The performance of our method is comparable to the classical exemplar-based methods $(\mathrm{E} = 20)$ , which shows that our scheme further reduces the impact of exemplars on CIL models. To provide further insight into the behaviors of different methods, we compare their average forgetting of all phases. As shown in Table 4, our method achieves much lower average forgetting, resisting catastrophic forgetting well in the absence of exemplars. + +Trend of accuracy. To analyze the trend of different methods, we show the detailed accuracy curves on three datasets. As shown in Fig. 7, our method is superior at almost all phases, striking a better stability-plasticity balance. It can be seen that the difficulty increases as the number of incremental phases (P) increases. In this process, the advantage of our method are even expanding, such as in TinyImageNet. Whether in the smaller CIFAR-100 or the + +larger ImageNet-Subset dataset, our method has a notable advantage, demonstrating its robustness. + +# 6. Conclusion and Discussion + +In this paper, a novel self-sustaining representation expansion scheme is presented for the NECIL task. A dynamic structure reorganization strategy is first proposed to optimize the newly incremental features in a side branch while maintaining the old feature distribution from the structurally expanded direction, and then the distillation process is arranged in the main branch. In particular, a prototype selection mechanism is integrated into the joint training to enhance the distinction between the old and new classes. Experimental results show that our method is superior in both performance and adaptability to the state-of-the-art methods, especially in the multi-phase process. + +Acknowledgments. Supported by National Key R&D Program of China under Grant 2020AAA0105700, National Natural Science Foundation of China (NSFC) under Grants 61872327 and U19B2038, Major Special Science and Technology Project of Anhui (No. 012223665049), the University Synergy Innovation Program of Anhui Province under Grants GXXT-2019-025. + +# References + +[1] Francisco M Castro, Manuel J Marín-Jiménez, Nicolas Guil, Cordelia Schmid, and Karteek Alahari. End-to-end incremental learning. In Proceedings of the European conference on computer vision (ECCV), pages 233-248, 2018. +[2] Nitesh V Chawla, Kevin W Bowyer, Lawrence O Hall, and W Philip Kegelmeyer. Smote: synthetic minority oversampling technique. Journal of artificial intelligence research, 16:321-357, 2002. +[3] Zhen Cheng, Zhiwei Xiong, Chang Chen, Dong Liu, and Zheng-Jun Zha. Light field super-resolution with zero-shot learning. 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At the heart of our framework lies an algorithm that investigates contexts of data on the embedding space to predict their class-equivalence relations as pseudo labels. The algorithm enables efficient end-to-end training since it demands no off-the-shelf module for pseudo labeling. Also, the class-equivalence relations provide rich supervisory signals for learning an embedding space. On standard benchmarks for metric learning, it clearly outperforms existing unsupervised learning methods and sometimes even beats supervised learning models using the same backbone network. It is also applied to semi-supervised metric learning as a way of exploiting additional unlabeled data, and achieves the state of the art by boosting performance of supervised learning substantially. + +# 1. Introduction + +Understanding similarities between data is at the heart of many machine learning tasks such as data retrieval [29, 37, 47, 48], face verification [35, 45], person re-identification [7, 56], few-shot learning [41, 46, 49], and representation learning [29, 52, 61]. Metric learning embodies the perception of similarity by learning an embedding space where the distance between a pair of data represents their inverse semantic similarity. Also, the mapping from data to such a space is typically modeled by deep neural networks. + +Recent advances in metric learning rely heavily on supervised learning using large-scale datasets. Manual annotation of such datasets is however costly, and thus could limit the class diversity of training data and in consequence the generalization capability of learned models. Unsupervised metric learning has been studied to resolve this issue. Exist- + +![](images/7a2a9b5a8007354d799ea96041af74391dbdbeb8c5441f7edc55bb7f26e93252.jpg) +Figure 1. Accuracy in Recall@1 versus embedding dimension on the CUB-200-2011 [54] dataset using GoogleNet [50] backbone. Superscripts denote embedding dimensions and $\dagger$ indicates supervised learning methods. Our model with 128 embedding dimensions outperforms all previous arts using higher embedding dimensions and sometimes surpasses supervised learning methods. + +ing methods in this line of research mainly synthesize class information of training data by assigning a surrogate class per training instance [13, 55, 59, 60] or discovering pseudo classes through $k$ -means clustering [3, 4, 26, 33, 34, 57], hierarchical clustering [57], or random walk [25]. Although these methods have demonstrated impressive results without using groundtruth labels in training, they often fail to capture intra-class variation [13, 55, 59, 60] or impose substantial computational burden due to the off-the-shelf techniques [3, 4, 25, 26, 33, 34, 57]. + +In this paper, we propose a new method for unsupervised metric learning that addresses the aforementioned limitations of previous work and achieves the state of the art as shown in Fig. 1. The major contribution of this paper is two-fold. First, we introduce a novel, end-to-end self-taught metric learning framework (STML), whose overall pipeline is illustrated in Fig. 2. Unlike the existing works, it predicts class-equivalence relations between data within each mini-batch by self-exploration and leverages the predicted relations as synthetic supervision for metric learning. Our framework manages two embedding networks, namely + +![](images/10e24862828d58973d5a179ed1ae349da288dcf48da1d659d8ac0876fc655628.jpg) +Figure 2. An overview of our STML framework. First, contextualized semantic similarity between a pair of data is estimated on the embedding space of the teacher network. The semantic similarity is then used as a pseudo label, and the student network is optimized by relaxed contrastive loss with KL divergence. Pink arrows represent backward gradient flows. Finally, the teacher network is updated by an exponential moving average of the student. The student network learns by iterating these steps a number of times, and its backbone and embedding layer in light green are considered as our final model. + +teacher and student whose backbone are initialized identically. Class-equivalence between a pair of data is approximately estimated as their semantic similarity on the embedding space of the teacher network. The predicted similarity is used as a soft pseudo label for learning the student model, and the teacher model is in turn updated by a momentum-based moving average of the student. Iterating this process evolves the student model progressively. + +The success of STML depends heavily on the quality of predicted semantic similarities, and our second contribution lies in the way of estimating semantic similarities using contexts. Specifically, given a pair of data, we compute their semantic similarity considering the overlap of their contexts (i.e., neighborhoods in the embedding space) as well as their pairwise distance. We found that the contextualized semantic similarity approximates class-equivalence precisely. Further, since it has a real value indicating the degree of semantic similarity, it provides rich information beyond binary class-equivalence. Also, since it requires no external module nor memory banks [20, 31], it makes STML efficient and concise. To further enhance the quality of predicted semantic similarity, we design the teacher network to learn a higher dimensional embedding space than the student counterpart. This asymmetric design of the two networks allows the teacher to provide more effective supervision thanks to its improved expression power while the student, i.e., our final model, remains compact. + +To the best of our knowledge, STML is the only unsupervised metric learning method that can consider semantic relations between data in end-to-end training without introducing off-the-shelf techniques. Compared to the instance-level surrogate classes [13, 55, 59, 60], pseudo labels generated and exploited by STML are more appropriate + +to capture semantic relations between data since they indicate class-equivalence relations. Also, unlike previous work based on pseudo labeling [3, 4, 25, 26, 33, 57], STML employs no external algorithm and thus allows training to be efficient, end-to-end, and less sensitive to hyper-parameters. Further, it is naturally applied to semi-supervised metric learning [14] as well as unsupervised metric learning. + +We first evaluate STML on standard benchmarks for metric learning [32, 48, 54], where it largely outperforms existing unsupervised learning methods. Surprisingly, sometimes it even beats some of supervised learning models using the same backbone network as shown in Fig. 1. Beyond that, its efficacy is demonstrated on two benchmarks for semi-supervised metric learning [14], where it substantially outperforms previous work as well. + +# 2. Related Work + +Unsupervised metric learning has been mainly addressed in two different directions, instance discrimination [13, 55, 59, 60] and pseudo labeling [3, 4, 25, 26, 33, 34, 57]. Following the contrastive learning strategy [2, 6, 8, 20], instance discrimination methods assign a unique label per training instance and learn embedding spaces where different instances are well discriminated. Unfortunately, they have a trouble modeling variations within each latent class. On the other hand, pseudo labeling methods discover pseudo classes by applying off-the-shelf algorithms like $k$ -means clustering [3, 4, 26, 33, 34], hierarchical clustering [57] and random walk [25] to unlabeled training data. Such methods can consider the class-equivalence relations between training data by utilizing existing supervised metric learning losses [19, 45, 53] with pseudo labels. How- + +ever, the major drawback of these methods is their prohibitively high complexity imposed by the auxiliary algorithms, which obstructs end-to-end training. + +Semi-supervised metric learning, recently introduced by Duan et al. [14], assumes that a training dataset consists of both labeled and unlabeled data. The previous work discovers and assigns pseudo labels to unlabeled training data via $k$ -means clustering. Unfortunately, it also suffers from the aforementioned drawbacks of the unsupervised learning using pseudo labeling. + +Self-supervised representation learning aims at learning high-quality intermediate features to generalize to other downstream tasks. To this end, various annotation-free pretext tasks have been proposed, e.g., rotation prediction [17], solving jigsaw puzzle [38], image colorization [62], and image inpainting [40]. Pseudo labeling also has been widely used as it allows to learn models using conventional losses; existing methods in this direction discover pseudo classes by clustering [4] or treat each training instance as a surrogate class [6, 13, 20, 55]. Also, as an extension of the surrogate class, nearest neighbors have been leveraged as a positive set for self-supervised learning [15, 23, 31], but they often produce noisy labels unless a sufficiently trained embedding space is provided in advance. + +# 3. Proposed Method + +This section first presents an overview of our self-taught metric learning framework, dubbed STML. We then describe the each step of STML in detail and how to estimate the contextualized semantic similarity, which is the synthetic supervision for our framework. + +# 3.1. Overview + +STML enables efficient end-to-end training without using any off-the-shelf technique, while capturing semantic relations between data by generating and exploiting pseudo labels that approximate their class-equivalence. + +Fig. 2 illustrates the overall pipeline of STML. It manages two embedding networks with the identically initialized backbone: a teacher and a student. The teacher network is used to estimate semantic similarities between data as their approximate class-equivalence relations, which are in turn used as synthetic supervision for training the student network. In particular, the teacher model leverages a high-dimensional (e.g., 1024 or 2048) embedding layer $g^t$ with the backbone encoder $\phi^t$ of the teacher. The use of the high dimensional space allows the teacher embedding layer to encode richer information and produce more reliable semantic similarity. Our student model has two parallel embedding layers $f^s$ and $g^s$ that share the backbone encoder $\phi^s$ . $f^s$ is the embedding layer of our final model, and has a lower dimension (e.g., 128 or 512) to learn a compact embedding space. $g^s$ is an auxiliary layer dedicated to + +Algorithm 1 Self-taught metric learning +Input: teacher model $t$ , student model $s$ , kernel bandwidth $\sigma$ , momentum $m$ , batch size $n$ . +1: set $\theta_t = \theta_{\phi^t} \cup \theta_{g^t}$ , $\theta_s = \theta_{\phi^s} \cup \theta_{g^s}$ +2: Identically initialize the backbone of $t$ and $s$ . +3: for number of epochs do +4: Construct mini-batches using nearest neighbor + batch construction. ▷ Step #1 +5: for number of iterations do +6: for all samples in a mini-batch $\{x_k\}_{k=1}^n$ do +7: $z_k^t \gets (g^t \circ \phi^t)(x_k)$ +8: $z_k^{f_s} \gets (f^s \circ \phi^s)(x_k)$ , $z_k^{g_s} \gets (g^s \circ \phi^s)(x_k)$ +9: end for +10: for all $i \in \{1, \dots, n\}$ and $j \in \{1, \dots, n\}$ do +11: $w_{ij}^P \gets \exp(-||z_i^t - z_j^t||_2^2/\sigma)$ +12: compute $w_{ij}^C$ using Eq. (7, 8, 9). +13: $w_{ij} \gets \frac{1}{2}(w_{ij}^P + w_{ij}^C)$ +14: end for +15: compute $\mathcal{L}_{\mathrm{STML}}$ using Eq. (3) and optimize $t$ . +16: $\theta_t \gets m\theta_t + (1 - m)\theta_s$ +17: end for +18: end for +19: return student model $s$ + +continually updating the teacher embedding layer $g^{t}$ , and thus having the same output dimension with that of $g^{t}$ . + +Algorithm 1 describes the procedure of STML in detail. First, the teacher network estimates semantic similarities that approximate class-equivalence relations between data, which are in turn used as synthetic supervision for training the student network. Then the teacher network is updated by the momentum-based moving average of the student. Our final model is the student network obtained by iterating this alternating optimization a predefined number of times. In the next section, we will elaborate each step of STML. + +# 3.2. Self-Taught Metric Learning Framework + +Step #1: Nearest neighbor batch construction. The way of constructing mini-batches for training has a massive impact on performance in metric learning [16, 44]. One of the most widely used methods for batch construction is the $pk$ -sampling: It randomly chooses $p$ unique classes, and then randomly samples $k$ instances per class. Since this method leverages class labels of training data, it is however prohibited in an unsupervised learning setting. We instead propose a new strategy based on the nearest neighbor search. For each mini-batch, it randomly samples $q$ queries and then searches for $k - 1$ nearest neighbors of each query; including both queries and their nearest neighbors, the mini-batch becomes of size $qk$ . Our strategy is simple, fast, yet allows mini-batches to include diverse and relevant samples. + +Step #2: Generating synthetic supervision. Supervised metric learning methods in general employ as supervision class-equivalence relations between data, which are how- + +ever not available in our setting. STML instead approximates the class-equivalence relations by semantic similarities between data on the teacher embedding space, which are used as synthetic soft supervision for learning the student model. The major challenge is that the teacher embedding space is not mature enough to grasp the semantic relations between data at early stages of unsupervised learning. We thus propose contextualized semantic similarity, which measures the similarity between a pair of data while considering their contexts on the teacher embedding space; its details are presented in Sec. 3.3. + +Step #3: Learning the student model. We simultaneously optimize the two branches of the student model using the contextualized semantic similarities as synthetic supervision. Since its value is soft, however, the contextualized semantic similarity cannot be incorporated with the ordinary metric learning losses that take discrete labels as supervision. We thus employ the relaxed contrastive loss [28], which is designed to utilize soft relational labels for metric learning. Let $w_{ij}$ be the contextualized semantic similarity between $x_i$ and $x_j$ , and $z_i^{f_s}$ denote the student embedding vector of $x_i$ generated by $f^s$ . Defining $d_{ij}^{f_s} := ||z_i^{f_s} - z_j^{f_s}||_2 / (\frac{1}{n}\sum_{k = 1}^n ||z_i^{f_s} - z_k^{f_s}||_2)$ as the relative distance between $f_i^s$ and $f_j^s$ , the loss is then given by + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {R C}} \left(\mathcal {Z} ^ {f _ {s}}\right) = \frac {1}{n} \sum_ {\substack {i = 1 \\ n}} ^ {n} \sum_ {\substack {j \neq i \\ n}} ^ {n} w _ {i j} \left(d _ {i j} ^ {f _ {s}}\right) ^ {2} \tag{1} \\ + \frac {1}{n} \sum_ {i = 1} ^ {n} \sum_ {j \neq i} ^ {n} (1 - w _ {i j}) \left[ \delta - d _ {i j} ^ {f _ {s}} \right] _ {+} ^ {2}, \\ \end{array} +$$ + +where $\mathcal{Z}^{f_s}$ is all student embedding vectors generated by $f^s$ , $n$ is the number of samples in the batch, and $\delta$ is a margin. The contextualized semantic similarity serves as the weights for the attracting and repelling terms of the loss, and thus determines the magnitude of the force that pulls or pushes a pair of data on the student embedding space. Note that $g_{s}$ is trained in the same manner on $f_{s}$ . We additionally apply self-distillation to further utilize complex higher dimensional information for lower dimensional space. Following [43], we use Kullback-Leibler divergence as objective of self-distillation: + +$$ +\mathcal {L} _ {\mathrm {K L}} \left(\mathcal {Z} ^ {f _ {s}}, \mathcal {Z} ^ {g _ {s}}\right) = \frac {1}{n} \sum_ {i = 1} ^ {n} \sum_ {j \neq i} ^ {n} \psi \left(- d _ {i j} ^ {g _ {s}}\right) \log \frac {\psi \left(- d _ {i j} ^ {g _ {s}}\right)}{\psi \left(- d _ {i j} ^ {f _ {s}}\right)}, \tag {2} +$$ + +where $\psi (\cdot)$ is softmax operation. Note that the gradientflow of $g_{s}$ is truncated. In summary, STML trains the two branches $f_{s}$ and $g_{s}$ of the student model by minimizing the overall loss defined as + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {S T M L}} \left(\mathcal {Z} ^ {f _ {s}}, \mathcal {Z} ^ {g _ {s}}\right) = \frac {1}{2} \left[ \mathcal {L} _ {\mathrm {R C}} \left(\mathcal {Z} ^ {f _ {s}}\right) + \mathcal {L} _ {\mathrm {R C}} \left(\mathcal {Z} ^ {g _ {s}}\right) \right] \tag {3} \\ + \mathcal {L} _ {\mathrm {K L}} \left(\mathcal {Z} ^ {f _ {s}}, \mathcal {Z} ^ {g _ {s}}\right). \\ \end{array} +$$ + +Step #4: Momentum update of the teacher model. The teacher model should be updated as the student model is trained so that the synthetic supervision computed from the teacher embedding space is enhanced progressively. The simplest update strategy is to replace the teacher model with the student counterpart at every iteration. However, this could deteriorate the consistency of the synthetic supervision over iterations, which leads to unstable training of the student model. We thus update the teacher model by the momentum-based moving average of the student, except for the embedding layer $f^{s}$ since the teacher model has only a high-dimensional one. Let $\theta_{t}$ be the parameters of the teacher model and $\theta_{t}$ be the parameters of $\phi_{t}$ and $g_{t}$ . Then $\theta_{t}$ is updated by + +$$ +\theta_ {t} \leftarrow m \theta_ {t} + (1 - m) \theta_ {s}, \tag {4} +$$ + +where $m \in [0,1]$ is the coefficient that controls the momentum update rate, slowing down the update of the teacher model as its value increases. + +# 3.3. Contextualized Semantic Similarity + +The quality of predicted semantic similarities is of vital importance in STML since they are the only supervision for training. However, it is not straightforward to compute reliable semantic similarities especially at early stages of unsupervised learning where the teacher network is significantly incomplete. To overcome this challenge, we propose to use context, i.e., neighborhood on a data manifold. + +Our key idea is not to rely on the relations considering two images of interest only, but to figure out their indirect semantic relations via their contexts. Their multiple indirect relations can contribute to capturing common patterns frequently observed within each class and thus understanding the underlying class-equivalence relations. To this end, we design the contextualized semantic similarity. Given a pair of samples, their contextualized semantic similarity is defined as a combination of their pairwise similarity and contextual similarity on the teacher embedding space. + +Pairwise similarity. The pairwise similarity of two samples $x_{i}$ and $x_{j}$ , denoted by $w_{ij}^{P}$ , is given by + +$$ +w _ {i j} ^ {P} = \exp \left(- \frac {\left| \left| z _ {i} ^ {t} - z _ {j} ^ {t} \right| \right| _ {2} ^ {2}}{\sigma}\right), \tag {5} +$$ + +where $z_{i}^{t}$ is the teacher embedding vector of $x_{i}$ and $\sigma$ is the Gaussian kernel bandwidth. This kind of similarity has been known to encode rich information about relations of $x_{i}$ and $x_{j}$ when the teacher embedding space is pre-trained in a fully supervised manner [28], but is often broken in unsupervised metric learning. We thus supplement it with the contextual similarity, which is detailed below. + +Contextual similarity. The underlying assumption of the contextual similarity is that the more two samples semantically similar, the larger their contexts overlap. One may + +consider nearest neighbors of a data point on the teacher embedding space as its context, but they often include irrelevant data when the embedding space is not sufficiently trained yet. We thus instead consider $k$ -reciprocal nearest neighbors as context since they are known to discover highly correlated candidates [42, 63]. The set of $k$ -reciprocal nearest neighbors of a data point $x_{i}$ is given by + +$$ +R _ {k} (i) = \{j | (j \in N _ {k} (i)) \wedge (i \in N _ {k} (j)) \}, \tag {6} +$$ + +where $N_{k}(i)$ is the $k$ -nearest neighbors of $x_{i}$ , including itself (i.e., $i \in N_{k}(i)$ ), in the current mini-batch. The initial form of contextual similarity measures the degree of overlap between $R_{k}(i)$ and $R_{k}(j)$ while considering whether $x_{i}$ and $x_{j}$ are in $k$ -reciprocal nearest neighbor relation. Since the size of the neighbor set of $x_{i}$ and $x_{j}$ would be different, we design an asymmetric Jaccard similarity as + +$$ +\tilde {w} _ {i j} ^ {C} = \left\{ \begin{array}{l l} \frac {\left| R _ {k} (i) \cap R _ {k} (j) \right|}{\left| R _ {k} (i) \right|}, & \text {i f} j \in R _ {k} (i), \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {7} +$$ + +In addition, we adopt the idea of query expansion [1, 10, 11] to further improve its reliability. Specifically, $\tilde{w}_{ij}^{C}$ is reformulated as the average of the contextual similarities between $x_{j}$ and nearest neighbors of $x_{i}$ as follows: + +$$ +\hat {w} _ {i j} ^ {C} = \frac {1}{| N _ {\frac {k}{2}} (i) |} \sum_ {h \in N _ {\frac {k}{2}} (i)} \tilde {w} _ {h j} ^ {C}. \tag {8} +$$ + +The expanded version in Eq. (8) is not symmetric anymore. To ensure symmetry, the final form of the contextual similarity is defined as the average of $\hat{w}_{ij}^{C}$ and its transpose, which is given by + +$$ +w _ {i j} ^ {C} = w _ {j i} ^ {C} = \frac {1}{2} \left(\hat {w} _ {i j} ^ {C} + \hat {w} _ {j i} ^ {C}\right). \tag {9} +$$ + +Contextualized semantic similarity. Finally, the contextualized semantic similarity between $x_{i}$ and $x_{j}$ is defined as the average of their pairwise similarity in Eq. (5) and contextual similarity in Eq. (9): + +$$ +w _ {i j} = \frac {1}{2} \left(w _ {i j} ^ {P} + w _ {i j} ^ {C}\right). \tag {10} +$$ + +Note that both of $w_{ij}^{P}$ and $w_{ij}^{C}$ lie within [0, 1] thus their scales are balanced. The contextualized semantic similarity effectively represents semantic relatedness between data by considering both of their pairwise relation and context. We found that the contextualized semantic similarity is highly correlated with groundtruth class-equivalence, which is empirically verified in Sec. 4.1.4. + +# 4. Experiments + +This section validates the effectiveness of STML on two metric learning tasks with lack of supervision, i.e., unsupervised metric learning and semi-supervised metric learning. + +# 4.1. Unsupervised Metric Learning + +We consider the student embedding model trained by STML as our final model, which is evaluated and compared with state-of-the-art unsupervised metric learning methods and representative self-supervised learning methods. + +# 4.1.1 Experimental Setup + +Datasets and evaluation. The models are evaluated and compared on three benchmark datasets, i.e., CUB-200-2011 (CUB) [54], Cars-196 (Cars) [32], and Stanford Online Product (SOP) [48]; for their train-test splits, we directly follow the standard protocol presented in [60]. Performance on these datasets is evaluated by $\mathrm{Recall}@\bar{k}$ , the fraction of queries that have at least one relevant sample in their $k$ -nearest neighbors on a learned embedding space. + +**Embedding networks.** For comparisons to previous work, we employ GoogleNet [50] and Inception-BN [24] as our teacher and student embedding model architecture. The dimension of embedding layers $g_{t}$ and $g_{s}$ are set as the output size of the last pooling, and that of $f_{s}$ follows each experimental setting. We append an $l_{2}$ normalization layer on top of the teacher so that the Euclidean distances in Eq. (5) are bounded for computing semantic similarities stably. + +Implementation details. The student model of STML is optimized by AdamP with Nesterov momentum [22] for 90 epochs on a single Titan RTX; the learning rate is initialized to $10^{-4}$ and scaled down by the cosine decay function [36]. Training images are randomly cropped to $227 \times 227$ and flipped horizontally at random while test images are resized to $256 \times 256$ then center cropped. For all experiments, $\sigma$ in Eq. (1) is set to 3. The margin $\delta$ , momentum coefficient $m$ and the number of nearest neighbors $k$ are 1.0, 0.999 and 10 on the CUB and Cars datasets, and 0.9, 0.9 and 4 on the SOP dataset. Note that $k$ in the nearest neighbor batch construction and that in Eq. (6) are identical. + +Batch construction. Nearest neighbors used to construct mini-batches in STML are computed on the student embedding space and update at every epoch. On the CUB and Cars datasets, each mini-batch consists of 120 images including 24 queries and their 4 nearest neighbors. Since the SOP dataset has a tiny number of samples per class, we construct a mini-batch with 60 queries and their top-1 neighbors on the dataset. Also, all images are randomly augmented twice following the multi-view augmentation strategy in [28]. + +# 4.1.2 Quantitative Results + +For fair comparisons to previous work, performance evaluation is done in the following settings: GoogleNet with 64/128/512 embedding dimensions, and Inception with BatchNorm with 512 embedding dimensions. All backbone networks in this experiment are pre-trained on ImageNet. The results on the three datasets are summarized in Table 1. + +
MethodsArch.CUBCarsSOP
R@1R@2R@4R@1R@2R@4R@1R@10R@100
Supervised
ABIER [39]G51257.569.778.382.089.093.274.286.994.0
ABE [30]G51263.074.583.385.290.594.076.388.494.8
MS [53]BN51265.777.086.384.190.494.078.290.596.0
PA [27]BN51269.178.986.186.491.995.079.290.796.2
Unsupervised (Using ImageNet pre-trained embedding networks)
MOM [25]G6445.357.868.6------
ROUL [26]G6452.064.074.5------
STMLG6455.067.578.642.054.465.964.979.689.3
MOM [25]G128---35.548.260.643.357.273.2
Exemplar [13]G12838.250.362.836.548.159.245.060.375.2
NCE [55]G12839.251.463.737.548.759.846.662.376.8
DeepCluster [4]G12842.954.165.632.643.857.034.652.666.8
ISIF [60]G12846.259.070.141.352.363.648.964.078.0
PSLR [59]G12848.160.171.843.754.866.151.166.579.8
ROUL [26]G12856.768.478.345.056.968.453.468.881.7
SAN [34]G12855.968.078.644.255.566.858.773.184.6
STMLG12859.771.281.049.060.471.365.880.189.9
UDML-SS [3]G51254.766.977.445.156.166.563.578.088.6
TAC-CCL [33]G51257.568.878.846.156.967.563.977.687.8
UHML [57]G51258.970.680.447.758.970.365.178.288.3
STMLG51260.671.781.550.561.871.765.379.889.8
UDML-SS [3]BN51263.775.083.8------
STMLBN51268.078.886.466.274.581.969.782.791.2
+ +Table 1. Performance of the unsupervised and supervised metric learning methods on the three datasets. Their network architectures are denoted by abbreviations, G-GoogleNet [50], BN-Inception with BatchNorm [24], where superscripts denote their embedding dimensions. + +
MethodsSOP
R@1R@10R@100
NCE [55]34.449.065.2
ISIF [60]39.754.971.0
PSLR [59]42.357.772.5
ROUL [26]45.460.574.8
SAN [34]46.361.977.0
STML60.774.885.2
+ +Table 2. Performance on the SOP dataset using ResNet18 without pre-trained weights. + +On all the datasets, our model achieves state-of-the-art performance in every setting. It improves the previous best score by a large margin, from $3.8\%$ to $7.1\%$ at $\text{Recall} @ 1$ with the 128 embedding dimensions. We note that our model clearly surpasses all existing models whose embedding dimension is 4 times higher on all the datasets, sometimes at 8 times higher. Moreover, on the CUB dataset, it even outperforms some of the supervised learning methods, e.g., ABIER [39] and MS [53], given the same embedding networks. These results suggest that our framework allows the model to learn compact yet effective embedding spaces by providing high-quality synthetic supervision. Last but + +not least, STML enables more efficient learning than existing pseudo labeling methods due to no use of off-the-shelf algorithms, especially on large-scale SOP dataset. + +# 4.1.3 Unsupervised Metric Learning from Scratch + +We demonstrate that STML is also effective for metric learning from scratch without pre-training on ImageNet. Following [60], we employ randomly initialized ResNet18 [21] with 128 embedding dimensions as the backbone network, and evaluate our model trained on the SOP dataset. As shown in Table 2, our model substantially outperforms existing methods including those for self-supervised representation learning in this setting. This result suggests that STML can generate reliable pseudo labels even on a randomly initialized embedding space, and our model trained by STML well generalizes to unseen class. + +# 4.1.4 In-depth Analysis + +Correlation between similarities and class-equivalence. To justify the contextualized semantic similarity, we compare our three similarity metrics (i.e., pairwise similarity $w_{ij}^{P}$ , contextual similarity $w_{ij}^{C}$ , contextualized semantic sim + +![](images/f02b85a3a303af82c53be02528798f259ef7ea3d79fe38a990bd56f7cf82098d.jpg) +Figure 3. Comparison between the contextualized semantic similarity and its two components in terms of class-equivalence prediction accuracy on the CUB dataset with pre-trained weights (left) and SOP dataset without pre-trained weights (right). + +
MethodsCUBCars
R@1R@1
STML60.650.5
w/o contextual pairwise similarity44.240.2
w/o pairwise similarity56.045.0
w/o relaxed contrastive loss53.438.7
w/o momentum update56.846.1
w/o NN batch construction54.644.8
w/o KL divergence59.249.4
+ +ality $w_{ij}$ ) in terms of how well they are correlated with class-equivalence, i.e., the groundtruth for supervised metric learning. Specifically, we predict class-equivalence of every pair of data by thresholding its semantic similarities, and count the accuracy of such predictions at various threshold settings. Fig. 3 presents AUROC scores of our contextualized semantic similarity and its two components during training. The results suggest that the accuracy of the pairwise similarity relies heavily on the quality of the teacher embedding space, while the contextual similarity helps infer class-equivalence correctly even at early stages of training without pre-trained weights. The contextualized semantic similarity achieves the best consistently, which also indicates that the pairwise and contextual similarities are complementary to each other. + +Ablation study. The impact of each component in STML is reported in Table 3. The results in the table are obtained by using GoogleNet with 512 embedding dimensions. The analysis reveals that the contextual similarity contributes most to the performance while the pairwise similarity has the minimum impact; Fig. 3 also supports this observation. Even if both similarities are used, the performance is largely degraded when using the conventional contrastive loss [19] instead of the relaxed version since the conventional one quantizes our semantic similarity into a binary value, leading to significant information loss. The momentum-based update of the teacher model and the nearest neighbor batch construction strategy also have significant impacts; the performance degrades substantially when the teacher model is + +![](images/a6fff14d7ae99f2b17e55e9a954054b3a67eccf2d467515e51557288951af676.jpg) +Figure 4. Recall@1 versus the hyper-parameters $k$ and $\sigma$ on the CUB and Cars datasets. Larger markers indicate our default experimental setting. + +Table 3. Ablation study of the components in STML on the CUB and Cars datasets. + +
MethodsArch.CUBCarsSOP
R@1R@1R@1
MoCo [20]G12848.337.253.3
BYOL [18]G12847.731.548.7
MSF [31]G12846.030.541.6
STMLG12859.749.065.8
MoCo [20]G51251.039.053.4
BYOL [18]G51250.938.551.2
MSF [31]G51249.632.547.8
STMLG51260.650.565.3
+ +Table 4. Comparison between STML and recent self-supervised representation learning methods using momentum encoder. + +updated directly by the student counterpart or the batch construction strategy is replaced with a random sampling. The KL divergence loss has relatively little influence compared to other components. + +Effect of hyper-parameters. We investigate how much sensitive STML is to the hyper-parameters $k$ and $\sigma$ . Specifically, we measure performance of STML employing GoogleNet with 512 embedding dimensions on the CUB and Cars datasets while varying values of $k$ and $\sigma$ . The results shown in Fig. 4 suggest that the performance of STML is consistently high when $k < 14$ , and $\sigma$ has virtually no effect on the performance if $\sigma > 1$ on both datasets. Moreover, whenever $k < 14$ our model outperforms all existing unsupervised metric learning methods. Note that our final results reported in Table 1 are not the best scores in Fig. 4 since we did not tune the hyper-parameters on the test splits. + +Comparison with recent SSL methods. STML has components used in recent self-supervised representation learning (SSL) methods such as the momentum encoder. To validate that the improvements of our framework do not originate from its structure, such methods are compared with STML under the same setting. Table 4 shows that MoCo and BYOL clearly underperform our method in all settings and achieve similar performance to unsupervised metric learning methods based on instance-level surrogate classes. Although they are structurally similar to STML, the reason for the degradation of performance is that they cannot capture intra-class variation unlike our method, and are + +
MethodsArch.Init.CUBCars
MAP@RRPR@1MAP@RRPR@1
Supervised
Contrastive [9]R50512ImageNet25.035.865.326.036.481.2
MS [53]R50512ImageNet26.437.566.328.338.385.2
Proxy-An anchor [27]R50512ImageNet28.339.169.930.539.987.7
Contrastive [9]R50512SwAV [5]29.339.871.231.741.288.1
MS [53]R50512SwAV [5]29.240.270.833.442.789.3
Proxy-An anchor [27]R50512SwAV [5]31.742.074.635.144.190.4
Semi-supervised (Labeled dataset + Additional unlabeled dataset)
SLADE (MS) [14]R50512ImageNet30.941.969.632.141.587.4
STML (MS)R50512ImageNet37.847.975.538.446.193.0
SLADE (MS) [14]R50512SwAV [5]33.944.474.138.046.991.5
STML (MS)R50512SwAV [5]35.245.376.238.246.593.2
+ +Table 5. Performance of the supervised and semi-supervised methods on the two datasets. Network architectures of the methods are all ResNet50 (R50) [21] and superscripts denote their embedding dimensions. Also, the column "Init." indicates whether the models are pre-trained on ImageNet or by SwAV. Our model and SLADE are all fine-tuned with the MS loss. + +limited in representing semantic similarities between data. + +# 4.2. Semi-supervised Metric Learning + +Semi-supervised metric learning aims to improve performance of supervised metric learning by exploiting additional unlabeled data [14]. STML can be employed for this task naturally since it provides a way of using the unlabeled data for training by predicting their class-equivalence relations as synthetic supervision. In this section, we validate the efficacy of STML for semi-supervised metric learning and compare it with SLADE [14], the first and only existing method for the task, on the CUB and Cars datasets. + +# 4.2.1 Experimental Setup + +Datasets and evaluation. We directly adopt the evaluation protocol of SLADE. Specifically, we employ two combinations of labeled and unlabeled datasets, {CUB [54], NABirds [51]} and {Cars [32], CompCars [58]}, and three performance metrics, MAP@R, RP, and Recall@1. + +Embedding networks. For comparisons to SLADE, we employ ResNet50 [21] with 512 embedding dimensions as the backbone network of the teacher and student models. Before applying STML, these models are pre-trained either on ImageNet [12] or by SwAV [5], then fine-tuned with the MS loss [53] on a labeled dataset (i.e., CUB or Cars). + +Implementation details. In this task, STML adopts an embedding model trained on a labeled dataset as the initial teacher and student models and trains them using both labeled and unlabeled data. Note that it computes and utilizes contextualized semantic similarities as supervision for labeled data as well as unlabeled data. For all experiments, $m$ in Eq. (4) and $\sigma$ in Eq. (10) are set to 0.9999 and 2, respectively, and the rest settings are the same as those for unsupervised metric learning. + +# 4.2.2 Results + +STML is compared with SLADE and state-of-the-art supervised metric learning methods on the two datasets. The results summarized in Table 5 show that STML improves performance of its supervised learning counterpart (i.e., MS) significantly regardless of the model initialization schemes. In particular, it enhances the performance by more than $5\%$ in Recall@1 on both datasets for ImageNet pre-trained setting. Also, STML clearly outperforms SLADE in all the settings except one, where their gap is only $0.4\%$ in RP. + +# 5. Conclusion + +We have proposed STML, a novel end-to-end unsupervised metric learning framework that estimates and exploits semantic relations between samples as pseudo labels. The pseudo labels in STML are estimated by investigating contexts of data as well as their pairwise distances on an embedding space. STML has achieved the state of the art on the three benchmark datasets for unsupervised metric learning, and demonstrated impressive performance even without pre-trained weights. Moreover, it has been applied to semi-supervised learning, and outperformed state of the art on the two benchmark datasets. Unfortunately, like other approaches, STML has a limitation in that it uses ImageNet pre-trained weights in some settings. In the future, we will explore extensions of our method where class labels are never involved in the training. + +Acknowledgement. This work was supported by the NRF grant, the IITP grant, and R&D program for Advanced Integratedintelligence for IDentification, funded by Ministry of Science and ICT, Korea (NRF-2021R1A2C3012728, NRF-2018R1A5-A1060031, NRF-2018M3E3A1057306, No.2019-0-01906 Artificial Intelligence Graduate School Program-POSTECH). + +# References + +[1] Relja Arandjelović and Andrew Zisserman. Three things everyone should know to improve object retrieval. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012. 5 +[2] Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. In Proc. Neural Information Processing Systems (NeurIPS), 2019. 2 +[3] Xuefei Cao, Bor-Chun Chen, and Ser-Nam Lim. Unsupervised deep metric learning via auxiliary rotation loss. arXiv preprint arXiv:1911.07072, 2019. 1, 2, 6 +[4] Mathilde Caron, Piotr Bojanowski, Armand Joulin, and Matthijs Douze. 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However, the over-reliance on these class-agnostic local geometric representations may raise confusion between local parts from different categories that are similar in appearance or spatially adjacent. To address this issue, we argue that mid-level features can be further enhanced with semantic information, and propose semantic-affine transformation that transforms features of mid-level points belonging to different categories with class-specific affine parameters. Based on this technique, we propose Se-maFFiNet for point cloud semantic segmentation, which utilizes the attention mechanism in the Transformer module to implicitly and explicitly capture global structural knowledge within local parts for overall comprehension of each category. We conduct extensive experiments on the ScanNetV2 and NYUv2 datasets, and evaluate semantic-affine transformation on various 3D point cloud and 2D image segmentation baselines, where both qualitative and quantitative results demonstrate the superiority and generalization ability of our proposed approach. Code is available at https://github.com/wangzy22/SemAffiNet. + +# 1. Introduction + +Point cloud semantic segmentation is a fundamental task for both structural representation learning [11, 45, 56] and stereoscopic scene understanding [15, 27, 49] in computer vision. It aims at partitioning the scene space into semanticmeaningful regions based on conformation and geometry knowledge inherited in point cloud layouts. Its successful applications in autonomous driving, robotic manipulation, and virtual reality have been motivating researchers to develop more fine-grained and more accurate solutions. + +![](images/43832e7d2972fffc20fc095346f080c96ba3bfff5e9b58893be1d7db1315fc09.jpg) +Figure 1. Illustration of Semantic-Affine Transformation. The left figure is the input point cloud, with different colors referring to different categories. We select one local part (red circle) and extract its mid-level features, resulting in the top-right figure. Some representations of the points from different categories are entangled with each other in the embedding space, which may be caused by the appearance similarities or spatial adjacency. We propose to perform the semantic-affine transformation on these mid-level features, predicting particular affine parameters for each category respectively. Therefore, once obtaining classification predictions of mid-level points, we can pull points from the same category closer while pushing points from different categories apart via semantic-affine transformation, as is shown in the bottom-right figure. + +Recent methods for point cloud segmentation usually adopt an encoder-decoder architecture as image semantic segmentation [4, 6, 7, 51, 69], ranging from voxel based-ones [11, 20, 52, 67, 71] to point-based ones [34, 46, 54, 60]. Despite the popularity of the encoder-decoder architecture, there still exists the local confusion problem as shown in Figure 1. On the one hand, there are local parts from different categories but with similar shapes, such as the similar + +legs of chairs and desks. On the other hand, adjacent local parts are blended in the input space and may obfuscate the model during segmentation, leaving ambiguous segment boundaries. The reasons are two folds: the heavy use of the local aggregation during feature processing, and the class-agnostic nature of the mid-level features. In the commonly-used encoder-decoder architecture, the mid-level features of the decoder are locally aggregated via convolution or set abstraction. The limitation of receptive fields produces similar feature vectors for visually-similar local parts, and the aggregation operation results in entangled mid-level features for spatially-adjacent local parts. Therefore, it is insufficient to use geometric-only information and the encoder-decoder architecture demands more knowledge to separate similar and entangled local representations. One possible solution to this problem is alleviating the reliance on geometric knowledge and introducing additional semantic information to enrich mid-level features. However, most existing literature fails to fully exploit semantic knowledge in the network design of the encoder-decoder architecture, as semantic annotations are mostly used for data augmentation [8,44,65] or supervision on final prediction [45,46,56]. Therefore, the mid-level features from the intermediate layers are only implicitly or weakly supervised via gradient descent, making them almost class-agnostic. + +To address the local confusion problem, we propose Semantic-Affine Transformation to transform mid-level decoder features with class-specific affine parameters that encode semantic information, which explicitly pulls features from the same category closer and pushes features from different categories apart. In this way, we enhance the semantic representation ability of mid-level features and boost semantic segmentation performance. Based on the proposed semantic-affine transformation, we design a semantic-aware network named SemAffiNet and introduce Transformer [55] to manage semantic information both implicitly and explicitly. The Transformer encoder implicitly communicates geometric information across modalities via the self-attention technique, while the special design of class queries in the Transformer decoder performs explicit semantic-aware reasoning to predict semantic-affine parameters via the cross-attention mechanism. We conduct extensive experiments on the ScanNetV2 [14] dataset and outperform the previous state-of-the-art BPNet [26] baselines. We also evaluate on the NYUv2 [43] dataset to verify the generalization ability of the SemAffiNet model. As the core of SemAffiNet, the proposed semantic-affine transformation is evaluated on both 3D point cloud and 2D image segmentation baselines under various settings, revealing the generalization ability of the proposed transformation. + +In conclusion, the contributions of our paper can be summarized as follows: (1) We propose Semantic-Affine Transformation to enhance the semantic representation ability of + +mid-level features in encoder-decoder segmentation architecture. (2) We propose SemAffiNet to perform semantic-aware segmentation both explicitly and implicitly via special designs of Transformer modules. (3) We conduct experiments on various datasets under different settings, revealing the superiority and generalization ability of our method. + +# 2. Related Work + +Point Cloud Semantic Segmentation. Existing point cloud semantic segmentation methods can be divided into four categories: voxel-based, point-based, projection-based, and hybrid models. Voxel-based methods aim at partitioning 3D space into ordered voxels and translating 2D convolutional encoder-decoder architectures to 3D conditions, leading by VoxNet [40]. The heavy time expense and memory cost have been addressed by later researches, including sparse convolution [11, 20], efficient data structure migration [32, 50] and novel voxelization techniques [52, 67, 71]. Point-based methods directly process points and aggregate local information instead of using conventional regular convolution kernel, leading by PointNet [45] and PointNet++ [46]. Nowadays point-based methods has become the mainstream of point cloud cognition tasks and has been developed into many branches, including MLP-based [16, 18, 25, 45, 46], convolution-based [34, 54, 60, 61] and graph-based [33, 56] posterity. Projection-based methods are mostly designed for efficient processing, including image projection [1, 13] and spherical projection [2, 42, 58, 59]. Hybrid methods are more complicated systems that combine different processing methods or fuse different modality information. Some approaches combine long-range correlations from voxel-based methods and meticulous details from point-based methods [10, 37, 53, 63], while other approaches fuse 2D and 3D knowledge [26, 48]. + +Semantic-Aware Segmentation. As semantic information is critical to the segmentation task, some works elaborately design special semantic-aware approaches to boost semantic segmentation performance [19, 39, 47]. Some methods aim at reasoning context relations differently between same-category pairs and distinct-categories pairs. DependencyNet [35] for image segmentation unifies dependency reasoning at three semantic levels: intra-class, inter-class and global. CGANet [39] for point cloud segmentation utilizes different aggregation strategies between the same category and different categories. Other methods propose multiscale supervision to realize comprehensive semantic guidance. In 2D vision, CPM [57] introduces intermediate supervision periodically while MSS-net [30] proposes layerwise loss. In 3D vision, RFCC [19] puts forward omnisupervision on all levels of the decoder layers. + +Different from the above methods, our method achieves comprehensive semantic awareness via semantic-affine + +![](images/a2cfb773cfb0e2da23e07042591fc229a232aa6972824735e965ceefc9105724.jpg) +(a) SemAffiNet + +![](images/5379c69136baad03800ba166ad96f792dae6f9b9753de8fb0abebb19569e9613.jpg) +(b) Semantic-Affine Transformation Module +Figure 2. Illustration of the proposed network architecture. $(a)$ shows the pipeline of the SemAffNet, which consists of two backbone branches (gray), an implicit semantic-aware module (ISAM, dark blue), and two explicit semantic-aware modules (ESAM, light blue dash square). Moreover, ESAM is composed of a Transformer decoder and a Semantic-Affine Transformation module, which is further illustrated in $(b)$ . We calculate the weighted sum of class-specific affine parameters to obtain semantic-affine parameters for mid-level points, with mid-level classification confidence as linear combination weights. + +transformation for mid-level features. Therefore, we don't need different aggregation modules that increase model scale. Additionally, our semantic guidance for intermediate layers is stronger than merely multi-level supervisions. + +Transformer for Segmentation. Transformer [55] has achieved a great success in many computer vision tasks, such as classification [17, 36], detection [5], and reconstruction [64]. Recent works employ the attention mechanism in Transformer to exploit long-range correlations for deeper context comprehension and better segmentation results [21, 68, 70]. Maskformer [9] proposes a mask classification model that utilizes Transformer to predict binary masks and unifies both semantic- and instance-level segmentation. SOTR [22] proposes to dynamically generating instance segmentation masks based on Transformer attention module. + +While we utilize a similar mask classification structure as Maskformer in our SemAffiNet, we migrate this idea from 2D image processing to 3D point cloud understanding, which is not trivial. Moreover, we propose semantic-affine transformation to further enhance the mask classification pipeline, which brings more progression than mask classification according to our ablation studies. + +# 3. Approach + +In the following section, we will first give an overview of the proposed SemAffiNet in Section 3.1. Then we will + +present details of the architecture, introducing the proposed semantic affine transformation in Section 3.2, revealing how we wrap it into a plug-and-play explicit semantic-aware module in Section 3.3, and presenting the auxiliary implicit semantic-aware module in Section 3.4. Finally, we will introduce the loss function design in Section 3.5. + +# 3.1. Overview + +We elaborately design SemAffiNet to perform the semantic-affine transformation on mid-level features from the conventional encoder-decoder model. Figure 2 shows the overall architecture, which can be divided into the following three parts: (1) Backbone, (2) the Explicit Semantic-Aware Module (ESAM), (3) the Implicit Semantic-Aware Module (ISAM). + +First of all, the backbone choice of SemAffiNet is flexible and our proposed modules can be easily added to any encoder-decoder segmentation architecture. We choose BPNet [26] that consists of two encoder-decoder branches for 2D and 3D modalities to evaluate our proposed semantic-affine transformation. Please refer to the BPNet paper or our supplementary material for further details. + +Most importantly, ESAM wraps our proposed semantic-affine transformation into a plug-and-play module, that explicitly exploits semantic information in mid-level features with specially designed Transformer decoders. As shown Figure 2, we employ two ESAM blocks in light + +![](images/a636109e59e38ba1c6d801923e8cb96704bd84a13a512c7312ce30daf612e33b.jpg) +Figure 3. Illustrations of the Semantic-Affine Transformation. (a) is the original representations of mid-level points. (b) is the underlying distinctive scales and bias for different categories. The arrow directions in (c) represent the regressed class-specific affine parameters. (d) shows the semantic-affine transformation results of mid-level features, which are more classification-friendly. + +blue dash square to manage semantic knowledge from different domains respectively. The Transformer decoder utilizes the cross-attention mechanism to obtain long-range dependencies for better semantic perception, while the following Semantic-Aware Transformation Module transforms mid-level features of backbone decoders with class-specific affine parameters to enlarge semantic distinctions across categories. + +Last but not least, ISAM utilizes the self-attention mechanism in the Transformer encoder to enhance high-level features that are outputs from the backbone encoder and inputs to ESAM. The proposed ISAM fuses multi-modality information and realizes implicit semantic awareness. + +# 3.2. Semantic-Affine Transformation + +As semantic-affine transformation is the key contribution of our paper, we will first introduce its conceptual and technical details in this sub-section. The core idea is predicting semantic-affine parameters for each category and then determining affine parameters for each point based on its classification prediction. + +Suppose there are $N$ classes and the shape of mid-level features $\mathbf{f}^i$ at layer $i$ is $(n_i,d_i)$ , indicating that there are $n_i$ points at layer $i$ and each point is represented by a $d_{i}$ -dim feature vector. From Section 3.3 we can predict categories for each point $p_j^i$ at layer $i$ and obtain a classification confidence vector $\mathbf{a}_j^i = [a_{j1}^i,a_{j2}^i,\dots ,a_{jN}^i],$ $0\leq a_{jk}^{i}\leq 1,1\leq j\leq n_{i},1\leq k\leq N,\sum_{k}a_{jk}^{i} = 1,$ where $a_{jk}^{i}$ denotes confidence of point $p_j$ at layer $i$ belonging to class $k$ . Simultaneously, we regress semantic-affine parameters for each class at layer $i$ , including scale factor $\mathbf{s}^i = \{s_k^i\in \mathbb{R}^{d_i},1\leq k\leq N,s_{kl}^i\geq 0,1\leq l\leq d_i\}$ and offset bias $\mathbf{b}^i = \{b_k^i\in \mathbb{R}^{d_i},1\leq k\leq N\}$ . Further technical details about the learning process of these semantic-aware parameters can be found in Section 3.3. + +Then we can obtain the semantic-specific affine parameters $S_{j}^{i}, B_{j}^{i}$ for each point $p_j$ at layer $i$ via linear combination of the affine parameters family $\mathbf{s}^i$ , $\mathbf{b}^i$ based on per-point + +classification confidence vector $\mathbf{a}_j^i$ : + +$$ +S _ {j} ^ {i} = \sum_ {k} a _ {j k} ^ {i} s _ {k} ^ {i}, \quad B _ {j} ^ {i} = \sum_ {k} a _ {j k} ^ {i} b _ {k} ^ {i} \tag {1} +$$ + +Once normalized with zero-mean and unit covariance, $\hat{f}_j^i = (f_j^i -\mu (f_j^i)) / \sigma (f_j^i)$ can be further enhanced with the semantic-affine transformation to obtain semantic-aware mid-level feature $\tilde{f}_j^i$ , which is used to replace $f_{j}^{i}$ .. + +$$ +\tilde {f} _ {j} ^ {i} = S _ {j} ^ {i} \hat {f} _ {j} ^ {i} + B _ {j} ^ {i} \tag {2} +$$ + +Note that we implement a soft semantic-affine parameters assignment that introduces a linear combination instead of a hard one that restricts the searching space within the exact value of $\mathbf{s},\mathbf{b}$ . In other words, the hard assignment strategy only considers the highest confidence scores of the category predictions and chooses the exact affine parameters accordingly. The reason is that the mid-level points are aggregation results of itself and its neighbors in the adjacent lower level, and the neighbors may have different categories from the center query point. Therefore, the mid-level points $p_i$ may represent multiple classes when its corresponding patch in lower levels lies at the edges. We will further discuss this issue in Section 3.5. + +We illustrate the principle of the semantic-affine transformation in Figure 3. The original representations of points from different categories in $(a)$ are entangled with each other. Then we train a network to capture the underlying distinctions of scales and bias between different categories, as is shown in $(b)$ . Then we express these distinctions with semantic-affine parameters, which are demonstrated as arrow directions in $(c)$ . Finally, in $(d)$ , the semantic-affine transformation explicitly transforms mid-level features with similar category distributions towards similar scales and offsets, thus pulling them closer. On the contrary, for mid-level features with distinctive category distributions, their discrepancy in scales and offsets pushes them further apart. + +According to the discussions above, the most important prerequisites for semantic-affine transformation are twofold. The first one is a precise class predictor, predicting accurate category distributions for mid-level points. The second one is a powerful semantic-aware module, regressing representative affine transformation parameters for each class. In Section 3.3, we show that these two prerequisites can be satisfied by a multi-layer Transformer decoder. + +# 3.3. The Explicit Semantic-Aware Module + +Our goal is to wrap the learnable parameters of semantic-aware transformation introduced above into a plug-and-play module that can be implemented in most encoder-decoder-style semantic segmentation architecture. We propose an Explicit Semantic-Aware Module (ESAM) as a multi-layer Transformer decoder module to jointly and explicitly inference semantic class masks and semantic affine parameters. + +Cross attention in Transformer decoder. The input to ESAM is the high-level feature $\mathbf{f}^0$ , which is the output from the backbone encoder. Particularly, we design $N$ learnable class queries $q^{(c)}$ to enquire semantic-specific knowledge. Then each layer of ESAM utilizes the attention mechanism to reason semantic information from $\mathbf{f}^0$ : + +$$ +\operatorname {A t t e n t i o n} (Q, K, V) = \operatorname {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d _ {k}}}\right) V \tag {3} +$$ + +where $d_{k}$ is the scaling factor, and $Q,K,V$ are queries, keys, and values matrix. We employ class queries $q^{(c)}$ as $Q$ , while $K,V$ are mapped embeddings of $\mathbf{f}^0$ . From each layer of ESAM, we can obtain class-specific features $h\in \mathbb{R}^{N\times d_h}$ of $d_h$ dimensions that encode both class-wise semantic knowledge from $q^{(c)}$ and geometry knowledge of the scene from $\mathbf{f}^0$ . + +Semantic-affine parameters. Based on the multi-layer Transformer decoder architecture of ESAM, we utilize the intermediate outputs from ESAM mid-level layers to calculate the semantic-affine parameters for mid-level layers of the backbone decoder: $\mathbf{s}_k^i = \mathrm{MLP}(h_k^u)$ , $\mathbf{b}_k^i = \mathrm{MLP}(h_k^u)$ where $1\leq k\leq N$ denotes class $k$ , and there is a one-to-one and order-preserved mapping between backbone decoder mid-layer $i$ and ESAM mid-layer $u$ . The principle is using output features of deeper ESAM layer $u$ to calculate semantic-affine parameters of deeper backbone decoder layer $i$ . Please refer to the supplementary material for detailed correspondence between $i$ and $u$ . The outcom ing scale and bias parameters s, b are then used to perform semantic-affine transformation introduced in Section 3.2. + +Semantic class masks. The segmentation masks $M = \{m_k \in \mathbb{R}^{d_m}, 1 \leq k \leq N\}$ for $N$ classes per-point classification are calculated via the output $h^{-1}$ from the final layer of ESAM: $m_k = \mathrm{MLP}(h_k^{-1})$ . Then we implement dot product on class mask $m_k$ and per-point feature $\mathbf{f}^i = \{f_j^i \in \mathbb{R}^{d_i}, 1 \leq j \leq n^i\}$ to calculate the confidence matrix $A^i = \{a_{jk}^i\}$ : $a_{jk}^i = m_k \cdot f_j^i$ , where $a_{jk}^i$ indicates the confidence of point $p_j$ at layer $i$ of the backbone decoder belonging to class $k$ and is utilized in Section 3.2. + +Note that in conventional per-point segmentation methods such as FCN [38] or encoder-decoder-style architecture UNet [51], per-point feature $\mathbf{f}^{-1}$ from the final layer of the decoder is further processed by an MLP block as segmentation head to obtain per-point class predictions. However, instead of linearly combining channel-wise values via fully connected layers to predict class confidence, we implement the above mask prediction and dot production with perpoint features to classify mid-level and final point features. The advantages of predicting class masks are two folds. On the one hand, the class masks have clearer interpretive meanings. Each mask $m_{k}$ represents the comprehensive feature of the class $k$ , and the dot product between $m_{k}$ + +![](images/f6cc84382ed650a632825f6fad9c509d21d6284e5ed32d0e1bb72c31b5aa162a.jpg) +Figure 4. Illustration of ShadowNet that is designed to trace multi-hot ground truth label for mid-level points. Column $(a)$ shows the local aggregation of stride operation in the backbone encoder. Column $(b)$ shows how we record the class distribution of the points at the higher layer according to the class distribution of its corresponding patch at the lower layer. + +![](images/484cb17d9aa69f8317cff2ff4f2f8fb4259ee38bb9c51a2c234ec67df003ddef.jpg) + +and the point feature measures the similarity between the point and the class. Therefore, the point is categorized into its most similar class. On the other hand, the class masks are more flexible to be implemented to predict categories of mid-level points. Once $M$ is obtained, the dot-product operation is more lightweight than the MLP forward calculation. Therefore, class mask prediction is more suitable to combine with our proposed semantic-affine transformation. + +In conclusion, ESAM explicitly predicts semantic class masks and semantic-affine parameters via a multi-layer Transformer decoder with learnable class queries. Each class query represents a category and inquires class-specific information in scene geometric representations. Then the semantic class masks are used to perform more flexible and lightweight multi-level per-point classification, while semantic-affine parameters are applied to transform mid-level features of the backbone decoder. + +# 3.4. The Implicit Semantic-Aware Module + +Besides ESAM that explicitly reasons semantic information via specially designed learnable class queries in the Transformer decoder, we also design ISAM to implicitly exploit and fuse semantic knowledge from multi-modalities. + +In our implementation, 2D high-level feature $\mathbf{f}^{0,2d}$ and 3D high-level feature $\mathbf{f}^{0,3d}$ are concatenated together to form mixed Transformer encoder input $\mathbf{f}^{0,mix}$ . Then queries, keys, and values matrix are obtained via three different linear transformations of the input mix feature $\mathbf{f}^{0,mix}$ . Therefore, the self-attention calculation in Equation (3) are performed at both inter-modality and intra-modality to obtain more representative high-level features $\bar{\mathbf{f}}^{0,2d}$ and $\bar{\mathbf{f}}^{0,3d}$ . On the one hand, the intra-modality self-attention reasons long-range dependencies between local parts from the same modality, attaching global information to local part features. On the other hand, the inter-modality self-attention captures similarities between parts from different modalities, creates soft correspondences, and merges knowledge from the other modal to local features. Therefore, the output features of ISAM acquire both long-range global knowledge and multi-modal information, making them more robust and more representative. Thus the implicit semantic-awareness + +is realized via intra-domain and inter-domain self-attention, where queries that are more semantic-similar to keys contribute more to updating the values matrix. + +# 3.5. The Loss Function + +Following conventional supervised segmentation approaches, we use the Cross Entropy loss for vanilla 2D per-pixel segmentation and 3D per-point segmentation. + +Additionally, since we predict category labels for mid-level points in backbone decoders, we calculate the Binary Cross Entropy loss for mid-level segmentation. In order to obtain the mid-level ground truth of backbone decoders, we design ShadowNets to trace the stride operation in their corresponding backbone encoders. As is shown in Figure 4, stride operation in the encoder aggregates points $\{p_j^i\}$ within a local patch $P_{j'}^i$ at layer $i$ into a meta-point $p_{j'}^{i+1}$ at higher layer $i+1$ . Suppose the one-hot label for point $p_j^i$ is $l_j^i$ , then our ShadowNet assigns the meta-point with multi-hot label $l_{j'}^{i+1}$ that records labels of all points within its corresponding patch $P_{j'}^i$ at the lower layer $i$ : + +$$ +l _ {j ^ {\prime}} ^ {i + 1} = \min \left(1, \sum_ {p _ {j} ^ {i} \in P _ {j ^ {\prime}} ^ {i}} l _ {j} ^ {i}\right) \tag {4} +$$ + +In this way, the multi-hot ground truth labels represent class distributions of points at mid-level layers. + +# 4. Experiments + +In this section, we conduct extensive experiments on various datasets to verify the superiority of the proposed semantic-affine transformation and the SemAffiNet architecture, calculating the class-wise mean intersection over union (mIoU) as evaluation metrics. In Section 4.1, we will present the quantitative and qualitative results of the SemAffiNet, comparing them with previous works. Then in Section 4.2, we will implement the semantic-affine transformation on both 3D point cloud and 2D image segmentation baselines under different conditions to prove its generalization ability. Furthermore, in Section 4.3, we will provide ablation studies to demonstrate the effectiveness of each proposed module. Finally, in Section 4.4, we will discuss the limitations of our proposed approach. Additionally, experiments setup including datasets introduction and implementation details can be found in supplementary materials. + +# 4.1. Main Results + +Following BPNet [26], we conduct semantic segmentation experiments on ScanNetV2, evaluating both 2cm and 5cm voxel settings on validation set. The quantitative results are shown in Table 1. Under 5cm settings, SemAffiNet exceeds BPNet baseline by $1.5\%$ and $3.1\%$ respectively on + +Table 1. Quantitative results on the ScanNetV2 dataset. We compare both 3D and 2D mIoU with our baseline method BPNet. We also compare 3D mIoU with other works that use point cloud as input. Methods marked with * use additional 2D image input. + +
Method3D mIoU(%)2D mIoU(%)
PointNet++ [46]53.5-
PointConv [60]61.0-
PointASNL [62]63.5-
MVPNet* [29]66.4-
KPConv [54]69.2-
SparseConvNet [20]69.3-
RFCR [19]70.2-
FAConv* [66]72.0-
MinkowskiNet [11]72.2-
Mix3D [44]73.6-
BPNet* [26] (5cm)70.665.1
SemAffiNet* (5cm)72.168.2
BPNet* (2cm)72.572.7
SemAffiNet* (2cm)74.574.2
+ +Table 2. NYUv2 2D image segmentation results (13-class task). We compare our SemAffiNet with typical RGB-D based methods and joint 2D-3D methods on dense pixel classification accuracy metric. Baseline results are from the BPNet [26] paper and the results of [14] is on the 11-class task. + +
MethodAccuracy(%)
SceneNet [23]52.5
Hermans et al. [24]54.3
SemanticFusion [41]59.2
ScanNet [14]60.7
3DMV [15]71.2
BPNet [26]73.5
SemAffiNet (Ours)78.3
+ +3D mIoU and 2D mIoU metrics. Under 2cm settings, SemAffiNet outperforms BPNet by $2.0\%$ and $1.5\%$ respectively on 3D and 2D segmentation results. We also surpass other previous 3D semantic segmentation methods that take point clouds as input [11, 19, 20, 44, 46, 54, 60, 62] or use point clouds and auxiliary 2D images as input [29, 66]. + +Besides ScanNetV2 which mainly focuses on 3D point cloud segmentation, we also conduct experiments on the NYUv2 [43] dataset that consists of RGB images and corresponding depth maps. We convert the depth image to pseudo point clouds according to camera pose and employ SemAffiNet. Following BPNet [26], we adopt the 13-class configuration and report the dense pixel classification accuracy. The experimental results are shown in Table 2, and our SemAffiNet outperforms those baselines by a large margin, + +![](images/51f2f97beb03d79266747a367c600ffada83a2f664a2812cc55f10b2a7b158a5.jpg) + +![](images/f3ef42c2f2ea4ca65b3664ab5609ef7dab59a6ec71ca5c84d1129f718e649d5c.jpg) + +![](images/aa9083bfceab3c038d1b988d430f7137580aa6969a322f4c77ebf40ab933bed4.jpg) + +![](images/3a9cdfee472f6fc222fb0741377fd6c1f19ac741e41a55b518c7ed0f2dcc55a6.jpg) + +![](images/264c5543b73225ab38cc2ceb73f022748adb43474baf276aae24c490f8f7f730.jpg) + +![](images/45748634cd97e92bf1ca1cbd54396435d0ccec3096357c8e6188f77b0a4be91a.jpg) + +![](images/ab7d9062693bbb4b490d1ec95976f7e1f7f95a4366dd775a6be5598a04671f51.jpg) + +![](images/497319c82a49f0fd2affde9183d982356e7041f3983346a7523779027a114448.jpg) + +![](images/3f8ca9596bcadb8187490757b4c1c126440540bc9f015a942215dd02606d7582.jpg) +Figure 5. Qualitative results of the SemAffiNet on ScanNetV2 point cloud semantic segmentation task. The first and second columns are the input point clouds and corresponding ground truth labels. The third and fourth columns are the segmentation results of BPNet baseline and our method SemAffiNet respectively. As is shown in the red rectangle in the first line, SemAffiNet is able to recognize chair crossbeam while BPNet cannot. From the second line, SemAffiNet correctly identifies that the object in the red rectangle is not chair, while BPNet fails. The final line shows the correspondence between categories and visualization colors. + +which verifies its superiority. + +The quantitative results are shown in Figure 5. From the first line example, our SemAffiNet is able to recognize the subtle chair crossbeam that BPNet baseline fails to correctly segment. From the second line example, our SemAffiNet correctly classifies the other furniture object which is visually similar to chair. From these qualitative results, we can prove the superiority of the SemAffiNet over the BPNet baseline. On the one hand, it has the ability to recognize subtle local parts that are easy to be confused with the background. On the other hand, it can correctly classify objects that are visually similar to other categories. + +# 4.2. Effects of Semantic-Affine Transformation + +Besides SemAffin architecture, we also evaluate the semantic-affine transformation independently by wrapping it as a plug-and-play module ESAM and inserting it into various 3D point cloud and 2D image encoder-decoder segmentation baselines. Point cloud methods can be further divided into voxel-based and point-based ones. + +For voxel-based 3D segmentation methods, we select MinkowskiNet [11] as the baseline given its efficiency and high performance. We conduct semantic segmentation on the ScanNetV2 [14] validation set under both $5\mathrm{cm}$ and $2\mathrm{cm}$ voxelization settings, and the results are shown in the first two lines of Table 3. By inserting ESAM into MinkowskiNet, we reach a higher performance on 3D mIoU results. + +For point-based 3D segmentation methods, we choose KPCov [54] (rigid) as the baseline, since it is one of + +Table 3. Quantitative results of inserting ESAM into various semantic segmentation baselines. The first two lines show results based on 3D voxel-based MinkowskiNet on the ScanNetV2 dataset. The third line shows results based on 3D point-based KPConv on the S3DIS dataset. The last two lines show results based on SemanticFPN on the 2D Cityscapes dataset. + +
MethodDatasetmIoU(%)
MinkowskiNet (5cm) [11]ScanNetV267.4
+ ESAMScanNetV268.8
MinkowskiNet (2cm)ScanNetV272.2
+ ESAMScanNetV274.0
KPConv [54]S3DIS65.8
+ ESAMS3DIS66.7
SemanticFPN (Res50) [31]Cityscapes76.1
+ ESAMCityscapes77.2
SemanticFPN (Res101)Cityscapes77.4
+ ESAMCityscapes79.0
+ +the most classical point-based approaches and has been analyzed as the baseline in many recently published papers [19, 44]. We conduct semantic segmentation on the S3DIS [3] dataset and the results are shown in the third line of Table 3. The qualitative results demonstrate the improvement made by ESAM, convincing the generalization ability of the semantic-affine transformation on both voxel-based + +Table 4. Ablation studies on individual contributions of SemAffiNet designs on the ScanNetV2 validation dataset under 5cm voxelization. + +
Ablation on ↓idxVNF.FCF.MM.FCM.MBNAdaINSAFuse2D mIoU3D mIoU
BackboneView Numa3✓xxx✓xxx65.170.6
b5✓xxx✓xxx65.570.1
ESAMMulti-level Segmentationc5x✓xx✓xxx65.870.3
d5x✓✓x✓xxx65.470.6
e5x✓x✓✓xxx67.270.8
SemAffinef5x✓x✓x✓xx66.871.2
g5x✓x✓xx✓x68.071.8
ISAMMulti-Modalityh5x✓x✓xx✓✓68.272.1
SemAffiNetView Numi3x✓x✓xx✓✓68.370.7
+ +and point-based point cloud segmentation methods. + +For 2D image segmentation methods, we choose the classical SemanticFPN [31] as the baseline, implementing ResNet-50 and ResNet-101 settings. We conduct semantic segmentation on the Cityscapes [12] dataset and the results are shown in the last two lines of Table 3. The quantitative results show that the proposed ESAM is not restricted within 3D domain and brings consistent improvements to 2D segmentation baseline under different settings. + +# 4.3. Ablation Studies + +In order to measure the contribution of each SemAffiNet module, we conduct ablation studies on the ScanNetV2 validation set under 5cm setting. ESAM can be divided into two parts: multi-level segmentation and semantic-affine transformation (SA). For multi-level segmentation, we incrementally add mid-level segmentation $(\hat{\mathbf{M}})$ besides final-level segmentation $(\hat{\mathrm{F}})$ and replace fully connected classifier (FC) with mask classifier (M). ISAM module fuses multi-modality information (Fuse). The ablation results are shown in Table 4 and we conclude that each block makes its own contribution to the overall progression, where semantic-affine transformation is the most effective one. + +Besides ablations on sub-modules of SemAffinet, we further explore the superiority of the semantic-affine transformation by replacing it with Adaptive Instance Normalization(AdaIN) [28], whose affine parameters are entirely learned with gradient descent and lack explicit semantic guidance. Comparing line $e$ , $f$ , $g$ in Table 4, AdaIN (line $f$ ) brings little improvement compared with the vanilla Batch Normalization (line $e$ ). However, semantic-affine transformation (line $g$ ) yields more significant progression. + +Furthermore, we also conduct ablation experiments on the number of 2D views (VN). According to line $a, b$ , adding views to BPNet [26] baseline doesn't lead to better results but adds computation burden. The reason might be that the potential of the network is exhausted when processing 3 views. However, according to our experiments (line $h$ and $i$ ), our SemAffiNet performs better on 3D semantic + +segmentation when increasing view numbers from 3 to 5. The experimental results show that our SemAffiNet reveals more semantic knowledge and has larger potential. + +# 4.4. Limitations + +Even though the proposed semantic-affine transformation is a general representation learning technique to enhance the semantic cognition ability of point clouds features, migrating and performing it on broader point cloud understanding tasks is a non-trivial problem. Since we need per-point supervision on mid-level points, we need to develop weakly-supervised or unsupervised learning techniques when the per-point annotation is inaccessible. + +# 5. Conclusions + +In this paper, we propose the semantic-affine transformation to explicitly map mid-level features of the backbone decoder to more semantic-distinct embeddings. Based on this technique, we build a semantic-aware segmentation network SemAffiNet. The ESAM explicitly predicts class masks and regresses semantic-affine parameters via the Transformer decoder with learnable query tokens, while the ISAM fuses multi-modal information via the self-attention mechanism. We conduct experiments with the SemAffiNet on the ScanNetV2 dataset and outperform the previous state-of-the-art BPNet. We also prove the generalization ability of the semantic-affine transformation by wrapping it into a plug-and-play ESAM and evaluating it on both 3D point cloud and 2D image segmentation baselines under various settings. 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With extreme data scarcity, current approaches explore various feature fusions to obtain directly transferable meta-knowledge. Yet, their performances are often unsatisfactory. In this paper, we attribute this to inappropriate correlation methods that misalign query-support semantics by overlooking spatial structures and scale variances. Upon analysis, we leverage the attention mechanism and propose a simple but effective architecture named Semantic-aligned Fusion Transformer (SaFT) to resolve these issues. Specifically, we equip SaFT with a vertical fusion module (VFM) for cross-scale semantic enhancement and a horizontal fusion module (HFM) for cross-sample feature fusion. Together, they broaden the vision for each feature point from the support to a whole augmented feature pyramid from the query, facilitating semantic-aligned associations. Extensive experiments on multiple benchmarks demonstrate the superiority of our framework. Without fine-tuning on novel classes, it brings significant performance gains to one-stage baselines, lifting state-of-the-art results to a higher level. + +# 1. Introduction + +Recent years have witnessed the flourish of large-scale perception systems like [3, 23]. Yet it has a long way to go towards real human-like intelligence. Being one of the underlying problems, few-shot learning received more and more interest from language [1, 17, 46, 58] to vision [15, 24, 37, 47, 49, 52, 54] related tasks. This scenario aims at learning a well-generalized model with scarcely labeled data, which challenges conventional learning paradigms. + +To bridge the aforementioned gap in few-shot object detection (FSD), existing literature suggests drawing support from transfer-learning [7, 16, 48, 54, 55, 65] or meta-learning [15, 24, 27, 28, 56, 57, 61]. Although the former is simple to conduct through pretraining on massive base classes and fine-tuning on scant novel ones, it suffers from the two-stage redundant procedures. The network should + +![](images/bd0168c8540425a3cf51ff01f0ad08a322545c1b4887b4e2999a80f454be5c73.jpg) +Figure 1. Comparison of semantic-aligned fusion and conventional fusion. Heatmaps and detection results of these two are based on our SaFT and a baseline with original cross-sample attention accordingly. Comparing the two schemes, semantic-aligned fusion activates more concentrated heatmaps on various feature levels and produces better OSD results. + +always utilize new-coming few-shot data to optimize parameters before it can well recognize these novel classes, thereby limiting its application. In contrast, the latter trend considers meta-knowledge extraction from sampled meta-tasks. This line of frameworks is expected to adapt directly to similarly organized tasks even without online fine-tuning, though it usually helps in performance. At present, this offline meta-learning paradigm is preferred by one-shot object detection (OSD) specific pipelines, with an out-of-the-box availability. + +In such a setting, the model should be well constructed to learn the relatedness between a given scene, i.e., the query, and an example patch, i.e., the support. To facilitate this, a series of works [15, 21, 24, 28, 38, 40, 57, 61] investigate cross-sample feature fusion, which augments query features with support representations via sample or ROI level correlation. However, neglecting semantic mismatches in space and scale limits their performances in one-shot scenarios. + +Concretely, the traditional paradigm suggests generating a prototype [15, 24] or a kernel [61] from the support to associate with query features. With most spatial information compressed, the long-range structure-dependent relation in between remains hardly mined. Although pooled prototypes in Fig. 2(b) and learned kernels in Fig. 2(c) are effec + +![](images/6244610afcd1e5966df1201dd53dd22e58db79cae071c5268fbca8b133a326bf.jpg) +Figure 2. Visualization of different fusion approaches. We present previous fusion schemes in (b), (c), (d), and our proposed semantic-aligned attention as a sort of semantic-aligned fusion in (e). Images are split into patches for illustration, with each patch representing the receptive field of a feature point. The only green patch indicates the query where a response is expected, blue patches are values that contribute to one feature point of the fusion result, and yellow ones are keys that interact with these values. Green lines in (e) suggest two pairs of ideal matches, where different granularities of query features are used. Support samples are scaled in reweighting and correlation schemes to visualize their compression in spatial information. + +tive in distinguishing one category from another, they contain fewer positioning priors and thus hinder their localization ability. Furthermore, these schemes match global support representations with local query contexts, regardless of semantic misalignment. An emerging trend [6, 22] seeks help from the attention mechanism for adaptive feature fusion. While easing problems discussed to some extent, they commonly focus on feature pairs on a single scale as shown in Fig. 2(d), leaving the multi-scale detection task for later anchor-based detector heads. Therefore, it makes no sense when targets are scattered on different scales. For instance, in Fig. 2(e), ideal matches for the bus wheel and rear windows lie in two distinct levels of query features, making any single-scale attempt sub-optimal. A simple multi-scale implementation cannot resolve it either, since it fuses the query and the support one scale at a time. Without cross-scale long-range interactions, this rigid manner is likely to fail in cases with semantic missing, such as occlusions or query-support inconsistencies in shape and size. + +To encourage more appropriate and sufficient feature interactions in OSD, we propose to adaptively fuse each feature point from the support with each from the query feature pyramid. Thus the original attention mechanism is extended to semantic-aligned attention as illustrated in Fig. 2(e). Features from each side are first deconstructed into semantic units, i.e., feature points. Then these units interact one another in a global manner, not only between query-support sample pairs (horizontally) but also among different scales (vertically). Since objects and parts of objects might exist in different scales and locations, the association process weighted collocates multiple semantic units to make a proper match. In this way, semantic-aligned attention enriches the semantic space that each feature point can utilize, thereby promoting better alignments between the query and + +the support. + +Our Semantic-aligned Fusion Transformer (SaFT) implements this fusion scheme, with Fig. 3 demonstrating its overall structure. It follows a one-stage proposal-free design and can be easily extended to two-stage pipelines through cascading proposal-based heads. Compared with allied frameworks that employ reweighting or correlation, SaFT alternatively contains a vertical fusion module (VFM) and a horizontal fusion module (HFM). The former is placed after the feature extractor to together form a Siamese backbone followed by the latter. VFM prepares scale-attended features via vertical attention (VA) in Fig. 5, and HFM utilizes them from query and support with horizontal attention (HA) in Fig. 4. Note that a single level of support feature interacts with multiple from the other side for a comprehensive view. Thanks to the cross-scale and cross-sample relatedness modeled by the attention mechanism, SaFT achieves remarkable performance gains in both PASCAL-VOC and MS-COCO datasets. + +We conclude our contributions as three-fold. + +1. To the best of our knowledge, our Semantic-aligned Fusion Transformer is the first to carry out the offline one-shot object detection task with proposal-free one-stage detectors, producing better performance than state-of-the-art two-stage models. +2. We discuss the problems of query-support feature fusion and propose a unified attention mechanism to tackle semantic misalignment in space and scale. Our implementation of this can be used as a general fusion neck. +3. Through qualitative and quantitative experiments, we prove that our novel semantic-aligned fusion is superior to conventional association methods by involving cross-scale long-range relations and collecting more comprehensive meta-knowledge. + +# 2. Related Work + +# 2.1. General Object Detection + +Given a plain image, general object detection aims to localize and classify the objects concerned. Modern detectors can be roughly divided into two categories, namely two-stage proposal-based methods and one-stage proposal-free ones. Two-stage pipelines [4, 8, 18, 19, 31, 44] generate a set of class-agnostic region proposals in the first stage and refine as well as classify them into final results in the second. In contrast, one-stage approaches use a class-aware locator to omit the second stage, mostly based on densely placed anchor boxes [32, 36, 43] or anchor points [12, 26, 50, 62]. Different from these, another line of work soaring recently leads a new trend of heuristic-free design. By introducing the attention mechanism, the DETR series [5, 9, 66] have achieved better performance while being fully end-to-end. Our model builds on one-stage detector FCOS [50] for simplicity, while is rather plug-and-play as a fusion neck. + +# 2.2. One/Few-shot Object Detection + +With sufficient data of base classes while limited samples of novel ones, few-shot scenarios bring more challenges to object detection. Recent work leads two main-streams in addressing this problem, using transfer-learning or meta-learning techniques. Transfer-learning-based methods [7, 16, 42, 48, 54, 55, 60, 63, 65] follow a two-stage training schema, which is pretraining and fine-tuning, to transfer knowledge from base classes to novel classes. By comparison, the latter trend [15, 22, 24, 27-29, 56, 57, 61] recasts the problem in a meta-learning form, encouraging efficient knowledge adaptation through meta-tasks sampling and region-based metric-learning. OSD is an extreme case of FSD with merely one label available for each class to detect. Less data needs more generalization, spawning a series of offline models [6, 21] further explore similarity metrics and abandon the fine-tuning phase. While with different task settings, these methods share a common regional similarity comparison strategy with most FSD networks adopting metric-learning [25, 27, 48, 56, 57]. In other words, they highly rely on region proposals, which can be unpredictable in low-shot scenarios. Different from above, our approach learns the metric in a proposal-free manner, facilitating higher efficiency and flexibility. + +# 2.3. Multi-scale Feature Fusion + +Unlike humans that are born with a continuously zooming field of vision, modern convolutional feature extractors usually down-sample images in a discrete way. To mitigate this, multi-scale feature fusion techniques are developed in detection networks, bringing remarkable performance boosts. Three paths in the feature pyramid are exploited, i.e., top-down [31], bottom-up [35] and within- + +scale [5, 53]. Recent work further enriches multi-level information interaction through dense as well as various aggregations [30] and the attention mechanism [59, 64]. Although cross-sample feature fusion is widely investigated in one/few-shot problems [6, 10, 21, 34, 38, 41, 49, 52, 56], its cross-scale counterpart is relatively scarce. Hence, we consider aggregating these two dimensions and propose a unified attention mechanism for feature fusion between samples and among scales. Compared with its counterparts, this design experimentally helps in semantic alignments. + +# 3. Method + +# 3.1. Problem Definition + +As in previous literature [6, 21], the one-shot object detection task constitutes of two sets of instances $\mathcal{D} = \mathcal{D}_{\text{base}} \cup \mathcal{D}_{\text{novel}}$ , where $\mathcal{D}_{\text{base}}$ denotes a large base set with numerous available annotations and $\mathcal{D}_{\text{novel}}$ stands for a small novel set including only one instance per category. Note that the base classes $\mathcal{C}_{\text{base}}$ in $\mathcal{D}_{\text{base}}$ and novel classes $\mathcal{C}_{\text{novel}}$ in $\mathcal{D}_{\text{novel}}$ are mutually exclusive, i.e., $\mathcal{C}_{\text{base}} \cap \mathcal{C}_{\text{novel}} = \emptyset$ . + +We consider this problem in a meta-learning fashion akin to [15, 24, 28] whilst omitting the fine-tuning phase to constrain the setting to fully offline like [6, 21]. Given a query image $Q$ and a support patch $S$ , the task is to find all instances of the same category as $S$ with their bounding boxes in $Q$ . The base set $\mathcal{D}_{base}$ is provided in training to generate both queries $Q_{base}$ and supports $S_{base}$ while the novel set $\mathcal{D}_{novel}$ is utilized in testing for supports $S_{novel}$ only. + +# 3.2. Framework + +We propose a concise framework, termed Semantic-aligned Fusion Transformer (SaFT), to settle our motivation. The overall architecture is sketched in Fig. 3. It adopts a Siamese backbone for aligned query-support feature extraction, a shared vertical fusion module (VFM) to enrich per-sample semantic hierarchically, and a subsequent horizontal fusion module (HFM) to aggregate information from both samples for later classification and regression. + +# 3.3. Feature Fusion via Dense Attention + +Initially introduced in natural language processing [51] and then borrowed to vision tasks [5,11,53], attention mechanism is known by its inductive bias in modeling long-range information. More specifically in location-aware tasks like detection, positional encodings [2, 5, 39] are adopted upon multi-head attention (MHA) to promote a permutation-variant architecture with + +$$ +\operatorname {P M A} (Q, K, V) = \operatorname {M H A} (Q + \operatorname {P} (Q), K + \operatorname {P} (K), V) \tag {1} +$$ + +where PMA abbreviates position-encoded multi-head attention and $\mathrm{P}$ represents positional encoding. + +![](images/001200f102527dd01077abb057e41ee14e3d0ed1e0f7e323fd8f7729c554dab4.jpg) +Figure 3. The architecture of Semantic-aligned Fusion Transformer for One-shot Object Detection. Darker color indicates features from deeper layers in backbone, the same in Fig. 5. VFM and HFM are vertical fusion module and horizontal fusion module separately. + +Based on Eq. (1), we express our dense attention (DA) as follows + +$$ +\mathrm {D A} (F ^ {Q}, F ^ {K}) = \mathrm {L N} (F ^ {Q} + \mathrm {P M A} (F ^ {Q}, F ^ {K}, F ^ {K})) \quad (2) +$$ + +where $F^Q \in \mathbb{R}^{h_Q w_Q \times d_Q}$ , $F^K \in \mathbb{R}^{h_K w_K \times d_K}$ , and LN denotes layer normalization. Akin to the decoder in [5] which captures a dense relationship between encoded features and object queries to decode, DA is expected to model a point-to-point correlation between $F^Q$ and $F^K$ , thus named as it is. We further extends DA in form of self-attention (SA) + +$$ +\mathrm {S A} \left(F ^ {Q}\right) = \mathrm {D A} \left(F ^ {Q}, F ^ {Q}\right) \tag {3} +$$ + +and cross-attention (CA) + +$$ +\mathrm {C A} \left(F ^ {Q}, F ^ {K}\right) = \mathrm {D A} \left(F ^ {Q}, F ^ {K}\right) = F ^ {K \rightarrow Q} \tag {4} +$$ + +$$ +\operatorname {C A F} \left(F ^ {Q}, F ^ {K}\right) = \operatorname {L N} \left(F ^ {K \rightarrow Q} + \operatorname {F F N} \left(F ^ {K \rightarrow Q}\right)\right) \tag {5} +$$ + +where CAF indicates CA with a consecutive feed-forward network (FFN) and an add-and-norm. + +Upon these, we propose two sorts of attention blocks, horizontal attention and vertical attention. The elemental procedure of both of them is consistent, with an SA before a CA. This design helps with adaptiveness since SA selectively expresses information from the query side, and CA weighted balances the two sides. + +# 3.4. Cross-sample Horizontal Attention + +DA-based cross-sample horizontal attention (HA) is designed for fusion between features from $Q$ and $S$ samples. For comparison, we first concisely review conventional convolution-based approaches in FSD/OSD tasks and then introduce our methods. + +Beginning with a pair of features $F^Q$ and $F^S$ extracted from the query and the support, traditional pair-wise operations either extract a prototype or learn a kernel of $S$ as + +$$ +\phi (F ^ {S}) = z ^ {S} \tag {6} +$$ + +and then obtain a class-specific enhanced feature with channel-wise multiplication as Fig. 2(b) or convolution as Fig. 2(c) + +$$ +\tilde {F} ^ {Q} = F ^ {Q} \odot z ^ {S} \tag {7} +$$ + +where $\tilde{F}^Q$ denotes the enhanced query feature. + +This schema highlights class-related information from support samples while discarding most of the spatial semantics. Furthermore, since the class-related $z^S$ represents the whole support patch while its target is a local area from the query, this global-to-local correlation process may lead to a misalignment in space and scale. + +In contrast, HA interacts every location pairs of $F^Q$ and $F^S$ as Fig. 2(d) shows. A single block of HA presented in Fig. 4 constitutes from a pair of SA and CAF + +$$ +\bar {F} _ {i + 1} ^ {Q} = \mathrm {S A} \left(\tilde {F} _ {i} ^ {Q}\right) \tag {8} +$$ + +$$ +\bar {F} _ {i + 1} ^ {S} = \mathrm {S A} \left(\tilde {F} _ {i} ^ {S}\right) \tag {9} +$$ + +$$ +\tilde {F} _ {i + 1} ^ {Q} = \operatorname {C A F} \left(\bar {F} _ {i + 1} ^ {Q}, \bar {F} _ {i + 1} ^ {S}\right) \tag {10} +$$ + +$$ +\tilde {F} _ {i + 1} ^ {S} = \operatorname {C A F} \left(\bar {F} _ {i + 1} ^ {S}, \bar {F} _ {i + 1} ^ {Q}\right) \tag {11} +$$ + +where overlines and tildes stand for self-attended features and cross-attended features accordingly. For more sufficient feature interactions, these operations conduct iteratively with initial $\tilde{F}_0^Q = F^Q$ , $\tilde{F}_0^S = F^S$ and $i = 0,\dots ,N - 1$ . Ending attention layers aggregate features from both sides + +$$ +\tilde {F} ^ {Q} = \mathrm {H A} \left(F ^ {Q}, F ^ {S}\right) = \operatorname {C A F} \left(\mathrm {S A} \left(\tilde {F} _ {N} ^ {Q}\right), \mathrm {S A} \left(\tilde {F} _ {N} ^ {S}\right)\right) \tag {12} +$$ + +We term these chained blocks of HA as a horizontal fusion module (HFM). + +Intuitively, HFM conducts global-to-global similarity matching and expression. One by one it associates each feature point from the query and one from the support, regardless of their positions. This schema aligns features from two sides in a deformable and reorganizable manner, thereby making them more comparable. + +![](images/098d9654b1ed62f4f779838b219eb60b25fd851a05b40ffbbcde1c2572cf27dc.jpg) +Figure 4. The horizontal attention (HA) block. HA includes two sequential processes. (a) Iterative two-way fusion process with pairs of SA and CAF. (b) Finalizing one-way aggregation process with SAs and a CAF. + +# 3.5. Cross-scale Vertical Attention + +Besides mutual interactions between $Q$ and $S$ on a single scale, we enhance multi-scale semantics of each sample with cross-scale vertical attention (VA). The whole procedure is shown in Fig. 3 with a close-up illustration in Fig. 5. To show its ability in semantic alignment, we begin with reviewing feature pyramid networks (FPN). + +Widely adopted in object detection, FPN is an efficient plug-in to tackle scale variances. Its building blocks can be written as + +$$ +\tilde {F} _ {j} = \operatorname {C o n v} _ {3 \times 3} \left(\operatorname {C o n v} _ {1 \times 1} \left(F _ {j}\right) + \operatorname {U p} _ {2 \times} \left(\tilde {F} _ {j + 1}\right)\right) \tag {13} +$$ + +where $F_{j}$ and $\tilde{F}_{j}$ are the level- $j$ feature extracted by backbone and the corresponding result after fusion between neighboring scales, separately. We notice that FPN gathers semantics from higher levels to replenish lower levels locally. Notwithstanding its enriched contexts, this in-place scheme falls short in capturing cross-scale long-range information which can be semantically complementary in OSD, e.g., people in a long line are of the same category while having distinct appearance features. + +To this end, we introduce VA. Given a feature pyramid $\{F_j|j = 3,\dots ,M\}$ having strides $\{2^j |j = 3,\ldots ,M\}$ extracted by backbone, VA starts from the self-enhancement of top level $M$ as + +$$ +\tilde {F} _ {M} = \operatorname {C o n v} _ {3 \times 3} (\mathrm {S A} (\operatorname {C o n v} _ {1 \times 1} (F _ {M}))) \tag {14} +$$ + +In a top-down hierarchy, VA adaptively inquires related information globally from upper levels + +$$ +\bar {F} _ {j} = \operatorname {S A} \left(\operatorname {C o n v} _ {1 \times 1} \left(F _ {j}\right)\right) \tag {15} +$$ + +![](images/f4d51c8b5a5fe0ceab89f190271b4967d22292937126e5789816d9edf50a1d22.jpg) +Figure 5. The vertical attention (VA) block. VA inserts an SA and CA pair between lateral and output convolutions of FPN. + +$$ +\begin{array}{l} \tilde {F} _ {j} = \mathrm {V A} \left(F _ {j}, \tilde {F} _ {j + 1}\right) \\ = \operatorname {C o n v} _ {3 \times 3} \left(\mathrm {C A} \left(\bar {F} _ {j}, \mathrm {U p} _ {2 \times} \left(\tilde {F} _ {j + 1}\right)\right)\right) \\ \end{array} +$$ + +where $\tilde{F}_j$ is the enhanced feature from level $j$ , which is up-sampled before fusion with the next level for alignment. This pyramidal process, named vertical fusion module (VFM), seeks to aggregate multi-scale global semantics. + +Compared with FPN in Eq. (13), VFM inserts attention layers between lateral and output convolutions. Rather than linearly combining features in the same position, VFM promotes more flexible cross-scale feature interactions and better matches between query-support representations. The query collects and enriches potential target semantics spread in different positions and scales, whereas the support highlights the main target consistent across scales and dims irrelevant backgrounds. Moreover, VFM cooperates with HFM to expand the attentive field of a support feature point from a single layer to multiple scales as in Fig. 2(e). With this point-to-pyramid connection, richer semantics and cross-scale long-range correlations are available in matching, thus aiding query-support alignments. + +# 4. Experiments + +# 4.1. Experimental Setting + +**Benchmarks.** We follow the previous work [6, 21] to train and evaluate our model on PASCAL-VOC [13, 14] and MS-COCO [33] with the same data splits. For VOC, a split of 20 classes partitions the whole dataset into 16 base classes and 4 novel classes. As for COCO, we divide the whole dataset of 80 classes into four groups, each having 20 classes. By turns, three groups are selected from the four as base classes for training and the remained 20 classes for evaluation. The original setting randomly samples query-support image pairs, which generates a different support patch each time a query image is given, in both training and testing. Differently, we keep the former but replace the latter with fixed seeds as in [24, 54, 56]. This strategy generates one random patch for each support class from COCO17 val and thus restricts the model to see merely one shot in testing rather than the whole set. Compared with the former evaluation, which is at risk of paralleling query and support with identical images, our proposed setting is closer to practical scenarios and de facto one-shot object detection. + +
Method / SetBaseNovel
PlantSofaTVCarBottleBoatChairPersonBusTrainHorseBikeDogBirdMbikeTableAvg.CowSheepCatAeroAvg.
\( FSCE^* [48] \)55.069.681.983.971.965.945.245.983.685.486.485.179.279.583.973.173.572.367.053.948.060.3
\( DeFRCN^* [42] \)51.774.478.387.170.867.652.461.685.085.887.683.182.083.882.864.074.970.759.158.843.057.9
CoAE [21]30.054.964.166.740.154.114.760.977.578.377.973.280.570.872.446.260.183.967.175.646.268.2
AIT [6]47.762.771.976.151.863.531.570.384.087.281.280.884.572.278.762.869.286.674.383.747.773.1
SaFT (Ours)59.781.382.486.973.072.062.383.785.988.186.787.787.783.586.175.180.188.177.084.348.574.5
+ +Table 1. Experimental results on the VOC 2007 test set in terms of AP50 (\%). We evaluate performances of our SaFT over multiple random runs. RED/BLUE indicate SOTA/the second best, the same below. The superscript * indicates results reproduced under the OSD setting. + +
Method / SplitBaseNovel
1234Avg.1234Avg.
CoAE [21]42.240.239.941.340.923.423.620.520.422.0
AIT [6]50.147.245.846.947.526.026.422.322.624.3
SaFT (Ours)49.247.247.949.048.327.827.621.023.024.9
+ +Implementation Details. Our approach employs FCOS [50] as our base detector with ResNet-101 [20] pretrained on ImageNet [45] as backbone. VFM outputs $\{\tilde{F}_4^Q, \tilde{F}_5^Q, \tilde{F}_6^Q\}$ with strides $\{16, 32, 64\}$ from the query while only the intermediate $\tilde{F}_5^S$ from the support for semantic-aligned fusion. HFM iterates $N = 6$ two-way HA blocks. To optimize our network, we use SGD with a mini-batch size of 8, momentum of 0.9 and weight decay of $1e - 4$ on both PASCAL-VOC and MS-COCO datasets without online fine-tuning. + +# 4.2. Comparison Results + +PASCAL-VOC. We provide performance comparison with current state-of-the-art on VOC in Tab. 1. The first two rows show results we reproduce with FSD methods under the OSD setting. Our SaFT consistently outperforms existing approaches, which demonstrates its effectiveness. We achieve around $5.2\%$ and $1.4\%$ improvements over the best method in base and novel classes respectively. To be specific, we observe a huge upswing in some categories, e.g., Chair with $9.9\%$ and Person with $13.4\%$ . One possible reason might be that objects in these classes have larger diversity in shape and size. Our method aligns query-support semantic units more effectively, thereby favoring these cases. It is also noteworthy that, among all the listed methods, our model is the only one adopting a one-stage framework. + +MS-COCO. Similarly, we report evaluation results of COCO on four different splits in Tab. 2. In spite of the challenge of COCO, our model achieves $24.9\%$ novel AP50, better than all existing methods. We further notice that performances on base classes and those on novel classes are not necessarily positively correlated. For example, although SaFT produces relatively low results on the first split of base classes, it brings a $1.8\%$ increase on novel classes over the current SOTA, demonstrating the strong generalization of our approach. + +Table 2. Experimental results on the COCO 2017 val set in terms of AP50 $(\%)$ . Our results are averaged over multiple runs. + +
Cross-scaleCross-sampleBaseNovel
w/oReweighting [24]61.853.7
w/oCorrelation [61]64.154.2
w/oHFM74.665.8
FPN [31]Reweighting72.362.9
FPNCorrelation76.661.6
FPNHFM79.669.2
VFMReweighting72.864.2
VFMCorrelation77.764.3
VFMHFM79.571.7
+ +Table 3. Ablation study for different modules of SaFT on VOC. Cross-scale and cross-sample are feature fusion techniques that interact among scales and between samples accordingly. + +# 4.3. Ablation Study + +We investigate into the effectiveness of various components of our proposed SaFT. Presented in Tabs. 3 and 4, all relative ablations are conducted on the VOC07 test set with half the batch size as our main experiment and less iterative HA blocks ( $N = 4$ ). Single-scale implementations in rows 1-3 of Tab. 3 utilize Res-4 feature by default, while the rest multi-scale ones use level-4,5,6 features as SaFT. + +Impact of different modules. In Tab. 3, reweighting [24] and correlation [61] are borrowed for substitution with HFM as our baseline cross-sample fusion operations. We adopt a $5 \times 5$ kernel for correlation and simply pool it to $1 \times 1$ to produce a reweighting prototype. As for cross-scale fusion, we implement pipelines without VFM in rows 1-3 as our baseline and add FPN in rows 4-6 for comparison. Upon these, we go through three phases to finish our exploration of SaFT. (1) Employ HFM for cross-sample fusion. Comparing the results in rows 1-3, we find that HFM improves by $10.5\% \sim 12.8\%$ and $11.6\% \sim 12.1\%$ respectively on base and novel classes. Similar conclusions can be drawn with respect to rows 4-6, showing the superiority of HFM in modeling cross-sample relatedness. With the help of the attention mechanism, HFM deconstructs support features so that they can be matched with the query deformably rather than always as a whole. In this way, semantics from both sides are more aligned. (2) Use FPN for cross-scale fusion. Before looking into VFM, we first extract multiscale features with FPN, thereby mitigating the problem + +
Cross-scaleCross-sampleQuerySupportBaseNovel
456456
FPN [31]Corresponding-scale✓✓✓✓✓✓77.468.7
FPNOne-to-all-scale✓✓✓✓79.669.2
VFMCorresponding-scale✓✓✓✓✓✓77.569.9
VFMOne-to-all-scale✓✓✓✓79.571.7
+ +Table 4. Ablation study for query-support fusion scales on VOC. One-to-all-scale means associating a single level of support features with all available query features, whereas corresponding-scale is limited to corresponding levels. All experiments use HFM for cross-sample fusion while with different corresponding rules. + +of scale variation. Besides the $3.4\% \sim 9.2\%$ performance boost on novel classes with FPN, we notice an interesting phenomenon. Cross-sample fusion approaches with larger receptive fields in the query gain more in single-scale performances, while FPNs attached upon them improve relatively less. This comes not only from the higher baselines they are on, but also from the aggregation of fine-to-coarse features that potentially increase the receptive field of lower levels. (3) Adopt VFM for semantic-aligned fusion. Comparison between rows 6 and 9 presents a $2.5\%$ promotion by replacing FPN with VFM, as a result of the more adaptive VA in VFM that collects and supplements semantics globally rather than locally. Baseline results also grow with $1.3\% \sim 2.7\%$ from rows 4-5 to rows 7-8. Finally, VFM and HFM collaborates in semantic-aligned attention and obtains a $17.5\% \sim 18.0\%$ soar, proving their effectiveness. + +Impact of query-support fusion scales. We examine the way to utilize different levels of features for fusion in Tab. 4. To begin with, we propose a simple corresponding-scale strategy that fuses each level of support feature with the same level of query feature. Its results are shown in the first and the third row. While with additional levels of support features participating in query-support fusion, its results turn out relatively lower. This counter-intuitive result might be due to a lack of generality in multi-level support features. Corresponding-scale fusion forces single-level fusion and detection, potentially causing multi-level connections to degrade by over-fitting to each level. In fact, a common down-sample ratio for each corresponding level of query-support feature means always searching targets of the same size. This not only undermines semantic alignments but also confuses multi-scale detection. Differently, since one-to-all-scale fusion matches the support with different sizes of targets on multiple scales, it learns more generalized meta-knowledge. This leads to $0.5\% \sim 1.8\%$ gains in novel classes after shifting from the corresponding-scale strategy. Also, a comparison between rows 2 and 3 shows that VFM with corresponding-scale query-support fusion outperforms FPN with a one-to-all-scale one. We attribute this to the cross-scale long-range correlation modeled by VFM, which mitigates cross-scale semantic misalignment. + +![](images/24d76a7759cf66738c09c283da4f491c2f8a0c85134ca1b5b227cb9fc2b856e8.jpg) +eey + +![](images/c3728504848de0974e1f373f3cf90fe13f21b873ce16b86f49ffb2c9cf1c821c.jpg) + +![](images/171542c518549c6bd638aef2ce8c59227957838be664b975c8bfec23998bc68a.jpg) + +![](images/bd0da502f78d160db1639055cb40f61bb7027e290ee8b4c6f89a2efa637ff602.jpg) + +![](images/f5c054ebe55d066b2fd76715c8d8ef3fd13151a327e5b9f0889cda089278c952.jpg) + +![](images/c05f98bd77b3a4e763375a028eaa9a8a2cdeb845186185501be11fbafaffa4a6.jpg) + +![](images/7ec5e9c8282f87389da551379b7b0889080673ddae0fc5bc8aa46232fa8421ce.jpg) + +![](images/8989fc15e3f106ac44fceb687020631b6339f72e78d8fb0d85fee96830d234e3.jpg) +Figure 6. Feature map responses of different fusion approaches. Vertically, the four columns are four different classes in the VOC07 test set. Horizontally, the top two rows are query and support samples for fusion, while the rest are feature map responses based on four fusion paradigms. Rows 3, 4, 5 show visualizations for three single-scale implementations. The last three lines demonstrate results of feature levels 4, 5, and 6 for our SaFT with VFM and HFM. These four configurations are respectively corresponding to rows 1-3 and 9 in Tab. 3. + +![](images/5a81c6a2b9e909d84343cb06629d6f999a970117bf97da61e06a9279cc0f9eb5.jpg) + +![](images/bbbfa831271ca73f5d98bd6eaf2659d7907c2fff246531d222c62d2c815c81d3.jpg) + +![](images/48439728da1cd6a26ba2f92ff102d99562626604fe1705ce9752bbb830dd0225.jpg) + +![](images/533c29c3e03b9288c366ea69f1d6a78fbad9e51e5dd879b513983445cce44b65.jpg) + +![](images/ee1b3c89c5ef3bdec859badd097a1039971d30f297c0ed1e357b4c9d29ae882f.jpg) + +![](images/9df6dcfba94eac19ecae3a410015b7ed8865c877a67521a14cbda64596f48d94.jpg) + +![](images/0681a5dd488c10581026e8d3585b33af0c0929db502e6a285435e269f8c7902a.jpg) + +![](images/a1798e0dc68e31cb36ddfc95d672c13b12865b3a8327f5cfc4ff4021f1756d6f.jpg) + +![](images/8555321e63018a36e0df48d17804d5e924b800a364e657a45feec5a63bab4335.jpg) + +![](images/882ecf8a8b2cce62f32e9548cc2c0372130b5ef37575e7db20b6c4fd1a750269.jpg) + +![](images/0682b4fd323ce7f572bc19ace00ef17c5a260917ed753eaf703a0eb05a878e95.jpg) + +![](images/d1c8c3443a8e08909a7f920c739850272dc7c37865b6df691b72cf12a7e121e5.jpg) + +![](images/9676c6fd833d4ddf399489bed681af009f5a520e6c73df534d3280a674600ea1.jpg) + +![](images/9b4e2c7079e93a26d1a8ce86e04a6766161cab602d4516000d446483ee2c8cdf.jpg) + +![](images/864e6e9a1366a518917ea3a9f03c349ebcecc2fa34c5d4d8d6e9081de958baa6.jpg) + +![](images/5f87364fad52db7c6d0a4931fbd064e41a2c7ba178f69f1bdcb291455f042a0e.jpg) + +![](images/568625f32ee72ccf4ea1c88d6ce3746a96f1b8f07c315d293a9484a41f2093a1.jpg) + +![](images/e589519f4b2a40d504f878270cc2f60cd06e9a1bb62b5fd6fff3d07b4c7fbf4f.jpg) + +![](images/ddeb2189cdf75cbe60b1be2c6728098429891b659e560c8e1b30c97239148674.jpg) + +![](images/e1db5e4278988a043bad4b88e0f8181a967b8501460e5ab7763e2c9fddcec566.jpg) + +![](images/f0adb8a7ba06779a7dd9abb2a93fec892bc4635e8a1c59854e6f14f9977a8b9d.jpg) + +![](images/99f09cfc1671f91359eae543cf58c68528202dc729641bba9e5a7fe5af019cc3.jpg) + +![](images/5577a982c3fde422d80ebb3d6ce41dd1db4d9a9cdc5accea1d0b51d629cda259.jpg) + +![](images/d85e9b8f69ea5ab8bc1818dd231c9e967eedcda4b2b7b7915bef821756c74306.jpg) + +# 4.4. Qualitative Analysis + +Feature map responses of different fusion approaches. To explore the behaviors of four fusion paradigms introduced in Fig. 2, we visualize their feature map responses in Fig. 6. These heatmaps are produced by averaging fusion features in all channels. Comparing row 3 with row 4, we can see that convolution-based methods tend to focus on objects that conform to their kernel sizes. Reweighting with a $1 \times 1$ kernel recognizes the tiny airplane in the first column while correlation with a $5 \times 5$ one hardly not. In larger objects, such as the cat in the third column, the heatmap of correlation activates more intensely than that of reweighting. Moreover, most related objects are partially focused due to the query-support mismatch. In contrast, attention-based HFM distributes its attention to more + +complete object regions. Yet, it activates some unrelated areas as well, especially in cases like the first and third columns, where the query shares a similar background with the support. We attribute the former to scale issues and the latter to the adaptive instinct of attention mechanisms, sometimes misleading. Generally, these conventional techniques are restricted in tackling appearance and scale variations, which leads to their activation biases compared with semantic-aligned attention. Illustrated in the three bottom rows, objects of distinct scales are activated differently in multi-scale heatmaps. As targets grow in size, fusion levels of interest shift from low to high. Clearly shown in the figure, the small-scale airplane, middle-scale sheep, and large-scale cat are highlighted in level 4, 5, and 6 heatmaps, accordingly. As a result, the attention mechanism works in tandem with the semantic-aligned fashion to address feature misalignment as well as scale discrepancies. + +Detection results of different fusion approaches. We demonstrate detection results in Fig. 7 for a more intuitive comparison. To be concrete, we explore the figure column by column. The first column clearly shows the differences between convolution-based techniques and attention-based ones. Matching the support patch in local areas of the query, reweighting and correlation are only capable of capturing bounding boxes that cover part of the object. In contrast, attention and semantic-aligned attention produce more accurate results, as they obtain a more global view of the query. Additionally, we can find more false positives in the results of traditional schemes. This is because their misalignment in scale wrongly focuses them on irrelevantness. Similar phenomena can be seen in the last column, where a human is recognized as a cow in rows 3-5. From top to bottom, networks successively give higher certainties to the cow and lower to the human. This also proves that space and scale alignments help in query-support associations. In the second column, we examine the ability of different approaches in resolving multi-scale issues. It is worth noticing that rows 3-5 show a downward trend in handling scale variances. Not difficult to understand, the discrepancy between reweighting and correlation is due to the inductive bias of their kernel sizes. With a smaller kernel size, reweighting is better at detecting smaller objects. In terms of attention, it fails to resolve scale variations solely dependent on single-scale matching. Thus, HFM in conjunction with VFM forming semantic-aligned attention presents better predictions. Next, we find an interesting anomaly in the third column. Despite the success of others, reweighting treats all humans as cats while ignoring the real cat. We attribute this to potential semantic conflicts in the support. As in this example, there is a human baby and a cat in the support patch. Then the compression of spatial structure is likely to distract detectors from the never-before-seen cat to the more familiar human that lies in base classes. By con + +![](images/8bfea87035713e1c704ba032f69836aa6c50e9a8d434e011daf47577c1c471a6.jpg) +Figure 7. Detection results of different fusion approaches. Four columns show original samples and detection results for each novel class in the VOC07 test set. Results in rows 3-6 are of configurations as rows 1-3 (previous schemes) and 9 (our novel scheme) in Tab. 3. + +trast, preserving structural information with larger convolution kernels or matching deformably with attention mechanisms remedies this. + +# 5. Limitation Discussion + +As an OSD-specific pipeline, our approach cannot be easily extended to more-shot circumstances. The Siamese design limits its inputs to a paired form, necessitating the construction of a dedicated feature extractor and aggregator for multiple support instances. Also, we notice that our model needs a small learning rate and a long schedule to converge. Hence, we adopt a learning rate of 0.001 instead of the common 0.02. Larger learning rates may result in instability in training. Future work can improve in these aspects. + +# 6. Conclusion + +In this paper, we look into the one-shot object detection task from the perspective of space and scale. The proposed Semantic-aligned Fusion Transformer substantially alleviates the underlying query-support misalignment in traditional feature fusion techniques employed by existing schemes. 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Torr $^{1}$ + +1 University of Oxford 2 Tsinghua-Berkeley Shenzhen Institute, Tsinghua University 3 Sun Yat-sen University + +{guangrun.wang,philip.torr}@eng.ox.ac.uk,tang.yansong@sz.tsinghua.edu.cn，linliang@ieee.org + +# Abstract + +The resurgence of unsupervised learning can be attributed to the remarkable progress of self-supervised learning, which includes generative $(\mathcal{G})$ and discriminative $(\mathcal{D})$ models. In computer vision, the mainstream self-supervised learning algorithms are $\mathcal{D}$ models. However, designing a $\mathcal{D}$ model could be over-complicated; also, some studies hinted that a $\mathcal{D}$ model might not be as general and interpretable as a $\mathcal{G}$ model. In this paper, we switch from $\mathcal{D}$ models to $\mathcal{G}$ models using the classical auto-encoder (AE). Note that a vanilla $\mathcal{G}$ model was far less efficient than a $\mathcal{D}$ model in self-supervised computer vision tasks, as it wastes model capability on overfitting semantic-agnostic high-frequency details. Inspired by perceptual learning that could use cross-view learning to perceive concepts and semantics1, we propose a novel AE that could learn semantic-aware representation via cross-view image reconstruction. We use one view of an image as the input and another view of the same image as the reconstruction target. This kind of AE has rarely been studied before, and the optimization is very difficult. To enhance learning ability and find a feasible solution, we propose a semantic aligner that uses geometric transformation knowledge to align the hidden code of AE to help optimization. These techniques significantly improve the representation learning ability of AE and make self-supervised learning with $\mathcal{G}$ models possible. Extensive experiments on many large-scale benchmarks (e.g., ImageNet, COCO 2017, and SYSU-30k) demonstrate the effectiveness of our methods. Code is available at https://github.com/wanggrun/Semantic-Aware-AE. + +# 1. Introduction + +Learning representations without human annotations is a long-standing vision full of expectations [5]. Although experiencing a downturn, it has gained a renaissance. Recently, the resurgence of unsupervised learning is attributed + +![](images/a121c16ce694ab965f3f825940c31efd2d4380aefdb9a340535f651ca135fae9.jpg) +(a) $\mathcal{D}$ model + +![](images/8bfa59ad3b85e0a8f553383c7e97f4593eaca764351c6f894cd81d7b6e777d07.jpg) +(b) semantic-agnostic model + +![](images/733a1cd5941829cef85f271d1d7713734ba2616382bee9add2a17cb7ed40c1e5.jpg) +(c) semantic-aware $\mathcal{G}$ model +Figure 1. A comparison among a discriminative model $(\mathcal{D}$ model), an existing semantic-agnostic generative model $(\mathcal{G}$ model), and our semantic-aware generative model. + +to the remarkable process of self-supervised learning (SSL), which can be divided into two groups, i.e., generative models $(\mathcal{G}$ models) and discriminative models $(\mathcal{D}$ models). + +In computer vision, the mainstream SSL algorithms belong to $\mathcal{D}$ models that learn representations via agent tasks, e.g., patch ordering [18], solving jigsaw puzzles [43], and rotation prediction [23]. Of all the agent tasks, contrastive learning [12-14, 25, 27] and metric learning [61] are currently the most successful, which randomly augments each image into different views and compares the (dis)similarity between different views (see Figure 1 (a)). But as pointed out by [4,27,61], without careful design, a contrastive learning algorithm would collapse. Special regularizations (e.g., losses [4], normalizations [27], centering [10]), unusual optimizations (e.g., gradient stopping [14], mean teacher [51]), and non-trivial architectures (e.g., additional predictors [25]) that are difficult to explain are often needed. Besides, some studies also suggested that a $\mathcal{D}$ model might hold some disadvantages compared to a $\mathcal{G}$ model in generalization and interpretability [3, 6, 26]. Specifically, $\mathcal{G}$ models might be more effective in pretraining foundation models [6] for fine-tuning tasks or downstream tasks, and the development of $\mathcal{G}$ models helps unify the pretraining paradigms in the CV and NLP domains [3, 17]. Moreover, with $\mathcal{G}$ models, one can further conduct a counterfactual intervention for explainability [1]. + +In this paper, we switch from $\mathcal{D}$ models to $\mathcal{G}$ models + +![](images/d2ac3a6d46d38df12b132e0f604298daa3466d469b69531df478844a55a4b22e.jpg) +Figure 2. Examples of the cross-view image generation by our semantic-aware AE on the validation set. In each triplet, the left is the input, the middle is our generated result, and the right is the reconstruction target. The generated image is similar to the reconstruction target. Although some may be slightly different from the reconstruction target, the generated images are reasonable (semantically plausible). + +using classical auto-encoders (AEs) $^2$ . Note that previous works seldom used a $\mathcal{G}$ model because it was not as efficient as a $\mathcal{D}$ model. For example, a typical $\mathcal{G}$ model BigBiGAN [19] with ResNet-50 [30] achieved a $55.4\%$ top-1 accuracy on the task of linear evaluation on ImageNet [48], which is 20.5 points lower than the triplet loss model [61], one of the best-performing $\mathcal{D}$ models. Similarly, the latest $\mathcal{G}$ model BEiT [3] with basic DeiT [52] only obtained $56.7\%$ top-1 accuracy, still holding a $19.2\%$ disadvantage compared to the $\mathcal{D}$ model. Actually, BEiT, iGPT [11], and MAE [26] can only perform well in pretraining tasks but fail to do well in direct discriminative representation learning tasks, e.g., a linear evaluation on ImageNet. A $\mathcal{G}$ model's inefficiency is caused by the waste of capability on overfitting semantic-agnostic local high-frequency details [3, 11, 19] and the ignorance to high-level semantics. For instance, a traditional AE uses an image as an input and the same image as the regression target, making the model overly focused on semantic-agnostic information compression rather than visual concepts (see Figure 1 (b)). + +To make $\mathcal{G}$ models feasible in SSL, we need to tackle the above semantic agnosticism problem. Fortunately, Becker & Hinton (1992) found that cross-view learning could enable models to perceive concepts and semantics, and they proposed perceptual learning [5]. Inspired by this prior art, we propose a novel AE that could learn semantic-aware representation via cross-view image reconstruction. We take a view of the image as input and force the AE to reconstruct another view of the image (see Figure 1 (c)). However, this + +rarely-explored AE model is hard to optimize in practice. To solve this problem, we further propose a novel semantic alignment technology. Using the geometric transformation knowledge, we can adjust the hidden code of AE to ensure that the code semantic is aligned with the reconstruction target, thereby improving the learning and optimization capabilities. These techniques significantly improve the representation learning ability of AE and make SSL with $\mathcal{G}$ models possible in computer vision, leading to a state-of-the-art performance in feature learning, generalizability, and explainability. Figure 2 shows some results of our cross-view image generation, which are promising. + +In summary, our contributions are three-fold. + +- We seek the possibility of replacing $\mathcal{D}$ models with $\mathcal{G}$ models in SSL in computer vision. We rethink the inefficiency of $\mathcal{G}$ models from the perspective of overfitting semantic-agnostic local high-frequency details and propose a novel semantic-aware AE inspired by perceptual learning. Our AE uses one image view as input and another view of the same image as the reconstruction target, which is rarely explored before. +- To help semantic-aware AE optimization, we propose a novel semantic alignment technique that uses the geometric transformation knowledge to semantically align the hidden AE codes to the reconstruction target. These technologies significantly improve the representation learning ability of AE and make the SSL with $\mathcal{G}$ model possible in computer vision. +- Extensive experiments show state-of-the-art performance of our method on several large-scale benchmarks (e.g., ImageNet [48], SYSU-30k [59], and COCO 2017 [40]) and varieties of tasks, demonstrating the effectiveness (e.g., feature learning, generalizability, and interpretability) of our method. + +# 2. Related work + +SSL. The idea of unsupervised representation learning dates back to many years ago, e.g., classical clustering [42]. It is highly anticipated at first, and then disappoints people due to unsatisfactory performance. Although experiencing a downturn, it has recently gained a renaissance. The resurgence of unsupervised learning is attributed to the enormous process of SSL, which achieved massive success in both NLP [7, 17] and computer vision [12-14, 25, 27, 61]. Generally, SSL can be divided into two groups, i.e., generative $(\mathcal{G})$ and discriminative $(\mathcal{D})$ models. + +$\mathcal{G}$ models in SSL. Although $\mathcal{G}$ models achieve good performance in pretraining language models in NLP [7, 17, 20], they are less effective in SSL tasks in computer vision. The first group of $\mathcal{G}$ models in computer vision are proxy generative tasks. Typical works include image denoising [53], image inpainting [44], and color jittering [64]. Although they contribute to the renaissance of SSL, their learned representations do not generalize well. The second group are pure generative methods. Representative work is BigBiGAN [19]. Its original intention is generative rather than discriminative representation learning; thus, its learned features are not very helpful in image recognition tasks. The third group are NLP-inspired generative models. Outstanding works include BEiT [3] and iGPT [11], which are inspired by BERT [20] and GPT [7], respectively. iGPT uses image tokens as inputs and targets, which are relatively low-level codes. Although BEiT combines masked language modeling with DALL-E codes [46], DALL-E codes still contain local dependencies used for image reconstruction. Thereby, these simple regression tasks (e.g., BEiT, iGPT, and MAE [26]) have difficulties in capturing high-level semantics. Hence, they can only perform well in pretraining tasks but fail to do well in direct discriminative representation learning tasks, e.g., a linear evaluation on ImageNet. + +Note that most of the above methods are AEs, whether based on CNN [37] or transformers [21]. The idea of AE dates back to several decades ago at an unclear/untraceable starting point [2, 36, 47]. Basically and traditionally, AEs are employed for generative representation learning whose purpose is dimensionality reduction. However, AEs are inefficient in discriminative representation learning because it wastes model capability on overfitting semantic-agnostic local high-frequency details [3, 11, 19] for reconstruction. + +$\mathcal{D}$ models in SSL. Similar to $\mathcal{G}$ models, the first group of $\mathcal{D}$ models in computer vision is proxy discriminative tasks. Typical works included patch ordering [18], solving jigsaw puzzles [43], and rotation prediction [23]. Since there was a gap between the proxy tasks and the main mission, their learned representations could not generalize well. The second group are currently the most effective methods, i.e., contrastive [12-14, 25, 27] and metric learning [61], which could be traced back to perceptual learning + +[5]. Lacking annotations, perceptual learning uses cross-view agreement to perceive concepts and semantics. Following it, contrastive-metric learning randomly augments each image into different views and compares the similarity between views. However, this way of representation learning often collapses [4, 27, 61]. To stabilize learning, careful designs are required. SimCLR [12] employs multi-node computing to enlarge the batch. MoCo v1/v2 [13, 27], triplet loss model [61], BYOL [25], DINO [10], and SimSiam [14] need gradient-free teachers (e.g., mean teachers [51] or gradient-stopping teachers). Triplet loss model, BYOL, and SimSiam [14] need additional predictors. DINO needs centering and sharpening of mean teachers. Most above methods benefit from synchronous batch normalization [32]. Although the recent VICReg [4] needs no normalization or predictor, it requires three special losses (i.e., variance, invariance, and covariance loss) for regularization. Also, the hyper-parameters in VICReg are uneasy to tune, and training VICReg is sometimes unstable. In summary, designing a workable $\mathcal{D}$ model could be over-complicated. + +Besides, the literature hinted that $\mathcal{D}$ models might be less general and explainable than $\mathcal{G}$ models [3, 6, 26]. Specifically, $\mathcal{D}$ models are less effective than $\mathcal{G}$ models in pretraining foundation models for fine-tuning tasks or downstream tasks [6], and $\mathcal{D}$ models hold a gap in the pretraining paradigms between computer vision and NLP domains [3, 17]. Moreover, $\mathcal{D}$ models have poorer interpretability than $\mathcal{G}$ models, e.g., in performing causal inference [1]. + +# 3. Method + +# 3.1. Vanilla AE (semantic-agnostic AE) + +AE is a classic model in the field of representation learning. Basically, a vanilla AE includes two modules, i.e., an encoder and a decoder (see Figure 3 (a)), which can be defined with two mappings $g$ and $f$ respectively, such that: + +$$ +\begin{array}{l} f: z \to h, \qquad g: h \to z, \\ f ^ {*}, g ^ {*} = \underset {f, g} {\arg \min } \mathcal {L} (z, (g \circ f) (z)), \tag {1} \\ \end{array} +$$ + +where $\circ$ denotes a composite function, and $\mathcal{L}$ denotes a loss function that can minimize the reconstruction errors (such as squared errors). $f^{*}$ and $g^{*}$ are the trained encoder and decoder. This formula shows that AE is to learn two complex mappings to minimize the error between input $z$ and output $(g\circ f)(z)$ . Therefore, the essential goal of AE is to learn a representation for information compression, and this representation learning is semantically ignorant. + +# 3.2. Semantic-aware AE + +To obtain semantic-aware AE, predecessors have made many efforts and proposed some outstanding works, including variational AE [35] and masked AE [3]. But these works + +![](images/b51a881e5df5787a39d99b1a216402f0384a54fad821d68202508c4bdff7f809.jpg) +(a) Vanilla AE (semantic-agnostic AE) + +![](images/e007a8f697a519d1aa241279cbf65a6613e91c127c3520f5491ecbc17d5b66a6.jpg) +Figure 3. A comparison between vanilla AE (i.e., semantic-agnostic AE) that achieves self-reconstruction and our semantic-aware AE achieving cross-view generation. + +are still inefficient in capturing semantics because they waste too much capacity on overfitting local high-frequency signals. We ask: could we learn semantic-aware representations without labels? Fortunately, this problem has been studied by Becker & Hinton (1992). They found that cross-view learning could enable models to perceive concepts and semantics, and they proposed perceptual learning [5]. Specifically, they perform two independent random augmentations on each image to get two different views. Then, semantic-aware representations are obtained by learning the similarity of two views of the same image and the dissimilarity of different images. Recently, perceptual learning has been the basis of $\mathcal{D}$ models (i.e., contrastive learning). + +Inspired by perceptual learning, we propose a novel AE that could learn semantic-aware representations via a new cross-view learning, i.e., cross-view image generation. As shown in Figure 3 (b), we perform two independent random data augmentations $\mathcal{T}_1$ and $\mathcal{T}_2$ for each image $x$ to obtain $z_1$ and $z_2$ , such that: $z_1 = \mathcal{T}_1(x)$ and $z_2 = \mathcal{T}_2(x)$ . Then, our goal is to reconstruct $z_2$ from $z_1$ . Overall, our semantic-aware AE is written as: + +$$ +z _ {1} = \mathcal {I} _ {1} (x), \qquad z _ {2} = \mathcal {I} _ {2} (x), +$$ + +$$ +f: z _ {1} \rightarrow h, \quad g: h \rightarrow z _ {2}, \tag {2} +$$ + +$$ +f ^ {*}, g ^ {*} = \underset {f, g} {\arg \min } \mathcal {L} (z _ {2}, (g \circ f) (z _ {1})). +$$ + +# 3.3. Semantic alignment + +Empirically, we found that it is extremely difficult to optimize the objective in Eqn. (2) straightforwardly; the training loss cannot converge (see Section 6). Therefore, it is uneasy to learn an effective semantic-aware representation with this formula. To help optimization, we introduce a novel semantic aligner below. + +Geometric transformation. To illustrate the semantic alignment process, we first present the difference between the input view (Figure 4 (a)) and the expected output view + +![](images/94b21f10954e764e1ac159de64df34435f0ec117f4771d30084c31909f3e3aa1.jpg) +(a) Input + +![](images/2a5cd03e69560077254eef677cd5cde21d30e05cc85186fba0f5d6f49430d270.jpg) +(b) output + +![](images/960ae1d85132ae1600a6def69524feca9b49e6c859214c759e718e294fab5514.jpg) +(c) Semantic alignment +Figure 4. An illustration of semantic alignment. (a-b) illustrate the geometric transformation between the input and the reconstruction target. (c) illustrates the semantic alignment process. + +(i.e., reconstruction target, see Figure 4 (b)). The geometric transformation between them are summarized as follows. (1) Random cropping: The two views are cropped from different locations of the original image, so the regional knowledge of interest is different. (2) Random scaling: The two views have different receptive fields due to different zooming scales. (3) Random flipping: There is a random difference in horizontal flip for the two views, so their mirror perception ability is also different. + +Our semantic aligner is placed at the end of the encoder, i.e., on the feature map. Specifically, we send the input $z_{1}$ into the encoder and get the intermediate code $f(z_{1})$ , which is in the form of a feature map. Then, having the geometric transformation between the input and the reconstruction target, we perform the following semantic alignment steps: (1) Zoom in/out $(\mathcal{Z}, i.e., \text{the "scaling"}$ in Figure 4 (c)): We resize the cropped code into the target size, i.e., $(\mathcal{Z} \circ f)(z_{1})$ . (2) Flipping $(\mathcal{F})$ : We perform horizontal flipping for the cropped code, i.e., $(\mathcal{F} \circ \mathcal{Z} \circ f)(z_{1})$ . (3) Replacing $(\mathcal{R})$ : we replace the transformed code in the appropriate coding position (the position corresponding to the area of interest in the reconstruction target), i.e., $(\mathcal{R} \circ \mathcal{F} \circ \mathcal{Z} \circ f)(z_{1})$ . Finally, the decoder will decode the latent code into the output space, where a reconstruction image can be obtained via cropping, i.e., $(\mathcal{C} \circ g \circ \mathcal{R} \circ \mathcal{F} \circ \mathcal{Z} \circ f)(z_{1})$ . An illustration of our semantic alignment process is shown in Figure 4 (c). + +# 3.4. Technical implementation details + +Encoder. Our encoder is a standard ViT [21]. We implement ViT following DeiT [52], which is the same as that in [3, 10]. Our ViT architecture is the most widely-used basic one (i.e., ViT-base). For more detail about the architecture protocol, please refer to Section 4.1. + +Decoder. Our decoder $g$ is composed of several simple transformer blocks. Having the output $(\mathcal{C} \circ g \circ \mathcal{R} \circ \mathcal{F} \circ \mathcal{Z} \circ f)(z_1)$ in Section 3.3, we can easily calculate the reconstruction error to get the reconstruction loss $\mathcal{L}(z_2, (\mathcal{C} \circ g \circ \mathcal{R} \circ \mathcal{F} \circ \mathcal{Z} \circ f)(z_1))$ , and use it to optimize our goal in Formula (2). Please see Section 6 for more details. + +Data augmentation. Our data augmentation methods are all standard methods, and the method we use is similar to the standard ImageNet supervised training, or even less. We did not use label smoothing [50] and did not use dropping paths [31]. For more data augmentation information, please see the "Training protocol" part of Section 4.1. + +Others. Besides, we have also thoroughly discussed the exclusion of global features in Section 6. + +# 4. Main results + +# 4.1. General protocols + +Architecture protocol. As is implied by [3, 10, 16], SSL has more potential in a vision transformer (ViT) [21], and thus a ViT is an ideal architecture to examine the effectiveness of SSL. Thereby, we focus on VITs to test the effectiveness of our method (see footnote3 for more reasons), similar to [3, 10, 16, 26]. We implement the ViT following DeiT [52], which is the same as that in [3, 10]. Our ViT architecture is the most widely-used basic one (i.e., ViT-base): Specifically, it takes a $224 \times 224$ image as input, and then divides it into $14 \times 14$ patches, each of which has $16 \times 16$ pixels. The encoder embeds each patch with a linear mapping into an embedding (including position codings), and then flattens these embeddings into 196 sequential vectors. These sequential vectors are input into 12 transformer blocks for processing. The hidden size of the transformer block is 768. + +Training protocol. In the unsupervised representation learning stage, we trained the model for 400 epochs, and we used the AdamW optimizer. Our learning rate adjustment scheme is cosine descent, and the basic learning rate is 5e-4. The learning rate is linearly warmed up during the first then epochs to its base. We set the weight decay factor as 4e-2. Our data augmentation is very common, including random scaling, cropping, and horizontal flips. Our model is trained using 1.28M training images on ImageNet, but we did not access its annotation information. Thanks to the simplicity of our method, we don't need complex training techniques as $\mathcal{D}$ models did. See our code for more details. + +Evaluation benchmarks. Since ViTs are data-hungry, we verify the effectiveness of our method by comparing it with the best existing methods in three large-scale benchmarks. The tasks include linear evaluation on ImageNet [48] (1.28M images), person re-ID on SYSU-30k [59] (30M images), object segmentation and instance detection evaluation on COCO 2017 [40] (123K images, 900K instances). + +Critical discussion on evaluation protocol. At present, linear evaluation is the most mainstream criterion to test the ability of SSL methods. The standard process is first to use an SSL method to train a backbone network and then freeze the trained model parameters. Next, people add a linear classifier to the top of the frozen backbone network and merely train this linear classifier for evaluation. [26] thinks that the occasional inconsistency between linear evaluation and fine-tuning indicates that fine-tuning should be emphasized (see footnote4). In contrast, we hold a slightly different opinion and believe that linear evaluation/probing can highly measure representation ability. + +- As shown in [10], representations with good linear evaluation performance can even be used to segment the object directly in an unsupervised manner. +- Classic visual matching tasks like face recognition and person re-ID also use linear query methods. +- Using fine-tuning will bring new unfairness because fine-tuning is highly dependent on hyperparameters (e.g., learning rate and training epochs). Fine-tuning will change the original parameters, and it is uneasy to standardize the extent to which parameters are allowed to be changed for evaluation. In fact, fine-tuning itself is still an open question [28, 41]. (see footnote5) + +What causes the occasional inconsistency between fine-tuning and linear evaluation may be complicated and multi- fold (see footnote for detail). We believe that the widely- used linear evaluation should still be valued by the community. Hence, we adopt this widely-used linear probing on ImageNet and SYSU-30k. Nevertheless, we also report the fine-tuning results on ImageNet. In addition, we follow the standard protocol to adopt fine-tuning evaluation on COCO. + +# 4.2. Linear evaluation on ImageNet + +We evaluate linear probes on ImageNet. In the unsupervised learning stage, we perform SSL with the 1.28M pictures on the ImageNet training set (but without their annotations). In the linear evaluation stage, all SSL methods are trained on the same training set and validated with 50k images on the validation set. The standard batch size is 256. A total of 100 epochs of training is adopted. This process does not use weight decay. The top-1 accuracy of the single-scale-center-crop scheme is used as the evaluation metric. Please see our code for more details. + +Table 1. Top-1 accuracy and training epochs of state-of-the-art methods on ImageNet using linear evaluation. + +
MethodTop-1EpochsBackbone#param.
D models
Random4.40R5023M
Ordering [18]38.8200R5023M
Rotation [23]47.0200R5023M
DeepCluster [8]46.9200R5023M
NPID [62]56.6200R5023M
ODC [63]53.4200R5023M
SimCLR [12]60.6200R5023M
SimCLR [12]69.31000R5023M
MoCo [27]61.9200R5023M
MoCo v2 [13]67.0200R5023M
MoCo v2 [13]71.1800R5023M
SwAV [9]72.7200R5023M
BYOL [25]71.5200R5023M
BYOL [25]72.5300R5023M
BYOL [25]74.31000R5023M
SimSiam [14]68.1100R5023M
SimSiam [14]70.0200R5023M
SimSiam [14]70.8400R5023M
SimSiam [14]71.3800R5023M
Triplet [61]75.9700R5023M
DINO [10]78.2400ViT-base86M
MoCo v3 [16]76.7600ViT-base86M
G models
BigBiGAN [19]55.4-R5023M
iGPT [11]65.2-ViT-super1362M
iGPT [11]65.2-ViT-super1362M
BEiT [3]56.7800ViT-base86M
MAE [26]68.01600ViT-base86M
Ours70.1400ViT-base86M
+ +Comparison with $\mathcal{G}$ models. As a new $\mathcal{G}$ model, we first compare our method with the existing $\mathcal{G}$ models. Due to the low efficiency of $\mathcal{G}$ models in recognition tasks, people were rarely interested in this task and thus, there are only a handful of $\mathcal{G}$ models that can be compared, including BigBiGAN [19], iGPT [11], BEiT [3], and MAE [26]. The comparison results are reported in Table 1. The performance of our method far exceeds the existing $\mathcal{G}$ models. For example, our accuracy is $70.1\%$ , which is significantly higher than the best method before (e.g., $56.7\%$ for BEiT). Note that the performance of the concurrent work MAE is also lower than our method (i.e., $68.0\%$ vs. $70.1\%$ ). These comparisons confirmed the superiority of our approach. + +Comparison with $\mathcal{D}$ models. In Table 1, we compare our method with the state-of-the-art methods. That is, our $\mathcal{G}$ model is compared with $\mathcal{D}$ models. We can observe that $\mathcal{G}$ models still have a long way to go. They have significantly lower learning efficiency than $\mathcal{D}$ models. But as shown in the table, our method is the closest to the $\mathcal{D}$ models. It is worth noting that DINO uses an extra multi-crop scheme that we didn't adopt, which has a significant gain (without + +Table 2. Top-1 accuracy of state-of-the-art methods on ImageNet using pretraining and fine-tuning evaluation. + +
RandMoCo v3 [16]DINO [10]BEiT [3]MAE [26]Ours
81.883.282.883.283.683.4
+ +multi-crop augmentation and Sinkhorn-Knopp, DINO only achieves $72.5\%$ ; see [10] for detail). + +# 4.3. Pretraining and fine-tuning on ImageNet + +As we have mentioned above, pretraining-finetuning evaluation has several shortcomings. Nevertheless, following [3] and [26], we also report the accuracies under this evaluation metric in Table 2. We have two observations. First, the fine-tuned result of our method is better than $\mathcal{D}$ models. Second, compared to $\mathcal{G}$ models, our result is slightly better than BEiT [3] and comparable to MAE [26]. + +# 4.4. Transfer to downstream tasks on COCO 2017 + +A goal of SSL is to learn general features. Thereby, we need to test the generalization ability of the learned features of our method by transferring them to downstream tasks. The downstream benchmark we adopt is COCO 2017 [40], which is currently one of the largest benchmarks for general object detection and segmentation, containing a total of 119k training images. Specifically, our ViT backbone is first trained using the above-mentioned unsupervised learning. Then these pretraining parameters are used as the initialization parameters of a Cascade Mask-RCNN [29], the widely-adopted framework for ViTs in object detection [65]. Next, we use the COCO 2017 training set to fine-tune all ViT layers. As suggested by [27,61], the distribution of features obtained by unsupervised pretraining is different from that of supervised pretraining. Therefore, in the fine-tuning stage, we use a larger learning rate than supervised pretraining counterparts. We report the accuracy on the COCO 2017 validation set. For the object detection task, we report the standard $\mathrm{AP}^{box}$ metric; for the instance segmentation task, we report the standard $\mathrm{AP}^{mask}$ metric. + +Comparison with $\mathcal{G}$ models. Table 3 shows that, in the COCO 2017 object detection and instance segmentation task, our SSL pretraining approach achieves state-of-the-art performance. Our approach is better than BEiT (e.g., $51.0\%$ vs. $50.1\%$ for the $\mathrm{AP^{Box}}$ metric, and $44.1\%$ vs. $43.5\%$ for the $\mathrm{AP^{Mask}}$ metric). It is worthy to note that all the $\mathcal{G}$ models outperform both $\mathcal{D}$ models and the supervised counterparts. These comparisons confirm the effectiveness of our method. Besides, we are unable to compare our method with MAE because their training protocol is missing. Note that MAE loads pretrained weights into a new windowed ViT [38] for fine-tuning, claiming MAE is superior to existing methods. We are really worried about this claim because loading weights into a new architecture puts existing methods at a disadvantage, as it introduces architecture + +Table 3. Object detection and instance segmentation on COCO 2017 for Mask-RCNN. + +
Method\(AP^{Box}\)(%)\(AP^{Mask}\)(%)
\(\mathcal{D}\ models\)
DINO [10]50.143.4
\(\mathcal{G}\ models\)
BEiT [3]50.143.5
Ours51.044.1
Supervised
supervised49.843.2
+ +gaps. Moreover, the code of [38] is unavailable. + +Comparison with $\mathcal{D}$ models. Different from the linear evaluation in ImageNet, in downstream segmentation and detection tasks, the current best-performing methods are $\mathcal{G}$ models rather than $\mathcal{D}$ models. For example, as Table 3 shows, our method is $0.9\%$ higher in $\mathrm{AP^{Box}}$ accuracy than the best $\mathcal{D}$ model DINO. Two reasons might account for this. First, our method learns more general features that are transferable to downstream tasks. Second, as a $\mathcal{G}$ model, our approach pays more attention to local dependencies that are beneficial for dense prediction tasks. + +Comparison with supervised learning. As shown in Table 3, our AE method fully surpasses the supervised pretraining method. Our $\mathrm{AP^{Box}}$ is $51.0\%$ , and the supervised counterpart is $49.8\%$ . These comparisons confirm the effectiveness of our method. Note that, in summary, $\mathcal{G}$ models are better than $\mathcal{D}$ models, and $\mathcal{D}$ models are close to the performance of the supervised model. + +# 4.5. Person re-identification on SYSU-30k + +Since ViTs are data-hungry models, we next verify the effectiveness of our method on a more extensive data set, SYSU-30k [59], that is 30 times larger than ImageNet both in terms of category number and image number. From a more general perspective, the above tasks (image classification, detection, and segmentation) are all visual classification tasks7. In view of this, the effectiveness of our method needs to be verified on more types of tasks. As mentioned in Section 4.1, if we can find a task to directly evaluate the features learned by SSL without fine-tuning network parameters, we will have a more transparent understanding of the effectiveness of SSL. Fortunately, person re-ID [22] is such a satisfying visual matching task8. Hence, we adopt the re-ID task for examination. The benchmark SYSU-30k is em + +Table 4. Comparison in re-ID tasks on SYSU-30k. + +
methodrank-1 (%)Backbone
D models
SimCLR [12]10.9R50
MoCo v2 [13]11.6R50
BYOL [25]12.7R50
Triplet [61]14.8R50
MoCo v3 [16]14.96ViT-base
G models
BEiT [3]8.3ViT-base
Ours11.8ViT-base
+ +ployed for three reasons. First, SYSU-30k is not only the largest re-ID dataset, but also one of the largest datasets in computer vision, containing 29,606,918 images of 30,508 pedestrians. Second, this dataset does not hold an exact label for each image. Evaluation on SYSU-30k means that we use its training set to perform SSL, and then the learned model is directly used to extract features for matching without any fine-tuning. This linear probing is more challenging than linear evaluation on ImageNet because linear evaluation on ImageNet can learn an extra classifier for recognition, but no extra classifier is allowed here. Third, another challenge in the linear probing is that there are 478,730 mismatching images as the wrong answer in the gallery. Evaluation using the SYSU-30k test set is like searching for a needle in a haystack. Unless being an extraordinary SSL feature learner, it is challenging to excel in this task. + +Comparison with SSL methods. We compare our method with existing SSL methods, including SimCLR [12], MoCo v2 [13], BYOL [25], MoCo v3 [16], and BEiT [3]. Among them, MoCo v3, BEiT, and our method use ViT-base [52] as the backbone, while others use ResNet-50 [30] as the backbone. Both BEiT and our method are $\mathcal{G}$ models; other methods are $\mathcal{D}$ models. The experimental results are shown in Table 4. We can see that our method has achieved a good performance (11.8%), which is comparable to $\mathcal{D}$ models. Overall, the performance of the $\mathcal{D}$ models is better than $\mathcal{G}$ models. Even so, our method is satisfactory. These comparisons prove that our method is an effective SSL visual feature learner. + +One thing that could not be ignored is that all SSL models perform unsatisfactorily on the challenging benchmark of SYSU-30k, i.e., the rank-1 values are very low. This is attributed to the challenge of the dataset, whereas warning us that SSL still has a long way to go. + +# 5. Visualization + +We show our image generation results in Figure 2 (Page 2) in the form of triplets. In each triplet, the left is the input image, the middle is our generated image, and the right is the ground truth. We can see that our generated images are very close to the ground truths. Even if some generated im + +![](images/ea02076db6144bbd85632c4c751016c5df5f937ce2472cd55e331be4ee182c2f.jpg) +Figure 5. Achieving interpretability via counterfactual intervention with the help of a $\mathcal{G}$ model. + +![](images/cede5ccc93e05dd0820708a9fd64e24a7d0edb148b4ef724a912dc2675bc2554.jpg) + +age is slightly different from the ground truth, the generated image is semantically plausible, indicating that our model has learned reasonably semantic representations. Besides, there is some grid effect in the visualization, similar to that in MAE [26]. We conjecture that this is attributed to two reasons. First, the loss is applied to the masked region. Second, it might be due to feature distortion. + +We have proven the generalizability of our method, e.g., in outperforming $\mathcal{D}$ models in pretraining tasks and dense prediction tasks and towards unifying pretraining methodology between CV and NLP. Next, we show the interpretability of our method. Our method can elegantly perform causal inference that is beyond the ability of $\mathcal{D}$ models. We conduct counterfactual interventions by masking an image to leave only one window at a time to exclude confounding factors for reconstruction. The reconstruction scores are visualized in Figure 5. As shown, the shark is successfully found via causal inference. + +# 6. Necessities, exclusions, and options + +The rest of this paper aims not to pursue state-of-the-art results but to gain insight into the role of different components of our method. Thus, we reduce the training epochs to 100 to fast access results. Other training protocol in this section is the same as in Section 4. This section only reports the linear evaluation results on ImageNet, because, as we said before, it is a general and reliable evaluation method. + +Necessity of semantic-aware generation. As described, our method inputs one view of the image and generates another view of it to perceive semantics. Now we removed this cross-view generation design and let the model perform self-regression, degenerating it back to a vanilla AE. Table 5 shows the result. It can be seen that after removing the semantic-aware generation, the performance of the visual feature learner plummeted from 46.4 to 6.1. This comparison confirms the necessity of semantic-aware generation. + +Necessity of semantic alignment. As mentioned, to train our semantic-aware AE, we need to align semantics. Specifically, we need to know the geometric transformation of the input and target and align them. Now we remove the aligner and directly regress the input into the target. This learning goal is different from all previous AEs, causing + +Table 5. Effectiveness analysis and insight of our method. + +
PropertiesTop-1 (%)
Semantic-aware AE (full)46.4
- Semantic-aware generation6.1 (-40.3)
Semantic-aware AE (full)46.4
- Semantic alignmentnot converge
Semantic-aware AE (full)46.4
+ Global featurenot converge
+ +huge learning difficulties. We observed that the training loss dropped quickly at the start, then it almost no longer declined (see Table 5). This comparison confirms that semantic alignment is necessary in a good feature learner. + +Exclusion of global feature. Unlike $\mathcal{D}$ models, existing state-of-the-art $\mathcal{G}$ models [3, 11, 26] do not have a global feature vector. As pointed out by [3, 11], lacking globality creates a gap between pretraining and linear evaluation. Here we insert a global pooling module at the end of the encoder and then increase the spatial size of the feature map using transformer decoder [45] and deconvolution [49] respectively to complete image reconstruction. As a result, the training loss cannot converge regardless of whether using a transformer decoder or deconvolution (see Table 5). + +# 7. Conclusion + +In NLP/NLU, $\mathcal{G}$ models play a vital role in SSL pretraining. But this role was absent in computer vision before, until [3, 26] came. This paper aims to bridge this gap. To tackle the problem that $\mathcal{G}$ models waste capacity in learning semantic-agnostic local signals, we propose a novel semantic-aware AE. Our AE uses one view of the image as input, but reconstructs another view of the image. In this way, our AE learns semantic representations, achieving good performance in many tasks. We hope that our approach will be inspiring for rethinking the new position of $\mathcal{G}$ models as a feature learner in computer vision, especially for closing the gap between NLP and computer vision. + +Broader impacts. This paper uses existing datasets, so the potential negative impact of the existing datasets will also be inherited. For example, the datasets ImageNet and SYSU-30k inevitably contain human photos. One limitation of this paper is that the proposed $\mathcal{G}$ still has a slight gap to the $\mathcal{D}$ models so far. The proposed method can generate non-existent images, which might be uncontrollable. + +# Acknowledgement + +This work is supported by the EPSRC/MURI grant EP/N019474/1, China National Key R&D Program grant 2021ZD0111600, China National Natural Science Foundation grant 61836012, and Guangdong Natural Science Foundation grant 2020A1515010423. We would also like to thank the Royal Academy of Engineering of the UK. + +# References + +[1] Arjun R Akula, Keze Wang, Changsong Liu, Sari Saba-Sadiya, Hongjing Lu, Sinisa Todorovic, Joyce Chai, and Song-Chun Zhu. Cx-tom: Counterfactual explanations with theory-of-mind for enhancing human trust in image recognition models. Iscience, 25(1):103581, 2022. 1, 3 +[2] Dana H. Ballard. Modular learning in neural networks. In Kenneth D. Forbus and Howard E. Shrobe, editors, Proceedings of the 6th National Conference on Artificial Intelligence. Seattle, WA, USA, July 1987, pages 279-284. Morgan Kaufmann, 1987. 3 +[3] Hangbo Bao, Li Dong, and Furu Wei. 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IEEE, 2018. 7 \ No newline at end of file diff --git a/semanticawareautoencodersforselfsupervisedrepresentationlearning/images.zip b/semanticawareautoencodersforselfsupervisedrepresentationlearning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f8c99e3f10e68e2555a0405f76c0bb2f652382e6 --- /dev/null +++ b/semanticawareautoencodersforselfsupervisedrepresentationlearning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7edbee0dfa7260f35d191181b8152846bd77589b9f51a4cc878395306d73656d +size 434115 diff --git a/semanticawareautoencodersforselfsupervisedrepresentationlearning/layout.json b/semanticawareautoencodersforselfsupervisedrepresentationlearning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..0eee3f966200319bb6244e484aa60f523dce25e4 --- /dev/null +++ b/semanticawareautoencodersforselfsupervisedrepresentationlearning/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:931ef9eaee6d462f76dfe00ccdd0846dc45f4bd239dfb64ebce5ed0b9275ec94 +size 490982 diff --git a/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_content_list.json b/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b9bb06e14f34a7956e81dea3bac8a42d0f994622 --- /dev/null +++ b/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a31cb73eb9e6627eba05dbc60a8f5053f60db659ba6ae20d7f0fc0c5233639ef +size 92737 diff --git a/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_model.json b/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e62db8aedfbb2c7fd60e68033491c7e6ea16ae88 --- /dev/null +++ b/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:63974ffa3b7183e04d6915117411b72dd8c9be12ac742b3f327e0e5398e71561 +size 116283 diff --git a/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_origin.pdf b/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..662d19abb6b4f83de1f02f5d57be535751e6aa6e --- /dev/null +++ b/semanticawaredomaingeneralizedsegmentation/94608522-5e84-46ae-8344-570079d103fe_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4db686be933a6fa4a0b8b1531762998be458b75cb5cb4f9f980964658ee08541 +size 1658530 diff --git a/semanticawaredomaingeneralizedsegmentation/full.md b/semanticawaredomaingeneralizedsegmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..813c886c709bd46a9c53e55286aea8ca239e5d9f --- /dev/null +++ b/semanticawaredomaingeneralizedsegmentation/full.md @@ -0,0 +1,387 @@ +# Semantic-Aware Domain Generalized Segmentation + +Duo Peng $^{1}$ Yinjie Lei $^{1,*}$ Munawar Hayat $^{2}$ Yulan Guo $^{3}$ Wen Li $^{4}$ $^{1}$ Sichuan University $^{2}$ Monash University $^{3}$ Sun Yat-sen University $^{4}$ University of Electronic Science and Technology of China + +duo_peng@stu.scu.edu.cn, yinjie@scu.edu.cn, munawar.hayat@monash.edu +guoyulan@sysu.edu.cn, liwenbnu@gmail.com + +![](images/73262d7235ad20e86e7d7839a12413fa00ceb5430e61c090bb0f0dcda13312f4.jpg) + +![](images/f775bbf2461c5102ae6f71d3518a2b8afd3ca7b3c99d8c117a8a61670801a3bd.jpg) + +![](images/8017a0c7697f37b1638d62d1a995ad9982e20794d96bae709574a3cefe23909d.jpg) + +![](images/cb070f81b6c907236977353c471ad046c37e28c42bded170fe41533941cbd303.jpg) + +![](images/f5fd5dc869248bc4088d42b71b8f30e1a92aac16a974fc691c8c2ad52ee3d1b6.jpg) + +![](images/bf31348bf6e992abf3d4dd28f5f1744264a2a6a89ca8f8e50d6abe1e04df73bc.jpg) +Figure 1. Illustration of existing Instance Normalization and Whitening methods and our proposed approach. (a-c) Existing methods broadly eliminate the global distribution variance but ignore the category-level semantic consistency resulting in limited feature discrimination. (d) Our proposed modules (SAN & SAW) encourage both intra-category compactness and inter-category separation through category-level feature alignment leading to both effective style elimination and powerful feature discrimination. + +# Abstract + +Deep models trained on source domain lack generalization when evaluated on unseen target domains with different data distributions. The problem becomes even more pronounced when we have no access to target domain samples for adaptation. In this paper, we address domain generalized semantic segmentation, where a segmentation model is trained to be domain-invariant without using any target domain data. Existing approaches to tackle this problem standardize data into a unified distribution. We argue that while such a standardization promotes global normalization, the resulting features are not discriminative enough to get clear segmentation boundaries. To enhance separation between categories while simultaneously promoting domain invariance, we propose a framework including two + +novel modules: Semantic-Aware Normalization (SAN) and Semantic-Aware Whitening (SAW). Specifically, SAN focuses on category-level center alignment between features from different image styles, while SAW enforces distributed alignment for the already center-aligned features. With the help of SAN and SAW, we encourage both intra-category compactness and inter-category separability. We validate our approach through extensive experiments on widely-used datasets (i.e. GTAV, SYNTHIA, Cityscapes, Mapillary and BDDS). Our approach shows significant improvements over existing state-of-the-art on various backbone networks. Code is available at https://github.com/leolyj/SAN-SAW + +# 1. Introduction + +Semantic segmentation is a critical machine vision task with multiple downstream applications, such as robotic nav + +igation [25, 36, 41, 64], autonomous vehicles [17, 27, 50, 63] and scene parsing [28, 68, 69, 71]. While the current fully supervised deep learning based segmentation methods can achieve promising results when they are trained and evaluated on data from same domains [1, 4-6, 21, 37, 40, 67, 70], their performance dramatically degrades when they are evaluated on unseen out-of-domain data. To enable generalization of models across domains, different domain adaptation techniques have been recently proposed [3, 15, 16, 23, 44, 46, 55, 62, 75]. However, a critical limitation of domain adaptation methods is their reliance on the availability of target domain in advance for training purposes. This is impractical for many real-world applications, where it is hard to acquire data for rarely occurring concepts. + +In this paper, we consider the challenging case of Domain Generalized Semantic Segmentation (DGSS), where we do not have access to any target domain data at the training time [9, 47, 48, 51, 66]. Existing methods tackle DGSS using two main approaches: (1) Domain Randomization [51, 66] which aims to increase the variety of training data by augmenting the source images to multiple domain styles. However, this is limiting since the augmentation schemes used are unable to cover different scenarios that may occur in the target domain. (2) Normalization and Whitening [9, 47, 48] which utilizes predefined Instance Normalization (IN) [61] or Instance Whitening (IW) [32] to standardize the feature distribution of different samples. IN separately standardizes features across each channel of individual images to alleviate the feature mismatch caused by style variations. However, as shown in Fig. 1 (a), IN only achieves center-level alignment and ignores the joint distribution among different channels. IW can remove linear correlation between channels, leading to well-clustered features of uniform distributions (see Fig. 1 (b)). Recent studies [9, 48] propose to combine IN and IW to achieve joint distributed feature alignment (see Fig. 1 (c)). Nevertheless, such global alignment strategy lacks the consideration of local feature distribution consistency. The features belonging to different object categories, which are originally well separated, are mapped together after normalization, leading to confusion among categories especially when generalizing to unseen target domains. Such semantic inconsistency inevitably results in sub-optimal training, causing performance degradation on unseen target domain and even the training domain (i.e. source domain). + +To address the inherent limitations of IN and IW, we propose two modules, Semantic-Aware Normalization (SAN) and Semantic-Aware Whitening (SAW), which collaboratively align category-level distributions aiming to enhance the discriminative strength of features (see Fig. 1 (d)). Compared with traditional IN&IW based methods, our approach brings two appealing benefits: First, it carefully integrates semantic-aware center alignment and distributed alignment, + +enabling both discriminative and compact matching of features from different styles. Therefore, our method can significantly enhance models' generalization to out-of-domain distributed data. Second, existing methods improve the generalization ability at the cost of source domain performance [9, 47]. Nevertheless, our approach enhances the semantic consistency while improving category-level discrimination, thus leading to effective generalization with negligible performance drop on source domain. + +Our extensive empirical evaluations on benchmark datasets show that our approach improves upon previous DGSS methods, setting new state-of-the-art performances. Remarkably, our method also performs favorably compared with existing SOTA domain adaptation methods that are trained using target domain data. In summary, followings are the major contributions of our work. + +- We propose effective feature alignment strategies to tackle out-of-domain generalization for segmentation, without access to target domain data for training. +- The proposed semantic-aware alignment modules, SAN and SAW, are plug-and-play and can easily be integrated with different backbone architectures, consistently improving their generalization performance. +- Through extensive empirical evaluations, and careful ablation analysis, we show the efficacy of our approach across different domains and backbones, where it significantly outperforms the current state-of-the-art. Remarkably, we even perform at par with approaches using target domain data for training purposes. + +# 2. Background + +Here, we discuss recent approaches developed for Domain Adaptation (DA) and Domain Generalization (DG) in the context of semantic segmentation. + +# 2.1. Domain Adaptation (DA) + +Domain Adaptation seeks to narrow the domain gap between the source and target domain data. It aims to enhance the generalization ability of the model by aligning the feature distributions between the source and target images [15, 16, 38, 39, 58-60]. Domain adaptation for semantic segmentation (DASS) was first studied in [24, 72], and since then has gained significant research attention. We can broadly categorize the existing approaches for DASS into Adversarial Training, and Self-Training based methods. Most of the existing work on DASS has been dominated by Adversarial Training based approaches [7, 15, 23, 56, 73]. Inspired by Generative Adversarial Networks [20], these approaches are generative in nature, and synthesize indistinguishable features which are domain-invariant and deceive the domain classifier. Self-Training based DASS approaches are relevant once labeled training data is scarce. + +These methods [35, 75] train the model with pseudo-labels which are generated from the previous models predictions. However, DA methods require access to the samples from the target domain, which limits their applicability on totally unseen target domain. + +# 2.2. Domain Generalization (DG) + +In contrast to Domain Adaptation, where the images in the target domain, although without labels, are accessible during the training process, Domain Generalization is evaluated on data from totally unseen domains [14, 43]. Domain generalization has been mostly explored on the image classification task, and a number of approaches have been proposed using as meta-learning [2, 29, 30, 34], adversarial training [31, 33, 52], autoencoders [18, 33], metric learning [12, 42] and data augmentation [19, 74]. The research on domain generalization for semantic segmentation (DGSS) is still in its infancy, with only a few existing approaches [9, 47, 48, 51, 66]. These existing DGSS methods mainly focus on two aspects: (1) Domain Randomization and (2) Normalization and Whitening. Domain Randomization based methods seek to synthesize images with different styles e.g. [66] leverages the advanced image-to-image translation to transfer a source domain image to multiple styles aiming to learn a model with high generalizability. Similarly, GTR [51] randomizes the synthetic images with the styles of unreal paintings in order to learn domain-invariant representations. Normalization and Whitening Methods apply different normalization techniques such as Instance Normalization (IN) [61] or whitening [48]. For example, based on the observation that Instance Normalization (IN) [61] prevents overfitting on domain-specific style of training data, [47] proposes to utilize IN to capture style-invariant information from appearance changes while preserving content related information. Inspired from [47], [47] proposes Switchable Whitening (SW), which combines IN with other whitening methods, aiming to achieve a flexible and generic features. In another recent approach [9], an instance selective whitening to disentangle domain-specific and domain-invariant properties is explored and only domain-specific features are normalized and whitened. However, all aforementioned methods perform a global alignment for features belong to different image categories. We aim to address this crucial limitation and propose an approach which enforces local semantic consistency during the trend of global style elimination. + +# 3. Preliminaries + +Let's denote an intermediate mini-batch feature map by $\mathbf{F} \in \mathbb{R}^{N \times K \times H \times W}$ , where $N, K, H$ and $W$ are the dimensions of the feature map, i.e. batch sample, channel, height and width, respectively. $\mathbf{F}_{n,k,h,w} \in \mathbf{F}$ represent the feature element, where $n, k, h, w$ respectively indicate + +the index of each dimension. Similarly, $\mathbf{F}_n\in \mathbb{R}^{K\times H\times W}$ denotes the features of $n$ -th sample from mini-batch, and $\mathbf{F}_{n,k}\in \mathbb{R}^{H\times W}$ denotes the $k$ -th channel of $n$ -th sample. + +Below, we first define Instance Normalization (IN) and Instance Whitening (IW), which have been commonly used by the existing approaches. + +Instance Normalization (IN) simply standardizes features using statistics (i.e. mean and standard deviation) computed over each individual channel from each individual sample, given by: + +$$ +\operatorname {I N} (\mathbf {F}) = \frac {\mathbf {F} _ {n , k} - \mu_ {n , k}}{\sigma_ {n , k} + \varepsilon}, \tag {1} +$$ + +where $\mathrm{IN}(\cdot)$ denotes the instance normalization process and $\varepsilon$ is a small value to avoid division by zero. The mean $\mu_{n,k}$ and standard deviation $\sigma_{n,k}$ of $n$ -th sample $k$ -th channel are computed as follows: + +$$ +\mu_ {n, k} = \frac {1}{H W} \sum_ {h = 1} ^ {H} \sum_ {w = 1} ^ {W} \mathbf {F} _ {n, k, h, w}, \tag {2} +$$ + +$$ +\sigma_ {n, k} = \sqrt {\frac {1}{H W} \sum_ {h = 1} ^ {H} \sum_ {w = 1} ^ {W} \left(\mathbf {F} _ {n , k , h , w} - \mu_ {n , k}\right) ^ {2}}. \tag {3} +$$ + +Using above operations, IN transforms the features from different image samples to have a standard distribution, i.e., zero mean and one standard deviation. However, even though the features of each channel are centered and scaled into standard distribution, the joint distribution between channels might be mismatched. + +Instance Whitening (IW) standardizes features by decorrelating the channels. As shown in Fig. 3 (a), it removes correlation between channels by making the covariance matrix close to the identity matrix through the following objective function: + +$$ +\mathcal {L} _ {\mathrm {I W}} = \sum_ {n = 1} ^ {N} | | \Psi (\mathbf {F} _ {n}) - \mathbf {I} | | _ {1}, \tag {4} +$$ + +where $\Psi (\cdot)$ and $\mathbf{I}$ denotes the channel correlation and identity matrix. $\Psi (\mathbf{F}_n)$ is defined as: + +$$ +\Psi (\mathbf {F} _ {n}) = \left[ \begin{array}{c c c} \operatorname {C o v} \left(\mathbf {F} _ {n, 1}, \mathbf {F} _ {n, 1}\right) & \dots & \operatorname {C o v} \left(\mathbf {F} _ {n, 1}, \mathbf {F} _ {n, K}\right) \\ \vdots & \ddots & \vdots \\ \operatorname {C o v} \left(\mathbf {F} _ {n, K}, \mathbf {F} _ {n, 1}\right) & \dots & \operatorname {C o v} \left(\mathbf {F} _ {n, K}, \mathbf {F} _ {n, K}\right) \end{array} \right], \tag {5} +$$ + +where $\operatorname{Cov}(\mathbf{F}_{n,i},\mathbf{F}_{n,j})$ is the covariance value between the $i$ -th channel and $j$ -th channel of feature $\mathbf{F}_n$ , given by: + +$$ +\operatorname {C o v} \left(\mathbf {F} _ {n, i}, \mathbf {F} _ {n, j}\right) = \frac {1}{H W} \sum_ {h = 1} ^ {H} \sum_ {w = 1} ^ {W} \left(\mathbf {F} _ {n, i, h, w} - \mu_ {n, i}\right) \left(\mathbf {F} _ {n, j, h, w} - \mu_ {n, j}\right). \tag {6} +$$ + +IW [32] is capable of unifying the joint distribution shape through channel decorrelation for each sample. Combined with IN [61], IW can make a unified joint distributed + +![](images/656e0e8315626c867b4901563e58b7a6b39205e5bce2cc0d842aa5a8087c5303.jpg) +Figure 2. The detailed architecture of our Semantic Aware Normalization (SAN) module. SAN adapts a multi-branch normalization strategy, aiming to transform the feature map $\mathbf{F}$ into the category-level normalized features $\bar{\mathbf{F}}$ , that are semantic-aware center aligned. + +![](images/9539a93b21f3cb9c3375013546ae6d3071a9e82cb3b44899fffd0c4544ecd5e5.jpg) + +alignment. However, such global matching might cause some features to be mapped to an incorrect semantic category, resulting in poor segmentation boundary decisions. In the following Sec. 4, we introduce our method which aims to tackle these problems, and preserve the semantic relationships between different categories. + +# 4. Proposed Method + +Our goal is to achieve semantic-aware center alignment and distributed alignment. For this, we introduce two novel modules, Semantic-Aware Normalization (SAN) and Semantic-Aware Whitening (SAW). We sequentially embed these two modules in our network as shown in Fig. 1. We discuss these modules in detail below. + +# 4.1. Semantic-Aware Normalization (SAN) + +Given an intermediate mini-batch feature map $\mathbf{F}$ , SAN transforms $\mathbf{F}$ into a feature map that is category-level centred. With the help of segmentation labels $Y$ , we can easily obtain the desired objective feature map $\mathbf{F}_{obj}$ as: + +$$ +\mathbf {F} _ {o b j} = \frac {\mathbf {F} _ {n , k} ^ {c} - \mu_ {n , k} ^ {c}}{\sigma_ {n , k} ^ {c} + \varepsilon} \cdot \gamma^ {c} + \beta^ {c}, \tag {7} +$$ + +$$ +\mu_ {n, k} ^ {c} = \frac {1}{| Y (c) |} \sum_ {Y (c)} \mathbf {F} _ {n, k} ^ {c}, \tag {8} +$$ + +$$ +\sigma_ {n, k} ^ {c} = \sqrt {\frac {1}{| Y (c) |} \sum_ {Y (c)} \left(\mathbf {F} _ {n , k} ^ {c} - \mu_ {n , k} ^ {c}\right) ^ {2}}, \tag {9} +$$ + +where $\mu_{n,k}^{c}$ and $\sigma_{n,k}^{c}$ are the mean and standard deviation computed from $c$ -th category features of $k$ -th channel, $n$ -th sample, and the $c$ -th category label $Y(c)$ . Features $\mathbf{F}_{n,k}^{c}$ belong to $c$ -th category in channel $\mathbf{F}_{nk}$ . The weights for scaling and shifting are denoted by $\gamma$ and $\beta$ , respectively, which + +are both learnable parameters. We separately allocate these affine parameters for each category (i.e. $\gamma^c$ and $\beta^c$ ) aiming to adjust the standardized features from different categories to distinct spaces, thus making our feature space more discriminative. Note that different samples in the mini-batch share the same affine parameters in order to cast features of same category into a same feature space, thus ensuring category-level center alignment. + +We utilize SAN to approximate Eq. (7) since the label $Y$ is unavailable when testing on target domains. We follow a series of steps to transform the input features $\mathbf{F}$ into the objective features $\mathbf{F}_{obj}$ as shown in Fig. 2. First, we leverage the segmentation masks generated from the classifier to highlight the category region while simultaneously suppressing other regions in each normalization branch. + +$$ +\mathbf {F} _ {c} ^ {\prime} = \mathbf {F} \otimes \mathbf {M} _ {c}, \tag {10} +$$ + +where $\mathbf{M}_c$ denotes the mask of the $c$ -th category, $\otimes$ denotes Hadamard product and $\mathbf{F}_c'$ represents the masked feature map in $c$ -th category branch. The generated mask can be too rough to precisely locate category features. We therefore introduce a Category-level Feature Refinement (CFR) block to adaptively adjust the highlighted features $\mathbf{F}_c'$ into $\mathbf{F}_c''$ , given by: + +$$ +\mathbf {F} _ {c} ^ {\prime \prime} = \operatorname {S i g m} \left(f ^ {3 \times 3} \left(\left[ \mathbf {F} _ {c, m a x} ^ {\prime}; \mathbf {F} _ {c, a v g} ^ {\prime}; \mathbf {M} _ {c} \right]\right)\right) \otimes \mathbf {F} _ {c} ^ {\prime}, \tag {11} +$$ + +where $f^{3 \times 3}(\cdot)$ and $\operatorname{Sigm}(\cdot)$ denote $3 \times 3$ convolution and sigmoid function, respectively. $\mathbf{F}_{c,\max}^{\prime}$ and $\mathbf{F}_{c,\text{avg}}^{\prime}$ are max-pooled and average-pooled features of feature map $\mathbf{F}_c^\prime$ . [a; b] is the concatenation of a and b along channel axis. + +In order to further refine the category-level center alignment, we design a Regional Normalization layer which normalizes features only within the category region instead of whole scene. After refinement, only the feature elements + +![](images/57cd95020325f812e69b5b076afb8484ee6481138a672ff835dcd0a1239ebf70.jpg) + +![](images/3479d4372405e4246539915c247d0229a7c31b11ed6cc69eb80edf3bbed5ae5f.jpg) + +![](images/9f8def368ba17fdf0ae5538cd0c6971c2c78f782fc291036b058d37500ce87a9.jpg) +(a) Instance Whitening (IW) [32] +(b) Group Instance Whitening (GIW) [8] +(c) Ours: Semantic-Aware Whitening (SAW) +Figure 3. Illustration of feature whitening in IW [32], GIW [8] and the proposed SAW. (a) IW de-correlates all channels from each other. (b) GIW only de-correlates the channels in the same group. (c) SAW allocates channels related to different categories in each group. + +with high value are assigned the category region. To flexibly identify feature elements, we apply $k$ -means clustering on the spatial feature map obtained by avgpooling along channel axis. After dividing the spatial elements into $k$ clusters, the clusters from the first to the $t$ -th are considered to be the category region, and the remaining clusters are considered as ignored region. We set $t$ to one and search the optimal $k$ through the hyper-parameter search. In this paper, $k$ is set to 5. See Sec. 5.5 for more details. + +Thus, we can assign the feature elements of $c$ -th branch into 2 clusters $\{\Phi_{\mathrm{low}}^c,\Phi_{\mathrm{high}}^c\}$ , where $\Phi_{\mathrm{high}}^c$ denotes the identified category region. We normalize features within the category region $\Phi_{\mathrm{high}}^c$ for each individual channel. Finally, all category branches are added together, then re-shifted and scaled by the learnable affine parameters: + +$$ +\widetilde {\mathbf {F}} = \sum_ {c = 1} ^ {C} \operatorname {R N} \left(\mathbf {F} _ {c} ^ {\prime \prime}, \Phi_ {\text {h i g h}} ^ {c}\right) \cdot \gamma^ {c} + \beta^ {c}, \tag {12} +$$ + +where $\mathrm{RN}(\cdot, \Phi_{\mathrm{high}}^c)$ denotes our regional normalization in $c$ -th branch, $\gamma^c$ and $\beta^c$ are affine parameters as per Eq. (7). In order to ensure the processed feature map $\widetilde{\mathbf{F}}$ are category-level-center-aligned as per Eq. (7), we optimize the following cross-entropy loss: + +$$ +\mathcal {L} _ {\mathrm {S A N}} = \operatorname {C E} (\mathbf {M}, Y) + \left\| \widetilde {\mathbf {F}} - \mathbf {F} _ {o b j} \right\| _ {1}, \tag {13} +$$ + +where $\mathbf{M} \in \{\mathbf{M}_1, \mathbf{M}_2, \dots, \mathbf{M}_C\}$ denotes the set of predicted segmentation masks. + +# 4.2. Semantic-Aware Whitening (SAW) + +We propose the Semantic-Aware Whitening (SAW) module, to further enhance channel decorrelation for the + +distributed alignment of the already semantic-centred features. Instance Whitening (IW) is capable of unifying the joint distribution, which is useful for distributed alignment. However, directly adopting IW is not feasible, since such strong whitening that strictly removes correlation between all channels may damage the semantic content, resulting in loss of crucial domain-invariant information. Group Instance Whitening (GIW [8], shown in Fig. 3(b)) is a simple solution to this problem. Given the feature map $\widetilde{\mathbf{F}}$ which is the output of SAN module, GIW is defined by: + +$$ +\mathbf {G} _ {n} ^ {m} = \left[ \widetilde {\mathbf {F}} _ {n, \frac {K (m - 1)}{M} + 1}; \widetilde {\mathbf {F}} _ {n, \frac {K (m - 1)}{M} + 2}; \dots ; \widetilde {\mathbf {F}} _ {n, \frac {K m}{M}} \right], \tag {14} +$$ + +$$ +\mathcal {L} _ {\mathrm {G I W}} = \frac {1}{N} \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {M} | | \Psi \left(\mathbf {G} _ {n} ^ {m}\right) - \mathbf {I} | | _ {1}, \tag {15} +$$ + +where $\mathbf{G}_n^m$ denotes the $m$ -th group of $n$ -th sample, $M$ is the number of groups, and $\Psi(\cdot)$ is the channel correlation matrix defined in Eq. (4). While GIW improves the generalization by partial (group) channel decorrelation, it strictly decorrelates neighboring channels, lacking the consideration of searching more appropriate channel combinations. It is well-known that the channels in convolution neural networks are highly related to semantics. To this end, we propose SAW module to rearrange channels, ensuring each group contains channels related to different categories. Compared with grouping same-category-related channels, decorrelation between channels from different categories is more reasonable, since different-category-related channels activate different regions. Removing the correlations between those channels not only enhances the representation + +capacity of each single channel, but also prevents the information loss, resulting in distributed alignment with minor changes to the semantic content. + +As for segmentation model, the segmentation results of each category are obtained by multiplying all the channels by their corresponding weights and then adding them up. The weight value determines the influence of channel on the category. Hence, to identify each channel belongs to which category, we utilize the classifier from the SAN module. As shown in Fig. 3 (c), for each category, there are $K$ weights corresponding to $K$ channels, i.e. $\{w_{\mathrm{class} c}^{1}, w_{\mathrm{class} c}^{2}, \dots, w_{\mathrm{class} c}^{K}\}$ where $c \in \{1, \dots, C\}$ . After turning them into absolute values. We rank the weights of each category from the largest to the smallest. Then in each category, the first $\frac{K}{C}$ weight indexes are selected. For the sake of clarity, we use $\mathcal{I} \in \mathbb{R}^{C \times \frac{K}{C}}$ to denote the all selected indexes, where $\mathcal{I}(i,j)$ represents the $j$ -th selected index of $i$ -th category, $i \in \{1, \dots, C\}$ and $j \in \{1, \dots, \frac{K}{C}\}$ . We arrange $\frac{K}{C}$ groups and allocate $C$ different-category-related channels for each group. Specifically, each channel is weighted by its corresponding classifier weight before grouping, aiming to execute adaptive whitening transformation. Therefore, the $m$ -th group of $n$ -th sample: $\mathbf{G}_n^m$ in Eq. (14) can be modified as $\bar{\mathbf{G}}_n^m$ : + +$$ +\begin{array}{l} \bar {\mathbf {G}} _ {n} ^ {m} = \left[ \widetilde {\mathbf {F}} _ {n, \mathcal {I} (1, m)} \cdot w _ {\text {c l a s s 1}} ^ {\mathcal {I} (1, m)}; \widetilde {\mathbf {F}} _ {n, \mathcal {I} (2, m)} \cdot w _ {\text {c l a s s 2}} ^ {\mathcal {I} (2, m)}; \right. \tag {16} \\ \ldots ; \widetilde {\mathbf {F}} _ {n, \mathcal {I} (C, m)} \cdot w _ {\mathrm {c l a s s C}} ^ {\mathcal {I} (C, m)} ]. \\ \end{array} +$$ + +Correspondingly, our whitening loss is formulated as: + +$$ +\mathcal {L} _ {\mathrm {S A W}} = \frac {1}{N} \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {\frac {K}{C}} | | \Psi (\bar {\mathbf {G}} _ {n} ^ {m}) - \mathbf {I} | | _ {1}. \tag {17} +$$ + +Note that operations of SAW module do not change the features of main network in forward pass. Therefore, different from SAN module, SAW is only applied during training. + +# 5. Experiments + +# 5.1. Datasets Description + +Synthetic Datasets. GTA5 [53] is a synthetic image dataset, which is collected by using GTA-V game engine. It contains 24966 images with a resolution of $1914 \times 1052$ along with their pixel-wise semantic labels. SYNTHIA [54] is a large synthetic dataset with pixel-level semantic annotations. The subset SYNTHIA-RANDCITYSCAPES [54] is used in our experiments which contains 9400 images with a high resolution of $1280 \times 760$ . + +Real-World Datasets. Cityscapes [10] is a high resolution dataset (i.e. $2048 \times 1024$ ) of 5000 vehicle-captured urban street images taken from 50 different cities primarily in Germany. BDDS [65] contains thousands of real-world dashcam video frames with accurate pixel-wise annotations, where 10000 images are provided with a resolution + +of $1280 \times 720$ . Mapillary [45] contains 25000 images with diverse resolutions. The annotations contain 66 object categories, but only 19 categories overlap with others. + +# 5.2. Implementation Details + +We initialize the weights of the feature extractor module with an ImageNet [11] pre-trained model. We use SGD [26] optimizer with an initial learning rate of 5e-4, a batch size of 2, a momentum of 0.9 and a weight decay of 5e-4. Besides, we follow the polynomial learning rate scheduling [6] with the power of 0.9. We train model for 200000 iterations. All datasets have 19 common categories, thus the parameter $C$ defined in both SAN and SAW is set to 19. However, since SAW arranges $\frac{K}{C}$ groups, $C$ can only be 2, 4, 8 or 16 to make $K$ (channel number) divisible by $C$ . Based on the results of ablation study on parameter $C$ (Sec. 5.5), we set $C = 4$ in both SAN and SAW. + +We implement our method on PyTorch [49] and use a single NVIDIA RTX 3090 GPU for our experiments. Following previous works, we use PASCAL VOC Intersection over Union (IoU) [13] as the evaluation metric. + +# 5.3. Comparison with DG and DA methods + +For brevity, we use G, S, C, B and M to denote GTA5 [53], SYNTHIA [54], Cityscapes [10], BDDS [65] and Mapillary [45], respectively. We extensively evaluate our method with different backbones including VGG-16 [57], ResNet-50 and ResNet-101 [22]. We repeat each experiment three times, and report the average results. Unlike existing synthetic-to-real generalization approaches, we propose to evaluate our model from an arbitrary domain to other unseen domains. Therefore, we conduct comprehensive experiments on five generalization settings, from (1) G to C, B, M & S; (2) S to C, B, M & G; (3) C to G, S, B & M; (4) B to G, S, C & M; (5) M to G, S, C & B. Our results reported in Tab. 1 on the first three settings, and Appendix A on the remaining 2 settings, suggest that our model consistently gains the best performance across all settings and backbones. Compared to the second best results (see underlined values), our method shows a large improvement. Visual samples for qualitative comparison are given in Fig. 4. Remarkably, our method performs favorably in comparison to the methods that have access to the target domain data, see results in Appendix B. + +# 5.4. Source Domain Performance Decay Analysis + +A common pitfall of the domain generalization methods is that their performance degrades on the source domain. To compare different methods for this aspect, we evaluate them on the test set of the source domain in Tab. 2. The results suggest that our method largely retains performance on the source domain, and performs comparably with the model trained without domain-generalization (Baseline in Tab. 2). + +Table 1. Performance comparison in terms of mIoU (%) between Domain Generalization methods. The best and second best results are highlighted and underlined, respectively. † denotes our re-implementation of the respective method. G, C, B, M and S denote GTA5 [53], Cityscapes [10], BDDS [65], Mapillary [45] and SYNTHIA [54], respectively. + +
MethodsPublicationBackboneTrain on GTA5 (G)Train on SYNTHIA (S)Train on Cityscapes (C)
→C→B→M→S→C→B→M→G→B→M→G→S
Baseline28.8925.4426.8725.7222.9023.1520.8125.2343.1550.9141.5322.36
IBN† [47]ECCV 201831.2531.6833.2726.4531.6828.3429.9726.0345.5553.6343.6424.78
SW [48]ICCV 2019VGG-1635.7027.1127.9826.6528.0026.8024.7025.8245.3753.0242.7923.97
DRPC [66]ICCV 201936.1131.5632.2526.8935.5229.4532.2726.3846.8655.8343.9824.84
GTR† [51]TIP 202136.1032.1434.3226.4536.0731.5730.6326.9345.9354.0843.7224.13
ISW† [9]CVPR 202134.3633.6834.6226.9936.2131.9431.8826.8147.2654.2142.0824.92
Ours38.2136.3036.8728.4538.3634.3233.2327.9449.1956.3745.7326.51
Baseline29.3225.7128.3326.1923.1824.5021.7926.3445.1751.5242.5824.32
IBN [47]ECCV 201833.8532.3037.7527.9032.0430.5732.1626.9048.5657.0445.0626.14
SW [48]ICCV 2019ResNet-5029.9127.4829.7127.6128.1627.1226.3126.5148.4955.8244.8726.10
DRPC [66]ICCV 201937.4232.1434.1228.0635.6531.5332.7428.7549.8656.3445.6226.58
GTR† [51]TIP 202137.5333.7534.5228.1736.8432.0232.8928.0250.7557.1645.7926.47
ISW [9]CVPR 202136.5835.2040.3328.3035.8331.6230.8427.6850.7358.6445.0026.20
Ours39.7537.3441.8630.7938.9235.2434.5229.1652.9559.8147.2828.32
Baseline30.6427.8228.6528.1523.8525.0121.8427.0646.2353.2342.9625.49
IBN† [47]ECCV 201837.4238.2838.2828.6934.1836.6336.1928.1550.2258.4246.3327.57
SW† [48]ICCV 2019ResNet-10136.1136.5632.5928.4331.6035.4829.3127.9750.1056.1645.2127.18
DRPC [66]ICCV 201942.5338.7238.0529.6737.5834.3434.1229.2451.4958.6246.8728.96
GTR [51]TIP 202143.7039.6039.1029.3239.7035.3036.4028.7151.6758.3746.7629.07
ISW† [9]CVPR 202142.8738.5339.0529.5837.2133.9835.8628.9850.9859.7046.2828.43
Ours45.3341.1840.7731.8440.8735.9837.2630.7954.7361.2748.8330.17
+ +![](images/5477d2b7e6182e810f22d803fb4d3bdcc36699f0430024fc97d2baae5f8ab010.jpg) +Figure 4. Visual comparison with different Domain Generalization methods on unseen domains i.e. Cityscapes [10], BDDS [65], Mapillary [45] and SYNTHIA [54], with the model trained on GTA5 [53]. The backbone network is ResNet-50. + +![](images/7263dc3f1821adae023a0ba4a06a6f9824e12ebdc6e3cc017b2aae02cbc9d367.jpg) + +![](images/3252efc76dd2552edaf3596afba0e8bac1813ac53b5003e95e9f472fe8bedc1f.jpg) + +![](images/b95ceac192b020157ada3d78de84c15e4ea83764320ea34709f86bfbd0794918.jpg) + +![](images/35c77c5ce1033dfe07f51cf5469b097f8241b81902743602b13d5e7013969314.jpg) + +![](images/553c153e742cfc5e1bf3a1978b4419ba55d6eac63437b13a0e54bf14a4af28f3.jpg) + +![](images/38cfa612e0e186f6f32d9f3fc8cb42a029f766ddee7c293b8efe9c8a943769f7.jpg) + +![](images/291eceb11e40199e6439491f8ca8ab45c9503afb56a237f444a01a695c09b95a.jpg) + +![](images/f076f4f9cc8651bfc145ec349f2be5bd35e6f3f9fe9401a75657f140eca1c40b.jpg) + +# 5.5. Ablation Study + +SAN and SAW. We investigate the individual contribution of SAN and SAW modules towards overall performance. Tab. 3 shows the mIoU improvement on ResNet-50 once we progressively integrate SAN and SAW. Experiments are conducted for generalization from GTA5 (G) to the other four datasets i.e. Cityscapes (C), BDDS (B), Mapillary (M) and SYNTHIA(S). In our case, each of them helps boost the generalization performance by a large margin. Specifically, we observe that SAN and SAW greatly achieve an average improvement of $8.71\%$ and $7.93\%$ , respectively. We further observe that the models with only SAW show slightly weaker generalization capacity than those with only SAN. This is because without category-level centering of SAN, SAW performs distributed align + +ment, which may lead to incorrect feature matching between different categories. Therefore, our SAW module is mainly proposed to complement SAN in an integrated approach. As shown in Tab. 3, the best performance is achieved with a combination of both SAN and SAW. + +CFR block in SAN. To demonstrate the effectiveness of the Category-level Feature Refinement (CFR) in SAN, we conducted an ablation experiment by removing the CFR block. As shown in Tab. 4 (top row), model without CFR consistently performs worse than model with SAN. With the help of CFR, SAN achieves an average gain of $2.30\%$ , which demonstrates its usefulness. + +Category-related Grouping in SAW. We perform ablations on different grouping strategies to verify their contributions. We conduct experiments on baseline with IW, GIW and SAW, respectively. The architectures of these + +![](images/93a85b043de4f85b0bbabe0b09386aca8cfb3dc2f86286e82fb6898be4771dc3.jpg) +(a) mIoU Performance According to $C$ + +![](images/e0c2fd2e3258248499fda8bdd406309f705a0be1019c9dc8f35534d02e53fe62.jpg) +(b) mIoU Performance According to $k$ +Figure 5. Change in performance with hyper-parameters: $C$ and $k$ . The experimental backbone is ResNet-50. + +three models are illustrated in Fig. 3. As shown in Tab. 4 (bottom row), by adopting the general grouping operation, GIW shows significant improvement compared to model with IW. When applying our proposed SAW which performs category-related grouping, the performance of network improves to $37.54\%$ , $34.97\%$ , $39.85\%$ & $28.46\%$ on G $\rightarrow$ C, B, M & S. This confirms the effectiveness of category-related grouping in SAW. + +Hyper-Parameter Analysis. $C$ decides on the number of categories for semantic-aware feature alignment in both SAN and SAW. Since we rank the categories according to the their respective proportions in training data, only the first $C$ categories are selected to handle category-level feature matching. To ensure that the channel dimension of feature maps is divisible by $C$ , we can only set $C \in \{2, 4, 6, 8, 16\}$ . Fig. 5 (a) shows compares results for different values, suggesting the optimal $C$ is 4. In CFR block, we adopt $k$ -means clustering to separate feature elements into category region and background. For searching the optimal parameter $k$ , we only choose the first cluster whose cluster center is highest as the category region. As shown in Fig. 5 (b), model performs best when adopting $k = 5$ . + +# 6. Conclusion and limitations + +In this manuscript, we present a domain generalization approach to address the out-of-domain generalization for semantic segmentation. We propose two novel modules: Semantic-Aware Normalization (SAN) and Semantic-Aware Whitening (SAW), which sequentially perform category-level center alignment and distributed alignment to achieve both domain-invariant and discriminative features. Comprehensive experiments demonstrate the effectiveness of SAN and SAW with state-of-the-art perfor + +Table 2. Comparison of different methods for performance drop on source domain. The performance drop $(\downarrow)$ is obtained with respect to the baseline. The best and second best values are highlighted and underlined, respectively. The network backbone is ResNet-50. + +
MethodsGTA5SYNTHIACityscapesBDDSMapillary
Baseline73.9570.8477.9379.6770.49
IBN† [47]↓1.05↓2.40↓1.38↓1.30↓2.25
SW [48]↓0.45↓1.71↓0.63↓1.52↓0.91
DRPC [66]↓2.37↓3.63↓2.72↓2.46↓3.05
GTR† [51]↓2.07↓2.11↓3.25↓3.64↓4.17
ISW† [9]↓1.85↓1.28↓1.52↓1.83↓1.23
Ours↓0.19↓0.08↓0.06↓0.23↓0.34
+ +Table 3. Ablation analysis of SAN (Sec. 4.1) and SAW (Sec. 4.2). + +
MethodsSANSAWTrain on GTA5 (G)
CBMS
Baseline29.3225.7128.3326.19
+ SAN✓38.9236.4340.1128.91
+ SAW✓37.5434.9739.8528.46
All✓✓39.7537.3441.8630.79
+ +Table 4. Ablation of different blocks in SAN and SAW + +
MethodsTrain on GTA5 (G)
CBMS
Baseline29.3225.7128.3326.19
Baseline + SAN (w/o CFR)35.5133.2438.6827.76
Baseline + SAN38.9236.4340.1128.91
Baseline + IW33.1931.2730.5526.55
Baseline + GIW35.7632.8836.9527.24
Baseline + SAW37.5434.9739.8528.46
+ +mance in both domain generalization and domain adaptation. Although the method effectively eliminates feature differences caused by style variations on source domain, the extracted style-invariant features may still contain source-domain specific cues, leading to significant performance delta between the source and target domain. Some interesting future directions to close this gap include learning how to model domain shift (meta-learning), integrating multiple domain-specific neural networks (ensemble learning) and teaching a model to perceive generic features regardless of the target task (disentangled representation learning). + +The datasets used in the paper lack diversity and have biases as they are mostly captured in the developed world. Beyond that, this paper has no ethical problem including personally identifiable information, human subject experimentation and military application. + +Acknowledgement: This work was partially supported by the National Natural Science Foundation of China (No. 61972435, U20A20185). M. Hayat is supported by ARC DECRA fellowship DE200101100. + +# References + +[1] Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla. Segnet: A deep convolutional encoder-decoder architecture for image segmentation. IEEE Transactions on Pattern Analysis & Machine Intelligence (TPAMI), 39(12):2481-2495, 2017. 2 +[2] Yogesh Balaji, Swami Sankaranarayanan, and Rama Chellappa. Metareg: Towards domain generalization using meta regularization. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), 31:998-1008, 2018. 3 +[3] Shai Ben-David, John Blitzer, Koby Crammer, Fernando Pereira, et al. Analysis of representations for domain adaptation. 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As a compromise, semantic segmentation has long been modeled as per-point prediction on dense regular grids. In this work, we present a novel and efficient modeling that starts from interpreting the image as a tessellation of learnable regions, each of which has flexible geometrics and carries homogeneous semantics. To model region-wise context, we exploit Transformer to encode regions in a sequence-to-sequence manner by applying multi-layer self-attention on the region embeddings, which serve as proxies of specific regions. Semantic segmentation is now carried out as per-region prediction on top of the encoded region embeddings using a single linear classifier, where a decoder is no longer needed. The proposed RegProxy model discards the common Cartesian feature layout and operates purely at region level. Hence, it exhibits the most competitive performance-efficiency trade-off compared with the conventional dense prediction methods. For example, on ADE20K, the small-sized RegProxy-S/16 outperforms the best CNN model using $25\%$ parameters and $4\%$ computation, while the largest RegProxy-L/16 achieves $52.9\mathrm{mIoU}$ which outperforms the state-of-the-art by $2.1\%$ with fewer resources. Codes and models are available at https://github.com/YiF-Zhang/RegionProxy. + +# 1. Introduction + +Semantic segmentation is one of the fundamental tasks in computer vision, and has been carried out using CNNs since the beginning of the deep learning era [10,17,21,27]. However, CNN is not the out-of-the-box solution for semantic segmentation considering two of its natures: 1) Limited context. CNN lacks of abilities to capture long range dependencies for context modeling, which is essential for semantic segmentation. 2) Coarse prediction. Due to its hierarchical nature, CNN outputs coarse feature which is inadequate for dense labeling. Fundamentally, the majority of semantic + +![](images/3eb00efaab096203be5c8aebe5badb14e4b1fd84c1462b22273154e7f38ba7a4.jpg) +pixel-wise features + +![](images/9fcbc19d57c2d5027b2881a713e3cf8cb6706f2acbce67cce57ce9814fc726f5.jpg) +regions tokens +Figure 1. Illustration of two different schemes for semantic segmentation. (Left) Conventional encoder-decoder models establish dense correspondence between input and output on structured pixel-level grid, and segment image in a per-pixel prediction fashion. (Right) We propose to interpret the image as a tessellation of learnable regions and represent it by region-level embeddings (i.e., proxies) at an early stage, and segment image by per-region prediction using sequence-to-sequence Transformer [11,41]. + +segmentation researches since FCN [27] have been centring on resolving these two issues. A great number of works have been proposed for better context modeling [19,50-52] and fine-grained feature prediction [6,34,43], which significantly advance the semantic segmentation research. + +Currently, the Transformer architecture [41] from natural language processing is introduced to the vision community and has gained significant research interest. The Vision Transformer (ViT) [11] partitions image into square patches and encodes their embeddings (i.e., tokens) in a sequence-to-sequence manner using stacked self-attention layers. Some of its variants [26, 44] adopt a hierarchical structure and restrict self-attention in local area for better scalability. Recently, several semantic segmentation works [38, 48, 53] adopt vision Transformers as backbone and achieve impressive performances. They learn better context with the help of the inherent advantages of vision Transformers, namely the attention mechanism. However, in these models, the vision Transformer serves transparently as feature extractor which extracts 2D coarse features exactly as its convolutional counterpart does, while its main character, a sequence-to-sequence encoder, is not touched. + +We revisit the aforementioned two issues: limited context and coarse prediction. While the former is a corollary + +of the local receptive field which can be alleviated by adopting Transformer architecture or previous CNN-based context modules, the latter is substantially induced by the inflexible regular (Cartesian) layout of network features, as it does not follow the structure of real world semantics: with the large strides of typical vision backbones, it carries jumbly semantics in grid cells and brings difficulties for dense labeling. Hence, a "decoder" is required to produce fine-grained features. These facts imply that regular grids may not be the optimal feature arrangement for semantic segmentation. + +In this work, we explore a novel modeling of semantic segmentation which we believe to be closer to its essence: we attempt to interpret image as a set of interrelated regions, where the region indicates a group of adjacent pixels with homogeneous semantics. As illustrated in Figure 1, we propose a simple RegProxy approach which learns regions at an early stage, explicitly models inter-region relations using Transformer [41], and encodes regions in a sequence-to-sequence fashion. We design a novel mechanism to describe region geometrics and ensure the tessellation of the entire region set, which enables us to conduct semantic segmentation by per-region prediction. The entire process is fully parameterized and differentiable which can be trained end-to-end efficiently. Here we present the major novelties and contributions of this work: 1) Instead of manipulating features on regular grids, we operate on a set of region embeddings throughout the entire network. Each of the region embeddings serves as the feature representation of a specific learnable region, namely the region proxy. 2) Instead of using Transformer to extract structured feature, we dive into its essence as a sequence-to-sequence encoder, and use it to explicitly model inter-region relations. 3) Instead of modeling semantic segmentation as per-pixel prediction using decoder, we segment images by directly predicting on the region embeddings using a linear classifier. + +We build our model on bare ViTs [11] for image classification by adding negligible overhead ( $\sim 0.5\%$ parameters and GFLOPs), and consistently achieves the state-of-the-art performances throughout different model sizes. Extensive experiments show the competitive performance-efficiency trade-off of RegProxy under various model capacities on multiple datasets. One may peek the results in Figure 2. + +# 2. Related Work + +Vision Transformer Transformer [41] was firstly introduced in machine translation and is currently the de-facto standard of most natural language processing (NLP) tasks. The proposed attention mechanism has also inspired a number of works in computer vision [18, 45, 46]. Notably, the attention works particularly well in semantic segmentation [13, 19, 22, 55] where contextual information is crucial. + +Recently, Dosovitskiy et al. [11] proposes the Vi- + +![](images/b99f67b61809d9b85c291d626615f5b8057eeb35d0aa9f8ede78a696bc83623a.jpg) +Figure 2. Performance vs. GFLOPs on ADE20K val split. We report results without multi-scale inference. RegProxy shows a highly competitive performance-efficiency trade-off among the state-of-the-art methods. Best viewed in color. + +vision Transformer (ViT) which directly inherits the Transformer [41] architecture from NLP and works as a standalone model. ViT is gaining significant research interest and a number of improved models have been proposed. Generally, the architecture of vision Transformers can be sequential or hierarchical. Sequential models (including the original ViT [11]) partition image into patches and encode inputs in a sequence-to-sequence fashion by computing the global self-attention. DeiT [39] successfully trains ViTs on ImageNet-1k [10] with the help of strong data augmentations and knowledge distillation. CaiT [40] proposes LayerScale technique and later class tokens for effective training of vision Transformers at depth. XCiT [12] proposes cross-covariance attention that operates on feature dimension to build more scalable vision Transformers. Hierarchical models [26, 44] borrow some of the image-specific inductive bias from CNNs, such as translation equivariance and 2D neighborhood structure on regular grid. They compute attentions within local windows and produce hierarchical 2D features. Swin Transformer [26] is one of the most successful hierarchical vision Transformers. With the shifted window design, it brings better efficiency while allowing cross-window connections for better feature extraction. + +Semantic Segmentation Semantic segmentation has been modeled as dense prediction since the emergence of fully conventional architectures. FCN [27] lays the foundation of modern semantic segmentation models, which is the first to adopt fully convolutional neural networks to segment images with arbitrary scales in an end-to-end manner. The + +
backbonemethod#params.FLOPsADE20KCityscapes
ViT-Ti/16Baseline5.7M3.8G39.0 / 37.872.3 / 68.1
Ours--40.9 (+1.9)74.1 (+1.8)
ViT-S/16Baseline22.0M14.9G45.4 / 44.276.1 / 71.8
Ours--46.0 (+0.6)75.9 (-0.2)
ViT-B/16Baseline86.6M58.8G47.1 / 45.678.5 / 75.1
Ours--47.3 (+0.2)77.3 (-1.2)
+ +Table 1. Pilot experiment results. We report baseline results with/without the bilinear upsampling of the final logits map. The baseline uses the original patch embedding [11] and works as a typical segmentation model with stride 16, while our prototype model embeds non-parametric regions (i.e., superpixels). + +following works inherit the fully convolutional design and focus on better context modeling. The efforts have been put on one or more aspects that significantly improve semantic segmentation performance: 1) Enlarge receptive field using larger kernels or dilated convolution [3,4,31,49]; 2) Integrate multi-scale features [5,6,20,52]; 3) Refine contextual information [24,50,51]; 4) Utilize attention [13,19,22,55]; 5) Search or design designated backbones [23,30,32,43]. + +Recently, several works exploit Transformer to conduct semantic segmentation. SETR [53] is the first to introduce vision Transformer backbones into semantic segmentation. Segmenter [38] exploits Transformer to predict per-class masks. SegFormer [48] and DPT [32] propose hierarchical vision Transformer backbones specifically designed for dense prediction tasks. MaskFormer [7] uses the Transformer Decoder [41] to query classes with their masks from a conventional encoder-decoder model. We emphasize that our work has significant difference with these approaches: we use bare Transformer to model inter-region relations instead of using it as replaceable or extra modules of existing dense-prediction architectures. + +# 3. Pilot Study of Region Proxy + +Before introducing our main model, we first present a naive instantiation of region proxy for a proof of concept. We revisit the classical superpixel segmentation [33]. Superpixels are an over-segmentation of images that is formed by grouping perceptually similar pixels together based on low-level information (e.g., colors). It provides a low/mid-level image representation for high-level vision tasks including semantic segmentation [14, 15, 36]. In our pilot study, we adopt widely used SLIC [1] method to generate non-parametric regions to validate our region proxy notion. + +Regions as Superpixels Essentially, we attempt to batch the pixel labeling by classifying superpixels. This implies that nearby pixels with similar low-level properties should be semantically homogeneous. This assumption will finally be analyzed in Section 5.3 along with our main model introduced in Section 4. At the moment, we build our prototype model under this premise. + +We modify the vanilla ViT [11] which encodes patches, making it feasible to encode superpixels: $N$ superpixels $\{\mathbf{s}_i\}$ are generated from input image $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ . The irregular superpixels are cropped by their enclosing bounding boxes and resized to fixed size patches $\{\mathbf{x}_i\}$ where $\mathbf{x}_i \in \mathbb{R}^{P \times P \times 3}$ , which is implemented using ROIAAlign [16]. We embed $\mathbf{x}_i$ using the exact linear patch embedding in the vanilla ViT, producing $N$ tokens with dimension $D$ , which are then encoded in a sequence-to-sequence manner. Instead of per-pixel prediction, We directly classify regions by applying a linear classifier on every tokens. For supervision, a soft label $\hat{\mathbf{y}}_i$ is applied on the $i$ -th token. We have + +$$ +\hat {\mathbf {y}} _ {i} [ c ] = \frac {| \left\{\mathbf {p} \in \mathbf {s} _ {i} \mid \hat {y} (\mathbf {p}) = c \right\} |}{| \mathbf {s} _ {i} |}, c \in \{0, 1, \dots , K - 1 \} \tag {1} +$$ + +where $\hat{y} (\mathbf{p})$ is the label of the pixel $\mathbf{p}$ , and $K$ is the number of classes. Namely, $\hat{\mathbf{y}}_i$ is the category histogram of pixels inside superpixel $\mathbf{s}_i$ . + +Experiment To set up the baseline, we apply the same linear classifier to the output tokens of the vanilla ViT. Hence the only difference between the baseline and our prototype model is the computation primitive: whether to be a square patch or a region. The training protocol is identical to our main experiments which is described in Section 5. In Table 1, We report results of three model variants ViT-{Ti/16, S/16, B/16} on ADE20K and Cityscapes. We observe evidential performance gains on smaller models, which vanish as the model getting larger. We hypothesize that the introduced low-level priori benefits small models, however, its intrinsic noise (i.e., inaccurate superpixels) becomes the bottleneck for larger models. We also notice the importance of the final bilinear interpolation as a standard practice: without it, the baseline model conducts patch classification which is a degeneration of the superpixel model, and yields worse performance. + +# 4. Method + +The aforementioned pilot experiments motivate us to explore for better instantiation of the region proxy modeling. In this section, we introduce the RegProxy model which computes on region embeddings (as tokens) that serve as computational proxies of specific learnable regions, and exploit Transformer [11, 41] to model region-wise context. + +We first provide basic information about the Transformer for region context modeling in Section 4.1. We introduce the learning of region geometrics and the embedding of region features in Section 4.2. Finally, we review RegProxy model from the system perspective and describe the training/inference as per-region prediction in Section 4.3. + +# 4.1. Transformer as Region Encoder + +Transformer is a type of sequence-to-sequence model, which applies multi-layer self-attention on its computation + +![](images/810038eb50049a3df18d61e68479035b75d9989a2d858c7663f712b3b0e1ab9e.jpg) +Figure 3. Overview of our RegProxy approach. The sequence-to-sequence Transformer encoder computes on region embeddings in the form of tokens, which serve as proxies of specific regions whose geometrics are described by the class-agnostic pixel-token association. Notably, we model global context completely at region-level without any typical "feature map". The region embedding and its geometrical description are jointly learned using the proxy head. A single linear classifier is adopted for per-region prediction. The region class logits are simply "painted" to the output plane according the corresponding region geometrics to yield final segmentation result. + +![](images/0b804282ed06af064366bbf5300d8170b01f9e11693122187d9b4652f7d9ae83.jpg) +Figure 4. More details of the RegProxy model. (a) Illustration of the proxy head, where $+$ stands for element-wise addition and $\rho$ stands for reshape and rearrange of dimensions. (b) Describing region geometrics by local pixel-region association. + +![](images/5fdfc22f8e122f0a53e008b1a4ce015ccc3ad34bd247deda859d222e449a9643.jpg) + +primitives, i.e. tokens. In this work, we take full advantage of the Transformer architecture to learn global context for image by directly modeling inter-region relations using self-attention. While the region learning and embedding will be discussed in Section 4.2, in this section, we briefly introduce the principle of the Transformer encoder. + +Supposing $N$ region embeddings has been produced, we write the Transformer input as a sequence of tokens: + +$$ +\mathbf {X} _ {0} = \left[ \mathbf {x} _ {\mathrm {c l s}} ^ {0}, \mathbf {x} _ {0} ^ {0}, \mathbf {x} _ {1} ^ {0}, \dots , \mathbf {x} _ {N - 1} ^ {0} \right] ^ {\top} \in \mathbb {R} ^ {(N + 1) \times D}, \quad (2) +$$ + +where $D$ is the embedding dimension and the class token $\mathbf{x}_{\mathrm{cls}}$ serves as a whole-image representation in image recognition tasks. A Transformer encoder is composed of $L$ stacked layers, each of which consists of a multi-head self-attention (MSA) block followed by a multi-layer perceptron (MLP) block with two linear projection layers. Layer normalization [2] and residual connections are applied for both MSA and MLP blocks. Mathematically, we can write the computation of layer $l$ as + +$$ +\mathbf {A} _ {l} = \operatorname {M S A} (\ln \left(\mathbf {X} _ {l - 1}\right)) + \mathbf {X} _ {l - 1}, \tag {3} +$$ + +$$ +\mathbf {Z} _ {l} = \operatorname {M L P} \left(\ln \left(\mathbf {A} _ {l - 1}\right)\right) + \mathbf {A} _ {l - 1}, +$$ + +where the output $\mathbf{Z}_l$ is used as input of the next layer. + +The Vision Transformer (ViT) inherits the exact architec + +ture from the Transformer in NLP [41], accompanied with a stem module designed for vision tasks. In this work, we follow the standard definition of the ViT models in [11, 39]. Our RegProxy- $\{\mathrm{Ti} / 16$ , S/16, B/16, L/16\} models are based on vanilla ViTs which use patch embedding stems, while our RegProxy- $\{\mathrm{R}26 + \mathrm{S} / 32$ , R50+L/32\} models are based on hybrid ViTs which use CNN stems. These ViTs vary from total strides and numbers of layers, embed dimensions and attention heads. The detailed specifications can be found in Table 2 and are described in Section 5. + +# 4.2. Learning Region Proxy + +As depicted in Figure 3, our region proxy method comes with two important components: the region feature and its geometrics. In this section, we introduce the region feature embedding and its geometrical description. + +Describing Region Geometrics Learning and describing region geometrics is not quite straightforward due to the irregular shape and various scales. An intuitive idea is to predict a binary mask for each region, either to be imagesized or within a local area. However, we find neither of the approaches practical for our sequence-to-sequence modeling. Predicting a full-sized mask for each token will be computationally expensive, while predicting small sized local masks cannot ensure the tessellation of regions, consequently causing overlapping and non-predicted areas. + +To this end, we propose a novel mechanism to describe region geometrics by pixel-to-token association. We start from an initial $H \times W$ grid where $H \times W = N$ . Each token lays on a single cell which serves as a "seed" of its corresponding region s. Note the cell itself is merely a token location indicator and has nothing to do with the actual region geometrics. We build the pixel-to-token association by assigning each pixel $\mathbf{p} = (u, v)$ to region s with a probability $q_{\mathrm{s}}(\mathbf{p})$ . It is unnecessary to apply this association globally. Instead, we associate pixel $\mathbf{p}$ only with tokens that lays + +in its neighborhood $\mathcal{N}_{\mathbf{p}}$ which satisfies + +$$ +\sum_ {\mathbf {s} \in \mathcal {N} _ {\mathbf {p}}} q _ {\mathbf {s}} (\mathbf {p}) = 1 \tag {4} +$$ + +This is illustrated in Figure 4b, as the pixel $\mathbf{p}$ is being assigned to one of the 9 region seeds (marked with red box) with in its surrounding neighborhood (in green box). Mathematically, we can write the association as a class-agnostic affinity map $\mathbf{Q} \in \mathbb{R}^{(Hh) \times (Ww) \times |\mathcal{N}_p|}$ at pixel-level which describe the actual geometries of all regions, where $(Hh) \times (Ww)$ matches the size of the output segmentation map and $(h, w)$ is the relative stride of the initial token grid. Empirically, we set the neighborhood size to $3 \times 3$ and $|\mathcal{N}_p| = 9$ , which works well through-out all model sizes. + +For an intuitive interpretation, the region is represented by a "core" (i.e., token's location on the initial $H \times W$ cell) and pixels surround it by probabilities. With the constraint of Eq. 4, the entire set of probabilistic regions forms a tessellation that covers the image plane with no overlaps and no gaps. Meanwhile, the regions learn to be highly semantically homogeneous even without explicit regularization, which will be discussed in Section 5.3. These facts enable us to segment image in a per-region prediction fashion. + +Embedding Regions We jointly embed region features and learn their geometrical description $\mathbf{Q}$ using the proxy head depicted in Figure 4a. To embed region features into tokens, we use a small part of the ViT backbone as token head. We take the exact stem module in [11] along with learnable position embeddings, which produces $N$ tokens of dimension $D$ where $N = H \times W$ . The stem module can be linear patch projection for vanilla ViT models, or CNNs for hybrid models (see Section 5). For our vanilla ViT models, we further apply the first $M$ Transformer layers for better feature extraction. + +To predict region geometrical description $\mathbf{Q}$ , we design a lightweight affinity head that is highly integrated with the ViT backbone, bringing negligible extra parameters and computations. As illustrated in Figure 4a, we predict the affinity map $\mathbf{Q}$ directly using features from the token head. Specifically, the token feature $\mathbf{T} \in \mathbb{R}^{N \times D}$ is reshaped to $\mathbf{T}' \in \mathbb{R}^{H \times W \times D}$ according to its initial layout, and then fed into a convolution module. The convolution module fuses local region-wise information and produces $H \times W \times (9hw)$ feature map, as we predict affinity vectors for all $hw$ pixels inside each cell in batches. The compact map is then "unpacked" to the pixel-level format, which finally yields the affinity map $\mathbf{Q} \in \mathbb{R}^{(Hh) \times (Ww) \times 9}$ . + +In details, the convolution module consists of one $3 \times 3$ depth-wise conv layer, followed by a $1 \times 1$ conv layer. The affinity map is activated by a Softmax to produce normalized probabilities. Notably, we discover some interesting facts about choices of the number of early layers $M$ for affinity prediction, which will be discussed in Section 5.3. + +# 4.3. Segmentation by Per-Region Prediction + +By our assumption, region embedding carries homogeneous semantics throughout the Transformer network. This enables us to directly predict on regions instead of pixels as opposed to conventional FCN-style models [6, 26, 27, 48], hence significantly reduces the number of predictions. As depicted in Figure 3, we apply a linear classifier on the last layer output $\mathbf{X}_L$ of the Transformer backbone, which we find sufficient to yield strong performance. The linear classifier produces class logits for all tokens except $\mathbf{x}_{\mathrm{cls}}$ : + +$$ +\mathbf {Y} = \left[ \mathbf {y} _ {0}, \mathbf {y} _ {1}, \dots , \mathbf {y} _ {N - 1} \right] ^ {\top} \in \mathbb {R} ^ {N \times K}, \tag {5} +$$ + +where $K$ is number of classes. + +We can easily attain the pixel-level segmentation result using the region geometrical description $\mathbf{Q}$ introduced in Section 4.2. We simply "paint" the token logits to the corresponding regions as illustrated in Figure 3. In practice, we paint in a per-pixel manner for efficient implementation. For pixel $\mathbf{p} = (u,v)$ , its class logits is calculated by + +$$ +\mathbf {Y} ^ {\prime} [ u, v ] = \sum_ {\mathbf {s} \in \mathcal {N} _ {\mathbf {p}}} \mathbf {y} (\mathbf {s}) \cdot q _ {\mathbf {s}} (\mathbf {p}), \tag {6} +$$ + +where $\mathbf{Y}' \in \mathbb{R}^{(Hh) \times (Ww) \times K}$ is the output logits map, $\mathbf{y}(\mathbf{s})$ is the class logits of the token corresponding to region s. In practice, we set $(h, w) = (4, 4)$ , yielding $\times 4$ stride logits map for RegProxy- $x/16$ models, and $\times 8$ stride logits map for RegProxy- $x/32$ models. Our model is trained end-to-end using cross-entropy loss without class balance or hard example mining. The output logits map is upsampled to ground-truth/Input size for supervision during training and prediction during inference following the standard practice. + +# 5. Experiments + +Datasets and Metrics We study RegProxy on three public datasets: ADE20K [54], Cityscapes [9] and Pascal Context [29]. ADE20K is a challenging scene parsing dataset with 150 classes, which contains 20210 images for training and 2000 images for validation. Cityscapes is a high-resolution street scene dataset with 19 classes. We train on the 5000 fine annotated training images and test on 500 validation images. Pascal Context contains 4996 training images and 5104 validation images with 60 classes (including one background class). We report Intersection over Union averaged over all classes (mIoU). + +ViT Backbones We build our model on the original ViTs as defined in [11,37]. We conduct extensive experiments on six variants: vanilla ViTs with four specs (tiny, small, base and large) and hybrid ViTs with two specs (small, large). Vanilla ViTs use patch embedding as stem which partitions an image into $P \times P$ patches, while each patch is flattened and linearly projected to an embedding with $D$ dimension. For hybrid ViTs, the projection is applied to the features ex + +
backbonestridestem#layersdim#heads#params
Ti/1616patch embed.1219236M
S/1616patch embed.12384622M
B/1616patch embed.127681286M
L/1616patch embed.24102416307M
R26+S/3232ResNet[2, 2, 2, 2]12384637M
R50+L/3232ResNet[3, 4, 6, 3]24102416330M
+ +tracted by a residual convolutional network [17], hence the patch size is equivalent to CNN's stride $S$ . We set $P = 16$ for vanilla ViTs and $S = 32$ for hybrid ones. Namely, the initial $H \times W$ token grid is of strides 16 and 32 respectively. Larger stride generally impairs performance while requiring less computation. The detailed configurations can be found in Table 2. We use weights pre-trained on ImageNet-21k [37] following recent works [26, 38, 53]. + +Implementation Details We implement our method using the public codebase mmsegmentation [8]. We introduce minimum changes to its default settings that are widely used by the community. For training, we use input sizes of $512 \times 512$ , $768 \times 768$ and $480 \times 480$ for ADE20K, Cityscapes and Pascal Context, respectively. We train our "Large" model on ADE20K using a $640 \times 640$ crop following [26, 38, 48]. We use AdamW [28] optimizer with an initial learning rate of $6 \times 10^{-5}$ , a weight decay of $10^{-2}$ and a "poly" learning rate scheduler [4] with power = 1.0 following [12, 26, 48]. We use a batch size of 16 and train for 160k, 80k, 40k iterations on ADE20K, Cityscapes and Pascal Context, respectively. We keep data augmentations and all other training settings identical to default settings in [8]. Training tricks such as hard example mining, auxiliary losses or class balance loss are not included. + +For testing, we use the sliding window mode with window sizes matching the crop sizes for training. We use default window strides in [8]. We report both single scale results and multi-scale + flipping results with scaling factors of $\{0.5, 0.75, 1.0, 1.25, 1.5, 1.75\}$ . + +# 5.1. Main Results + +Baselines To setup the baseline, we simply append a linear classifier to the bare ViTs to produce per-patch prediction $\mathbf{Y} \in \mathbb{R}^{N \times K}$ . Then the patch-wise logits are reshaped to their original 2D layout $\mathbf{Y}' \in \mathbb{R}^{H \times W \times K}$ and upsampled to image size for training and inference following the standard segmentation pipeline. It can be interpreted as a typical segmentation model of stride 16. This setting is identical to the "Linear" baseline in [38], and we produce similar results by our implementation. Since they have no structural difference with the vanilla ViTs [11] for image classification, we simply refer to the baseline models as ViT- $x/16$ where $x \in \{\mathrm{Ti}, \mathrm{S}, \mathrm{M}, \mathrm{L}\}$ . + +Table 2. Configurations of ViT variants. (Top) Vanilla ViTs use patch embedding. (Bottom) Hybrid ViTs use ResNet [17] stem. + +
methodFLOPs#params.ADE20K (SS/MS)Cityscapes (SS/MS)
ViT-Ti/163.8G5.7M39.039.872.374.1
+Mask.T+1.0G+1.0M38.1 (-0.9)38.8 (-1.0)--
+Ours+0.1G+0.1M42.1 (+3.1)43.1 (+3.3)76.5 (+4.2)77.7 (+3.6)
ViT-S/1614.9G22.0M45.445.976.178.0
+Mask.T+4.2G+4.1M45.3 (-0.1)46.9 (+1.0)--
+Ours+0.2G+0.2M47.6 (+2.2)48.4 (+2.5)79.8 (+3.7)81.5 (+3.5)
ViT-B/1658.8G86.6M47.148.178.580.5
+UperNet+336G+57.6M47.9 (+0.8)49.5 (+1.4)79.6 (+1.1)80.9 (+0.4)
+Mask.T+17.1G+16.0M48.7 (+1.6)50.1 (+2.0)-80.6 (+0.1)
+Ours+0.7G+0.7M49.8 (+2.7)50.5 (+2.4)80.9 (+2.4)82.2 (+1.7)
ViT-L/16325.0G304.3M50.751.878.480.7
+Mask.T+44.5G+28.5M51.8 (+1.1)53.6 (+1.8)-81.3 (+0.6)
+Ours+0.9G+1.8M52.9 (+2.2)53.4 (+1.6)81.4 (+3.0)82.7 (+2.0)
SETR [53]325.1G305.6M48.148.877.9-
+MLA+8.7G+4.0M48.6 (+0.5)50.3 (+1.5)77.2 (-0.7)-
+PUP+97.5G+11.7M48.6 (+0.5)50.1 (+1.3)79.3 (+1.4)-
+ +* In green are the gaps of at least +2.0 mIoU. + +Table 3. Compare different integrations of vision Transformer. We report the results of the baseline, the state-of-the-art Mask Transformer from Segmenter [38], UperNet [47] and our Reg-Proxy. We also report numbers from SETR [53] for reference. + +Results We compare different integrations of vision Transformer for semantic segmentation. Table 3 summarizes the results. Our RegProxy approach brings consistent performance gains throughout all model sizes with an evidential gap (2~3 mIoU on ADE20K and 2~4 mIoU on Cityscapes), while costing negligible overhead (less than 2 M parameters and 1 GFLOPs computation for the largest model). It also significantly outperforms the Segmenter [38] which carries a heavy decoder. Moreover, we notice the performance degeneration of Segmenter on smaller models, which is not observed on our approach. As a reference, we also report results from SETR [53] which appends different convolutional decoders to the ViT-L/16 backbone and the UperNet [47] results ran by us. By these results, we may suggest that our region proxy modeling is a more effective and efficient way to exploit vision Transformers in semantic segmentation compared with the encoder-decoder scheme. + +# 5.2. Comparison across Architectures + +ADE20K We conduct comprehensive comparisons with the state-of-the-art methods on ADE20K. Results in Figure 2 show that the RegProxy is among the most competitive models in terms of performance-efficiency trade-off. RegProxy consistently outperforms the state-of-the-art Segmenter [38] by a large margin, which uses the same ViT backbones and pre-training as ours. It also shows significant superiority compared with recent SegFormer [38], SwinTransformer [26] and SETR [53]. Table 4 gives a more detailed comparison with respect to parameters, GFLOPs, inference speed and performance. The smallest RegProxy-Ti/16 achieves $42.1\mathrm{mIoU}$ with only $5.8\mathrm{M}$ parameters and 3.9 GFLOPs, and runs at a speed of 38.9 FPS, which out- + +![](images/8137d66cc04910fd0b5e0c242c7a078ae76021a5d92414a62bb5ee4a673fe59f.jpg) +Figure 5. Qualitative comparison on ADE20K and Cityscapes. Our model produces much more accurate contour (in white box) compared to Segmenter [38] and captures more consistent context (in yellow box) compared to DeepLabV3+ [6]. Best viewed zoom in. + +![](images/2fa06877023f71c38f6fe4a028498a2f2e487f5297242965f55fcf4d5736cd30.jpg) + +![](images/1946c9c01ce53e76b6520531bdc26a77b330c46c9b07ca15496298f28dcc758c.jpg) + +![](images/edc2acdecffb86caea57aa95311a9510c9332b7bafe2b108a227ea2b4e8ce200.jpg) + +![](images/7c610517c56714c1c655fd3d63de49deeba59d288c60c6f4c2b50ecd4dd6722b.jpg) + +
methodbackboneFLOPs#params.mIoUFPS
FCN [27]MobileNetV239.6G9.8M19.7 / -64.4
D.LabV3+ [6]MobileNetV269.4G15.4M34.0 / -43.1
SegFormer [48]MiT-B08.4G3.8M37.4/38.050.5
Segmenter [38]ViT-Ti/164.9G6.7M38.1/38.8-
RegProxyViT-Ti/163.9G5.8M42.1/43.138.9
OCRNet [50]HRNet-W1855G12M39.3/40.818.9
SegFormer [48]MiT-B116G14M42.2/43.147.7
Segmenter [38]ViT-S/1619G26M45.3/46.929.8
MaskFormer [7]Swin-T55G42M46.7/48.822.1
RegProxyViT-S/1615G22M47.6/48.532.1
RegProxyR26+ViT-S/3216G36M47.8/49.128.5
OCRNet [50]HRNet-W48165G71M43.2/44.917.0
D.LabV3+ [6]ResNet-101255G63M45.5/46.414.1
D.LabV3+ [6]ResNeSt-200345G88M- /48.4-
Segmenter [38]ViT-B/1676G103M48.7/50.114.6
RegProxyViT-B/1659G87M49.8/50.520.1
DPT [32]DPT-Hybrid-123M- 49.0-
SETR [53]ViT-L/16422G318M48.6/50.14.5
SegFormer [48]MiT-B5183G85M51.0/51.89.8
Segmenter [38]ViT-L/16370G333M51.8/53.6-
RegProxyR50+ViT-L/3282G323M51.0/51.712.7
RegProxyViT-L/16326G306M52.9/53.46.6
+ +* All models in the last group except DPT use a larger ${640} \times {640}$ crop. +Table 4. Comparison to state-of-the-art methods on ADE20K val split. We report both single/multi-scale results. We group the methods based on model capacities and computational costs for fine-grained comparison. Cross group comparison is welcomed. + +performs the best efficient models by large margins (greater than $4.0\mathrm{mIoU}$ ). Our small model RegProxy-S/16 has surpassed the heaviest CNN model (DeepLabV3+ w/ ResNeSt-200) using only $25\%$ parameters and $4\%$ computation. The medium sized RegProxy-B/16 significantly outperforms all CNN models with much less computation. The largest RegProxy-L/16 achieves $52.9\mathrm{mIoU}$ without multi-scale inference, outperforms Segmenter [38] by $1.1\mathrm{mIoU}$ . The hybrid models also achieve notable results even with a large-stride backbone. The RegProxy- $[R26+S/32]$ achieves $47.8/49.1\mathrm{mIoU}$ , and the RegProxy- $[R50+L/32]$ achieves a comparable $51.0/51.7\mathrm{mIoU}$ among jumbo Transformer-based models using only 1/4 computations. And gener + +
methodbackbonecropFLOPs#params.mIoU
D.LabV3+ [6]ResNet-187692992G12M76.3/77.9
OCRNet [50]HRNet-W18full424G12M78.6/80.5
SegFormer [48]MiT-B0768252G4M75.3/ -
SegFormer [48]MiT-B110242244G14M78.5/80.0
RegProxyViT-Ti/16768269G6M76.5/77.7
RegProxyViT-S/167682270G23M79.8/81.5
OCRNet [50]HRNet-W48full1297G70M80.7/81.9
Auto-D.Lab [25]NAS-F487692-44M- /80.4
Axial-D.Lab [42]Axial-D.Lab-XL-2447G173M- /81.1
D.LabV3+ [6]ResNeSt-200full-88M- /82.7
SETR [53]ViT-B/167682-98M79.5/ -
SETR [53]ViT-L/167682-318M79.3/82.2
Segmenter [38]ViT-B/1676821344G103M- /80.6
Segmenter [38]ViT-L/167682-337M79.1/81.3
RegProxyViT-B/1676821064G88M81.0/82.2
RegProxyViT-L/167682-307M81.4/82.7
+ +Table 5. Comparison to state-of-the-art methods on Cityscapes val split. The "full" crop indicates the whole image inference, while others indicate the sliding window protocol. + +ously, our RegProxy runs at a significantly higher frame rate among different sized models thanks to the concise design. + +Cityscapes and Pascal Context In Table 5 we compare the state-of-the-art methods on Cityscapes. We observe similar results as on ADE20K. Our RegProxy- $\{\mathrm{Ti} / 16, \mathrm{S} / 16\}$ outperform their counterparts with a $\sim 1.2 \mathrm{mIoU}$ margin. Our RegProxy- $\{\mathrm{B} / 16, \mathrm{L} / 16\}$ also achieve state-of-the-art performances compared to larger models. Notably, they outperform SETR [53] and Segmenter [38] by $\sim 2 \mathrm{mIoU}$ using identical backbones. We notice that on Cityscapes, the performance gained from model capacities tends to saturate on larger models. RegProxy-L/16 is only $0.4 \mathrm{mIoU}$ higher than RegProxy-B/16 (the gap on ADE20K is $2.2 \mathrm{mIoU}$ using both $512 \times 512$ crops). This is also observed on SETR [53] and Segmenter [38]. We hypothesize that this is due to the simpler context of Cityscapes. We report results on Pascal Context in Table 6. RegProxy-L/16 achieves $58.4 \mathrm{mIoU}$ and significantly outperforms the state-of-the-art CNN models, and achieves comparable performance with Segmenter [38] using less resources. We present qualitative comparison in Figure 5 and supplemental material. + +
methodbackboneFLOPs#params.mIoU
DeepLabV3+ [6]ResNet-101224G63M47.2/48.3
OCRNet [50]HRNet-W48144G71M- /56.2
SETR [53]ViT-L/16238G318M54.9/55.8
Segmenter [38]ViT-B/1667G102M- /55.0
Segmenter [38]ViT-L/16210G333M58.1/59.0
RegProxyViT-B/1652G87M55.2/55.4
RegProxyViT-L/16183G305M58.4/58.8
+ +# 5.3. Analysis and Ablation Study + +In this section, we present the most significant analysis and ablation studies. Due to limited space, we present more of them in the supplemental material. + +Region Semantics We analyze the semantical homogeneity of regions, which is described using "region entropy": we calculate the per-pixel category histogram within every regions using Eq. 1 and compute their entropies [35]. We analyze the distribution of region entropies on the entire ADE20K val split, with regard to three sources: regular cell used by conventional segmentation model such as [38], superpixels used in our pilot study, and learned regions from our RegProxy approach. The results are shown in Figure 6. Although we do not apply any explicit regularization, the learned regions still exhibit highly compact semantics compared to regular cells and superpixels. In the right part of Figure 6, we visualize the leaned probabilistic regions of a number of tokens on tiny crops of Cityscapes validation images. Note the regions are class-agnostic (as association of pixels and nearby tokens) and leaned from shallow features. However, they still capture fine-grained boundaries of high level classes. This suggest that the computation primitives in our model (i.e., tokens) carries more uniformed semantics compared to CNNs or other vision Transformer models that compute on structured features, which probably leads to easier optimization hence the better performances. + +Per-Class Performance In Figure 7, we analyze per-class performance on Cityscapes. Compared to Transformer-based Segmenter [38], DeepLabV3+ [6] is good at handling small/thin classes (e.g., traffic sign, pole) thanks to its small stride, yet fails more on confusing classes (e.g., bus, wall) which require wider context. Our region proxy modeling possesses both of their merits and consistently outperforms or being comparable to both of the methods on all classes. + +![](images/05891e972db2216d4a62aacdd4260a606c26d0d4af9c62d1eafeca6a041c8b01.jpg) +Figure 6. (Left) Distribution of region entropies estimated by kernel density estimation (KDE). Regions with entropy of 0 are ignored. (Right) Geometrics of the class-agnostic regions and its corresponding tokens (marked using white cell). + +![](images/88d37aa99f3c0c4451b5199117f99b8bc8e6c87c6ae06f1b2070640d818b223e.jpg) + +![](images/483d8d66a63d83b5c4eef42c11a71b5f71a609e6a0c1e0bc4806ffaa72e08d39.jpg) +Figure 7. Per-class performance on Cityscapes. We report relative mIoU of DeepLabV3+ and our RegProxy-L/16 model compared with Segmenter-L/16 [38]. + +This is credited to the early region design that captures fine regions in advance and models region-wise relations afterwards, hence learns global context without loss of details. + +Depth of Token Head As illustrated in Figure 4a, we use the first $M$ Transformer layers in the token head. $M$ is set to 0 for our hybrid models since the convolutional stem is strong enough for region learning and embedding. Here we investigate the $M$ setting for vanilla ViT based models. The results are displayed in Table 7. We find that using early layers (e.g., 3~5 layers) generously works well, while setting $M$ to 0 (a too shallow token head) will harm the performance. Interestingly and importantly, we also find that a too deep token head will cause a significant performance drop. To the extreme, setting $M = 12$ (uses all Transformer layers, the proxy head degenerates to a typical decoder) will yield a performance no better than the baseline's. This indicates the importance of the Transformer layers after the proxy head, which model context for learned regions. + +Table 6. Comparison to state-of-the-art methods on Pascal Context val split. + +
depth M03456912baseline
ADE20K46.347.147.047.246.846.645.745.0
Cityscapes76.879.078.878.277.776.175.275.4
+ +Table 7. Ablation on depth of token features used for region learning. We report single scale mIoU results of RegProxy-S/16 on ADE20K and Cityscapes using half of the training schedule. + +# 6. Conclusion + +In this paper, we present region proxy, a novel and efficient modeling of semantic segmentation. It interprets the image as a tessellation of learnable regions, each of which has flexible geometrics and carries homogeneous semantics. We conduct semantic segmentation by per-region prediction on top of region embeddings, which are encoded using Transformer in a sequence-to-sequence fashion. Without a decoder, the RegProxy segmentation models still exhibit the most competitive performance-efficiently trade-off among its dense prediction counterparts. We hope our region proxy modeling provide an inspiring perspective of efficient image representation for semantic segmentation and other vision tasks. + +# 7. Acknowledgement + +This work was supported by the National Key Research and Development Project of China (No. 2021ZD0110700), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), Shanghai Qi Zhi Institute, and SHEITC (2018-RGZN-02046). + +# References + +[1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süssrunk. Slic superpixels compared to state-of-the-art superpixel methods. IEEE transactions on pattern analysis and machine intelligence, 34(11):2274-2282, 2012. 3 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016. 4 +[3] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Semantic image segmentation with deep convolutional nets and fully connected crfs. arXiv preprint arXiv:1412.7062, 2014. 3 +[4] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. 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Most previous methods focus on exploiting the given semantic map, which just captures an object-level layout for an image. Obviously, a fine-grained part-level semantic layout will benefit object details generation, and it can be roughly inferred from an object's shape. In order to exploit the part-level layouts, we propose a Shape-aware Position Descriptor (SPD) to describe each pixel's positional feature, where object shape is explicitly encoded into the SPD feature. Furthermore, a Semantic-shape Adaptive Feature Modulation (SAFM) block is proposed to combine the given semantic map and our positional features to produce adaptively modulated features. Extensive experiments demonstrate that the proposed SPD and SAFM significantly improve the generation of objects with rich details. Moreover, our method performs favorably against the SOTA methods in terms of quantitative and qualitative evaluation. The source code and model are available at SAFM. + +# 1. Introduction + +Semantic image synthesis is a kind of conditional image generation task, which aims to generate semantically aligned and photo-realistic images with the given semantic maps. Compared to unconditional image generation, it has significant flexibility in image generation since we can flexibly control the generated image content by drawing or editing the input semantic maps. Semantic image synthesis has been widely used in many practical scenarios, e.g., content creation and image editing [7, 28, 33, 42]. + +Recently, Generative Adversarial Networks (GANs) [10] are broadly adopted to solve this problem and achieve impressive results. Most works attempt to model the mapping between different semantic classes and visual appearances. Park et al. [28] propose to use spatially-adaptive transformations (SPADE) learned from the input semantic layouts to modulate the activations in the generator. + +![](images/65f46fbdcdc3907eebe5e92bf1b249cb204786bdc16d55d5d0dca5ccb0ba3b92.jpg) +Object-level layout + +![](images/b014faff03ff7032e9ddb4349c8ed681d0873843ebaa59af7528230dd9c8709d.jpg) +Part-level laypout + +![](images/3b90ccb980ee8dc05e3d657608541d63aa9b9367c830efca33690b7bb6ad5583.jpg) + +![](images/620996d6c18545cf7170b90e89607b89651ee7deb7afb25e313407d1fa27b44c.jpg) +Our SPD +Figure 1. The given semantic map only provides an object-level layout, which is too coarse for generating images with rich details. The part-level semantic layout is implied in the shape/contour of an object instance. By encoding object shape into the proposed SPD feature, we can effectively exploit such part-level layouts for better image details generation. + +CC-FPSE [21] subsequently extends SPADE by predicting spatially-varying conditional convolution kernels from the semantic layouts. Most recently, SC-GAN [36] exploits the learned semantic vectors to get spatially-variant and appearance-correlated convolution kernels and normalization parameters for the semantic stylization. + +A semantic map has not only semantic labels but also a spatial layout. Such a spatial layout can be used to regularize the semantic image synthesis. Generally, one object instance is composed of some object parts, and pixels from the same object part should have a similar appearance while pixels from distinct object parts should not. For instance, an object 'car' is composed of 'window', 'wheel', etc. Thus, the pixels from the 'window' should look different from those from the 'wheel'. In contrast, two pixels both from the 'window' should look similar to each other. By exploiting such a spatial layout, we can suppress artifacts and generate coherent image details. + +Semantic layouts have been effectively exploited to improve image synthesis in previous methods. However, the given semantic map just captures an object-level layout for an image, which describes whether two pixels belong to the same object instance or not. It is too coarse to capture the + +fine-grained structure of an object instance. If we could subtly exploit a part-level semantic layout, it will benefit the generation of image high-frequency details. + +Obviously, the shape/contour of each object instance can be easily identified from the object-level semantic layout. On the other hand, given the shape/contour of an object (e.g., a car), its part-level layout (e.g., the position of 'window' or 'wheel') can be roughly inferred according to the prior knowledge of an object's structure, as shown in Fig. 1. Therefore, there is a strong connection between an object's shape and its part-level layout, i.e., an object's shape implies its part-level layout. Thus, the exploitation of an object's part-level layout can be implicitly achieved by modeling its shape. + +In this paper, we propose a Shape-aware Position Descriptor (SPD) to describe each pixel's positional feature. Our SPD describes the relative relations (distance and angle) between each pixel inside an object instance and pixels on its contour, as shown in Figure. 2 (a). Thus, the information of object shape has been encoded into each pixel's SPD feature. In other words, the clue of an object's part-level layout has been implicitly encoded into the SPD feature. + +Next, we design the Semantic-shape Adaptive Feature Modulation (SAFM) block to combine the given semantic map and our SPD features together, and modulate the input features adaptively. Specifically, our SAFM block first conditionally produces semantic-specific convolution kernels, and then performs semantic-specific convolution on the SPD features. At last, the SAFM block accepts input feature maps, adaptively modulates them, and forwards them to the next block, as shown in Figure. 2 (b). + +Note that our SPD is inspired by the shape context descriptor [2] which describes the relations of pixels just on the shape contour, but our SPD describes the relations between pixels inside an object and pixels on the contour. + +Our main contributions can be summarized as follows: + +- We propose a Shape-aware Position Descriptor (SPD) to describe the pixel's positional feature, where the object's part-level layout can be exploited and leveraged. +- We design a Semantic-shape Adaptive Feature Modulation (SAFM) block, which combines the semantic maps and SPD features to produce adaptively modulated feature maps. +- Experimental results show that our method performs favorably on Cityscapes, COCO-stuff, and ADE20K datasets against SOTA methods and can generate more photo-realistic results with rich details. + +# 2. Related Work + +# 2.1. Semantic Image Synthesis + +Generative Adversarial Networks (GANs) [10] have achieved impressive results on unconditional image generation related tasks [4, 13, 14]. Subsequently, by introducing + +external information, such as class labels [22, 26, 27], natural language descriptions [17, 18, 40], or semantic maps [28, 35], many kinds of conditional GANs are proposed to improve the controllability of image generation. + +Semantic image synthesis is a task that takes semantic segmentation maps as input, which provides pixel-level class labels. Pix2Pix [12] is first proposed to use an encoder-decoder generator and PatchGAN discriminator to conduct semantic image generation. Pix2PixHD [35] improved it by adopting a coarse-to-fine generator and multi-scale discriminators to generate vivid details at high-resolution space. Particularly, Pix2PixHD introduced the instance-level boundary map as extra input to separate different instances for sharper boundaries. Further, panoptic aware convolutions and upsampling layers [9] are utilized to differentiate occluded instances. + +Recently, most works focus on how to sufficiently leverage the given semantic layouts. SPADE [28] proposed to modulate the activations with spatially-adaptive transformations learned from semantic layouts. CC-FPSE [21] learned to predict conditional convolution kernels based on the given semantic layouts. Additionally, a feature pyramid semantic-embedding discriminator is employed to enable the generator to synthesize semantically aligned images with high-quality details. Similarly, Ntavelis et al. [25] proposed a two-stream discriminator by using semantic features to guide the scores of the discriminator. LGGAN [33] proposed a local class-specific and global image-level generative adversarial network to separately learn the global appearance distribution and generation of different object classes. EdgeGAN [32] generated edges from semantic layouts to introduce detailed structure information for image synthesis. Most recently, SCGAN [36] learned semantic vectors to parameterize spatially conditional convolution and normalization. Besides, OASIS [31] re-designed the discriminator with a segmentation-based network for synthesizing semantically aligned images with higher fidelity. + +Except for these GAN-based methods, CRN [7] adopted a cascaded refinement network for semantic image synthesis. Qi et al. [29] proposed a semi-parametric approach, which retrieved compatible fragments and composited them to assist the semantic image synthesis. + +Most of those methods just exploit object-level semantic layouts, which are too coarse to capture the part-level structure of object instances. Although the part-level layouts are unknown, they can be roughly inferred from objects' shapes. In our work, such part-level layouts are effectively exploited by encoding objects' shapes into our SPD descriptors. + +# 2.2. Shape Context Descriptor + +Shape context descriptor was first proposed by Belongie et al. [2] for category-level shape matching and object recognition. Through counting the histogram of the relative position distribution of other shape points, a rich + +![](images/4973fc4294e05cc212b96af9c5117389bd9d2fed4ee1933037171dd5d0305837.jpg) +(a) The calculation process of shape-aware position descriptor + +![](images/1d42412a0c9bad401d695daf40a4b9ce31cbb32b2dfd6ec801341048fea4614e.jpg) +(b) Architecture of our network +Figure 2. Overview of our proposed method. (a) shows the calculation process of the SPD features of a certain point in a car instance (denoted by a blue $\triangle$ ). After calculating all points inside the instances, we get a SPD map, as shown in (a) (right). (b) illustrates the architecture of our generator network, where SAFM is mainly constructed by conditional convolutions. + +local descriptor that implies the global shape points can be obtained for each point. After that, Thayananthan et al. [34] propose an efficient dynamic programming scheme to constrain the figural continuity of shape context matching. Instead of Euclidean distance, Ling et al. [20] adopt inner-distance to measure the spatial relation between shape points, which can better capture the structure of complex shapes with articulations. + +The shape context descriptor can bring sufficient information that captures the relative locations within the whole instance beyond the point itself. Due to the robustness and discrimination in reducing the ambiguity in class matching, these types of descriptors have been widely employed for different object recognition problems [3,24], but are seldom exploited in semantic image synthesis tasks. In this work, we extend the shape context descriptor [2] to characterize the position of each point inside an object instance, where object shapes are explicitly exploited and leveraged. + +# 3. Method + +Given a semantic layout $S \in \mathbb{R}^{H \times W \times C}$ with $C$ class labels, our goal is to synthesize a photo-realistic image + +$I_{s} \in \mathbb{R}^{H \times W \times 3}$ , which is semantically aligned with $S$ . Following [35], we adopt the instance-level segmentation map as supplementary input to obtain each instance region. + +In the following, we first introduce the Shape-aware Position Descriptor (SPD), where object shapes are exploited and leveraged. Next, we design the Semantic-shape Adaptive Feature Modulation (SAFM) block to combine the semantic maps and SPD features to adaptively modulate the input feature maps. + +# 3.1. Shape-aware Position Descriptor + +The shape of an object instance implies its part-level layout, as shown in Fig. 1. In our approach, we propose the Shape-aware Position Descriptor (SPD) to describe each pixel's positional feature, where the object shape is explicitly considered. In this way, the clue of an object's part-level layout could be effectively exploited and leveraged. + +To balance the computation cost and the robustness of the descriptor, we only use the contour point set of an object instance to describe its shape information, instead of using all the points inside the segmentation region. + +Calculation process of the SPD. Figure. 2 (a) illustrates + +the calculation process of our proposed SPD. Taking the rear-view car in the semantic map as an example, we can easily get its contour shape $T \in \{0,1\}^{H \times W}$ according to its segmentation map, where the points on the contour are denoted by label 1 and the rest are set to 0. Further, the contour shape of the car can be discretely represented as a point set $P = \{(x,y)|T(x,y) = 1\}$ . + +For any point $o = (x_o, y_o)$ inside the instance, we calculate its positional descriptor through the following steps. Firstly, we take the point $o$ as the pole to construct a polar coordinate space around it. And then we divide this coordinate into $m \times n$ bins $B$ with $m$ polar radius intervals and $n$ polar angle intervals (in this work $m = 12$ and $n = 6$ ). Each bin $B_{i,j}$ should satisfy the following condition: + +$$ +B _ {i, j} = \left\{\left(r, \theta\right) \mid r _ {i - 1} < = r < r _ {i}, \theta_ {j - 1} < = \theta < \theta_ {j} \right\}. \tag {1} +$$ + +In order to make the descriptor more sensitive to the nearby points relative to the farther ones, we use bins that are uniform in log-polar space. + +After that, the distance and angle distribution of each point in the contour point set $P$ relative to the pole $o$ can be formulated as $P^{\prime} = \{(r_{i},\theta_{i})|_{i = 1}^{|P|}\}$ . Finally, we count the number of the points in the contour point set $P^{\prime}$ that fall in each bin $B_{i,j}$ , denoted as $H_{i,j}$ : + +$$ +H _ {i, j} = | \{p | p \in P ^ {\prime}, p \in B _ {i, j} \} |, \tag {2} +$$ + +where $|\cdot |$ denotes the quantization operation. By integrating the number of contour points in all $m\times n$ bins and flattening it, we can get a vector $v_{o}\in \mathbb{R}^{m\times n}$ about point $o$ that stores the contour point distribution. The final SPD $\hat{v}_o$ for point $o$ can be obtained through the normalization: + +$$ +\hat {v} _ {o} = \frac {v _ {o}}{| P ^ {\prime} |}. \tag {3} +$$ + +After calculating the descriptor for all the points inside each instance, we can get a SPD map that explicitly represents the detailed position for each point. + +Discussion about the SPD. For example, there are three rear-view cars in Fig. 3 (a), which have similar shape contours but different spatial locations and scales. Intuitively, the corresponding points at the same object part should have consistent SPD features. In contrast, the points from different object parts should have different SPD features. + +Taking the points on the left wheel as an example (denoted by blue $\triangle$ ), the SPDs of the two points are shown in Fig. 3 (b) and (c). Another example is the points at the center of car (denoted by blue $\star$ ), their SPD features are shown in Fig. 3 (d) and (e). + +We can observe that: (i) For the corresponding positions of different instances, their SPD features look similar to each other (b vs c and d vs e). (ii) For different positions of the same instance, there are obvious differences between their SPD features (c vs d). (iii) Even if the absolute location or scale of an instance changes, we can still get similar SPD features, which indicates our SPD is only dependent on object shape (d vs e). In other words, object shapes are + +![](images/1d9685d20716eeb63d3eb60659c3c4c46fafe776b5c3408fc37e89cbde77495a.jpg) +Figure 3. Visualization of the SPD features of the car instances. There are three different rear-view cars with similar shapes in (a). (b-e) show the descriptor of blue $\triangle$ and $\star$ points in (a). (f) illustrates the descriptor compressed to 1D by t-SNE. + +robust and discriminatively encoded into our SPD features. + +Furthermore, we also jointly consider the SPD features of all pixels inside an object instance. Specifically, we use t-SNE to compress each pixel's SPD feature as a scalar, and hence we obtain a compact 2D map corresponding to all pixels inside an object instance, as shown in (f). We can see that all the three cars share similar patterns in the compact 2D map. More importantly, for each instance, the compact 2D map could well describe the part-level layout of a car. Thus, we claim that our SPD features could implicitly exploit an object's part-level layout. + +# 3.2. Semantic-Shape Adaptive Feature Modulation + +Another thing should be noticed is that different classes of object instances may have similar shapes. For example, the painting and washer shown in Fig. 4 (a) are both rectangular, and the patterns of their SPD features are quite similar (compact 2D map), but their appearance and structure are different, which will confuse the image synthesis. + +To circumvent this issue, we designed the Semantic-shape Adaptive Feature Modulation (SAFM) block (Fig. 2 (b)), which combines the semantic information and our SPD features to compensate each other. For instance, the proposed SPD features can bring more detailed descriptions about the point positions to the semantic layouts, while the semantic layouts can bring complementary semantic information to the SPD features. And then the SAFM yields semantic-shape adaptive modulation parameters for different positions of different classes, so as to subtly guide the semantic image synthesis. + +In the SAFM block, semantic layouts and SPD features are first scaled to the same size. Then semantic layouts are fed into two convolution layers to predict two sets of semantic-adaptive $3 \times 3$ convolution kernels, which vary with the class label of spatial position. After that, through depthwise convolution layers, the semantics information of + +![](images/ef914022622f54f07ca9c84b258e38d542c8d0450bcaafca228e3210e4a35479.jpg) +Figure 4. The (a) appearance, (b) shape and (c) the compact 2D map of the painting and washer instances. + +![](images/08a05f62c3976b124601fb27495cfd147807ee42578d32b39d03bea2a99c45d7.jpg) + +![](images/e79bad4f89fbdf6466e0f47e5a37a1315205c7fa0799e58d8f5156140d7e6ac7.jpg) + +![](images/941c70c923fcaa8ff00f2093473a1c1235bf2f4a3304270e5f43b5ec1dbe8392.jpg) +Figure 5. The distribution of the SPD of points in the painting and washer before and after using SAFM block.(mapping by t-SNE). + +![](images/b180318cd605147a1f8e1aa84fde9bbbf06b86216881701f2abcace1fe7fac2b.jpg) + +each spatial position is fused into the corresponding position in the SPD features. Finally, it yields semantic-shape adaptive modulation parameters with the fused features for feature modulation. + +With the SAFM block, semantic information and spatial position information can be integrated together. Fig. 5 shows the distribution of the SPD features without and with the SAFM block. Note that the light green dots represent the washer, while the orange dots stand for the painting. One can see that by incorporating the SAFM block, the washer and painting points tend to be better separated, which shows the effectiveness of the SAFM block in combining the SPD features and semantic features. + +# 3.3. Learning Objective + +In our approach, we adopt adversarial loss $\mathcal{L}_{adv}$ , feature matching loss $\mathcal{L}_{fm}$ , and perceptual loss $\mathcal{L}_{perc}$ to achieve high fidelity and realness of generation. In addition, $\mathcal{L}_{seg}$ is suggested from the pre-trained segmentation model for constraining the semantic alignment. + +Adversarial Loss. Adversarial learning can effectively keep the generated images staying at the real image manifold and has been widely used in many image generation tasks [4, 13, 22]. In this work, we adopt the hinge-based adversarial loss [19, 23, 39] and the optimization of generator $G$ and discriminator $D$ can be formulated as: + +$$ +\begin{array}{l} \mathcal {L} _ {a d v} ^ {D} = - \mathbb {E} _ {(I, S)} [ \min (0, - 1 + D (I, S)) ] \tag {4} \\ - \mathbb {E} _ {(z, S)} [ m i n (0, - 1 - D (G (z, S), S)) ], \\ \end{array} +$$ + +$$ +\mathcal {L} _ {a d v} ^ {G} = - \mathbb {E} _ {(z, S)} D (G (z, S), S), \tag {5} +$$ + +where $I$ is the real image, $S$ is the corresponding semantic layouts, and $z$ is the noise map fed into the generator. + +Feature Matching Loss. Following [35], we adopt the feature matching loss $\mathcal{L}_{fm}$ to enhance the supervision for stabilizing the training process which constrains the features of synthesized images to be close to the real one in different feature spaces of discriminator $D$ . This can be defined as: + +$$ +\mathcal {L} _ {f m} = \sum_ {i = 1} ^ {n} \frac {1}{N _ {i}} | | D _ {i} (I, S) - D _ {i} (G (z, S), S) | | _ {1}, \tag {6} +$$ + +where $N_{i}$ is the number of elements in feature $D_{i}(I,S)$ . + +Perceptual Loss. We adopt the pre-trained VGG19 model $\Phi$ [30] to separately extract the features from the real image $I$ and the generated images $\hat{I}$ . The perceptual loss $L_{perc}$ is computed in multi-scale feature space and is formulated as: + +$$ +\mathcal {L} _ {p e r c} = \sum_ {k = 1} ^ {K} | | \Phi_ {k} (\hat {I}) - \Phi_ {k} (I) | | _ {1}, \tag {7} +$$ + +where $\phi_{k}$ denotes the $k$ -th feature map extracted from the VGG19 model $\Phi$ . In our implementation, we set $K = 5$ . + +Semantic Alignment Loss. In order to explicitly constrain the semantic consistency between the generated image and the given semantic layout, we further introduce the semantic alignment loss $\mathcal{L}_{seg}$ to optimize the learning process: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {s e g}} = - \sum_ {i = 1} ^ {C} w _ {i} \sum_ {j = 1} ^ {H} \sum_ {k = 1} ^ {W} S _ {i, j, k} [ \log \operatorname {S e g} (I) _ {i, j, k} + \log \operatorname {S e g} (\hat {I}) _ {i, j, k} ], (8) \\ w _ {i} = \frac {H \times W}{\sum_ {j = 1} ^ {H} \sum_ {k = 1} ^ {W} S _ {i , j , k}}, (9) \\ \end{array} +$$ + +where $Seg$ is a pre-trained segmentation model [1]. + +The overall learning objective can be summarized as: + +$$ +\mathcal {L} = \lambda_ {a d v} \mathcal {L} _ {a d v} ^ {G} + \lambda_ {f m} \mathcal {L} _ {f m} + \lambda_ {p e r c} \mathcal {L} _ {p e r c} + \lambda_ {s e g} \mathcal {L} _ {s e g}, \tag {10} +$$ + +where $\lambda_{adv}$ , $\lambda_{fm}$ , $\lambda_{perc}$ , and $\lambda_{seg}$ are trade-off parameters. + +# 4. Experiments + +Extensive experiments are conducted to evaluate the effectiveness of our proposed SPD features and SAFM block. We report the quantitative and qualitative results in comparison with the competing methods, including CRN [7], SIMS [29], Pix2PixHD [35], SPADE [28], CC-FPSE [21], OASIS [31], LGGAN [33] and SC-GAN [36]. Besides, the ablation study is further conducted to explore the benefits of each component of our method that bring to the results. + +# 4.1. Dataset and Experimental Details + +Dataset. Our experiments are conducted on three challenging datasets, i.e., Cityscapes [8], ADE20K [41], and COCO-Stuff [5]. The Cityscapes dataset contains images of urban street scenarios, which has 3,000 images for training and 500 for validation. The ADE20K dataset has 20,210 images for training and 2,000 for validation each of which has 150 semantic classes, covering indoor and outdoor scenarios. Similarly, The COCO-Stuff contains 182 classes + +
MethodsCityscapesADE20KCOCO-Stuff
mIoU ↑Acc ↑FID ↓mIoU ↑Acc ↑FID ↓mIoU ↑Acc ↑FID ↓
CRN [7]52.477.1104.722.468.873.323.740.470.4
SIMS [29]47.275.549.7N/AN/AN/AN/AN/AN/A
pix2pixHD [35]58.381.495.020.369.281.814.645.7111.5
SPADE [28]62.381.971.838.579.933.937.467.922.6
CC-FPSE [21]65.682.354.343.782.931.741.670.719.2
LGGAN [33]68.483.057.741.681.8N/AN/AN/AN/A
OASIS [31]69.3N/A47.748.3N/A28.344.1N/A17.0
SC-GAN [36]66.982.549.545.283.829.342.072.018.1
Ours70.483.149.550.186.632.843.373.424.6
+ +Table 1. The quantitative comparison with the competing methods on different datasets. $\uparrow \left( \downarrow \right)$ indicates higher (lower) is better. + +that cover diverse scenarios and provides 118,000 images for training and 5,000 for validation. The real images and their corresponding semantic layouts in ADE20K and COCO-Stuff are resized and cropped to $256 \times 256$ while those in Cityscapes are processed to $256 \times 512$ . + +Experimental Details. We adopt the generator of SPADE [28] and SESAME [25] discriminator as baseline model. Following SPADE, Spectral Norm [23] is incorporated in all convolutional layers in our model. We adopt the ADAM [15] optimizer with $\beta_{1} = 0, \beta_{2} = 0.999$ , and the learning rate is set to $1 \times 10^{-4}$ and $4 \times 10^{-4}$ for generator and discriminator, respectively. Our model is trained on ADE20K and Cityscapes for 200 epochs, and 100 epochs on COCO-Stuff. The trade-off parameters $\lambda_{adv}$ , $\lambda_{fm}$ , $\lambda_{perc}$ , and $\lambda_{seg}$ are set to 1, 10, 10, 1, respectively. The experiments are carried out on a server with 4 2080Ti GPUs. + +Evaluation Metrics. Following previous semantic synthesis works [21, 28], we use three metrics to quantitatively evaluate the performance, i.e., Fréchet Inception Distance (FID) [11], mean Intersection-over-Union (mIoU), and pixel accuracy (Acc). Among these metrics, FID is introduced to assess the realism of the synthesized images by computing the Wasserstein-2 distance between the distributions of the synthesized and real images. Acc and mIoU are proposed to measure the differences of semantic labels between the synthesized images and the input semantic layouts. Following [28], we use the pre-trained semantic segmentation models DRN-D-105 [38], UperUnet101 [37] and DeepLabV2 [6] for the semantic evaluation of Cityscapes, ADE20K and COCO-Stuff, respectively. In addition, we demonstrate the generated results for visual comparison with other competing methods. Finally, a user study is reported to further evaluate the effectiveness of our method. + +# 4.2. Quantitative and Qualitative Results + +Quantitative comparisons. Table 1 lists the semantic segmentation and FID performance of our model and the competing methods on the Cityscapes, ADE20k, and COCO-Stuff datasets. In terms of semantic alignment, the mIoU of our method achieves 70.4 and 50.1 on Cityscapes and ADE20K, respectively (at least 1.1 and 1.8 higher than the second-best one). In addition, our method obtains the com + +parable FID scores, which ensures the distribution consistency between the generated results and the real images. The best semantic segmentation performance of our method indicates that the results of our method are not only more consistent with the target layout, but also photo-realistic in appearance, both of which can be attributed to the introduction of the SPD feature and the SAFM block. + +Note that OASIS achieves nearly the best performance on the COCO-Stuff dataset, but performs inferior to ours on the Cityscapes and ADE20K datasets, we analyze that the COCO-stuff dataset has more stuff classes without part-level semantics (91 stuff classes that cover about $66\%$ of the pixels), which makes the superiority of our SPD features for object instances not obvious in the quantitative results. + +Qualitative comparisons. Fig. 6 gives the qualitative comparisons on the Cityscapes, ADE20K, and COCO-Stuff datasets, from which we can observe that (i) with the SPD, our method can generate more realistic details (e.g. the washing machine in the 3-rd row), which is benefited from the discriminative and effective spatial position characterization. (ii) From the 4-th to 6-th rows, our method can well handle the instances of the same class with different shapes, while others fail to generate plausible results, indicating the effectiveness of our SPD features and SAFM block. (iii) With the constraints of semantic alignment, our method also performs well in unstructured textures, contributing to better visual quality, which can be seen from the 1-st row. + +User Study. Following [28], we conduct a user study to further compare our method with SPADE, CC-FPSE, LGGAN, and OASIS on the Cityscapes and ADE20K datasets. For each set of experiments, participants with computer vision backgrounds1 are required to select the image that has better performance in semantic alignment and photo-realistic appearance. From Table 2 we can see that users are more likely to favor our results, especially on the Cityscapes. + +Multi-modal synthesis. Following SPADE [28], we train an additional encoder for multi-modal synthesis or style-guided image with the KL Divergence loss in the way of VAE [16]. By controlling the mean and variance vector to + +![](images/4c933b4651180d7b32ae16602ef215ceadf42bf43d2c34dfc7d3c06b5026381d.jpg) +Figure 6. Visual comparisons on the COCO-Stuff (1-st $\sim$ 2-nd rows), ADE20K (3-rd row) and Cityscapes (4-th $\sim$ 6-th rows) datasets. + +
MethodsCityscapesADE20K
Ours > SPADE74.76%63.32%
Ours > CC-FPSE63.20%58.24%
Ours > LGGAN68.48%58.96%
Ours > OASIS65.24%56.76%
+ +Table 2. User study. The numbers represent the percentage of our method favored by users relative to competing methods. + +sample different random noises, our generator can also synthesize images with diverse and photo-realistic appearances for the given input segmentation mask, as shown in Fig. 8. + +Results with segmentation-based discriminator. Noting the success of the segmentation-based discriminator in OASIS, we verified the effectiveness of SPD with the discriminator and training tricks of OASIS. Specifically, we use SPD to replace the 3D noise in the OASIS generator, resulting in improved results for the Cityscapes dataset (FID: 43.81 and mIoU: 71.8). More qualitative results are shown in the supplementary materials. + +# 4.3. Ablation Study + +We conduct the ablation study on the Cityscapes dataset to evaluate the effectiveness of our SPD feature and SAFM block, which contains the following variants. (1) Base + +line: by adopting SPADE [28] generator and SESAME [25] discriminator as the baseline model. (2) Baseline $+\mathcal{L}_{seg}$ : by adding the semantic alignment loss upon the Baseline model. (3) Baseline $+SPD$ : by concatenating the SPD features with semantic layouts and feeding them into the SPADE block to generate spatially adaptive modulation parameters. (4) Baseline $+SPD + SAFM$ : by introducing the SAFM block to the generator to exploit the SPD features instead of directly concatenating them. (5) Ours-Full: by incorporating the Baseline, $\mathcal{L}_{seg}$ , SPD features and SAFM block together. The quantitative results and visual comparisons are shown in Table 3 and Fig. 7, respectively. + +We can see that (i) although $\mathcal{L}_{seg}$ equally promotes the realistic texture generation of object classes (e.g. car, washer classes) and stuff classes (e.g. sky, earth classes), the mIoU of object classes (mO) and stuff classes (mS) increase by 2.9 and 3.7, respectively, which greatly improves the performance of the synthesized images on mIoU and Acc metrics (3.4 and 0.5 higher than Baseline), it still can not promote the generator to synthesize rich structural details. Intuitively, its FID score has been slightly improved. (ii) The generator by introducing SPD as an additional condition can synthesize richer details, such as realistic car windows and lights, thereby greatly improving the mIoU, Acc, + +![](images/c6f01b174df53c1c2f5bdd8346b36d3ad156477195ba6056eeee76babf2674d4.jpg) +Figure 7. Visual comparisons of different variants. + +![](images/6d10ff6fd87cdfb7da3bb529eae95fc786a249e1439bbe3933dc2819426ec3b8.jpg) +Figure 8. Visual results of multi-modal synthesis. + +and FID scores of the generated results (see Baseline VS. Baseline+SPD). From Table 3 we can see that the mIoU of the object classes of the Baseline+SPD model increased by 3.3 compared to the Baseline model, and the FID reduced from 54.2 to 50.1, which indicates the effectiveness of our proposed SPD. (iii) The SAFM block enables the generator to better model the mapping between the SPD features and the shape appearance, which further improves the performance of our model, especially on the mIoU of object classes. (iv) By incorporating the SPD features, SAFM block, and $\mathcal{L}_{seg}$ , the performance of Ours-Full achieved the best performance, indicating the effectiveness of each component of our method in the synthesizing process. + +# 4.4. Limitation and Impact + +Limitation. Since the part-level semantic layouts for each object class are learning from data, the performance of our + +
MethodsmIoU ↑mS ↑mO ↑Acc ↑FID ↓
Baseline66.070.060.782.554.2
+Lseg69.473.763.683.053.2
+SPD68.571.864.082.750.1
+SPD+SAFM69.471.566.482.850.6
Ours-Full70.474.265.383.149.5
+ +Table 3. Quantitative comparison of five variants on Cityscapes. Here, mS (mO) represents the mIoU of Stuff (object) classes. + +approach heavily depends on the quantity of training data. Thus, the rare object classes or the rare shape patterns cannot be well modeled. For instance, non-rigid human bodies sometimes have uncommon posture and shape, from which it is hard to infer the implied part-level layout with insufficient training samples. Nevertheless, our method cloud significantly improve the quality of image synthesis for common object classes and common shape patterns. + +Impact. This paper proposes a method for semantic image synthesis which can synthesize or edit images based on semantic maps. Malicious usage of semantic image synthesis models may have adverse social repercussions, such as the synthesis of images for the purpose of spreading fake news. + +# 5. Conclusion + +In this paper, the shape of object instances is explicitly encoded into the proposed SPD features. Thus, the object's part-level layouts could be exploited to improve the generation of images with rich details. Furthermore, the SAFM block is proposed to combine the semantic map and SPD features through conditional convolution operation, which could adaptively modulate the input features. The quantitative and qualitative results demonstrate the superior performance of our method in synthesizing semantically aligned images with rich as well as photo-realistic details. + +Acknowledgments. This work was supported in part by National Key R&D Program of China under Grant No. 2020AAA0104500, and by the National Natural Science Foundation of China (NSFC) under Grant No.s U19A2073 and 62006064. + +# References + +[1] Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla. Segnet: A deep convolutional encoder-decoder architecture for image segmentation. 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SemanticStyleGAN factorizes its latent space based on semantic regions. Here, we show the results of style mixing by swapping local latent codes. Note that our models also disentangles shape and texture but we are simultaneously changing both here. + +# Abstract + +Recent studies have shown that StyleGANs provide promising prior models for downstream tasks on image synthesis and editing. However, since the latent codes of StyleGANs are designed to control global styles, it is hard to achieve a fine-grained control over synthesized images. We present SemanticStyleGAN, where a generator is trained to model local semantic parts separately and synthesizes images in a compositional way. The structure and texture of different local parts are controlled by corresponding latent codes. Experimental results demonstrate that our model provides a strong disentanglement between different spatial areas. When combined with editing methods designed for StyleGANs, it can achieve a more fine-grained control to edit synthesized or real images. The model can also be extended to other domains via transfer learning. Thus, as a generic prior model with built-in disentanglement, it could facilitate the development of GAN-based applications and enable more potential downstream tasks. + +# 1. Introduction + +Recent studies on Generative Adversarial Networks (GANs) have made impressive progress on image synthesis, where photo-realistic images can be generated from random codes in a latent space [11, 35-37]. These models provide powerful generative priors for downstream tasks by serving as neural renderers. However, their synthesis procedure is usually stochastic and no user control is naturally promised. Thus, it is still a challenging problem to achieve controllable image synthesis and editing utilizing generative priors. + +One of the most famous work among such generative priors is the StyleGAN series [35-37], where each generated image is conditioned on a set of coarse-to-fine latent codes (See Fig. 2). However, the meanings of these latent codes are still relatively ambiguous. Thus, a plethora of studies have attempted to further investigate into the latent space of StyleGAN to improve controllability. It is shown that by learning a linear boundary or a neu + +ral network in the latent space of StyleGAN, one could control the global attributes [4, 26, 59, 60] or 3D structure [64] of the generated images. Furthermore, by using an optimization/encoder-based method, real images can also be embedded into the latent space to create a unified synthesis/editing model [2, 3, 5, 55, 65, 67, 75]. However, as pure learning-based methods, these solutions inevitability suffer from the biases in the StyleGAN latent space. For example, since different attributes could be correlated in StyleGAN, it often happens that unexpected attributes or local parts are changed while one wants to edit a certain attribute or area. + +To obtain a more precise control, another solution is to train a new GAN model from scratch by introducing additional supervision or inductive biases. For example, by using 3D rendered faces, CONFIG [39] and DiscoFaceGAN [18] aim to build a GAN where pose, 3D information are factorized in the latent space. GAN-Control [61] disentangles the latent space by incorporating pre-trained attribute models for contrastive learning. Given the recent progress on neural rendering, it has also been shown that 3D-controllable GANs can be trained from images by injecting volumetric rendering into the synthesis procedure [13, 25, 46, 58, 74]. However, a major limitation of above-mentioned models is that they are designed for holistic attributes and there is no fine-grained local editability. + +In this work, we propose SemanticStyleGAN, which introduces a new type of generative prior for controllable image synthesis. Unlike prior work, the latent space of SemanticStyleGAN is factorized based on semantic parts defined by semantic segmentation masks (Fig. 2 (b)). Each semantic part is modulated individually with corresponding local latent codes and an image is synthesized by composing local feature maps. Different from layout-to-image translation methods [14, 69, 76], our local latent codes are able to control both the structure and texture of semantic parts (See Fig. 1). Compared to attribute-conditional GANs [18, 39, 61], our model is not designed for any specific task and can serve as a generic prior like StyleGAN. Thus, it can be combined with latent manipulation methods designed for StyleGAN to edit output images while providing more precise local controls. The contributions of this work can be summarized as follows: + +- A compositional generator architecture that disentangles the latent space into different semantic areas to control the structure and texture of local parts. +- A GAN training framework that learns the joint modeling of image and semantic segmentation masks. +- Experiments showing that our generator can be combined with existing latent manipulation methods to edit images in a more controllable fashion. +- Experiments showing that our generator can be adapted to other domains with only limited images while preserving spatial disentanglement. + +![](images/bf1d4682bcb46c03bf041ec98514da3226d2482c7103d9e56f634fcda84c4e0c.jpg) +(a) StyleGAN + +![](images/abd9ae6d5064700d0597556a7717c6b0199c9e948a4443a82324259279c219bd.jpg) +(b) SemanticStyleGAN +Figure 2. Abstract illustration of our method. Unlike StyleGAN, whose latent codes are associated with different granularity. The latent space of SemanticStyleGAN is factorized over different regions, which controls both local shape and texture. + +# 2. Related Work + +# 2.1. GAN Latent Space for Image Editing + +Given the success of GANs on synthesizing high quality images [11, 36, 37], many studies have attempted to utilize GANs as a image prior to achieve controllable image synthesis and editing. These studies can be categorized into two types. The first type aims to learn a model to manipulate the latent space of a pre-trained GAN network to achieve editability. For example, InterFaceGAN [59], GANSpace [26] and StyleFlow [4] trains a attribute model in the StyleGAN latent space to control binary attributes. StyleRig [64] learns a set of latent space networks to change the pose and lighting. Similarly, StyleFusion [33] learns to fuse semantic parts from different images in the latent space. The second type aims to learn a GAN with more disentangled latent space using additional supervision. For example, CONFIG [39] and DiscoFaceGAN [18] uses 3D-rendered data to disentangle pose, identity, expression from other information. GAN-Control [61] separates attributes like identity and age in the latent space by utilizing pretrained attribute models. Besides these, StyleMapGAN [38] propose to use style maps to modulate a synthesis network, but the meaning of each style pixel is unclear. Different from prior works, we propose a new type of factorization in the GAN latent space according to semantic labels. Our disentangled latent codes could independently control the shape and texture of each semantic part in the output image. + +# 2.2. Compositional Image Synthesis + +A plethora of studies have investigated how to build generative models to mimic the compositional nature of the world. To achieve compositionality, some studies propose to take images as input and compose a complicated scene with elements from real images [8, 10, 57]. On the other side, the majority studies aim to build a generative model that unsupervisedly discovered different objects in the training images and then synthesize them from independent latent codes. Most of these methods assume that objects are positioned independently in the scene and a compositional generative model is designed to discover such objects [6,12,19,20,23,24,31,66,71,72]. Some other methods + +![](images/85fb290e78acb174a250493efeb8d1a17e0f6e715ed72fca3c50445962431613.jpg) +Figure 3. Overview of our training framework. A MLP first maps randomly sampled codes into $\mathcal{W}$ space. The $\mathbf{w}$ code is used to modulate the weights of local generators. Each local generator $g_{k}$ outputs a feature map $\mathbf{f}_k$ and a pseudo-depth map $\mathbf{d}_k$ , which are fused into a coarse segmentation mask $\mathbf{m}$ and a global feature map $\mathbf{f}$ for image synthesis. The render network $R$ , which is only conditioned on the feature map, refines upsampled $\mathbf{m}$ into a high-resolution segmentation mask by learning a residual $\Delta \mathbf{m}$ and generates the fake image. A dual-branch discriminator models the joint distribution of RGB images and semantic segmentation masks. + +approach the compositional synthesis from a 3D perspective and disentangles objects and background by leraning multiview datasets [28, 45, 47, 48]. Similar to these work, we inject composition as an inductive-bias to encourage disentanglement. However, we focus on semantic parts that are defined by humans. This allows us to decompose highly correlated local parts below object level (e.g. hair and face) and enables more fine-grained control during synthesis. + +# 2.3. Layout-based Generators for Local Editing + +In the layout-to-image translation problem, a layout image is provided as the condition for controllable image synthesis. The layout image can be a semantic segmentation mask [14, 15, 42, 49, 53, 68, 69, 76, 77], a sketch image [16, 55, 68], etc. Among these, some studies have attempted to represent different semantic parts with latent codes [14, 76, 77]. But since the layout is controlled by the input segmentation mask, they are only able to control the local texture. Our method also shares similarity with prior research that utilizes semantic masks as intermediate representations for generation [9, 30, 32], but they are engineered to serve conditional generation tasks and not able to generate images from scratch. Recently, some researchers have also analyzed the correlation between StyleGAN style space and semantic masks [17, 33, 70] or supervise the latent manipulation with segmentation masks [21, 41, 51] to achieve local editing. In contrast to these methods, we build a semantic-aware generator that directly associates different local areas with latent codes, these codes can then be used to edit both local structure and texture. + +# 3. Methodology + +A typical GAN framework learns a generator that maps a vector $\mathbf{z} \sim \mathcal{Z}$ to an image, where $\mathcal{Z}$ is usually a standard normal distribution. In StyleGANs [36, 37], to handle the + +non-linearity of data distribution, $\mathbf{z}$ is first mapped into a latent code $\mathbf{w} \sim \mathcal{W}$ with an MLP. This $\mathcal{W}$ space is then extended into a $\mathcal{W}^+$ space that controls the output styles at different resolutions [36]. However, these latent codes do not have a strictly defined meaning and can hardly be used individually. + +We propose to build a generator whose $\mathcal{W}^+$ space is disentangled for different semantic areas. Formally, given a labeled dataset $D = \{(x_{1},y_{1}),(x_{2},y_{2})\ldots ,(x_{n},y_{n})\}$ , where $y_{i}\in \{0,1\}^{H\times W\times K}$ is the semantic segmentation mask of image $x_{i}$ and $K$ is the number of semantic classes, our generator gives a factorized $\mathcal{W}^+$ such that: + +$$ +\mathcal {W} ^ {+} = \mathcal {W} ^ {\text {b a s e}} \times \mathcal {W} ^ {1} \times \mathcal {W} ^ {2} \times \dots \times \mathcal {W} ^ {K}. \tag {1} +$$ + +Here each local latent code $\mathbf{w}^k\in \mathcal{W}^k$ controls the shape and texture of $k_{th}$ semantic area defined in segmentation labels while $\mathbf{w}^{\mathrm{base}}\in \mathcal{W}^{\mathrm{base}}$ is a shared code that controls the coarse structure, such as pose. Each $\mathbf{w}^k$ is further decomposed into a shape code $\mathbf{w}_s^k$ and a texture code $\mathbf{w}_t^k$ . The generator $G:\mathcal{W}^{+}\to \mathcal{X}\times \mathcal{Y}$ maps the latent codes to an RGB image and a semantic segmentation mask. To this end, we identify two major challenges: + +1. How to decouple different local areas? +2. How to ensure the semantic meanings of these areas? + +For the first problem, inspired by compositional generative models [12, 23, 48], we introduce local generators and a compositional synthesis procedure as the inductive bias. For the second problem, we use a dual-branch discriminator $D: \mathcal{X} \times \mathcal{Y} \to \mathbb{R}$ that models the joint distribution $p(x, y)$ to supervise the shapes of local parts after composition. + +# 3.1. Generator + +The overall structure of our generator is shown in Figure 3. Similar to StyleGAN2 [36, 37], an 8-layer MLP first maps $\mathbf{z}$ to the intermediate code $\mathbf{w}$ . Then, $K$ local generators are introduced to model different semantic parts using + +![](images/d60daa7f80ba4f5fde994507a83d6d79097d708cf0e90f883dbff8937e031148.jpg) +Figure 4. The architecture of local generator. Blue blocks are modulated $1 \times 1$ convolution layers whose weights are conditioned on input latent codes. Purple blocks are linear transformation layers. + +w. A render net $R$ takes in the fused results from local generators and outputs an RGB image and a corresponding semantic segmentation mask. + +Local Generator Following recent work on continuous image rendering [7, 62, 74], we use modulated MLPs for local generators (Fig. 4), which allows explicit spatial control over synthesized output. Given Fourier features [63] (position encoding) $\mathbf{p}$ and latent codes as inputs, a local generator $g_{k}$ outputs a feature map $\mathbf{f}_k$ and a pseudo-depth map $\mathbf{d}_k$ : + +$$ +g _ {k}: \left(\mathbf {p}, \mathbf {w} ^ {\text {b a s e}}, \mathbf {w} _ {s} ^ {k}, \mathbf {w} _ {t} ^ {k}\right) \mapsto \left(\mathbf {f} _ {k}, \mathbf {d} _ {k}\right). \tag {2} +$$ + +Here, to reduce the computation cost, the input Fourier feature map as well as the outputs are of a reduced size $H^{c} \times W^{c}$ , smaller than the final output image. In practice, we choose it to be $64 \times 64$ to balance the efficiency and quality. During training, style mixing [36] is conducted independently within each local generator between $\mathbf{w}_{s}^{k}$ , $\mathbf{w}_{t}^{k}$ and $\mathbf{w}_{t}^{k}$ such that different local parts and different shapes and textures could work collaboratively for synthesis. We note that the pseudo-depth maps here are not strictly depth maps, we call them "depth" because the they are used for a composition strategy that mimics the z-buffering process. + +Fusion In the fusion step, we first generate a coarse segmentation mask $\mathbf{m} \in \mathbb{R}^{K \times H^c \times W^c}$ from pseudo-depth maps. Following prior work on compositional generation [12, 23], the pseudo-depth maps are used as logits for softmax function: + +$$ +\mathbf {m} _ {k} (i, j) = \frac {\exp \left(\mathbf {d} _ {k} (i , j)\right)}{\sum_ {k ^ {\prime}} ^ {K} \exp \left(\mathbf {d} _ {k ^ {\prime}} (i , j)\right)}, \tag {3} +$$ + +where $\mathbf{m}_k(i,j)$ denotes the pixel $(i,j)$ in the $k_{th}$ class of mask $\mathbf{m}$ and similarly for $\mathbf{d}_k(i,j)$ . The feature maps are then aggregated by: + +$$ +\mathbf {f} = \sum_ {k = 1} ^ {K} \mathbf {m} _ {k} \odot \mathbf {f} _ {k}. \tag {4} +$$ + +Here $\odot$ denotes element-wise multiplication. The aggregated feature map $\mathbf{f}$ contains all the information about the output image and is sent into $R$ for rendering. We note + +that directly using $\mathbf{m}$ for feature aggregation could be problematic when some classes are transparent. Thus, we use a modified version $\tilde{\mathbf{m}}$ for feature aggregation in case of transparent classes, e.g. glasses (See appendix for details). + +Render Net The render net $R$ is similar to the original StyleGAN2 generator with a few modifications. First, it does not use modulated convolution layers and the output is purely conditioned on the input feature map. Second, we input the feature map at both $16 \times 16$ and $64 \times 64$ resolutions, where feature concatenation is conducted at $64 \times 64$ . The additional input of low-resolution feature map allows a better blending between different parts. Last, we find that directly training with $\mathbf{m}$ is difficult due to the intrinsic gap between softmax outputs and real segmentation masks. Thus, besides the ToRGB branch after each convolution layer, we have an additional ToSeg branch as in SemanticGAN [40] to output residuals to refine the coarse segmentation mask $\mathbf{m}$ into the final mask $\hat{y} = \text{upsample}(\mathbf{m}) + \Delta \mathbf{m}$ that has the same size as output image. Here a regularization loss is needed such that the final mask would not deviate too much from the coarse mask: + +$$ +\mathcal {L} _ {\text {m a s k}} = \left\| \Delta \mathbf {m} \right\| ^ {2}. \tag {5} +$$ + +# 3.2. Discriminator and Learning Framework + +In order to model the joint distribution $p(x,y)$ , the discriminator needs to take both RGB images and segmentation masks as input. We found that a simple concatenation does not work due to the large gradient magnitude on segmentation masks. Thus, we propose to use a dual-branch discriminator $D(x,y)$ that has two convolution branches for $x$ and $y$ , respectively. The outputs are then summed up for fully connected layers. Such a design allows us to separately regularize the gradient norm of the segmentation branch with an additional R1 regularization loss $\mathcal{L}_{R1seg}$ . The resulting training framework is similar to StyleGAN2 with the loss function: + +$$ +\mathcal {L} _ {a l l} = \mathcal {L} _ {\text {S t y l e G A N 2}} + \lambda_ {\text {m a s k}} \mathcal {L} _ {\text {m a s k}} + \lambda_ {R 1 _ {\text {s e g}}} \mathcal {L} _ {R 1 _ {\text {s e g}}}, \tag {6} +$$ + +where $\mathcal{L}_{StyleGAN2}$ denotes the loss functions used in the original StyleGAN2. + +# 4. Implementation Details + +We implement our methods using PyTorch 1.15 library. We use the same optimizer and batch settings as in StyleGAN2. $\lambda_{R1img}$ , $\lambda_{R1seg}$ , $\lambda_{mask}$ are set to 10, 1000 and 100, respectively. Style mixing probability and path regularization are reduced to 0.3 and 0.5, respectively. For some experiments, we fine-tune our models on image-only datasets. In such cases, we drop the segmentation branch in discriminator and use the original StyleGAN2 loss functions to fine-tune the model. Due to the space limit, more details about network architectures are given in appendix. + +![](images/f0f330551340a3c0daf8d4047970240a206357851b5b49dcbc567ec0b7275989.jpg) +Figure 5. Illustration of compositional synthesis. Starting from background, we gradually add more components into the feature map. The second row shows the pseudo-depth map of each corresponding component used for fusion. Note that the "hair" generator outputs a complete shape even though it is covered by the face. During synthesis, all pseudo-depth maps are fused without an order. + +
MethodDataCompositionalFID↓IS↑
StyleGAN2img×4.453.40
SemanticGANimg&seg×18.542.77
+ proposed trainingimg&seg×7.503.51
SemanticStyleGAN (ours)img&seg✓6.423.21
+ +Table 1. Quantitative evaluation on synthesis quality. All the models are trained on CelebAMask-HQ at $256 \times 256$ . "img" and "seg" refer to RGB image and segmentation mask, respectively. + +![](images/62b4bef2df5b0dee205176a50e40b8f892d7a11cb00e36a8ea6b20ed1feb6645.jpg) +Figure 6. Example generation results of our model trained on CelebAMask-HQ. The images are generated at a resolution of $512 \times 512$ with a truncation of 0.7. + +# 5. Experiments + +# 5.1. Semantic-aware and Disentangled Generation + +We first evaluate our model on the synthesis quality and its local disentanglement. For synthesis quality, we compare our model with StyleGAN2 [37] and SemanticGAN [40]. The original StyleGAN2, which neither models segmentation masks nor provides local controllability, is compared against as an upper bound of synthesis quality. SemanticGAN modifies StyleGAN2 into a joint training framework to output both image and segmentation masks. Since its goal is to conduct segmentation, it does not allows local control either. All the models are trained on the the first 28,000 images of CelebAMask-HQ resized to + +![](images/aee234b0ab30bb188b6894346598cee983b02850d8a0cc3a91d9d6d2b78287e2.jpg) +Figure 7. Results of latent interpolation on the whole latent space and specified subspaces. Here, "Face" refers to all the components relevant to face, including eyes, mouth, etc. + +$256 \times 256$ . Fréchet Inception Distance (FID) [29] and Inception Score (IS) [56] are used to measure the synthesis quality. + +Our project is initially built on SemanticGAN framework for learning a semantic-aware model. The original SemanticGAN is semi-supervised and we change it to use all the training labels. As shown in Tab. 1, SemanticGAN achieves much lower quality compared to original StyleGAN, indicating that learning a joint model of images and segmentation masks is a challenging task. Hypothesizing that the main bottleneck of SemanticGAN is the additional patch discriminator used for learning segmentation masks, we replace it with the proposed dual-branch discriminator. The new training framework achieves much better synthesis score. We further replace the SemanticGAN generator with our SemanticStyleGAN generator. Compared to SemanticGAN generator, our model shows a similar synthesis quality while providing additional controllability on each semantic area. We then extend our model to $512 \times 512$ resolution and + +![](images/d934fd499dfa613e79129a1735c620ca6c41a988f0c7127cf80e08bd412d5660.jpg) +Figure 8. Image composition and transformation via Fourier feature manipulation. Real images are used as background for synthesis and inverted into feature maps. Then foreground can be synthesized on this real image in the feature space. The location and size of foreground can be controlled via Fourier features. + +achieve a FID and IS of 7.22 and 3.47, respectively. For reference, the StyleGAN2 generator achieves a FID and IS of 6.47 and 3.55, respectively. Fig. 6 shows the synthesis results of the $512 \times 512$ model. + +To interpret the compositional synthesis of our model, Fig. 5 shows the results of synthesis with limited components. We first disable all the foreground generators and gradually add them into the forward process. It can be seen that these local generators can work independently to generate a semantic part. The pseudo-depth maps, in spite of the lack of 3D supervision, learn meaningful shapes that could be used to collaboratively compose different faces. + +Fig. 7 shows the results of latent interpolation of our generator model. The first row shows that our model could interpolate smoothly between two randomly sampled images. Besides, we can interpolate on a specific semantic area by changing the corresponding latent codes, e.g. face or hair, while fixing irrelevant parts. The results indicate that our model has learned a smooth and disentangled latent space for semantic editing. Overall, even though there is no explicit constraint during training, we observe that our model could disentangle most local shapes and textures. We also refer the readers to the appendix for more results on semantic local style mixing. We note that unlike traditional GANs that generates a complete image, such a compositional process also allows our model to generate the foreground only and control it by manipulating the Fourier features (See Fig. 8). + +# 5.2. Controlled Synthesis and Image Editing + +With the semantic decomposition in the latent space, our model provides a more disentangled generative prior for image editing. Here, we evaluate our model on downstream editing tasks and compares it to StyleGAN2. We use the pytorch conversion of official StyleGAN2 (config-F on FFHQ 1024x1024) as our baseline, which is widely used in relevant studies on image editing. The $512 \times 512$ model is used for our method. + +# 5.2.1 Encoding and Editing Real Images + +To evaluate the editing results on real images, we first need to embed such images into the GAN latent space. Here, + +
MethodMSE↓ID↑LPIPS↓
StyleGAN2 (FFHQ)0.031±0.0150.654±0.0970.309±0.046
StyleGAN20.029±0.0160.575±0.1190.330±0.052
SemanticStyleGAN0.031±0.0170.602±0.1220.335±0.051
+ +Table 2. Quantitative evaluation of reconstruction performance using Restyle (psp) encoder. The bottom two rows (StyleGAN2 and Ours) are trained on the same split of CelebAMask-HQ. + +we adopt a state-of-the-art GAN encoder, i.e. Restylepsp [5], for both StyleGAN2 and our model. We use the official model from Restyle authors for StyleGAN2 while a new encoder is trained for our model with default hyperparameters. For reference, we also train a encoder for our StyleGAN2 that is trained on CelebAMask-HQ. Tab. 2 shows the quantitative results of image reconstruction using restyle encoders. Overall, our model achieves a comparable performance in terms of reconstruction. + +The next question is whether our model can be applied to local editing on these reconstructed images. Here, we adopt two popular editing methods that were proposed for StyleGAN2: InterFaceGAN [59] and StyleFlow [4]. Both methods need to generate a set of fake images and label their attributes to train a latent manipulation model. In particular, InterFaceGAN learns a linear SVM while StyleFlow uses a conditional continuous normalizing flow [22] to model the latent attribute manipulation. For both generators, we randomly synthesize 50,000 images for labeling. Following InterFaceGAN, a ResNet-50 [27] is trained on CelebA dataset [44] to label these images. During the experiments, we found that our model trained on CelebAMask-HQ exhibits a much lower diversity compared to FFHQ-based StyleGAN2. Thus, we fine-tune our model on FFHQ for 1,000 steps (See Sec. 4), for which we observe a sufficient improvement of diversity without loss of controllability. + +We choose 4 local attributes covering different parts of the face image for editing experiments, namely smile, baldness, beard and bangs, and test on the last 1,000 images of CelebAMask-HQ, which were not used for training. For StyleGAN2, we keep the original selection of latent dimensions in these methods for content preservation. For ours, we manually choose relevant areas for editing, e.g. hair for baldness and face for beard, which can be regarded as a trivial step during deployment. Fig. 9 shows the qualitative results of applying InterFaceGAN to StyleGAN2 and our model. Although InterFaceGAN successfully edits the attributes on StyleGAN2, irrelevant parts are inevitably altered due to the entanglement in the latent space. In comparison, our model focuses only on specified semantic areas. We also conduct a quantitative evaluation of the editing task. For each image, we control the degree of manipulation to generate 10 images. Then a "preservation-score" curve is plotted using the attribute classifier. Here, score gain refers to the average gain in classification score of the tar + +![](images/c28c6e0009e2865bbf5dde897a11ae906c8e8443602520ce07504943c94af5d7.jpg) +Figure 9. Results of GAN inversion and editing. For each attribute and method, we show the inversion result of Restyle encoder, the edited image and the difference map between them. + +![](images/79cc04d3b11abce9a2b5e1546771c21f95a5dd8981f4b568c881aec4ff433c12.jpg) + +![](images/d9799f693e41d0b484a39ce4609a04c2420c7c75b327ef48d22998d6b53814d2.jpg) + +![](images/504ffae3a918fa1afc9a2f882e888e4f26e01817b3396bd692d0792eb653980b.jpg) +Figure 10. Quantitative comparison of local attribute editing using StyleGAN2 and our model when combined with StyleFlow and InterFaceGAN. + +![](images/60a383f07f42cf7bef85a6fefd9281be16cbb19c6f780ef8a4cc48567054784c.jpg) + +get attribute. pixel preservation refers to 1 minus the $\ell 1$ loss between the two images. The $\ell 1$ loss is an approximation of $\ell 0$ loss, which computes the number of pixels that has been altered. In our experiments, we found this simple metric best correlates with the spatial difference between images. From Fig. 10, it can be seen that our model achieves a better overall performance. Note that for baldness, our model stops when it removes all hairs, but InterFaceGAN+StyleGAN2 keeps increasing the score by adapting into correlated attributes (such as aging). For bangs, our model tends to increase the overall length of hairs, which could be an inherited bias from original training data. Besides, we found that StyleFlow is more sensitive to label imbalance. Thus, given the small number of bald examples, it fails to learn the baldness attribute for both generators. + +![](images/9b76b13eb53a76f25cec8ddd6731e3176f97693a82b202ea879954e746929b52.jpg) +Figure 11. Results of text-guided image synthesis under sequential editing. Starting from an average fake face, the first row (from left to right) shows the results of sequentially applying optimization-based StyleCLIP [50] with StyleGAN2 while the second row shows the results of our model with the same input texts. + +# 5.2.2 Text-guided Synthesis + +Recent work have shown that one could use a text-image embedding, such as CLIP [54], to guide the synthesis of StyleGAN2 for controlled synthesis [50]. Similar to attribute editing, StyleGAN2 suffers from the local disentanglement problem on. Fig. 11 shows a few examples of using StyleCLIP [50] to manipulate a synthesized image with a sequence of text prompts. Here, we use the optimization-based version of StyleCLIP as it is flexible for any input text. It can be seen that the original StyleCLIP often modifies the whole image while the text is trying to change only a specified area. Our model, by additionally let the user to choose relevant areas, can faithfully constrain the editing to local parts. The results indicate that our model could be a more suitable tool for text-guided portrait synthesis where detailed descriptions are provided. + +![](images/41b97af46f46ea40e8f6beb6a73e1edb12d2bed47c4ddec01c45fa83f9c13737.jpg) +Figure 12. Examples of changing hair styles on adapted new domains. The first four and last three columns show the results of different latent codes for hair shapes and textures, respectively. + +![](images/af50224578911a58e7d8e84ceb47338bdf17ad06f85bafd37a7661687a5f9d1f.jpg) +Figure 13. Controlled generation results on the DeepFashion dataset. Our model can generate various style for different parts. + +# 5.3. Results on Other Domains + +Training our model from scratch requires access to images and segmentation masks at the same time, which might not be feasible in some cases. Thus, we would like to ask whether the model can be fine-tuned on image-only datasets while preserving the local disentanglement (See Sec. 4 for fine-tuning). Fig. 12 shows the results after fine-tuning our model on the Toonify [52], MetFaces dataset [34] and BitMoji [1]. All of these datasets have a much smaller number of images compared to CelebAMask-HQ and no segmentation masks. We train our model for hundreds of steps until perceptually good results are generated. It can be seen that, for datasets with a limited domain gap, our model is able to maintain local controllability even after fine-tuning. + +In spite of the experiments on face datasets so far, our method indeed does not include any module that is designed for face only and hence can be applied to other objects as well. Fig. 13 shows the results of training our model on the DeepFashion dataset [43], for which we obtain the labels from [77]. With the default hyper-parameters, we find that + +our model can be successfully trained on fashion datasets and we can similarly control the structure and texture of different semantic parts in the latent space. + +# 6. Limitations and Discussion + +Applicable Datasets Although we have shown that our method can be applied to other domains beyond face photos, we still see a limitation caused by the design and supervision. Since we need to build a local generator for each class, the method would not scale to datasets that have too many semantic classes, such as scenes [73]. Besides, for the purpose of synthesis quality, we change the semi-supervised framework of SemanticGAN [40] into fully-supervised, which limits our model from training on image-only datasets from scratch. It would be beneficial to develop a semi-supervised version of our method in the future. + +Disentanglement As the disentanglement between pose, shape and texture is only enforced by the design of layer separation in local generators, we see that the boundary between them is still sometimes ambiguous. For example, the shared coarse structure code could encode some information about expression and the shape code could affect the beard. However, in this work, we mainly focus on the spatial disentanglement between different semantic parts and we believe additional regularization losses or architecture tuning could be incorporated in the future to better decouple those information. + +Societal Impact Our work focuses on the technical problem of improving controllability of GANs and is not specifically designed for any malicious uses. This being said, we do see that the method could be potentially extended into controversial applications such as generating fake profiles. Therefore, we believe that the images synthesized using our approach should present itself as synthetic. + +# 7. Conclusion + +In this paper, we present a new type of GAN method that synthesizes images in a controllable way. Through the design of local generators, masked feature aggregation and joint modeling of images and segmentation masks, we are able to model the structure and texture of different semantic areas separately. Experiments show that our method is able to synthesize high-quality images while disentangling different local parts. By combining our model with other editing methods, we can edit synthesized images with a more fine-grained control. Experiments also show that our model can be adapted to image-only datasets while preserving disentanglement capability. We believe the proposed method presents a new and interesting direction of GAN priors for controllable image synthesis, which could shed light on many potential downstream tasks. + +# References + +[1] Bitmoji dataset. https://www.kaggle.com/mostafamozafari/bitmoji-faces/version/1, 2013. Released under CC BY 4.0.8 +[2] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? 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However, the massive expansion of semiconductor manufacturing and the development of new technology will bring many defect wafers. If these defect wafers have not been correctly inspected, the ineffective semiconductor processing on these defect wafers will cause additional impact to our environment, such as excessive carbon dioxide emission and energy consumption. + +In this paper, we utilize the information processing advantages of quantum computing to promote the defect learning defect review (DLDR). We propose a classical-quantum hybrid algorithm for deep learning on near-term quantum processors. By tuning parameters implemented on it, quantum circuit driven by our framework learns a given DLDR task, include of wafer defect map classification, defect pattern classification, and hotspot detection. In addition, we explore parametrized quantum circuits with different expressibility and entangling capacities. These results can be used to build a future roadmap to develop circuit-based quantum deep learning for semiconductor defect detection. + +# 1. Introduction + +The industry presents a paradox. The achievement of global climate goals will depend on semiconductors. They are an integral part of solar arrays, wind turbines, and electric vehicles. But chip manufacturing requires huge amounts of energy and water, and it emit a lot of exhaust gas during the production process. In addition to switching to renewables, chipmakers could also implement efficiencies in fabs to reduce their carbon footprint, including ineffective processing on the defect wafer. + +In the semiconductor manufacturing, there are three main types of defects: wafer defect map, defect pattern, and hotspot. Wafer defect map is used to visualize the distribution of defect patterns and identify potential process and tool issues. Continuous-monitoring wafer + +defect maps are crucial for yield management because a sudden increase in the problematic patterns can be feedback to operation engineers to resolve the related issue. Generally, it is known that conventional defect patterns such as cluster, scratch, and ring are closely related to a certain type of process. For example, as shown in Figure 1, the defect map "Edge" is caused by the damaged low thermal mass (LTM) pad. LTM is an industrial grade self-regulating heating cable used for pipelines and chambers. Under the high temperature and high pressure of chemical vapor deposition (CVD) process, LTM pad will gradually get aged and cracked. Then, it will produce particles that fall on the edge of wafer surface. Another example "Cluster" is a mass of particles on the wafer surface during the Etching process. This defect is usually caused by the aged component of side O-ring. When this defect maps are detected, it means that the chamber needs to maintenance and replace aging parts with new ones. + +![](images/a87dc615363525ea14903b025008fb061d037cb03f8a5a122abfec8d4f9c441d.jpg) +Defect Map + +![](images/aeb97af29848b7f4049eee2ff0a83795982d4b116e7b9ab5fa6a3f3ffdbb00ec.jpg) +Root Cause + +![](images/448ee3718086f7862eb94188c84f03bb22e4ee963d5e4867d80889f205fd2e1e.jpg) + +Side O-ring + +![](images/8abe42f88699ef98df4237bff9dee3be4b9de51fd843c63d1fdc8ab4e32a9879.jpg) +Figure 1: Defect map and its root cause. + +![](images/9cf8e936a8eedcdc87abb92f801b88f595fe70a600268bd2720e801f99368c5c.jpg) + +![](images/6e22be975320adf6dcef1d8459b4f958641fcaa22eca14142aec28790dbeb2ab.jpg) + +Side O-ring + +The defect pattern is the unit that composes the wafer map, which image is obtained by a higher resolution inspection tool. Each defect pattern signals the root cause, and engineers can diagnose the failure and prevent it from happening again. As shown in Figure 2, the defect pattern "Multi-dots" mainly occurs in the WET Etching chamber pipeline and is caused by the dirty nozzles of xFlow. Another example is "Fallon" that often occurs on the CVD chamber. The main reason is the fall on particle caused by the damage of the point-of-use (POU) filter. The damage component must be replaced immediately to avoid this defect from happening again. + +![](images/b203884690397ef9a80c518b7053e9dea4674ab62f007ab4ef0067c1ead563c7.jpg) +Defect Pattern +Root Cause +Figure 2: Defect pattern and its root cause + +A hotspot is the region of mask layout patterns where failures including open and short circuits are more likely to happen during semiconductor manufacturing. Hotspot detection is used to check potential circuit failures at the post optical proximity correction (OPC) stage when transferring designed patterns onto silicon wafers. Figure-3 show the example of Epitaxy (EPI) hotspot and its root cause. We can find that this wafer has the layout pattern of SiGe wavy. This hotspot usually caused by tungsten loss (W loss) in the CVD process. In addition, the lithography (LIT) hotspot has received much attention in the recent years. LIT hotspots caused by light diffraction during manufacturing procedure due to a substantial mismatch between lithography wavelength and semiconductor technology feature size. + +![](images/7428be1bc699c60f40025330a16c2cea6c4c62784b904367b8ceb60bd6809651.jpg) +Figure 3: Hotspot and its root cause. + +![](images/8b9b67d3f7b8b62c9012452c9a34b61b0a28e6043e082531efa2bfa03d3edde2.jpg) + +Deep learning as a hot computer vision technology has been actively realized in many fields. Although it has been serving the semiconductor industry in many areas, the contribution of deep learning in semiconductor defect detection is tremendous. However, deep learning algorithms tend to give probabilistic results and contain correlated components but at the same time suffer computational bottlenecks due to the curse of dimensionality. Similar to deep learning, quantum computing (QC) provides probabilistic results based on measurements formed by intrinsically coupled quantum systems. QC can provide potentially exponential speedups due to their ability to perform massively parallel computations on the superposition of quantum states. + +In addition, each artificial neuron is usually constructed by linear connected layers, with non-linear activation functions connected at the end. In this work, we replace the + +linear part by the quantum circuit to take advantage of possible speedup in quantum computation. We propose the hybrid classical-quantum deep learning (HCQDL) based on quantum circuit for the above various types of defect inspection. Our HCQDL consists of classical and quantum layers. The classical layers implemented by the combination of self-proliferation and self-attention block. Self-proliferation block used a series of linear transformations to generate more feature maps at a cheaper computing cost. Then, self-attention block learned a wealth of information about long-range dependencies from this generated feature. + +The quantum layer implemented by various quantum circuit built in the continuous-variable architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. By tuning parameters implemented on it, quantum circuit driven by our framework learns a given DLDR task, include of wafer defect map classification, defect pattern classification, and hotspot detection. The main contributions of the paper are: + +(1) We introduce a new network architecture, SelfProliferation-and-Attention block (SP&A Block), which can perform feature engineering in a more efficient way. +(2) We present the parametrized quantum circuit (PQC) with different expressibility and entangling capacities, and compare their training performance to quantify the expected benefits. +(3) We provide a future roadmap to develop circuit-based hybrid quantum-classical deep learning for semiconductor defect detection. + +The rest of the paper has been organized as follows: Section 2 describes the related works of deep learning defect review (DLDR) and quantum machine learning. Section 3 presents our proposed HCQDL model and explore it in detail theoretically. Section 4 compares the results of latest DLDR models and our proposed method according to different metrics through several experiments. Finally, we conclude with some final thoughts and give future work recommendations in section 5. + +# 2. Related works + +In this section, we briefly discuss DLDR and quantum machine learning backgrounds. + +# 2.1. Defect learning defect review + +Wafer Defect Map. Wafer defect map is used to visualize defect patterns, identify potential process issues, and provide yield engineers with vital information to help them identify the root cause of die failures during semiconductor manufacturing processes. Nakata et al. [1] proposed the big data analysis enables comprehensive and long-term monitoring automation. They make use of fast and scalable methods of clustering and pattern mining and realize daily + +comprehensive monitoring with massive manufacturing data. They also apply deep learning to classification of wafer failure map patterns. Their deep learning model was a retrainable, one-class classifier with five layers whose parameters were determined empirically. They used to train it on the frequently occurring pattern, employing unlabeled images to monitor if that defect pattern emerges again. Nakazawa and Kulkarni [2] proposed the convolutional neural network (CNN) for wafer map defect classification and retrieval of similar maps. They demonstrate that by using only synthetic data for network training, real wafer maps can be classified with high accuracy. Kyeong and Kim [3] proposed a mixed defect classification system consisting of four CNN models for four basic defect types of the dataset. The proposed model was able to identify 16 defect types as combinations of four basic types. Kim et al. [4] presented a neural network-based bin coloring method and built a four-layered CNN to distinguish good and bad wafers. However, they did not classify the defect wafers into their respective defect types, which is a necessary step to analyze the root cause of the defects. di Bella et al. [5] adopted submanifold sparse CNN as a binary classifier for sparse data of larger images. They also used oversampling to overcome class imbalance, such as rotations, flips, and noise injection. Kong and Ni [6] proposed a multi-step detection system for multi-defect wafers classification. First, a binary CNN is used to classify wafers with overlapping and non-overlapping patterns. The wafer maps with a single pattern or non-overlapping mixed-type pattern were segmented into single pattern maps and then classified by a CNN. In the latest research, deep learning architecture has become the mainstream [8-10] on wafer defect map classification task. We plan to combine the advantages of deep learning and quantum computing as a roadmap for future research. + +Defect Pattern. The defect pattern is the unit that composes the wafer map. It is the image obtained by a higher resolution inspection tool. Defect pattern recognition is suited to deep learning, a powerful supervised learning technique that does not need manual feature design. Beuth et al. [11] used a biological visual attention method to perform the deep learning defect review. This biological visual attention mechanism is mainly to realize the boundary search of the defect chip by simulating the signal of the pre-frontal cortex (PFC). However, the attention mechanism of this study has two problems: 1. The PFC of this model is only applicable to the search of geometric shapes, and not for textures. 2. The model cannot adaptively learn the attention area of attention. Therefore, how to develop an adaptive attention mechanism (self-attention) for defect pattern classification is the direction of future research. Chen et al. [12] proposed a lightweight network called WDD-Net. The method refers to MobileNet-V2, using depthwise separable convolutions to reduce parameters and calculations. The experimental + +results show that the detection speed of WDD-Net is 5 times faster than that of VGG-16. Yang and Sun [13] proposed a new DLDR architecture, named self-proliferating neural network (SPNet), which can effectively generate more feature maps with a lower computational cost. + +Hotspot. Hotspot detection is defined as the procedure of finding the hotspots from the layout that would cause printability issues during lithograph. F. Yang et al. [14] used support vector machine (SVM) as the lithography hotspot classifier. They adopted spectral clustering for feature extraction, and their accuracy reached $95.66\%$ on the public dataset ICCAD-2012. V. S. Ajna and N. George [15] proposed a method of layout hot spot detection based on deep learning. This method achieves $93\%$ accuracy with the least number of false alarms. In subsequent research, deep learning became the main model architecture of hotspot detection [16-18]. X. Huang et al. [19] proposed an ensemble deep learning based on multiple sub-models. This method achieves recall rate $98.8\%$ on the ICCAD-2012. + +Quantum computation is a paradigm that furthermore includes nonclassical effects such as superposition, interference, and entanglement, giving it potential advantages over classical computing models. Therefore, we introduce the application of quantum machine learning in the next section, hoping to improve the weakness of classical deep learning by using quantum computing. + +# 2.2. Quantum machine learning + +Recent developments in quantum computing allowed scientists to look at computational problems from a new perspective. Researchers have been investigating quantum computing tools for a computational advantage for the deep learning problem. As near-term quantum devices move beyond the point of classical stimulability, also known as quantum supremacy [20], it is of utmost importance to discover new applications for noisy intermediate scale quantum (NISQ) devices [21] which are expected to be available in the next few years. Among the most promising applications for quantum computing is Quantum Machine Learning (QML) [22-23]. Recent advances in QML have been dominated by a class of algorithms called hybrid quantum-classical variational algorithms. Sasaki and Carlini [24] have delved into the notion of semi-classical and universal strategies whereby, in the former, classical methods are adapted to work on quantum systems whereas in the latter the methods are purely quantum in nature. A. Ajagekar and F. You [25] proposed the fault diagnosis deep learning method based on quantum computing. This method enjoys superior performance with an average fault diagnosis rate of $80\%$ and tremendously low false alarm rates for the monitoring of Tennessee Eastman process. + +In this paper, we present quantum computing based deep + +learning methods for semiconductor defect detection that are capable of overcoming the computational challenges faced by conventional techniques performed on classical computers. The proposed model effectively detects defect pattern by leveraging the superior feature extraction of self-proliferation and self-attention to facilitate proper classification between normal and defect wafers. Then, a quantum computing assisted generative training process followed by supervised discriminative training is used to train this model. + +# 3. Method + +Our technique, called hybrid classical-quantum deep learning (HCQDL), uses quantum circuits to nonlinearly transform classical inputs into features that can then be used in a number of deep learning algorithms. HCQDL consists of classical layer, quantum layer, and fully connection layer (as shown in Figure 4). The classical layer is implemented by the self-proliferation and self-attention (SP&A) block that used to extract feature maps effectively. The quantum layer is composed of the quantum circuit that can generate highly complex kernels whose calculations could be classically intractable. The fully connection layer is implemented by the non-linear activation functions to calculate the probability of various semiconductor defect. To demonstrate the power of the proposed method, we present results of using HCQDL to generate eigenstates of simple molecules, complex entangled ground states, and ground states of the transverse Hamiltonian with varying local fields and spin-spin couplings. The approach achieved high accurate results and can be generalized for creating quantum states of complex systems. + +![](images/bd0a1a9735c05467ca3089019eebc99b901f3213d8e019c652f7699da890f714.jpg) +Figure 4: Architecture of hybrid classical-quantum deep learning. + +# 3.1. Classical Layer + +The classical layer is mainly composed of two parts: self-proliferation block and self-attention block. Self-proliferation block used a series of linear transformations to generate more feature maps at a cheaper cost. Self-attention block learned a wealth of information about long + +range dependencies from this generated feature maps. + +Self-Proliferation Block. Traditional convolution is a series of convolution operations to increase the feature depth. Self-proliferation block generates the same number of features through linear transform. The process is similar to DNA unzipping and replication, which can effectively increase the number of features. The process of Self-proliferation is as follows (as shown in Figure 5). + +The first step of self-proliferation is a small amount of classical convolution which can be built upon a transformation $f \in \mathbb{R}^{c \times k \times k \times n}$ mapping an input $M \in \mathbb{R}^{c \times h \times w}$ to feature maps $M' \in \mathbb{R}^{h' \times w' \times n}$ : + +$$ +M ^ {\prime} = M \otimes f \tag {1} +$$ + +where $\otimes$ denotes convolution, $c$ and $n$ is the number of input and out channels, $h$ and $h^\prime$ is the height of the input and out data, $w$ and $w^{\prime}$ is the width of the input and out data. we can obtain n feature maps by classical convolution. + +The second step is a cheap operation, represented by $\rho$ in the Eq. 2. This is a linear transformation that uses depthwise convolution to further obtain $n$ feature maps according to the following function: + +$$ +u _ {i, j} = \rho_ {i, j} \left(m _ {i} ^ {\prime}\right), \forall i = 1, \dots , s, j = 1, \dots , t \tag {2} +$$ + +Where $m_i'$ is the $i$ -th unit of feature map $M'$ generated by Eq. 1., $\rho_{i,j}$ is the $j$ -th linear transformation for generating the $j$ -th feature map $u_{i,j}$ . If 12 feature maps are generated, self-proliferation can generate 6 of them (as shown in Figure 5). Therefore, the computation cost can be reduced by half. + +![](images/c9250e046931e502f18d26a87334c6e88081259b95503f576a059fb8e90f08b6.jpg) +Figure 5: Self-proliferation process. + +Self-Attention Block. The self-attention block aims at strengthening the features of the query position via aggregating information from other positions. The basic architecture formulated as: + +$$ +y _ {i} = x _ {i} + w _ {e 2} R e L U (L N \left(w _ {e 1} \sum_ {j = 1} ^ {h \times w} \frac {e ^ {w _ {g} x _ {j}}}{\sum_ {m = 1} ^ {h \times w} e ^ {w _ {g} x _ {m}}}\right)) (3) +$$ + +We denote $x_{i}$ as the feature map of on input instance (e.g., defect pattern), where $h$ and $w$ is the height and width of input $x$ . $w_{e1}$ and $w_{e2}$ denote linear transform matrices $(1 \times 1$ convolution) which is used to bottleneck transform. $w_{g}$ is the weight for global attention pooling. $LN$ denotes + +the layer normalization, which is utilized to filter the redundant information and refine the obtained contextual information. Specifically, our self-attention block consists of 3 parts (as shown in Figure 6): (a) global attention pooling for context modeling; (b) bottleneck transform to capture channel-wise dependencies; and (c) denotes the fusion function to broadcast element-wise addition for feature fusion. This function can aggregate the global context features to the features of each position [30]. + +![](images/dac62b651a9dab3773a5d2c532b05ed072600d007f71ae1547585c496e6c9802.jpg) +Figure 6: Architecture of self-attention. + +![](images/a972fda04dfcf80eec857087f187dfab1271db22c6cfbe942b6e543a777262cd.jpg) +Figure 7: Architecture of self-proliferation-and-attention block. + +Self-Proliferation-and-Attention Block. It consists of 4 parts (as shown in Figure 7): (a) expansion layer used self-proliferation block to increase input dimension to generate more feature maps at a cheaper cost. (b) depthwise convolution are used for feature extraction and self-attention are used to capture long-range dependencies. (c) compression layer used to reduce feature dimension to be the same as input feature. Then, we can transform spatial information with low computation. Finally, in (d) we refer to MobileNetV2 [26] to build inverted residuals. The residuals architecture was first proposed by He et al. in ResNet [27]. Its design concept is to learn residuals on the network to avoid gradient vanishing problems. ResNet's architecture is to compress first then expand. MobileNet's architecture is the opposite of ResNet that expand first then compress. The idea of MobileNet is to "capture features in high dimensions and transfer information in low dimensions". + +![](images/2c6c1ba0acc92d4c56f6e715046a31a2e1644f353ef292225cde40cffd822b48.jpg) +Figure 8: An example of quantum circuit with 4 qubits. Each qubit uses the rotation gate $R(\theta)$ by the angle $\theta$ around $x, y, z$ . CNOT gate are used for every 2 qubits in order. + +# 3.2.Quantum Layer + +The quantum layer implemented by various quantum circuit built in the continuous-variable architecture. It consists of three consecutive parts (as shown in Figure 8). An encoding circuit encodes classical data to states of the qubits followed by a parametrized quantum circuit (PQC) that is applied to transform these states to their optimal location on the Hilbert space (as shown in Figure 9). Finally, measure the output of PQC along the $z$ -axis with the $\sigma_z$ operator. + +# 3.2.1 Encoding Circuit + +The encoding circuit is used to encode the classical data into the physical states of Hilbert space [28] for quantum computing. In this paper, we applied 3 encoding methods, including basis encoding, amplitude encoding, and angle encoding. + +Basis Encoding. In basis encoding, the data has to be in form of a binary string to get encoding. Approximating a scalar value to its binary form and then transforming it to a quantum state. For example, if we have a classical dataset containing two examples $x_{k} = 01$ and $x_{k + 1} = 11$ , the corresponding quantum state after basis encoding is $|x_{k}\rangle = |01\rangle$ and $|x_{k + 1}\rangle = |11\rangle$ . In short, Basis encoding encodes an n-bit binary string $x_{k}$ to an $n$ -qubit quantum state as: + +$$ +\left| x _ {k} \right\rangle = \left| i _ {x} \right\rangle \tag {4} +$$ + +where $|i_x\rangle$ is a computational basis state, and every binary string has a unique integer representation $i_{x} = \sum_{k = 0}^{n - 1}2^{k}x_{k}$ . + +Amplitude Encoding. The amplitude encoding is also known as wave function embedding. The amplitude is the height of a wave. In the amplitude encoding, the data points are transformed into amplitudes of the quantum state. A normalized classical $N$ -dimensional $x_{k}$ is represented by the amplitudes of a $n$ -qubit quantum state $|x_{k}\rangle$ as: + +$$ +\left| x _ {k} \right\rangle = \sum_ {k = 0} ^ {N} x _ {k} \left| i _ {x} \right\rangle \tag {5} +$$ + +where $\mathbf{N}$ is the length of vector $x_{k}$ into amplitudes of an n-qubit quantum state with $n = \log_2(N)$ . $\{|i_x\rangle \}$ is the computational basis for the Hilbert space. Since the + +classical information forms the amplitudes of a quantum state, the input needs to satisfy the normalization condition: $|x|^2 = 1$ . + +Angle Encoding. Angle encoding makes use of rotation gates to encode classical information $x_{k} \in \mathbb{R}^{N}$ without any normalization condition. The classical information determines angles of rotation gates: + +$$ +\left| x _ {k} \right\rangle = \otimes_ {k = 0} ^ {N} R \left(x _ {k}\right) \left| 0 ^ {N} \right\rangle \tag {6} +$$ + +Where $N$ is the number of qubits, $R$ can be one of $R_{x}, R_{y}, R_{z}$ . Usually, $N$ used for encoding is equal to the dimension of vector $x_{k}$ . Since it is $2\pi$ -periodic one may want to limit $\mathbb{R}^N$ to the hypercube $[0, 2\pi]^{\otimes n}$ . The $i$ -th feature $x_{k}$ is encoded into the $k$ -th qubit via a Pauli-X rotation. Figure 9 shows the angle encoding with a rotation angle of $\theta$ around $z$ -axis on the Hilbert space. After activation function $\tanh(x)$ , the output $x_{k} \in [-1, 1]$ from the end of classical layer. Then, the rotation angle is mapped between $\theta \in [0, \pi]$ due to the periodicity of the cosine function. This is relevant since the expectation value is taken with respect to the $\sigma_z$ operator at the end of the circuit execution. + +![](images/906d13842aa2f22f97932612930b510ea3402cb8d1cf2e538b77a074938d777d.jpg) +Figure 9: Angle encoding with a rotation angle of $\theta$ around $z$ -axis on the Hilbert space. + +# 3.2.2 Parametrized Quantum Circuit + +A parameterized quantum circuit is a quantum circuit consisting of parameterized gates with fixed depth. These circuits have free parameters: the rotation angle of the quantum state. We use quantum circuits and repeat multiple times with different random parameters, instead of using the large and complex classical neural networks. The parameterized quantum circuit also consists of one-qubit gates as well as Controlled Not (CNOT). Some more complicated gates may also be used in PQC which can be decomposed into one qubit gates and CNOT. In general, an $n$ qubits PQC can be written as: + +$$ +u (\hat {\theta}) | \varphi \rangle = \left(\prod_ {i = 1} ^ {m} u _ {i}\right) | \varphi \rangle \tag {7} +$$ + +where $u(\hat{\theta})$ is the set of unitary gates and $m$ is the number of quantum gate. $\hat{\theta}$ is the set of parameters $\{\theta_0, \theta_1, \dots, \theta_k\}$ , where $k$ is the total number of parameters and $|\varphi\rangle$ is the initial quantum state after data encoding. The unitary gate + +taking parameters is rotation gate $R(\hat{\theta})$ , given by: + +$$ +R _ {x} (\hat {\theta}) = e ^ {- i \frac {\hat {\theta}}{2} \sigma_ {x}}, R _ {y} (\hat {\theta}) = e ^ {- i \frac {\hat {\theta}}{2} \sigma_ {y}}, R _ {z} (\hat {\theta}) = e ^ {- i \frac {\hat {\theta}}{2} \sigma_ {z}} \tag {8} +$$ + +where $\{\sigma_x, \sigma_y, \sigma_z\}$ is Pauli matrices. The operation of $u$ can be modified by changing parameters $\hat{\theta}$ . Thus, the output state can be optimized to approximate the wanted state by changing parameter $\hat{\theta}$ . By optimizing the parameters used in $u(\hat{\theta})$ , PQC approximates the wanted quantum states. To achieve better entanglement of the qubits before appending nonlinear operations, the $n$ qubits PQC has $n$ repeated layers in our model. By optimizing the parameters, the general PQC tries to approximate arbitrary states so that it can be used for different specific molecules. + +In order to provide computational speedup by orchestrating constructive and destructive interference of the amplitudes in quantum computing, we constructed m rotation gates $R_{x}$ on the n qubits PQC as our basic quantum circuit, which can be written as: + +$$ +\prod_ {i = 1} ^ {n} \left(\otimes_ {j = 0} ^ {m} R _ {x} \left(\theta_ {i + n \times j}\right) C N O T _ {i, i + 1}\right) \tag {9} +$$ + +where $R_{x}$ represents the unitary gate of rotation- $x$ . $\theta_{i + n\times j}$ is adjustable parameter of unitary gates. $CNOT_{i,i + 1}$ represents $CNOT$ gate with $m$ as the control qubit, and $n$ is the total number of qubits. Figure 10 show the basic quantum circuit with $n = 4$ and $m = 3$ . Each qubit uses the rotation gate $R(\theta)$ by the angle $\theta$ around $x$ -axis on the Hilbert space, and $CNOT$ gate is used for every 2 qubits. + +![](images/43cc1c5b7df34213f72b64a8d8f084ade7b0c3570f1f64f7226c4614b5190096.jpg) +Figure 10: Basic quantum circuit with $n = 4$ , $m = 3$ + +# 3.3. Fully Connection Layer + +After obtaining all features from PQC, we feed them into a fully connection (FC) layer. We use the softmax activation function, so the output of FC layer will be a probability distribution. The i-th element of the output is the probability that this data point belongs to the i-th category, and we predict that this data point belongs to the category with the highest probability. In order to predict the actual label, we calculate the cumulative distance between the predicted label and the actual label as the loss function to be optimized: + +$$ +\mathcal {L} (\omega^ {1}, b ^ {1}, \theta , \omega^ {2}, b ^ {2}) = - \frac {1}{N} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {K} y _ {j} ^ {i} \log \tilde {y} _ {j} ^ {i} (1 0) +$$ + +where $\omega^1, b^1$ is the parameter of classical layer. $\theta$ is the parameter of quantum layer. $\omega^2, b^2$ is the parameter of FC layer. Perform the above procedure enough times to get a good estimate of the expected value of $\tilde{y}_j^i$ with minimum loss function. + +# 4. Results + +# 4.1. Experiment Circuits + +In deep learning, it is very useful to transform data into a higher-dimensional feature space. In the same way, there are two strategies for using quantum circuits to generate higher dimensional features: entangling more and more qubits. However, quantum computers are now in their infancy, the available qubits are limited. In this experiment, we adopt different entangling strategies to verify our method on the 4 qubits circuit system. In addition to the basic quantum circuit (as shown in Figure-10), we also chose Circuit-5/6/16/17 provided by Sim et al. [29], which has better expressive ability and entanglement ability, as the parametrized quantum circuit (as shown in Figure 11). + +Table 1: Ablation Study of Defect Pattern Classification + +
ModelClassical LayerQuantum Layer
Feature ExtractionEncodingCircuit
Basic561617
HybridResNet50 [27]Basic93.7395.4295.0394.4293.94
Amplitude93.7495.4395.0494.4393.95
Angle93.8195.5095.1194.5194.02
Classical-92.76
HybridSENet [45]Basic95.0996.7596.4396.0495.85
Amplitude95.2796.9496.6196.2296.03
Angle95.4297.0896.7596.3696.17
Classical-93.55
HybridMobileNetV3 [31]Basic92.9394.1393.7093.2493.40
Amplitude93.0294.2193.7993.3393.49
Angle93.3994.5894.1593.7093.86
Classical-92.09
HybridSP&A-Net (proposed model)Basic95.9297.8597.0596.5496.11
Amplitude96.0697.9997.1996.6896.25
Angle96.5598.4797.6897.1796.73
Classical-94.27
+ +# 4.2. Ablation Study + +To demonstrate the usefulness of quantum circuit, our model had been verified on two industry data sets, defect pattern and EPI hotspot. We performed a rigorous ablation study and showed the quantitative comparison in Table 1. We refer to ResNet50, SENet, MobileNetV3 and our proposed model as the basic model to integrate with various quantum circuits. In addition to the basic circuit we + +![](images/88d5a874e37e5ce8ca0469464058c668bf4538f523c32b8fe34c3d8f19f9f424.jpg) + +![](images/9523957625cedfe2f06bc5ce875f4e6abf43922e8ad041215a4fd65da07b1f94.jpg) + +![](images/abefd186594ba5c6ee4634bb1e7b7e4c64d56f8d8c119257958111331335209b.jpg) +Figure 11: Quantum Circuit by Sim et al. [29]. + +![](images/ea593938463a9fe59462dab6f36fd8f2b801cc0aeb2c4396bef618d4432091f0.jpg) + +![](images/0cb8182d3c8f49eefd772e59e875edfe9ae1d0fc931b5159d4111e1bbb12bd5d.jpg) +Figure 12: ResNet50 [27] with Different Strategy of Quantum Circuit for Defect Pattern Classification + +![](images/f575d1194f1ab643cb9f0dc8bc7a667728630aa5013c7a0c123b521c5ce32850.jpg) +Figure 13: SENet [45] with Different Strategy of Quantum Circuit for EPI Hotspot Classification + +proposed, we added the Circuit-5/6/16/17 presented in the previous section. We also adopted four encoding strategy: basic, amplitude, and angle encoding. + +Ablation results yielded many significant findings. First, Circuit 5 and Circuit 6 is a fully connected graph + +arrangement of qubits which led to both favorable expressibility and entangling capability. Therefore, the network model with Circuit 5 and Circuit 6 has high accuracy regardless of semiconductor defect detect task (as shown in Figure 12 and Figure 13). Second, Circuit 5 and Circuit 16 with controlled Z-rotation $(CRz)$ gates is better than Circuit 6 and 17, respectively. It because that $CRz$ operations in the entangling block commute with each other and thus the effective unitary operation comprised of $CRz$ gates can be expressed using unique generator terms that are fewer than the number of parameters for these gates. Finally, the basic circuit without any controlled rotation gate has the lowest accuracy among the 4 classification tasks. This suggests that, if one is trying to design a PQC to increase expressibility, it is better to insert single-qubit gates which skew the controlled gate rotation axis away from the control axis. + +# 4.3. Experiment Results + +We compare our proposed model on the public dataset of LIT hotspot (ICCAD-2012) and defect wafer map (WM811K) with the state-of-art method in the last 4 years. Table 2 and table 3 shows that our proposed model (HCQDL) has a higher test accuracy, which shows the advantages of quantum computing. It mean that small quantum circuits provide significant performance lift over standard linear classical algorithms, improving classification accuracy rates from around $98\%$ to $99.12\%$ , and from around $96\%$ to $98.10\%$ in these two public datasets, respectively. + +Table 2: Comparison of state-of-the-art methods on ICCAD-2012 + +
AuthorsModelFeature ExtractionData AugmentationAccuracy
H. Yang, et al. [32]CNNFeature Tensor ExtractionMirroring, Flipping98.88%
H. Yang, et al. [33]CNN-Mirroring, Flipping, Upsampling98.20%
Y. Tomioka, et al. [34]Real AdaBoostHistogram of Oriented Light PropagationRotating, Reflecting99.01%
F. Yang, et al. [35]Efficient SVMSpectral Clustering-95.66%
V. Borisov and J. Scheible [36]CNN-Flipping, Gaussian filter98.94%
H. Yang, et al. [37]CNN--97.36%
V.S. Ajna and N. George [15]CNN--93.00%
X. Huang, et al. [19]Ensemble CNNCombine Physical Features-98.80%
X. Lin, et al. [38]Heterogeneous Federated LearningFeature Tensor Extraction-97.90%
Our Proposed ModelHybrid Classical-Quantum CNNSelf-Proliferate Self-AttentionMirroring, Flipping, Rotating99.12%
+ +Table 3: Comparison of state-of-the-art methods on WM-811K + +
AuthorsModelFeature ExtractionData AugmentationAccuracy
T. Nakazawa and D. V. Kulkarni, [2]CNN--96.30%
N. Yu, Q. Xu and H. Wang [7]CNNPCA-93.25%
J. Yu and J. Liu [10]CNNAE+PCA-97.30%
J. Yu, X. Zheng and J. Liu [39]CNNAE-95.13%
J. Yu [40]SVMAE-89.50%
T.-H. Tsai and Y.-C. Lee [8]MobileNetV2-AE97.01%
M. B. Alawieh et al. [9]CNN-AE94.00%
S. Kang [41]CNN-Rotation92.13%
U. Batool et al. [42]CNN-Flipping, Brightness90.44%
M. Saqlain et al. [43]CNN-Rotation, flipping, shifting, zooming96.20%
D. Kim and P. Kang [44]CNN--96.40%
Our Proposed ModelHybrid Classical-Quantum CNNSelf-Proliferate Self-AttentionMirroring, Flipping, Rotating98.10%
+ +# 5. Conclusion + +Our experiments in this work were designed to highlight the novelties introduced by the quantum deep learning: the generalizability of convolutional layers inside a typical CNN architecture, the ability to use this quantum circuit on semiconductor defect datasets, and the potential use of features introduced by the parametrized quantum circuit. The experimental results show that our framework outperforms the existing deep learning techniques. In addition, based on recent progress, we reasonably believes that quantum advantage is achievable within the next 5-10 years. Quantum computers promise access to fast linear algebra processing capabilities which are in principle able to deliver the polynomial speed-up that allows kernel methods to process big data without relying on approximations and heuristics. + +Moreover, there is much to be learned about how to select these parameterized circuits, how to choose the random numbers to mix with the input data, and how to optimize the number of qubits to get good performance. Many of our existing deep learning algorithms could be translated into hybrid classical-quantum deep learning, allowing them take advantage of new properties like entanglement, superposition and parallel computing. It's only a matter of time before these algorithms are changing the world. We hope this paper can be a demonstration that quantum machine learning has the potential to provide satisfactory solutions for semiconductor defect detection. + +# References + +[1] K. Nakata, R. Orihara, Y. Mizuoka and K. 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Lee, "A deep convolutional neural network for wafer defect identification on an imbalanced dataset in semiconductor manufacturing processes," in IEEE Transactions on Semiconductor Manufacturing, vol. 33, no. 3, pp. 436-444, Aug. 2020. +[44] D. Kim and P. Kang, "Dynamic Clustering for Wafer Map Patterns using Self-Supervised Learning on Convolutional Autoencoders," in IEEE Transactions on Semiconductor Manufacturing, 2021. +[45] J. Hu, L. Shen and G. 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Recently, semi-supervised few-shot learning has been developed to obtain pseudo-labels of unlabeled samples for expanding the support set. However, the relationship between unlabeled and labeled data is not well exploited in generating pseudo labels, the noise of which will directly harm the model learning. In this paper, we propose a Clustering-based semi-supervised Few-Shot Learning (cluster-FSL) method to solve the above problems in image classification. By using multi-factor collaborative representation, a novel Multi-Factor Clustering (MFC) is designed to fuse the information of few-shot data distribution, which can generate soft and hard pseudo-labels for unlabeled samples based on labeled data. And we exploit the pseudo labels of unlabeled samples by MFC to expand the support set for obtaining more distribution information. Furthermore, robust data augmentation is used for support set in the fine-tuning phase to increase the labeled samples' diversity. We verified the validity of the cluster-FSL by comparing it with other few-shot learning methods on three popular benchmark datasets, miniImageNet, tieredImageNet, and CUB-200-2011. The ablation experiments further demonstrate that our MFC can effectively fuse distribution information of labeled samples and provide high-quality pseudo-labels. Our code is available at: https://gitlab.com/smartllvlab/cluster-fsl + +# 1. Introduction + +Deep learning methods based on neural networks [34] have made great breakthroughs and been widely used in the field of computer vision [15] [32] [23]. Unfortunately, deep learning models require a massive amount of labeled data to learn huge-scale parameters. Moreover, the scenes in real life are complex and diverse. For instance, in some + +practical problems, there exist objects that are rarely observed, such as the faces of the suspects, rare animal photos, and so on, which makes it difficult to collect labeled data. With the inspiration of the human vision system, much attention has been paid to the development of few-shot learning [29] [38] [27] [7], which can release the strong demand for data used for training deep models to some extent. + +The goal of few-shot learning is to learn a new concept or behavior from a very small number of samples based on experience. Due to the particularity of few-shot learning, how to alleviate the overfitting problem that the model hardly fits the distribution of the categories caused by the scarcity of samples, has always been the focus and difficulty of few-shot learning. With the development of few-shot learning, methods have been proposed to solve the above difficulty from three perspectives: model, data, and learning algorithm. Model-based methods [28] [39] aim to learn the interactive information between samples by designing a model that adapts to the few-shot case. As for data, researchers have explored various methods to enrich training data, such as data augmentation [28] [1] [48], which preprocesses data through flipping, cropping, translation, rotation, and zooming. However, data augmentation requires expensive labor costs and relies heavily on domain knowledge, resulting in some data augmentation methods being specific to datasets. Few-shot image classification based on learning methods [45] [14] [38] aim to improve the generalization of the model by using meta-learning or transfer learning strategy, which learns meta-knowledge or transferrable knowledge shared in different subtasks. However, the performance of few-shot learning is still far from satisfactory because the small set of labeled data cannot provide rich and essential information for recent model learning. + +When the task has few-shot labeled samples and additional unlabeled data for new categories, a straightforward approach is to utilize the unlabeled samples to alleviate the scarcity of labeled samples. Unlabeled data has been effectively explored by semi-supervised learning methods, including a combination of weak data augmentation and strong augmentation [37], consistent regularization [16], + +adversarial perturbation regularization [40], achieving very exciting performance without using a large number of annotated samples. If unlabeled data can be explored by combining semi-supervised learning with few-shot learning (e.g., mining pseudo-labels of unlabeled samples), problems such as data scarcity can be solved to some extent. Recent few-shot image classification combined with semi-supervised learning [31] [22] [38] focuses on improving the accuracy of pseudo-label prediction for unlabeled samples and is expected to obtain more correct pseudo-labels to expand the training set. However, existing methods cannot obtain completely correct pseudo-labels. How to avoid the influence of false pseudo-labels on model training and how to use sample distribution information to assist the acquisition of pseudo-labels are still current challenges. + +To solve the aforementioned issues, we propose a Clustering-based semi-supervised Few-Shot Learning (cluster-FSL) method in image classification. By introducing labeled samples as factors of a cluster and representing unlabeled data on a multi-factor dictionary, we propose Multi-Factor Clustering (MFC) to guide the acquisition of pseudo-labels of unlabeled samples, which combines the distribution information of labeled and unlabeled samples for assisting clustering and obtaining more accurate pseudo-labels. In the fine-tuning stage, we design robust data augmentation to augment the support set and adopt the MFC module to predict soft labels of query samples, learning more discriminative feature distribution. In the testing stage, we use MFC instead of label propagation to assign more accurate pseudo-labels to unlabeled samples for expanding the test support set. The experimental results have shown that our cluster-FSL has achieved state-of-the-art performance (e.g., $2.45\%$ improvement in the 5-way 1-shot scene of miniImageNet when the backbone is ResNet-12) on miniImageNet, tiered-ImageNet, and CUB-200-2011. + +Our main contributions can be summarized as follows. + +1. A novel multiple factor clustering (MFC) algorithm, which includes factors of labeled and unlabeled samples and exploits the distribution information among these factors via a multi-factor dictionary, is proposed, generating more accurate clustering results. +2. The proposed MFC is integrated into the fine-tuning stage and testing stage in a new way, with outputting high-quality pseudo labels for expanding the query and test support set effectively. + +# 2. Related Works + +# 2.1. Learning-based Few-shot Image Classification + +Learning-based few-shot image classification algorithm aims to design a training and update mode suitable for few-shot scenarios. Transfer learning and meta-learning methods have been successfully applied to few-shot classifica + +tion recently. + +The transfer-learning-based methods pre-train the model on a large amount of data from the base class and adapt the pre-trained model to the few-shot learning task of identifying new categories. Kozerawski et al. [14] learn a transfer function that maps the embedding features extracted by the pre-trained model to the classification decision boundary. In [45], Yoo et al. identify groups of neurons within each layer of a deep network that shares similar activation patterns, and then use a training set for fine-tuning by group-by-group backward propagation. Transfer-learning-based methods can train a feature extractor with a powerful representation ability. To take advantage of these methods, We fine-tune a pre-trained model with the aid of the proposed MFC to improve the performance of our method. + +Meta-learning-based methods, also known as learning to learn, aim to learn a paradigm that can be adapted to recognize new categories using few-shot train examples [46]. Researchers improve the meta-learning-based methods from the following aspects: the embedded module and shared distance measurement method [41] [36] [39], the initial distribution of model parameters [4] [25], and update strategies and rules of model parameters [21] [30]. As a classic and commonly used and effective method for solving few-shot classification tasks, although these methods have achieved rapid development, the problem of sample scarcity is still a remaining challenge. + +Recently, Rodríguez et al. [33] propose the use of Embedding Propagation (EP) as an unsupervised non-parametric regularizer for manifold smoothing and apply EP to a transductive classifier. However, this method has a limited expansion of the labeled samples, which prevents further improvement of the performance. To solve the issue of EPNet [24], we use the proposed MFC module to obtain pseudo-labels of unlabeled samples, which can alleviate the scarcity of labeled samples effectively. + +# 2.2. Semi-supervised Few-shot Methods Based on Pseudo-label Acquisition + +The few-shot image classification methods combined with semi-supervised learning expand the labeled data by obtaining the pseudo-labels of the unlabeled data and alleviates the problem of sample scarcity, such as introducing class prototypes into the distribution of unlabeled samples to predict pseudo-labels in [31], using label propagation to obtain pseudo-labels in [22], using a pre-trained classifier to predict pseudo-labels in [46], and leveraging the manifold structure of labeled and unlabeled data distribution to predict pseudo-labels in [17]. After obtaining the pseudo-labels, these methods directly use them as labeled samples for model fine-tuning and training. However, they ignore the impact of incorrectly pseudo-labeled data on model training. + +To reduce the impact of incorrect pseudo labels, Wu et al. [44] set a priority to select informative unlabeled samples to be used in the subsequent training process, while Sun et al. [20] proposed to limit the number of unlabeled samples selected in each round of optimization and preferentially select pseudo-labeled samples with high confidence. Huang et al. [11] presented a pseudo-loss confidence metric (PLCM), which maps pseudo-labeled data of different tasks to a unified metric space and estimates the confidence of pseudolabeled according to the distribution component confidence of its pseudo-loss. However, the method of using a trained classifier to predict unlabeled samples one by one individually ignores the information at the data distribution level. The influence of the intra-class and inter-class relationship between unlabeled samples and the distribution information of unlabeled samples and labeled samples on the acquisition of pseudo-labels is not considered. + +Recently, Huang et al. proposed Poisson Transfer Network (PTN) [10], which is a transfer-learning-based semisupervised few-shot method. PTN model improves the capacity of mining the relations between the labeled and unlabeled data for graph-based few-shot learning, and our cluster-FSL is similarly dedicated to enhancing such capacity. However, our proposed MFC utilizes multiple factors to build a feature dictionary, which allows the overall clustering to effectively strengthen the relationship between labeled and unlabeled data, making the clustering being more concise and more interpretable. Wang et al. [42] proposed that the model iteratively selects the pseudo-labeled instances according to its credibility measured by Instance Credibility Inference (ICI) for classifier training. However, if the quality of pseudo-labels is not directly improved, the impact of incorrectly pseudo-labels on the model cannot be reduced. In addition, ICI focuses on solving a linear regression hypothesis by increasing the sparsity of the incidental parameters and ranking the pseudo-labeled instances with their sparsity degree, while our MFC constructs a dictionary by fusing the distribution of the labeled data, and uses the reconstruction error to calculate the distance when clustering. + +# 3. Clustering-based semi-supervised Few-Shot Learning + +Obtaining pseudo-labels of unlabeled samples with high confidence is a major challenge that the semi-supervised few-shot learning model needs to solve. To effectively solve the above challenge, we propose a novel model of clustered-based semi-supervised few-shot learning (cluster-FSL), which uses multi-factor clustering to obtain the high-quality pseudo labels of unlabeled data. Furthermore, our proposed cluster-FSL utilizes robust data augmentation and MFC modules to learn more discriminative features for improving performance. Here we first present a multi-factor + +clustering and then introduce three stages (e.g., pre-training, fine-tuning, and testing) of cluster-FSL in detail. + +# 3.1. Problem Definition + +In the few-shot classification task, the dataset is divided into training set, validation set, and test set, namely $\mathcal{D} = \{\mathcal{D}^{train},\mathcal{D}^{val},\mathcal{D}^{test}\}$ . where $\mathcal{D}^{train} = \{X^{train},Y^{train}\}$ contains all training data and corresponding labels, and $\mathcal{D}^{test} = \{X^{test},Y^{test}\}$ contains all test data and corresponding labels. All categories in the training set and test set are denoted by $\mathcal{C}^{train}$ and $\mathcal{C}^{test}$ , respectively, such that $\mathcal{C}^{train} \cap \mathcal{C}^{test} = \emptyset$ . The categories in the validation set do not overlap with $\mathcal{C}^{train}$ and $\mathcal{C}^{test}$ . Referring to episodic learning, we construct $n$ independent few-shot tasks to form episodic set $\Gamma = \{T_i^{tr},T_i^{test}\}_{i = 1}^n$ . For each training task $T_{i}^{tr}$ , we randomly select $N$ categories from the training set, and randomly select $K$ samples from each category to form a training support set $S^{tr} = \{x_{i}^{s},y_{i}^{s}\}_{i = 1}^{N\times K}$ , where $x_{i}^{s} \in X^{train}$ and $y_{i}^{s} \in Y^{train}$ . From the same $N$ categories, we select $q$ non-repeated samples to form the training query set $Q^{tr} = \{x_{i}^{q},y_{i}^{q}\}_{i = 1}^{N\times q}$ , where $x_{i}^{q} \in X^{train}$ and $y_{i}^{q} \in Y^{train}$ . The validation set $\mathcal{D}^{val}$ is used to determine the best model, and the model with the highest accuracy on the validation set will be selected. For each testing task $T_{i}^{test}$ , the model also randomly selects $N$ categories from the test set, and randomly select $K$ samples from each category to obtain the test support set $S^{test} = \{x_{j}^{s},y_{j}^{s}\}_{j = 1}^{N\times K}$ , and select $q$ non-repeated samples from each category to form the test query set $Q^{test} = \{x_{j}^{q},y_{j}^{q}\}_{j = 1}^{N\times q}$ . In addition, we randomly select $u$ samples from the unselected samples under the $N$ categories included in the test set, and remove the labels to form an unlabeled set $U^{test} = \{x_{j}^{u}\}_{j = 1}^{N\times u}$ . + +![](images/be5788b81fd4a556f98e0f9bd515cebcf617dbd2b1985cd8b70d646ca6b3fffa.jpg) +Figure 1. The clustering process of MFC. Among them, black dots represent the cluster centers after the update, and gray-black dots represent the cluster center before the update. + +# 3.2. Multi-Factor Clustering + +Given a labeled set $L$ and an unlabeled set $U$ , we propose a clustering method called multi-factor clustering (MFC) to predict the pseudo-labels of samples in $U$ by using the distance between samples and factors (e.g. cluster center and + +labeled samples). By utilizing multiple factors to construct a feature dictionary and using reconstruction error as a distance measurement, our MFC is suitable for the few-shot scenario to obtain pseudo-labels of unlabeled samples. + +Pseudo-label Acquisition There are a small number of labeled samples in the few-shot learning task, and the number of categories is known. Under the setting of $N$ -way $K$ -shot, the clusters in MFC are expressed as $C = \{C_i\}_{i=1}^N$ , where $N$ is the number of clusters. The center of each cluster is initialized to the within-class mean of the labeled samples by + +$$ +\boldsymbol {c} _ {i} ^ {*} = \frac {1}{K} \sum_ {j = 1} ^ {K} l _ {j} ^ {i} \tag {1} +$$ + +where $l_{j}^{i} \in L$ is the $j^{th}$ embedding representation of the $i^{th}$ category labeled sample and $c_{i}^{*}$ represents the center of $i^{th}$ cluster. + +Traditional clustering method [31] only considers the distance between an unlabeled sample and each cluster center, while ignoring data distribution information and the feature information of the $K$ labeled samples belonging to the same category. We regard the factor of a cluster as an embedded representation that can represent the cluster (e.g. the cluster center and a labeled sample) and then propose multifactor clustering (MFC), which sets up multiple factors for each cluster and improves the calculation method of the distance from the unlabeled sample to each cluster. + +The factors $\pmb{F}$ of the $i^{th}$ cluster in MFC are defined as $\pmb{F}_i = [l_1^i,\dots ,l_K^i,\pmb {c}_i^* ]$ , which includes a cluster center and the samples belonging to $i^{th}$ cluster in the labeled set $L$ + +To release the small-sample-size problem, the proposed MFC adopts all class-specific factors as a dictionary to collaboratively represent an unlabeled sample $\pmb{u}_i\in U$ : + +$$ +\tilde {\boldsymbol {\beta}} _ {i} = \underset {\boldsymbol {\beta} _ {i}} {\arg \min } \| \boldsymbol {u} _ {i} - \boldsymbol {F} \boldsymbol {\beta} _ {i} \| _ {2} ^ {2} + \epsilon \| \boldsymbol {\beta} _ {i} \| _ {2} ^ {2} \tag {2} +$$ + +where $\epsilon$ is a constant of 0.01 to regularize the representation, $\tilde{\beta}_i = [\tilde{\beta}_{i,1},\tilde{\beta}_{i,2},\dots ,\tilde{\beta}_{i,N}]^T$ , $\tilde{\beta}_{i,j}\in \mathbb{R}^{(K + 1)\times 1}$ is the sub-coefficient vector associated to the $j^{th}$ cluster. We refer to the solution in collaborative representation [47] to solve the $\tilde{\beta}_i$ in Eq. 2. Then we use the reconstruction errors associated with each cluster as the distance from the unlabeled sample to the cluster as shown in Fig.1. The reconstruction error is defined as: + +$$ +d _ {i, j} = \left\| \boldsymbol {u} _ {i} - \boldsymbol {F} _ {j} \tilde {\boldsymbol {\beta}} _ {i, j} \right\| _ {2} ^ {2} \tag {3} +$$ + +Calculating this reconstruction error takes into account the factors of all categories, which make different cluster factors competitively represent the unlabeled data, outputting a more robust clustering. + +According to the minimum reconstruction error from the unlabeled data $\pmb{u}_i$ to each cluster, the clustering result is + +Algorithm 1 Process description of Multi-Factor Clustering +Input: Labeled set $L = \{l_i, y_i\}_{i=1}^{N \times K}$ , unlabeled set $U = \{\pmb{u}_i\}_{i=1}^{N \times u}$ +Output: Pseudo-labels of samples in unlabeled set $P = \{p_i, \tilde{y}_i\}_{i=1}^{N \times u}$ +1: while True do +2: for Each unlabeled sample $u_i \in U$ do +3: Compute the reconstruction error $d_{i,j}$ by Eq.(3) +4: Obtain the clustering result $\alpha_i = \arg \min_{1 \leq j \leq N} d_{i,j}$ +5: Update the clusters and the cluster centers by Eq.(4) +6: end for +7: if The cluster centers remain unchanged then +8: Calculate the soft pseudo label $p_i$ and hard pseudo label $\tilde{y}_i$ by Eq.(5). +9: Break +10: end if +11: end while + +$\alpha_{i} = \arg \min_{1\leq j\leq N}d_{i,j}$ . And each cluster is updated by, + +$$ +\tilde {C} _ {\alpha_ {i}} = C _ {\alpha_ {i}} \cup \left\{\boldsymbol {u} _ {i} \right\} +$$ + +$$ +\boldsymbol {c} _ {j} ^ {*} = \frac {1}{| \tilde {C} _ {j} |} \sum_ {\boldsymbol {z} _ {k} \in \tilde {C} _ {j}} \boldsymbol {z} _ {k} \quad \forall j = 1, 2, \dots , N \tag {4} +$$ + +where $c_{j}^{*}$ is the $j^{th}$ cluster center, which is used to update the cluster factor. + +Multiple factors can make the clustering more accurate compared to only one factor because they can better represent the embedding manifold of the cluster. After several iterations, when the clusters and cluster centers do not change, the cluster is denoted as $C = \{C_1, C_2, \dots, C_N\}$ . We take the clustering result of the last iteration to obtain soft labels and hard labels for unlabeled data. The soft label $p_i = [p_{i,1}, p_{i,2}, \dots, p_{i,N}]$ of the unlabeled sample $u_i$ are defined as: + +$$ +p _ {i, j} = \frac {e ^ {- \log \left(d _ {i , j} / \tau\right)}}{\sum_ {k = 1} ^ {N} e ^ {- \log \left(d _ {i , k} / \tau\right)}} \tag {5} +$$ + +where $\tau$ is a temperature parameter and $p_{i,j}$ denotes the probability that the unlabeled sample $\mathbf{u}_i$ is predicted to be the $j^{th}$ class. Thus, the hard label is $\tilde{y}_i = \arg \max_j p_{i,j}$ . The procedure details of MFC are shown in Algorithm 1. + +# 3.3. Training procedure + +To train a model with good generalization ability, we firstly use $\mathcal{D}^{train}$ to train a pre-trained model by fully-supervised learning and self-supervised learning. Then we use the episode set $\Gamma$ to fine-tune the pre-trained model by multi-factor clustering and label propagation [12]. + +![](images/681e968dc8840e18d4a48079af334caaccbfbda81e124f8c5587133df6d746b1.jpg) +Figure 2. The framework of the fine-tuning phase. At first, we use more robust data augmentation to augment the support set. The samples from the augmented support set and the query set undergo feature extraction and embedding propagation to obtain features $\tilde{z}$ . Then based on the support set, the MFC module and the label propagation module obtain the soft labels of the query set samples. + +# 3.3.1 Pre-training phase + +We use the cross-entropy loss to fit the model's classification predictions to the ground-truth labels. For self-supervised learning, another classifier that predicts image rotations is added to this model which is same as [33]. In this case, the pre-trained model can extract representative embedding from an image for few-shot tasks. + +# 3.3.2 Fine-tuning with data augmentation and MFC + +In this phase as shown in Fig.2, we introduce data augmentation for support set and a cross-entropy loss based on MFC to learn an encoder with good generalization that can extract powerful embeddings. We retain the encoder of the pre-trained model and discard its classifiers to fine-tune the encoder by episodic learning. For a training task $T_{i}$ , it contains a support set $S^{tr}$ and a query set $Q^{tr}$ . We use Randaugment [3] for support set to avoid over-fitting. Because the size of the support set is too small in few-shot learning, the model can easily overfit a small amount of data. However, Randaugment can dramatically change the image to increase the difficulty of the model to fit data distribution. The augmented support set is $ag(S^{tr}) = \{ag(x_i^s), y_i^s\}_{i=1}^{N \times K}$ . After the model extracts embeddings for all samples of the augmented support set and the query set, we use embedding propagation [33] to process these features: + +$$ +\tilde {z} _ {i} = e p \left(z _ {i}, Z\right) \tag {6} +$$ + +where $\mathbf{Z} = \{z_1, z_2, \dots, z_{N \times (K + q)}\}$ denotes the embedding set of the images from $ag(S^{tr})$ and $Q^{tr}$ . $ep(:,.)$ is the embedding propagation which can increase the smoothness + +of the embedding manifold by the Euclidean distances between embeddings. + +We construct two cross-entropy losses based on multifactor clustering and label propagation [12], respectively: + +$$ +l _ {f t} = \lambda l _ {M F C} + (1 - \lambda) l _ {L P} \tag {7} +$$ + +where $\lambda$ is a hyperparameter, $l_{MFC}$ is the cross-entropy loss based on multi-factor clustering, and $l_{LP}$ is the cross-entropy loss based on label propagation. + +For multi-factor clustering, $ag(S^{tr})$ can be considered as labeled set and $Q^{tr}$ can be considered as unlabeled set in a training task $T_{i}$ . We can obtain the soft pseudo-labels of training query samples by MFC, and then use ground-truth labels to calculate the cross-entropy loss: + +$$ +l _ {M F C} = - \frac {1}{q} \sum_ {i = 1} ^ {q} \log p _ {i, y _ {i} ^ {q}} \tag {8} +$$ + +where $p_{i,y_i^q}$ denotes the probability that the $i^{th}$ query sample is predicted to be the $y_i^q$ category in the MFC. The probability $p_{i,j}$ is defined in Eq.(5). + +Similarly, the cross-entropy loss based on label propagation is defined as: + +$$ +l _ {L P} = - \frac {1}{q} \sum_ {i = 1} ^ {q} \log \tilde {p} _ {i, y _ {i} ^ {q}} \tag {9} +$$ + +where $\tilde{p}_{i,y_i^q}$ is the predicted probability obtained by label propagation [12]. + +# 3.3.3 Expanding support set by MFC in testing phase + +In this phase as shown in Fig.3, we exploit the samples in the test support set $S^{test}$ and the unlabeled set $U^{test}$ to infer + +![](images/2fe5253f6cb5b757622fdb9e9bb4b9397e696a725c0bf6a31247972e5d65ffa7.jpg) +Figure 3. The framework of the testing phase. After features extraction of unlabeled samples and supporting samples, the MFC module is used to obtain pseudo-labels of unlabeled samples to expand the support set. The expanded support set is used for label propagation with the query set, and the labels of the query set samples are obtained. + +the categories of samples in the test query set $Q^{test}$ . Different from EPNet [33], we use MFC to assign pseudo-labels to unlabeled data and expand the test support set. And then the categories of samples in test query set $Q^{test}$ are obtained by label propagation using the expanded support set. The advantage of using MFC is that MFC can generate high-quality pseudo-labels for unlabeled data in few-shot tasks. + +We extract the embedding representations by the trained encoder from $\{S^{test}, Q^{test}, U^{test}\}$ , and apply embedding propagation on these embedding representations. $S^{test}$ is viewed as the labeled set to cluster unlabeled data in $U^{test}$ by MFC. We select the unlabeled data with high-confidence pseudo-labels to form a subset by: + +$$ +\tilde {U} ^ {\text {t e s t}} = \left\{\left(x _ {i} ^ {u}, \tilde {y} _ {i}\right) \mid x _ {i} ^ {u} \in U ^ {\text {t e s t}} \right\} \tag {10} +$$ + +where $\tilde{y}_i$ is the hard pseudo-label obtained by MFC for $x_i^u$ . The test support set is updated by: + +$$ +S ^ {\prime} = S ^ {t e s t} \cup \tilde {U} ^ {t e s t} \tag {11} +$$ + +At last, we predict the labels of the data in $Q^{test}$ by label propagation based on expanded test support set $S'$ . + +# 4. Experiment + +# 4.1. Datasets + +The miniImageNet dataset is a subset extracted from the ImageNet [34] dataset by Vinyals et al. [41]. Our experiment uses all 60,000 images in the dataset, and according to the standard of the traditional few-shot learning methods [41] [39] [5] [13], the 100 categories are divided into 64 training categories, 16 verification categories and 20 test categories. + +The tieredImageNet is proposed by Ren et al. [31] for few-shot learning, and is a subset extracted from the ImageNet [34] dataset. It contains 34 superclasses which can be divided into 608 categories, with a total of 779,165 images. Our experiments use all the image data in this dataset and divide these superclasses into 20 training superclasses (351 categories), 6 validation superclasses (97 categories) and 8 test superclasses (160 categories), following the traditional few-shot learning methods [6] [35]. + +The CUB [2] [8] dataset is a fine-grained dataset based on CUB200 [43], which contains 200 classes and 11,788 images split in 100 base, 50 validation and 50 novel classes. + +# 4.2. Model Settings + +In the pre-training phase, the cluster-FSL model is trained on 200 epochs with a batch size of 128, using all training categories and data. The dropout rate is 0.1, the weight decay is 0.0005, and the momentum is 0.9. The pre-trained network is updated using the stochastic gradient descent algorithm, with an initial learning rate of 0.1. The learning rate is multiplied by 0.1 when the model reaches a plateau that the validation loss had not improved for 10 epochs. When the structure of the feature extractor is ResNet-12, the output feature dimension $n$ is 512. When the structure is WRN-28-10, the output feature dimension $n$ is 640. In the fine-tuning phase, the cluster-FSL model is trained on 200 epochs, the number of iterations is 600, the weight decay is 0.0005, and the momentum is 0.9. The model is updated using the stochastic gradient descent method. The learning rate is 0.001, and it is multiplied by 0.1 when the model reaches a plateau. In the testing phase, the cluster-FSL model is tested on 1000 epochs, and the average of the accuracy of the model classification results is used as the evaluation result. The number of categories in each few-shot task $N$ is 5. For each category, the number of supported samples $K$ is 1 and 5, the number of query samples $q$ is 15, and the number of unlabeled samples $u$ is 100. The hyperparameter $\lambda$ is 0.8, the temperature parameter $\tau$ is 0.1 and the hyperparameter $\epsilon$ is 0.01. The number of iterations of the clustering process is 10. + +# 4.3. Comparative Experiment + +The baseline models for comparative experiment are EPNet [33], ICI [42] and some classic or state-of-the-art few-shot learning methods, which are TADAM [26], MTL [38], MetaOpt-SVM [18], CAN [9], LST [39] and LEO [35]; semi-supervised few-shot learning methods, which are TPN [22], TransMatch [46] and PLAIN [19]; and graph-network-based method, wDAE-GNN [6]. In addition, comparative experiments were conducted for PTN [10] and for clustering methods proposed by Ren et al. [31], such as Soft K-Means, Soft K-Means+Cluster, Masked Soft K-Means. We use quantitative analysis and comparison meth + +Table 1. The average classification accuracy of 1000 few-shot tasks in the 5-way 1-shot and 5-way 5-shot scenarios of the cluster-FSL model on the miniImageNet dataset. + +
Methods5-way 1-shot5-way 5-shot
ResNet-12
TADAM58.50±0.30%76.70±0.30%
MTL61.20±1.80%75.50±0.80%
MetaOpt-SVM62.64±0.61%78.60±0.46%
CAN67.19±0.55%80.64±0.35%
LST70.10±1.90%78.70±0.80%
EPNet66.50±0.89%81.06±0.60%
TPN59.46%75.65%
PLAIN74.38±2.06%82.02±1.08%
EPNet-SSL75.36±1.01%84.07±0.60%
cluster-FSL(our)77.81±0.81%85.55±0.41%
WRN-28-10
Soft K-Means50.09±0.45%64.59±0.28%
Soft K-Means+Cluster49.03±0.24%63.08±0.18%
Masked Soft K-Means50.41±0.31%64.39±0.24%
LEO61.76±0.08%77.59±0.12%
wDAE-GNN62.96±0.62%78.85±0.10%
EPNet70.74±0.85%84.34±0.53%
TransMatch62.93±1.11%82.24±0.59%
ICI71.41%81.12%
EPNet-SSL79.22±0.92%88.05±0.51%
PTN81.57±0.94%87.17±0.58%
cluster-FSL(our)82.63±0.79%89.16±0.35%
+ +ods to test the classification accuracy of the cluster-FSL model and evaluate the performance of the model. And we conduct experiments in two scenarios, 5-way 1-shot and 5-way 5-shot, which are two common scenarios in the field of few-shot learning. Using ResNet-12 and WRN-28-10 as the backbone, we get the comparative experimental results on miniImageNet, tieredImage and CUB-200-2011 datasets as shown in Table 1, Table 2 and Table 3. + +In Table 1, compared with the best performance EPNet-SSL [33] on the miniImageNet dataset, when the backbone is ResNet-12, the cluster-FSL model achieves $2.45\%$ and $1.48\%$ improvement in the 1-shot and 5-shot scenes respectively. When the backbone is WRN-28-10, our cluster-FSL achieves $1.06\%$ and $0.73\%$ improvement at 1-shot and 5-shot scenes, respectively. Table 2 shows the comparative experimental results on the tieredImageNet dataset. Our cluster-FSL achieves $2.10\%$ and $1.46\%$ improvement at the 1-shot and 5-shot when the backbone is ResNet-12, which is the state-of-the-art performances. When the backbone is WRN-28-10, our cluster-FSL also shows a $1.04\%$ and $1.04\%$ improvement under 1-shot and 5-shot, respectively. On CUB-200-2011 dataset, Table 3 shows the improvement of our cluster-FSL compared to EPNet [33] and ICI [42]. + +The results of comparative experiments illustrate that our + +Table 2. The average classification accuracy of 1000 few-shot tasks in the 5-way 1-shot and 5-way 5-shot scenarios of the cluster-FSL model on the tieredImageNet dataset. + +
Methods5-way 1-shot5-way 5-shot
ResNet-12
MetaOpt-SVM65.99±0.72%81.56±0.53%
CAN73.21±0.58%84.93±0.38%
LST77.70±1.60%85.20±0.80%
EPNet76.53±0.87%87.32±0.64%
PLAIN82.91±2.09%88.29±1.25%
EPNet-SSL81.79±0.97%88.45±0.61%
cluster-FSL(our)83.89±0.81%89.94±0.46%
WRN-28-10
Soft K-Means51.52±0.36%70.25±0.31%
Soft K-Means+Cluster51.85±0.25%69.42±0.17%
Masked Soft K-Means52.39±0.44%69.88±0.20%
LEO66.33±0.05%81.44±0.09%
wDAE-GNN68.16±0.16%83.09±0.12%
EPNet78.50±0.91%88.36±0.57%
ICI85.44%89.12%
EPNet-SSL83.68±0.99%89.34±0.59%
PTN84.70±1.14%89.14±0.71%
cluster-FSL(our)85.74±0.76%90.18±0.43%
+ +Table 3. The average classification accuracy of 1000 few-shot tasks in the 5-way 1-shot and 5-way 5-shot scenarios of the cluster-FSL model on the CUB-200-2011 dataset. $(\cdot)\dagger$ denotes this method uses ResNet-12 as the backbone, while $(\cdot)\ddagger$ denotes this method uses WRN-28-10 as the backbone. + +
Methods5-way 1-shot5-way 5-shot
EPNet†82.85±0.81%91.32±0.41%
cluster-FSL(our)†87.36±0.71%92.17±0.31%
ICI‡91.11%92.98%
EPNet‡87.75±0.70%94.03±0.33%
cluster-FSL(our)‡91.80±0.58%95.07±0.23%
+ +Table 4. In 5-way 5-shot setting, the impact of different methods of obtaining pseudo-labels based oncluseter-FSL. + +
MethodsminiImageNettieredImageNet
Label propagation87.99±0.37%89.45±0.45%
Kmeans88.05±0.40%88.48±0.53%
MFC(our)89.16±0.35%90.18±0.43%
+ +cluster-FSL has excellent performance under both 1-shot and 5-shot. Moreover, our MFC has stronger ability to strengthen the relationship between multiple factors. + +# 4.4. Ablation Studies + +In this section, we have done a series of complete ablation experiments for the role of each module at each stage, + +Table 5. In 5-way 1-shot setting, the impact of MFC and label propagation (LP) on fine-tuning and testing phase of cluseter-FSL. + +
SettingsFine-tune
LPMFCMFC + LP
TestLP78.71%79.32%79.81%
MFC + LP80.88%82.56%82.70%
+ +Table 6. In 5-way 1-shot setting, the impact of MFC and data augmentation on fine-tuning phase of cluseter-FSL. + +
Data AugmentationMFCACC
××79.87±1.10%
✓×80.88±1.07%
×✓81.73±1.09%
✓✓82.70±1.03%
+ +which are unified with WRN-28-10 as the backbone and evaluate the accuracy under 5-way 1-shot or 5-way 5-shot. To verify that MFC is effective in obtaining pseudo-labels with higher correctness, we compared different methods of obtaining pseudo-labels, such as label-propagation [33] and Kmeans, on the miniImageNet and tieredImageNet under the cluster-FSL, as shown in Table 4. The experimental results show that compared with label propagation and Kmeans clustering, the MFC module has improvements on the miniImageNet and tieredImageNet datasets, which shows that multiple factors contain more sample distribution information and improve classification accuracy. + +In order to verify that the MFC and label propagation modules included in the cluster-FSL play a crucial role in the experimental results, a full-scale ablation experiment is conducted for each component of the fine-tuning and testing phases, as shown in Table 5. For the fine-tuning stage, we compared the model with only label propagation, only MFC module, and both. For the three situations of the fine-tuning stage, we explored the impact of different settings in the testing stage on performance. For testing stage, the "MFC+LP" in Table 5 means that the testing model uses the MFC to obtain the expanded support set and then uses the label propagation to predict the labels of the query set. And the "LP" means that we only use label propagation to infer the labels of the query set. The results show that the MFC plays a important role in the model, and it can improve the performance of the model. + +During the fine-tuning phase of the model, the support set was extended with data augmentation and the query samples were predicted by MFC module. Therefore, we carry out ablation experiments for both parts and the results are shown in Table 6, which shows the effect of both data augmentation and MFC. + +![](images/42777af91e51aa4be4f0f5447bd7832700999874ac86e3ec670349739191ec10.jpg) +Figure 4. The impact of different $\lambda$ on the miniImageNet dataset in 5-way 1-shot setting. + +# 4.5. Parameters Analysis + +Our cluster-FSL model has one hyperparameter, $\lambda$ , where $\lambda$ in Eq.(7) is used to control the proportion of MFC and label propagation during the fine-tuning phase. The parameter analysis experiment is done on the miniImageNet dataset with WRN-28-10 as the backbone, and the 5-way 1-shot setting is adopted. As shown in Fig.4, the best accuracy is obtained at 0.8, which can achieve $82.70\%$ . When the value of $\lambda$ is 0 or 1, it corresponds to not considering the effect of MFC or label propagation in Eq.(7) during the fine-tuning phase of the model. + +# 5. Conclusion + +We proposed a novel clustering-based semi-supervised few-shot learning (cluster-FSL) image classification method, which has effectively alleviated the problem of sample scarcity. In cluster-FSL, we presented a multifactor clustering (MFC) algorithm by integrating factors of labeled and unlabeled data, which effectively improve the quality of pseudo-labels. Furthermore, in the model fine-tuning stage, we used more robust data augmentation to further augment the dataset and learned the model with the joint supervision of multi-factor clustering and label propagation. On the three benchmark datasets, our cluster-FSL has state-of-the-art performances than other few-shot learning methods. + +Limitations: our proposed cluster-FSL needs to introduce extra unlabeled data and make an assumption that unlabeled data and labeled data are implicitly embedded in a manifold to ensure the generation of pseudo-labels. + +Acknowledgement: This work was partially supported by the National Natural Science Foundation of China (Grants no. 62176271 and 61772568) and Guangdong Basic and Applied Basic Research Foundation (Grant no. 2019A1515012029). + +# References + +[1] Sagie Benaim and Lior Wolf. One-shot unsupervised cross domain translation. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, pages 2108-2118, 2018. 1 +[2] Wei-Yu Chen, Yen-Cheng Liu, Zsolt Kira, Yu-Chiang Frank Wang, and Jia-Bin Huang. A closer look at few-shot classification. 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Traditionally, a supervised learning was used for training the models, which required tremendous manually-labeled data, while some methods suggested a self-supervised or weakly-supervised learning to mitigate the reliance on the labeled data, but with limited performance. + +In this paper, we present a simple, but effective solution for semantic correspondence that learns the networks in a semi-supervised manner by supplementing few ground-truth correspondences via utilization of a large amount of confident correspondences as pseudo-labels, called SemiMatch. Specifically, our framework generates the pseudo-labels using the model's prediction itself between source and weakly-augmented target, and uses pseudo-labels to learn the model again between source and strongly-augmented target, which improves the robustness of the model. We also present a novel confidence measure for pseudo-labels and data augmentation tailored for semantic correspondence. In experiments, SemiMatch achieves state-of-the-art performance on various benchmarks. + +# 1. Introduction + +Establishing dense correspondences across semantically similar images, depicting different instances of the same object or scene category, can facilitate many Computer Vision applications such as semantic segmentation [42,52,61], object detection [34], or image editing [25,33]. Unlike classical dense correspondence problems such stereo matching or optical flow [21,58], semantic correspondence poses additional challenges from large intra-class appearance and ge + +![](images/63392c92cc065644436733265f6a0699c879e9d6c611cd71ca41f689f26870c7.jpg) + +![](images/cbb9d2217cf525ef0d341458f55aba7f92fc34facb098499a3a38fda429a43aa.jpg) + +![](images/8baf329b804b36f08f525b75f36335fa65c827fd08b166eac6cbc22bd408ad0f.jpg) +(a) Supervised loss +(c) Unsupervised loss (Ours) +Figure 1. Comparison of semantic correspondence methods in terms of different formulation of supervision. Conventional methods leverage either (a) supervised loss using sparse ground-truth keypoint matches [16,43,45] or (b) self-supervised loss using synthetic flow field with random geometric parameters [40,48,63]. Unlike them, we present (c) unsupervised loss using pseudo-labels from a matching probability and (d) semi-supervised loss using both sparse ground-truth keypoints and confident pseudo-labels. + +![](images/4aaf4405f26309c5c3875edfb2417e2055c0a4fe4f1b58758ef702ff58520132.jpg) +(b) Self-supervised loss +(d) Semi-supervised loss (Ours) + +ometric variations [10, 16, 23]. + +Although formulated in various ways, most recent approaches [9,36,40,41,43,45,48,49,51,54,63,64] addressed these challenges by carefully designing deep neural networks, such as CNNs [36,40,43,45,48,49,51,54,63,64] or Transformers [9, 59], based models. The most straightforward way to formulate a mapping function is to use groundtruth correspondences between the image pairs. Recent approaches [9, 70], including conventional approaches, have been formulated in a supervised fashion (Fig. 1a). However, ground-truth keypoint pairs on the most standard benchmarks [15,44] can be the inherent bottleneck [10, 16, 43, 45] because they are annotated subjectively and sparsely. + +To alleviate the reliance on the ground-truth data, some methods [40, 48, 63, 64] presented a self-supervised learning framework (Fig. 1b), using synthetic geometric warps of an image to generate a synthetic image pair. Although it turns out that it is an appealing alternative, using synthetic image pairs cannot account for extreme intra-class appear + +ance variations in semantic correspondence [48,55]. On the other hand, some other methods [20, 23, 25, 45] presented a weakly-supervised learning framework that casts this task as a feature reconstruction between the images, but the loss function often fails to explain the correspondences across severely different instances among the same class. + +On the other hand, most recent approaches in image classification task [3, 4, 19, 27, 57] have been popularly formulated in a semi-supervised learning framework, which enables learning the model on a large amount of unlabeled data with a few labeled data, and showed outstanding performance. Most recent trends of semi-supervised learning [3, 4, 19, 27, 57] integrate consistency regularization [2] and pseudo-labeling [29]. For instance, FixMatch [57] first generates a pseudo-label using the model's prediction on weakly-augmented unlabeled data and then encourages the prediction from strongly-augmented unlabeled data to follow the pseudo-label with confidence thresholding. This learning framework has become a promising solution to mitigate the reliance on large labeled data [18, 38, 57], but directly applying these techniques to semantic correspondence is challenging in that learning the matching networks requires pixel-level pseudo-labels. + +In this paper, we present a novel semi-supervised learning framework, called SemiMatch, that generates pixel-level pseudo-labels using the model's prediction itself between source and weakly-augmented target and then encourages the model to predict the pseudo-label again between source and strongly-augmented target, as illustrated in Fig. 2. To account for the observation that all of the pseudo-labels may not help to boost performance, we introduce a novel confidence measure for pseudo-labels by considering object-centric foreground, forward-backward consistency, and uncertainty of probability itself. Tailored for semantic correspondence, we also present a matching-specialized augmentation that exploits a keypoint-aware cutout, helping the network to learn distinctive feature representations around the keypoints. + +We evaluate our method on several benchmarks [15, 44]. Experimental results on various benchmarks show that using our novel loss function with sparsely-supervised loss function consistently improves the performance compared to the latest methods for semantic correspondence. We also provide an extensive ablation study to validate and analyze components in our learning framework. + +# 2. Related works + +Semantic Correspondence. The objective of semantic correspondence [10, 15, 24, 49] is to find correspondences across semantically similar images. Recent methods [9, 10, 16, 43, 45, 70] showed great progress by supervised loss, but they are limited by the availability of sparse ground-truth annotation. On the other hand, some methods [40, 48, 63, 64] + +address the aforementioned limitations by training the network in a self-supervised manner, relying on synthetic warps of real images, without ground-truth flow and [32] presents a teacher-student model where the student model exploits the teacher model's generalized knowledge learned from synthetic data. Their improvement is mainly due to self-supervised training data, but synthetic geometric deformation cannot model intra-class appearance variations and realistic scene generation. Another alternative is to use a training loss that only requires a weak-level of supervision, given for each image pair as either positive (the same class) or negative (different class), as in [20, 45, 51]. While it [45] can achieve higher performance than strongly-supervised methods, it has fundamental limitations to supervise locating matches. Unlike the methods above, we present for the first time a semi-supervised learning framework which overcomes the lack of labeled ground-truth keypoints by utilizing a large amount of confident correspondences as pseudo-labels. + +Semi-Supervised Learning. The most recent methods for semi-supervised learning have followed two trends; pseudo-labeling and consistency regularization. Pseudolabeling [1, 29, 47, 56, 67, 71] encourages a model to follow the pseudo-label from the model's prediction itself closely related to entropy minimization [13] where the model's predictions are encouraged to be low-entropy (i.e., high-confidence) on unlabeled data. On the other hand, consistency regularization [2, 53, 62, 67] encourages the model to produce the same prediction when perturbations are applied to the input or the model. Consistency regularization-based methods, enforcing invariant representations across augmentations, rely heavily on the usage of strong data augmentation, so it is important which strong augmentations are used and how strong they are. Very recently, some state-of-the-art methods [3, 19, 27, 57, 67] combine pseudolabeling and consistency regularization by a confidence-based strategy and separate weak and strong augmentations, but there still remains the problem of ignoring a large amount of unlabeled data due to reliance on fixed high thresholding to compute the unsupervised loss. Most aforementioned methods have focused on solving an image-level task, e.g., image classification, but methods for pixel-level tasks such as semantic correspondence are done limitedly and cannot be applied directly. + +Uncertainty Estimation. Predicting uncertainty in the field of Computer Vision has been widely explored [7, 26, 28, 37], even before the expansion of deep learning. There are two approaches in uncertainty estimation: empirical and predictive. The former method [5, 14] approximates the uncertainty by sampling a finite number of weight configurations for a given network and computing the mean and variance of the predictions. In the latter method [46], a network + +![](images/064a2d4be21303994a5cfa2b7003e72159e7e93ab95e71ac3a31956c6e307000.jpg) +Figure 2. Overview of our semi-supervised learning framework for semantic correspondence. SemiMatch first augments the target image into a weakly-augmented one and a strongly-augmented one. The backbone matching networks extract features from these images, compute correlation cost, followed by aggregation. The aggregated cost between source and weakly-augmented target images is transformed by the same geometry warp used in strong augmentation and sharpened to generate a pseudo-label. The overall loss function is composed of supervised loss which uses the sparse ground-truth label and unsupervised loss which uses the pseudo-label. + +is trained to infer the mean and variance of the distribution by design. + +In semi-supervised learning in image classification, there were some approaches, such as Dash [68] and FlexMatch [69], to measure the uncertainty of pseudo-labels by applying a different threshold to each sample, unlike FixMatch [57] which assumes that the samples exceed the hand-crafted confidence threshold. In contrast to the existing semi-supervised method [57, 68, 69] which assumes that all pseudo-labels are certain without considering the uncertainty of the generated pseudo-label, we improve the performance by considering the uncertainty of the pseudo-label. + +# 3. Methodology + +# 3.1. Motivation + +Given a pair of images, i.e., source $I_{s}$ and target $I_{t}$ , which represent semantically similar images, the goal of semantic correspondence is to establish matches between the two images at each pixel. To achieve this, most predominant methods with CNNs [36, 40, 43, 45, 48, 49, 51, 54, 63, 64] consist of two steps, including feature extraction and cost aggregation. First of all, feature extraction networks extract a feature $F \in \mathbb{R}^{h \times w \times d}$ , where $h \times w$ is the spatial resolution and $d$ is the channels. The similarities between feature maps, called cost volume, can be estimated by $\mathcal{C}(i,j) = F_t(i)^T F_s(j)$ , where $i \in \{1,.., h_tw_t\}$ and $j \in \{1,.., h_kw_s\}$ . However, initial cost volume itself is vulnerable to ambiguous, repetitive, or textureless matches. To disambiguate these, recent methods [9, 31, 36, 41] employ the cost aggregation networks for refining the initial matching similarities to achieve the aggregated cost $\mathcal{C}'(i,j)$ . + +Although existing methods [9, 31, 36, 41, 70] can be formulated in various ways, their outputs $\mathcal{C}$ or $\mathcal{C}'$ can be con + +sidered as a matching probability through a simple SoftMax function [30] such that $P(i) = p(I_s, I_t(i); \theta) \in \mathbb{R}^{h_s w_s \times 1}$ with the network parameters $\theta$ , defined across all the points in $I_s$ for point $i$ in $I_t$ . Learning such networks in a supervised manner requires manually annotated ground-truth correspondences $P_{\mathrm{GT}}$ , which are extremely labor-intensive and involves subjectivity [9, 45, 70]. Thus, in semantic correspondence, only sparsely-annotated ground-truths are available, and the supervised loss function is defined such that + +$$ +\mathcal {L} _ {\sup } = \sum_ {i} c (i) \mathcal {D} \left(p \left(I _ {s}, I _ {t} (i); \theta\right), P _ {\mathrm {G T}} (i)\right), \tag {1} +$$ + +where $c(i)$ is a binary indicator for representing the existence of ground-truth $P_{\mathrm{GT}}(i)$ , $P_{\mathrm{GT}}(i)$ is an one-hot vector form, and $\mathcal{D}(\cdot, \cdot)$ is the distance function, e.g., L2 distance [40] or cross-entropy [23, 51]. Due to the inherent nature of using sparse ground-truths, the distance function yields a limited performance [9, 70]. To alleviate the reliance on large ground-truth data, self-supervised learning methods [40, 48, 63, 64] have been popularly used, which generates synthetic matching pairs by applying a geometric warping on a single image. In specific, target image $I_t$ (or source image $I_s$ ) is transformed by geometry warping operator $\mathcal{G}(\cdot; \phi)$ with a randomly-defined warping field $\phi$ , e.g., generated by affine [66] or thin-plate-spline (TPS) [6] transformation. The synthetic image pairs are then defined as $I_t$ and $\mathcal{G}(I_t; \phi)$ , and $\phi$ is used as a pseudo-label for them. + +The self-supervised loss function is then defined as + +$$ +\mathcal {L} _ {\text {s e l f - s u p}} = \sum_ {i} \mathcal {D} \left(p \left(\mathcal {G} \left(I _ {t}; \phi\right), I _ {t} (i); \theta\right), P _ {\phi} (i)\right). \tag {2} +$$ + +where $P_{\phi}$ is one-hot vector form of $\phi$ . Since this loss function does not require annotated ground-truths, and enables + +![](images/aa0288741e74388ba8158b0bb7507fe0b027e59da27b141850c66c603ebe1096.jpg) +(a) $I_{s}$ + +![](images/dd9e441497be7ffb257650d6530c469368405cebbd2589b93d9269428e477a01.jpg) +(b) $I_{t}$ + +![](images/8fd3d021c160d3335e10c6212b821a3473ed9469807b0a24a9b3e4412f3fdc23.jpg) +(c) $\alpha (I_t)$ + +![](images/f0ec8354ef54e4e674c861a358313465b09b47acde3904a4f6bb11f98ece0e75.jpg) +(d) $\mathcal{G}(\mathcal{A}(I_t))$ +Figure 3. Examples of augmented images in semi-supervised learning: (a) source image $I_{s}$ , (b) target image $I_{t}$ (c) weakly-augmented target image $\alpha(I_{t})$ , and (d) strongly-augmented target image $\mathcal{G}(\mathcal{A}(I_{t}))$ . + +learning with dense labels, it can be an alternative to data hungry from sparse annotations [9, 70]. However, such synthetic image pairs cannot contain realistic appearance variations across the two images and model moving objects or occlusion, which limits the performance in semantic correspondence that often poses challenges by intra-class appearance and shape variations [30, 41]. + +# 3.2. Formulation + +We present a novel semi-supervised learning framework, SemiMatch, for learning a matching model on a large amount of unlabeled pixels with few labeled pixels between source and target images. Following recent trends of semi-supervised learning in image classification [57, 67] that have not been applied in semantic correspondence yet, we present to extend the consistency regularization between two differently augmented instances from the same image [57] to semantic correspondence. They are commonly based on the assumption that when perturbations are applied to the input, the prediction should not change significantly. However, it is difficult to adapt the existing consistency regularization techniques [3,4,57] to semantic correspondence directly, predicting dense probabilities because they were designed for image classification task. + +In this section, we study how to formulate the loss function for unsupervised learning within semantic correspondence framework that can be simultaneously used with sparsely supervised loss function for semi-supervised learning. First of all, as shown in Fig. 3 given source $I_{s}$ and target $I_{t}$ images, we build a triplet $\{I_s,\alpha (I_t),\mathcal{G}(\mathcal{A}(I_t))\}$ where $\alpha (\cdot)$ and $\mathcal{A}(\cdot)$ represent weak and strong photometric and geometric augmentations, respectively. Our key ingredient is to exploit the difference in difficulty levels of matching weak pairs and strong pairs, i.e., the weak pairs are easier to generate pseudo-labels for the strong pairs, inspired by [57]. However, without the geometric augmentation, the performance of trained models may be sub-optimal because the models may lack the robustness to geometric variations, which frequently occur in semantic correspondence. But if the geometric augmentation is applied simultaneously, direct consistency regularization cannot be formed,i.e., to perform consistency regularization on the geometrically warped image pairs, it is necessary to find the + +![](images/c922e1f940300ba23c5480b00be2456e9d456fdcf386bc219dba49b16482fb16.jpg) +Figure 4. Comparison of matching difficulty between weak branch and strong branch. The yellow and red lines show the result of the weak and strong branch, respectively. The green lines show when the weak branch and strong branch results are the same. Weak branch gives more accurate results. + +![](images/60ed1f12b47fb91b9db0a09b83f3819b34c2bd65ced7c048be15bb16dd9ca65b.jpg) + +pseudo labels in the misaligned image pair. + +To overcome the aforementioned issues, we present a novel unsupervised loss function that jointly leverages photometric and geometric augmentations, defined such that + +$$ +\mathcal {L} _ {\text {u n - s u p}} = \sum_ {i} m (i) \mathcal {D} \left(p \left(I _ {s}, \mathcal {G} \left(\mathcal {A} \left(I _ {t} (i)\right); \phi\right); \theta\right), Q (i)\right), \tag {3} +$$ + +where $Q(i)$ is a pseudo-label defined as + +$$ +Q (i) = \mathcal {G} \left(p \left(I _ {s}, \alpha \left(I _ {t} (i)\right); \theta\right); \phi\right), \tag {4} +$$ + +which means the geometrically-warped matching probabilities between weak pairs with $\phi$ . And the same geometric warping applied to the target image, such that $\mathcal{G}(\mathcal{A}(I_t);\phi)$ . Like previous consistency regularization methods [2], we generate pseudo-labels from better correspondences of the weak pairs than the strong pairs as shown in Fig. 4. By geometrically-warping the pseudo-labels, we can align matching probability for strong pairs, enabling the model to achieve robustness to strong augmentation as well. + +In the following section, we will explain how to achieve the confidence $m(i)$ of pseudo-label. + +# 3.3. Confidence of Pseudo-Label + +Matching probabilities inferred from the weak branch are used to define pseudo-labels in the strong branch. However, incorrect pseudo-labels may hinder performance boosting, which is called confirmation bias [1] problem. To overcome this, some semi-supervised learning methods for image classification use simple thresholding of the probability value itself, e.g., FixMatch [57]. This is too a strong constraint in early iterations of training in that most false positives cannot be captured. + +To alleviate this, we present three constraints to measure the confidence of pseudo-labels. First of all, we utilize a binary object mask of source and target images, which helps to limit the matching candidates within object-centric regions. In specific, since the pseudo-labels are defined at geometrically-warped regions, we define $M_{\mathrm{mask}}$ as a binary foreground object mask for target image $I_{t}$ . Note that the object mask is synthesized using the min and max values of ground-truth keypoints. + +![](images/76fbda1567ba9259dadeedf18706904cc07742e44677729b4a3c6583c7248f33.jpg) +(a) Source + +![](images/57b214f48b73d20cd98af028405aeedc3a94b4786c35ecf894b705896567a6c3.jpg) +(b) Target + +![](images/39e0ec8ca8178d4cde366faeaab6fec6b6d31e50e1b562532ca9dff12b278541.jpg) +(c) Mask intersection + +![](images/38b4cb3c3c2f99ba81b42b3a385c9823704c44a317f40a2ba40d3b933dce84e2.jpg) +(d) $M_{\mathrm{mask}}$ + +![](images/f2884a880bb921fd793f53a5c38e81290a8d6a9252ce9aa520a10fa3ec1b1781.jpg) +(e) $M_{\mathrm{fb}}$ + +![](images/51cb4c4b3fa5c8dda1e701bdadc412f0443dc1a937a743cace7b53b294b15e0d.jpg) +(f) $M_{\mathrm{thres}}$ +Figure 5. Visualization of our confidence mask: (a) source, (b) target, (c) mask intersection, (d) $M_{\mathrm{mask}}$ , (e) $M_{\mathrm{fb}}$ , and (f) $M_{\mathrm{thres}}$ . Sampled pixels by mask intersection belong to object-centric and discriminative image regions. + +Secondly, we also utilize forward-backward consistency checking [35, 39, 60]. In specific, by estimating correspondences between $\{I_s, \alpha(I_t)\}$ in forward and backward directions simultaneously and checking the consistency between them, we determine the reliability of pseudo-labels based on the observation that if this consistency constraint is not satisfied, the points in $\alpha(I_t)$ are occluded at the matches in $I_s$ (or vice-versa), and the estimated flow vector is incorrect. This constraint is denoted by $M_{\mathrm{fb}}$ . + +Finally, unlike existing consistency regularization methods [57], using a few samples through high thresholding with a pre-defined scalar value $\tau$ , we present uncertainty-based weighting on the loss function itself. This lets a considerable amount of unlabeled data, especially at the early iteration of training phase, be used as pseudo-labels according to their different learning status. Specifically, we measure the uncertainty $u(i)$ of matching probabilities $P(i)$ as + +$$ +u (i) = 1 / \exp \left(\sum_ {j} P (i, j) \log P (i, j)\right), \tag {5} +$$ + +where $P(i,j)$ is $j$ -th component of $P(i)$ . $M_{\mathrm{thres}}(i)$ is then measured by $(1 / u(i)) \odot 1$ ( $\max(P(i)) \geq \tau$ ) to weight loss function depending on uncertainty where $\odot$ denotes Hadamard product. + +Our final confidence $m$ is determined by $\mathcal{G}(M_{\mathrm{mask}}\odot M_{\mathrm{fb}}\odot M_{\mathrm{thres}};\phi)$ . We visualize each mask component belonging to the intersection of the masks in Fig. 5. + +# 3.4. Augmentation + +Consistency regularization-based methods [2], enforcing invariant representations across augmentations, greatly depend on what kind of transformations are used for strongly-augmented images. Even though any kind of augmentation can be used in this framework, for semantic correspond + +![](images/cb7b6d1ce51b6ad254c54c5235e8ee8714a3a821c3eaf1427e5ae2cf2313bad2.jpg) +(a) Image pair + +![](images/327693a7bc259f5a112d761d14fb5722c3dad739f09d78b75150ad475163546a.jpg) +(b) Keypoint pair +Figure 6. Visualization of KeyOut augmentation: (a) image pair, (b) keypoints, and (c) keyOut applied to the target image. + +![](images/f7f727c09efa28d057d12adb8abbeb118ede323d9de4cba464c71ff9468154c2.jpg) +(c) KeyOut pair + +dence, augmentation should be more focused on discriminative local parts of an object to infer the matches. + +In this section, we propose a matching-specialized augmentation, called keypoint-guided CutOut (KeyOut), which cuts and removes boxes of a certain size around the keypoint location as shown in Fig. 6. It allows the model to learn to find the keypoint locations by integrating keypoint peripheral information. + +# 3.5. Loss Functions + +Finally, we propose two loss functions to train our model using different supervision, including supervised loss and semi-supervised regimes. As described above, any distance function $\mathcal{D}$ can be used for loss functions. In specific, following the common practice [40], $L_{\mathrm{sup}}$ is defined as the L2 distance such that + +$$ +\mathcal {L} _ {\sup } = \sum_ {i} c (i) \| \xi \left(p \left(I _ {s}, I _ {t} (i); \theta\right)\right) - \xi \left(P _ {\mathrm {G T}} (i)\right) \|, \tag {6} +$$ + +where $\xi (\cdot)$ is denoted as general max function including soft argmax and hard argmax. In addition, $L_{\mathrm{un - sup}}$ is formulated with the contrastive loss function [65] as + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {u n - s u p}} \\ = - \sum_ {i} m (i) \log \left(\frac {\exp \left(p \left(I _ {s} \left(i ^ {\prime}\right) , G (i) ; \theta\right) / \gamma\right)}{\sum_ {j} \exp \left(p \left(I _ {s} (j) , G (i) ; \theta\right) / \gamma\right)}\right), \tag {7} \\ \end{array} +$$ + +where $G = \mathcal{G}(\mathcal{A}(I_t);\phi)$ , $i'$ and $j$ represent the locations in source image, respectively, $i'$ is determined as $\xi(Q(i))$ , and $\gamma$ is the temperature hyper-parameter. + +Our total loss $\mathcal{L}_{\mathrm{total}} = \mathcal{L}_{\mathrm{sup}} + \lambda \mathcal{L}_{\mathrm{un - sup}}$ where $\lambda$ is a weight that is adaptively determined by the ratio between $\mathcal{L}_{\mathrm{sup}}$ and $\mathcal{L}_{\mathrm{un - sup}}$ such that $\lambda = \mathcal{L}_{\mathrm{sup}}^{*} / \mathcal{L}_{\mathrm{un - sup}}^{*}$ , where $\mathcal{L}^*$ is the loss value itself and no back propagation happens. + +# 3.6. Network Architecture + +Our semi-supervised learning framework can be used in any deep networks for semantic correspondence [9, 22, 31, 36, 41, 43, 50, 51]. In this paper, we leverage the recent state-of-the-art network, especially focusing on cost aggregation stage, CATs [9] that explores global consensus among initial correlation map with the help of Transformer-based aggregator. By considering the outputs of the networks as matching probabilities, it directly leverages the proposed unsupervised loss, as well as supervised loss. Our overall architecture is shown in Fig. 2. + +
MethodSupervisionLearning signalPF-PASCALPF-WillowSPair-71k 0.1
0.050.10.150.050.10.15
\( PF_{HOG} \) [15]None-31.462.579.528.456.868.2-
CNNGeoResNet-101 [48]A2NetResNet-101 [55]Self-sup.synthetic pairs41.069.580.436.969.277.820.6
42.870.883.336.368.884.422.3
SF-NetResNet-101 [30]Weak-sup.bbox53.681.990.646.374.084.2-
WeakalignResNet-101 [49]images49.074.884.037.070.279.920.9
RTNsResNet-101 [23]55.275.985.241.371.986.225.7
NC-NetResNet-101 [51]54.378.986.033.867.083.720.1
DCC-NetResNet-101 [20]55.682.390.543.673.886.5-
DHPFResNet-101 [45]56.182.191.150.280.291.137.3
SCNetvGG-16 [16]ANC-NetResNet-101-FCN [31]Sup.keypoints36.272.282.038.670.485.3-
-86.1----28.7
HPFResNet-101 [43]60.184.892.745.974.485.628.2
DHPFResNet-101 [45]75.790.795.049.577.689.137.3
CHMNetResNet-101 [41]80.191.694.952.779.487.546.3
MMNetResNet-101 [70]77.689.194.3---40.9
CATs†ResNet-101 [9]67.589.194.946.675.687.542.4
CATSResNet-101 [9]75.492.696.450.379.290.349.9
SemiMatch†SemiMatchSemi-sup.keypoints75.091.795.647.476.388.243.0
80.193.596.654.082.192.150.7
+ +Table 1. Quantitative evaluation on PF-PASCAL and PF-Willow [15] and SPair-71k [44]. Subscripts of each method's name indicate the feature backbone used. The best results in bold, and the second best results are underlined. CATs† means without fine-tuning feature. + +
Methodsaero.bikebirdboatbott.buscarcatchai.cowdoghors.mbik.pers.plan.shee.trail.tvall
CNNGeo [48]23.416.740.214.336.427.726.032.712.727.422.813.720.921.017.510.230.834.120.6
A2Net [55]22.618.542.016.437.930.826.535.613.329.624.316.021.622.820.513.531.436.522.3
WeakAlign [49]22.217.641.915.138.127.427.231.812.826.822.614.220.022.217.910.432.235.120.9
NC-Net [51]17.912.232.111.729.019.916.139.29.923.918.815.717.415.914.89.624.231.120.1
HPF [43]25.218.952.115.738.022.819.152.917.933.032.820.624.427.921.115.931.535.628.2
SCOT [36]34.920.763.821.143.527.321.363.120.042.942.531.129.835.027.724.448.440.835.6
DHPF [45]38.423.868.318.942.627.920.161.622.046.946.133.527.640.127.628.149.546.537.3
CHMNet [41]49.133.664.532.744.647.543.557.821.061.354.643.835.143.738.133.570.655.946.3
MMNet [70]43.527.062.427.340.150.137.560.021.056.350.341.330.919.230.133.264.243.640.9
\(CATs^†\) [9]46.526.969.124.344.338.530.262.715.953.752.246.732.735.232.231.268.049.142.4
CATs [9]52.034.772.234.349.957.543.666.524.463.256.552.042.641.743.033.672.658.049.9
SemiMatch†47.829.070.624.044.537.629.865.217.254.752.847.135.237.629.932.768.549.443.0
SemiMatch53.637.074.632.347.557.742.467.423.764.257.351.743.840.445.333.174.165.950.7
+ +Table 2. Per-class quantitative evaluation on SPair-71k dataset [44]. The best results are in bold, and the second best results are underlined + +# 4. Experiments + +# 4.1. Implementation Details + +In experiments, we evaluate our framework with the state-of-the-art network, CATs [9]. For a fair comparison, we use the same hyper-parameters and photometric augmentation lists following CATs [9]. For geometric transformation [30,48,63], we apply a combination of affine and thin-plate-spline with random transformation parameters in range $[0,1]^{*}t_{scale}$ (0.15 for affine, and 0.4 for tps). To generate matching-specialized augmentations, we add blur as in [8] and KeyOut on strong augmentation. We set $\gamma = 0.1$ and $\tau = 0.5$ . + +# 4.2. Experimental Settings + +In this section, we conduct comprehensive experiments for semantic correspondence, by evaluating our framework through comparisons to state-of-the-art methods including HOG [15], CNNGeo [48], A2Net [55], SFNet [30], WeakAlign [49], SCNet [16], RTNs [23], NC-Net [51], DCC-Net [20], HPF [43], DHPF [45], SCOT [36], ANC-Net [31], CHM [41], CATs [9], MMNet [70]. + +Dataset. We extensively conduct experiments on three popular benchmarks for semantic correspondence: PF-PASCAL [15], PF-WILLOW [15], SPair-71k [44]. PF-PASCAL contains 1,351 semantically related image pairs from 20 categories of the PASCAL VOC dataset [12]. PF-Wilow contains 900 image pairs from 4 categories. SPair + +![](images/c02731ae4021831665a3825bab9a9233011c6f8c13a17cc76ff335cc36228b43.jpg) + +![](images/257d3f26d8e39ca578f3c5cc1f42e9f8cab10cdc9a5d7c602c29968b414db0b5.jpg) + +![](images/9c70c9479eddcc2135b7677943387d3d45827d1104d2ea780962419f839a5d70.jpg) + +![](images/13827830b4522d42ffbfe53e8b1d7d1468c82ce23c8751558893c9421611c908.jpg) + +![](images/018c89bef141590542dc6d9dc502a475a50dcf86e92e9b59ecf2b5b3504af43a.jpg) +(a) CHMNet [70] + +![](images/839f0cfa93b9259c1323fc63466d0d6a834ea9bb731fcf627e719b59b1f06baa.jpg) +(b) CATs [9] + +![](images/475ab26acc17455e2b8e097985b2f1eaadb46138ec462126aad1b592e6b97d2d.jpg) +(c) SemiMatch +Figure 7. Qualitative results on PF-PASCAL [15]. (a) CHMNet [41] (b) CATs [9] (c) SemiMatch, and (d) sparse GT keypoints. + +![](images/caa1efc89ddb9cbde475953b6a6b08edeebd926366ade45d33f1dc1eb5a43e3b.jpg) +(d) GT keypoints + +
ComponentPF-PASCALPF-Willow
0.050.10.050.1
(I)SemiMatch80.193.554.082.1
(II)(I) w/o \(M_{mask}\)73.992.051.479.7
(III)(I) w/o \(M_{fb}\)78.793.152.981.9
(IV)(I) w/o \(M_{thres}\)72.391.352.181.5
+ +Table 3. Ablation study of mask elements. + +71k consists of total 70,958 image pairs in 18 categories with diverse view-point and scale variations. We used the same split proposed in [44]. + +Evaluation Metric. Following the standard experimental protocol [15, 44], we use the percentage of correct keypoint (PCK@ $\alpha$ ), computed as the ratio of estimated keypoints within the threshold from ground-truths to the total number of keypoints. Given a set of predicted and ground-truth keypoint pairs $\mathcal{K} = \{(k_{\mathrm{pred}}(m), k_{\mathrm{GT}}(m))\}$ , PCK can be defined as $\mathrm{PCK}(\mathcal{K}) = \frac{1}{M} \sum_{m}^{M} d(k_{\mathrm{pred}}(m), k_{\mathrm{GT}}(m)) \leq \alpha_k \cdot \max(H, W)$ , where $M$ is the number of keypoint pairs, $d(\cdot)$ is Euclidean distance; a threshold is scaled by $\alpha_k \cdot \max(H, W)$ in proportion to the larger portion of image for PF-PASCAL [15], and the object's bounding box for PF-Willow [15], and SPair-71k [44]. + +# 4.3. Matching Results + +For fair comparisons with our baseline, CATs [9], and previous state-of-the-art methods, we exploit the same network architecture, ResNet-101 [17] pretrained on ImageNet [11]. As shown in Table 1, for PF-PASCAL [15], SemiMatch records state-of-the-art results with $80.1\%$ PCK@0.05, $93.5\%$ PCK@0.1 and $96.6\%$ PCK@0.15. Without and with fine-tuning feature extraction backbone, SemiMatch outperforms CATs [9] by $7.5\% /4.7\%$ PCK@0.05, $2.6\% /0.9\%$ PCK@0.1, and $0.7\% /0.2\%$ PCK@0.15. It demonstrates the effectiveness of our semi-supervised framework with the confidence constraints of pseudo-labels and matching-specialized augmentation. Compared to CATs, it can operate more sensitively + +at local regions through the significant performance improvement in PCK@0.05, which is the most strict matching criterion in PF-PASCAL. Experiments show that a large amount of pseudo-labels provide information on neighboring keypoints that cannot be provided by sparse keypoints. Generalization power of SemiMatch can be proven through the best performance in PF-willow for all PCKs by $1.3\%$ , $1.9\%$ and $1.0\%$ , respectively compared to the previous state-of-the-art results. Finally, we also record the best performance with $50.7\%$ PCK@0.1 even in SPair-71k [44] having large-scale variation. To show the effectiveness and robustness of our framework in detail, we compare per-class accuracy in Table 2 and our approach outperforms all state-of-the-art networks on 11 of the 18 classes. Our qualitative results are shown in Fig. 7. + +# 4.4. Ablation Study + +We conduct ablation analyses to investigate the effectiveness of components in our framework and also explore the effect of pseudo-labeling compared to CATs [9]. All experiments are conducted on PF-PASCAL dataset [15] and validated on PF-PASCAL and PF-Willow. + +Effects of Confidence Mask. In Table 3, we evaluate each mask constraint in SemiMatch baseline (I) by removing each from the entire constraints. From (I) to (II), PCK decline shows that the network can learn more representative information of the object by foreground samples separated from the background. A large performance drop in (IV) compared to (III) shows that it is important to adjust a weighting on the loss function proportionally according to the uncertainty. + +Effects of Keypoint-Based Augmentation. We also evaluate additional strong augmentation by CutOut, KeyOut with low probability and small box regions (KeyOutweak) and KeyOut with high probability and large box regions (KeyOutstrong). As shown in Table 4, we can prove the effectiveness of our KeyOut, cutout regions based on keypoint locations by comparing (II) and (III)-(IV). Especially + +![](images/c5215f176ac66e6a3d0140e570a046f2d45a4df92819e722bb9e85ae8d6d1d04.jpg) +(a) PCK@0.1 on PF-PASCAL + +![](images/9dc4c16b0adf90ff897ea97d9045e4657a85e685f9e7f8c2913cfb94d92b3821.jpg) +(b) PCK@0.05 on PF-PASCAL +Figure 8. PCK results of CATs [9] and SemiMatch on PF-PASCAL and PF-Willow with various label fractions: (a) PCK@0.1 on PF-PASCAL, (b) PCK@0.05 on PF-PASCAL, (c) PCK@0.1 on PF-Willow, and (d) PCK@0.05 on PF-Willow. + +![](images/6f33b3e134674dfcdd75a84fb774db35f43f86918fc7e6ffe12f3eaf27bfd100.jpg) +(c) PCK@0.1 on PF-Willow + +![](images/b5780b781007e53b3b9fbb2dd8757d79c7458090473a0d8e26030f7f0790be9a.jpg) +(d) PCK@0.05 on PF-Willow + +
ComponentPF-PASCALPF-Willow
0.050.10.050.1
(I)SemiMatchBase79.893.352.981.5
(II)w/ CutOutweak79.893.251.881.1
(III)w/ KeyOutweak80.193.654.082.1
(IV)w/ KeyOutstrong79.893.453.681.9
+ +on PF-Willow, (III) shows powerful generalization power compared to (I) and (II) by $1.1\%$ and $2.2\%$ . + +Experiments with Label Fraction. We investigate the performance gap between CATs and SemiMatch according to the label fraction of PF-PASCAL dataset, referring to the percentage of data in entire image pairs. We conduct ablation experiments using labels of $5\%$ , $10\%$ , $20\%$ , and $30\%$ of the total dataset. Fig. 8 shows that SemiMatch is consistently $\sim 4.5\%$ better than CATs in any label fraction setting on both PF-PASCAL and PF-Willow. Note that SemiMatch using $5\%$ , $10\%$ , $20\%$ , and $30\%$ of labels surpasses CATs using all labels by $0.9\%$ , $1.3\%$ , $1.2\%$ and $2.3\%$ PCK@0.1 for PF-Willow, respectively. Also, SemiMatch using $5\%$ , $10\%$ , $20\%$ , and $30\%$ of labels surpasses CATs using all labels by $0.9\%$ , $1.7\%$ , $2.2\%$ , and $2.9\%$ PCK@0.05 for PF-Willow. + +Experiments with Warm-Up stage. The fundamental problem of pseudo-labeling is that in the early stages of the training, the model is hindered by incorrect pseudolabels caused by parameter initialization, which is called confirmation bias [1]. Therefore, semi-supervised frameworks based on pseudo-labeling generally have a warm-up stage using only the labeled data. We evaluate the effect of warm-up stage results, which is 20 epochs of training with supervised loss. In experiments, there is no significant difference in performance with or without the warm-up, as shown in Table 5. It can be interpreted that our network explores the effectiveness of utilizing unlabeled data according to the model's learning status by uncertainty-based confidence measurement. + +Table 4. Ablation study of types of data augmentation. + +
Warm-upPF-PASCALPF-Willow
0.050.10.150.050.10.15
✓80.193.696.654.082.192.1
X78.993.596.853.982.392.7
+ +Table 5. Ablation study of warm-up stage. + +
Loss functionPF-PASCALPF-Willow
0.050.10.150.050.10.15
AEPE78.992.796.453.682.192.2
Contrastive80.193.696.654.082.192.1
+ +Table 6. Ablation study of loss function. + +Comparison of Distance Function. A distance function for unsupervised loss in our semi-supervised framework can be defined as either AEPE or Contrastive loss. It should be noted that, SemiMatch shows better performance than CATs, our baseline, regardless of loss formulation. We experimentally observed that using Contrastive loss performs better than using AEPE as shown in Table 6. + +# 5. Conclusion + +In this paper, we have presented a novel semi-supervised learning framework, called SemiMatch, that exploits the pixel-level pseudo-label generated by source and weakly-augmented target to learn a model again by taking source and strongly-augmented target as input. We introduce a novel confidence measure for pseudo-labels to ignore incorrect pseudo-labels and augmentation tailored for semantic matching, exploiting keypoint locations, to learn the model to integrate keypoint peripheral information. We have shown that SemiMatch achieves state-of-the-art performance over the latest methods in several benchmarks. + +Acknowledgements. This research was supported by the MSIT, Korea (IITP-2022-2020-0-01819, ICT Creative Consilience program), National Research Foundation of Korea (NRF-2021R1C1C1006897), and the Research and Development Program for Advanced Integrated Intelligence for Identification (AIID) (NRF-2018M3E3A1057288). + +# References + +[1] Eric Arazo, Diego Ortego, Paul Albert, Noel E O'Connor, and Kevin McGuinness. Pseudo-labeling and confirmation bias in deep semi-supervised learning. In 2020 International Joint Conference on Neural Networks, pages 1-8. IEEE, 2020. 2, 4, 8 +[2] Philip Bachman, Ouais Alsharif, and Doina Precup. Learning with pseudo-ensembles. Advances in neural information processing systems, 27:3365-3373, 2014. 2, 4, 5 +[3] David Berthelot, Nicholas Carlini, Ekin D Cubuk, Alex Kurakin, Kihyuk Sohn, Han Zhang, and Colin Raffel. 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Current pseudo-labeling-based SSOD methods individually learn from labeled data and unlabeled data, without considering the relation between them. To make full use of labeled data, we propose a Multi-instance Alignment model which enhances the prediction consistency based on Global Class Prototypes (MA-GCP). Specifically, we impose the consistency between pseudo ground-truths and their high-IoU candidates by minimizing the cross-entropy loss of their class distributions computed based on global class prototypes. These global class prototypes are estimated with the whole labeled dataset via the exponential moving average algorithm. To evaluate the proposed MA-GCP model, we integrate it into the state-of-the-art SSOD framework and experiments on two benchmark datasets demonstrate the effectiveness of our MA-GCP approach. + +# 1. Introduction + +With a large amount of labeled data available, deep learning has shown superior performance when solving object detection task. However, it is very costly to collect sufficient labeled data for each object category. Fortunately, there are large amounts of unlabeled data available which can be collected from social media and websites. Semi-supervised object detection (SSOD) is proposed to improve the generalization ability of object detectors with largescale unlabeled images [8, 18, 23, 28, 31]. In SSOD, we are given a labeled dataset and an unlabeled dataset. SSOD aims to learn a object detector with good generalization ability by using these labeled and unlabeled images. + +To achieve this goal, existing SSOD approaches usually adopt two strategies: consistency-based SSOD [12, 13, 30] and pseudo-labeling-based SSOD [18, 22, 26-29, 31]. Consistency-based approaches train the target detec + +tor by minimizing inconsistency between prediction results of unlabeled data with different perturbations. Their performance highly depends on the design of perturbations and the measurement of consistency. Recently, pseudolabeling-based approaches become popular. As shown in the yellow box of Figure 1, they adopt a teacher-student learning framework. Specifically, the pseudo labels of unlabeled images are first estimated by using a teacher detector followed by a label refinement module. Then, they jointly train a student detector with both labeled and unlabeled images. The detection losses of labeled and unlabeled images are used to optimize the parameters of student detector. Teacher detector's parameters are updated with the parameters of student detector via Exponential Moving Average (EMA) algorithm or pretrained with all labeled images. However, these models individually train the student detector with labeled data and unlabeled data. That is, their detection losses of labeled and unlabeled data update the student detector individually, without considering the relation between them. + +This work fully leverages the labeled images to improve SSOD by developing a Multi-instance Alignment model with Global Class Prototypes (MA-GCP). Our key insight is to better estimate prediction consistency of unlabeled images by using the reliable information learned from all labeled images. By enforcing the consistency regularization in the pseudo-labeling-based framework, our approach can improve its detection performance. + +Specifically, we assume each class is represented by a prototype in the feature space. As shown in the green box of Figure 1, each prototype is progressed with region features of the corresponding category via EMA algorithm. Since each prototype is updated with all labeled instances during the whole training process, we call it global class prototype. Then, we compute the class distributions of unlabeled images' proposals based on its visual similarity with each global class prototype. After that, we impose consistency between each pseudo ground-truth proposal and its candidate proposals with high Intersection-of-Union (IoU) scores by minimizing the cross-entropy loss of their class + +![](images/df10d34a42bbe5506aa02ece2b517a82d1651da81710616467d204e3082d3177.jpg) +Figure 1. Illustration of the proposed approach. Our approach is implemented based on a pseudo-labeling-based SSOD framework, as shown in the yellow box. It estimates the pseudo labels for unlabeled images using a teacher detector followed by a label refinement module and then jointly trains a student detector with both labeled and unlabeled images. As shown in the green box, to make full use of labeled images, we propose a multi-instance alignment model based on global class prototypes which are learned with all labeled images via EMA algorithm. The detection loss of labeled images $\mathcal{L}_{det}^s$ and unlabeled images $\mathcal{L}_{det}^u$ and multi-instance alignment loss $\mathcal{L}_{aln}^u$ are used to train the student detector, and teacher detector's parameters are updated with student detector's parameters via EMA algorithm. + +distributions. Different from previous consistency-based SSOD [2, 12, 13] which use batch-wise prototypes as references or directly compute prediction results without references, our model leverages these global class prototypes to produce more reliable consistency regularization and thus improves the detection accuracy of SSOD. + +To evaluate the performance of our MA-GCP approach, we integrate it into the state-of-the-art pseudo-labeling-based framework. Experimental results on the PASCAL VOC and MSCOCO datasets demonstrate that our approach outperforms the competing models, and thus obtains the state-of-the-art results. + +In summary, our main contributions are as follows: + +- We propose a multi-instance alignment model with global class prototypes to enhance prediction consistency of pseudo-labeling-based SSOD approaches. +- We propose to learn global class prototypes with all labeled images via the EMA algorithm and then employ them to estimate prediction consistency of unlabeled images. These global class prototypes help to estimate more reliable prediction consistency and thus benefit SSOD. +- Extensive experiments demonstrate that our MA-GCP approach has achieved a consistent improvement on two benchmark datasets and obtains the state-of-the-art results. + +# 2. Related Work + +Semi-supervised image classification (SSIC) aims to exploit a large amount of unlabeled data to improve classi + +fication accuracy [4, 11, 14, 19, 24]. Most of them adopt consistency regularization which penalizes the inconsistency of prediction results of an unlabeled image of different augmentation views [1, 9, 19, 24]. Recently, some data-augmentation methods are designed to tackle semi-supervised image classification and have shown superior performance [3, 4, 25]. This work aims to tackle a more challenging task - SSOD, where not only classification task but location task needs to be dealt with. + +Existing SSOD approaches are grouped into two categories: consistency-based approaches [12, 13, 30] and pseudo-labeling-based approaches [18, 22, 28, 29, 31]. Consistency-based approaches follow semi-supervised classification and learn from unlabeled data by enforcing the prediction consistency between unlabeled images in different augmentation views. For example, Jeong et al. imposed a prediction consistency between each unlabeled image and its horizontally flipped variant [12]. They further developed an interpolation-based SSOD (ISD) approach which produces reliable mix-up patches from two input images and maximizes the consistency between mix-up patches and original patches [13]. They combine this ISD method with previous consistency-based approach to promote the detection performance. These aforementioned approaches focus on the design of the augmentation method to improve sample diversity. Our approach not only improves spatial diversity by introducing high-IoU candidates of pseudo ground-truth proposals, but also proposes to strengthen the consistency based on reliable global class prototypes. + +Recently, pseudo labeling (or self-training) strategy becomes popular in SSOD. Sohn et al. pre-trained a teacher + +detector using labeled images and generated pseudo-labels of unlabeled images to fine-tune the target(student) detector [21]. Their pseudo-labels are generated only once and are fixed through out the rest of training. Many follow-up work propose to simultaneously update teacher detector and student detector in an end-to-end manner. Liu et al. employed EMA strategy to train a student detector and a gradually progressing teacher in a mutually-beneficial manner [18]. Tang et al. also utilized EMA to update teacher detector and proposed a data ensemble method to produce reliable pseudo labels for unlabeled images [22]. Xu et al. developed an end-to-end soft teacher mechanism where the classification loss of each unlabeled bounding box is weighed by the classification score produced by the teacher network [27]. However, these approaches individually learn from labeled and unlabeled data. To make full use of labeled data, we propose a multi-instance alignment model based on global class prototypes. By inserting the proposed alignment model into a teacher-student training framework, our approach can improve its detection accuracy. + +# 3. Method + +In this section, we first provide the formulation of SSOD and a popular teacher-student framework. Then, an overview briefly introduces the proposed model. After that, we give technical details of two key components, i.e., global class prototypes and multi-instance alignment. The overall training objective is finally provided. + +# 3.1. Preliminary: Teacher-Student Framework for Semi-Supervised Object Detection + +Before introducing SSOD approaches, we first provide the definition of SSOD. In SSOD, we are given a set of labeled images $D_{s} = \{(x_{i}^{s},y_{i}^{s})\}_{i = 1}^{N_{s}}$ and a set of unlabeled images $D_{u} = \{x_{j}^{u}\}_{j = 1}^{N_{u}}$ , where $N_{s}$ and $N_{u}$ are the total number of labeled and unlabeled images, respectively. Here, $y_{i}^{s}$ denotes the image annotation of image $x_{i}^{s}$ . The goal of SSOD is to learn a good detector with $D_{s}$ and $D_{u}$ . + +Recent attempts [18, 22, 26, 27, 29, 31] exploit teacher-student framework to address SSOD. Specifically, as shown in the yellow box of Figure 1, given an unlabeled image $\boldsymbol{x}_i^u$ , we first feed it into a weak augmentation model $\mathbf{T}_w$ and a strong augmentation module $\mathbf{T}_s$ to obtain the inputs of teacher detector $\mathbf{M}_t$ and student detector $\mathbf{M}_s$ , respectively. Then, we feed the weak augmented image $\mathbf{T}_w(\boldsymbol{x}_i^u)$ into the teacher detector $\mathbf{M}_t$ followed by a label refinement post-processing module $\mathbf{H}$ to produce pseudo labels for each unlabeled image. After that, the strong augmented image $\mathbf{T}_s(\boldsymbol{x}_i^u)$ is fed into student model $\mathbf{M}_s$ to predict detection results. A detection loss of unlabeled image $\mathcal{L}_{\text{det}}^u$ is used to minimize the differences between prediction results $\mathbf{M}_s(\mathbf{T}_s(\boldsymbol{x}_i^u))$ and pseudo labels. Simultaneously, each labeled image $\boldsymbol{x}_j^s$ is fed into student detector $\mathbf{M}_s$ to predict + +detection result and a detection loss $\mathcal{L}_{det}^{s}$ is used to minimize the difference between its prediction result and its ground-truth label. By combining the two losses together, given an unlabeled image set $D_{u}$ and a labeled image set $D_{s}$ , we compute the total loss of the teacher-student framework $\mathcal{L}_{det}^{st}$ , which is formulated in Equation (1). + +$$ +\mathcal {L} _ {d e t} ^ {s t} \left(\boldsymbol {D} _ {s}, \boldsymbol {D} _ {u}\right) = \mathcal {L} _ {d e t} ^ {s} \left(\boldsymbol {D} _ {s}\right) + \lambda_ {u} \mathcal {L} _ {d e t} ^ {u} \left(\boldsymbol {D} _ {u}\right). \tag {1} +$$ + +where $\lambda_{u}$ is a hyper-parameter to balance the detection losses of labeled and unlabeled images. During the training stage, the total loss is used to optimize the parameters of student detector and label refinement module. The teacher detector and student detector share the same network architecture. The parameters of teacher detector are pretrained by all labeled images and then fixed or slowly progressed with student detector parameters via EMA algorithm. During the test stage, the student detector is used to predict detection results of test images. + +# 3.2. Overview + +Although the teacher-student framework has achieved promising results in SSOD, it didn't consider the relations between labeled and unlabeled images. To make full use of labeled images, we propose a multi-instance alignment model which enforces the proposal-level consistency based on global class prototypes learned from all labeled images. Our MA-GCP approach benefits from the reliable global class prototypes and can learn more robust visual features for object detection. We insert our MA-GCP model into the SOTA SSOD model [27] and employ it as an additional consistency regularization for performance improvement. + +# 3.3. Global Class Prototype Learning + +In our model, we represent each class with a global prototype. These global class representations are initialized by Gaussian noise and then updated with features of ground-truth proposals via EMA algorithm. Specifically, during each training iteration, given a labeled image $\boldsymbol{x}_i^s$ , we first compute its RoI feature set of ground-truth proposals by using the RoI head of student detector. The set of RoI features is denoted by $\pmb{F}_i^{gt} = \{(f_{i,j}^{gt}, y_{i,j}^{gt})\}$ , where $f_{i,j}^{gt}$ denotes the RoI feature of $j$ -th ground-truth proposal, $y_{i,j}^{gt} \in C$ denotes its class label and $C$ denotes the set of all training object categories. After that, we average these RoI features by class and obtain a local prototype for each class: + +$$ +\boldsymbol {v} _ {k} = \left\{ \begin{array}{l l} \frac {\sum_ {i , j} \boldsymbol {f} _ {i j} ^ {g t} \mathbb {1} \left(\boldsymbol {y} _ {i , j} ^ {g t} = k\right)}{\sum_ {i , j} \mathbb {1} \left(\boldsymbol {y} _ {i , j} ^ {g t} = k\right)} & \sum_ {i} \mathbb {1} \left(\boldsymbol {y} _ {i, j} ^ {g t} = k\right) > 0, \\ \boldsymbol {0} & \sum_ {i} \mathbb {1} \left(\boldsymbol {y} _ {i, j} ^ {g t} = k\right) = 0. \end{array} \right. \tag {2} +$$ + +where $\pmb{v}_k$ denotes the local prototype of $k$ -th class in $\pmb{C}$ , $\mathbf{0}$ denotes a zero vector and $\mathbb{1}$ denotes an indicator opera + +![](images/b83da05176169dbb789e5395afd33202101274c86d1abc1bdc94b2006dd13210.jpg) +Figure 2. Illustration of the proposed multi-instance alignment model. The multi-instance alignment model takes as inputs the pseudo ground-truth proposals obtained by teacher detector and candidate proposals obtained by the student detector, and enforces their consistency by minimizing the cross-entropy loss between their class distributions based on global class prototypes. + +tor. The global class prototypes are updated with local prototypes via the EMA algorithm. The process of updating global class prototypes is formulated in Equation (3). + +$$ +\boldsymbol {g} _ {k} = \alpha \cdot \boldsymbol {g} _ {k} + (1 - \alpha) \cdot \boldsymbol {v} _ {k}. \tag {3} +$$ + +where $g_{k}$ denotes the global prototype of the $k$ -th class in $C$ . $\alpha$ is momentum parameter and empirically set to be 0.99. By doing so, we obtain a set of global class prototypes and will employ it as reference for multi-instance alignment. + +# 3.4. Multi-instance Alignment + +With these global class prototypes, we propose a multi-instance alignment model which minimizes the difference between the class distributions of pseudo ground-truth proposals and their high-IoU candidate proposals, as illustrated in Figure 2. These class distributions are computed with global class prototypes as references. Specifically, the alignment model takes as inputs the pseudo ground-truth proposals obtained by the label refinement module, RoI proposals obtained by the student detector and global class prototypes. For each pseudo ground-truth proposal $\pmb{r}_{i,j}^{pgt}$ of a given unlabeled image $\pmb{x}_i^u$ , RoI proposals with a high intersection-of-union(IoU) score are selected to construct its candidate proposal set, which is denoted by $R_{i,j}^{c} = \{r_{i,j,z}^{c}\}$ . Then, we feed these pseudo ground-truth proposals and their candidate proposal sets into the RoI head of student detector, and obtain their RoI features, which are denoted by $\{\pmb{f}_{i,j}^{pgt}\}$ and $F_{i,j}^{c} = \{\pmb{f}_{i,j,z}^{c}\}$ , respectively. Here, + +$j$ is the index of pseudo ground-truth proposals for unlabeled image $\boldsymbol{x}_i^u$ and $z$ is the index of candidate proposals of the $j$ -th pseudo ground-truth proposals. After that, we produce the class distribution of $\boldsymbol{f}_i^{pgt}$ based on a softmax over its similarities with the global class prototypes in the feature space: + +$$ +p (y = k \mid \boldsymbol {f} _ {i, j} ^ {p g t}) = \frac {\exp \left(\operatorname {s i m} \left(\boldsymbol {f} _ {i , j} ^ {p g t} , \boldsymbol {g} _ {k}\right)\right)}{\sum_ {k} \exp \left(\operatorname {s i m} \left(\boldsymbol {f} _ {i , j} ^ {p g t} , \boldsymbol {g} _ {k}\right)\right)}. \tag {4} +$$ + +where $sim$ denotes the similarity metric between RoI features and global class prototypes. Here, we empirically use cosine similarity and the diagnosis study of its form is provided in Section 4.4. In the same way, we can obtain the class distribution of candidate proposals. For each pseudo ground-truth proposal, we enforce its prediction consistency with its candidate proposals by minimizing the cross-entropy loss $\mathcal{L}_{aln}^{u}$ between their class distributions. The formulation of $\mathcal{L}_{aln}^{u}$ and the outline of computing $\mathcal{L}_{aln}^{u}$ is given in Algorithm 1. + +$$ +\mathcal {L} _ {a l n} ^ {u} = \sum_ {j} \sum_ {z} \sum_ {k \in C} - p (y = k | \boldsymbol {f} _ {i, j} ^ {p g t}) \log p (y = k | \boldsymbol {f} _ {i, j, z} ^ {c}). \tag {5} +$$ + +Note that, the proposed multi-instance alignment model is different from previous consistency-based SSOD approaches [2, 12, 13, 30] from two aspects: (1) We enforce the consistency between pseudo ground-truth proposals and their candidates with high IoU scores, rather than the same candidate proposals cropped from images and their horizontal- + +Algorithm 1 Multi-instance Alignment Loss Computation +Require: labeled dataset $D_{s} = \{(x_{i}^{s},y_{i}^{s})\}$ , unlabeled dataset $D_{u} = \{x_{i}^{u}\}$ , object category set $C$ student detector $\mathbf{M}_s$ , teacher detector $\mathbf{M}_t$ , label refinement module H. + +Ensure: Multi-instance alignment loss $\mathcal{L}_{aln}$ . +1: for each $(\pmb{x}_i^s,\pmb{y}_i^s)\in D_s$ do +2: Extract $f_{i,j}^{gt}$ of ground-truth proposals by using $\mathbf{M}_s$ +3: for $k\in C$ do +4: Compute local prototype $\pmb{v}_{k}$ according to Eq. (2); +5: Update global prototype $\pmb{g}_k$ according to Eq. (3); +6: end for +7: end for +8: for each $\pmb{x}_i^u\in D_u$ do +9: Obtain pseudo ground-truth proposals $\pmb{r}_{i,j}^{pgt}$ by using $\mathbf{M}_t$ followed by $\mathbf{H}$ +10: Obtain candidate proposal set $\pmb{R}_{i,j}^{c} = \{\pmb{r}_{i,j,z}^{c}\}$ with high IoU scores by using $\mathbf{M}_s$ +11: Compute RoI features $\pmb{f}_{i,j}^{pgt}$ of $\pmb{r}_{i,j}^{pgt}$ by using $\mathbf{M}_s$ +12: Compute RoI features $\pmb{f}_{i,j,z}^{c}$ of $\pmb{r}_{i,j,z}^{c}$ by using $\mathbf{M}_s$ +13: for $k\in C$ do +14: Compute class distributions $p(y = k|\pmb{f}_{i,j}^{pgt})$ and $p(y = k|\pmb{f}_{i,j,z}^{c})$ according to Eq. (4); +15: end for +16: Compute $\mathcal{L}_{aln}^{u}$ according to Eq. (5). +17: end for + +flipped variants [12]. In this way, we increase the diversity of input proposal pairs and thus benefits SSOD. (2) The consistency is computed based on global class prototypes learned from labeled images, while previous approaches either use batch-wise prototypes [2] or directly compute consistency without any references of labeled image [12, 13, 30], which are less reliable and suffer from class imbalance issue. + +# 3.5. The Overall Training Objective Function + +The proposed multi-instance alignment model can be flexibly incorporated with the teacher-student framework to enhance its detection performance. By combining the detection loss $\mathcal{L}_{det}^{st}$ of original detector with $\mathcal{L}_{aln}$ , the overall objective function is formulated in Equation (6). + +$$ +\mathcal {L} _ {\text {o v e r a l}} = \mathcal {L} _ {\text {d e t}} ^ {s t} + \lambda_ {a} \mathcal {L} _ {\text {a l n}} ^ {u}. \tag {6} +$$ + +where $\lambda_{a}$ denotes the weight of multi-instance alignment loss $\mathcal{L}_{aln}$ and a diagnosis study of $\lambda_{a}$ is provided in Section 4.4. + +# 4. Experimental Results and Discussion + +In this section, to evaluate the effectiveness of our approach, we conduct three groups of experiments: 1) Comparison with state-of-the-art SSOD approaches; 2) Ablation + +study to test the effectiveness of key components and select hyper-parameters; 3) Qualitative analysis. + +# 4.1. Experimental Setup + +We evaluate our approach on two benchmark datasets, i.e., PASCAL VOC [7] and MSCOCO [17] datasets. PASCAL VOC consists of 20 object categories. In SSOD, 5,011 labeled images from trainval set of VOC2007 and 11,540 unlabeled images from trainval set of VOC2012 dataset are used for training, and 4,952 images from VOC2007 test set for testing. As in [12, 13], the mean average precision (mAP) with IoU threshold 0.5 is used as the evaluation metric. MSCOCO is more challenging dataset which consists of 80 object categories. There are $118\mathrm{k}$ , $5\mathrm{k}$ , and $123\mathrm{k}$ images in its training, validation and unlabeled sets, respectively. Following [21,27], there are two data splits for SSOD: partially-labeled split and fully-labeled split. The partially-labeled split randomly selects $1\%$ , $5\%$ or $10\%$ labeled images from training set of MSCOCO as labeled dataset and the remaining images in the training set are used to construct the unlabeled dataset. The fully-labeled split is more practical, which uses the whole training set of MSCOCO as the labeled dataset and the whole unlabeled set of MSCOCO as the unlabeled dataset. In both data splits, the test set for evaluation is the validation set of MSCOCO. The mean average precision with IoU threshold ranging from 0.5 to 0.95 is used for evaluation metric as in [27]. To avoid sampling randomness in the partially-labeled split, we report averaged results over 5 data folds as in recent SSOD approaches [18, 27]. + +# 4.2. Implementation Details + +Our approach is implemented based on a recent pseudolabeling-based SSOD [27] which achieves the state-of-the-art results on benchmark datasets. The baseline detection framework is Faster RCNN [20] equipped with Pyramid Feature Network [16]. The backbone is ResNet50 [20]. For PASCAL VOC dataset, the model is trained for 60k iterations on 8 GPUs with 5 image per GPU. For each training iteration, the ratio of the number of labeled and unlabeled samples is 0.25. We train the whole model by using SGD [15] with momentum. The learning rate is initialized to 0.01 and is divided by 10 at 40k iteration and 50k iteration. The weight decay and the momentum are set to 0.0001 and 0.9, respectively. For MSCOCO dataset, We train our full model with the same learning scheme as in [27]. + +# 4.3. Comparison with State-of-the-Arts + +PASCAL VOC. Table 1 provides comparative results on the PASCAL VOC dataset. From this table, we can observe that our approach outperforms the SoftTeacher baseline and achieves state-of-the-art results. Specifically, our approach exceeds the SoftTeacher baseline over $1.40\%$ ab + +
SettingsModelsLabeled datasetUnlabeled datasetmAP(%)
Fully-SupervisedFaster RCNN+FPNVOC2007None76.30
Faster RCNN+FPNVOC2007+VOC2012None82.17
Semi-SupervisedCSD [12]VOC2007VOC201274.70
STAC [21]VOC2007VOC201277.45
ISD [13]VOC2007VOC201274.40
ISMT [29]VOC2007VOC201277.23
UGMP [26]VOC2007VOC201278.60
UnbiasedTeacher [18]VOC2007VOC201277.37
HumbleTeacher [22]VOC2007VOC201280.94
Instant-Teaching [31]VOC2007VOC201279.90
SoftTeacher* [27]VOC2007VOC201280.32
MA-GCP(Ours)VOC2007VOC201281.72
+ +Table 1. Results on Pascal VOC, evaluated on the VOC07 test set. Soft Teacher* denotes the results obtained by the official implementation of [27] with the same training scheme as ours. The mAP with IoU threshold 0.5 is used as the evaluation metric. Our approach not only outperforms competing SSOD models and achieves comparable results with fully-supervised baseline trained with all samples from both VOC2007 and VOC2012 datasets. + +
Model1% labeled samples5% labeled samples10% labeled samples
STAC [21]13.97± 0.3524.38± 0.1228.64± 0.21
ISMT [29]18.88± 0.7426.37± 0.2430.53± 0.52
Unbiased Teacher [18]20.75 ± 0.1228.27± 0.1131.50± 0.10
HumbleTeacher [22]16.96± 0.3827.70± 0.1531.61± 0.28
Instant-Teaching [31]18.05± 0.1526.75± 0.0530.40± 0.05
SoftTeacher [27]20.46± 0.3930.74± 0.0834.04± 0.14
MA-GCP(Ours)21.30± 0.2831.67± 0.1635.02± 0.26
+ +Table 2. Results on MSCOCO under the partially-labeled setting, evaluated on the MSCOCO's validation set. The $\mathrm{mAP}(\%)$ with IoU threshold ranging from 0.5 to 0.95 is used as the evaluation metric. We report averaged results over 5 data folds as in most recent SSOD approaches [21, 27]. Our approach consistently outperforms competing SSOD models under different ratios of labeled images. + +
ModelAP0.5:0.95(%)
STAC [21]39.20
ISMT [29]39.64
UnbiasedTeacher [18]41.30
HumbleTeacher [22]42.37
Instant-Teaching [31]40.20
SoftTeacher [27]44.50
MA-GCP(Ours)45.92
+ +Table 3. Results on MSCOCO under the fully-labeled setting, where the whole training set of MSCOCO is used as labeled dataset and the whole unlabeled set of MSCOCO is used unlabeled dataset. The evaluation metric is the same as that of Table 2. Our approaches yields better results than competing SSOD approaches. + +solute points in terms of mAP and outperforms the supervised baseline over $5.43\%$ absolute points. Furthermore, our approach achieves comparable results with the super + +vised baseline trained with all labeled samples from both VOC2007 and VOC2012 dataset. This demonstrates the effectiveness of our MA-GCP approach in SSOD. + +MSCOCO. Tables 2&3 provide comparative results under partially-labeled and fully-labeled settings on the MSCOCO dataset, respectively. For more challenging MSCOCO dataset, our approach still consistently outperforms competing SSOD models under both two settings. Compared with the state-of-the-art SoftTeacher, our approach yields 0.84, 0.93, and 0.98 points improvement under $1\%$ , $5\%$ and $10\%$ labeled settings, respectively. Our approach is shown to be more effective when the ratio of labeled images are larger. It can be expected – more labeled samples help to learn more reliable global class prototypes and thus lead to more benefit to SSOD. For more practical fully-labeled setting, our MA-GCP model achieves $45.92\%$ mAP, which outperforms SoftTeacher by 1.42 absolute points, which is bigger than that of partial-labeled setting. This indicates the benefit leaded by our MA-GCP + +
ModelmAP(%)
Baseline80.32
Baseline+MA(Contrast)80.53
Baseline+MA(Siamese)80.79
Baseline+MA(GCP)81.72
+ +model will not diminish when more labeled images are available. That is, our approach is suitable for practical scenarios where both large-scale labeled and unlabeled dataset are available. + +# 4.4. Ablation Studies + +Effect of Key Components. We first conduct ablation studies to validate the effectiveness of key components in our MA-GCP approach. Here, we compare our full model with three stripe-down versions: The simplest version is 'Baseline', i.e., the state-of-the-art SSOD [27]. The other two strip-down versions align the RoI features of pseudo ground-truth proposals and their high-IoU candidates by visual similarity, rather than class distributions over global class prototypes. Specifically, we follow the recent self-supervised learning approaches and develop two ways to measure their visual similarities. The first way is based on contrastive learning [5, 10], which is denoted by 'MA(Costrastive)': we feed these RoI features into a projection head $\mathbf{B}$ and then add a contrastive loss on these projected RoI features. The alignment loss formulated in Equation (5) is reformulated as follows. + +$$ +\mathcal {L} _ {C t A l n} ^ {u} = - \sum_ {j} \sum_ {z} \log \frac {\exp \left(\mathbf {B} \left(\boldsymbol {f} _ {i , j , z} ^ {c}\right) , \mathbf {B} \left(\boldsymbol {f} _ {i , j} ^ {p g t}\right)\right)}{\sum_ {k \neq j} \exp \left(\mathbf {B} \left(\boldsymbol {f} _ {i , k , z} ^ {c}\right) , \mathbf {B} \left(\boldsymbol {f} _ {i , j} ^ {p g t}\right)\right)} \tag {7} +$$ + +The second way is based on Siamese learning [6], which is denoted by 'MA(Siamese)': we first feed these RoI features into a projection head $\mathbf{B}$ and then feed the projected RoI features of candidate proposals into a predictor head $\mathbf{S}$ . We optimize the model with a new alignment loss which maximizes the cosine distance between projected RoI features of pseudo ground-truth proposals and predicted RoI features of their candidate proposals. The new alignment + +Table 4. Ablation study on contribution of key components of our model on the PASCAL VOC dataset. The evaluation metric is the same as that of Table 1. Notations: 'Baseline' – the state-of-the-art SSOD model [27]; 'MA(Costrastive)' – the multi-instance alignment model which aligns the RoI features of pseudo ground-truth proposals and their high-IoU candidates by contrastive learning; 'MA(Siamese)' – the multi-instance alignment model which aligns the RoI features of pseudo ground-truth proposals and their high-IoU candidates by Siamese learning; 'GCP' – the global class prototypes proposed in Section 3.3. The consistently improvement over Baseline shows the effectiveness of the key components proposed in our MA-GCP model. + +
ModelmAP(%)
Negative L2-Distance81.04
Cosine Similarity (ours)81.72
+ +Table 5. The diagnosis study of the different form of similarity functions. The evaluation metric is exactly same as in Table 4. Notations: 'Negative $L_{2}$ -Distance' - negative $L_{2}$ norm of differences between two inputs, which is formulated in Equation (10); 'Cosine(ours)' - cosine similarity formulated in Equation (9). + +![](images/47c7330852d3aa149bd7334c6eaa6c9f930dd7487ab1e0145782930287627050.jpg) +Figure 3. Diagnosis experiment over the hyper-parameter $\lambda_{a}$ in Equation (6). The evaluation metric is the same as in Table 4. + +loss is defined in Equation (8). + +$$ +\mathcal {L} _ {S e A l n} ^ {u} = - \sum_ {j} \sum_ {z} \cos \left(\mathbf {S} \left(\mathbf {B} \left(\boldsymbol {f} _ {i, j, z} ^ {c}\right)\right), \mathbf {B} \left(\boldsymbol {f} _ {i, j} ^ {p g t}\right)\right) \tag {8} +$$ + +In Equation (8), $\cos(\cdot, \cdot)$ denotes the cosine distance between two inputs. As in [6], the projected RoI features of pseudo ground-truth proposals $\mathbf{B}(\pmb{f}_{i,j}^{pgt})$ doesn't backpropagate the gradients. + +Table 4 provides the comparative results of these models on the PASCAL VOC dataset. From this table, we can observe that: 1) Multi-instance alignment implemented by three different ways can improve the detection accuracy of Baseline model. This indicates the proposed alignment model is effective for SSOD. 2) Our alignment based on global class prototypes achieves much better results then those based on contrastive learning or Siamese learning. These results demonstrate the superior of the proposed global class prototypes, which is one of key contributions of this work. This can be expected - the global class prototypes learned from labeled images provide reliable guidance to consistency regularization and thus lead to better detection performance. + +The Form of Similarity Function. In our experiments, we implement our similarity function as a cosine similarity between two input feature vectors, which is formulated in Equation (9). + +$$ +\operatorname {s i m} \left(\boldsymbol {f} _ {i, j} ^ {\text {p g t}}, \boldsymbol {g} ^ {k}\right) = \frac {\boldsymbol {f} _ {i , j} ^ {\text {p g t}} \left(\boldsymbol {g} ^ {k}\right) ^ {T}}{\| \boldsymbol {g} ^ {k} \| \cdot \| \boldsymbol {f} _ {i , j} ^ {\text {p g t}} \|.} \tag {9} +$$ + +![](images/c25bfb8a5010527294426e429f2a789a56e8862e8c93cd1079eb79449e698233.jpg) +Figure 4. Qualitative visualizations of the detected novel objects obtained by baseline models and our approach on the PASCAL VOC dataset. We show our model achieves much better detection result than baseline model. + +An alternative way is using the negative $L_{2}$ norm of differences between two inputs as their similarity, which is formulated as in Equation (10). + +$$ +\operatorname {s i m} \left(\boldsymbol {f} _ {i, j} ^ {p g t}, \boldsymbol {g} ^ {k}\right) = - \left\| \boldsymbol {f} _ {i, j} ^ {p g t} - \boldsymbol {g} ^ {k} \right\|. \tag {10} +$$ + +Table. 5 provides the comparative results of the alternative methods and our solution on PASCAL VOC dataset. We can observe that our method consistently outperforms the negative $L_{2}$ distance strategy. This demonstrate that our cosine similarity solution is more suitable than the negative $L_{2}$ -distance. + +The Weight of Multi-instance Alignment Loss. We conduct a diagnosis experiment over the important hyperparameter $\lambda_{a}$ in Equation (6). The results of different $\lambda_{a}$ values are illustrated in Figure 3. We can observe that we obtained the best performance when $\lambda_{a} = 0.8$ . Thus, we set $\lambda_{a}$ to be 0.8 in our experiments. + +# 4.5. Qualitative Results + +We provide qualitative visualizations of the detected results on unlabeled set and test set of PASCAL VOC in Figure 4. We show our model achieves much better detec + +tion result than baseline model, thanks to the multi-instance alignment model based on reliable global class prototypes. Moreover, we also illustrate some failure cases of our approach and discuss these failure cases in the supplementary material. We can observe that our approach struggles in detecting objects in complex backgrounds or rare views. This might be a future direction that needs to be investigated. Please be careful to apply this model in the situation where failures lead to serious adverse consequences. + +# 5. Conclusion + +In this paper, we propose to make full use of labeled images in SSOD by developing a multi-instance alignment model based on global class prototypes. The global class prototypes learned by using all labeled training images are shown to be the reliable guidance for improving SSOD. With the reliable guidance, we can enhance the consistency between prediction results of teacher detector and student detector. By inserting our MA-GCP approach into the state-of-the-art SSOD model, we obtain a strong solution for object detection. + +# References + +[1] Abulikemu Abuduweili, Xingjian Li, Humphrey Shi, ChengZhong Xu, and Dejing Dou. Adaptive consistency regularization for semi-supervised transfer learning. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR, pages 6923-6932, 2021. 2 +[2] Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Armand Joulin, Nicolas Ballas, and Michael G. Rabbat. 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A common practice is to select the highly confident predictions as the pseudo ground-truth, but it leads to a problem that most pixels may be left unused due to their unreliability. We argue that every pixel matters to the model training, even its prediction is ambiguous. Intuitively, an unreliable prediction may get confused among the top classes (i.e., those with the highest probabilities), however, it should be confident about the pixel not belonging to the remaining classes. Hence, such a pixel can be convincingly treated as a negative sample to those most unlikely categories. Based on this insight, we develop an effective pipeline to make sufficient use of unlabeled data. Concretely, we separate reliable and unreliable pixels via the entropy of predictions, push each unreliable pixel to a category-wise queue that consists of negative samples, and manage to train the model with all candidate pixels. Considering the training evolution, where the prediction becomes more and more accurate, we adaptively adjust the threshold for the reliable-unreliable partition. Experimental results on various benchmarks and training settings demonstrate the superiority of our approach over the state-of-the-art alternatives.1 + +# 1. Introduction + +Semantic segmentation is a fundamental task in the computer vision field, and has been significantly advanced along + +![](images/c3bb09ab53c2bf88208777f8f7deafb453d3b50afd39084a77f427c7a1adb235.jpg) +Figure 1. Category-wise performance and statistics on number of pixels with reliable and unreliable predictions. Model is trained using 732 labeled images on PASCAL VOC 2012 [16] and evaluated on the remaining 9,850 images. + +with the rise of deep neural networks [7,30,36,47]. Existing supervised approaches rely on large-scale annotated data, which can be too costly to acquire in practice. To alleviate this problem, many attempts [1,4,11,17,23,34,44,49] have been made towards semi-supervised semantic segmentation, which learns a model with only a few labeled samples and numerous unlabeled ones. Under such a setting, how to adequately leverage the unlabeled data becomes critical. + +A typical solution is to assign pseudo-labels to the pixels without annotations. Concretely, given an unlabeled image, prior arts [28,42] borrow predictions from the model trained on labeled data, and use the pixel-wise prediction as the "ground-truth" to in turn boost the supervised model. To mitigate the problem of confirmation bias [2], where the model may suffer from incorrect pseudo-labels, existing approaches propose to filter the predictions with their confidence scores [43, 44, 51, 52]. In other words, only the highly confident predictions are used as the pseudo-labels, while the ambiguous ones are discarded. + +However, one potential problem caused by only using reliable predictions is that some pixels may never be learned + +in the entire training process. For example, if the model cannot satisfyingly predict some certain class (e.g., chair in Fig. 1), it becomes difficult to assign accurate pseudolabels to the pixels regarding such a class, which may lead to insufficient and categorically imbalanced training. From this perspective, we argue that, to make full use of the unlabeled data, every pixel should be properly utilized. + +As discussed above, directly using the unreliable predictions as the pseudo-labels will cause the performance degradation [2]. In this paper, we propose an alternative way of Using Unreliable Pseudo-Labels. We call our framework as $\mathrm{U}^2\mathrm{PL}$ . First, we observe that, an unreliable prediction usually gets confused among only a few classes instead of all classes. Taking Fig. 2 as an instance, the pixel with white cross receives similar probabilities on class motorbike and person, but the model is pretty sure about this pixel not belonging to class car and train. Based on this observation, we reconsider the confusing pixels as the negative samples to those unlikely categories. Specifically, after getting the prediction from an unlabeled image, we employ the per-pixel entropy as the metric (see Fig. 2) to separate all pixels into two groups, i.e., a reliable one and an unreliable one. All reliable predictions are used to derive positive pseudo-labels, while the pixels with unreliable predictions are pushed into a memory bank, which is full of negative samples. To avoid all negative pseudo-labels only coming from a subset of categories, we employ a queue for each category. Such a design ensures that the number of negative samples for each class is balanced. Meanwhile, considering that the quality of pseudo-labels becomes higher along with the model gets more and more accurate, we come up with a strategy to adaptively adjust the threshold for the partition of reliable and unreliable pixels. + +We evaluate the proposed $\mathrm{U}^2\mathrm{PL}$ on PASCAL VOC 2012 [16] and Cityscapes [12] under a wide range of training settings, where our approach surpasses the state-of-the-art competitors. Furthermore, through visualizing the segmentation results, we find that our method achieves much better performance on those ambiguous regions (e.g., the border between different objects), thanks to our adequate use of the unreliable pseudo-labels. + +# 2. Related Work + +Semi-Supervised Learning has two typical paradigms: consistency regularization [3, 17, 34, 37, 43] and entropy minimization [4, 18]. Recently, a more intuitive but effective framework: self-training [28], has become the mainstream. Several methods [17, 44, 45] utilize strong data augmentation such as CutOut [15], CutMix [46], and ClassMix [32] based on self-training. However, these methods do not pay much attention to the characteristics of semantic segmentation, while our method focuses on those + +![](images/783525642c11ffd2b970f4e4ea8f62b81c3cbf25df06c6f60682d0e65e9af976.jpg) +(a) Input image with entropy map. + +![](images/d0f2d7538c8fe09cf5694d26ec70570347e65c971d89a351d3f60c5b84639f3a.jpg) +(b) Pseudo-label after filtering. + +![](images/a67f14d63cffe944914b1a18fd2e584ac26405973bca3b617702016d72512dd0.jpg) +(c) Reliable prediction (yellow cross). +Figure 2. Illustration on unreliable pseudo-labels. (a) Pixel-wise entropy predicted from an unlabeled image, where low-entropy pixels and high-entropy pixels indicate reliable and unreliable predictions, respectively. (b) Pixel-wise pseudo-labels from reliable predictions only, where pixels within the white region are not assigned a pseudo-label. (c) Category-wise probability of a reliable prediction (i.e., the yellow cross), which is confident enough for supervising the class person. (d) Category-wise probability of an unreliable prediction (i.e., the white cross), which hovers between motorbike and person, yet is confident enough of not belonging to car and train. + +![](images/c9d9a0ea0020b04dd46566abbf5dcf851577875c98a218c61bdda24093767f1f.jpg) +(d) Unreliable prediction (white cross). + +unreliable pixels which will be filtered out by most of self-training based methods [35, 44, 45]. + +Pseudo-Labeling is applied to prevent overfitting to incorrect pseudo-labels when generating predictions of input images from the teacher network [2, 28]. FixMatch [38] utilizes a confidence threshold to select reliable pseudolabels. UPS [35], a method based on FixMatch [38], takes model uncertainty and data uncertainty into consideration. However, in semi-supervised semantic segmentation, our experiments show including unreliable pixels into training can boost performance. + +Model Uncertainty in computer vision is mostly measured by Bayesian deep learning approaches [14, 25, 31]. In our settings, we do not focus on how to measure uncertainty. We simply use the entropy of pixel-wise probability distribution to be the metric. + +Contrastive Learning is applied by many successful works in self-supervised learning [9, 10, 19]. In semantic segmentation, contrastive learning has become a promising new paradigm [1, 29, 41, 48, 50]. However, these methods ignore the common false negative samples in semi-supervised + +segmentation, and unreliable pixels may be wrongly pushed away in contrastive loss. Discriminating the unlikely categories of unreliable pixels can address this problem. + +Negative Learning aims at decreasing the risk of incorrect information by lowering the probability of negative samples [26, 27, 35, 40], but those negative samples are selected with high confidence. In other words, these methods still utilizes pixels with reliable predictions. By contrast, we propose to make sufficient use of those unreliable predictions for learning instead of filtering them out. + +# 3. Method + +In this section, we establish our problem mathematically and give an overview of our proposed method in Sec. 3.1 first. Our strategies about filtering reliable pseudo-labels are introduced in Sec. 3.2. Finally, we describe how to use unreliable pseudo-labels in Sec. 3.3. + +# 3.1. Overview + +Given a labeled set $\mathcal{D}_l = \left\{(\mathbf{x}_i^l,\mathbf{y}_i^l)\right\}_{i = 1}^{N_l}$ and a much larger unlabeled set $\mathcal{D}_u = \{\mathbf{x}_i^u\}_{i = 1}^{N_u}$ , our goal is to train a semantic segmentation model by leveraging both a large amount of unlabeled data and a smaller set of labeled data. + +Fig. 3 gives an overview of $\mathrm{U}^2\mathrm{PL}$ , which follows the typical self-training framework with two models of the same architecture, named teacher and student respectively. The two models differ only when updating their weights. The student model's weights $\theta_{s}$ are updated consistent with the common practice and the teacher model's weights $\theta_{t}$ are exponential moving average (EMA) updated by the student model's weights. Each model consists of a CNN-based encoder $h$ , a decoder with a segmentation head $f$ , and a representation head $g$ . At each training step, we equally sample $B$ labeled images $\mathcal{B}_l$ and $B$ unlabeled images $\mathcal{B}_u$ . For every labeled image, our goal is to minimize the standard cross-entropy loss in Eq. (2). As for each unlabeled image, we first take it into the teacher model and get predictions. Then, based on pixel-level entropy, we ignore unreliable pixel-level pseudo-labels when computing unsupervised loss in Eq. (3). This part will be introduced in section Sec. 3.2 in detail. Finally, we use the contrastive loss to make full use of the unreliable pixels excluded in the unsupervised loss, which will be introduced in Sec. 3.3. + +Our optimization target is to minimize the overall loss, which can be formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {s} + \lambda_ {u} \mathcal {L} _ {u} + \lambda_ {c} \mathcal {L} _ {c}, \tag {1} +$$ + +where $\mathcal{L}_s$ and $\mathcal{L}_u$ represent supervised loss and unsupervised loss applied on labeled images and unlabeled images respectively, and $\mathcal{L}_c$ is the contrastive loss to make full use of unreliable pseudo-labels. $\lambda_{u}$ and $\lambda_{c}$ are weights of + +unsupervised loss and contrastive loss respectively. Both $\mathcal{L}_s$ and $\mathcal{L}_u$ are cross-entropy (CE) loss: + +$$ +\mathcal {L} _ {s} = \frac {1}{| \mathcal {B} _ {l} |} \sum_ {\left(\mathbf {x} _ {i} ^ {l}, \mathbf {y} _ {i} ^ {l}\right) \in \mathcal {B} _ {l}} \ell_ {c e} \left(f \circ h \left(\mathbf {x} _ {i} ^ {l}; \theta\right), \mathbf {y} _ {i} ^ {l}\right), \tag {2} +$$ + +$$ +\mathcal {L} _ {u} = \frac {1}{| \mathcal {B} _ {u} |} \sum_ {\mathbf {x} _ {i} ^ {u} \in \mathcal {B} _ {u}} \ell_ {c e} \left(f \circ h \left(\mathbf {x} _ {i} ^ {u}; \theta , \hat {\mathbf {y}} _ {i} ^ {u}\right), \right. \tag {3} +$$ + +where $\mathbf{y}_i^l$ represents the hand-annotated mask label for the $i$ -th labeled image, and $\hat{\mathbf{y}}_i^u$ is the pseudo-label for the $i$ -th unlabeled image. $f \circ h$ is the composition function of $h$ and $f$ , which means the images are first fed into $h$ and then $f$ to get segmentation results. $\mathcal{L}_c$ is the pixel-level InfoNCE [33] loss defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {c} = - \frac {1}{C \times M} \sum_ {c = 0} ^ {C - 1} \sum_ {i = 1} ^ {M} \\ \log \left[ \frac {e ^ {\langle \mathbf {z} _ {c i} , \mathbf {z} _ {c i} ^ {+} \rangle / \tau}}{e ^ {\langle \mathbf {z} _ {c i} , \mathbf {z} _ {c i} ^ {+} \rangle / \tau} + \sum_ {j = 1} ^ {N} e ^ {\langle \mathbf {z} _ {c i} , \mathbf {z} _ {c i j} ^ {-} \rangle / \tau}} \right], \tag {4} \\ \end{array} +$$ + +where $M$ is the total number of anchor pixels, and $\mathbf{z}_{ci}$ denotes the representation of the $i$ -th anchor of class $c$ . Each anchor pixel is followed with a positive sample and $N$ negative samples, whose representations are $\mathbf{z}_{ci}^{+}$ and $\mathbf{z}_{cij}^{-}$ respectively. Note that $\mathbf{z} = g \circ h(\mathbf{x})$ , which is the output of the representation head. $\langle \cdot, \cdot \rangle$ is the cosine similarity between features from two different pixels, whose range is limited between $-1$ to 1, hence the need of temperature $\tau$ . Following [29], $M = 50$ , $N = 256$ and $\tau = 0.5$ . + +# 3.2. Pseudo-Labeling + +To avoid overfitting incorrect pseudo-labels, we utilize entropy of every pixel's probability distribution to filter high quality pseudo-labels for further supervision. Specifically, we denote $\mathbf{p}_{ij} \in \mathbb{R}^C$ as the softmax probabilities generated by the segmentation head of the teacher model for the $i$ -th unlabeled image at pixel $j$ , where $C$ is the number of classes. Its entropy is computed by: + +$$ +\mathcal {H} \left(\mathbf {p} _ {i j}\right) = - \sum_ {c = 0} ^ {C - 1} p _ {i j} (c) \log p _ {i j} (c), \tag {5} +$$ + +where $p_{ij}(c)$ is the value of $\mathbf{p}_{ij}$ at $c$ -th dimension. + +Then, we define pixels whose entropy on top $\alpha_{t}$ as unreliable pseudo-labels at training epoch $t$ . Such unreliable pseudo-labels are not qualified for supervision. Therefore, we define the pseudo-label for the $i$ -th unlabeled image at pixel $j$ as: + +$$ +\hat {y} _ {i j} ^ {u} = \left\{ \begin{array}{l l} \arg \max _ {c} p _ {i j} (c), & \text {i f} \mathcal {H} (\mathbf {p} _ {i j}) < \gamma_ {t}, \\ \text {i g n o r e ,} & \text {o t h e r w i s e ,} \end{array} \right. \tag {6} +$$ + +![](images/068eb74d1f9cc0d604710c0e5e8846882d1a0ed240f4d3cd7a0884c6e9d20d61.jpg) +Figure 3. An overview of our proposed $\mathbf{U}^2\mathbf{PL}$ method. $\mathrm{U}^2\mathrm{PL}$ contains a student network and a teacher network, where the teacher is momentum-updated with the student. Labeled data is directly fed into the student network for supervised training. Given an unlabeled image, we first use the teacher model to make a prediction, and then separate the pixels into reliable ones and unreliable ones based on their entropy. Such a process is formulated as Eq. (6). The reliable predictions are directly used as the pseudo-labels to advise the student, while each unreliable prediction is pushed into a category-wise memory bank. Pixels in each memory bank are regarded as the negative samples to the corresponding class, which is formulated as Eq. (4). + +where $\gamma_{t}$ represents the entropy threshold at $t$ -th training step. We set $\gamma_{t}$ as the quantile corresponding to $\alpha_{t}$ to limit unreliable pixels with top $\alpha_{t}$ entropy, i.e., $\gamma_{t} = \text{np-percentile}(\text{H.flatten}), 100 * (1 - \alpha_{t}))$ , where $\text{H}$ is per-pixel entropy map. We adopt the following adjustment strategies in the pseudo-labeling process for better performance. + +Dynamic Partition Adjustment. During the training procedure, the pseudo-labels tend to be reliable gradually. Based on this intuition, we adjust unreliable pixels' proportion $\alpha_{t}$ with linear strategy every epoch: + +$$ +\alpha_ {t} = \alpha_ {0} \cdot \left(1 - \frac {t}{\text {t o t a l e p o c h}}\right), \tag {7} +$$ + +where $\alpha_0$ is the initial proportion and is set to $20\%$ , and $t$ is the current training epoch. + +Adaptive Weight Adjustment. After obtaining reliable pseudo-labels, we involve them in the unsupervised loss in Eq. (3). The weight $\lambda_{u}$ for this loss is defined as the reciprocal of the percentage of pixels with entropy smaller than threshold $\gamma_{t}$ in the current mini-batch multiplied by a base weight $\eta$ : + +$$ +\lambda_ {u} = \eta \cdot \frac {\left| \mathcal {B} _ {u} \right| \times H \times W}{\sum_ {i = 1} ^ {\left| \mathcal {B} _ {u} \right|} \sum_ {j = 1} ^ {H \times W} \mathbb {1} \left[ \hat {y} _ {i j} ^ {u} \neq \text {i g n o r e} \right]}, \tag {8} +$$ + +where $\mathbb{1}(\cdot)$ is the indicator function and $\eta$ is set to 1. + +# 3.3. Using Unreliable Pseudo-Labels + +In semi-supervised learning tasks, discarding unreliable pseudo-labels or reducing their weights is widely used to prevent degradation of model's performance [5, 6, 38, 42, + +44, 51]. We follow this intuition by filtering out unreliable pseudo-labels based on Eq. (6). + +However, such contempt for unreliable pseudo-labels may result in information loss. It is obvious that unreliable pseudo-labels can provide information for better discrimination. For example, the white cross in Fig. 2, is a typical unreliable pixel. Its distribution demonstrates model's uncertainty to distinguish between class person and class motorbike. However, this distribution also demonstrates model's certainty to not to discriminate this pixel as class car, class train, class bicycle and so on. Such characteristic gives us the main insight to propose our $\mathrm{U}^2\mathrm{PL}$ to use unreliable pseudo-labels for semi-supervised semantic segmentation. + +$\mathrm{U}^2\mathrm{PL}$ , with a goal to use the information of unreliable pseudo-labels for better discrimination, coincides with recent popular contrastive learning paradigm in distinguishing representation. But due to the lack of labeled images in semi-supervised semantic segmentation tasks, our $\mathrm{U}^2\mathrm{PL}$ is built on more complicated strategies. $\mathrm{U}^2\mathrm{PL}$ has three components, named anchor pixels, positive candidates and negative candidates. These components are obtained in a sampling manner from certain sets to alleviate huge computational cost. Next, we will introduce how to selecting: (a) anchor pixels (queries); (b) positive samples for each anchor; (c) negative samples for each anchor. + +Anchor Pixels. During training, we sample anchor pixels (queries) for each class that appears in the current mini batch. We denote the set of features of all labeled candidate anchor pixels for class $c$ as $\mathcal{A}_c^l$ , + +$$ +\mathcal {A} _ {c} ^ {l} = \left\{\mathbf {z} _ {i j} \mid y _ {i j} = c, p _ {i j} (c) > \delta_ {p} \right\}, \tag {9} +$$ + +where $y_{ij}$ is the ground-truth for the $j$ -th pixel of labeled image $i$ , and $\delta_p$ denotes the positive threshold for a particular class and is set to 0.3 following [29]. $\mathbf{z}_{ij}$ means the representation of the $j$ -th pixel of labeled image $i$ . For unlabeled data, counterpart $\mathcal{A}_c^u$ can be computed as: + +$$ +\mathcal {A} _ {c} ^ {u} = \left\{\mathbf {z} _ {i j} \mid \hat {y} _ {i j} = c, p _ {i j} (c) > \delta_ {p} \right\}. \tag {10} +$$ + +It is similar to $\mathcal{A}_c^l$ , and the only difference is that we use pseudo-label $\hat{y}_{ij}$ based on Eq. (6) rather than hand-annotated label, which implies that qualified anchor pixels are reliable, i.e., $\mathcal{H}(\mathbf{p}_{ij}) \leq \gamma_t$ . Therefore, for class $c$ , the set of all qualified anchors is + +$$ +\mathcal {A} _ {c} = \mathcal {A} _ {c} ^ {l} \cup \mathcal {A} _ {c} ^ {u}. \tag {11} +$$ + +Positive Samples. The positive sample is the same for all anchors from the same class. It is the center of all possible anchors: + +$$ +\mathbf {z} _ {c} ^ {+} = \frac {1}{| \mathcal {A} _ {c} |} \sum_ {\mathbf {z} _ {c} \in \mathcal {A} _ {c}} \mathbf {z} _ {c}. \tag {12} +$$ + +Negative Samples. We define a binary variable $n_{ij}(c)$ to identify whether the $j$ -th pixel of image $i$ is qualified to be negative samples of class $c$ . + +$$ +n _ {i j} (c) = \left\{ \begin{array}{l l} n _ {i j} ^ {l} (c), & \text {i f i m a g e i i s l a b e l e d}, \\ n _ {i j} ^ {u} (c), & \text {o t h e r w i s e}, \end{array} \right. \tag {13} +$$ + +where $n_{ij}^{l}(c)$ and $n_{ij}^{u}(c)$ are indicators of whether the $j$ -th pixel of labeled and unlabeled image $i$ is qualified to be negative samples of class $c$ respectively. + +For $i$ -th labeled image, a qualified negative sample for class $c$ should be: (a) not belonging to class $c$ ; (b) difficult to distinguish between class $c$ and its ground-truth category. Therefore, we introduce the pixel-level category order $\mathcal{O}_{ij} = \operatorname{argsort}(\mathbf{p}_{ij})$ . Obviously, we have $\mathcal{O}_{ij}(\arg \max_{i} \mathbf{p}_{ij}) = 0$ and $\mathcal{O}_{ij}(\arg \min_{i} \mathbf{p}_{ij}) = C - 1$ . + +$$ +n _ {i j} ^ {l} (c) = \mathbb {1} [ y _ {i j} \neq c ] \cdot \mathbb {1} [ 0 \leq \mathcal {O} _ {i j} (c) < r _ {l} ], \tag {14} +$$ + +where $r_l$ is the low rank threshold and is set to 3. The two indicators reflect feature (a) and (b) respectively. + +For $i$ -th unlabeled image, a qualified negative sample for class $c$ should: (a) be unreliable; (b) probably not belongs to class $c$ ; (c) not belongs to most unlikely classes. Similarly, we also use $\mathcal{O}_{ij}$ to define $n_{ij}^{u}(c)$ : + +$$ +n _ {i j} ^ {u} (c) = \mathbb {1} \left[ \mathcal {H} \left(\mathbf {p} _ {i j}\right) > \gamma_ {t} \right] \cdot \mathbb {1} \left[ r _ {l} \leq \mathcal {O} _ {i j} (c) < r _ {h} \right], \tag {15} +$$ + +where $r_h$ is the high rank threshold and is set to 20. Finally, the set of negative samples of class $c$ is + +$$ +\mathcal {N} _ {c} = \left\{\mathbf {z} _ {i j} \mid n _ {i j} (c) = 1 \right\}. \tag {16} +$$ + +Category-wise Memory Bank. Due to the long tail phenomenon of the dataset, negative candidates in some + +Algorithm 1: Using Unreliable Pseudo-Labels +1 Initialize $\mathcal{L}\gets 0$ +2 Sample labeled images $\mathcal{B}_l$ and unlabeled images $\mathcal{B}_u$ . +3 for $\mathbf{x}_i\in \mathcal{B}_l\cup \mathcal{B}_u$ do +4 Get probabilities: $\mathbf{p}_i\gets f\circ h(\mathbf{x}_i;\theta_t)$ +5 Get representations: $\mathbf{z}_i\gets g\circ h(\mathbf{x}_i;\theta_s)$ +6 for $c\gets 0$ to $C - 1$ do +7 Get anchors $\mathcal{A}_c$ based on Eq. (11); +8 Sample $M$ anchors: $\mathcal{B}_A\gets$ sample $(\mathcal{A}_c)$ +9 Get negatives $\mathcal{N}_c$ based on Eq. (16); +10 Push $\mathcal{N}_c$ into memory bank $\mathcal{Q}_c$ +11 Pop oldest ones out of $\mathcal{Q}_c$ if necessary; +12 Sample $N$ negatives: $\mathcal{B}_N\gets$ sample $(\mathcal{Q}_c)$ +13 Get $\mathbf{z}^{+}$ based on Eq. (12); +14 $\mathcal{L}\leftarrow \mathcal{L} + \ell (\mathcal{B}_A,\mathcal{B}_N,\mathbf{z}^{+})$ based on Eq. (4); +15 end +16 end Output: contrastive loss $\mathcal{L}_c\gets \frac{1}{|\mathcal{B}| \times C}\mathcal{L}$ + +particular categories are extremely limited in a mini-batch. In order to maintain a stable number of negative samples, we use category-wise memory bank $\mathcal{Q}_c$ (FIFO queue) to store the negative samples for class $c$ . + +Finally, the whole process to use unreliable pseudolabels is shown in Algorithm 1. All features of anchors are attach to gradient, come from student hence, while features of positive and negative samples are from teacher. + +# 4. Experiments + +# 4.1. Setup + +Datasets. PASCAL VOC 2012 [16] Dataset is a standard semantic segmentation benchmark with 20 semantic classes of objects and 1 class of background. The training set and the validation set include 1,464 and 1,449 images respectively. Following [11,23,44], we use SBD [20] as the augmented set with 9,118 additional training images. Since the SBD [20] dataset is coarsely annotated, PseudoSeg [51] takes only the standard 1,464 images as the whole labeled set, while other methods [11,23] take all 10,582 images as candidate labeled data. Therefore, we evaluate our method on both the classic set (1,464 candidate labeled images) and the blender set (10,582 candidate labeled images). Cityscapes [12], a dataset designed for urban scene understanding, consists of 2,975 training images with fine-annotated masks and 500 validation images. For each dataset, we compare U $^2$ PL with other methods under $1/2$ , $1/4$ , $1/8$ , and $1/16$ partition protocols. + +Network Structure. We use ResNet-101 [21] pre-trained on ImageNet [13] as the backbone and DeepLabv3+ [8] as the decoder. Both of the segmentation head and the rep + +Table 1. Comparison with state-of-the-art methods on classic PASCAL VOC 2012 val set under different partition protocols. The labeled images are selected from the original VOC train set, which consists of 1,464 samples in total. The fractions denote the percentage of labeled data used for training, followed by the actual number of images. All the images from SBD [20] are regarded as unlabeled data. "SupOnly" stands for supervised training without using any unlabeled data. $\dagger$ means we reproduce the approach. + +
Method1/16 (92)1/8 (183)1/4 (366)1/2 (732)Full (1464)
SupOnly45.7754.9265.8871.6972.50
\(MT^{\dagger}\)[39]51.7258.9363.8669.5170.96
\(CutMix^{\dagger}\)[17]52.1663.4769.4673.7376.54
PseudoSeg [51]57.6065.5069.1472.4173.23
\(PC^2Seg\) [49]57.0066.2869.7873.0574.15
\(U^2PL(w/CutMix)\)67.98 (+15.82)69.15 (+5.68)73.66 (+4.20)76.16 (+2.43)79.49 (+2.95)
+ +representation head consists of two Conv-BN-ReLU blocks, where both blocks preserve the feature map resolution and the first block halves the number of channels. The segmentation head can be seen as a pixel-level classifier, mapping the 512 dimensional features output from ASPP module into $C$ classes. The representation head maps the same features into 256 dimensional representation space. + +Evaluation. Following previous methods [17, 23, 34, 49], the images are center cropped into a fixed resolution for PASCAL VOC 2012. For Cityscapes, previous methods apply slide window evaluation, so do we. Then we adopt the mean of Intersection over Union (mIoU) as the metric to evaluate these cropped images. All results are measured on the val set on both Cityscapes [12] and PASCAL VOC 2012 [16]. Ablation studies are conducted on the blender PASCAL VOC 2012 [16] val set under $1/4$ and $1/8$ partition protocol. + +Implementation Details. For the training on the blender and classic PASCAL VOC 2012 dataset, we use stochastic gradient descent (SGD) optimizer with initial learning rate 0.001, weight decay as 0.0001, crop size as $513 \times 513$ , batch size as 16 and training epochs as 80. For the training on the Cityscapes dataset, we also use stochastic gradient descent (SGD) optimizer with initial learning rate 0.01, weight decay as 0.0005, crop size as $769 \times 769$ , batch size as 16 and training epochs as 200. In all experiments, the decoder's learning rate is ten times that of the backbone. We use the poly scheduling to decay the learning rate during the training process: $lr = lr_{\mathrm{base}} \cdot \left(1 - \frac{\mathrm{iter}}{\mathrm{total\_iter}}\right)^{0.9}$ . + +# 4.2. Comparison with Existing Alternatives + +We compare our method with following recent semi-supervised semantic segmentation methods: Mean Teacher (MT) [39], CCT [34], GCT [24], PseudoSeg [51], CutMix [17], CPS [11], $\mathrm{PC^2Seg}$ [49], AEL [23]. We re-implement MT [39], CutMix [46] for a fair comparison. For Cityscapes [12], we also reproduce CPS [11] and AEL [23]. All results are equipped with the same network architecture (DeepLabv3+ as decoder and ResNet-101 as encoder). It is + +Table 2. Comparison with state-of-the-art methods on blender PASCAL VOC 2012 val set under different partition protocols. All labeled images are selected from the augmented VOC train set, which consists of 10,582 samples in total. "SupOnly" stands for supervised training without using any unlabeled data. $\dagger$ means we reproduce the approach. + +
Method1/16 (662)1/8 (1323)1/4 (2646)1/2 (5291)
SupOnly67.8771.5575.8077.13
\( MT^{\dagger} \)[39]70.5171.5373.0276.58
\( CutMix^{\dagger} \)[17]71.6675.5177.3378.21
CCT [34]71.8673.6876.5177.40
GCT [24]70.9073.2976.6677.98
CPS [11]74.4876.4477.6878.64
AEL [23]77.2077.5778.0680.29
\( U^{2}PL(w/CutMix) \)77.21 (+5.55)79.01 (+3.50)79.30 (+1.97)80.50 (+2.29)
+ +Table 3. Comparison with state-of-the-art methods on Cityscapes val set under different partition protocols. All labeled images are selected from the Cityscapes train set, which consists of 2,975 samples in total. "SupOnly" stands for supervised training without using any unlabeled data. $\dagger$ means we reproduce the approach. + +
Method1/16 (186)1/8 (372)1/4 (744)1/2 (1488)
SupOnly65.7472.5374.4377.83
\( MT^{\dagger} \)[39]69.0372.0674.2078.15
\( CutMix^{\dagger} \)[17]67.0671.8376.3678.25
CCT [34]69.3274.1275.9978.10
GCT [24]66.7572.6676.1178.34
\( CPS^{\dagger} \)[11]69.7874.3174.5876.81
\( AEL^{\dagger} \)[23]74.4575.5577.4879.01
\( U^{2}PL(w/CutMix) \)70.30 (+3.24)74.37 (+2.54)76.47 (+0.11)79.05 (+0.80)
\( U^{2}PL(w/AEL) \)74.90 (+0.45)76.48 (+0.93)78.51 (+1.03)79.12 (+0.11)
+ +important to note the classic PASCAL VOC 2012 Dataset and blender PASCAL VOC 2012 Dataset only differ in training set. Their validation set are the same common one with 1,449 images. + +Results on classic PASCAL VOC 2012 Dataset. Tab. 1 compares our method with the other state-of-the-art methods on classic PASCAL VOC 2012 Dataset. $\mathrm{U}^2\mathrm{PL}$ outperforms the supervised baseline by $+22.21\%$ $+14.23\%$ $+7.78\%$ and $+4.47\%$ under 1/16, 1/8, 1/4 and 1/2 partition protocols respectively. For a fair comparison, we only list the methods tested on classic PASCAL VOC + +2012. Our method $\mathrm{U}^2\mathrm{PL}$ outperform $\mathrm{PC}^2\mathrm{Seg}$ under all partition protocols by $+10.98\%$ , $+2.87\%$ , $+3.88\%$ and $+3.11\%$ under 1/16, 1/8, 1/4 and 1/2 partition protocols respectively. Even under full supervision, our method outperform $\mathrm{PC}^2\mathrm{Seg}$ by $+5.34\%$ . + +Results on blender PASCAL VOC 2012 Dataset. Tab. 2 shows the comparison results on blender PASCAL VOC 2012 Dataset. Our method $\mathrm{U}^2\mathrm{PL}$ outperforms all the other methods under most partition protocols. Compared with the baseline model (trained with only supervised data), $\mathrm{U}^2\mathrm{PL}$ achieves all improvements of $+9.34\%$ $+7.46\%$ $+3.50\%$ and $+3.37\%$ under 1/16, 1/8, 1/4 and 1/2 partition protocols respectively. Compared with the existing state-of-the-art methods, $\mathrm{U}^2\mathrm{PL}$ surpasses them under all partition protocols. Especially under 1/8 protocol and 1/4 protocol, $\mathrm{U}^2\mathrm{PL}$ outperforms AEL by $+1.44\%$ and $+1.24\%$ . + +Results on Cityscapes Dataset. Tab. 3 illustrates the comparison results on the Cityscapes val set. $\mathrm{U}^2\mathrm{PL}$ achieves consistent performance gains over the supervised only baseline by $+9.16\%$ , $+3.95\%$ , $+4.08\%$ and $+1.29\%$ under 1/16, 1/8, 1/4 and 1/2 partition protocols. $\mathrm{U}^2\mathrm{PL}$ outperforms the existing state-of-the-art method by a notable margin. In particular, $\mathrm{U}^2\mathrm{PL}$ outperforms AEL by $+0.45\%$ , $+0.93\%$ , $+1.03\%$ and $+0.11\%$ under 1/16, 1/8, 1/4 and 1/2 partition protocols. + +Note that when labeled data is extremely limited, e.g., when we only have 92 labeled data, our $\mathrm{U}^2\mathrm{PL}$ outperforms previous methods by a large margin $(+10.98\%)$ under $1/16$ split for classic PASCAL VOC 2012), proofing the efficiency of using unreliable pseudo-labels. + +# 4.3. Ablation Studies + +Effectiveness of Using Unreliable Pseudo-Labels. To prove our core insight, i.e., using unreliable pseudolabels promotes semi-supervised semantic segmentation, we conduct experiments about selecting negative candidates (Sec. 3.3) with different reliability. Tab. 4 demonstrates the mIoU results on PASCAL VOC 2012 val set. "Unreliable" outperforms other options, proving using unreliable pseudo-labels does help. + +Effectiveness of Probability Rank Threshold. Sec. 3.3 proposes to use probability rank threshold to balance informativeness and confusion caused by unreliable pixels. Tab. 5 provides a verification that such balance promotes the performance. $r_l = 3$ and $r_h = 20$ outperform other options by a large margin. When $r_l = 1$ , false negative candidates would not be filtered out, causing the intra-class features of pixels incorrectly distinguished by $\mathcal{L}_c$ . When $r_l = 10$ , negative candidates tend to become irrelevant with corresponding anchor pixels in semantic, making such discrimination less informative. + +Effectiveness of Components. We conduct experiments in Tab. 6 to ablate each component of $\mathrm{U}^2\mathrm{PL}$ step by step. For + +Table 4. Ablation study on using pseudo pixels with different reliability, which is measured by the entropy of pixel-wise prediction (see Sec. 3.3). "Unreliable" denotes selecting negative candidates from pixels with top $20\%$ highest entropy scores. "Reliable" denotes the bottom $20\%$ counterpart. "All" denotes sampling regardless of entropy. + +
UnreliableReliableAll
1/8 (1323)79.0177.3077.40
1/4 (2646)79.3077.3577.57
+ +Table 5. Ablation study on the probability rank threshold, which is described in Sec. 3.3. + +
rlrh1/8 (1323)1/4 (2646)
1378.5779.03
12078.6479.07
31078.2778.91
32079.0179.30
102078.6278.94
+ +Table 6. Ablation study on the effectiveness of various components in our $\mathbf{U}^2\mathbf{PL}$ , including unsupervised loss $\mathcal{L}_u$ , contrastive loss $\mathcal{L}_c$ , category-wise memory bank $\mathcal{Q}_c$ , Dynamic Partition Adjustment (DPA), Probability Rank Threshold (PRT), and high entropy filtering (Unreliable). + +
\( \mathcal{L}_c \)\( Q_c \)DPAPRTUnreliable1/4 (2646)
73.02
✓77.08
✓✓✓✓78.49
✓✓✓✓79.07
✓✓✓✓77.57
✓✓✓✓✓79.30
+ +Table 7. Ablation study on $\alpha_0$ in Eq. (7), which controls the initial proportion between reliable and unreliable pixels. + +
α040%30%20%10%
1/8 (1323)76.7777.3479.0177.80
1/4 (2646)76.9277.3879.3077.95
+ +a fair comparison, all the ablations are under 1/4 partition protocol on blender PASCAL VOC 2012 Dataset. Above all, we use no $\mathcal{L}_c$ trained model as our baseline, achieving mIoU of $73.02\%$ (MT in Tab. 2). Simply adding $\mathcal{L}_c$ without DPA strategy improves the baseline by $+4.06\%$ . Category-wise memory bank $\mathcal{Q}_c$ , along with PRT and high entropy filtering brings an improvement by $+5.47\%$ to baseline. Dynamic Partition Adjustment (DPA) together with high entropy filtering, brings an improvement by $+6.05\%$ to baseline. Note that DPA is a linear adjustment without tuning (refer to Eq. (7)), which is simple yet efficient. For Probability Rank Threshold (PRT) component, we set corresponding parameter according to Tab. 5. Without high + +![](images/969c69d78f72162d69d3a29703565e7edfa331105e8f0a90c8b408da825a3e0f.jpg) + +![](images/8a633c2f6ccd6e64a78fc56d38b808644fc40f5bef980b10e5a9930e25348ce6.jpg) + +![](images/cb74dc90bfc3dc4e8545cd92e23a1b57706fc7e337eaa3ac809e2bd2656f26d9.jpg) + +![](images/481ed6d4558d125fa5fdc99b413aaf4319de497442a2f534a2715100bbcba38b.jpg) + +![](images/6a98af9d00e880a9ba36e70e6cb7f40519e856a29d7050325d6212623a51ace7.jpg) + +![](images/88c6c6f123d988168b6ca27e22da09bf6159b58d48e7becd736a44be364ef12a.jpg) + +![](images/c898fda02fb44f0c075e83f75d5bd547d0ffd87b9dd1fca60a5bdfe35650c3ec.jpg) + +![](images/c1f6257ed2cc6c033e52939459f55856c324c9e7606d7d6ca14a2493a609c2dd.jpg) + +![](images/303652afa68115b04fd975e60f885103a9d888781d0ab4747121c0f614f800db.jpg) + +![](images/eccb3c3d92220fa3d36c6fb0742fd372ded4420b81b7e58362da88cf76c6d146.jpg) + +![](images/1b0e4a3d3ef8729c99f7b95499819b9377bc82e2df044820fe50915a413dc115.jpg) + +![](images/72a23f13faedf8c594a7d8d4d4d9dbed4197d2fe3794d09d0a6221f7b3cc2149.jpg) + +![](images/8fcda1b9107c97f24728cb790f5e8b1e173b70192e7177f8ffabeb80843d5e95.jpg) + +![](images/ef2a8b7579df7ffaff6ff2c950c0090660052e2ae6ea313a0a4d8f8aa29cc0df.jpg) + +![](images/efa1e4a6eec31a5eb85791f799784de4c001f7a3380b20b026f0edf94b5da12d.jpg) + +![](images/46b1f4624fa2f2224474aeb18697df4d5f3635b831511de30a83753b5e5f482b.jpg) +(a) Image + +![](images/4c046b6d83ba67b2788e043324f4803c7f335203da5f9123c1bedbbdbb345492.jpg) +(b) Ground-Truth + +![](images/5c707e18ff9ab09443751029ee38900a959bb5c76ebc79619d9a15dbeee38fc4.jpg) +(c) Supervised Only +Figure 4. Qualitative results on PASCAL VOC 2012 val set. All models are trained under the $1/4$ partition protocol of blender set, which contains 2,646 labeled images and 7,396 unlabeled images. (a) Input images. (b) Hand-annotated labels for the corresponding image. (c) Only labeled images are used for training without any unlabeled data. (d) The vanilla contrastive learning framework, where all pixels are used as negative samples without entropy filtering. (e) Predictions from our $\mathrm{U}^2\mathrm{PL}$ . Yellow rectangles highlight the promotion of segmentation results by adequately using unreliable pseudo-labels. + +![](images/1f9b8d92c7b7fcb0dba7a57368046ccb86208c8ceded8805adbf8e354a89af11.jpg) +(d) Plain $\mathcal{L}_c$ + +![](images/d3bced8a0a552b724b8fbdac14dc132b73824e39ab343b5fbf851f7ed7c06080.jpg) +(e) $\mathrm{U}^2\mathrm{PL}$ + +entropy filtering, the improvement decreased significantly at $+4.55\%$ . Finally, when adding all the contribution together, our method achieves state-of-the-art result under 1/4 partition protocol with mIoU of $79.30\%$ . Following this result, we apply these components and corresponding parameters in all experiments on Tab. 2 and Tab. 1. + +Ablation Study on Hyper-parameters. We ablate following important parameter for $\mathrm{U}^2\mathrm{PL}$ . Tab. 7 studies the impact of different initial reliable-unreliable partition. This parameter $\alpha_0$ have a certain impact on performance. We find $\alpha_0 = 20\%$ achieves the best performance. Small $\alpha_0$ will introduce incorrect pseudo labels for supervision, and large $\alpha_0$ will make the information of some high-confidence samples underutilized. The studies on other hyper-parameters can be found in Supplementary Material. + +# 4.4. Qualitative Results + +Fig. 4 shows the results of different methods on the PASCAL VOC 2012 val set. Benefiting from using unreliable pseudo-labels, $\mathrm{U}^2\mathrm{PL}$ outperforms other methods. Note that using contrastive learning without filtering those unreliable pixels, sometimes does harm to the model (see row 2 and row 4 in Fig. 4), leading to worse results than those when the model is trained only by labeled data. + +Furthermore, through visualizing the segmentation re + +sults, we find that our method achieves much better performance on those ambiguous regions (e.g., the border between different objects). Such visual difference proves that our method finally makes the reliability of unreliable prediction labels stronger. + +# 5. Conclusion + +We propose a semi-supervised semantic segmentation framework $\mathrm{U}^2\mathrm{PL}$ by including unreliable pseudo-labels into training, which outperforms many existing state-of-the-art methods, suggesting our framework provide a new promising paradigm in semi-supervised learning research. Our ablation experiments prove the insight of this work is quite solid. Qualitative result gives a visual proof for its effectiveness, especially the better performance on borders between semantic objects or other ambiguous regions. + +The training of our method is time-consuming compared with fully-supervised methods [7, 8, 30, 36, 47], which is a common disadvantage for semi-supervised learning tasks [11, 22, 23, 34, 44, 49]. Due to the extreme lack of labels, the semi-supervised learning frameworks commonly need to pay a price in time for higher accuracy. + +Acknowledgment. This work is also sponsored by Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone: HZQB-KCZYZ-2021045. + +# References + +[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. Semi-supervised semantic segmentation with pixel-level contrastive learning from a class-wise memory bank. In Int. Conf. Comput. 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The unlabeled images are usually assigned pseudo labels to be used in training, which however often causes the risk of performance degradation due to the confirmation bias towards errors on the pseudo labels. We present a novel method that resolves this chronic issue of pseudo labeling. At the heart of our method lies error localization network (ELN), an auxiliary module that takes an image and its segmentation prediction as input and identifies pixels whose pseudo labels are likely to be wrong. ELN enables semi-supervised learning to be robust against inaccurate pseudo labels by disregarding label noises during training and can be naturally integrated with self-training and contrastive learning. Moreover, we introduce a new learning strategy for ELN that simulates plausible and diverse segmentation errors during training of ELN to enhance its generalization. Our method is evaluated on PASCAL VOC 2012 and Cityscapes, where it outperforms all existing methods in every evaluation setting. + +# 1. Introduction + +Recent advances in semantic segmentation have been attributed to supervised learning of deep neural networks [6, 7, 33, 37, 50] on large-scale datasets [10, 12, 15, 32]. However, collecting training data for semantic segmentation is labour-intensive and time-consuming due to the prohibitive cost of pixel-wise class labeling, which often leads to a dataset limited in terms of the number of annotated data and class diversity. To address this issue, label efficient learning, such as semi-supervised learning [3, 5, 19, 24, 26, 27, 29, 30, 35, 36], unsupervised learning [9, 46], weakly supervised learning [1, 2, 4, 11, 23, 28, 42, 48], and synthetic-to-real domain adaptation [20, 25, 31, 44, 45, 47, 53], has been proposed for semantic segmentation. + +This paper studies semi-supervised learning of semantic segmentation, which assumes that only a subset of train- + +ing images are assigned segmentation labels while the others remain unlabeled. Undoubtedly, the key to the success of this task is to utilize the unlabeled images effectively. Self-training [5, 27, 35, 49] and contrastive learning [3, 29, 51, 52] are techniques commonly used for the purpose in literature. Self-training generates pseudo labels of unlabeled images using a model trained on labeled ones, and uses them for supervised learning. Meanwhile, contrastive learning forces feature vectors corresponding to the same pseudo label to be close to each other. Although these techniques have improved the performance of semi-supervised semantic segmentation substantially, they share a common drawback: Since predictions for unlabeled images are usually corrupted by errors, learning using such predictions as supervision causes confirmation bias towards the errors and returns corrupted models consequently. Most existing methods alleviate this issue simply by not using uncertain predictions as supervision [3, 19, 29, 36], but their performance depends heavily on hand-tuned thresholds. + +A recent approach deals with errors on pseudo labels by learning and exploiting an auxiliary network that corrects the errors [27, 35]; this model, called error correction network (ECN), learns from the difference between predictions of the main segmentation network and their ground truth labels on the labeled subset of training images. Ideally, ECN can significantly improve the quality of pseudo labels, but in practice, its advantage is often limited due to the challenges in its training. Since the segmentation network is quickly overfitted to a small number of labeled images, its outputs used as input to ECN do not cover a wide variety of prediction errors that ECN faces in testing, which results in limited generalization capability of ECN. + +We present a novel method that is also dedicated to handling errors on pseudo labels yet better generalizes to those of arbitrary unlabeled images. The core of our method is the error localization network (ELN), which identifies pixels with erroneous pseudo labels in the form of binary segmentation. As will be demonstrated empirically, simply disregarding invalid pseudo labels, instead of correcting them, is sufficient to alleviate the confirmation bias and to learn accurate segmentation models. More importantly, since er + +![](images/0b3a96ab166f44a9f6526b73ac06313c83efcce3459cd5fad81bbaa6b137e8ab.jpg) +Figure 1. Our semi-supervised learning framework incorporating ELN. It employs two segmentation networks, the student $(s)$ , which will be our final model, and the teacher $(t)$ used for generating pseudo labels. The student is trained using the pseudo labels of the teacher in two different ways, self-training and contrastive learning. To be specific, the decoder has two heads, one for segmentation $(Seg)$ and the other for feature embedding $(Proj)$ ; self-training and contrastive learning are applied to outputs of the $Seg$ and $Proj$ heads, respectively. Then the teacher is updated by an exponential moving average (EMA) of the student. ELN allows both self-training and contrastive learning to be robust against noises on pseudo labels by identifying and disregarding pixels whose pseudo labels are likely to be noisy. + +ror localization is a class-agnostic subproblem of error correction and accordingly easier to solve, it is more straightforward to train an accurate and well-generalizable network for the target task. + +Moreover, we design a novel training strategy for ELN to further improve its generalization. Specifically, we attach multiple auxiliary decoders to the main segmentation network and train them to achieve different accuracy levels so that they simulate the segmentation network at different training stages. ELN is then trained to localize errors on the predictions given by the auxiliary decoders as well as the main segmentation network. This strategy improves generalization of ELN since such predictions used as input to ELN potentially exhibit error patterns that the segmentation network causes during self-training with unlabeled images. + +The trained ELN is then used for semi-supervised learning of semantic segmentation; the overall pipeline incorporating ELN is illustrated in Fig. 1. Our framework exploits unlabeled images in two ways: self-training and contrastive learning, both relying on pseudo labels. To this end, we adopt two segmentation networks: A student network, which will be our final model, and a teacher network generating pseudo labels and updated by an exponential moving average of the student. Self-training is done by learning the student using pseudo labels produced by the teacher. Meanwhile, contrastive learning encourages embedding vectors of the student and teacher to be similar if their pseudo labels are identical. ELN helps improve the effect of both + +self-training and contrastive learning by filtering out potentially erroneous pseudo labels. + +Following the convention, the proposed method is evaluated on the PASCAL VOC 2012 [12] and Cityscapes [10] datasets while varying the number of labeled training images, and it demonstrates superior performance to previous work on both of the datasets. In brief, our main contribution is three-fold. + +- We propose error localization, a new approach to dealing with errors on pseudo labels. It is simple yet effective and can be naturally incorporated with self-training and contrastive learning. Moreover, we empirically demonstrate the superiority of error localization to error correction. +- We develop a new strategy for generating diverse and plausible prediction errors intentionally during the training of ELN. This improves the generalization of ELN even using a small number of labeled data for training. +- Segmentation networks trained by our method achieves the state of the art on two benchmark datasets, PASCAL VOC 2012 and Cityscapes, in every setting. + +# 2. Related Work + +Semantic segmentation. The goal of semantic segmentation is to generate dense pixel-wise classification. Starting with FCN [21], which replaced the classifier's last fully-connected layer with a fully convolutional layer for the + +![](images/2df610cedbd2a62f8ec9630fbb8370dbede6a37fdf30e3a7c11656976406ec9c.jpg) +$\oplus$ Concatenate $\longrightarrow$ Forward/Backward $\longrightarrow$ Forward Only + +![](images/8213dbb9714eaedfe206743b81b92a80e9556bd279ab41348fd97ea6d52418ad.jpg) +Figure 2. Training ELN along with the main segmentation network and the auxiliary decoders. (left) The main segmentation network is trained with the ordinary cross-entropy loss $\mathcal{L}_{sup}$ , but the auxiliary decoders are trained with constrained cross-entropy losses $\mathcal{L}_{aux}$ so that they are inferior to the main segmentation network, and their predictions contain plausible and diverse errors intentionally. (right) All predictions from the decoders are used as training input to ELN, which learns to localize errors on the predictions. Note that ELN and other components are trained simultaneously, although their training processes are drawn separately in this figure for brevity. + +first time, various approaches have been studied early. An encoder-decoder structure has been proposed to obtain an accurate high-resolution output [37, 40], and structures such as ASPP [6] and PSPNet [50] have been exploited to obtain more diverse spatial contexts. An attention mechanism has been studied to obtain a global relation [13, 22]. However, the success of these models requires a large amount of data, which costs expensive labour. + +Semi-supervised semantic segmentation. Attempts to reduce the cost by applying a semi-supervised learning scheme have been studied intensely. Several methods [24, 30, 36] based on GAN and adversarial learning have been studied to reduce the gap between prediction on unlabeled and labeled data. One of the techniques frequently used in semi-supervised learning [14, 26, 39, 41] is consistency regularization. It allows the decision boundary to be located in a low-density region by using constraints to make the outputs of various perturbed inputs consistent with each other. Another approach [5, 27, 35, 49], self-training, is a method of generating pseudo labels with unlabeled data by pre-trained model and training the model with both labeled and pseudo labeled data. Recently, various methods [3, 29, 51, 52] have applied contrastive learning [16] to semantic segmentation in a semi-supervised manner, showing significant performance improvement. + +Self-correction networks for semi-supervised semantic segmentation. The idea of correcting pseudo labels by an auxiliary network has been studied in [27, 35]. They presented networks that correct errors of pseudo labels by learning the difference between predicted and ground truth segmentation labels. However, it is challenging to train such networks effectively in the semi-supervised learning setting + +since the segmentation network is quickly overfitted to the labeled data, leading to a poor generalization of correction networks. To address this generalization issue of the previous work, we introduce a new auxiliary task called error localization, and present ELN and its training strategy. + +# 3. Proposed Method + +Our framework consists of two-stage, learning ELN using labeled data and semi-supervised learning with ELN. The major issue in the first stage is the lack of diversity in predictions of the main network, which leads to a poor generalization of ELN. To address this issue, in addition to the main segmentation network (encoder $\mathcal{E}$ , decoder $\mathcal{D}$ ), we employ auxiliary decoders $(\mathcal{D}_{aux}^{1}, \dots, \mathcal{D}_{aux}^{K})$ that are learned to be inferior to the main segmentation network intentionally; predictions of the auxiliary decoders will depict plausible and diverse errors. ELN is learned along with the segmentation network and auxiliary decoders to identify errors on their predictions. The overall procedure of ELN training is illustrated in Fig. 2. + +In the second stage, the trained ELN is then used for semi-supervised learning of semantic segmentation, where unlabeled images are exploited in two ways, self-training, and contrastive learning. The role of ELN is to identify pixels whose pseudo labels are likely to be erroneous so that we disregard such pixels in the process of self-training and contrastive learning for stable and effective training. + +The remainder of this section presents details of the two stages of our method. + +# 3.1. Learning ELN Using Labeled Data + +At first, the main segmentation network is pre-trained with the standard pixel-wise cross-entropy loss $\mathcal{L}_{sup}$ on the set of labeled images $D_{L}$ . Let $\mathcal{L}_{ce}(P,Y)$ denote the standard pixel-wise cross-entropy between segmentation prediction $P$ and its ground truth label $Y$ : + +$$ +\mathcal {L} _ {c e} (P, Y) = - \sum_ {i} Y _ {i} ^ {\top} \log (P _ {i}), \tag {1} +$$ + +where $i$ is the index indicating each pixel of the input and $Y_{i}$ is the one-hot vector of the ground truth for pixel $i$ . Let $P = \mathcal{D}(\mathcal{E}(X))$ denote segmentation prediction of the main network for an image $X$ . $\mathcal{L}_{sup}$ is then given by + +$$ +\mathcal {L} _ {s u p} = \frac {1}{| D _ {L} |} \sum_ {X \in D _ {L}} \mathcal {L} _ {c e} (P, Y), \tag {2} +$$ + +where $Y$ is the ground truth of the input image $X$ . + +When the pre-training is completed, each auxiliary decoder is trained similarly to the main network but with a constrained cross-entropy loss, which is minimized only up to a certain multiple of $\mathcal{L}_{ce}(P,Y)$ and its gradient is not propagated beyond the auxiliary decoder. Let $K$ be the number of all auxiliary decoders and $k$ be their index. Then the total loss for the $K$ auxiliary decoders, denoted by $\mathcal{L}_{aux}$ , is given by + +$$ +\begin{array}{l} \mathcal {L} _ {a u x} = \frac {1}{| D _ {L} |} \sum_ {X \in D _ {L}} \sum_ {k = 1} ^ {K} \\ \mathbb {1} \left\{\mathcal {L} _ {c e} \left(P ^ {k}, Y\right) > \alpha^ {k} \cdot \mathcal {L} _ {c e} (P, Y) \right\} \cdot \mathcal {L} _ {c e} \left(P ^ {k}, Y\right), \tag {3} \\ \end{array} +$$ + +where $P^k = \mathcal{D}^k(\mathcal{E}(X))$ denotes segmentation prediction of the $k$ th decoder, and $\alpha^k$ indicates a scale hyper-parameter for constraining the loss applied to the $k$ th auxiliary decoder. Training the auxiliary decoders in this way enables them to produce plausibly erroneous predictions, which are used as training input to ELN. + +Given an image and its segmentation prediction as input, ELN is trained to localize errors on the prediction through supervised learning, where true locations of the errors are revealed by comparing the prediction with its ground truth counterpart. Let $E^{k}$ be the pixel-wise entropy map of $P^{k}$ and $B^{k} = \mathrm{ELN}(X\oplus P^{k}\oplus E^{k})$ denote the prediction of ELN in the form of binary segmentation map, where $\oplus$ represents channel-wise matrix concatenation. Then the binary cross-entropy loss for ELN, $\mathcal{L}_{\mathrm{ELN}}$ , is given by + +$$ +\mathcal {L} _ {\mathrm {E L N}} = \frac {1}{| D _ {L} | \cdot (K + 1)} \sum_ {X \in D _ {L}} \sum_ {k = 0} ^ {K} \mathcal {L} _ {c e} \left(B ^ {k}, M ^ {k}\right), \tag {4} +$$ + +where $M^k$ denotes the ground truth mask of $B^k$ ; $M_i^k$ is 1 if the prediction of pixel $i$ is correct and 0 otherwise. Note that $k = 0$ denotes the main decoder. + +Despite using the auxiliary decoders, the population of pixel-level binary labels in $M^k$ is typically biased to 1 (correct), which impairs the error identification ability of ELN. To alleviate this, a re-weighting factor is applied to pixels with incorrect predictions in $\mathcal{L}_{\mathrm{ELN}}$ for balanced training. Let $\mathcal{L}_{wce}$ denote a weight re-adjusted pixel-wise cross-entropy between segmentation prediction $P$ and its binary ground truth label $Y$ : + +$$ +\begin{array}{l} \mathcal {L} _ {w c e} (P, Y) = \\ - \sum_ {i} \left(\mathbb {1} \{Y _ {i} = 0 \} \frac {\sum_ {j} \mathbb {1} \{Y _ {j} = 1 \}}{\sum_ {j} \mathbb {1} \{Y _ {j} = 0 \}} Y _ {i} ^ {\top} \log (P _ {i}) \right. \\ \left. + \mathbb {1} \left\{Y _ {i} = 1 \right\} Y _ {i} ^ {\top} \log \left(P _ {i}\right)\right). \tag {5} \\ \end{array} +$$ + +Then the loss in Eq. (4) is revised as + +$$ +\mathcal {L} _ {\mathrm {E L N}} = \frac {1}{| D _ {L} | \cdot (K + 1)} \sum_ {X \in D _ {L}} \sum_ {k = 0} ^ {K} \mathcal {L} _ {w c e} \left(B ^ {k}, M ^ {k}\right). \tag {6} +$$ + +The total loss minimized in the first stage for labeled data is as follows: + +$$ +\mathcal {L} _ {\text {l a b e l e d}} = \mathcal {L} _ {\sup } + \mathcal {L} _ {\text {a u x}} + \mathcal {L} _ {\text {E L N}}. \tag {7} +$$ + +Note that losses in $\mathcal{L}_{\text{labeled}}$ are jointly optimized in the first stage, although in pre-training $\mathcal{L}_{\text{sup}}$ is solely minimized. + +# 3.2. Semi-supervised Learning with ELN + +After learning ELN, the main segmentation network is trained on the set of unlabeled images $D_U$ with two losses, a self-training loss and a pixel-wise contrastive loss. We adopt the mean teacher framework [43], which allows the teacher network to provide more stable pseudo supervision to the student network. Weights $\tilde{\theta}$ of the teacher $(\tilde{\mathcal{E}},\tilde{\mathcal{D}})$ are updated by the exponential moving average of weights $\theta$ of the student $(\mathcal{E},\mathcal{D})$ with an update ratio $\beta$ : + +$$ +\tilde {\theta} _ {t} = \beta \tilde {\theta} _ {t - 1} + (1 - \beta) \theta_ {t}. \tag {8} +$$ + +The proposed self-training loss $\mathcal{L}_{pseudo}$ is the pixelwise cross-entropy loss like $\mathcal{L}_{sup}$ , but is applied only to valid pixels identified by ELN. Let $\tilde{P} = \tilde{\mathcal{D}} (\tilde{\mathcal{E}} (X))$ denote segmentation prediction of the teacher network and $P^{a} = \mathcal{D}(\mathcal{E}(A\cdot X))$ denote that of the student network, where $A$ is the perturbation operator applied to the input image $X$ . Also, let $\tilde{B} = \mathrm{ELN}(X\oplus \tilde{P}\oplus \tilde{E})$ be the binary segmentation output of ELN. Then $\mathcal{L}_{pseudo}$ is given by + +$$ +\mathcal {L} _ {\text {p s e u d o}} = - \frac {1}{| D _ {U} |} \sum_ {X \in D _ {U}} \sum_ {i} [ \tilde {B} ] _ {i} \cdot \hat {Y} _ {i} ^ {\top} \log \left(P _ {i} ^ {a}\right), \tag {9} +$$ + +where $\lfloor \cdot \rfloor$ is a function rounding to the nearest integer and $\hat{Y}_i$ denotes the one-hot vector of the pseudo label for pixel + +$i$ . Through the rounded binary mask, the main segmentation network can be trained on valid pixels only. + +In order to further improve the quality of learned features, we adopt a pixel-wise contrastive loss $\mathcal{L}_{contra}$ . Specifically, in this loss, features whose pseudo labels are the same attract each other while those from different categories are pushed away in the feature space. Instead of applying the loss on a single image, we expand its range to the whole input batch for considering various feature relations, leading to a significant performance improvement. For a given input, let $\Omega_p^i$ denote a set of pixels belonging to the class of pixel $i$ and $\Omega_n^i$ denote a set of pixels that do not belong to the class of pixel $i$ . Also, let $\mathbf{d}$ represent a distance function, $\mathbf{d}(f_1,f_2) = \exp (\cos (f_1,f_2) / \tau)$ , where $\cos$ means the cosine similarity and $\tau$ is a temperature hyperparameter. The pixel-wise contrastive loss $\mathcal{L}_{contra}$ is then given by + +$$ +\begin{array}{l} \mathcal {L} _ {\text {c o n t r a}} = \\ - \frac {1}{| V |} \sum_ {i \in V} \sum_ {j \in \Omega_ {p} ^ {i}} \log \frac {\mathbf {d} \left(f _ {i} , \tilde {f} _ {j}\right)}{\mathbf {d} \left(f _ {i} , \tilde {f} _ {j}\right) + \sum_ {k \in \Omega_ {n} ^ {i}} \mathbf {d} \left(f _ {i} , \tilde {f} _ {k}\right)}, \tag {10} \\ \end{array} +$$ + +where $V$ denotes the set of valid pixels on $D_U$ , $f_i$ and $\tilde{f}_i$ are feature embeddings of pixel $i$ from the student and teacher networks, respectively. + +The total loss for unlabeled data is as follows: + +$$ +\mathcal {L} _ {\text {u n l a b e l e d}} = \mathcal {L} _ {\text {p s e u d o}} + \mathcal {L} _ {\text {c o n t r a}}. \tag {11} +$$ + +Note that labeled data are also involved in training through $\mathcal{L}_{\text{labeled}}$ . When training is completed, only the student network is used at inference since the others, including ELN, are all auxiliary modules that support semi-supervised learning of the student. + +# 4. Experiments + +# 4.1. Network Architecture + +We use DeepLab v3+ [8] with ResNet [18] backbone as our segmentation network since it has been adopted in recent papers [3, 29, 35] and shares a similar structure with Deeplab v2 [6], that has been widely used in literature [14, 27, 36, 38]. + +The proposed model mainly consists of two types of networks, the main segmentation network and the ELN. Each network is formed with an encoder and decoder. The encoder includes a ResNet [18] backbone, and the decoder (including the auxiliary decoders) contains sub-modules such as an atrous spatial pyramid pooling layer [6], a pixel-wise classifier for segmentation (Seg in Fig. 1), and a projector for feature embedding (Proj in Fig. 1). The last two modules are implemented by two $1 \times 1$ convolutional layers and one intermediate ReLU activation layer. + +
MethodSegNetBackbone1/201/81/4Full
CutMix [14]DL2R10166.4867.60-72.54
S4GAN+MLMT [36]DL2R10162.967.3-73.2
GCT [27]DL2R101-72.1473.6275.73
Alonso et al. [3]DL2R10167.869.9-72.6
BaselineDL3+R5059.8867.6370.5676.6
ECS [35]DL3+R50-70.2272.6076.29
Xin et al. [29]DL3+R50-72.474.076.5
Alonso et al. [3]DL3+R5069.171.8-75.9
OursDL3+R5070.5273.2074.63-
BaselineDL3+R10164.4769.5272.9578.24
CutMix [14]DL3+R10169.5772.45-76.73
Xin et al. [29]DL3+R101-74.676.378.2
OursDL3+R10172.5275.1076.58-
+ +Table 1. mIoU value in the PASCAL VOC 2012 val set with different labeled unlabeled ratios. All results of our experiments are averaged from three different subsets of the same ratio. + +
MethodSegNetBackbone1/81/41/2Full
CutMix [14]DL2R10160.3463.87-67.68
S4GAN [36]DL2R10159.361.9-65.8
Alonso et al. [3]DL2R10163.064.8-66.4
BaselineDL3+R5059.8861.8667.6377.70
ECS [35]DL3+R5067.3870.7072.8974.76
Xin et al. [29]DL3+R5069.772.7-77.5
Alonso et al. [3]DL3+R5070.071.6-74.2
OursDL3+R5070.3373.5275.33-
+ +Table 2. mIoU value in the Cityscapes val set with different labeled-unlabeled ratios. All results of our experiments are averaged from three different subsets of the same ratio. + +We adopt ResNet-50 or ResNet-101 as the backbone of the main network, and ResNet-34 for ELN. The backbones are pre-trained on ImageNet, but since the input to ELN is the concatenation of an image and tensors, its first convolutional layer is accordingly re-designed and fine-tuned. + +# 4.2. Implementation Details + +Datasets. We conduct experiments on two different datasets, PASCAL VOC 2012 [12] and Cityscapes [10]. PASCAL VOC 2012 is a standard semantic segmentation dataset consisting of 21 classes including the background class. The dataset has three separate subsets for training, validation, and testing; the subsets consist of 1464, 1449, 1456 images, respectively. Following the common practice, we use additional 9118 training images from the Segmentation Boundary (SBD) Dataset [17]. During training on PASCAL VOC 2012, we resize images to $512 \times 512$ pixels. Cityscapes [10] is a dataset of urban driving scenes with 19 classes for objects and background stuffs. It consists of training, validation, and testing splits with 2975, 500, and 1525 images, respectively. Images of the dataset is randomly cropped to $512 \times 1024$ . + +Data augmentation. Random horizontal flip is applied to both training datasets with the probability of 0.5. As the perturbation operator for the semi-supervised learning, we adopt color jittering and random grayscale with the probability of 0.2. + +Optimizer. AdamW [34] is adopted with learning rate 1e-4 and weight decay 1e-5. + +Hyper-parameters. For both labeled and unlabeled data, the size of a mini-batch is 6 on PASCAL VOC 2012 and 4 on Cityscapes. We assign 20 and 50 to the first and second auxiliary decoders, respectively. The temperature value $\tau$ of $\mathcal{L}_{\text{contra}}$ is set to 0.5. The update ratio $\beta$ is set to 0.995. + +Evaluation Metrics. We adopt the mean Intersection-over-Union (mIoU) as an evaluation metric. During evaluation, image of PASCAL VOC 2012 are resized to $512 \times 512$ and those of Cityscapes are used as-is. We conduct experiments on several proportions of labeled data to unlabeled data for validating our method under different conditions. For PASCAL VOC 2012, we use three ratios, 1/20, 1/8, and 1/4, while 1/8, 1/4, and 1/2 are used for Cityscapes. + +# 4.3. Results + +To demonstrate the superior performance of our method, we compare the method with recent state-of-the-art models and training on labeled data only (Baseline). The results of our method on PASCAL VOC 2012 are listed in Table 1. We abbreviate Deeplab v2 to DL2, Deeplab v3+ to DL3+ and ResNet-50 to R50, ResNet-101 to R101. To test the performance of our method under various conditions, we conduct experiments on three ratios (1/20, 1/8, 1/4) with ResNet-50 and ResNet-101 as a backbone network, respectively. As we can see from the table, our method achieves superior performance over all other works for both backbone networks. It is considered that our error localization concept is much more effective than error correction in the semi-supervised scheme from the comparison of results between ECS [35] and Ours. We achieve higher performance than ECS with less labeled data; note that the performance of ECS is 70.22 in the 1/8 ratio, while Ours is 70.52 in the 1/20. Moreover, we conduct experiments on Cityscapes on three ratios (1/8, 1/4, 1/2) to show the generalization capability of our method. The results are displayed in Table 2, showing that our method still outperforms other methods. Fig. 3 and 4 show qualitative results of our method under various ratio conditions. + +Performance analysis on error localization network. We further conduct additional experiments to compare our method with two similar approaches to demonstrate the effectiveness of ELN. We conduct experiments on the ratio of 1/20 to PASCAL VOC 2012 with ResNet-50 as a backbone network. As the first thing to compare, we consider a simple error correction network (s-ECN) which has a sim + +
MethodELNs-ECNThreshold
mIoU70.5267.1467.77
+ +Table 3. mIoU value of ELN, $s$ -ECN and confidence score threshold method. The experiment is conducted in a val set of PASCAL VOC 2012. + +
MethodELNs-ECNThreshold
Precision0.69610.70600.7054
Recall0.96730.82940.8783
F1 score0.78810.74240.7627
+ +Table 4. Precision, Recall, and F1 score of the ELN, $s$ -ECN, and confidence score threshold method. Reported scores are averages of all the results of each image. To compare $s$ -ECN, we only consider its error localization ability, not a correction. The experiment is conducted on the unlabeled data of the given ratio of 1/20 to PASCAL VOC 2012. + +
# of aux. decoders0123
α-2020,5020,50,100
mIoU69.8970.2070.5271.13
+ +Table 5. An ablation study for the model performance according to the number of decoders and loss constrain parameter $\alpha$ . + +ilar learning strategy as ELN; $s$ -ECN is trained with pixelwise cross-entropy loss and yields a corrected segmentation prediction as an output, not a binary mask. We choose another method, performing confidence score threshold on the output of segmentation prediction after softmax layer, without an additional network. As we can see from Table 3, ELN achieves the highest mIoU value over the other two approaches. We also conduct another experiment to understand how well each method performs error localization to unseen data. In Table 4, ELN shows the highest F1 score among methods. Note that results of $s$ -ECN are worse than Threshold; it emphasizes the limitations of the error correction scheme, implying that it does not work as intended due to its harsh training condition. In Fig. 5 and 6, we display our qualitative results of segmentation prediction and its binary mask. + +# 4.4. Ablation Studies + +We conduct ablation studies to investigate the impacts of each component of the proposed method. The experiment is based on PASCAL VOC 2012 with the ratio of 1/20, and results are averaged over three times. We use ResNet-50 as the backbone of the main segmentation network. + +Different number of auxiliary decoders. The auxiliary + +![](images/afe6518345eb81bf9e65040cff530d055d8702432b581b7ba08dab2e08f361dd.jpg) +Input Image + +![](images/16ca76896afa7bca3f119a8162921921420719161ef570d3e696ec54403cd5ee.jpg) +GT + +![](images/ee226ec2c90e491c59ced065a7e661deab176d9ddbbf5db3f102a281c9a1a8d2.jpg) +1/4 + +![](images/2954f0ba21dc618aadd6d3108a53f68f561f29d44ac560d9d7e064fc24034130.jpg) +1/8 + +![](images/41816633d341edccdb30db8a50ed5015b3cdb0cbdcd83e5e9dc9a453859210f3.jpg) +1/20 + +![](images/de550e48fc672d0afd5ce9b25f0bb2fc51d2a70117e50f1fc675890756eb36fa.jpg) +Figure 3. Qualitative results on a val set of PASCAL VOC 2012 in various proportions of labeled data to unlabeled data. +Input Image +Figure 4. Qualitative results on a val set of Cityscapes in various proportions of labeled data to unlabeled data. + +![](images/43c0a6e436c6e2505c46876072a4720105233bf4c894c993bd793b2881d1b055.jpg) +GT + +![](images/fcb2bf76851e6f6aba3ecafb6f24930b5f1cdbb648e124540e0f7fbf1a356a44.jpg) +1/2 + +![](images/0bb3d97bb0636cff9b4d8640c20b7323ae5c52f3dd86690b153507ee3246da1e.jpg) +1/4 + +![](images/d6413b6a0843a18b4fe043ab07c3993f41a5edc2a973749e020040b3e6097ba6.jpg) +1/8 + +decoder plays a critical role in ELN learning. We experiment with how the auxiliary decoders affect the overall performance by changing the number of auxiliary decoders and constraints parameters. The result is listed in Table 5. As reported from the experiments, the performance improves as the number of decoders increases and a high loss constrain value is applied. It shows that various quality of segmentation predictions helps the effective learning of the ELN. Note that we could achieve sufficient performance improvement with only two auxiliary decoders. + +Different loss combination in Eq. (11). In the semi-supervised learning stage, $\mathcal{L}_{pseudo}$ and $\mathcal{L}_{contra}$ are jointly + +
ThresholdLpseudoLcontraLpseudo + Lcontra
67.7769.1469.3070.52
+ +Table 6. An ablation study on different loss combinations in mIoU. "Threshold" in the table is the method using none of the two losses associated with ELN but applying a confidence score threshold. + +optimized. The proposed pixel-wise contrastive loss, $\mathcal{L}_{\text {contra }}$ , enables the training of feature embeddings in more diverse contexts by learning the relation between images in a batch with a standard pixel-wise cross-entropy loss + +![](images/4ba9d2c9c70e64d01db53ff84866482edba5ceb3a6c5fb4f22a1531a455786d1.jpg) +Input Image + +![](images/574e8e343e517db355d5e0e1bf7a92947559deca595bfa76fdadeb120acdf1cd.jpg) +GT + +![](images/0133510b02da2c9b31dacd5f227cb28bbbe50a161115011be3b7b75a88339696.jpg) +(a) + +![](images/4e7aec89fc5797fe2b9e0867109f28522ecc7c331edf3b863ced85a08abf0577.jpg) + +![](images/b43fdf922de2be7e11e8298878f03c122e53053dea0d1862905eda2c6fea4bf9.jpg) + +![](images/8a74ef0a28b688fa5fd09ad7e584518e5614a4edeeb632025fcf99f0ec5b2bfe.jpg) + +![](images/f832e646207ae61edbd3b5f2a3378ad5cb05cf4ec2e53af729fc9be1531fd3e5.jpg) +(b) + +![](images/2946dff99a1044d9bc21983ecc0b1af40c93be5ed642f3b2e9deaf5920bcc1cd.jpg) +(c) + +![](images/0fe01ffb89d2ed04051c57149543aaaf2ab2b8526600866ced0a692edcca4f63.jpg) +(d) + +![](images/0c884872bf954ab48a70a177d865b2316759da35934e05eb598626d29bff7233.jpg) +Figure 5. Qualitative results on unlabeled data of training set on PASCAL VOC 2012 in the labeled ratio of 1/20. (a) Segmentation prediction from the main segmentation network. (b) Ground truth binary mask. (c) Binary mask predicted by ELN. (d) Filtered segmentation prediction by the predicted binary mask. Erroneous predictions colored in white in (d) are not used as pseudo labels. +Input Image +Figure 6. Qualitative results on unlabeled data of training set on Cityscapes in the labeled ratio of 1/8. (a) Segmentation prediction from the main segmentation network. (b) Ground truth binary mask. (c) Binary mask predicted by ELN. (d) Filtered segmentation prediction by the predicted binary mask. Erroneous predictions colored in white in (d) are not used as pseudo labels. + +![](images/59abb5c7d28c9b187f7f81cb12fcbc173d6891576301b00af482dd07ec3209d5.jpg) +GT + +![](images/dc9225720b9d3702d1f9c8e82eb8790637f8aed16badf628fd94fe40c235abe0.jpg) +(a) + +![](images/ac0fab46a83e0915d3cf230dc20826d6687a66f903c189cbd81fdd3100626d64.jpg) +(b) + +![](images/1bed8b875374fc406a1e79ea487a6238d3333ff0126fac354880a731fbc4671f.jpg) +(c) + +![](images/bf9a9c984f8a7c5c545c2586c3e6ba80057ae52508836cf3a8305e1cae500978.jpg) +(d) + +$\mathcal{L}_{pseudo}$ . We make a comparison to investigate effect of each loss term in Eq. (11). As shown in Table 6, each term contributes to the performance, and using both of them improves the most. + +# 5. Conclusion + +We have presented a novel training framework suitable for semi-supervised semantic segmentation tasks. To mitigate the performance degradation caused by confirmation bias due to invalid pseudo labels, we have proposed error localization network (ELN) and its training scheme. Our experiments validated that ELN effectively removes error of pseudo labels for unseen data, which demonstrate that our + +learning strategy using erroneous predictions simulated by auxiliary decoders is helpful. Our method achieved the state of the art on both of the PASCAL VOC 2012 and Cityscapes datasets with high generalization capability. + +limitations. Due to the additional auxiliary networks, our method needs a relatively larger amount of GPU memory during training, and as the number of auxiliary decoders increases, larger memory footprint is required. ELN sometimes failed to indicate erroneous predictions that the main segmentation network has strong confidence (i.e., low-entropy). + +Acknowledgement. This work was supported by Samsung Electronics Co., Ltd (IO201210-07948-01). + +# References + +[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019. 1 +[2] Jiwoon Ahn and Suha Kwak. Learning pixel-level semantic affinity with image-level supervision for weakly supervised semantic segmentation. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018. 1 +[3] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. Semi-supervised semantic segmentation with pixel-level contrastive learning from a class-wise memory bank. In Proc. IEEE International Conference on Computer Vision (ICCV), 2021. 1, 3, 5 +[4] Liyi Chen, Weiwei Wu, Chenchen Fu, Xiao Han, and Yuntao Zhang. Weakly supervised semantic segmentation with boundary exploration. In Proc. 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Most previous works focus on Video Sentence Grounding (VSG), which localizes the moment with a sentence query. Recently, researchers extended this task to Video Paragraph Grounding (VPG) by retrieving multiple events with a paragraph. However, we find the existing VPG methods may not perform well on context modeling and highly rely on video-paragraph annotations. To tackle this problem, we propose a novel VPG method termed Semi-supervised Video-Paragraph Transformer (SVPTR), which can more effectively exploit contextual information in paragraphs and significantly reduce the dependency on annotated data. Our SVPTR method consists of two key components: (1) a base model VPTR that learns the videoparagraph alignment with contrastive encoders and tackles the lack of sentence-level contextual interactions and (2) a semi-supervised learning framework with multimodal feature perturbations that reduces the requirements of annotated training data. We evaluate our model on three widely-used video grounding datasets, i.e., ActivityNet-Caption, Charades-CD-OOD, and TACoS. The experimental results show that our SVPTR method establishes the new state-of-the-art performance on all datasets. Even under the conditions of fewer annotations, it can also achieve competitive results compared with recent VPG methods. + +# 1. Introduction + +Localizing events in a given untrimmed video is one of the challenging video understanding tasks, which is first proposed by [1, 7]. Following their works, a list of promising methods [16, 20, 45-47, 50] has been proposed. However, most existing methods focus on Video Sentence Grounding (VSG), addressing this problem in "single-multi" approaches (as shown in Fig. 1(a)), they ground a moment from a video that consists of several dif + +![](images/4712edf96d72e17f2ee6564cb573d34625c4663efd4a470f82e7a7a060567908.jpg) +(a) Video Sentence Grounding + +# Paragraph: + +① Two young girls are standing in the kitchen preparing to cook. +They then open a box of brownies...get an egg out of the fridge. +After, the two continue to stir the contents ... placing them on a pan. +④ Once the cookies are ... watch the cookies bake. +⑤ When they are done, they ... begin eating. + +![](images/35bf027aac6eb8b8eb08832895018ba2034384d8ac3159602a02e51ce4260073.jpg) + +![](images/e1ee7167c8ff06c0698678c1217a207e50806f8fec0f99a34e4dd36f803b9614.jpg) +Figure 1. An illustrative example of VSG and VPG: (a) VSG aims at retrieving a particular moment with a single sentence. (b) VPG receives a paragraph consisting of multiple sentences as a query and localizes multiple events in the untrimmed video. + +ferent events according to an individual sentence query. Contrastively, as illustrated in Fig. 1(b), Video Paragraph Grounding (VPG), which is recently proposed by [2], addresses the video events grounding task in the "multi-multi" manner. Specifically, in the VPG task, given a paragraph describing multiple events instead of a single sentence, it is expected to localize all of the related moments in an untrimmed video. Since a paragraph consisting of multiple sentences in time order contains more temporal information compared with the single sentence input, it is more informative for retrieving moments in videos. + +The previous VPG methods [2,6,50] first generate proposals for each sentence, then learn temporal order and semantic relations among these proposals to select desired candidates. Nevertheless, these methods exist three problems. Firstly, they rely on the temporal information of paragraphs but hardly exploit the contextual information well from the perspective of text modality. For example, shown in Fig. 1(b), all the sentences in the paragraph are describ- + +ing two girls cooking in the kitchen and each of the sentences is related to others contextually around the cooking topic. Recently, the informal work [30] tried to tackle VPG with Transformer [34], which proved the global contexts worked in this task. However, these methods including [30] still fall into the second defect: with the paragraph input, they only focus on the proposal-sentence matching but ignore the video-paragraph matching, which may lead to misalignment on cross-modal fusion. Lastly, compared with moment-sentence annotation, the video-paragraph annotated data are more expensive and hard to generate. All these VPG methods are required to be trained with temporal labeled data, which brings heavy costs to this task. Although there are also some weakly-supervised video grounding methods [5, 19, 43], most of them are "single-multi" methods and the performance is much worse than fully-supervised methods. + +To tackle these problems, we first propose a novel base model termed Video-Paragraph Transformer (VPTR), which introduces contrastive learning and semi-supervised learning into VPG. We further extend it to the semi-supervised version, the Semi-supervised Video-Paragraph Transformer (SVPTR), to reduce the dependency on temporal annotations. Specifically, as the general framework of our proposed SVPTR method shown in Fig. 2, to explore the contextual information hidden in paragraphs, we extract hierarchical text features and design a sentence-based query mechanism in the decoder. The individual sentence queries interact with particular words and other sentences with such designs thus we can extract more contextual information. Moreover, to avoid misalignment between proposal moments and sentences, contrastive learning is introduced into the multimodal encoder to guide the cross-modal fusion at the video-paragraph level. As is shown in Fig. 2, the contrastive encoder separately encodes the two modalities and projects them into a common space via self-supervised learning. Finally, we develop an advanced semi-supervised learning VPG method SVPTR that is based on the teacher-student framework, which effectively reduces the consumption of video-paragraph temporal annotations. + +The primary contributions in this work are as follows: + +- We explore contextual information in the paragraph query with hierarchical text features and the sentence-based query mechanism. It effectively improves the precision of localizing events in untrimmed videos. +- We combine self-supervised learning to optimize the cross-modal fusion in video paragraph grounding. Particularly, we design a contrastive loss at the videoparagraph level without proposing moment candidates. +- We design a semi-supervised learning framework for VPG and achieve promising results with less annotated + +data. To the best of our knowledge, we are the first to explore the semi-supervised learning on video paragraph grounding. + +To evaluate the proposed SVPTR method, we conduct extensive experiments on three widely-used datasets: ActivityNet-Caption [12], Charades-CD-OOD [44], and TACoS [27]. The comprehensive results demonstrate the superiority of our SVPTR method compared with a handful of state-of-the-art VPG approaches under both fully-supervised and semi-supervised settings. + +# 2. Related Work + +Video Sentence Grounding. Video Sentence Grounding (VSG) is first proposed by [1,7], which determines the start and end time points of a single event by a query sentence. Early works in VSG [1, 7, 8, 45, 48, 50] adopt a two-stage model that first generates proposal candidates then models these video segments and sentence queries jointly. Meanwhile, a part of VSG methods [15, 20, 22, 47] follow the proposal-free model and treat the VSG as a regression task that predicts the timestamps directly. Recently, researchers [16, 39, 49, 51] are studying new frameworks to localize the target events. Notably, Zhang et al. [49] introduced Transformer [34] into VSG to improve the quality of cross-modal modeling, which proved its effectiveness for video grounding task. Additionally, there are also weakly-supervised methods [5, 19, 43] tackling the VSG problem from the perspective of overcoming the costs of temporal annotations. Since the lack of location information, these methods usually perform much worse than popular fully-supervised methods. Recently, an informal work [18] proposed a novel VSG framework that achieves a trade-off between annotation costs and performance with semi-supervised learning. Nevertheless, most of these methods above are limited in single event grounding and not suitable for localizing multiple events at the same time. + +Video Paragraph Grounding. Different from VSG, Video Paragraph Grounding (VPG) treats video events grounding as a "multi-multi" problem. Specifically, the natural language query in VPG is a long paragraph, which describes multiple events in the untrimmed video. The VPG is first defined by Bao et al. [2] as the inverse problem of the Dense Video Caption [35]. In this initial work [2] for VPG, they first extended two previous methods [6, 50] to baselines, then designed a novel VPG model DepNet. Following that, a recent informal work [30] proposed a method that utilized Transformer [34] to tackle this task. Although these methods above have achieved promising improvement compared with conventional VSG methods, they ignore crucial contextual information hidden in paragraphs or the high costs of annotations caused by paragraph input, which motivates us to develop this work. + +![](images/70a067cf88d3ef0cc8699eb15d55d308bde5b43cc06bdf06e5fb687275c5fa70.jpg) +Figure 2. An overview of our SVPTR method. The first part on the top shows the semi-supervised framework of our method, which maintains a teacher model and a student model. Two models receive different inputs via multimodal feature perturbations. We update the teacher model with Exponential Moving Average (EMA) instead of backpropagation. The second part in the yellow box illustrates the details of the proposed base model VPTR. + +Semi-supervised Learning. Semi-supervised Learning (SSL) is a class of dominant methods in machine learning to learn from limited labeled data and massive unlabeled data. In general, it can be roughly categorized into two types: pseudo label generation and consistency regularization. The former [14, 25, 40] usually make predictions from a model trained on labeled data to impute approximate labels for unlabeled data, while the latter [13, 31] encourage models to reduce the discrepancy between predictions made perturbed data points. Recently, some works [10, 18, 37] introduced semi-supervised learning into video understanding task. Ji et al. [10] designed two sequential perturbations based on the mean teacher framework. Wang et al. [37] combined self-supervised learning and SSL to reduce the reliance on labeled data for Temporal Action Proposal. Meanwhile, Luo et al. [18] recently explored the SSL in VSG, which is the most related to our work. + +# 3. Proposed Method + +# 3.1. Problem Formulation + +Given an untrimmed video $\mathrm{V}$ and a paragraph $\mathrm{P}$ consisting of $\mathbf{K}$ sentences, our goal is to localize timestamps of $\mathbf{K}$ events in the video which are most related to these sentences respectively. Specifically, we represent the untrimmed video $\mathrm{V}$ as $\mathrm{V} = \{\mathrm{v}_i\}_{i=1}^{l^{\mathrm{V}}}$ , where $l^{\mathrm{V}}$ is the frame number of $\mathrm{V}$ . The paragraph $\mathrm{P}$ is presented as $\mathrm{P} = \{\mathrm{S}_i\}_{i=1}^{\mathrm{K}}$ where $\mathrm{S}_i$ denotes $i$ -th sentence in the paragraph. Let $t_{\mathrm{s}}$ and $t_{\mathrm{e}}$ be the start time and end time of one target video segment re + +spectively, the VPG task can be formulated as follows: + +$$ +\mathrm {M} _ {\mathrm {V P G}} (\mathrm {V}, \mathrm {P}) \rightarrow \left\{\left(t _ {\mathrm {s}}, t _ {\mathrm {e}}\right) _ {i} \right\} _ {i = 1} ^ {\mathrm {K}}, \quad t _ {\mathrm {s}} < t _ {\mathrm {e}}, \tag {1} +$$ + +where $(t_{\mathrm{s}}, t_{\mathrm{e}})_i$ is the retrieved result for $i$ -th sentence in P. + +# 3.2. Video-Paragraph TRansformer + +Depicted in Fig. 2, we first propose a base model VPTR, which tackles the problems of learning contextual information and aligning the two modalities. + +Video Modality. Given an untrimmed video V with $l^{\mathrm{V}}$ frames, we divide them into a group of small clips without overlap and each clip contains the same constant number of frames. Afterward, we extract visual features with pre-trained C3D backbones [32], where $l^{F}$ denotes the total length of video features. Let $m_{v}(\cdot)$ be the 3D CNN backbone and $\phi_v(\cdot)$ be the projecting layer with normalization, the video feature extraction can be expressed as $\mathbf{F}_v = \phi_v(m_v(V)) = \{\mathbf{f}_i\}_{i=1}^{l^F}$ . + +Text Modality. Most existing works in VSG [15, 16, 51] denote the query into a group of word-level features. However, in VPG, we receive multiple sentences from the paragraph query, where each sentence contains different semantics. To this end, we hierarchically extract the text features from paragraph input. Specifically, we first extract the word-level features from the whole paragraph to learn global semantics. Following that, we extract the sentence-level features from each sentence individually. Given a paragraph query $\mathrm{P} = \{\mathrm{S}_i\}_{i=1}^{l^{\mathrm{S}}} = \{\mathrm{W}_j\}_{j=1}^{l^{\mathrm{W}}}$ , we use 2-layer bidirectional GRUs to obtain the word-level features + +$\mathbf{F}_w = \{\mathbf{w}_j\}_{j=1}^{l^{\mathrm{W}}}$ , where $l^{\mathrm{S}}$ , $l^{\mathrm{W}}$ denote the number of sentences and words in the paragraph respectively and $w_j$ denote $j$ -th word features. Moreover, we split the paragraph into sentences and each sentence is encoded by the GRUs individually. The sentence-level feature of $i$ -th sentence in the paragraph is obtained by the concatenation of hidden states in both directions, which is denoted as $\mathbf{s}_i$ . Hence, we obtain the sentence-level features of the whole paragraph $\mathbf{F}_s = \{\mathbf{s}_i\}_{i=1}^s$ . Formally, the language feature extraction can be represented as following: + +$$ +\left\{ \begin{array}{l} \mathbf {s} _ {i} = \operatorname {B i G R U} \left(\mathbf {w} _ {k} ^ {i}, h _ {k - 1} ^ {i}\right), \\ \mathbf {w} _ {j} = \operatorname {B i G R U} \left(\mathbf {w} _ {j}, h _ {j - 1}\right), \end{array} \right. \tag {2} +$$ + +where $\mathbf{w}_k^i$ represents the $k$ -th word in $i$ -th sentence and the $h$ is the hidden state of GRUs. Afterward, the word-level features $\mathbf{F}_w$ are processed by a projecting layer with normalization $\phi_w(\cdot)$ , which is similar to video modality. + +Contrastive Encoder. Inspired by the success of multimodal Transformer [33], the recent work [49] introduces it into VSG and achieves competitive results. However, we observed that the mixed input of encoders results in degeneration of learning intra-modality information. To maintain the intra-modality modeling and obtain inter-modality aligning for VPG, we design a contrastive encoder, learning the semantic consistency [42] via self-supervision. As illustrated in Fig. 3(a), our contrastive encoder projects the video features $\mathbf{F}_v$ and word-level text features $\mathbf{F}_w$ into a common subspace for semantic alignment [41]. The objective of our contrastive encoder is to pull the positive video and paragraph pairs together and push the negative pairs away. Specifically, as depicted in Fig. 2, we apply the transformer encoder [3] $\Phi (\cdot)$ and normalization layer Norm to acquire the transferred video feature $\tilde{\mathbf{F}}_v = \mathrm{Norm}(\Phi (F_v))$ and text features $\tilde{\mathbf{F}}_w = \mathrm{Norm}(\Phi (\mathbf{F}_w))$ . Additionally, we construct a triplet tuple $\left(\tilde{\mathbf{F}}_v^+, \tilde{\mathbf{F}}_w^+, \tilde{\mathbf{F}}_w^-\right)$ , where $\left(\tilde{\mathbf{F}}_v^+, \tilde{\mathbf{F}}_w^+\right)$ is a positive pair and $\left(\tilde{\mathbf{F}}_v^+, \tilde{\mathbf{F}}_w^-\right)$ a negative pair, for our contrastive learning. Let $\mathcal{T}_{\mathrm{v}}$ and $\mathcal{T}_{\mathrm{w}}$ represent triplet tuples $\left(\tilde{\mathbf{F}}_v^+, \tilde{\mathbf{F}}_w^+, \tilde{\mathbf{F}}_w^-\right)$ and $\left(\tilde{\mathbf{F}}_w^+, \tilde{\mathbf{F}}_v^+, \tilde{\mathbf{F}}_v^-\right)$ respectively, the contrastive loss can be expressed as: + +$$ +\mathcal {L} _ {C T} = \sum_ {\left(\tilde {\mathbf {F}} _ {v} ^ {+}, \tilde {\mathbf {F}} _ {w} ^ {+}\right)} \left\{\sum_ {\tilde {\mathbf {F}} _ {w} ^ {-}} \mathcal {L} _ {T} \left(\mathcal {T} _ {\mathrm {v}}\right) + \sum_ {\tilde {\mathbf {F}} _ {v} ^ {-}} \mathcal {L} _ {T} \left(\mathcal {T} _ {\mathrm {w}}\right) \right\}, \tag {3} +$$ + +where $\mathcal{L}_T(\cdot)$ [19] ensures the positive pair's similarity score is better than the negative pair's by at least a margin. Meanwhile, we concatenate the encoded features of video and paragraph together, which are used as the memory of decoder. Let $[\cdot ;]$ denote the concatenating operation, we obtain the multimodal memory $\mathbf{F}_{\mathrm{mem}} = [\mathbf{F}_v;\mathbf{F}_w]$ . + +Sentence-based Decoder. In previous work [2], multiple sentences brought more temporal information, however, the + +![](images/68e71569ab5e54bfd0a5e6bd8e6632cb43033991f6c624270ccda207dce678f0.jpg) +(a) An illustration of Contrastive Encoder + +![](images/de12259eb974e13aff92dc36f53fe2cd9f67704c49c482b5985f8201780d22cb.jpg) +(b) Sentence-level Context Modeling +Figure 3. A detailed illustration for VPTR. (a) The contrastive encoder projects multimodal pairs with similar semantics closer. The circles and triangles represent text features and video features respectively. (b) The sentence-based decoder maintains sentence-level temporal and contextual information. The thickness of lines represents the strength of contextual connection. + +contextual information among these sentences was mined insufficiently. To overcome this defect, our decoder receives sentence-level features from the paragraph query rather than learnable embeddings. As depicted in Fig. 3(b), this mechanism conducts the sentence-level context modeling, turning each sentence gets related temporally and contextually. Concretely, given the sentence-level features $\mathbf{F}_s = \{\mathbf{s}_i\}_{i=1}^{l^S}$ , we first use the position embedding layer to encode temporal information, and then the interactions among sentences are conducted by the self-attention layers. Following that, each sentence query generates a feature for describing events from the multimodal memory via cross-attention layers. With the hierarchical text features, the sentence-level features can also interact with particular words, allowing the decoder to learn more contextual information. Finally, a parallel regression layer is employed to compute the timestamps of each sentence-wise feature. The procedures of sentence-based decoder are formulated as follows: + +$$ +\mathbf {T} = \operatorname {M L P} \left(\Psi \left(\mathbf {F} _ {\text {m e m}}, \mathbf {F} _ {s}\right)\right), \tag {4} +$$ + +where the $\Psi (\cdot)$ represents the decoders of transformer which conduct the position embedding on sentence level. $\mathbf{T}$ is the localizing results consisting of $l^S$ valid timestamps. + +# 3.3. Semi-supervised VPTR + +Based on the teacher-student framework, we extend our VPTR to Semi-supervised VPTR (SVPTR), which consists of two base models and a multimodal feature perturbation module. With such a semi-supervised learning pipeline, we significantly reduce the consumption of annotated data. + +Feature Perturbations. In previous works on semi-supervised learning [31, 37], stochastic perturbations have been found effective for improving the robustness of models. Moreover, the perturbations can also be regarded as data augmentation that helps self-supervised learning. Illustrated in Fig. 2, we conduct the feature perturbations both on two modalities. For video modality, we follow [37] and employ the random temporal shift as our video perturbation module. Concretely, we randomly choose $\mu$ channels first, then $\mu /2$ feature channels are moved forward and the other $\mu /2$ channels are moved backward. Different from the conventional temporal shift, the random selection brings more diversity into the perturbation, which augments the video modality features for semi-supervised learning and self-supervised learning. As for text modality, inspired by BERT [4], we randomly mask a part of words from the whole paragraph. Furthermore, we also apply dropout strategy with probability hyperparameter $\lambda$ on both modalities. Mean Teacher Framework. Mean Teacher [31] is a semi-supervised learning method based on consistency regularization. As illustrated in Fig. 2, two base models are maintained: a student VPTR model $\Gamma$ and the teacher VPTR model $\Gamma^{\prime}$ . The student model $\Gamma$ learns from the annotated data, and the Contrastive Encoder also allows us to train it with self-supervised learning. The teacher model $\Gamma^{\prime}$ is a duplicate of the student model, whose weights are updated with a sequence of student models during training via the Exponential Moving Average (EMA) strategy. Specifically, the Mean Teacher Framework can be formulated as follow: + +$$ +\Gamma_ {t} ^ {\prime} = \tau \Gamma_ {t - 1} ^ {\prime} + (1 - \tau) \Gamma_ {t}, \tag {5} +$$ + +where $t$ , $\tau$ denote the number of training iterations and smoothing coefficient respectively. + +The input of each iteration consists of labeled and unlabeled data. During the training, the student VPTR receives input from the feature perturbation module and predicts the timestamps, while the teacher VPTR is fed by the original data to get predictions. Using the predictions from the two models, we compute a consistency loss, which induces our model to learn from labeled and unlabeled data jointly: + +$$ +\mathcal {L} _ {\mathrm {C S}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left\| \Gamma (X) _ {i} - \Gamma^ {\prime} \left(X ^ {\prime}\right) _ {i} \right\| ^ {2}, \tag {6} +$$ + +where $X$ and $X'$ represent agumented features and original features respectively, and $N$ denotes the total number of events in each input. + +# 3.4. Objective Function + +The loss function of the proposed SVPTR method consists of three parts: supervised loss, contrastive loss and consistency loss. We represent the overall loss as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \alpha \mathcal {L} _ {\mathrm {S P}} + \beta \mathcal {L} _ {\mathrm {C T}} + \gamma \mathcal {L} _ {\mathrm {C S}}. \tag {7} +$$ + +The supervised loss guides our model to learn location information from the annotated data. Concretely, for total $N$ events, we denote the supervised loss as follows: + +$$ +\mathcal {L} _ {\mathrm {S P}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left(\left\| T _ {i} - \hat {T} _ {i} \right\| _ {1} + \mathcal {L} _ {\mathrm {i o u}} \left(T _ {i}, \hat {T} _ {i}\right) + \mathcal {L} _ {\mathrm {a t t n}} \left(a _ {i}, \hat {a} _ {i}\right)\right), \tag {8} +$$ + +where the $T_{i}$ , $\hat{T}_i$ represent the predictions and ground truth respectively. $\mathcal{L}_{\mathrm{iou}}$ is temporal IoU loss which based GIoU loss [28]. $\mathcal{L}_{\mathrm{attn}}$ is the attention guided loss for crossattention layers in decoder referring to [20], where $a_i$ and $\hat{a}_i$ represent the attention weights of valid video features and the fine-grained one-hot ground truth in $i$ -th event. $\alpha, \beta, \gamma$ are hyperparameters for balancing different part of losses. + +# 4. Experiments + +# 4.1. Experimental Settings + +Following the previous VPG methods [2, 50], we evaluate our SVPTR method on three benchmark datasets: ActivityNet-Caption (Activity). [12] It is the largest dataset in video grounding task, which contains around $20\mathrm{k}$ open domain videos. On average, each video contains 3.65 queries, and each query has an average of 13.48 words. Since the original test set is not released, we follow the previous work [2] and split the dataset into the training, val_1, val_2 of 10009/37421, 4917/17505, and 4885/17031 video/sentence respectively, where the val_2 is used for test. + +Charades-CD-OOD (Charades). [7, 44] The dataset contains 6672 indoor daily life videos and is first released by Gao et al. [7] namely Charades-STA. To better evaluate the effectiveness of existing VSG methods, Yuan et al. [44] re-organizes the original dataset and splits it into train, val, and test_ood with 4563/11071, 333/859, and 1442/3375 video/sentence respectively, in which the training and testing data are designed to have different distributions. + +TACoS. [27, 29] It is based on MPII Cooking Composite Activities video corpus [29] and enriched by Regneri et al. [27] with natural language descriptions and temporal annotations. All the videos are in kitchen room and the videos are much longer than the other two datasets. A standard split consists of 75/10146, 27/4589, and 25/4083 video/sentence pairs for training, validation, and testing. + +Implementation Details. Following the previous work [2, 7, 50], we use pre-trained C3D [32] model without fine-tuning to extract the video features, and employ GLoVe embeddings [24] to receive the text vector representations. For Activity, the video features are preprocessed by PCA [12]. All the video features are sampled evenly to a fixed length $L$ first. As for the videos which are shorter than $L$ , we apply the zero padding and avoid the invalid padding features with padding masks. We set the number of encoder and decoder layers to 2 for all datasets. The smoothing coeffi + +cient for EMA in Mean Teacher is set to 0.999. In feature perturbations, $\mu$ and $\lambda$ are set to 64 and 0.2 respectively. We train the model with Adam optimizer [11], which has a fixed learning rate $4 \times 10^{-5}$ . The weight decay factors are set to $1 \times 10^{-5}$ for three datasets. Moreover, we follow the metrics adopted in most video grounding works, which is denoted as $\text{Recall} @ k$ , $IoU = m$ , where $k$ is the number of generated candidates and $m$ is the threshold. In our methods, $k$ is set to 1 since the SVPTR predicts the timestamps directly, while $m$ is set to $\{0.3, 0.5, 0.7\}$ , $\{0.3, 0.5, 0.7\}$ , and $\{0.1, 0.3, 0.5\}$ for Activity, Charades, and TACoS respectively. We also adopt the $mIoU$ metric, which shows the average effect of our model. More detailed implementations are reported in the supplementary materials. + +# 4.2. Overall Comparison Results + +We compare our proposed SVPTR with the existing state-of-the-art VPG methods DepNet [2], and two natural extension methods Beam Search and 3D-TPN, which are reported by Bao et al. [2]. Moreover, to show the superiority of exploring the contextual information hidden in paragraph, we also compare our model with recent VSG methods, including CTRL [7], ACRN [17], WSSL [5], ABLR [46], [38], 2D-TAN [50], DRN [47], CBP [36], LGI [20], CPNet [15], BPNet [39], CBLN [16], DeNet [51], MATN [49], $\mathrm{I}^2\mathrm{N}$ [21]. Furthermore, Luo et al. [18] introduces semi-supervised learning into VSG recently, we compare their informal work on Charades under the same settings. Note that the experiments on *DepNet are implemented by us based on the open source project [2]. The results of compared VSG methods on Charades refer to [44]. + +Table 1. Comparisons with state-of-the-arts on the Activity. + +
MethodIoU=0.3IoU=0.5IoU=0.7mIoU
LGI [20] (CVPR'20)58.5341.5123.0741.13
DRN [47] (CVPR'20)-45.4524.36-
CPNet [15] (AAAI'21)-40.5621.6340.65
BPNet [39] (AAAI'21)58.9842.0724.6942.11
CBLN [16] (CVPR'21)66.3448.1227.6-
DeNet [51] (CVPR'21)61.9343.79--
MATN [49] (CVPR'21)-48.0231.78-
Beam Search [6]62.5346.4327.12-
3D-TPN [50] (AAAI'20)67.5651.4930.92-
DepNet [2] (AAAI'21)72.8155.9133.46-
SVPTR (Ours)78.0761.7038.3655.91
+ +Comparison with Fully-supervised Learning. For fair comparisons, we first train our method with $100\%$ labeled data and compare the test results with recent SOTA fully-supervised methods. The experimental results on Activity, Charades, and TACoS are reported in Table 1, Table 2, and Table 3 respectively. Based on these results, we list following observations: (1) On all datasets, our proposed SVPTR outperforms recent state-of-the-art VPG methods on most metrics under the same labeled proportion. No- + +Table 2. Comparisons with state-of-the-arts on the Charades. + +
MethodIoU=0.3IoU=0.5IoU=0.7mIoU
CTRL [7] (ICCV'17)44.9730.7311.97-
ACRN [17] (SIGIR'18)44.6930.0311.89-
ABLR [46] (AAAI'19)44.6231.5711.38-
TSP-PRL [38] (AAAI'20)31.9319.376.20-
2D-TAN [50] (AAAI'20)43.4530.7711.75-
DRN [47] (CVPR'20)40.4530.4315.91-
STLG [18] (arXiv'21)48.3030.399.79-
*DepNet [2] (AAAI'21)45.6127.5910.6929.30
SVPTR (Ours)55.1432.4415.5336.01
+ +Table 3. Comparisons with state-of-the-arts on the TACoS. + +
MethodIoU=0.1IoU=0.3IoU=0.5mIoU
DRN [47] (CVPR'20)--23.17-
FIAN [26] (MM'20)39.5533.87--
2D-TAN [50] (AAAI'20)47.5937.29--
BPNet [39] (AAAI'21)-25.9620.9619.53
I²N [21] (TIP'21)-31.4729.25-
CBLN [16] (CVPR'21)49.1638.9827.65-
CPNet [15] (AAAI'21)-42.6128.2928.69
Beam Search [6]48.4638.1425.72-
3D-TPN [50] (AAAI'20)55.0540.3126.54-
DepNet [2] (AAAI'21)56.1041.3427.16-
SVPTR (Ours)67.9147.8928.2231.42
+ +tably, shown in Table 1, with $100\%$ labeled data, our method brings at least $4.9\%$ improvement on all the metrics compared with DepNet (2) Compared with VSG methods, our SVPTR method also shows obvious advantages. The reason is that our SVPTR method receives a paragraph as input rather than an individual sentence. By the well-designed sentence-based decoder, our SVPTR method effectively mines the contextual information among the sentences and learns more temporal features from the two modalities jointly. (3) Compared with the previous works, our SVPTR method reveals superiority on $mIoU$ metric. It demonstrates our method also has more stable performance and localizes events more precisely. + +Comparison with Semi-supervised Learning. We list the semi-supervised training results of our SVPTR method and compare them with several state-of-the-art methods in Table 4, where the $\{\rho_1,\rho_2,\rho_3\}$ follows the same settings above for the three datasets. "FS", "SS", "WS" represent fully-supervised learning, semi-supervised learning, and weakly-supervised learning methods, respectively. From the results, we can observe that: (1) Our SVPTR method successfully utilizes the unlabeled data and significantly improves the grounding performance. Specifically, under the same situation, our SVPTR method clearly outperforms DepNet on all the datasets. (2) Using much less labeled data only, our method achieves similar or higher even performance compared with fully-supervised methods. It proves the superiority of our SVPTR method that reduces the dependency on expensive video-paragraph annotations and utilizes the labeled data more effectively. (3) The proposed method + +SVPTR finds a fair trade-off between temporal annotation costs and performance. Compared with the weakly-supervised methods, our method brings more than $20\%$ improvement on Activity and $5\%$ approximately on Charades under the metric of R1@IoU=0.5. (4) It reveals the superiority of semi-supervised learning strategy that our SVPTR method achieves better performance than the base model VPTR does. However, we also note that on the TACoS dataset, the advantages of VPTR are weakened. One probable reason is the diversity of videos is poor in this dataset, which has a negative influence on training robust models. + +Table 4. Comparisons with state-of-the-arts methods using fewer temporal annotations. + +
DatasetsTypesMethodsIoU=ρ1IoU=ρ2IoU=ρ3mIoU
ActivityFS3D-TPN67.5651.4930.92-
DepNet@100%72.8155.9133.46-
WSWSSL41.9823.34-28.23
SS*DepNet@10%61.4645.1426.7844.11
VPTR@10%72.8053.1429.0750.08
SVPTR@10%73.3956.7232.7851.98
CharadesFSSTLG@100%48.3030.399.79-
*DepNet@100%45.6127.5910.6929.30
WSWSSL35.8623.678.27-
SSSTLG@30%46.1529.439.38-
*DepNet@30%43.0325.0710.1428.09
VPTR@30%45.1324.9810.2228.92
SVPTR@30%50.3128.5012.2732.13
TACOSFS3D-TPN55.0540.3126.54-
DepNet@100%56.141.3427.16-
SS*DepNet@50%40.2726.9516.5418.68
VPTR@50%61.3140.5921.3926.59
SVPTR@50%63.0640.1920.0526.10
+ +# 4.3. Further Analysis + +Effectiveness of Structures. To learn how each module of SVPTR performs in grounding, we conduct the structure ablation studies on Activity and Charades datasets with $10\%$ and $30\%$ labeled data respectively. As depicted in Table 5, we study the effectiveness of following components: sentence-level query (S.Q.), multimodal encoding (M.E.), contrastive loss $(\mathcal{L}_{\mathrm{CT}})$ , consistency loss $(\mathcal{L}_{\mathrm{CS}})$ , and feature perturbations (F.P.). According to the results, we can observe that: (1) The multimodal encoding performs a significant role in VPG. Specifically, with multimodal encoding, the precision on most metrics gets improved on the two datasets. The reason is that it allows the fine-grained cross-modal interactions between word-level text features and clip-level video features. (2) The consistency loss $\mathcal{L}_{\mathrm{CS}}$ is essential for the whole semi-supervised learning framework. Without $\mathcal{L}_{\mathrm{CS}}$ , the generalization of models on unlabeled data will be degraded greatly thus leading to worse performance under semi-supervised conditions. (3) Using contrastive loss with the feature perturbations boosts the final results. A probable reason is that video perturbations bring more diversity into multimodal features, which has been proved [9, 23] to be crucial for contrastive learning. + +Effectiveness of Annotation Proportions. To study the + +![](images/b0cc6040bac2beb3ff4384c3a769eeec2a630af90b10facec6b9d5239925959f.jpg) +Figure 4. Analysis with respect to the proportion of annotations on Activity dataset. + +![](images/98962a5225f4639573f561091df9c3c03092dcf1fae66503afbe9e0580e9359a.jpg) + +quality of the semi-supervised learning framework, we evaluate our VPTR and SVPTR on different proportions of labeled data. For fair comparisons, we also train the recent method DepNet under the same conditions. Limited by the space, we report the experimental results on Activity. For more results on Charades, please refer to the supplementary materials. As illustrated in Fig. 4, we list following observations: (1) Our two models, VPTR and the complete model SVPTR, both outperform the previous method DepNet significantly, which reveals the robustness and effectiveness of our method. (2) The SVPTR achieves promising improvement compared with the base model VPTR, especially under the situation of less annotated data. It demonstrates the superiority of our SVPTR method that reduces the requirements of annotated data again. (3) The performance of our method can be improved with more labeled data. Specifically, with $100\%$ labeled data, our SVPTR method achieves about $5\%$ higher both on the two metrics compared with the results of $10\%$ labeled data. + +![](images/5ab7438aa4dc63bef6d42ac2332b7431e8a06d6e645346281ba4c31e3173ed83.jpg) +Figure 5. Analysis with respect to the sentence-level contexts. + +![](images/403d5cc62d596e5623b28a4f6b938200a0103369e7d071b4c910a17536b999b2.jpg) + +Effectiveness of Contexts. We design four ablated models to study how the contextual information of paragraph influence the grounding quality, which is shown in Fig. 5: (1) "No Contexts": no sentence-level contexts are utilized and the model degenerates to a conventional VSG model. (2) "Temporal Shuffle": the order of sentences in a paragraph is shuffled randomly. (3) "No Temporal": we disable the sentence-level position embedding in a decoder. (4) "Unidirectional": the contexts are limited in the single direction. + +Comparing these results, we can observe that our complete model achieves significant improvement on grounding precision, which proves again that contextual information is + +Table 5. Ablation study on Activity with ${10}\%$ labeled data and Charades with ${30}\%$ labeled data. + +
S.Q.M.E.\( \mathcal{L}_{\text{CT}} \)\( \mathcal{L}_{\text{CS}} \)F.P.ActivityCharades
IoU=0.3IoU=0.5IoU=0.7mIoUIoU=0.3IoU=0.5IoU=0.7mIoU
✓73.2452.9828.4550.0246.0126.1611.6730.25
✓✓73.6753.4128.5650.3447.3828.3610.6730.81
✓✓✓72.8053.1429.0750.1445.1324.9810.2228.92
✓✓✓74.3654.5030.0051.0449.0129.5411.4431.71
✓✓✓✓73.4653.7829.5750.4249.4429.8710.9431.51
✓✓✓✓74.6955.9831.6351.7046.8727.0210.8130.25
✓✓✓✓✓73.3956.7232.7851.9850.3128.5012.2732.14
+ +crucial for localizing events in untrimmed videos. However, we also note that "No Contexts" version performs better on Charades than it does on Activity. One essential reason is, compared with the latter, Charades contains a large number of videos consisting of sparse events. It thus leads to a deficiency of sentence-level contextual information, weakening the advantages of our SVPTR method. + +$①$ A man stands in a bull ring. $②$ A bull runs towards the man. $③$ The man gets hit by the bull. $④$ The man then runs around being chased by the bull. + +![](images/94cdeb99673d0e1810a428c150444ab403b52c5333cb963cdfd9f87135767eb0.jpg) + +① A kid is skate boarding down an empty street. ② Another kid skate boards behind the first kid. ③ They both then zig zag down the street together. + +![](images/38cc703a7c063bfd7059e50201e2edc609250ffacfd619026b2f6bb3878c268c.jpg) +Figure 6. Visualization of two examples on Activity dataset. + +![](images/3ec42a4b731b7fdd51bf99a81125725519b5789fe062acb994986970005126ed.jpg) +Figure 7. Visualization of cross-modal attention weights. + +Qualitative Analysis. To illustrate the localizing quality of the proposed SVPTR method, we visualize two local- + +izing examples with different length of videos and compare them with the results of DepNet [2]. In Fig. 6(a), our proposed SVPTR method precisely localizes all the target moments, while the previous method DepNet fails to retrieve the second event. Moreover, as described in Fig. 6(b), the long video example is more challenging since the high demand on understanding the contexts. Focusing the proposal-sentence matching and ignoring crucial contexts in paragraph, the DepNet gives an absolutely incorrect result on the first event, which contains the whole video almost. Contrastively, our SVPTR method avoids this fatal defect effectively with the video-paragraph alignment and sentence-level context modeling. Additionally, to show how the proposed method SVPTR works, we visualize the crossattention weights between sentence and video features from sentence-based decoders. As illustrated in Fig. 7, we can observe that each sentence gains more attention on the related moments and maintains the temporal order correctly. + +# 5. Conclusion + +In this work, we have introduced a novel Video Paragraph Grounding (VPG) framework dubbed Semi-supervised Video-Paragraph Transformer (SVPTR) that learns contextual information from paragraphs and significantly reduces the dependency on annotated data. We evaluated our SVPTR method on three public datasets and conduct extensive experiments to prove its effectiveness and robustness. The results show that our proposed SVPTR model achieves competitive results with less annotated data. Moreover, with fully-supervised training, SVPTR outperforms the latest VPG methods. For future work, we will study furtherly the trade-off between performance and costs based on this work, and we believe it will inspire more research on video events grounding. + +# 6. Acknowledgement + +This work was supported in part by National Natural Science Foundation of China under Grants (No. 61976049 and 62072080); Sichuan Science and Technology Program, China (No. 2019ZDZX0008, 2020YYS0057) and Meituan. + +# References + +[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In IEEE International Conference on Computer Vision, pages 5803-5812, 2017. 1, 2 +[2] Peijun Bao, Qian Zheng, and Yadong Mu. Dense events grounding in video. 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Existing semi-supervised methods attempt to exploit unlabeled data in model training, but they just regard video as a set of independent images. To better explore semi-supervised segmentation problem with video data, we formulate a semi-supervised video semantic segmentation task in this paper. For this task, we observe that the overfitting is surprisingly severe between labeled and unlabeled frames within a training video although they are very similar in style and contents. This is called inner-video overfitting, and it would actually lead to inferior performance. To tackle this issue, we propose a novel interframe feature reconstruction (IFR) technique to leverage the ground-truth labels to supervise the model training on unlabeled frames. IFR is essentially to utilize the internal relevance of different frames within a video. During training, IFR would enforce the feature distributions between labeled and unlabeled frames to be narrowed. Consequently, the inner-video overfitting issue can be effectively alleviated. We conduct extensive experiments on Cityscapes and CamVid, and the results demonstrate the superiority of our proposed method to previous state-of-the-art methods. The code is available at https://github.com/jfzhuang/IFR. + +# 1. Introduction + +As a fundamental task in computer vision, image semantic segmentation has benefited numerous downstream applications. However, the training data for semantic segmentation requires pixel-level labeling, which is very expensive and time-consuming. Recently, semi-supervised image segmentation (SSIS) is proposed to train models with a limited number of labeled images and additional unla + +![](images/01ad5db0860dc71a11d8f0638c0fa830d12a4fcc258f458b26adad458b676d8b.jpg) +Figure 1. Illustration of expanded training data. As commonly adopted in SSIS, only one frame from each video is sampled and used as the training data. These frames are divided into labeled and unlabeled ones. To fully utilize video data, we propose to supplement the remaining video frames into unlabeled data for training. + +beled images. Besides regular supervised learning on labeled images, SSIS methods usually construct extra supervision signals for unlabeled images, e.g., consistency constraint [17, 23] and pseudo label [4, 32]. It is shown that they can bring considerable performance improvement on the challenging datasets, e.g., PASCAL VOC [8]. + +In real-world scenarios, we can usually collect the video data conveniently and economically, but only a few videos would be annotated with a single frames due to the high expense of human labor. For example, Cityscapes [6] as a representative dataset contains 2975 videos in the training subset, and only the 20th frame in each video is annotated. That is, there are actually many unlabeled frames that can be utilized for model training. However, the existing SSIS methods [4,17,23] do not fully exploit video data, in which only one frame is sampled from each video for model training and a large amount of unlabeled frames are ignored. To better explore unlabeled videos, we propose to expand the training data setting of SSIS by leveraging remaining video frames, as shown in Figure 1. + +A nature way to utilize extra unlabeled frames is to perform SSIS with adding the remaining frames into unlabeled training data. Here we particularly implement two SOTA SSIS methods, i.e., CAC [17] and CPS [4]. Table 1 gives the + +
MethodSampled FramesAll Frames
Baseline66.00-
+ CAC69.7069.80 (+0.10)
Baseline70.32-
+ CPS74.3974.66 (+0.27)
+ +Table 1. Performance of SOTA methods with all video frames. We implement CAC [17] and CPS [4] by adding remaining video frames into unlabeled training data. However, no obvious improvement is gained. Here, Cityscapes with 1/8 labeled data is used, and Deeplabv3+ with the ResNet50 backbone is adopted as segmentation model. The baseline performances are different due to adopting different training settings. + +
IDAccel+ CAC+ CPS
T2081.580.179.7
1569.8↓11.769.9↓10.268.1↓11.6
1065.3↓16.265.5↓14.665.1↓14.6
560.6↓20.961.9↓18.261.8↓17.9
V2049.8↓31.751.1↓29.051.3↓28.4
+ +Table 2. Performance on Cityscapes-VPS. T and V represent the training and validation subsets, respectively. ID indicates the frame id. The model is trained on the 20th frame in the training subset. $\downarrow$ represents the accuracy gap comparing to that on the training frames. Performance gap exists not only between two subsets but also within each training video. + +results on Cityscapes. It can be seen that there is no obvious performance improvement. The primary reason may be the homogenization of video data, i.e., the contents of different frames within a video are often similar. Given one frame from each video, therefore, the existing semi-supervised methods cannot capture much more information from the remaining frames using a simple extension on training data. Evidently, how to effectively boost the segmentation performance with unlabeled video data is challenging. + +Next we first formulate the semi-supervised video segmentation (SSVS) task addressed in this work. There are two main differences comparing to the SSIS task. The first is the training data. During training, only one frame sampled from each video is used in SSIS, while all video frames are accessible in SSVS, as shown in Figure 1. The second is the baseline model. SSIS focuses on improving image segmentation models, e.g., PSPNet [28], while SSVS concentrates on video segmentation models, e.g., Accel [15]. Since the video models are usually designed for exploiting video characteristics, e.g., feature propagation by utilizing the temporal consistency, we particularly consider the learning method by further exploring video data in this paper. + +The overfitting is a key challenge in SSIS, as demonstrated in existing works [17, 23]. Here we investigate the + +![](images/d7a37965d915f0b90cb05a2d616b7c7611fafc3bc260227d0856673918cca983.jpg) +Figure 2. Illustration of inner-video overfitting. The commonly concerned overfitting issue is the performance gap between training and test videos. However, we find that overfitting also exists between labeled and unlabeled frames within each training video, which is called inner-video overfitting. + +overfitting issue in SSVS with a popular VSS model, i.e., Accel [15]. In particular, we conduct a study experiment on the Cityscapes-VPS dataset [16]. The dataset contains 500 videos, where each video contains 30 frames and every 5 frame is annotated. We randomly select 100 videos for training and the remaining are for validation. To be specific, only the annotation on the 20th frame is used for each video during training. We evaluate the model on both the training and validation subsets, as shown in Table 2. From the results, we have two observations. First, the performance gap exists between the training and validation frames, which is the commonly concerned overfitting issue. Second, the gap also occurs between the training and other frames within the training videos, though they have no significant visual difference as shown in Figure 2. We called this phenomenon as inner-video overfitting. + +In this work, we argue that the inner-video overfitting is mainly caused by the lack of accurate supervision signals for unlabeled frames, which results in inconsistent performance. Specifically, the model trained on the labeled frames is supervised by the ground-truth labels, which can provide accurate semantic signals. But the model trained on unlabeled frames is either not considered as in Accel or supervised by some constructed signals. Actually, these signals can only provide an indirect constraint like consistency in CAC or noisy semantic supervision like pseudo labels in CPS, which cannot effectively supervise model training on unlabeled frames. + +Then a natural question arises: can we use ground-truth + +labels to train model on the unlabeled frames? Here we particularly utilize the internal relevance of different frames within a video, as they share similar semantic contents and styles. Following this idea, we propose a novel inter-frame feature reconstruction (IFR) method. The main idea is to reconstruct features of the labeled frame $\mathbf{f}_L$ using the information from features of the unlabeled frame $\mathbf{f}_U$ . After that, we apply supervised learning on the reconstructed feature $\mathbf{f}_R$ with the ground-truth label, which actually imposes supervision on $\mathbf{f}_U$ implicitly. During training, $\mathbf{f}_R$ would become similar to $\mathbf{f}_L$ as they are supervised by the same objective. As a result, the feature distribution discrepancy between $\mathbf{f}_L$ and $\mathbf{f}_U$ would be narrowed, and further the inner-video overfitting would be alleviated. In this way, we can also improve the generalization capacity of the model on unseen scenes, i.e., testing data. In one word, IFR has two main advantages comparing to other methods. First, it uses the ground-truth labels to train model on unlabeled data rather than the generated pseudo labels [4] or consistency constraint [17, 23], which can provide much more accurate semantic supervision. Second, it collaborates the training on labeled and unlabeled data through the same objective, which are processed separately in the existing methods. + +We experimentally evaluate the proposed method on the Cityscapes and CamVid datasets. The results validate the effectiveness of our IFR in alleviating the inner-video overfitting issue, and it can bring a significant performance improvement for mainstream video semantic segmentation methods. The contributions of this work are summarized as follows. + +- We formulate the semi-supervised video semantic segmentation task and discover the inner-video overfitting issue is one of the main challenges damaging the performance of SSVS. +- We propose a novel inter-frame feature reconstruction method to alleviate the inner-video overfitting and further boost the performance. IFR essentially utilizes the internal relevance of different frames within a video. +- We experimentally evaluate the effectiveness of our proposed method, and the results on Cityscapes and CamVid demonstrate the superiority of our method to previous state-of-the-art methods. + +# 2. Related Work + +Image semantic segmentation. Image semantic segmentation targets to assign each pixel in scene images a semantic class, which is a fundamental yet rather challenging task. Modern deep learning methods for semantic segmentation are mainly based on fully convolutional network (FCN) [20]. FCN firstly uses convolutional layers to replace fully-connected layers and can achieve better performance. + +To further enhance segmentation results, the dilation convolution [3], pyramid pooling [28], and attention mechanism [10, 13, 29] are proposed to model object relationships and aggregate context information. Besides, HRNet [25] is designed to maintain high resolution feature maps. With the development of transformer, some transformer-based segmentation models [5, 19, 26] are proposed and outperform current CNN-based networks. Despite the success of these models, they are often impeded in practical deployment due to requiring sufficient pixel-wise annotations for learning. + +Semi-supervised semantic segmentation. To achieve good representation learning with limited annotations, semi-supervised semantic segmentation is studied by exploring unlabeled data. Existing methods can be roughly divided into three families. The adversarial based methods, e.g., AdvSemiSeg [14] and S4GAN [21], utilize a discriminator to distinguish the confidence maps from labeled and unlabeled data predictions. The consistency based methods enforce the consistency of the predictions or intermediate features with various perturbations. The perturbations can be conducted on input images, e.g., CutMix [9], ClassMix [22], and CAC [17], and feature space, e.g., CCT [23]. The self-learning based methods generate pseudo segmentation maps on unlabeled data. [2, 11, 27] propose to generate pseudo labels in an offline manner and retrain the model iteratively. While PseudoSeg [32] and CPS [4] follow the FixMatch [24] scheme and design an online pseudo labeling mechanism. Note that Naive-Student et al. [2] proposes to leverage self-learning in extra unlabeled video sequences to improve the performance of full-supervised image segmentation models. Different from that, our work focuses on improving representation learning of video segmentation models with limited annotations. + +However, existing methods are not designed for video data, which only regards unlabeled videos as a collection of independent images. As shown in Table 1, more extra frames cannot bring considerable improvement due to severe data homogeneity. In this paper, we propose a novel approach to explore the internal relevance of video data. + +Video semantic segmentation. Video semantic segmentation aims to predict pixel-level semantics for each video frame. Different from static images, videos embody rich temporal information that can be exploited to improve semantic segmentation performance. DFF [30] firstly proposes feature propagation to reuse key frame features under the guidance of estimated optical flows, which can reduce the average computational cost. Inspired by DFF, Accel [15] proposes an adaptive fusion policy to effectively integrate the predictions from the key and current frames. DAVSS [31] proposes to correct the distorted features caused by inaccurate optical flow when propagating + +![](images/8680659657de1fb16ed32a83b64f5feb104805fccbad908b4806ca9fbdf1a96f.jpg) +Figure 3. Overview of Inter-Frame Feature Reconstruction. For a labeled video, we sample the annotated frame $\hat{x}_{t_1}^L$ , a random frame $x_{t_2}^L$ and the given label $y_{t_1}$ to construct a training sample. $t_1$ and $t_2$ represent different timestamps. During training, after feature extraction, we generate class prototypes on $\mathbf{f}_{t_2}$ and $\mathbf{f}_{t_2}^s$ based on pseudo label $\tilde{y}_{t_2}$ . Then, prototypes $P_{t_2}$ and $P_{t_2}^s$ are used to reconstruct $\mathbf{f}_{t_1}$ , resulting in $\widetilde{\mathbf{f}}_{t_2}$ and $\widetilde{\mathbf{f}}_{t_2}^s$ . Finally, cross entropy loss $\widetilde{L}$ and $\widetilde{L}_s$ are calculated on logits $L_{t_s}$ and $\widetilde{L}_{t_s}$ with $y_{t_1}$ , respectively. To be notice, IFR can also be applied on unlabeled videos by only replacing label $y_{t_1}$ with pseudo label $\tilde{y}_{t_1}$ of the sampled frame. Best viewed in color and zoom in. + +features. Besides the feature propagation paradigm, some recent works propose to improve the performance of lightweight models with temporal constraints [7, 18] and attention mechanism [12]. + +Different from the image-based methods, video segmentation methods can use unlabeled frames nearby the labeled frame for training. However, existing methods still require sufficient annotated frames, and other unlabeled videos are not fully explored. To the best of our knowledge, this work is the first attempt to design a semi-supervised learning method for video segmentation methods. + +# 3. Method + +# 3.1. Problem Definition + +In this work, we focus on the semi-supervised video semantic segmentation problem. Formally, assume a small set of labeled videos with one frame annotated and a large set of unlabeled videos are provided. Let $\mathcal{V} = \{x_1,\dots ,x_l\}$ represents $l$ frames in a video with $x_{i}$ as the $i$ th frame with spatial resolution of $H\times W$ . Let $\mathcal{D}_L = \{(\mathcal{V}_1^L,\hat{x}_1,y_1),\dots ,(\mathcal{V}_{n_L}^L,\hat{x}_L,y_{n_L})\}$ represents the $n_L$ labeled videos, where $\hat{x}_i$ is the annotated frame of the $i$ th video, $y_{i}\in \mathbb{R}^{C\times H\times W}$ corresponds to the pixel-level one-hot label, and $C$ is the number of classes. Let $\mathcal{D}_U = \{\mathcal{V}_1^U,\dots ,\mathcal{V}_{n_U}^U\}$ represents the $n_U$ unlabeled videos. Besides, another set of labeled videos $\mathcal{D}_V = \{(\mathcal{V}_1^V,\hat{x}_1,y_1),\dots ,(\mathcal{V}_{n_V}^V,\hat{x}_{n_V},y_{n_V})\}$ is used for perfor + +mance evaluation. + +Our work aims to learn a segmentation model from $\mathcal{D}_L$ and $\mathcal{D}_U$ , and generalize it to $\mathcal{D}_V$ . Generally, a segmentation network $\mathrm{Net} = \mathrm{Net}_B \circ \mathrm{Net}_C$ can be regarded as a composition of the backbone $\mathrm{Net}_B$ for feature extraction and the classifier $\mathrm{Net}_C$ for semantic prediction. Following previous methods [4,9,17,22,23,32], the objective of semi-supervised learning can generally be summarized as two loss functions. The first one is a regular cross-entropy loss on the labeled data: + +$$ +L _ {s u p} = - \mathbb {E} _ {(\hat {x}, y) \in \mathcal {D} _ {L}} \sum_ {i = 1} ^ {H \times W} \sum_ {c = 1} ^ {C} y ^ {(i, c)} \log p ^ {(i, c)}, \tag {1} +$$ + +where $p = \mathsf{Net}(\hat{x})$ and $p^{(i,c)}$ represents the softmax probability of the pixel $i$ belonging to the $c$ th class. The second loss aims to train model on unlabeled data with some constructed supervision signals, e.g., consistency constraint or pseudo label, which is denoted by $L_{unsup}$ in this paper. Then the overall training objective can be presented as follows + +$$ +L = L _ {s u p} + \lambda L _ {u n s u p}, \tag {2} +$$ + +where $\lambda$ is a trade-off parameter. + +# 3.2. Inter-Frame Feature Reconstruction + +In this work, we mainly focus on addressing the innerservice overfitting and present a novel inter-frame feature reconstruction (IFR) method. Instead of leveraging the labeled and unlabeled data via different loss functions, IFR + +involves unlabeled frames in supervised learning of labeled frames and consequently can narrow the feature distribution discrepancy between different frames within a video. The overview of our solution is illustrated in Figure 3. To make it clear, we first elaborate on the core component of our method on labeled video data, and then explain two extensions to strong augmented data and unlabeled video data. + +Specifically, we sample an annotated frame $\hat{x}_{t_1}^L$ with the label $y_{t_1}$ and an unlabeled frame $x_{t_2}^L$ from a labeled video to construct a training sample, denoted by $(x_{t_1}, x_{t_2}, y_{t_1})$ , where the superscripts $L$ and $\hat{\cdot}$ are omitted to simplify the notations. Firstly, we extract the features on $x_{t_1}$ and $x_{t_2}$ with a shared backbone, resulting in $\mathbf{f}_{t_1}$ and $\mathbf{f}_{t_2}$ . The key idea of our IFR is to reconstruct $\mathbf{f}_{t_1}$ with the information of $\mathbf{f}_{t_2}$ and then conduct supervised learning with the given labels on the reconstructed features. Since different frames within a video contain similar semantic content, we consider using the class prototypes generated from $\mathbf{f}_{t_2}$ for feature reconstruction. Here the class prototypes refer to the class-wise feature centroids that commonly represent class semantics. Specifically, we calculate the pseudo label $\check{y}_{t_2}$ of $\mathbf{f}_{t_2}$ as + +$$ +\check {y} _ {t _ {2}} = \operatorname {a r g m a x} \left(\operatorname {N e t} _ {C} \left(\mathbf {f} _ {t _ {2}}\right)\right). \tag {3} +$$ + +Then, we group the pixel-wise features in $\mathbf{f}_{t_2}$ belonging to the same class according to $\tilde{y}_{t_2}$ , i.e., + +$$ +P _ {t _ {2}} ^ {(c)} = \frac {\sum_ {i} \mathbf {f} _ {t _ {2}} ^ {(p)} * \mathbb {1} (\check {y} _ {t _ {2}} ^ {(i , c)} = = 1)}{\sum_ {i} \mathbb {1} (\check {y} _ {t _ {2}} ^ {(i , c)} = = 1)}, \tag {4} +$$ + +where $\mathbb{1}$ is an indicator function and $\check{y}_{t_2}^{(i,c)}$ represents the one-hot label of pixel $i$ belonging to the cth class. To represent $\mathbf{f}_{t_1}$ with the generated class prototypes $P_{t_2}$ , we consider adopting the commonly used attention mechanism + +$$ +s ^ {(i, c)} = \bar {\mathbf {f}} _ {t _ {1}} ^ {(i) T} \bar {P} _ {t _ {2}} ^ {(c)}, \tag {5} +$$ + +$$ +s ^ {(i, c)} = \frac {e ^ {s ^ {(i , c)} / \tau_ {r e}}}{\sum_ {c = 1} ^ {C} e ^ {s ^ {(i , c)} / \tau_ {r e}}}, \tag {6} +$$ + +$$ +\widetilde {\mathbf {f}} _ {t _ {2}} ^ {(i)} = \sum_ {c = 1} ^ {C} s ^ {(i, c)} P _ {t _ {2}} ^ {(c)}, \tag {7} +$$ + +where $\mathbf{f}^{(\bar{i})} = \mathbf{f}^{(i)} / \| \mathbf{f}^{(i)}\|$ is the L2 normalization. Here we adjust the softmax operation by dividing by a temperature $\tau_{re}$ . + +After that, we generate the classification probabilities $\widetilde{p} = \sigma (\mathsf{Net}_C(\widetilde{\mathbf{f}}_{t_2}))$ , where $\sigma$ indicates a softmax function. To perform supervised learning similar to labeled frames, we adopt the cross-entropy with the given label $y_{t_1}$ as follows + +$$ +\widetilde {L} = - \mathbb {E} \sum_ {i = 1} ^ {H \times W} \sum_ {c = 1} ^ {C} y _ {t _ {1}} ^ {(i, c)} \log \widetilde {p} ^ {(i, c)}. \tag {8} +$$ + +Then the overall training objective can be presented as + +$$ +L = L _ {s u p} + \lambda \widetilde {L}. \tag {9} +$$ + +During training, $\widetilde{\mathbf{f}}_{t_2}$ would become similar to $\mathbf{f}_{t_1}$ since they are enforced by the same loss function and supervision signal. Therefore, the model is encouraged to narrow the distribution between $\mathbf{f}_{t_2}$ and $\mathbf{f}_{t_1}$ , i.e., keep the feature consistency of different frames within a video. + +# 3.3. Extended Solution + +Strong Augmented Data. Existing works [9, 22, 23, 27] have shown that strong data augmentation on unlabeled data can effectively improve model generalization in semi-supervised learning. As shown in the lower half of Figure 3, we extend the IFR training on strong augmented frames. Specifically, taking the labeled video data as an example, we impose strong augmentation, e.g., color jitter, on $x_{t_2}^L$ to get $x_{t_2}^{Ls}$ . After feature extraction, we also use $\mathbf{f}_{t_2}^s$ to perform feature reconstruction. Differently, when generating the prototypes, we use the pseudo label of $\mathbf{f}_{t_2}$ rather than $\mathbf{f}_{t_2}^s$ for more accurate semantic prediction. After that, a regular IFR training procedure is adopted with $\widetilde{L}_L^s$ . Essentially, we impose an implicit consistency constraint on $\mathbf{f}_{t_2}$ and $\mathbf{f}_{t_2}^s$ , since we narrow their distribution discrepancy with $\mathbf{f}_{t_1}$ . Finally, the overall training objective can be presented as + +$$ +L = L _ {s u p} + \lambda \left(\widetilde {L} + \lambda_ {s} \widetilde {L} ^ {s}\right), \tag {10} +$$ + +where $\lambda_{s}$ is an extra control parameter. + +Unlabeled Video Data. By far, our proposed IFR is only applied to labeled videos. To further explore a large amount of unlabeled videos, we make a simple extension to the IFR solution. Specifically, we randomly sample two frames $x_{t_1}^U$ and $x_{t_2}^U$ from each unlabeled video. Similarly, strong augmentation is applied on $x_{t_2}^U$ , resulting in $x_{t_2}^{Us}$ . Since no frame label is provided, we need to build supervision signal for reconstructed features. In particular, we adopt the pseudo label $\check{y}_{t_1}$ of $x_{t_1}^U$ . Then a training sample $(x_{t_1}^U, x_{t_2}^U, x_{t_2}^{Us}, \check{y}_{t_1})$ is obtained and naturally it can be used in the IFR training procedure as for the labeled samples. Finally, the overall training objective can be presented as + +$$ +L = L _ {s u p} + \lambda_ {L} \left(\widetilde {L} _ {L} + \lambda_ {s} \widetilde {L} _ {L} ^ {s}\right) + \lambda_ {U} \left(\widetilde {L} _ {U} + \lambda_ {s} \widetilde {L} _ {U} ^ {s}\right), \tag {11} +$$ + +where subscripts $L$ and $U$ represent loss terms calculated on the labeled and unlabeled videos, respectively. $\lambda_{L}$ and $\lambda_{U}$ correspond to their trade-off parameters. + +# 4. Experiments + +# 4.1. Dataset + +Cityscapes [6] is a representative dataset in semantic segmentation and autonomous driving domain. It focuses + +
Method1/30 (100)1/16 (186)1/8 (372)1/4 (744)1/2 (1488)
Accel45.7352.1057.1260.5562.83
+ CCT [23]48.05 (+2.32)53.25 (+1.15)58.88 (+1.76)62.00 (+1.45)64.02 (+1.19)
+ CAC [17]48.83 (+3.10)54.56 (+2.46)58.55 (+1.43)62.78 (+2.23)63.87 (+1.04)
+ CPS [4]48.97 (+3.24)54.69 (+2.59)58.97 (+1.85)62.43 (+1.88)63.74 (+0.91)
+ Ours52.86 (+7.13)56.39 (+4.29)60.08 (+2.96)63.45 (+2.90)64.53 (+1.70)
+ +Table 3. Comparison with state-of-the-art methods on the Cityscapes validation subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data. + +
Method1/30 (15)1/16 (29)1/8 (58)1/4 (117)1/2 (234)
Accel42.3747.5750.7856.4059.37
+ CCT [23]47.09 (+4.72)52.45 (+4.88)54.50 (+3.72)58.69 (+2.29)61.58 (+2.21)
+ CAC [17]46.85 (+4.48)52.16 (+4.59)54.03 (+3.25)59.67 (+3.27)63.17 (+3.80)
+ CPS [4]46.05 (+3.68)52.04 (+4.47)55.30 (+4.52)59.02 (+2.62)62.49 (+3.12)
+ Ours49.50 (+7.13)53.71 (+6.14)57.37 (+6.59)61.27 (+4.87)63.86 (+4.49)
+ +Table 4. Comparison with state-of-the-art methods on the CamVid test subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data. + +on semantic understanding to urban street scenes. The training and validation subsets contain 2,975 and 500 videos, respectively, and each video contains 30 frames at a resolution of $1024 \times 2048$ . The 20th frame in each is annotated by pixel-level semantic labels with 19 categories. + +CamVid [1] also focuses on the semantic understanding to urban street scenes, but it contains less data than Cityscapes. It has four driving videos and each video contains frames ranging from 3,600 to 11,000 at a resolution of $720 \times 960$ . Every 30th frame of videos is annotated with 11 semantic classes, which results in a total of 701 samples. Similar to Cityscapes, we split videos into 701 videos and each video contains 30 frames. All videos are divided into the trainval set with 468 videos and test set with 233 videos. + +We follow the partition protocols of CutMix [9] and CPS [4] and divide the whole training set via randomly sub-sampling $1/2$ , $1/4$ , $1/8$ , $1/16$ , and $1/30$ of all training videos, i.e., 2975 videos in Cityscapes and 468 videos in CamVid, as the labeled set and regard the remaining videos as the unlabeled set. In the implementation, we follow [2] to add the labeled set into the unlabeled set for unsupervised learning, which can slightly improve performance. Following [9, 14, 21-23], we apply bilinear interpolation to resize every video frame in Cityscapes and CamVid to $512 * 1024$ and $360 * 480$ for the efficiency of training and inference, respectively. + +# 4.2. Implementation Details + +Here we particularly adopt Accel [15] as video semantic segmentation architecture due to its good performance. It consists of two segmentation branches, i.e., a heavy reference branch and a light-weight update branch, an optical + +flow network, and a score fusion layer. To be consistent with previous works [9,17,23], we adopt PSPNet [28] to implement the segmentation branches. Specifically, ResNet-101 and ResNet-18 are adopted as the backbone of reference and update branches, respectively. + +Accel uses a two-stage training procedure. In stage one, two segmentation branches are trained separately on a specific dataset, e.g., Cityscapes [6]. To improve representation learning with limited annotations, we apply semi-supervised methods to this stage. The segmentation model is trained using a SGD optimizer with a momentum of 0.9 and a weight decay of $10^{-4}$ . The learning rate is set at $10^{-3}$ for the backbone parameters and $10^{-2}$ for others, which is annealed following the poly learning rate policy. In stage two, two segmentation branches are fixed, and the classifier is jointly trained with the optical flow network and the score fusion layer by following the standard supervised learning paradigm. The training settings follow the original Accel implementation. Actually, the training in the stage two also suffers from limited annotations. However, how to design a suitable semi-supervised learning method for optical flow network is beyond the scope of this work, which can be explored in the future. + +We evaluate the segmentation performance on the validation videos, i.e., validation subset in Cityscapes and test set in CamVid. Following Accel, for each test video, we conduct the reference branch on a selected key frame and update branch on the annotated frame. The segmentation results are predicted via the feature propagation and score fusion. We evaluate different methods with mean Intersection-over-Union (mIoU) as metric. The key frame interval is set as 5 throughout the experiments. + +For our IFR, there are three trade-off hyperparameters in Eq. 11 and one temperature in Eq. 6, i.e., $\lambda_{L}, \lambda_{U}, \lambda_{s}$ and $\tau_{re}$ . We set $\lambda_{L} = 0.01$ , $\lambda_{U} = 0.001$ , $\lambda_{s} = 0.1$ and $\tau_{re} = 0.5$ for all experiments. + +# 4.3. Performance Comparison + +To demonstrate the superiority of our method, we make a comparison with recent state-of-the-art methods, i.e., two consistency based SSIS methods including CCT [23] and CAC [17], and one self-learning based SSIS method CPS [4]. However, it is hard to directly compare with these methods since they are implemented under different settings, e.g., segmentation models, data splits, and training settings. Besides, these methods are not applied to our used video semantic segmentation model Accel. Therefore, we reproduce these methods according to their official codes, where all of them are equipped with the same base segmentation model, i.e., PSPNet, and trained with the same data splits and training settings (i.e., optimizer and hyperparameters). In addition, different data augmentations are adopted in existing works, e.g., random cropping and flipping in [23], and extra random scaling in [17] and cutmix in [4]. For fair comparison, we adopt the same random cropping and flipping for supervised learning of all comparison methods while keeping their original implementations for unsupervised learning. In this way, we can fairly compare the improvement brought by different methods on the basis of the same baseline with supervised learning. + +The comparison on Cityscapes and CamVid is shown in Table 3 and Table 4. From the results, we have the following two observations. First, our IFR can bring significant performance improvement under all partition protocols comparing to the baseline that only uses the labeled data. A larger gain is achieved for the cases with less labeled data, e.g., $7.13\%$ mIoU gain with 100 samples in Cityscapes and $7.14\%$ mIoU gain with 15 samples in CamVid. Such experimental results well verify that IFR can effectively improve the generalization of models. Second, our method surpasses other state-of-the-art methods, including CCT [23], CAC [17], and CPS [4], by a large margin. For example, it outperforms CPS by $3.98\%$ and $3.46\%$ under 1/30 partition protocol on Cityscapes and CamVid, respectively. It shows that IFR can better utilize the unlabeled video data in training model. + +# 4.4. Ablation Study + +In this subsection, we conduct experiments to reveal the effectiveness of our proposed method. All experiments are particularly conducted with 1/30 labeled data on Cityscapes. For efficient training, we adopt PSPNet with ResNet18 as the segmentation network by default. + +Effect of Components. To reveal the contribution of our proposed components, we conduct an extensive study by + +
LsupL̅LL̅UL̅sL + L̅sUmIoU (%)
✓43.68
✓✓46.13 (+2.45)
✓✓46.81 (+3.13)
✓✓46.66 (+2.98)
✓✓✓47.51 (+3.83)
✓✓✓✓48.40 (+4.72)
+ +Table 5. Ablation study on our proposed components. Each component can bring performance improvement comparing to the baseline, and their combination performs best. + +
MethodStage OneStage Two
PSPNet18PSPNet101
Baseline43.6850.2445.73
+ CCT45.60 (+1.92)52.60 (+2.36)48.05 (+2.32)
+ CAC46.50 (+2.82)53.50 (+3.26)48.83 (+3.10)
+ CPS46.81 (+3.13)53.26 (+3.02)48.97 (+3.24)
+ Ours48.40 (+4.72)54.40 (+4.16)52.86 (+7.13)
+ +Table 6. Ablation study on improvement in multi-stage training. Following Accel, stage one involves the training of image segmentation model while stage two mainly involves the training of optical flow network and score fusion. Comparing to others, our method can bring more gains in both training stages. + +evaluating their combinations, and the results are shown in Table 5. It can be seen that each component can bring performance improvement comparing to the baseline. In particular, the feature reconstruction on both the labeled and unlabeled frames can achieve higher accuracy than the setting only equipped with each of them. Finally, the combination of all components performs best. + +Improvement in Two Stages. The used Accel is trained in a two-stage manner. Here we investigate the performance improvement in the two-stage training, and the results are shown in Table 6. In stage one, only image segmentation models, i.e., PSPNet18 and PSPNet101, are involved. Comparing to other methods, our method can obtain more gain over the baseline due to better utilization of unlabeled videos. In stage two, the training of optical flow network and score fusion layer are involved, i.e., no semi-supervised method is introduced in this stage. However, we observe an interesting phenomenon that our trained segmentation model can further bring performance improvement over the baseline, while other models only almost maintain improvement brought in stage one. It is because our method can help the segmentation model to extract features with a similar distribution for different frames, which is important for the feature fusion in Accel. + +Performance with Different VSS Architectures. To study the generalization ability of our method, we further apply it + +![](images/098d84154edaa64ab76f5303eeacc63f431ceb2626f96518cade4d69da0c474c.jpg) +Figure 4. Qualitative results comparison on the Cityscapes dataset using 1/30 labeled samples. The proposed IFR produces better results than the baseline and other methods. We highlight the details with the yellow boxes. Best viewed in color and zoom in. + +
MethodBaseline+ Ours
DFF [30]44.1949.97 (+5.78)
DAVSS [31]46.5151.97 (+5.46)
+ +Table 7. Performance on different VSS architectures. Our method can bring significant improvement for different video semantic segmentation architectures consistently. + +
IDAccel+ CAC+ CPS+ Ours
T2081.580.179.776.5
1569.8↓11.769.9↓10.268.1↓11.671.0↓5.5
1065.3↓16.265.5↓14.665.1↓14.667.4↓9.1
560.6↓20.961.9↓18.261.8↓17.966.8↓9.7
V2049.8↓31.751.1↓29.051.3↓28.453.9↓22.6
+ +to different video semantic segmentation architectures. We particularly adopt two widely adopted video segmentation architectures, i.e., DFF [30] and DAVSS [31]. As shown in Table 7, our proposed method can bring significant performance improvement consistently. + +Effectiveness on Alleviating Overfitting. To verify the effectiveness of our method on tackling the overfitting, we conduct an analysis experiment on Cityscapes-VPS, in which each video is annotated with multiple frames, and the results are shown in Table 8. Comparing to the baseline, it can be seen that our method can significantly reduce the accuracy gap not only between training and validation videos but also within training videos. It verifies that our method can effectively alleviate the overfitting issue in video semantic segmentation. + +Effectiveness on Temporal Consistency. It is important + +Table 8. Performance on Cityscapes-VPS. T and V represent training and validation subsets, respectively. ID represents for frame id. Model is trained on the 20th frame in training subset. $\downarrow$ represents the accuracy gap comparing to trained frames. Obviously, our method can significantly reduce both overfitting and inner-video overfitting issues. + +
MethodAccel+ CCT+ CAC+ CPS+ Ours
TC70.0471.4371.4770.7473.88
+ +Table 9. Comparison on Temporal Consistency. We evaluate different methods with temporal consistency (TC) score [18]. Our proposed method can bring a significantly improvement. + +for VSS methods to produce temporally stable predictions. Thus, we further verify the effectiveness of our method on improving temporal consistency. Particularly, we follow [18] and adopt temporal consistency (TC) score as the evaluation metric. As shown in Table. 9, our method can bring a significant improvement, since consistent predictions among different frames can be achieved. + +Qualitative Results. Figure 4 presents the visual comparison with the baseline and other semi-supervised methods. We can observe that the results of our method are commonly superior to others. + +# 5. Conclusion + +In this paper, we focus on the semi-supervised video semantic segmentation problem, and propose a novel interframe feature reconstruction approach. Our IFR exploits a large number of unlabeled frames by cooperating them into supervised learning of labeled frames, which essentially narrows the feature distribution of different frames within a video. Furthermore, we propose two extensions on strong augmented data and unlabeled videos. IFR can effectively alleviate the inner-video overfitting, and extensive experiments on Cityscapes and CamVid validate the effectiveness of our method, which outperforms previous state-of-the-art methods. + +# Acknowledge + +This work is supported by the National Natural Science Foundation of China under Grant No.62176246 and No.61836008. We acknowledge the support of GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC. + +# References + +[1] Gabriel J Brostow, Julien Fauqueur, and Roberto Cipolla. Semantic object classes in video: A high-definition ground truth database. 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Pseudoseg: Designing pseudo labels for semantic segmentation. arXiv preprint arXiv:2010.09713, 2020. 1, 3, 4 \ No newline at end of file diff --git a/semisupervisedvideosemanticsegmentationwithinterframefeaturereconstruction/images.zip b/semisupervisedvideosemanticsegmentationwithinterframefeaturereconstruction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..46f7f934ecc9a0ad52e9df90558fc0c3eb710f53 --- /dev/null +++ b/semisupervisedvideosemanticsegmentationwithinterframefeaturereconstruction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:821d2ccb43ad5b7e26e7d4753d3efa090b6e2fb73089e6b86933c232727a2725 +size 488438 diff --git a/semisupervisedvideosemanticsegmentationwithinterframefeaturereconstruction/layout.json b/semisupervisedvideosemanticsegmentationwithinterframefeaturereconstruction/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d8d2e4bfb6b7753741467dacbd8986ca5a478bbc --- /dev/null +++ b/semisupervisedvideosemanticsegmentationwithinterframefeaturereconstruction/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:86ecd7f75717a30b0ab309f49943d356fb73d66bccf43f237939c2c6b2e21cae +size 378270 diff --git a/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_content_list.json b/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c3e36ed60f6bd3836cca0e6ba835b18f8e055dd4 --- /dev/null +++ b/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bfc515096a38a70ec7d4653a541baab96fd6fdbc78e0fb2b4d60fb71a4650c0d +size 78391 diff --git a/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_model.json b/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..902ebf6eb0413797c8b7374aba08188179524a49 --- /dev/null +++ b/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f12250ea50298878839186ece41acea7259fad62aedb035e2323e4935c6d2a07 +size 95674 diff --git a/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_origin.pdf b/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5820573ce2bf4352c238ec2587695e149665d247 --- /dev/null +++ b/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/fe0e3ca2-8a83-4dde-9232-f9bd607381eb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:420f5b42d6523ba1974638bbc95111b5b84df7abaa32d3ff820cea57e524fc30 +size 8639585 diff --git a/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/full.md b/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ffb0448b7e7fb2e5be208a7c896d075d49051e4c --- /dev/null +++ b/semisupervisedwideangleportraitscorrectionbymultiscaletransformer/full.md @@ -0,0 +1,367 @@ +# Semi-Supervised Wide-Angle Portraits Correction by Multi-Scale Transformer + +Fushun Zhu $^{1*}$ Shan Zhao $^{2*}$ Peng Wang $^{2*}$ Hao Wang $^{2}$ Hua Yan $^{1\dagger}$ Shuaicheng Liu $^{3,2\dagger}$ $^{1}$ Sichuan University + $^{2}$ Megvii Technology + $^{3}$ University of Electronic Science and Technology of China + +# Abstract + +We propose a semi-supervised network for wide-angle portraits correction. Wide-angle images often suffer from skew and distortion affected by perspective distortion, especially noticeable at the face regions. Previous deep learning based approaches need the ground-truth correction flow maps for training guidance. However, such labels are expensive, which can only be obtained manually. In this work, we design a semi-supervised scheme and build a high-quality unlabeled dataset with rich scenarios, allowing us to simultaneously use labeled and unlabeled data to improve performance. Specifically, our semi-supervised scheme takes advantage of the consistency mechanism, with several novel components such as direction and range consistency (DRC) and regression consistency (RC). Furthermore, different from the existing methods, we propose the Multi-Scale Swin-Unet (MS-Unet) based on the multi-scale swin transformer block (MSTB), which can simultaneously learn short-distance and long-distance information to avoid artifacts. Extensive experiments demonstrate that the proposed method is superior to the state-of-the-art methods and other representative baselines. The source code and dataset are available at https://github.com/megvii-research/Portraits_Correction + +# 1. Introduction + +In recent years, a growing number of smartphones have been equipped with wide-angle cameras, which take wide-angle images with rich contents. However, a wider FOV camera often causes severe perspective distortions, which bends straight edges on buildings, and distorts faces, as shown in Fig. 1(a). Therefore, an ideal intelligent algorithm is required to correct the distortion image. After correction, the faces will look more natural while the curved lines in the background are also corrected, as shown in Fig. 1(b). + +The traditional undistortion methods apply perspective projection using calibrated camera parameters, which cor + +![](images/50380cfc54c3d2d738622680dfc9c48ac37bcfd692486eb14712681bc91a3b63.jpg) +Figure 1. An example of our method. (a) the original wide-angle image with curved lines and distorted faces. (b) result by the proposed semi-supervised method, both lines and faces are corrected. + +![](images/e021611fe2698fd0754fb05be571213ce659d7359d8ead8df202087896566978.jpg) + +![](images/3ca42ae02cb16392906ac85b42befb493aed89603f44d1f150c4b7c28109712c.jpg) + +rectly warp the lines at the background to straight [3,8,24]. Nevertheless, faces on the image are stretched unnaturally due to incorrect projection as a plane. Compared to perspective projection, the mercator and stereographic projections [28] can preserve the shape of faces locally, but they also bend linear structures in the background [4]. + +It is obvious that facial regions and background need two different types of projections for the wide-angle image correction. Carroll et al. [4] presented a content-preserving approach that finds an optimal mapping solution according to the user-specified lines. Recently, Shih et al. [26] designed an optimization problem to create a mesh that adapts stereographic projection on facial regions regionally and applies perspective projection on background, enabling a smooth transition between portraits and background by solving the optimization problem automatically. However, the method [26] sometimes causes distorted architectures nearby corrected faces. In addition, it requires portraits segmentation mask and camera parameters as additional inputs. + +Tan et al. [29] proposed the first fully-supervised CNN-based method for wide-angle image correction, which consists of a line correction network and a portraits correction network. Tan's method obtained satisfactory results with the distorted image as input. However, there still exists disadvantages in their work. First, it needs many training pho + +tos under rich scenarios, and each face in the photo must be manually undistorted by specific tools. Meanwhile, errors may occur in manual annotation, causing uneven annotation quality or introducing dirty data. Therefore, the whole data preparation procedure is complex and expensive, making it unrealistic to improve performance by enlarging the training dataset. Second, Tan's method also creates artifacts in some cases because it does not use long-range semantic information for local variations of faces. + +To address the above problems, we attempt to leverage a novel semi-supervised strategy, aiming to reduce the cost of preparing an expensive manual corrected dataset. Specifically, we adopt the semi-supervised strategy, containing direction and range consistency (DRC) and regression consistency (RC), to make full use of both labeled and unlabeled data by introducing a surrogate task (segmentation). Besides, compared with Tan et al. [29], we develop a novel network based on the multi-scale swim transformer block (MSTB), dubbed as Multi-Scale Swin-Unet (MS-Unet) which is better suitable for portraits correction. In particular, we also collect more than 5,000 unlabeled distortion images from different phones and scenes to train MS-Unet by the semi-supervised strategy. Experimental results show that our approach can correct distortions in wide-angle portraits with superior performance than previous methods, and it only needs a small amount of manually labeled data. In summary, our main contributions are: + +- We propose the first semi-supervised learning strategy for wide-angle portraits correction, which dramatically reduces the requirement of labeled training data. +- We develop a novel transformer-based network called MS-Unet, based on MSTB, to fully utilize both local-scale and long-range semantic information interaction for wide-angle portraits correction. +- We provide a high-quality unlabeled dataset that can be used to train semi-supervised wide-angle portraits correction algorithms. + +# 2. Related Works + +# 2.1. Wide-Angle Portraits Correction + +Early wide-angle portraits correction methods always relied on traditional algorithms [4, 40]. Tehrani et al. [31, 32] presented methods to remove faces distortions and preserve background features during this process, but their solutions require user assistance. Shih et al. [26] proposed a mesh-based algorithm that can strike a balance between straight lines and faces correction effects automatically. Nevertheless, it requires the camera parameters and portraits segmentation as inputs. Recently, Tan et al. [29] proposed a two-stage deep neural network to complete wide-angle portraits correction with only an image as input. However, this + +fully-supervised method is limited to the number of labeled data that requires high-cost manual screening and processing. Fortunately, our method greatly reduces the limitation of the amount of labeled training dataset and learns the correction flow maps from distortion image to usual image. + +# 2.2. Deep Semi-Supervised Learning + +Deep semi-supervised learning provides a practical and effective approach to fully utilizing the mixture dataset containing labeled and unlabeled images. It has been widely used in image classification [13,36,37], semantic segmentation [1,35,38], machine translation [6,9,12], crowd counting [21,23], text classification [15,17,18], text segmentation [30,34] and so on. These works have proved that the semi-supervised method can promote the accuracy. Therefore, we introduce the semi-supervised strategy into the portraits correction domain and make a beautiful breakthrough. + +# 2.3. Visual Transformer + +The proposal of transformer [33] has been widely used in natural language processing (NLP). Inspired by their outstanding achievements, researchers have gradually applied transformers to the computer vision field recently [11, 16]. More impressively, Liu et al. [22] proposed an excellent hierarchical transformer structure called Swin Transformer, which is established upon shifted window partitioning mechanism. It has advanced performance on various vision tasks, including image classification, object detection, and semantic segmentation. Hu et al. [2] also devised a U-shaped transformer block called Swin-Unet, which focused on medical image segmentation and achieved surpassing results. Based on these works, we propose a new transformer network that can meet the need for long-distance semantic information of wide-angle portraits correction. + +# 3. Method + +Fig. 2 shows a pipeline of the proposed method. We devise a novel semi-supervised scheme to solve the problem of limited training data by utilizing both labeled and unlabeled data. As shown, we assume a single distortion image as input. Then, we get the correction flow maps and the segmentation mask as intermediate outputs. The correction flow maps are used to project the distortion image into a correction image. The segmentation mask is the bridge between labeled and unlabeled data. + +# 3.1. Semi-supervised Learning Algorithm + +As shown in Fig. 2, in our problem settings, we have a set of unlabeled images noted as $U = (I_{th}^{u})$ and a set of labeled images $L = (I_{th}^{l}, F_{th})$ , where $F_{th}$ represents the labels. We mix these images and adopt them to train the correction network through the semi-supervised method composed of DRC and RC, which are described in detail below. + +![](images/1ae7a206be38d0014e455862ba018b4e95c072f98d4bc1e3ae4742487c40377b.jpg) +(a) The training strategy for labeled images + +![](images/779ae0d0a9a4cced12ac2761dfa940548a7871eb15ca16be86d570ae41055181.jpg) +(b) The training strategy for unlabeled images +Figure 2. The pipeline of semi-supervised wide-angle portraits correction framework with the surrogate task (segmentation). (a) The network training strategy by utilizing the labeled images. (b) Utilize the unlabeled images to train our network. The training strategy consists of direction and range consistency (DRC), regression consistency (RC). For an unlabeled image $I_{th}^{u}$ , when it is sent to the siamese network, the estimated segmentation mask and the correction flow map are utilized to compute the DRC loss $\mathcal{L}_{DRC}$ and RC loss $\mathcal{L}_{RC}$ . + +
S/S1''/S2''Segmentation Mask by TranslationIthLabeled ImageLCRCRC LossAugData Augmentation
S'/S1'/S2'Segmentation Mask by PredictionIu thUnlabeled ImageLCDRCDRC LossLm1Mask based L1 Loss
F'/F1'/F2'Correction Flow Map by PredictionFGround Truth Correction Flow MapLceCross-Entropy LossLmsMask based Sobel Loss
+ +# 3.1.1 Direction and Range Consistency (DRC) + +Many existing methods have proved that the estimation accuracy can be further improved by introducing approximate surrogate tasks [10, 23]. Inspired by the success, we attempt to present a surrogate task (segmentation) into the network that is different from the existing fully-supervised wide-angle portraits correction method [29]. In particular, the segmentation mask from the surrogate task can assist the network to construct a novel direction and range consistency learning strategy, which is helpful to improve the accuracy of wide-angle portraits correction. + +This design is mainly motivated by four aspects: 1) The portraits correction flow maps represent the offset and direction of each pixel for correcting distortion images. By introducing the segmentation task to flow maps, the network pays more attention to learning the direction change of each pixel. It is conducive to the network to understand the portraits correction better. 2) If we generate a binary mask, the network will pay more attention to the guiding role of direction but ignore the importance of regional consistency. Thus the multi-category mask is generated by multiple thresholds to supervise the segmentation task. In the segmentation mask, the pixels classified into the same category represent that their values change within the same threshold range. In other words, the segmentation mask is also helpful to guide the network to learn the information of regional consistency, so that the correction flow map predicted by the network will also become smoother. 3) As shown in Fig. 2, the predicted correction flow map can also be converted to the segmentation mask. Hence the loss function can be constructed between portraits correction and segmentation, making it feasible to introduce unlabeled data for our semi- + +supervised scheme. 4) Meanwhile, the segmentation mask can be generated without extra costs. It is conducive for the transformation between the flow map and segmentation mask so. In addition, the unlabeled data can be fully utilized when conducting our DRC learning strategy. + +Semantic segmentation and portraits correction have similar characteristics, making it possible to learn the consistency between them. When the semantic segmentation is deployed as the surrogate task in this paper, it predicts whether the flow map value $F(i,j)$ meets the given direction and range. We judge the offset by the threshold $\delta \in \mathbb{N}^{+}$ , the pixels whose offset is in the range $(-\infty, -\delta]$ or $[\delta, +\infty)$ keep negative or positive directions, and the offset in the range $(-\delta, \delta)$ are merged into one set which indicates slight movement. The prediction target of the segmentation task is defined as follows: + +$$ +S (i, j) = \left\{ \begin{array}{l l} 0, & i f \quad F (i, j) \leqslant - \delta \\ 1, & i f \quad - \delta < F (i, j) < \delta \\ 2, & i f \quad F (i, j) \geqslant \delta \end{array} , \right. \tag {1} +$$ + +where $S(i,j)$ denotes the segmentation mask, $(i,j)$ is the pixel position of mask or flow map, and $\delta$ represents the predefined threshold is set to 5 in our experiments. + +The proposed DRC learning strategy is shown in Fig. 2. As mentioned above, by introducing the surrogate task, the network can vigorously supervise direction and regional consistency. For labeled data, the ground truth of the correction flow map is used for training the portraits correction task. Meanwhile, it also converts into a multi-classification mask, which is utilized for training the surrogate task. As for the unlabeled data, no ground truth is available. Nevertheless, the predicted correction flow map can also generate + +![](images/c33a9f65e04427f5e56e5784da74e20180bc167d9ab2dd22769b1ec51af4a843.jpg) +Figure 3. (a) The overview of our proposed Multi-Scale Swin-Unet (MS-Unet). The network mainly consists of encoder, decoder, bottleneck and skip fusion blocks (SFB). (b) The architecture of two successive MSTBs. The primary difference between them is the windowing configurations (window partition and shifted window partition). (c) The detailed architecture of SFB. + +the segmentation mask through the multiple thresholds. The unlabeled data is still allowed to train the network by DRC loss, and the details will be given in Section 3.3. + +# 3.1.2 Regression Consistency (RC) + +Besides the DRC, we also introduce the regression consistency (RC) to improve the network robustness. Fig.2 illustrates the details of RC. Specifically, we can obtain two different images $I_{th}^{u1}$ and $I_{th}^{u2}$ with various augmentation methods (e.g., noise, smoothing, and sharpening), from an unlabeled image $I_{th}^{u}$ . Many previous works have stated that an image with different perturbations can obtain similar predictions through a robust network. Therefore, we expand the MS-Unet into a shared-weight siamese structure. The unlabeled images $I_{th}^{u1}$ and $I_{th}^{u2}$ are respectively fed into the two networks, and a consistent loss is established between their outputs. The detailed loss implementation of RC will be given in Section 3.3. + +# 3.2. Multi-Scale Swin-Unet (MS-Unet) + +# 3.2.1 Architecture Overview + +Although the semi-supervised scheme can significantly boost the performance, the portraits correction depends on a superior network. Motivated by the success of vision transformers [2,7,11,16], we develop the MS-Unet, derived from Swin-Unet [2], for the wide-angle portraits correction task. As shown in Fig. 3(a), our proposed MS-Unet can be divided into four major parts: encoder, decoder, bottleneck + +and skip fusion blocks. + +Overall, there are two primary differences between MS-Unet and Swin-Unet. First, as the core unit of Swin-Unet, the swin transformer block ignores the importance of local-scale information, which leads to some objects (e.g., faces with different sizes) being distorted after correction. Second, directly employing the skip connection may not be the optimal scheme for hierarchical features fusion owing to their difference. To alleviate these issues, we leverage the MSTB as the basic unit of our MS-Unet to integrate local-scale and long-range information. Furthermore, the simple yet efficient SFB is designed to replace the skip connection. + +# 3.2.2 Multi-Scale Swin-Transformer Block (MSTB) + +Similar to EMSA of RestT [39], we develop the dense connection module (DCM) into the MSTB for local multiscale information extraction. In Fig.3 (b), two successive MSTBs are presented. Each MSTB contains the DCM, layernorm (LN), multi-head self-attention (MSA), skip connection, and multi-layer perceptron (MLP). The window partitioning (WP) and shifted window partitioning (SWP) are used in two successive MSTBs. + +When the features $X \in \mathbb{R}^{C \times H \times W}$ with a height of $H$ and a width of $W$ are fed into the MSTB, they will pass through two parallel branches for computing the input of MSA (the query $Q$ , key $K$ , and value $V$ ). In the left branch, $X$ are split into non-overlapping windows with a size of $h \times w$ by (S)WP. The features are flattened and reshaped as $X_{f} \in \mathbb{R}^{N \times C}$ , where $N = h \times w$ . Then a full con + +nction layer is applied to obtain query $Q \in \mathbb{R}^{N \times d}$ , where $d = C / k$ and $k$ is the head number. In the right branch, the features $X$ are first utilized to extract local-scale information by DCM. Inspired by [14], the DCM consists of two $1 \times 1$ layers, and three $3 \times 3$ depthwise separable convolution layers with different dilation rates $D = (1,2,3)$ . To be specific, the $1 \times 1$ convolution layers are employed to change the feature dimension. Each $3 \times 3$ depthwise separable convolution layer will receive the features from all preceding layers (i.e., $x_0, \ldots, x_{r-1}$ ) as input: + +$$ +x _ {r} = C _ {r} ([ x _ {0}, \dots , x _ {r - 1} ]), \tag {2} +$$ + +where $C_r$ denotes the concatenation operation. Then we apply the same operations like the left branch on these features from the DCM to generate $X_m \in \mathbb{R}^{N \times C}$ . The key $K \in \mathbb{R}^{N \times d}$ , and value $V \in \mathbb{R}^{N \times d}$ are obtained through $X_m$ . Afterward, the MSA can be calculated as follows: + +$$ +M S A (Q, K, V) = \operatorname {S o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d}} + B\right) V, \tag {3} +$$ + +where $B\in \mathbb{R}^{N\times N}$ refers to learnable relative position bias. + +# 3.2.3 Skip Fusion Block (SFB) + +As mentioned above, the crucial difference among features from different hierarchical stages will be ignored when directly adopting skip connection. Hence, we designed the simple yet efficient skip fusion block (SFB) to replace the skip connection. As shown in Fig. 3 (c), before the features $X^{i} \in \mathbb{R}^{N \times C}$ , $X^{j} \in \mathbb{R}^{N \times C}$ (from the $i^{th}$ stage of encoder, and the $j^{th}$ stage of decoder) are sent to the next stage of decoder, they pass through the SFB to form new features $X_{SFB}^{ij}$ with dimension $\mathbb{R}^{N \times C}$ . The whole calculation process is defined as follows: + +$$ +X _ {S F B} ^ {i j} = D \left(C O N \left(C \left[ D \left(X ^ {i}\right), D \left(X ^ {j}\right) \right]\right)\right), \tag {4} +$$ + +where $D(\cdot)$ is dimension permuting, $C[\cdot]$ refers to the concatenation, and $CON(\cdot)$ is 1D convolution layer. + +# 3.3. Loss Function + +In practice, the MS-Unet is optimized by adopting the supervised losses on the labeled data $L$ , and the semi-supervised losses on the unlabeled data $U$ . + +# 3.3.1 Supervised Loss + +Our constructed supervised loss $\mathcal{L}_s$ is composed of three parts, including mask-based $L1$ loss $\mathcal{L}_{m1}$ , mask-based sobel loss $\mathcal{L}_{ms}$ , and the cross-entropy loss $\mathcal{L}_{ce}$ . The detailed definitions are described as follows: + +a) $\mathcal{L}_{m1}$ Loss: In our method, we introduce the weighted mask, which uses the weight value of the portraits area to be + +greater than that of the background so that the network will pay more attention to the distorted portraits. Eq. 5 gives the definition of this loss. + +$$ +\mathcal {L} _ {m 1} = \left| F ^ {\prime} - F \right| M, \tag {5} +$$ + +where $F$ and $F^{\prime}$ represent the ground truth and estimated flow maps, respectively, $M$ denotes the weighted mask. + +b) $\mathcal{L}_{ms}$ Loss: In portraits correction, the object edges directly affect the overall visual effects of a correction image. Therefore, we introduce the sobel loss, which can be expressed as follows: + +$$ +\mathcal {L} _ {m s} = \left[ \left| G _ {x} \left(F ^ {\prime}\right) - G _ {x} (F) \right| + \left| G _ {y} \left(F ^ {\prime}\right) - G _ {y} (F) \right| \right] M, \tag {6} +$$ + +where the $G_{x}$ and $G_{y}$ mean the sobel operator in horizontal and vertical direction, respectively. + +c) $\mathcal{L}_{ce} \text{Loss}$ : To supervise the mask generated from the segmentation task, we convert the ground truth flow map into a mask label and deploy the cross-entropy loss. The loss function is defined as follows: + +$$ +\mathcal {L} _ {c e} = S \log \left(S ^ {\prime}\right) + (1 - S) \log \left(1 - S ^ {\prime}\right), \tag {7} +$$ + +where the $S$ is the ground truth mask converted from the flow map, and the $S^{\prime}$ refer to the estimated mask. To sum up, the training loss for a labeled image is: + +$$ +\mathcal {L} _ {s} = \mathcal {L} _ {m 1} + \lambda_ {1} \mathcal {L} _ {m s} + \lambda_ {2} \mathcal {L} _ {c e}, \tag {8} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are hyper-parameters of $\mathcal{L}_{ms}$ loss and $\mathcal{L}_{ce}$ loss respectively, both being set to 10 in our experiments. + +# 3.3.2 Semi-Supervised Loss + +For an unlabeled image, we construct the unsupervised loss $\mathcal{L}_u$ based on the surrogate (segmentation) task and flow map task, which is used to guide the prediction consistency of the network. Specifically, The unsupervised loss contains two parts: the loss of DRC $\mathcal{L}_{DRC}$ and RC $\mathcal{L}_{RC}$ . + +$$ +\begin{array}{l} \mathcal {L} _ {u} = \mathcal {L} _ {R C} + \mathcal {L} _ {D R C} \\ = \left[ \mathcal {L} _ {m 1} \left(F _ {1} ^ {\prime}, F _ {2} ^ {\prime}\right) + \lambda_ {2} \mathcal {L} _ {m s} \left(F _ {1} ^ {\prime}, F _ {2} ^ {\prime}\right) \right] + \tag {9} \\ \end{array} +$$ + +$$ +[ \mathcal {L} _ {c e} (S _ {1} ^ {\prime}, S _ {1} ^ {\prime \prime}) + \mathcal {L} _ {c e} (S _ {2} ^ {\prime}, S _ {2} ^ {\prime \prime}) ], +$$ + +where the $F_{1}^{\prime}$ and $F_{2}^{\prime}$ are the estimated flow maps from both the branches of the siamese network, $S_{1}^{\prime}$ and $S_{2}^{\prime}$ refer to the segmentation mask converted from $F_{1}^{\prime}$ and $F_{2}^{\prime}$ , while the $S_{1}^{\prime \prime}$ and $S_{2}^{\prime \prime}$ indicate the output of the siamese network. + +# 4. Experiments + +# 4.1. Implementation Details + +# 4.1.1 Datasets + +Following the existing method [29], we conduct extensive experiments on the wide-angle dataset [29], captured + +![](images/02357a748435258c81729c321520e2ab67e640476c57164277e63c260396e3ce.jpg) + +![](images/aaf9ce42972db621ec004e0da8707733666c7b1067584de95bf8cc9c32aca73b.jpg) + +![](images/429dee6ad26ff66de477bcf54b68bf2f529f33a8884977486bc1639db8d0223d.jpg) + +![](images/cdb477fa93743f469b9564cffaacbeb8fb772872c4e8d09a540a426a83c12875.jpg) + +![](images/bfd5c86678c4baf7baae602101656e2568a1124ab076aeda1c712debd0b7be96.jpg) +(a) Projection Image + +![](images/83912f21c7f033e43484651e41e5f4608ba1e32d83326a8c66f8cebcf2fe4b2d.jpg) +(b) Shih's Result + +![](images/81f84b2c5dca3265ef3fe8cc7d33e65ce756547b1d88c7e8ee68329dbfbf2383.jpg) +(c) Tan's Result +Figure 4. Qualitative results of different correction methods. Notice the coordination of lines and face area marked with red boxes. + +![](images/1dcfd58688fbf5b024d3c0348b21df91e518d5ec55aa0c4491394a975974ac79.jpg) +(d) Our Result + +with 5 different smartphones. The training dataset contains over 5,000 images and 129 in the testing dataset. Many kinds of labels are provided for each image in the dataset, containing the face mask, correction flow maps, and landmarks. In addition, we collected more than 5,000 images by 4 different smartphones (including Samsung Note 10, Xiaomi 11, vivo X23 and vivo iQOO) as the unlabeled set. + +# 4.1.2 Training Details + +We train the MS-Unet via a two-step scheme. Similar to [29], the input size is set as $512 \times 384$ . Before the semi-supervised strategy starts, we need to train a correction flow map predictor, which can provide the pseudo labels for the surrogate task when both labeled and unlabeled images are utilized. We found that the predictor can achieve good results with only 200 epochs. Then, we introduce the surrogate task (segmentation) to the network, which can enhance the learning ability of the network. Based on the surrogate task, the semi-supervised method can further improve the network's performance. In this stage, the total training epoch is set to 1,000. Notably, the supervised loss is utilized for labeled images, while the unsupervised loss is for unlabeled images. To compute the loss conveniently, each batch only contains the labeled images or unlabeled images. For both steps, we use Adam to optimize our model with an initial learning rate of $1 \times 10^{-4}$ , and the weight decay of $2 \times 10^{-4}$ . We trained the MS-Unet (8.82 GFLOPs, Parameters: 8.79M) using 4 Geforce RTX 2080Ti, and tested it with only one GPU, which can run at around 40 FPS. + +# 4.1.3 Evaluation Metrics + +We use the same evaluation metrics (LineAcc and ShapeAcc) as [29] to evaluate the performance of our method. + +More specifically, LineAcc is used to evaluate the curvature variation of the marked lines and defined as follows: + +$$ +L S = 1 - \frac {1}{n} \sum_ {i = 0} ^ {n - 1} \left(\frac {y _ {d _ {i}} - y _ {d _ {i - 1}}}{x _ {d _ {i}} - x _ {d _ {i - 1}}} - \frac {y _ {g _ {0}} - y _ {g _ {n}}}{x _ {g _ {0}} - x _ {g _ {n}}}\right), \tag {10} +$$ + +where $LS$ denotes the similarity between slope of these two lines, $n$ is the number of uniformly sampled points in each line. $(x_{g_i},y_{g_i})$ and $(x_{d_i},y_{d_i})$ indicate the coordinate of the corresponding point in the reference and distortion image. + +ShapeAcc aims to evaluate the face similarity between the correction image and the reference image. Based on face landmarks, the ShapeAcc is described as follows: + +$$ +F C = \frac {1}{n} \sum_ {i = 0} ^ {n - 1} \| L _ {g _ {i}} \| \| L _ {d _ {i}} \| \cos \theta , \tag {11} +$$ + +where $FC$ is the similarity between the corrected and target face, $n$ is the number of fixed sampled points in each face. $L_{g}$ and $L_{d}$ are the corresponding face landmarks in the correction image and the reference image. + +# 4.2. Ablation Study + +In order to verify the influence of different factors on our proposed method, we conducted some ablation experiments on Tan's dataset [29] and our unlabeled dataset. Notably, the network structure, the semi-supervised strategy, and the number of unlabeled samples are all considered below. + +# 4.2.1 Effect of the Correction Network + +We explore that how the proposed modules affect the network performance using fully-supervised method. Specifically, we utilize the Swin-Unet as our baseline, and the performance of three different networks is evaluated. 1) Baseline: directly employ the Swin-Unet; 2) Baseline+MSTB: + +based on 1), the MSTB is considered to replace the swim transformer block; 3) Baseline+MSTB+SFB (MS-Unet): the SFB is added to fuse the hierarchical features, and Table 1 presents the results. We can observe that the performance boosts significantly with the addition of each module from the table. Oddly, when both MSTB and SFB are added to the network, the full MS-Unet can achieve the best LineAcc (66.825) and ShapeAcc (97.491). These experiments demonstrate that MSTB indeed promotes the network to extract more complementary information, which boosts the correction ability dramatically. Meanwhile, SFB provides a better feature fusion strategy than skip connections. + +In addition, we compared MS-Unet and Tan's method under the same conditions, and the experiment shows that the accuracy of MS-Unet is slightly higher than Tan's network (LineAcc: 66.784, ShapeAcc: 97.490). + +Table 1. Ablations on the structure of proposed MS-Unet. + +
IndexBaselineMSTBSFBLineAccShapeAcc
1)✓--66.51497.460
2)✓✓-66.76397.487
3)✓✓✓66.82597.491
+ +# 4.2.2 Effect of the Semi-Supervised Strategy + +Several experiments are conducted to evaluate the impact of our proposed semi-supervised scheme. In practice, we first utilize the fully-supervised method to train our MS-Unet with only Tan's dataset [29]. The training result is regarded as the baseline for comparison, and we present it in the first row shown in Table 2. Then we add the surrogate task to the network and train the two-task MS-Unet. The second row in Table 2 reports the results of the two-task MS-Unet. Compared with the baseline, it shows a slight improvement after adding the surrogate task (LineAcc: $66.825 \rightarrow 66.871$ , ShapeAcc: $97.491 \rightarrow 97.493$ ). The result indicates that introducing a surrogate task plays a guiding role in networking training to a certain extent. Afterward, both labeled (Tan's dataset) and unlabeled data are deployed to accomplish the experiments about semi-supervised strategy. The DRC is conducted based on the segmentation task, and the third row in Table 2 lists the comparison result. Compared with the two-task MS-Unet, adding DRC can further improve the estimation accuracy of the correction flow maps, especially the LineAcc (from 66.871 to 67.154). Besides, the effect of RC is also evaluated, and the result is presented in the fourth row of Table 2. The result also outperforms the single-task MS-Unet, which is only trained by the fully-supervised scheme. The MS-Unet attains the best result (LineAcc: 67.209, ShapeAcc: 97.500) when DRC and RC are employed during the semi-supervised training. These experiment results prove + +Table 2. Performance comparison of different semi-supervised strategies. 'Seg' indicates a segmentation task without direction and range consistency. 'DRC' refers to the direction and range consistency, and 'RC' refers to the Regression Consistency. + +
BaselineSegDRCRCLineAccShapAcc
1)✓---66.82597.491
2)✓✓--66.87197.493
3)✓✓✓-67.15497.494
4)✓--✓66.84897.497
5)✓✓✓✓67.20997.500
+ +that our proposed semi-supervised strategy can assist the consistency learning between portraits correction task and surrogate and improve the correction performance. + +# 4.2.3 Effect of the Number of Unlabeled Samples + +We examine the influence of the number of unlabeled images on network performance through Tan's dataset [29] and our unlabeled data. We change the number of unlabeled images from 0 to 5,000 while the number of labeled images is fixed. The results are listed in Table 3, where it shows our MS-Unet trained with semi-supervised strategy obtains consistent superior performance compared with that using the fully-supervised scheme. Meanwhile, we can draw that in a specific range, the performance of the MS-Unet will improve as the amount of unlabeled images increases. + +Table 3. The impact of the number of unlabeled images. + +
IndexnumbersLineAccShapeAcc
1)066.87197.493
2)100066.92997.493
3)200066.99997.494
4)300067.10597.497
5)400067.15597.496
6)500067.20997.500
+ +# 4.3. Comparison with Other Methods + +We also compare our method with previous state-of-the-art methods on Tan's and Google's test sets. Table 4 illustrates that our method obtains the highest metric results in both two test sets. The visual comparisons in Fig. 4 also confirm the results. Note that the projection image can correct lines but make faces distorted seriously. Shih [26] and Tan [29] try to seek the optimal trade-off between the faces and the background. Unfortunately, several bent structures still exist in the background, and a few faces are still distorted. From our results, the faces are more natural than other methods, and the corrected lines in the background are satisfactory. Generally, both quantitative and qualitative results verify the superior performance of our method. + +![](images/442fd8aa1b73b9596a2a1fdf8990a898735d47d429571a13a9f0560d4c6985ea.jpg) +(a) Distortion Image + +![](images/4ef8cc74e97efba14180a0f9cd724f1a20f79e951eba3eb938b4cfd8b41e5d6a.jpg) +(b) Projection Image + +![](images/55b26405a09bf9354a286f212ef0ea1e708b1a6d0bb562e045b8806cfd1a6ba9.jpg) +(c) iPhone12's Result +Figure 5. Visual comparison between our method and some wide-angle portraits correction methods from smartphones. + +![](images/c52f235a65c15ed8c47d5ed9c0eab9f31f90efa9dfe8c60c66c002c0f05ff7c2.jpg) +(d) Xiaomi11 ultra's Result + +![](images/0d18edd03ac3152c78856a970db8c7d2cefe139b88153d51decf3f49534bb530.jpg) +(e) Our Result + +Table 4. The results of our proposed method and the two classic methods on two wide-angle portraits correction test sets. + +
MethodTan's test setGoogle's test set
LineAccShapeAccLineAccShapeAcc
Shih [26]66.14397.25361.55197.464
Tan [29]66.78497.49064.65097.499
Ours67.20997.50066.09897.512
+ +Fig. 5 depicts the results of our method and other famous portraits correction algorithms from smartphones (i.e., Xiaomi 11 ultra, and iPhone 12). We can observe that serious stretching of portraits appears in iPhone 12. Although Xiaomi 11 ultra improves over the distortion image, there is still slight deformation on the face and curved lines in the background. Our method shows better results, as the face is natural while correcting the lines in the background. + +Only a few wide-angle portraits correction works employ the deep learning methods due to its challenge. Based on the correction flow maps, the correction task is regarded as a pixel-level regression problem, which is closely related to some other tasks, such as crowd counting [10, 21] and semantic segmentation [2, 5]. Hence, we introduce some efficient networks from these fields to predict the correction flow maps. All the networks are trained by the fully-supervised scheme, and Table 5 shows the results. Notably, our proposed MS-Unet surpasses all the methods. The primary reason is that the CNN-based networks focus on learning local-scale information while the transformer-based networks concentrate on long-range information. For wide-angle portraits, the long-range information can ensure the corrected image generally looks more natural, and the face corrected by local information is more authentic. Therefore, combining both advantages, the MS-Unet will capture multi-scale information for more accurate estimation. + +Finally, our proposed semi-supervised strategy is used to train these networks. Different from the original network architecture, the surrogate task is added to the network during + +Table 5. The effectiveness evaluation of the proposed semi-supervised scheme on different networks. + +
MethodFully-SupervisedSemi-Supervised
LineAccShapeAccLineAccShapeAcc
RefineNet [20]66.34897.44966.56997.455
UNet [25]65.24697.47366.53497.475
CSRNet [19]65.96797.46966.23697.471
Deeplab v3+ [5]66.20097.48266.56597.487
Swin-Unet [2]66.51497.46066.85997.469
HRNet [27]66.74897.47766.80597.491
Ours66.82597.49167.20997.500
+ +the training process. And all the semi-supervised results are listed in Table 5. We can observe that the accuracy of these networks assisted by both labeled and unlabeled data is improved compared with the conventional fully-supervised scheme. The experimental results also demonstrate the generalization ability of our semi-supervised method. + +# 5. Conclusion + +In this paper, we develop a novel semi-supervised wide-angle portraits correction method using a multi-scale transformer. By combining DRC and RC in our semi-supervised manner, we can solve the limitations of labeled data and fully utilize unlabeled data. In addition, four kinds of smartphones are adopted to collect unlabeled data. Furthermore, we especially propose the MS-Unet, built upon the MSTB, to capture both local-scale and long-range information for improving artifacts around portraits. Extensive experimental results show that our proposed method is much better than the existing advanced methods and can be popularized in the application of wide-angle portraits correction. + +Acknowledgement This work was supported by the National Natural Science Foundation of China (NSFC) under grants No.61872067 and No.62172032. + +# References + +[1] Yauhen Babakhin, Artsiom Sanakoyeu, and Hirotoshi Kitamura. Semi-supervised segmentation of salt bodies in seismic images using an ensemble of convolutional neural networks. In German Conference on Pattern Recognition, pages 218-231, 2019. 2 +[2] Hu Cao, Yueyue Wang, Joy Chen, Dongsheng Jiang, Xiaopeng Zhang, Qi Tian, and Manning Wang. Swin-unet: Unet-like pure transformer for medical image segmentation. arXiv preprint arXiv:2105.05537, 2021. 2, 4, 8 +[3] Robert Carroll, Aseem Agarwala, and Maneesh Agrawala. Image warps for artistic perspective manipulation. ACM Trans. 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We propose a general SWSL framework that can efficiently learn from both types of videos and can leverage any of the existing weakly-supervised action segmentation methods. Our key observation is that the distance between the transcript of an unlabeled video and those of the weakly-labeled videos from the same task is small yet often nonzero. Therefore, we develop a Soft Restricted Edit (SRE) loss to encourage small variations between the predicted transcripts of unlabeled videos and ground-truth transcripts of the weakly-labeled videos of the same task. To compute the SRE loss, we develop a flexible transcript prediction (FTP) method that uses the output of the action classifier to find both the length of the transcript and the sequence of actions occurring in an unlabeled video. We propose an efficient learning scheme in which we alternate between minimizing our proposed loss and generating pseudo-transcripts for unlabeled videos. By experiments on two benchmark datasets, we demonstrate that our approach can significantly improve the performance by using unlabeled videos, especially when the number of weakly-labeled videos is small. + +# 1. Introduction + +Many of humans everyday tasks are procedural, where a task consists of a sequence of actions that must be followed to achieve the desired goal. Therefore, there has been an explosion of instructional videos on the web, teaching how to perform tasks, such as cooking recipes, repairing devices, assembling furnitures, performing emergency first aid, etc. [1, 10, 15, 23, 38, 56, 66, 67]. Automatic learning of procedural tasks from instructional videos has important applications, such as teaching intelligent agents to perform + +![](images/3c1c30c2d5d5b2725d01014fcda59c0e02be99255d9f3d41b4e0314a2ff1ef9e.jpg) +Figure 1. Transcript variation within each task for three different tasks. + +complex tasks, constructing large knowledge bases of compact instructions, and automatic performance evaluation for executing tasks. Over the past several years, we have seen great advances on different aspects of learning from instructions [1,4,8,15,19,20,33,35-37,49,50,56,66,67]. + +A major challenge in learning from instructional videos is that videos are long and have many actions, therefore annotation is costly and complex. This poses a major challenge for scaling the learning to a large number of tasks and videos. Therefore, while a few fully-supervised methods have studied learning from densely-annotated videos [24, 27, 45, 49, 51, 53, 64, 66], the majority of existing works have focused on using less supervision. Specifically, weakly-supervised methods assume that each training video is accompanied with its transcript (ordered list of actions) [5, 7, 12, 30, 35, 44, 67] or action-set (unordered list of actions) [16, 31, 32, 36, 43]. While using weak supervision reduces the annotation cost by removing the need for specifying temporal boundaries of actions, it still requires annotators to watch entire videos. On the other hand, unsupervised methods remove the need for annotation by using unlabeled videos and leveraging the similarity of videos of the same task. However, existing similarity constraints, e.g., videos following the same sequence of actions or the same pairwise action ordering, are limiting and often violated in videos (see Figure 1). This has led to performance of unsupervised methods significantly lagging behind that of the weakly-supervised algorithms. + +Paper Contributions. Motivated by the above discussion, we study a new action segmentation problem in which we assume having access to a small number of weakly-labeled + +training videos and a large number of unannotated videos (with only task labels) from multiple tasks. We refer to this setting as Semi-Weakly-Supervised Learning (SWSL) of actions, whose goal is to learn a video segmentation model using both types of training videos. Using unlabeled videos allows us to effectively regularize learning from a small number of weakly-labeled videos, which would be insufficient for learning action segmentation/classifier using current methods. On the other hand, using weakly-labeled videos allows us to guide learning from unlabeled videos by leveraging a few transcripts of each task. + +We propose an SWSL method to find the parameters of a video feature learning module and an action classifier by simultaneously learning from weakly-labeled and unlabeled videos. Our key observation is that transcripts of unlabeled videos often have small but nonzero distances to the transcripts of the weakly-labeled videos from the same task, accounting for small variations by which the task could be accomplished. Therefore, we develop a differentiable Soft Restricted Edit (SRE) loss, which allows us to predict a transcript for an unlabeled video that is close to ground-truth transcripts of the weakly-labeled videos of the same task, yet could be different from them. To compute the SRE loss, we develop a flexible transcript prediction (FTP) method that uses the output of the action classifier to find both the length of the transcript and the sequence of actions occurring in an unlabeled video. Motivated by prior works on self-training [28, 62, 63], we propose a learning scheme in which we alternate between i) minimizing our proposed loss (sum of the weakly-supervised and SRE losses) on both types of videos; ii) adding a few most confident unlabeled videos and their pseudo-transcripts to the weakly labeled set. An advantage of our method is that it can use any existing weakly-supervised method. By experiments on two benchmark datasets of Breakfast [23] and CrossTask [67], we demonstrate the effectiveness of our approach. + +# 2. Related Works + +Action Segmentation. Depending on the supervision type, existing works on action segmentation in instructional videos can be divided into three categories. First, fully-supervised methods assume that frame-wise annotations of actions in videos are given [24, 27, 45, 49, 51, 53, 64, 66]. Second, weakly-supervised methods assume each training video comes with an ordered or unordered list of its actions [5, 7, 30, 31, 35, 36, 43, 44, 67] or its summary [39, 60]. Third, unsupervised learning methods exploit the common structure, cross-modality consistency or temporal information of videos of the same task to discover and localize actions [14, 15, 18, 25, 48, 50]. In this paper, we propose the new setup of semi-weakly-supervised learning from instructional videos, which has not been explored yet. + +Weakly-supervised action segmentation methods mostly + +use the transcripts to learn a mapping from video features to framewise action class probabilities, so the major difference among prior works is the choice of mapping functions and loss functions. In the paper, we leverage two existing weakly-supervised methods [30, 54]. Specifically, [30] uses a GRU layer with a fully-connected layer as the mapping function, while [54] uses a deep convolutional neural network. As for the loss functions, [30] uses a constrained discriminative forward loss (CDFL) to distinguish the valid frame labelings, consistent with the ground-truth transcripts, from invalid labelings. [54] has a module to predict the class and length of segments and uses the mutual consistency (MuCon) loss to enforce the consistency of the frame-wise probabilities and predicted segments. + +Semi-supervised learning (SSL) approaches aim to learn from both labeled and unlabeled data [21, 34, 41, 46, 61, 63, 65]. In video understanding, SSL has been studied for temporal action proposals, human pose estimation, salient object detection, action recognition, etc. [42, 52, 59, 62] There are two major directions in SSL: self-training and consistency regularization. Self-training based methods [28, 62, 63] first train a model using supervised methods and then predict pseudo-labels for unlabeled data. Consistency regularization, first proposed by [3] and extended in several works including temporal ensembling [26] and mean teacher [57], minimizes the discrepancy between predictions of perturbed input data. + +Sequence Alignment. Our work is related to sequence alignment. Dynamic Time Warping (DTW) is a classic algorithm to measure the distance between two temporal sequences [47]. Recent variants of DTW include differentiable approximations [9, 19] and allowing skipping outliers [13]. Weak sequence alignment algorithm (WSA) [50] performs one-to-one alignment while allowing some items to be unmatched, and is extended to be differentiable. However, all of these works require the alignment to strictly obey a temporal order. Order-preserving Wasserstein distance [55] can tackle local temporal distortion via optimal transport, but it is multiple-to-multiple or one-to-multiple alignment and not differentiable. Our work is motivated by edit distance, which measures the distance between two strings. Levenshtein distance [2,29] is a specific-type of edit distance that allows deletion, insertion and substitution, and can be computed by Needleman-Wunsch [40] algorithm. [22] extends the inputs of Needleman-Wunsch algorithm from strings to time series and makes it differentiable, but it does not allow adjacent transposition. Restricted Edit Distance and Damerau-Levenshtein distance [11, 17] allow the transposition of two adjacent characters, but neither of them are differentiable. Our proposed SRE loss is an extension of restricted edit distance, which can be applied to temporal sequences and is differentiable. + +![](images/b1db8390c9a56868d276f9859c8598fe5279a7a3b219667d4a01cf3ad0f5cbdb.jpg) +Figure 2. Alignment of two transcripts by different methods. + +Illustrative Example: To better highlight the difference between the Restricted Edit distance and other sequence alignment methods, Figure 2 shows the alignment between two transcripts by different methods. DTW strictly aligns every entry in the two sequences, leading to many false alignments. While Edit Distance or WSA can obtain a one-to-one alignment and skip some unmatched items, they strictly follow temporal ordering and cannot handle the transposition from "crack egg" to "add salt and pepper". In contrast, the Restricted Edit distance can handle outlier elements and the transposition of adjacent items. + +# 3. Problem Statement + +In the semi-weakly-supervised learning of actions, we assume there are $N$ weakly-labeled videos, $\{X_n^w\}_{n=1}^N$ , and $M$ unlabeled videos, $\{X_m^u\}_{m=1}^M$ . The videos come from multiple tasks and each video consists of a sequence of actions required to achieve the underlying task. Let $O$ denote the number of tasks and $A$ denote the number of action classes across all videos. Our goal is to learn a model that segments a test video into different actions and recognizes the action of each segment and the underlying task of the video. + +More specifically, for weakly-labeled training videos, we assume we have triplets $\{(X_n^w,G_n^w,y_n^w)\}_{n = 1}^N$ of video features, transcripts and task labels, + +$$ +\boldsymbol {X} _ {n} ^ {w} = \left(\boldsymbol {x} _ {n, 1} ^ {w}, \boldsymbol {x} _ {n, 2} ^ {w}, \dots , \boldsymbol {x} _ {n, T _ {n} ^ {w}} ^ {w}\right), +$$ + +$$ +\boldsymbol {G} _ {n} ^ {w} = \left(\boldsymbol {g} _ {n, 1}, \boldsymbol {g} _ {n, 2}, \dots , \boldsymbol {g} _ {n, L _ {n}}\right), \tag {1} +$$ + +$$ +y _ {n} ^ {w} \in \{1, \dots , O \}, +$$ + +where $\pmb{x}_{n,i}^{w} \in \mathbb{R}^{d}$ is the $d$ -dimensional feature of the $i$ -th frame in the $n$ -th weakly-labeled video and $T_{n}^{w}$ is the length of the $n$ -th video. Also, $G_{n}^{w}$ is the video transcript (weak label), with the one-hot encoding $g_{n,l} \in \{0,1\}^{A}$ denoting the $l$ -th action in the $n$ -th video, $L_{n}$ is the length of the transcript, and $y_{n}^{w}$ is the task label. For each task $o \in \{1,\dots,O\}$ , we denote the set of transcripts of all weakly-labeled videos from the task by $\mathcal{G}_o$ , i.e., + +$$ +\mathcal {G} _ {o} = \left\{\boldsymbol {G} _ {n} ^ {w} \mid \text {i f} y _ {n} ^ {w} = o, \forall n \right\}. \tag {2} +$$ + +![](images/09de01e8231b6704ee405d8e932227e214c4811ff9c55795472f141bb3103984.jpg) +Figure 3. Our proposed framework for learning from both weakly-labeled and unlabeled instructional videos of multiple tasks. + +On the other hand, for unlabeled videos, we have pairs $\{(X_m^u,y_m^u)\}_{m = 1}^M$ of video features and task labels, + +$$ +\boldsymbol {X} _ {m} ^ {u} = \left(\boldsymbol {x} _ {m, 1} ^ {u}, \boldsymbol {x} _ {m, 2} ^ {u}, \dots , \boldsymbol {x} _ {m, T _ {m} ^ {u}} ^ {u}\right), \tag {3} +$$ + +$$ +y _ {m} ^ {u} \in \{1, \dots , O \}, +$$ + +where $\pmb{x}_{m,i}^{u}$ is the feature of the $i$ -th frame in the $m$ -th unlabeled video, and $T_{m}^{u}$ is the length of the $m$ -th video. + +# 4. Semi-Weakly-Supervised Action Learning + +# 4.1. Overview of Proposed Framework + +We propose a general framework for jointly learning from (small) weakly-labeled and (large) unlabeled videos. As shown in Figure 3, our framework consists of two branches for learning from both types of training videos while using a shared action classifier. For weakly-labeled videos, in our proposed framework, we can flexibly use any existing weakly-supervised method. Let $\mathcal{L}_{weak}$ denote the associated loss, which is introduced in Sec. 4.2. + +For unlabeled videos, given the video features as inputs, we use the action classifier to output a framewise probability matrix $P \in [0,1]^{T \times A}$ that captures the probability of each frame belonging to each action. To predict the transcript of each unlabeled video, we propose a Flexible Transcript Prediction (FTP) algorithm that takes $P$ as input and outputs the transcript of the video and the associated segmentation. We use the key observation that the predicted transcript of an unlabeled video should have a small distance to the transcripts of the weakly-labeled videos of the same task, corresponding to small variations by which a task could be accomplished. Therefore, we propose the Soft Restricted Edit (SRE) distance, a differentiable loss that allows insertion, deletion, substitution and adjacent transposition for computing the distance between the predicted transcript and the training transcript set. Thus, we can predict transcripts of unlabeled videos that are sufficiently close to those of the weakly-labeled videos, instead of enforcing the predicted transcript to coincide with the training transcripts. + +As training proceeds, we generate pseudo-transcripts for the unlabeled videos and gradually add the videos with the most confident transcripts into the weakly-labeled set. This self-training strategy is introduced in Sec. 4.5. + +# 4.2. Weakly-Supervised Action Segmentation + +To learn from weakly-labeled training videos, whose set is denoted by $\mathcal{W}$ , weakly-supervised action segmentation learns a mapping $\mathcal{F}_{\Theta}:\mathbb{R}^{T\times d}\to \mathbb{R}^{T\times A}$ from the features of each video to framewise action class probabilities, $P$ , and uses the provided transcript, $G$ , for supervision, i.e., + +$$ +\min _ {\Theta} \sum_ {\mathcal {W}} \mathcal {L} _ {\text {w e a k}} (\boldsymbol {P}, \boldsymbol {G}), \text {w h e r e} \boldsymbol {P} = \mathcal {F} _ {\Theta} (\boldsymbol {X}). ^ {2} \tag {4} +$$ + +As an advantage of our framework, we can leverage any existing weakly-supervised method and use unlabeled videos to significantly improve its performance, especially when the number of weakly-labeled videos is small. In the paper, we use two state-of-the-art methods, MuCon [54] and CDFL [30], which we reviewed in Sec. 2. + +# 4.3. Flexible Transcript Prediction (FTP) + +Given the framewise probability matrix $\pmb{P} \in [0,1]^{T \times A}$ of a video, where $T$ is the number of frames and $A$ is the number of action classes, our goal is to predict the transcript probability, denoted by $Q \in [0,1]^{L \times A}$ , where $L$ is the predicted transcript length, i.e., the number of actions in the video. The $i$ -th row of $Q$ indicates the probabilities that the entry $i$ in the transcript will be each of the $A$ actions. Notice that both the transcript length and the sequence of actions are unknown. Therefore, we propose a Flexible Transcript Prediction (FTP) algorithm to estimate both. + +To tackle the problem, first notice that, given a fixed transcript length $L$ , we can find the segmentation boundary points $(t_0, t_1, t_2, \ldots, t_L)$ and the classes of segments $(a_1, a_2, \ldots, a_L)$ by solving + +$$ +\max _ {\left\{t _ {i} \right\}, \left\{a _ {i} \right\}} \prod_ {i = 1} ^ {L} \prod_ {j = t _ {i - 1} + 1} ^ {t _ {i}} p _ {j, a _ {i}} \quad \text {s . t .} \quad t _ {0} = 0, t _ {L} = T. \tag {5} +$$ + +In other words, we simultaneously search for the segmentation and the assignment of each segment $(t_{i-1} + 1, t_i)$ to an action class $a_i$ that gives the maximum likelihood. Given that the transcript length, $L$ , is itself unknown, we modify the problem to also search for a transcript of sufficiently small length. Thus, we add $L$ as a penalty to the negative log-likelihood in (5) and solve + +$$ +\min _ {\left\{t _ {i} \right\}, \left\{a _ {i} \right\}, L} - \frac {1}{T} \sum_ {i = 1} ^ {L} \sum_ {j = t _ {i - 1} + 1} ^ {t _ {i}} \log p _ {j, a _ {i}} + \lambda L \tag {6} +$$ + +$$ +\begin{array}{l} \text {s . t .} \quad t _ {0} = 0, t _ {L} = T, \ell_ {\min } \leq L \leq \ell_ {\max }, \end{array} +$$ + +# Algorithm 1: Flexible Transcript Prediction (FTP) + +input : Probability matrix $\mathbf{P} \in \left\lbrack {0,1}\right\rbrack {^T} \times A$ + +1 Compute cumulative sum of negative log-likelihood: + +$$ +s _ {t, a} = \sum_ {t ^ {\prime} \leq t} - \log q _ {t ^ {\prime}, a}; +$$ + +2 Compute the minimal cost of each segment: + +$$ +c _ {t _ {1}, t _ {2}} = \min _ {a} \left(s _ {t _ {2}, a} - s _ {t _ {1} - 1, a}\right), 1 \leq t _ {1} \leq t _ {2} \leq T; +$$ + +3 Dynamic program: $d_{t,l} = \min_{t' < t}(d_{t',l-1} + c_{t' + 1,t}),$ $t \in \{1, \dots, T\}, l \in \{1, \dots, \ell_{max}\}$ ; + +4 Optimal length: $L = \operatorname*{argmin}_{\ell_{\text{min}} \leq l \leq \ell_{\text{max}}} \frac{d_{T,l}}{T} + \lambda l$ ; +5 Back-tracking: $t_L = T$ + +$$ +t _ {i - 1} = \operatorname {a r g m i n} _ {t < t _ {i}} \left(d _ {t, i - 1} + c _ {t + 1, t _ {i}}\right), i \in \{L, \dots , 1 \}; +$$ + +$$ +\text {o u t p u t}: \text {S e g m a t i o n b o u n d a r y p o i n t s} \left(t _ {0}, \dots , t _ {L}\right). +$$ + +where $(\ell_{min},\ell_{max})$ is a predefined range for the transcript length (which can be estimated from weakly-labeled videos), and $\lambda$ is a regularization hyperparameter. + +To solve (6), we develop a dynamic programming-based method, shown in Algorithm 1. For each possible segment $(t_1,t_2)$ , we define a cost $c_{t_1,t_2} = \min_a\sum_{t = t_1}^{t_2} - \log p_{t,a}$ which corresponds to the inner summation of the first term in (6) and represents the negative log-likelihood of assigning the segment to its most likely action. We can calculate $c_{t_1,t_2}$ efficiently by precomputing the cumulative sum of negative log-likelihood. We then dynamically update $d_{t,l}$ , which computes the minimal cost value for the first $t$ frames and $l$ segments, via step 3, where we find an optimal boundary point $t^\prime$ that minimizes the cost of splitting the first $t^\prime$ frames into $l - 1$ segments and setting $(t^{\prime} + 1,t)$ as a segment. Here, $d_{T,l}$ denotes the minimal cost of splitting the video into $l$ segments, so we find the optimal length $L$ that minimizes (6). Finally, we recover the segmentation boundary points by back-tracking. + +After solving (6), we compute the probability matrix $Q$ of the predicted transcript using the geometric average of the probabilities within each predicted segment, i.e., + +$$ +q _ {i, a} = \left(\prod_ {t = t _ {i - 1} + 1} ^ {t _ {i}} p _ {t, a}\right) ^ {\frac {1}{t _ {i} - t _ {i - 1}}}. \tag {7} +$$ + +Computational Complexity. In Algorithm 1, the complexity of step 1 is $\mathcal{O}(T^2)$ , step 2 is $\mathcal{O}(T^2A)$ , step 3 is $\mathcal{O}(T^2\ell_{max})$ , step 4 is $\mathcal{O}(\ell_{max})$ and step 5 is $\mathcal{O}(L)$ . Thus, the overall complexity is $\mathcal{O}(T^2(\ell_{max} + A))$ . We can also significantly improve the complexity by a factor of $1 / S^2$ through applying a temporal average pooling with stride $S$ to $P$ , which we investigate in the experiments. + +# 4.4. Soft Restricted Edit (SRE) Distance + +We develop the differentiable Soft Restricted Edit (SRE) loss that finds the distance between two sequences while allowing the operations of insertion, deletion, substitution and adjacent transposition. This allows us to obtain + +a predicted transcript for an unlabeled video, $Q = (q_{1},\dots ,q_{L})$ , that has a small distance to the transcripts of the weakly-labeled videos of the same task. More specifically, with $\mathcal{G}$ denoting the set of transcripts $G = (g_{1},\dots ,g_{L^{\prime}})\in \{0,1\}^{L^{\prime}\times A}$ of the weakly-labeled videos of the same task, we propose to minimize $\mathcal{L}_{sre}$ defined as + +$$ +\mathcal {L} _ {s r e} (\mathcal {G}, \boldsymbol {Q}) \triangleq \min _ {\boldsymbol {G} \in \mathcal {G}} \operatorname {S R E} (\boldsymbol {G}, \boldsymbol {Q}). \tag {8} +$$ + +To motivate our method for computing SRE loss, we start with the toy example of restricted edit distance between two strings, and then generalize it to arbitrary sequences. + +Motivating Example. Consider the two strings of $\pmb{x} =$ (' $p'$ , ' $a'$ , ' $r'$ , ' $s'$ , ' $e'$ ) and $\pmb{y} =$ (' $e'$ , ' $r'$ , ' $a'$ , ' $s'$ , ' $e'$ , ' $r'$ '). Our goal is to find the least number of operations to convert one string into the other, where the admissible edit operations are insertion, deletion, substitution and transposition of two adjacent characters. As shown in Figure 4 (left), the restricted edit distance between the two strings is 3. + +To compute the restricted edit distance between two strings $\mathbf{x}$ and $\mathbf{y}$ , of lengths $L_{x}$ and $L_{y}$ , we use dynamic programming. We compute a cumulative cost matrix $\mathbf{E} = [e_{i,j}] \in \mathbb{R}^{L_x + 1 \times L_y + 1}$ whose entry $e_{i,j}$ is the distance between the first $i - 1$ entries of $\mathbf{x}$ and the first $j - 1$ entries of $\mathbf{y}$ , see Figure 4 (right). As a result, the last entry of $\mathbf{E}$ , i.e., $e_{L_x + 1,L_y + 1}$ corresponds to the restricted edit distance between the two sequences. We can recursively compute $e_{i,j}$ as the minimum among + +$$ +\left\{ \begin{array}{l} e _ {i - 1, j} + 1 (\text {d e l e t i o n}) \\ e _ {i, j - 1} + 1 (\text {i n s e r t i o n}) \\ e _ {i - 1, j - 1} + \mathbb {1} \left(\boldsymbol {x} _ {i - 1} \neq \boldsymbol {y} _ {j - 1}\right) (\text {s u b s t i t u t i o n}) \\ e _ {i - 2, j - 2} + 1, \text {i f} \left(\boldsymbol {x} _ {i - 2} = \boldsymbol {y} _ {j - 1}, \boldsymbol {x} _ {i - 1} = \boldsymbol {y} _ {j - 2}\right) (\text {t r a n s p o s i t i o n}) \end{array} \right. \tag {9} +$$ + +where $\mathbb{1}(\cdot)$ is an indicator function, which is one when its argument is true and is zero otherwise. Notice that the last entry in (9) is the cost of adjacent transposition. In our toy example, see Figure 4 (right), if we want to update the $(4,4)$ -th entry of $E$ (the blue box), we check if the $2nd$ and $3rd$ characters in the two strings are the same but swapped. Since they are, we move two steps back and take the value of the $(2,2)$ -th entry (the orange box), which is 1, and increment it by one for the adjacent transposition cost. + +SRE Forward Propagation. We make the restricted edit distance to be differentiable (for efficient classifier and video feature learning) and extend it to handle the more general case of computing distances between sequences of vectors. In our case, the two sequences are the ground-truth transcript of a weakly-labeled video, $\pmb{G} = (g_{1},\dots ,g_{L^{\prime}})$ , and the predicted transcript of an unlabeled video, $Q =$ + +![](images/411f833b3d564c99352cbe8adf6fcc49760daacbd4f33d4d13fa09b5a3fe0203.jpg) +Figure 4. Left: restricted edit distance between two strings. Right: Cumulative cost matrix. The last entry is the distance between sequences. + +$(q_{1},\dots ,q_{L})$ . To achieve this, we modify (9) as + +$$ +e _ {i, j} = \min _ {\beta} \left\{ \begin{array}{l} e _ {i - 1, j} + c _ {D}, \\ e _ {i, j - 1} + c _ {I}, \\ e _ {i - 1, j - 1} + \delta_ {i - 1, j - 1}, \\ e _ {i - 2, j - 2} + \delta_ {i - 2, j - 1} + \delta_ {i - 1, j - 2} + c _ {T} (\forall i, j \geq 3), \end{array} \right. \tag {10} +$$ + +where i) we change the cost of edit operations from 1 to positive constant costs of $c_{D}, c_{I}, c_{T}$ for deletion, insertion and adjacent transposition, respectively; ii) for substitution, we use a continuous distance function $\delta$ between two vectors, instead of the indicator function; iii) to make the distance differentiable, we replace the minimum operation with soft-min, defined as $\min_{\beta} \{\alpha_{1}, \alpha_{2}, \ldots\} = -\beta \log \sum_{k} e^{-\alpha_{k} / \beta}$ , where $\beta$ is a smoothing hyperparameter. The Soft Restricted Edit (SRE) loss will be the last entry of cumulative matrix $E$ , + +$$ +\operatorname {S R E} (\boldsymbol {G}, \boldsymbol {Q}) = e _ {L ^ {\prime} + 1, L + 1}. \tag {11} +$$ + +Algorithm 2 summarizes the forward propagation steps for computing the SRE loss. + +In the paper, we compute the distance $\delta_{i,j}$ between the entry $i$ in the weakly-labeled transcript $\pmb{G}$ and the entry $j$ in the predicted transcript $\pmb{Q}$ using the inner product + +$$ +\delta_ {i, j} = - \left\langle \boldsymbol {g} _ {i}, \log \boldsymbol {q} _ {j} \right\rangle , \tag {12} +$$ + +which is the negative log-likelihood that the j-th action in the predicted transcript is the same as the i-th action in weakly-labeled transcript. + +SRE Backward Propagation. Given that an input to the SRE distance is $Q$ , which is obtained using the framewise probabilities from the action classifier, not only we can find the best alignment between the predicted transcript and weakly-labeled transcripts, but also supervise the learning of video features and action classifier to get a better alignment. Hence, to update $\Theta$ (parameters of the feature learning and classifier modules), we need to compute + +$$ +\nabla_ {\Theta} \operatorname {S R E} (\boldsymbol {G}, \boldsymbol {Q}) = \left(\frac {\partial \boldsymbol {Q}}{\partial \Theta}\right) ^ {T} \nabla_ {\boldsymbol {Q}} \operatorname {S R E} (\boldsymbol {G}, \boldsymbol {Q}). \tag {13} +$$ + +Let $J \triangleq \operatorname{SRE}(\mathbf{G}, \mathbf{Q})$ . We first define two intermediate variables $r_{i,j} = \frac{\partial J}{\partial \delta_{i,j}}$ and $h_{i,j} = \frac{\partial J}{\partial e_{i,j}}$ . As we show in the + +Algorithm 2: Forward Propagation for SRE +input: Pairwise cost matrix $\Delta = [\delta_{i,j}] \in \mathbb{R}^{L' \times L}$ ; $c_D, c_I, c_T, \beta \geq 0$ . +1 $e_{i,1} = (i - 1) \cdot c_D, i \in \{1,2,\ldots,L' + 1\}$ +2 $e_{1,j} = (j - 1) \cdot c_I, j \in \{2,\ldots,L + 1\}$ +3 for $i \gets 2$ to $L' + 1$ do +4 for $j \gets 2$ to $L + 1$ do +5 update $e_{i,j}$ via (10); +output: SRE Loss, $\mathcal{L}_{sre} = e_{L' + 1,L + 1}$ + +Algorithm 3: Backward Propagation for SRE +input: Pairwise cost $\Delta = [\delta_{i,j}]\in \mathbb{R}^{L^{\prime}\times L}$ cumulative cost $E = [e_{i,j}]\in \mathbb{R}^{L^{\prime} + 1\times L + 1};$ $c_{I},c_{D},c_{T},\beta \geq 0.$ +1 $h_{L^{\prime} + 1,L + 1} = 1$ +2 for $i\gets L^{\prime} + 1$ to 1 do +3 for $j\gets L + 1$ to 1 do +4 update $a_{i,j},b_{i,j},h_{i,j}$ via Eq. (13) in the supplementary material; +5 Update $r_{i,j}$ via (4.4) and set $\pmb {R} = [r_{i,j}]$ output: $\nabla_{Q}\mathrm{SRE}(\pmb {G},\pmb {Q}) = \left(\frac{\partial\pmb{\Delta}(\pmb{G},\pmb{Q})}{\partial\pmb{Q}}\right)^{T}\pmb{R}$ + +supplementary materials, we can efficiently compute $r_{i,j}$ using $h_{i,j}$ , and two auxiliary gradient matrices with entries defined as $a_{i,j} = \frac{\partial e_{i+1,j+1}}{\partial e_{i,j}}$ and $b_{i,j} = \frac{\partial e_{i+2,j+2}}{\partial e_{i,j}}$ , where + +$$ +r _ {i, j} = h _ {i + 1, j + 1} \cdot a _ {i, j} + h _ {i + 1, j + 2} \cdot b _ {i - 1, j} + h _ {i + 2, j + 1} \cdot b _ {i, j - 1}. +$$ + +We also show that $h_{i,j}, a_{i,j}, b_{i,j}$ can be recursively updated starting from the last row and column of $\pmb{E}$ . Algorithm 3 shows the backward propagation for computing the gradient with respect to $\pmb{Q}$ . Once finished, we can back-propagate the gradient w.r.t. $\Theta$ by using (13). + +# 4.5. Training and Inference + +To jointly learn from both weakly-labeled and unlabeled videos, we propose to minimize + +$$ +\mathcal {L} _ {s w s l} = \sum_ {n} \mathcal {L} _ {w e a k} \left(\boldsymbol {X} _ {n} ^ {w}, \boldsymbol {G} _ {n} ^ {w}\right) + \rho \sum_ {m} \mathcal {L} _ {s r e} \left(\mathcal {G} _ {y _ {m} ^ {u}}, \boldsymbol {Q} _ {m} ^ {u}\right), \tag {14} +$$ + +over the parameters of the feature learning and action classifier modules as well as searching over the predicted transcripts, shown in Figure 3, where $\rho \geq 0$ is a hyperparameter. The first term in (14) minimizes the distance between each weakly-labeled video and its ground-truth transcript, while the second term minimizes the distance between the predicted transcript of each unlabeled video and the set of weakly-labeled transcripts of the same task. + +Motivated by works on self-training [28, 62, 63], we propose a training strategy which alternates between minimizing $\mathcal{L}_{swsl}$ and moving some of the unlabeled videos and + +their predicted transcripts to the weakly-supervised set. We show that this approach works better than optimizing (14) once. More specifically, we minimize $\mathcal{L}_{swsl}$ using both the current weakly-labeled videos and unlabeled videos. We then generate pseudo-transcripts for unlabeled videos and add the unlabeled videos with the most confident pseudotranscripts to the weakly-labeled set (see below for details) and retrain the model by minimizing $\mathcal{L}_{swsl}$ , and so on. In the last iteration, all unlabeled videos have been moved to the weakly-labeled set, therefore, we minimize $\mathcal{L}_{weak}$ . + +For self-training, given an unlabeled video, we compute $\mathcal{L}_{weak}$ between the video and all transcripts in the weakly-labeled set, and find the transcript $G^{*} \in \{0,1\}^{L^{\prime} \times A}$ with the minimum loss. We use the transcript probability $Q \in [0,1]^{L \times A}$ produced by FTP, and compute the restricted edit distance between $G^{*}$ and $Q$ to find their alignment $M \in \{0,1\}^{L^{\prime} \times L}$ , where $m_{i,j} = 1$ indicates that the $i$ -th action in the transcript occurs in the $j$ -th segment in $Q$ . We then generate the one-hot pseudo-transcript for the unlabeled video using $\tilde{Q} = M^T G^{*}$ . Finally, we choose a few videos with the smallest loss values and add them along with their pseudo-transcript to the weakly-labeled set. + +Remark 1 A conventional self-training approach has two major differences with our method. First, it only minimizes the first term of (14), i.e., $\rho = 0$ . Second, it generates a pseudo-label for an unlabeled video using the most probable transcript from the training videos. However, this enforces the unlabeled videos to have exactly the same transcript as weakly-labeled videos, which is limiting, especially when the number of weakly-labeled videos is small. In the experiment, we show that this strategy does not perform well compared to our method. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets. For our experiments, we use two benchmark datasets of Breakfast [23] and CrossTask [67]. Breakfast consists of 1,712 videos of people making breakfast with 10 cooking tasks. The dataset contains 48 actions in total and on average, about 7 action instances are performed in each video. We use the existing 4 training/testing data splits in the dataset and report the average performance on the 4 splits. CrossTask consists of videos from 18 primary tasks. We follow [35] and use the 14 cooking-related tasks, which contains 2,552 videos and 80 classes of actions. We use the same training/testing split as in [35], with $90\%$ training and $10\%$ testing videos. For each dataset, we randomly split the training set into two subsets: one subset with weak labels (action transcripts and task labels), and the other subset with only task labels, and evaluate the performance on testing set. We investigate the effect of using different ratios of the number of weakly-labeled videos to the total number of videos used, including $1\%$ , $2\%$ , $5\%$ , $10\%$ , $20\%$ . + +Evaluation. For a comprehensive analysis of the results, we report multiple evaluation metrics. Following most works in action segmentation [25,30,35,54], we compute Mean over Frame (MoF), i.e., frame-wise accuracy, and intersection over union (IoU). Since in CrossTask, over $70\%$ of frames are background, simply predicting all frames as background will lead to a high MoF. Thus, to avoid this undesired effect, we also report the F1-score [14, 50] on CrossTask. + +Implementation Details. To show that our proposed framework can leverage any existing weakly-supervised action segmentation methods, we use MuCon [54] and CDFL [30]. To be consistent with prior works, on Breakfast, we use the 2048-dimensional RGB+Flow I3D features [6] for MuCon, and the 64-dimensional improved dense trajectory features [58] for CDFL. On CrossTask, we use the 3200-dimensional released features [67] for MuCon and, following [35], reduce the feature dimension to 64 via PCA for CDFL. The average number of frames on Breakfast is over 2000, so we apply a temporal average pooling with stride 8 before inputting the frame-wise probabilities into our Flexible Transcript Prediction (FTP) module. We start the training for several epochs using weakly-labeled videos, and then use both weakly-labeled and unlabeled videos to optimize (14). We generate pseudo-transcripts for the unlabeled videos in three rounds, each round adding $1/3$ of the unlabeled videos and their learned pseudo-transcripts to the weakly-labeled set. We keep the same setups as in the original works on MuCon and CDFL [30,54]. Due to space limitation, other details such as hyperparameter values are reported in the supplementary materials. + +Baselines. We mainly compare four methods: i) Weakly-Supervised Learning (WSL): we apply $\mathcal{L}_{weak}$ (MuCon or CDFL loss) on weakly-labeled videos only; ii) Semi-Weakly-Supervised Learning (SWSL): we apply $\mathcal{L}_{swsl}$ for all videos without generating pseudo-transcripts (i.e., without self-training); iii) WSL+Self: we use self-training in weakly-supervised methods, where we minimize only $\mathcal{L}_{weak}$ and iteratively generate pseudo-transcripts of unlabeled videos and add them to the weakly-labeled set and retrain the model; iv) SWSL+Self: our final approach, where we minimize our proposed $\mathcal{L}_{swsl}$ loss, while iteratively increasing the weakly-labeled set using self-training. + +# 5.2. Experimental Results + +Action Segmentation Performance. Tables 1 and 2 show the average performances of different methods on Breakfast and CrossTask when we use, respectively, MuCon [54] and CDFL [30] as the backbone weakly-supervised module in our framework. First, notice that using unlabeled videos always improves the performance of WSL. In particular, in Table 1, when the number of labeled videos is extremely small (1%), our method (SWSL+Self) improves the MoF by $14.0\%$ , IoU by $16.3\%$ on Breakfast, and MoF by $9.9\%$ . + +
WPUPBreakfastCrossTask
MoFIoUMoFIoUF1
WSL1%011.013.538.214.62.6
SWSL1%99%23.121.847.716.66.3
WSL+Self1%99%22.326.140.516.08.0
SWSL+Self1%99%25.029.848.117.98.9
WSL2%012.914.844.015.85.3
SWSL2%98%21.223.552.318.98.3
WSL+Self2%98%26.527.841.716.09.9
SWSL+Self2%98%26.730.644.617.811.3
WSL5%023.125.842.316.18.3
SWSL5%95%28.123.551.318.010.3
WSL+Self5%95%32.731.045.316.511.4
SWSL+Self5%95%32.531.750.618.311.5
WSL10%028.028.842.116.79.9
SWSL10%90%33.931.248.317.49.7
WSL+Self10%90%36.732.145.016.511.6
SWSL+Self10%90%36.333.449.018.012.1
WSL20%035.233.444.417.711.0
SWSL20%80%36.733.646.717.310.7
WSL+Self20%80%38.634.746.317.011.5
SWSL+Self20%80%39.836.154.519.311.8
WSL100%048.5†39.1*48.4*21.0*16.7*
+ +Table 1. Performance on Breakfast and CrossTask, when using MuCon as the backbone weakly-supervised module in our framework. (WP: Weakly-labeled video Percentage. UP: Unlabeled video Percentage. † reported in [54]; * obtained in our experiments.) + +IoU by $3.3\%$ and F1 by $6.3\%$ on CrossTask. Additionally, SWSL+Self significantly improves over WSL+Self, e.g., improves MoF by $2.7\%$ , IoU by $3.7\%$ on Breakfast, and MoF by $7.6\%$ , IoU by $1.9\%$ , F1 by $0.9\%$ on CrossTask. This shows the effectiveness of our proposed $\mathcal{L}_{sre}$ loss and simultaneously learning the model from both weakly-labeled and unlabeled videos. Finally, notice that combining self-training with our method (SWSL+Self vs SWSL) improves MoF by $1.9\%$ , IoU by $8.0\%$ on Breakfast, and MoF by $0.4\%$ , IoU by $1.3\%$ , F1 by $2.6\%$ on CrossTask. + +Transcript Prediction. Table 3 shows the normalized edit distance (smaller is better) between the predicted transcript and the ground-truth transcript on the test set. Notice that our SWSL+Self method performs better than WSL+Self in all cases. Given that the difference between the two methods is in using our proposed $\mathcal{L}_{sre}$ loss, the improvement shows that encouraging the transcript of unlabeled videos to have a small distance to the transcripts of weakly-labeled videos (instead of enforcing them to coincide) is beneficial for transcript prediction, especially when the number of labeled videos is small. Besides, the improvement is more remarkable on CrossTask than Breakfast, because CrossTask has more diverse transcripts and benefits more from allowing flexible transcripts. + +Comparison with Soft Edit distance. Table 4 compares the performance of our proposed Soft Restricted Edit (SRE) distance with Soft Edit (SE) distance, which does not allow adjacent transposition. Notice that, generally, SRE performs better than SE, especially when the number of weakly-labeled videos is small. This comes from the fact + +
WPUPBreakfastCrossTask
MoFIoUMoFIoUF1
WSL1%010.916.920.78.63.0
SWSL1%99%13.420.424.510.74.4
WSL+Self1%99%18.621.827.810.69.2
SWSL+Self1%99%32.429.521.89.29.9
WSL2%010.917.420.58.65.3
SWSL2%98%16.322.426.911.47.8
WSL+Self2%98%27.626.222.39.69.5
SWSL+Self2%98%35.430.021.49.110.1
WSL5%013.419.720.48.75.1
SWSL5%95%24.425.723.510.47.9
WSL+Self5%95%37.131.820.78.88.3
SWSL+Self5%95%39.631.322.69.111.3
WSL10%020.420.923.29.07.8
SWSL10%90%24.724.223.29.89.0
WSL+Self10%90%38.331.420.58.510.0
SWSL+Self10%90%40.432.424.09.311.7
WSL20%031.726.423.69.08.1
SWSL20%80%33.928.922.69.410.9
WSL+Self20%80%42.333.022.08.512.4
SWSL+Self20%80%43.533.024.89.013.2
WSL100%050.2†35.9*31.5*13.2*18.8*
+ +Table 2. Performance on Breakfast and CrossTask, when using CDFL as the backbone weakly-supervised module in our framework. (WP: Weakly-labeled video Percentage. UP: Unlabeled video Percentage. † reported in [30]; * obtained in our experiments.) + +
WPBreakfastCrossTask
WSL+SelfSWSL+SelfWSL+SelfSWSL+Self
1%0.4370.4220.5380.499
2%0.4190.4030.5100.468
5%0.3580.3350.4880.458
10%0.3640.3180.4810.424
20%0.3220.3120.4510.406
+ +Table 3. Normalized edit distance (smaller is better) between the predicted transcript and ground-truth transcript on the test set for MuCon. + +
WPMoFIoU
SESRESESRE
1%24.325.029.229.8
2%25.326.729.930.6
5%31.132.530.831.7
10%33.536.333.433.4
20%39.239.835.836.1
+ +Table 4. Comparison on Soft Edit distance (disallow adjacent transposition) and our proposed Soft Restricted Edit distance (allow adjacent transposition) for MuCon on Breakfast with respect to different Weakly-labeled video Percentage (WP). + +that when we have fewer labeled videos, the size of the weakly-labeled transcript set would be small, therefore, it is more likely that the order of adjacent actions in unlabeled videos would be different from that in the transcript set. + +Training Effect. Figure 5 shows the performance of two methods (SWSL+Self and SWSL) on the Breakfast test set as a function of training epochs. We train the model using weakly-labeled videos for 60 epochs and then add unlabeled videos for training. For SWSL+Self, we generate pseudotranscripts for unlabeled videos and add a subset of them to the weakly-labeled set in epoch 80, 100, 120. Notice that at epoch 60, adding unlabeled videos significantly improves the performance. For SWSL (right), the model converges + +![](images/2d765366c1d1ad46089901b5c1a3ef08e1f1dd0a2fcd9c817da89f9aa8a0fb49.jpg) +Figure 5. IoU of different methods on the Breakfast test set as a function of the number of training epochs. Left: SWSL+Self. Right: SWSL. + +![](images/0fa20f8736827930aa3d83825fa54d7022870ddf66bf2a26fc638c107eafbb5e.jpg) + +![](images/bdbf3c9c775e6d3af701e55c070a6aeacabff672bef7aaf20224ce1e35627dc6.jpg) +Figure 6. Segmentation results for a test video from the task 'make scrambled egg' in the Breakfast dataset. + +or even overfits after epoch 80. But if we generate pseudotranscripts for unlabeled videos (left), the performance still improves after each update. Besides, the improvement is more significant when we have $1\%$ weakly-labeled videos, which shows the effectiveness of our method in the case of an extremely small number of weakly-labeled videos. See supplementary materials for the plots of other methods. + +Qualitative Results. Figure 6 shows the segmentation of a test video from 'make scrambled egg' by different methods. This is a challenging case where the transcript of the test video is not present in the weakly-labeled training videos. WSL or WSL+Self will produce transcripts very different from the ground-truth, while the transcript predicted by SWSL or SWSL+Self is more close to the ground-truth. Furthermore, compared with SWSL, the boundary localization of SWSL+Self is more accurate, which shows the advantages of self-training. + +# 6. Conclusions + +We studied the new problem of semi-weakly supervised action learning from instructional videos. We proposed a Soft Restricted Edit distance that leverages unlabeled videos for training by encouraging the transcript of unlabeled videos to be close, yet possibly different, from those of the weakly-labeled videos of the same task. 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Kitani + +Carnegie Mellon University + +# Abstract + +A key component of understanding hand-object interactions is the ability to identify the active object – the object that is being manipulated by the human hand. In order to accurately localize the active object, any method must reason using information encoded by each image pixel, such as whether it belongs to the hand, the object, or the background. To leverage each pixel as evidence to determine the bounding box of the active object, we propose a pixel-wise voting function. Our pixel-wise voting function takes an initial bounding box as input and produces an improved bounding box of the active object as output. The voting function is designed so that each pixel inside of the input bounding box votes for an improved bounding box, and the box with the majority vote is selected as the output. We call the collection of bounding boxes generated inside of the voting function, the Relational Box Field, as it characterizes a field of bounding boxes defined in relationship to the current bounding box. While our voting function is able to improve the bounding box of the active object, one round of voting is typically not enough to accurately localize the active object. Therefore, we repeatedly apply the voting function to sequentially improve the location of the bounding box. However, since it is known that repeatedly applying a one-step predictor (i.e., auto-regressive processing with our voting function) can cause a data distribution shift, we mitigate this issue using reinforcement learning (RL). We adopt standard RL to learn the voting function parameters and show that it provides a meaningful improvement over a standard supervised learning approach. We perform experiments on two large-scale datasets: 100DOH and MECCANO, improving AP50 performance by $8\%$ and $30\%$ , respectively, over the state of the art. The project page with code and visualizations can be found at https://fuqichen1998.github.io/SequentialVotingDet/. + +# 1. Introduction + +Finding the active object – the object that is being manipulated by the human hand – is a crucial task towards under- + +![](images/3cc9b4f39a740ec0e1f555a5c33d1b4f3c933bb26b8e6426661a9e961705d1f8.jpg) + +![](images/cbafb8f13eded6e981c536a248e7b927131f7c308577333454131b156e041690.jpg) + +![](images/8d35c31a74d46a84c80797af2e74e5ab85a3e3400435314852b1c96d4c54e2c0.jpg) +Figure 1. Relational Box Field and Pixel-wise Voting visualization. Each green bounding box is an estimated active object bounding box for a pixel inside the blue input bounding box (initialized with a detected hand box). The voting function selects the majority vote prediction (red) as the improved active object bounding box estimate. To ensure visibility, we only show 200 sampled predictions. + +![](images/cbeda2797bbf0082cbb3d195bcd2ebeeac1ee530ecfde4100fbf80206bb5fc7d.jpg) + +![](images/a896d8eee1a25b2bcb8b846360246f2c7888946c81f0dab41ccbe4f18b3484dc.jpg) + +![](images/c574629f3c4be660afcd9bb93a5af3976807b1f7b81d2961caac27ab36c24fea.jpg) + +standing human-object interactions, especially in egocentric videos where hands are the only visible human parts. It is also an essential step to a variety of downstream tasks including joint hand-object pose estimation [6, 7, 19, 25, 33], reconstruction [5, 14], activity recognition [10, 20, 22], and imitation learning [34]. However, an accurate localization of the active object can be challenging due to natural occlusions caused by the hands during interactions. During a hand-object interaction, it is common for the hand to occlude most of the object in order to grasp the object. On one hand, this makes it hard to detect active objects. On the other hand, the appearance of the hand actually contains important information about the location, shape, size, and pose of the active object. It is important to develop computer vision algorithms that can leverage each pixel of the image, especially the hands and objects, to accurately esti + +mate a bounding box around the active object. + +To advance the state of art in active object detection, we introduce a pixel-wise voting function to improve the active object bounding box estimate while being robust to occlusion. The voting function takes as input an initial bounding box estimate of the active object (typically seeded by bounding box around the hand region), and then predicts an improved bounding box, where the improved bounding box is tighter and more centered around the active object. Inside the voting function, we predict a large set of improved active object bounding boxes, by allowing each pixel inside the input box to regress a new bounding box. We call the collection of active object bounding boxes as the Relational Box Field (RBF), as they represent a field of bounding boxes related to pixels inside the input bounding box. As we can observe in Fig. 1, the pixel-wise predictions can be quite diverse because they depend on features from different locations in the input image. Our method overcomes inconsistencies across the RBF by using a technique similar to [9,26,32,36], where our voting function finds the consensus from pixel-wise predictions by selecting the bounding box with a majority vote. Similar to the Hough transform, our voting scheme is able to minimize the influence of outliers and generate stable predictions through the power of aggregation. We also show later in our experiments that our voting scheme is more robust when compared to standard regression methods. + +While the voting function can provide a better active object bounding box estimation, one round of voting is typically not enough to accurately localize the active object. Similar to the idea of boosting [12] where one uses a sequence of computational units to iteratively improve prediction performance, we apply multiple rounds of the voting function to progressively obtain a more accurate active object bounding box. However, repeatedly applying a function trained for one-step prediction (i.e., supervised learning or behavior cloning) can result in a data distribution shift, also known as covariate shift [31]. For example, each time a one-step predictor is used in an auto-regressive manner (i.e., the output is passed as input for the next sequence), it can introduce small errors which can compound over the prediction sequence, leading to a data distribution shift, which can lead to bad performance towards the end of a sequence. In order to mitigate this issue, we use reinforcement learning (RL) to learn the proposed voting function. RL is designed to account for distribution shifts in auto-regressive processes by evaluating and optimizing over sequences. Specifically, we use a Markov Decision Process (MDP) to model the sequential decision-making process of obtaining an optimal active object bounding. In each step of the sequential decision-making process, the voting function (the MDP policy) takes an initial estimate of the active object bounding box as input (the MDP state) and predicts a new improved active object + +![](images/da76123da826770da3a2fa1ca301959be68ff19e0efbf14d56bd0c94eeb8d376.jpg) +Figure 2. Previous methods detect active object by first detecting hands and objects independently, followed by an interaction detection to match active objects and hands. Our method directly detects the active object corresponding to each hand a sequential decision-making process dependent on hand. + +![](images/c039dcf4cff2e4c1dace4fbbcb6ceba7ddd3c4cdddc9abcca6514b12e17b8507.jpg) + +bounding box (the MDP action and next state). Interestingly, we find that the first estimate of the bounding box of the active object can be seeded using a hand bounding box since active objects are usually near the hands. We demonstrate that using reinforcement learning provides a meaningful improvement over standard supervised learning models for active object detection. + +Our approach is evaluated on two large-scale hand-object interaction datasets: 100DOH [30] and MECCANO [27] datasets. Experiments show that our method achieves new state-of-the-art performance on both hand-object detection and active object detection tasks. We also demonstrate the better generalization ability of our model by evaluating its performance across the datasets. Last, we provide a comprehensive ablation study for our design choices. + +# 2. Related Work + +Human-object Interaction Detection As shown in Fig. 2, existing approaches [9,13,17,30] in human(or hand)-object interaction usually detect active objects in two steps: (1) detecting hand and object independently with a classical detector [3,8,28,37], followed by (2) an hand-object interaction detection to match hands and objects detected in the first step. One limitation of using classical object detectors is that they are not designed to detect objects under occlusions. Meanwhile, in these methods, the important relation- + +![](images/03275f9cd7d327b6fdd253b6db5d9b9f2be5dc812eb29238283c6821516f30fd.jpg) +Figure 3. Overview of the sequential decision-making process for active object detection. Our approach, seeded using a hand bounding box, progressively refines the current active object bounding box towards an optimal active object estimation. In each step, we use a voting function on the Relational Box Fields to predict a better active object bounding box based on the current input. + +ship between hand and object is also not considered when localizing the active object. Instead, our method achieves an accurate localization of the active object in a sequential decision-process dependent on hand, which is robust to occlusions and fully exploits the feature of hand, object, and their inter-dependency like human perception [11, 24]. + +Object Detection with Reinforcement Learning Different from classic object detection methods [8, 28, 37], RL-based detection approaches [2, 15, 21] progressively narrow down the scope from the initial guess to the object bounding box in a top-down sequential process based on the current observation and historical paths. Some RL methods [2, 15, 21] localize the visual objects in scenes using top-down sequential policies. Some methods [18, 35] combine RL with classical detectors to improve object detection performance or efficiency. For instance, [35] uses RL to efficiently generate bounding box proposals to replace the first stage of two-stage detectors like [28]. Similar to [2] training a localization agent that starts with the whole scene and narrows down to the object, we design an agent which starts from the hand box and progressively moves to the object touched by the hand. The key difference is our agent does not directly predict a single action that deforms the bounding box using translation and scaling. Instead, we propose a voting function that allows each pixel to have a different prediction and then finds the consensus from pixel-wise predictions, which essentially enables the agent to ignore noisy observation caused by occlusions. + +Dense Methods Most dense methods make a prediction for each pixel or patch in the image, then use voting to aggregate the results into a robust estimation. [26, 36] use pixel-wise predictions with Hough voting to localize keypoint for pose estimation. [32] uses patch-based voting to remove false-positive hypotheses from the background for joint object detection and depth recovery. [9] uses bounding-box-wise voting for human-object interaction detection. Different from the above methods, our proposed method progressively performs pixel-wise voting on the Relational Box Field to predict and improve the active object estimation from hand. + +# 3. Method + +The overview structure of our framework is illustrated in Fig. 3. To achieve robust object localization, especially under occlusion, we propose a voting function with the Relational Box Field that allows each pixel in the image to vote for a bounding box of the active object. To further refine the active bounding box estimation, we repeatedly apply the voting function until the bounding box converges. + +In the following subsections, we first explain the Relational Box Field with Pixel-wise Voting for improving the active object bounding box estimation. Then we describe how to use an MDP to model the sequential decision-making process that progressively obtains a more accurate active object bounding box. Finally, we describe the implementation details of the model and the hybrid training + +strategy consisting of imitation learning and reinforcement learning to learn an optimal policy efficiently. + +# 3.1. Relational Box Field with Pixel-wise Voting + +We describe a voting function for estimating an improved bounding box of an object from the input box. Specifically, we first predict a Relational Box Field which encodes bounding box predictions for every pixel inside the image. Then the predictions from the pixels inside the input box are aggregated into a single improved object box through pixel-wise voting. + +Relational Box Field The Relational Box Field $F$ is a field of active object bounding boxes in relationship to each pixel inside the image. Specifically, the estimated Relational Box Field $\hat{F} \in \mathbb{R}^{H \times W \times 5}$ has the same spatial resolution as the input image $I \in \mathbb{R}^{H \times W \times 3}$ . For a location $(u, v) \in \mathbb{R}^2$ , $\hat{F}_{u,v} \in \mathbb{R}^5$ represents its related object box in the form of + +$$ +\hat {F} _ {u, v} = \left[ \hat {r} _ {u, v}, \hat {\theta} _ {u, v}, \hat {h} _ {u, v}, \hat {w} _ {u, v}, \hat {c} _ {u, v} \right] \tag {1} +$$ + +where $\hat{r}_{u,v} \in \mathbb{R}^{+}$ and $\hat{\theta}_{u,v} \in [0,2\pi)$ represent the predicted relative displacement from $(u,v)$ to its related bounding box center in polar coordinate system. $\hat{h}_{u,v} \in (0,H]$ and $\hat{w}_{u,v} \in (0,W]$ are the height and width of the bounding box prediction at $(u,v)$ . $\hat{c}_{u,v} \in [0,1]$ is the confidence score of the prediction at $(u,v)$ . + +Loss for Relational Box Field During training, we supervise the Relational Box Field with respect to the set of ground truth bounding boxes $\mathcal{A}$ . Note that bounding boxes may overlap with each other. To alleviate the confusion due to overlapping, we remove the overlapped regions from each bounding box $a \in \mathcal{A}$ during training as clipped bounding boxes $a^{\star}$ : + +$$ +a ^ {\star} = a \cap (\coprod \mathcal {A}) \tag {2} +$$ + +where $\coprod$ denotes the disjoint union, i.e., the union of nonoverlapped areas in $\mathcal{A}$ . + +For each pixel $(u,v)$ inside the clipped bounding box $a^{\star}$ , we apply localization loss $L_{u,v}^{loc} - \text{smooth-} L_1$ regression loss on the predicted box parameters $(\hat{r}_{u,v},\hat{\theta}_{u,v},\hat{h}_{u,v},\hat{w}_{u,v})$ , and Focal Loss $L_{u,v}^{C}$ on the predicted confidence score $\hat{c}_{u,v}$ . Both $L_{u,v}^{loc}$ and $L_{u,v}^{C}$ are only applied in $a^{\star}$ . Given predicted $\hat{F}$ , the overall loss applied to a bounding box $a$ is the average of pixel-wise losses: + +$$ +L _ {\hat {F}} (a) = \frac {\sum_ {u , v \in a ^ {\star}} L _ {u , v} ^ {l o c} + L _ {u , v} ^ {C}}{| a ^ {\star} |} \tag {3} +$$ + +To reduce the bias towards large bounding boxes, we compute the total loss of Relational Box Field by averaging the loss of each bounding box + +$$ +L _ {\hat {F}} (\mathcal {A}) = \frac {\sum_ {a \in \mathcal {A}} L _ {\hat {F}} (a)}{| \mathcal {A} |} \tag {4} +$$ + +Weighted Pixel-wise Voting To improve the robustness against noise in the Relational Box Field prediction, we use pixel-wise voting to aggregate the predicted bounding box results. The voting function summarizes the bounding box predictions from all pixels belonging to the input box $a$ into an improved bounding box estimation $(\hat{x}^a, \hat{y}^a, \hat{h}^a, \hat{w}^a)$ as + +$$ +\hat {x} ^ {a}, \hat {y} ^ {a}, \hat {h} ^ {a}, \hat {w} ^ {a} = \operatorname {V o t e} _ {\hat {F}} (a) \tag {5} +$$ + +To identify the best location of the improved bounding box, we create a histogram of votes over bounding box parameters, where the predictions with larger confidence scores $\hat{c}_{u,v}$ contributes with larger weights. Specifically, we compute the voting scores of the target object box center $S_{\mathrm{center}}^a\in \mathbb{R}^{H\times W}$ , width $S_{\mathrm{width}}^a\in \mathbb{R}^W$ , and height $S_{\mathrm{height}}^a\in \mathbb{R}^H$ for the improved bounding box estimation from the input box $a$ as + +$$ +S _ {\text {c e n t e r}} ^ {a} (x, y) = \sum_ {u, v \in a} \hat {c} _ {u, v} \cdot \mathbb {1} (\left\lfloor u + \hat {r} _ {u, v} \sin (\hat {\theta} _ {u, v}) \right\rfloor = y). +$$ + +$$ +\mathbb {1} \left(\left\lfloor v + \hat {r} _ {u, v} \cos \left(\hat {\theta} _ {u, v}\right) \right\rfloor = x\right) +$$ + +$$ +S _ {\mathrm {w i d t h}} ^ {a} (w) = \sum_ {u, v \in a} \hat {c} _ {u, v} \cdot \mathbb {1} (\lfloor \hat {w} _ {u, v} \rceil = w) +$$ + +$$ +S _ {\text {h e i g h t}} ^ {a} (h) = \sum_ {u, v \in a} \hat {c} _ {u, v} \cdot \mathbb {1} (\lfloor \hat {h} _ {u, v} \rceil = h) \tag {6} +$$ + +where $\mathbb{1}(\cdot)$ is the indicator function and $\lfloor \cdot \rfloor$ is the function of rounding to the nearest integer. The optimal bounding box parameters $(\hat{x}_a,\hat{y}_a,\hat{h}_a,\hat{w}_a)$ are then obtained by retrieving the candidate with maximum voting score in $S_{\mathrm{center}}^a,S_{\mathrm{width}}^a,S_{\mathrm{height}}^a$ respectively. + +As shown in Fig. 4, the informative patterns (such as fingers and objects) produce more consistent predictions compared to irrelevant information such as background and occlusions. Since the voting function picks the box with the most votes as output, it allows the model to explicitly focus on informative patterns instead of irrelevant information. + +# 3.2.MDP + +Recall the goal of our method is to localize the active object bounding box $b^{o} = [x^{o},y^{o},w^{o},h^{o}] \in \mathbb{R}^{4}$ corresponding to a hand bounding box $b^{h} = [x^{h},y^{h},w^{h},h^{h}] \in \mathbb{R}^{4}$ in an image $I$ , where the $(x^{o},y^{o})$ and $(x^{h},y^{h})$ are the centers of the active object and hand box, and $w^{o},h^{o},w^{h},h^{h}$ stand + +for their widths and heights. Considering the remarkable success in hand detection [1, 23, 30], we assume the hand boxes is given. As the grasp appearance of human hands is highly indicative of the location and shape of the object being manipulated, we leverage this important clue by first generating an active object bounding box hypothesis using visual clues inside the hand bounding box. However, the object hypothesis based on only hand appearance could be ambiguous because a similar hand grasp could hold various objects. Thus, it is important to further refine the object estimation by incorporating object patterns from the estimated object bounding box as direct evidence. + +We find only one step of pixel-wise voting from the Relational Box Field could be insufficient to localize the active object accurately. Therefore, we propose to further refine the active object localization based on the updated estimation of the bounding box in a sequential decision-making process, which is modeled by an MDP. The state, action, dynamics, policy, and reward of the MDP are defined as follows. + +State The state $s_t$ at each timestamp $t$ consists of two parts: a local state and a global state feature which is consistent throughout the sequence. We use the current active object bounding box estimation $\hat{b}_t^o = [\hat{x}_t^o, \hat{y}_t^o, \hat{w}_t^o, \hat{h}_t^o] \in \mathbb{R}^4$ as the local state, where $(\hat{x}_t^o, \hat{y}_t^o)$ represents the center of estimated bounding box and $\hat{w}_t^o, \hat{h}_t^o$ stand for its width and height. The global state representation is a combination of the detected hand bounding box $b^h$ and the image feature $\mathcal{F} \in \mathbb{R}^{H \times W \times 256}$ extracted from image $I$ . + +$$ +s _ {t} = \left(\hat {b} _ {t} ^ {o}, b ^ {h}, \mathcal {F}\right) \tag {7} +$$ + +Our method does not require an initial active object bounding box guess. Instead, we exploit the visual clue inside the hand bounding box to generate the initial active object bounding box hypothesis. In other words, the local state $\hat{b}_0^o$ at timestamp $t = 0$ can be arbitrary initialized because it is ignored by the policy. + +Action Each action at timestamp $t$ is in the format of $a_{t} = [\Delta x_{t},\Delta y_{t},\Delta w_{t},\Delta h_{t}]\in \mathbb{R}^{4}$ , which are the offsets to update the center coordinate, width and height of the active bounding box estimation. + +Actions that do not significantly change the bounding box lead to the terminal state. We use the relative changes of the center, height, and width of the bounding box as the criterion for termination. Specifically, we check: + +$$ +\frac {\left| \Delta x _ {t} \right|}{\hat {w} _ {t} ^ {o}}, \frac {\left| \Delta y _ {t} \right|}{\hat {h} _ {t} ^ {o}}, \frac {\left| \Delta w _ {t} \right|}{\hat {w} _ {t} ^ {o}}, \frac {\left| \Delta h _ {t} \right|}{\hat {h} _ {t} ^ {o}} \tag {8} +$$ + +The terminal state will be triggered if all the relative changes are below a threshold. We set the threshold value to 0.05 in all of our experiments. + +Dynamics Our state transition dynamics $h:(s_t,a_t)\mapsto s_{t + 1}$ is a deterministic function, which leads to exactly one next state from one state-action pair. It updates the current state $s_t$ by adding the action $a_{t}$ (the offsets for bounding box parameters) to the current active object bounding box estimation $\hat{b}_t^o$ . Except when timestamp $t = 0$ , the action is applied to the hand bounding box $b^{h}$ since our method is conditioned on the hand location and appearance for the initial active object hypothesis. + +Policy The policy generates an action $a_{t}$ by applying the voting function on two relational box fields: hand-to-object box field $\hat{F}^{ho}$ and object refinement box field $\hat{F}^{oo}$ , which are predicted based on the image feature $\mathcal{F}$ in the current state $s^t$ . + +The hand-to-object box field $F^{ho}$ addresses the contact relation, which is used to generate an initial hypothesis of the active object box $\hat{b}_1^o$ . Specifically, $F^{ho}$ encodes the mapping from the hand pixels to the corresponding active object bounding box + +$$ +F ^ {h o}: (u, v) \mapsto \left(x ^ {o}, y ^ {o}, w ^ {o}, h ^ {o}\right) \quad \text {f o r} u, v \in b ^ {h} \tag {9} +$$ + +In $F^{ho}$ , the ground truth confidence score of contact relation $c_{u,v}^{ho} = 1$ if $(u, v)$ lies in a hand which is touching an object, while $c_{u,v}^{ho} = 0$ otherwise. + +The object refinement relational box field $F^{oo}$ exploits object local patterns inside the current object box estimation to further improve it. Specifically, $F^{oo}$ encodes the mapping from the pixels of active objects to their box center, width, and height. + +$$ +F ^ {o o}: (u, v) \mapsto \left(x ^ {o}, y ^ {o}, w ^ {o}, h ^ {o}\right) \quad \text {f o r} u, v \in b ^ {o} \tag {10} +$$ + +To summarize, at $t = 0$ , the policy generates an initial active object hypothesis by applying the voting in Eq. (5) to bounding box predictions within $\hat{F}^{ho}$ from pixels belonging to the hand bounding box $h^t$ . When $t > 0$ , the policy applies the voting in Eq. (5) to predictions within $\hat{F}^{oo}$ from pixels belonging to the current active object estimation $\hat{b}_t^o$ to vote for a refined active object bounding box. Specifically, the policy finds a local optimal active object bounding box estimation $\hat{b}_{t + 1}^o$ as: + +$$ +\hat {b} _ {t + 1} ^ {o} = \left\{ \begin{array}{l l} \operatorname {V o t e} _ {\hat {F} ^ {h o}} \left(b ^ {h}\right) & \text {i f} t = 0 \\ \operatorname {V o t e} _ {\hat {F} ^ {o o}} \left(\hat {b} _ {t} ^ {o}\right) & \text {o t h e r w i s e} \end{array} \right. \tag {11} +$$ + +where $\hat{b}_t^o$ is the local state and $b^{h}$ belongs to the global state representation in $s_t$ defined in Eq. (7). + +The output action of the policy $a_{t} = \pi (s_{t})$ is defined as the displacement towards the local optimal active object bounding box estimation $\hat{b}_{t + 1}^{o}$ from either current estimation $\hat{b}_t^o$ when $t > 0$ , or the hand bounding box $b^{h}$ when $t = 0$ . + +![](images/cbee894b1c7e55d26908778e14d783887d8262d273a8d4015c03b4776234770f.jpg) + +![](images/f98d823ccea14d1ba8f804f1ba5d8c2594136d7c071d2d6bd1e17e93015b2002.jpg) +Figure 4. We visualize the IoU (red indicates higher IoU) between the final active object box estimation (red) and the pixel-wise predictions inside the hand bounding box (blue). This figure shows voting is able to adapt predictions from informative hand parts like fingers as opposed to irrelevant parts like wrist and background. + +![](images/1bffb39842552a8829a7a317927be8dab78445a7655b1530a5fadb811b1d9687.jpg) + +![](images/4f64ee6fc75c7ae0f748a5bf97159c9a934577a39001104a7ee4655c4ccba320.jpg) + +![](images/8debff15c4bb5cace9b49a7db454d1cc8565084c98517114263eea75bc7458cf.jpg) + +![](images/35454efcff775244ed0fc278982981c2328338f668f59c8107aa7c1c81f8ad61.jpg) + +![](images/c71665459b6c57b8c15d07ba3eeb0a132ac2a7fa37fc9088cd8a551f1eef604f.jpg) + +![](images/694fed639cafb53f64503de77dcd9993fd49d715535721adadcc1615cd65c83f.jpg) + +![](images/4f5e464cec0d887602dda0929b1465ef2afdb596353326543dd29131c5d297de.jpg) + +![](images/7d4f35070c7389c1140bd490330784af6aaa092287213aaa251af1b8f5625f6d.jpg) + +Reward We design the reward $r$ as the accuracy of the active object bounding box estimation. As the action $a_{t}$ updates the active object bounding box from $\hat{b}_{t}^{o}$ to $\hat{b}_{t+1}^{o}$ , we use the GIoU [29] between $b_{t+1}^{o}$ and the ground truth $b_{o}$ as the reward at timestamp $t$ + +$$ +r \left(s _ {t}, a _ {t}\right) = \operatorname {G I o U} \left(\hat {b} _ {t + 1} ^ {o}, b ^ {o}\right) \tag {12} +$$ + +# 3.3. Implementation Details + +In this subsection, we describe the implementation details of our image feature extractor and the policy model. + +Image Feature Extractor Our image feature extractor $f$ is in an encoder-decoder style with self-attention. The network takes an input image $I \in \mathbb{R}^{H \times W \times 3}$ and outputs a feature map $\mathcal{F} \in \mathbb{R}^{H \times W \times 256}$ . For the encoder, we use a pretrained ResNet101 on ImageNet and modify it by changing the last two layers into dilated convolution to increase the spatial size of the feature map. To further exploit the synergy between hand and object, we apply one layer of image-wide self-attention (with details in the supplementary) on the deep feature before forwarding it to the decoder. In the decoder, the Atrous Spatial Pyramid Pooling from DeepLabV3+ [4] and bi-linear up-sampling are repeatedly performed to efficiently expand the feature map until its size matches the input size. + +Policy Model Our light-weighed policy model is a $1 \times 1$ convolution layer with an input channel of size 256 and an output channel of size 14. The policy model takes the image feature $\mathcal{F}$ and outputs the prediction of hand-to-object relational box field $F^{ho}$ and object refinement relational box field $F^{oo}$ . + +# 3.4. Finding a Policy with Hybrid Training + +It is challenging to learn the image feature extractor and policy model from scratch: a massive amount of random actions, in the beginning, provide weak training signals, and optimizing the image feature extractor for each state is slow. + +While our policy uses a deterministic voting scheme to predict the action, a set of optimal hand-to-object relational box field $F^{ho}$ and object refinement relational box field $F^{oo}$ would generate the same desired behavior as learning by the reward function. This design enables us to first use imitation learning to learn these two relational box fields in a fully supervised mode. Specifically, we perform multi-task training with an overall objective which is a linear combination of losses from hand-to-object and object refinement box fields following Eq. (4) to jointly pretrain the image feature extractor and policy model + +$$ +L _ {I L} = L _ {F ^ {h o}} (\mathcal {H}) + L _ {F ^ {\infty}} (\mathcal {O}) \tag {13} +$$ + +where $\mathcal{H}$ and $\mathcal{O}$ are the set of hand bounding boxes and active object bounding boxes in the image. In imitation learning, we use a batch size of 28 and an initial learning rate of $10^{-4}$ for 100 epochs with $10\times$ learning rate drop every 30 epochs. + +After pretraining, we freeze the weights in the image feature extractor and further train the policy model using reinforcement learning (RL) on the sequential predictions for the active object $b_{o}$ . We follow the standard policy gradient on the cumulative reward. For computational efficiency, we set the horizon $T = 5$ . In consistent with the ultimate objective of getting a final accurate active object, we do not discount the future reward by setting a discount factor $\gamma = 1$ . To improve the training stability, we add the losses of relational box fields as an auxiliary loss + +$$ +L _ {R L} = \sum_ {t = 0} ^ {T} \left(1 - r \left(s ^ {t}, a ^ {t}\right)\right) + L _ {F ^ {h o}} \left(b ^ {h}\right) + L _ {F ^ {o o}} \left(b ^ {o}\right) \tag {14} +$$ + +For reinforcement learning, we use a batch size of 48 and a learning rate of $10^{-5}$ for 5 epochs. We show that RL boosts the precision of localization in the supplementary. + +# 4. Experiments + +In this section, we demonstrate the performance of our approach on hand-object detection and active object detect- + +![](images/4b79ed8a78b9acd4d085e7d449d252aa93b40d0e8ecad4f32868d89991375cba.jpg) +Proposed HO Detector Ground Truth + +![](images/f1b87e195b467e339794f0c7176cd3763855d6216a070ffed82cccbe60caa6ee.jpg) +Figure 5. Comparison of qualitative hand-object interaction detection results on the 100DOH dataset, where HO Detector denotes 100DOH Detector [30]. The differences are highlighted using bold yellow arrows. It demonstrates our method not only provides more precise object localization (col. 1) but also is more robust to the scenes where objects are overlapped (col. 2, 3) or occluded by hands (col. 2, 3, 4, 5). + +![](images/5c351764f96e001528386a84025bce16616075fef36d97a831cd5352946fe436.jpg) + +![](images/13f662fdf90d504dde4b469fceef39a36f2bdd7ebd93950281a54581b1f1bfd8.jpg) + +![](images/ce82e781f349058b0a16a79c6e264a27381a8793d2e6838c032d2998a4e28e8e.jpg) + +
MethodsBackbone# of ParamsHand SourceAP50handAP75AP50AP25
Simple BaselineR10147MFasterRCNN [28]89.5928.1544.7347.57
100DOH Detector [30]R10147MFasterRCNN [28]89.5928.5046.9551.80
PPDM [17]DLA3421MCenterNet [37]89.6426.8945.8053.04
HOTR [16]R5051MDETR [3]90.2629.3049.2757.80
OursR10148MFasterRCNN [28]89.5929.9053.0257.15
Simple BaselineR10147MGround Truth10034.5144.6852.35
OursR10148MGround Truth10040.0554.8264.86
+ +Table 1. Results of hand-object interaction detection on 100DOH. The Simple Baseline method is described in Sec. 4.1. + +tion tasks. In order to show our method is capable of tackling both third-person and egocentric real-life applications, we evaluate on two challenging datasets: 100DOH [30] and MECCANO [27]. + +# 4.1. Experiments on 100DOH + +100DOH [30] is a large-scale benchmark for hand-object interaction. It has 99,899 frames (79,921 for training, 9,995 for validation and 9,983 for testing). Among the dataset, there are 189.6K annotated hands with 110.1K objects. For each hand, it is either paired with an active object bounding box or has no object. + +We use the same hand-object detection evaluation metrics used in [30], which calculates the average precision (AP) of the tuple (hand, object). Specifically, a tuple is considered as true positive if and only if: 1) the IoU between the predicted hand bounding box and ground truth is greater than or equal to the IoU threshold; and 2) the IoU between the predicted object bounding box and ground truth is greater than or equal to the IoU threshold. + +Since active objects are usually close to hands, we construct a Simple Baseline by first detecting hands and objects independently using Faster-CNN [28], and then assigning the closest object (in terms of box center Euclidean dis + +tance) to each hand as the active object. Besides Simple Baseline and the baseline in the dataset paper, we also adapt two recent methods on human-object interaction detection, PPDM [17] and HOTR [16], to our task by changing the subject from human to hand. We assign the object with the highest score in detected interaction tuple (hand, object) to the corresponding hand for evaluation. + +We report the AP at IoU thresholds of 0.75, 0.5, and 0.25. As a fair comparison against the baselines, we use detected hand bounding boxes from Faster-RCNN [28] as the input of the proposed method. As illustrated in Tab. 1, our method outperforms all baseline with similar hand detection as input. We also exhibit the maximum performance when ground truth hand bounding boxes are available. Some qualitative results with comparisons are displayed in Fig. 5, which shows the proposed method not only provides more precise object localization but also is more robust to occlusions. More qualitative results and visualization of object refinement are shown in the supplementary. + +# 4.2. Experiments on MECCANO + +MECCANO [27] is an egocentric dataset for human-object interaction understanding. It contains 64,349 frames which are annotated with active object boxes. Since there + +
MethodBackboneFinetuneAP75AP50AP25
100DOH Detector [30]R101X-11.17-
OursR101X9.0916.6123.97
100DOH Detector [30]R101✓-20.18-
OursR101✓12.9926.2534.88
+ +Table 2. Results of active object detection on MECCANO. We compare our method against 100DOH Detector [30]. + +
DatasetAggregation\(AP^{75}\)\(AP^{50}\)\(AP^{25}\)
100DOHCenter25.0052.3156.88
100DOHAverage25.5951.7756.41
100DOHVote29.9053.0257.15
MECCANOCenter9.5922.8532.78
MECCANOAverage12.8325.7634.66
MECCANOVote12.9926.2534.88
+ +is no hand bounding box and hand-object correspondence annotation in the MECCANO dataset, we perform Pseudo labeling in two steps to train our model. First, we adapt the pre-trained hand detector [30] to detect hands in all frames. Second, we assign the closest annotated active object to each hand box in terms of box centers. There is no human annotation involved in the Pseudo labeling, which leads to a fair comparison. + +Since MECCANO does not have the interaction annotation to train PPDM [17] and HOTR [16], we compare our methods against 100DOH Detector [30] in terms of standard object detection metrics: average precision (AP) at IoU thresholds of 0.75, 0.5, and 0.25. We first compare the generalization ability by directly evaluating models trained on 100DOH. Then we compare the performance by retraining the proposed method using automatically generated pseudo labels of MECCANO. Tab. 2 shows that our method has a better generalization ability when adapted to a new dataset without retraining, and better performance after retraining on the MECCANO dataset. More qualitative results and visualization of object refinement are shown in the supplementary. + +# 4.3. Ablation Studies + +We perform ablation studies on both 100DOH and MEC-CANO datasets. Specifically, we examine the effects of pixel-wise voting and the sequential decision-making process. More ablation study, runtime analysis, and discussion about limitations are included in the supplementary. + +Effect of Pixel-wise Voting The pixel-wise weighted voting is the key component of the proposed method to retrieve a single bounding box estimation from dense predictions + +Table 3. Ablation studies on different aggregation methods to retrieve estimation from dense predictions. + +
Dataset# of Voting\(AP^{75}\)\(AP^{50}\)\(AP^{25}\)
100DOH129.1849.5853.11
100DOH229.8053.1157.47
100DOH329.9253.1057.23
100DOH∞29.9053.0257.15
MECCANO17.3322.6132.94
MECCANO28.9722.5632.46
MECCANO310.3823.9133.03
MECCANO∞12.9926.2534.88
+ +Table 4. Ablation studies on the number of voting of the sequential decision-making process. + +while being robust to occlusions. To understand the effect of pixel-wise weighted voting, we visualize the heatmap of the IoU between pixel-wise bounding box predictions and the final predicted bounding box after voting aggregation in Fig. 4. As expected, voting picks the final estimated bounding box mostly based on the predictions in the regions of informative patterns such as fingers and objects as opposed to irrelevant information such as the background. We further quantitatively examine the effectiveness of pixel-wise voting by comparing it with two aggregation methods: 1) using the prediction from the central pixel of the input box, and 2) averaging the bounding box parameters of all predictions inside the input box. Table 3 reveals the superiority of using voting to aggregate dense predictions. + +Effect of Sequential Decision-Making Process We analyze whether applying the voting function multiple times could sequentially improve the active object bounding box estimation. Specifically, we report the performance after applying different numbers of the voting function. The results are shown in Tab. 4. For the 100DOH dataset, the performance converges after applying the voting function two times. On the MECCANO dataset, the performance is progressively improved with more iterations of voting. + +# 5. Conclusion + +In this paper, we propose a voting function with Relational Box Field to leverage each pixel as evidence to robustly predict the bounding box of the active object, despite under occlusions. The voting function is applied repeatedly to improve the active object estimation. 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Our key observation is that videos within the same task have similar ordering of actions, which can be leveraged for effective learning. Therefore, we propose an attention-based method with a new Pairwise Ordering Consistency (POC) loss that encourages that for each common action pair in two videos of the same task, the attentions of actions follow a similar ordering. Unlike existing sequence alignment methods, which misalign actions in videos with different orderings or cannot reliably separate more from less consistent orderings, our POC loss efficiently aligns videos with different action orders and is differentiable, which enables end-to-end training. In addition, it avoids the time-consuming pseudo-label generation of prior works. Our method efficiently learns the actions and their temporal locations, therefore, extends the existing attention-based action localization methods from learning one action per video to multiple actions using our POC loss along with video-level and frame-level losses. By experiments on three datasets, we demonstrate that our method significantly improves the state of the art. We also show that our method, with a small modification, can effectively address the transcript-supervised action learning task, where actions and their ordering are available during training.1 + +# 1. Introduction + +Learning actions by partitioning long and untrimmed procedural videos into action segments has recently drawn increasing attention in video understanding. Fully-supervised methods [23, 26, 46, 55, 57, 62] require dense annotation of training videos with framewise action labels, which is costly and unscalable. Therefore, weakly-supervised methods [5, 9, 13, 30, 31, 33, 37, 44, 45, 52, 58] learn from weak labels, in the form of action transcripts, + +![](images/b6046ea5d8e98b79867c49f714790b208a0a2e2ee2ad4285f9ffe3059904faa9.jpg) +Figure 1. Our attention-based framework with pairwise ordering consistency for set-supervised action learning. + +i.e., ordered lists of actions in videos, or action sets, i.e., sets of unique actions in videos (obtained from video narrations, captions or meta-tags). For action transcripts/sets, learning faces the major challenge of finding the temporal regions of actions in videos during the training. Learning from action sets, referred to as set-supervised action learning, additionally faces the challenge of not knowing the ground-truth action orderings in training videos. + +Most prior works on set-supervised action learning [31, 33, 44] alternate between three steps: i) generating action-transcripts from action-sets, ii) generating pseudo-labels from transcripts using Viterbi decoding, iii) training the model using pseudo-labels. However, generating transcripts and pseudo-labels is costly, slowing down the training and inference speeds, while the often erroneous pseudo-labels in early training iterations degrade the performance. [13] proposes a two-branch CNN that co-supervise each other and directly predicts the label and length of each video segment. Despite faster training/inference speed, [13] uses a fixed ra + +tio of the number of segments to the video length, which cannot handle dense action regions, i.e., it may undersegment short videos that contain many actions. More importantly, it predicts the labels of segments independently, which ignores the ordering between actions and similar transcripts of training videos of each task. + +In fact, videos of the same task often have similar transcripts. For example, in videos of 'make fried-egg', the step of 'cracking egg' is followed by 'frying egg'. While such similar ordering has been the key in the development and success of unsupervised action learning methods [1, 11, 12, 15, 25, 53, 64], it has not been exploited for set-supervised action learning. On the other hand, temporal attention is a powerful mechanism for finding temporal regions of actions in videos. However, existing works based on attention [27, 28, 38-40, 54, 63], assume one action is present in the video, which must be distinguished from the background frames. Therefore, extending temporal attention to videos of complex tasks with multiple actions and regulating it according to ordering consistency within and across videos remains a major challenge. + +Paper Contributions. In this paper, we propose a temporal attention-based method for set-supervised action learning by leveraging the similarity of action ordering of videos of each task, see Figure 1. We design a new loss function, referred to as Pairwise Ordering Consistency (POC) loss, which encourages that for each common pair of actions in videos of the same task, attention predictions follow the same ordering across videos. Our work has the following advantages with respect to the state of the art: + +- Our new POC loss resolves drawbacks of Dynamic Time Warping (DTW) [48] and Edit Distance (ED) [29]. Unlike DTW, which misaligns actions when applied to videos with different transcripts (action orderings), our method correctly aligns actions and brings the representations of the same action closer to each other. Unlike ED, which may not properly distinguish different inconsistent orderings from one another, our method efficiently distinguishes different consistency levels of action orderings by comparing the percentage of inconsistent action pairs. Additionally, our POC loss is differentiable, enabling feature learning, and its computational complexity is linear in the number of videos, thereby is scalable to large training sets. + +- Unlike three-step approaches [31, 33, 44], our method has a single step of minimizing a new loss, hence, enjoys faster training/inference and does not suffer from error amplification. Unlike [13], our method uses similarity of a task's videos, gives frame predictions, handles short videos with many actions and has much smaller number of parameters. + +- We extend the existing works on attention-based action localization, from one to multiple actions in each videos. Our POC loss penalizes the overlap between attentions of dif + +ferent actions for better localization and enforces consistent ordering between actions, which has not been addressed in prior works on attention-based action localization. Unlike existing works, our method does not assume that the length of each action is a fixed ratio of the total number of video frames and alternatively learns it via video-level action recognition, where the attention of an action is enforced to cover every possible frame of it. + +- Last, but not least, by extensive experiments on three datasets, we show that our proposed method outperforms existing set-supervised algorithms. We show that, with a small modification, our method can also effectively address transcript-supervised action learning, where the actions and their orderings are available during training. + +# 2. Related Works + +Action Learning with Set Supervision. Many long untrimmed videos [7, 14, 41, 51, 56, 64] and the high cost of gathering framewise action annotations have motivated many works on localization and classification of actions using minimum supervision. Set-supervised methods learn a model from the ground-truth sets of actions in training videos. [44] generates video transcripts from action-sets and runs Viterbi decoding based on HMM to produce framewise action labels. [31] proposed a Set-Constrained Viterbi algorithm to ensure the optimal segmentation covers all actions in the action-set. Building on this idea, [33] treats the most confident frames of each action as anchors to exclude unreliable segmentations to improve the training complexity and performance. On the other hand, [13] directly predicts actions and their lengths without Viterbi decoding to improve the inference speed. Since action-sets have no information about localization, consistent action ordering is an important assumption to improve action learning. [31,33,44] learn ordering via the transition model of an HMM. However, Viterbi decoding results in large computational cost. Our method does not use Viterbi decoding and learns consistent orderings by enforcing pairwise ordering similarity. + +Action Learning with Other Weak Supervision. Some works have studied action segmentation using video transcripts [2, 5, 9, 18, 30, 31, 37, 44, 45, 64] or video summaries [42, 61]. Earlier works exploit using transcripts via speech recognition techniques [24, 43], two-step optimization schemes [20, 21, 24, 43], connectionist temporal classification [18, 36] and iteratively boundary refinement [9]. Also, [5, 30, 45] perform Viterbi decoding between a video and its transcript. [58] studies a two-branch CNN with co-supervision between branches. [37] models actions using low-dimensional subspaces, which allows adjusting subspace dimensions based on complexities of actions. To remove or further reduce the need for annotation, [1, 11, 12, 16, 25, 32, 49, 50, 53] have studied unsupervised segmentation by leveraging the shared structure of + +![](images/8e6884e588d8908f24b21248a6cc7576c58aeacddf8865869068538ddf75440f.jpg) +Figure 2. Illustration of Dynamic Time Warping, Edit Distance and Pairwise Ordering Consistency applied on videos with different action orderings. + +![](images/b9fed51d33084ec2cde78138e3d09b448de856395dae1f019bbee1889378c22f.jpg) + +![](images/010e870f7724a43007bd25b875beb10c135722dd9431474eb9ebba0f5d16eafc.jpg) + +videos from similar tasks, while the recent work in [52] has studied the new setup of semi-weakly-supervised learning. Also, [35] has explored timestamp supervision, where each action is annotated with one frame. + +Sequence Alignment Distances. Two major classes of sequence alignment methods are Dynamic Time Warping [48] and Edit Distance [29]. DTW finds element-wise ordered alignment between two sequences and has been generalized to a differentiable setting [5,6,17]. However, standard DTW aligns sequences by assuming that they follow the same ordering. Therefore, it leads to misalignment between actions when applied to videos with different action orderings, as shown in Figure 2 (left). [10, 53] allow some elements to stay unmatched, yet the unmatched elements and their relative orderings are ignored in optimizing the alignment and cannot be improved. + +ED measures the pairwise sequence distance as the minimum number of edit operations to transform one sequence into the other and has been generalized to a differentiable distance in [19]. However, ED may not distinguish more from less consistent orderings under certain scenarios. For example, in Figure 2 (middle), the ordering between $\{a_1, a_2, a_3\}$ is more consistent between videos $(\mathcal{V}_1, \mathcal{V}_2)$ than $(\mathcal{V}_1, \mathcal{V}_3)$ as the first only has one violating action pair, $(a_1, a_2)$ , and the second has two violating pairs, $(a_1, a_2)$ and $(a_1, a_3)$ . However, ED of both video pairs is 4 (the number of deleted elements), thus fails to capture the differences in order consistencies of these video pairs. Also, ED incurs a cost if two videos contain uncommon actions, such as $\{a_5, a_6\}$ in our toy example. Minimizing ED implies videos must have the same action-sets, while in fact videos of the same task can have slightly different action-sets. Finally, [8] extends ED to allow for transposition between adjacent elements, yet it is not differentiable. In contrast, our POC loss is differentiable, respects the difference in action-sets and can accurately measure the ordering discrepancy by comparing the ordering between action pairs. + +# 3. Set-supervised Action Learning via Pairwise Order Consistency + +# 3.1. Problem Statement + +Assume we have $N$ videos of various tasks, e.g., from making different recipes in the cooking domain. For each + +video $\mathcal{V}^i$ of length $T^i$ , we have a set of pre-extracted framewise features $\mathcal{X}^i = \{\pmb{x}_1^i,\dots,\pmb{x}_{T^i}^i\}$ and the action-set $\mathcal{A}^i = \{a_1^i,\dots,a_{|\mathcal{A}^i|}^i\}$ . The action-set contains the list of actions occurring in the video with $a_j^i\in \{1,2,\ldots ,A\}$ . Here, $|\mathcal{A}^i|$ denotes the number of actions in the $i$ -th video and $A$ denotes the total number of actions across all videos. Present actions in the action-set, $a\in \mathcal{A}^i$ , are often referred to as positive actions and the others as negative actions. For simplicity of notation, we drop the superscript $i$ (when referring to video $i$ ) when it is clear from the context. The goal of set-supervised action learning is to learn a segmentation model that predicts the action of each frame during testing, using training videos that are weakly-labeled by their action-sets. + +# 3.2. Proposed Method + +We propose an attention-based network with pairwise ordering consistency for set-supervised action learning. Our framework consists of the following components. + +# 3.2.1 Feature Learning and Temporal Attention + +We use a fully convolutional network for feature learning followed by $A$ attention modules for localizing actions in videos. More specifically, we use a WaveNet backbone [60] for feature learning to capture the temporal information among frame features, + +$$ +\left(\boldsymbol {h} _ {1}, \dots , \boldsymbol {h} _ {T ^ {\prime}}\right) = \operatorname {W a v e N e t} \left(\left(\boldsymbol {x} _ {1}, \dots , \boldsymbol {x} _ {T}\right)\right). \tag {1} +$$ + +We have $T' \leq T$ when we use a MaxPooling layer. We use an attention module, $\mathcal{F}^{\mathrm{att}}$ , to compute the score/probability of each timestamp belonging to each action, + +$$ +\boldsymbol {\Gamma} = \mathcal {F} ^ {\text {a t t}} \left(\left(\boldsymbol {h} _ {1}, \dots , \boldsymbol {h} _ {T ^ {\prime}}\right)\right) \in \mathbb {R} ^ {A \times T ^ {\prime}}, \tag {2} +$$ + +$$ +\boldsymbol {W} = \operatorname {s o f t m a x} (\boldsymbol {\Gamma}) \in [ 0, 1 ] ^ {A \times T ^ {\prime}}, +$$ + +where $\Gamma$ and $W$ denote, respectively, the unnormalized and normalized attention weights, where $\sum_{a} W_{a,t} = 1$ . The value of $W_{a,t}$ being close to 1 indicates that frame $t$ is likely to belong to action $a$ . We compute the estimated length of action $a$ as $\tau_{a} = \sum_{t} W_{a,t} \in [0, T']$ . To learn the parameters of our model, we propose a novel loss function that consists of several components as follows. + +# 3.2.2 Pairwise Order Consistency (POC) + +Motivation. A key observation in our work is that for videos of the same task, the pairwise ordering of common + +![](images/57018241544c3c074ae9ee3b02ce4503956ea8632983ad5150fcab29990badca.jpg) +Figure 3. Illustration of our order score encoding the relative positions between actions. Top: $O(a_{u}, a_{v}) = 1$ as $a_{u}$ occurs before $a_{v}$ . Bottom: $O(a_{u}, a_{v}) = 0.3$ as $a_{u}$ occurs after the start of $a_{v}$ , yet it overlaps with the later part of $a_{v}$ . + +actions are similar. Indeed, for the videos of the same task in Breakfast [22], CrossTask [64] and MPII Cooking 2 [47] datasets, respectively, $88\%$ , $66\%$ and $67\%$ of the common action pairs have consistent ordering. Therefore, our goal is to learn attention models of actions so that predictions for pairs of common actions in videos of each task follow a consistent ordering. To achieve the goal, we measure the ordering difference between two videos as the percentage of common action pairs that have an inconsistent order. For example, in Figure 2 (right), both $(\mathcal{V}^1,\mathcal{V}^2)$ and $(\mathcal{V}^1,\mathcal{V}^3)$ have 4 common actions $\{a_1,a_2,a_3,a_4\}$ , thus 6 common action pairs. Notice that the ordering of $\mathcal{V}_2$ is more similar to $\mathcal{V}_1$ than $\mathcal{V}_3$ as $(\mathcal{V}^1,\mathcal{V}^2)$ only has one violating action pair (the ordering difference is $\frac{1}{6}$ ), while $(\mathcal{V}^1,\mathcal{V}^3)$ has two violating pairs (the ordering difference is $\frac{1}{3}$ ). To allow for different action-sets, we do not consider the ordering of the uncommon actions, such as $\{a_5,a_6\}$ . Therefore, unlike DTW, we can effectively handle videos with different orderings. Unlike ED, we efficiently separate the more from less consistent orderings by comparing the pairwise action orders while respecting the difference between action-sets. + +A main challenge is how to measure if an action $a_u$ occurs before an action $a_v$ using attention outputs, which are probabilities. To tackle this, we propose to find the ordering score of $(a_u, a_v)$ , denoted by $O(a_u, a_v)$ , as the probability of $a_u$ occurring before $a_v$ . To do so, first we compute + +$$ +\beta_ {a _ {v}, t} = \frac {1}{\tau_ {a _ {v}}} \sum_ {k = t + 1} ^ {T ^ {\prime}} \boldsymbol {W} _ {a _ {v}, k} \in [ 0, 1 ], \tag {3} +$$ + +which measures the probability of action $a_v$ starting after time $t$ . We then compute the ordering score as + +$$ +O \left(a _ {u}, a _ {v}\right) = \frac {1}{\tau_ {a _ {u}}} \sum_ {t} W _ {a _ {u}, t} \beta_ {a _ {v}, t} \in [ 0, 1 ]. \tag {4} +$$ + +For example, given two attention outputs for actions $a_u$ and $a_v$ shown in Figure 3 (top), $\beta_{a_v,t}$ would be 1 for the first 80 frames, during which action $a_u$ started and finished. Therefore, $O(a_u,a_v)$ according to (4) would be 1, as desired. On the other hand, in Figure 3 (bottom), $a_u$ occurs from frame 80 to 140, after the start of $a_v$ , yet overlaps with the later part of $a_v$ . Thus, $O(a_v,a_u) = 0.3$ is a small but non-zero value, indicating their relative ordering and overlap. + +POC Loss. Given the output of the attentions for video $i$ , we compute an ordering score between each pair of its actions. More specifically, for $a_u, a_v \in \mathcal{A}^i$ , we compute the ordering score $O^i(a_u, a_v) \in [0,1]$ , which is the probability of $a_u$ happening before $a_v$ . Our goal is to ensure that the ordering of $a_u, a_v$ would be consistent across all videos that contain this pair of actions. Let $\Lambda(a_u, a_v)$ denote the set of all videos that have both $a_u$ and $a_v$ in their action sets. We define a reference ordering score between $(a_u, a_v)$ by computing the average of $O^i(a_u, a_v)$ across all videos, + +$$ +O ^ {\star} \left(a _ {u}, a _ {v}\right) = \frac {1}{\left| \Lambda \left(a _ {u} , a _ {v}\right) \right|} \sum_ {i \in \Lambda \left(a _ {u}, a _ {v}\right)} O ^ {i} \left(a _ {u}, a _ {v}\right). \tag {5} +$$ + +We define the discrepancy between the ordering in each video $i$ and the reference as + +$$ +\begin{array}{l} \pi^ {i} \left(a _ {u}, a _ {v}\right) = 1 - O ^ {i} \left(a _ {u}, a _ {v}\right) O ^ {\star} \left(a _ {u}, a _ {v}\right) \\ - O ^ {i} \left(a _ {v}, a _ {u}\right) O ^ {\star} \left(a _ {v}, a _ {u}\right). \tag {6} \\ \end{array} +$$ + +Notice that $\pi^i$ will be close to 0 when the attention prediction of $a_{u}$ is before/after $a_{v}$ in both the video and the reference ordering, while $\pi^i$ would be close to one when the ordering in the video and the reference disagree. Finally, we define the Pairwise Order Consistency (POC) loss as + +$$ +\mathcal {L} _ {\mathrm {p o c}} \left(\left\{\mathcal {V} ^ {i} \right\}\right) = \frac {1}{N} \sum_ {i = 1} ^ {N} \frac {1}{| \mathcal {A} ^ {i} | ^ {2}} \sum_ {a _ {u}, a _ {v} \in \mathcal {A} ^ {i}} \pi^ {i} \left(a _ {u}, a _ {v}\right), \tag {7} +$$ + +which measures the aggregated discrepancy between action ordering between each video and the reference. As a result, minimizing this loss not only enforces a consistent ordering of common action pairs across videos, but also reduces the overlap between action attentions. Thanks to the differentiability of our loss, we also obtain an end-to-end framework for learning actions, therefore avoiding the high computational complexity of the Viterbi decoding and pseudolabel generation as in the prior works [31, 33, 44]. Our POC loss is directly computed from attentions and minimizing it guides the learning of attention modules and the network parameters. Notice also that POC loss can be applied to any networks that predict framewise action labels of videos. + +Remark 1 A main advantage of computing a reference ordering as in (5) and computing the loss as in (7) is linear computational complexity with respect to the number of + +videos. Alternatively, we could compute the discrepancy between every pair of videos. However, this leads to quadratic complexity with respect to the number of videos (similar to DTW and ED), and performed worse in our experiments than using the reference ordering. + +In the supplementary materials, we discuss that our loss can handle repeated actions and varied action ordering and provides more analysis of computation complexity and the effect of using the reference ordering on the optimal solution. + +# 3.2.3 Frame-Level and Video-Level Losses + +For action recognition, we will use the attention features to build video-level action features that will be given to a classifier, which will be learned using video-level losses. Additionally, we regularize the learning of the classifier by defining frame-level losses on the attentions. + +Frame-Level Losses. We use a framewise attention ranking loss to ensure that, for each training video, the attentions of positive actions are higher than those of negative actions at each time instant, + +$$ +\mathcal {L} _ {\mathrm {f - r k}} (\mathcal {V}) = \frac {1}{T ^ {\prime}} \sum_ {t} \log \left(1 + \sum_ {a \in \mathcal {A}, a ^ {\prime} \notin \mathcal {A}} e ^ {\left(\Gamma_ {a ^ {\prime}, t} - \Gamma_ {a, t}\right)}\right). \tag {8} +$$ + +In procedural videos, some frames do not belong to any action, hence referred to as background $^2$ frames. Therefore, we also use a 'background' action class. Previous works [10, 25, 53] have shown that regularizing the percentage of background frames has a large impact on the performance. Thus, we propose a background length loss, + +$$ +\mathcal {L} _ {\mathrm {f - b g}} (\mathcal {V}) = \left\{ \begin{array}{l l} \log \left(\tau_ {\min } / \tau_ {\mathrm {b g}}\right), & \text {i f} \tau_ {\mathrm {b g}} < \tau_ {\min }, \\ 0, & \text {i f} \tau_ {\min } \leq \tau_ {\mathrm {b g}} \leq \tau_ {\max }, \\ \log \left(\tau_ {\mathrm {b g}} / \tau_ {\max }\right), & \text {i f} \tau_ {\mathrm {b g}} > \tau_ {\max }, \end{array} \right. \tag {9} +$$ + +which promotes that $\tau_{\mathrm{bg}} \triangleq \sum_{t} W_{t, a_{\mathrm{bg}}}$ , which is the estimated length of the background action using the associated attention module, will be between the two predefined thresholds of $\tau_{\mathrm{min}}$ and $\tau_{\mathrm{max}}$ . + +A challenge when learning temporal attention is that the predicted frames for an action could be scattered in the video, instead of forming one or a few segments. To overcome this, we propose a centering loss + +$$ +\mathcal {L} _ {\mathrm {f - c r}} (\mathcal {V}) = \frac {1}{| \mathcal {A} | \cdot T ^ {\prime}} \sum_ {a \in \mathcal {A}, a \neq a _ {\mathrm {b g}}} \sum_ {t} W _ {a, t} (t - \bar {t} _ {a}) ^ {2}, \tag {10} +$$ + +where $\bar{t}_a \triangleq (\sum_t t \cdot W_{a,t}) / (\sum_t W_{a,t})$ is the temporal center of action $a$ .3 This loss imposes a large penalty if $W_{a,t}$ is large for frames that are far from the action temporal center. + +Video-Level Losses. For action recognition, we build a video-level feature for each action $a$ using its attention, + +$$ +\boldsymbol {g} _ {a} = \frac {1}{T ^ {\prime}} \sum_ {t} \boldsymbol {W} _ {a, t} \boldsymbol {h} _ {t}, \tag {11} +$$ + +which will be fed into an action classifier $\mathcal{F}^{\mathrm{cls}}$ . We consider two losses for supervising the action classifier [34]. First, we use a ranking loss, + +$$ +\mathcal {L} _ {\mathrm {v - r k}} (\mathcal {V}) = \log \left(1 + \sum_ {a \in \mathcal {A}, a ^ {\prime} \notin \mathcal {A}} e ^ {\left(\mathcal {F} ^ {\operatorname {c l s}} \left(\boldsymbol {g} _ {a ^ {\prime}}\right) - \mathcal {F} ^ {\operatorname {c l s}} \left(\boldsymbol {g} _ {a}\right)\right)}\right), \tag {12} +$$ + +where $\mathcal{F}^{\mathrm{cls}}(g_a)$ is the probability logit without passing it through the sigmoid function. Since set-supervised action recognition is a multi-label learning problem, the ranking loss resolves the positive and negative sample imbalance. However, its drawback is requiring to tune a threshold on the probability logit to separate the positive from negative actions. To resolve this issue, we use a binary cross-entropy loss with a dynamically estimated action threshold, + +$$ +p _ {a} = \operatorname {s i g m o i d} \left(\mathcal {F} ^ {\mathrm {c l s}} (\boldsymbol {g} _ {a}) - \mathcal {F} ^ {\mathrm {t h r}} (\boldsymbol {g} _ {a})\right), +$$ + +$$ +\mathcal {L} _ {\mathrm {v - c e}} (\mathcal {V}) = - \sum_ {a \in \mathcal {A}} \log \left(p _ {a}\right) - \sum_ {a ^ {\prime} \notin \mathcal {A}} \log \left(1 - p _ {a ^ {\prime}}\right). \tag {13} +$$ + +Here, $\mathcal{F}^{\mathrm{thr}}(g_a)$ is the estimated threshold for action $a$ via a sub-network $\mathcal{F}^{\mathrm{thr}}$ , which is then used to compute the action probability $p_a$ . + +# 3.2.4 Training and Inference + +Our final loss function is the weighted sum of the POC, frame-level and video-level losses, discussed above. In each iteration of the training, we sample a batch of videos from the same task to learn action ordering. We do not consider the ordering between 'background' and other actions as background can occur anywhere. For testing, we consider two scenarios: action segmentation, where we assume the action-sets of test videos are unknown, and action alignment, where the action-sets are known. For action segmentation, we first estimate the action-set of a test videos as $\hat{\mathcal{A}} = \{a|p_a\geq 0.5\}$ . We obtain the action label $\hat{y}_t$ of frame $t$ by finding the maximum attention value over $\hat{\mathcal{A}}$ , i.e., $\hat{y}_t = \operatorname*{argmax}_{a\in \hat{\mathcal{A}}}W_{a,t}$ . For action alignment, we directly compute the argmax over the ground-truth $\mathcal{A}$ , which is assumed to be given. + +# 4. Experiments + +We evaluate the performance of our proposed method for action segmentation and action alignment tasks, against prior set-supervised methods. We also compare with the state-of-the-art attention-based action localization method + +UM [28]. Additionally, we demonstrate that a simple modification of our method can address transcript-supervised action learning, where we know the transcripts (sequence of actions) in videos during the training time. We also perform ablation studies to investigate the effect of each of our proposed loss functions, compare the performance of POC loss under different scenarios and show qualitative results for video segmentation using our method. + +# 4.1. Experimental Setup + +Datasets. We use three video datasets for evaluations. The Breakfast [22] dataset contains 1,712 videos of 10 cooking activities with 48 different actions. On average, each video has 5.2 unique actions and 6.9 action segments, as $10\%$ of the actions have multiple occurrences. The CrossTask [64] dataset consists of videos from 18 tasks. Following [37], we train on the 14 cooking-related tasks, which have 2,522 videos and 80 actions. On average each video has 6.1 actions and 14.4 action segments, with $25\%$ actions having multiple occurrences. The MPII Cooking 2 (MC2) [47] is a smaller dataset with 273 videos from 74 recipes and 68 actions. On average each video has 16.7 actions and 95.2 action segments, with $50\%$ of actions having multiple occurrences. The datasets become more challenging from Breakfast to CrossTask and then to MC2, as their videos have more segments, action repetitions and background frames. + +Evaluation Metrics. We use three evaluation metrics: 1) Mean-over-Frame (MoF), which is the percentage of frames whose action labels are predicted correctly. 2) Intersection over Union (IoU), defined as $\frac{1}{A}\sum_{a}|GT_{a}\cap D_{a}| / |GT_{a}\cup D_{a}|$ where $GT_{a}$ and $D_{a}$ are the ground-truth and predicted set of frames for action $a$ . We follow the implementation in [37]. 3) Midpoint Hit Metric (MidH), as the percentage of predicted action segments whose middle frames belong to the ground-truth segment of the action. + +Implementation Details. Consistent with prior works, we use the released four train/test splits for Breakfast and the one train/test split for CrossTask and MC2. Meanwhile, we use the I3D features [4] extracted by [13] on Breakfast and the released 3,200-dimension features on CrossTask. Since [13] has not released their extracted I3D features from MC2, we extract I3D features ourselves. + +To adapt our method to the transcript-supervised learning task, we will estimate the reference order $O^{\star}$ in (6) from the ground-truth transcripts instead of attentions of the videos. Following [30, 37, 45], for action alignment, we run Viterbi decoding between videos and the given transcripts to predict the framewise action label. Due to the nature of the weak supervision, the performance of all transcript/set-supervised models changes for different initializations. Most prior works only report the results of their best run, see [37, 59]. Similar to [37], we run our + +method for three runs and report the best run results for a fair comparison and the averaged results over runs for thorough evaluation. We include more performance statistics in the supplementary material. + +# 4.2. Experimental Results + +In Table 1, we report the best run results for the prior set-supervised action segmentation methods and the results of our POC for the best run and the average over three runs, denoted as $POC(best)$ and $POC(average)$ , respectively. Since the action localization method UM [28] does not evaluate on the datasets we use, we show the results of our replication using its released code, denoted by UM. Meanwhile, prior set-supervised action segmentation methods have not reported IoU and have not tested on CrossTask. For a fair comparison, we replicate the state-of-the-art model SCT [13] on all three datasets with its released code, whose result is denoted by SCT. Notice we also collect the scores of SCT on Breakfast and MC2 from its paper, but our replication obtain higher accuracy than those reported in that paper. + +In Table 2, we show the best run results for prior transcript-supervised action segmentation methods and the best and average results of our method. MuCon [58] does not report the best run results; we include their reported average results and standard deviation. For the transcript-supervised segmentation, we do not compare on MC2 as no prior transcript-supervised method evaluated on the dataset. + +Set-Supervised Action Learning. As Table 1 shows, POC outperforms the all set-supervised methods on the three datasets for both action segmentation and action alignment tasks. UM has low performance as it assumes each video contains only one action, thus its attention does not learn distinct locations for different actions. In contrast, our POC loss penalizes the overlap between attentions. Our method also exceeds SCT as it does not consider the ordering between action as we do in our POC loss. + +Notice that on Breakfast, POC improves the MoF and IoU for action segmentation by $7.6\%$ and $16.2\%$ , respectively, over the second best results (SCT), showing the effectiveness of consistent action ordering in learning action localization. On CrossTask, our method improves over SCT by $6.7\%$ on MoF and $4.8\%$ on IoU on action segmentation. On MC2, although $50\%$ of the actions in a video have multiple occurrences, our POC loss is still able to model the action orderings efficiently. We improve the MidH by $1.6\%$ on action segmentation and $3.5\%$ on action alignment. Without the POC loss, the MidH of our model drops by $5.3\%$ and $4.7\%$ for action segmentation and alignment, respectively. + +On the other hand, the set-supervised pseudo-label based methods [31, 33, 44] have a big performance gap between action segmentation and action alignment tasks, e.g., ACV has a $11.7\%$ gap for MoF on Breakfast. In comparison, the gap of our POC at MoF is $3.9\%$ on Breakfast and only $0.1\%$ + +
SegmentationAlignment
BreakfastMoFIoUMoFIoU
Action Set [44]23.328.4
UM [28]29.115.829.516.8
SCV [31]30.240.8
SCT [13]30.4
SCT [13]34.817.337.919.2
ACV [33]33.445.1
POC (best)42.433.546.336.7
POC (average)40.132.543.635.8
CrossTaskMoFIoUMoFIoU
UM [28]35.810.540.313.0
SCT [13]37.311.440.412.6
POC (best)44.016.244.116.2
POC (average)42.915.642.615.6
MC2MidHIoUMidHIoU
Action Set [44]10.610.6
UM [28]12.13.912.55.1
SCV [31]14.515.1
SCT [13]14.3
SCT [13]14.74.715.94.8
ACV [33]15.516.2
POC (best)17.19.019.710.0
POC (average)13.15.716.06.0
+ +on CrossTask. This comes from the fact that pseudo-label based methods cannot directly predict the action-set of a test video, but compare a video with each training action-set to find the most likely one, which is often erroneous or only partially correct. Our method accurately predicts the action-sets of test videos, thanks to the action classifier learned with our video-level losses, hence boosts the performance of action segmentation. Thus, our set-supervised POC, despite not having access to ground-truth action orderings of training videos, achieves competitive results with transcript-supervised methods (compare results of POC in Table 1 with results of existing works in Table 2). POC with set supervision achieves a similar MoF as NNV and a similar IoU as CDFL on Breakfast and even surpasses the state-of-the-art TASL on CrossTask for action segmentation. + +Transcript-Supervised Action Learning. In Table 2, we show POC trained with ground-truth transcripts achieves competitive results w.r.t. the state-of-the-art transcript-supervised methods, even obtaining the best results for some cases. For action segmentation, POC successfully exceeds TASL at IoU by $2.8\%$ on Breakfast and $1.4\%$ on CrossTask. It is because POC can accurately predict the actions in a test video while pseudo-label based methods [30, 37, 45] compute the similarity between the video and each training transcript with Viterbi decoding and consider the most similar one as the test transcript, which is often partially or fully incorrect. Learning and inference with Viterbi decoding also makes those methods time + +Table 1. Set-Supervised action segmentation and alignment results. + +
SegmentationAlignment
BreakfastMoFIoUMoFIoU
OCDC [2]8.9
CTC [18]21.8
HTK [23]25.99.843.926.6
ECTC [18]27.735.0
HMM/RNN [43]33.3
TCFPN [9]38.424.253.535.3
NNV [45]43.0
D3TW [5]45.757.0
CDFL [30]50.233.763.045.8
MuCon [58]48.5±1.8
TASL [37]49.936.665.849.9
POC (best)47.139.456.146.7
POC (average)45.738.354.446.4
CrossTaskMoFIoUMoFIoU
NNV [45]27.011.034.615.3
CDFL [30]32.511.846.717.2
TASL [37]42.714.957.119.1
POC (best)44.116.353.318.9
POC (average)42.815.653.018.4
+ +Table 2. Transcript-supervised action segmentation and alignment results. + +
BreakfastCrossTask
action-set0.2640.412
transcript0.1470.332
+ +Table 3. Ordering discrepancy between model predictions and ground-truth on test videos under different supervision. + +and computationally expensive. In contrast, our method is lightweight, learning actions with video-level losses and action ordering with the POC loss. The average inference time of CDFL and TASL is 56 seconds per video, while POC only takes 0.014 seconds. On the other hand, having ground-truth transcripts for action alignment, transcript-supervised methods achieve higher results as they separately estimate the temporal region for each occurrence of an action while this is not learned by modeling the pairwise action ordering via the POC Loss. Yet, POC exceeds CDFL at IoU on Breakfast and at both MoF and IoU on CrossTask, thanks to we end-to-endly train a deep network, enabled by differentiability of the POC loss, thus learn better action features. + +Notice that using transcripts rather than action-sets greatly improves the performance of POC on Breakfast, showing the efficacy of POC loss in learning ordering. On CrossTask, the result for action segmentation is similar when using action-sets or transcripts, because videos have many 'background' segments between action segments, thus action ordering provides limited information about their locations. However, we show that POC uses the ground-truth transcripts to learn a better ordering. In Table 3, we report average order discrepancy defined in (6) between model predictions and ground-truth labels, i.e., reference ordering $O^{\star}$ is computed from the true labels. Using transcript supervision successfully reduces the discrepancy on both datasets. + +![](images/02d7df7ca01aa1d8898b1fba8812d1ae6df5520bd655c322d3c8db55545a5b88.jpg) + +![](images/5f95cb4b2b1aec6c59b118440e06c92aa23c478b22725b29de9e63f2e48cff8e.jpg) + +![](images/221fe8c85e85c5932a9a90677233d176bd50d715deeba367886450f9240f130d.jpg) +Figure 4. Left: ordering discrepancy between model predictions and ground-truth for each recipe in Breakfast. Middle: a global transcript (a single transcript for all videos) of the task scrambled egg estimated from transcripts of videos and learned by action ordering (red shows actions with incorrect positions). Right: action segmentation results by SCT and POC against ground-truth on Breakfast. + +
Lv-rkLv-ceLf-rkLf-bkLf-crLpocMoFIoU
✓✓××××15.59.3
✓✓✓×××36.628.7
✓✓✓✓××36.829.4
✓✓✓✓×✓38.531.7
✓✓✓✓✓×37.030.3
✓×✓✓✓✓32.520.8
×○✓✓✓✓32.725.2
✓✓✓✓✓✓40.132.5
+ +Table 4. Effect of proposed losses for action segmentation on Breakfast. + +Ablation Studies. In Table 4, we summarize the contribution of each of our proposed loss functions by showing the average performance over three runs. The first row shows the baseline model with only video-level losses while last row is the complete model with all losses. First, adding $\mathcal{L}_{\mathrm{f - rk}}$ improves the baseline by a factor of 2 and 3 on, respectively, MoF and IoU. Notice that with $\mathcal{L}_{\mathrm{f - rk}}$ , our model already outperforms ACV and SCT for action segmentation. Also, comparing the fourth and the last row shows that removing $\mathcal{L}_{\mathrm{f - cr}}$ reduces MoF and IoU by $1.6\%$ and $0.8\%$ respectively. Comparing the fifth and last row shows removing $\mathcal{L}_{\mathrm{poc}}$ reduces MoF and IoU by $3.1\%$ and $2.2\%$ respectively. Finally, as the fifth and sixth rows show, we test learning action recognition with only the ranking loss $\mathcal{L}_{\mathrm{rank}}$ or the standard cross entropy loss without threshold estimation, denoted by $\circ$ . In both cases, MoF drops by $7\%$ . + +Effect of POC Loss. First, to understand the impact of POC loss under different scenarios, we show the ordering discrepancy defined in (6) between the ground-truth labels and our model predictions, i.e., $O^{\star}$ is computed from true labels in Figure 4 (left). We compare our model learned without POC loss (blue) and with POC loss (green) for each task (recipe) in Breakfast. Notice that the green bar is lower than blue bar for all recipes, including hard recipes like fried egg, scrambled egg and especially sandwich. The videos of the tasks are long videos with many actions. Both blue and green bars are high on salad and pancake, where actions often occur multiple times in a video, showing repeated action is a major challenge in learning action ordering. + +To visualize the difference in the learned action ordering, in Figure 4 (middle), we show the global transcript (a single + +transcript for all videos) of the recipe scrambled egg estimated from our model without and with the POC loss. The global transcript is estimated via Bradley-Terry model [3] thanks to our ordering score $O(a_{u}, a_{v})$ in (4), which can be viewed as the probability of $a_{u}$ being before $a_{v}$ . Without POC loss, 4 actions in the global transcript have incorrect positions, especially for take plate and crack egg, resulting in 7 wrong-ordered action pairs. In contrast, with the POC loss, there are only 2 incorrect ordering, between (stir egg, add salt pepper) and (stir egg, pour egg to pan). + +Qualitative Results. In Figure 4 (right), we visualize the action segmentation results by SCT and POC against the ground-truth (GT). Notice that for the top example, SCT predicts a wrong ordering between stir milk and other actions while POC learns the correct ordering, thus, significantly improves the segmentation result. The bottom example shows a failure case of the set-supervised methods where SCT and POC predict the correct actions and ordering, yet the localizations do not align with the ground-truth. However, compared with SCT, POC predicts more accurate action boundaries between non-background actions. + +# 5. Conclusions + +We addressed the problem of set-supervised action learning in procedural task videos. We proposed an attention-based method with a novel differentiable pairwise ordering consistency loss that enforces similar action ordering for videos of the same task, resolving the drawbacks of conventional sequence alignment methods. 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One popular approach for physical-world attacks is to adopt the "sticker-pasting" strategy, which however suffers from some limitations, including difficulties in access to the target or printing by valid colors. A new type of non-invasive attacks emerged recently, which attempt to cast perturbation onto the target by optics based tools, such as laser beam and projector. However, the added optical patterns are artificial but not natural. Thus, they are still conspicuous and attention-grabbed, and can be easily noticed by humans. In this paper, we study a new type of optical adversarial examples, in which the perturbations are generated by a very common natural phenomenon, shadow, to achieve naturalistic and stealthy physical-world adversarial attack under the black-box setting. We extensively evaluate the effectiveness of this new attack on both simulated and real-world environments. Experimental results on traffic sign recognition demonstrate that our algorithm can generate adversarial examples effectively, reaching $98.23\%$ and $90.47\%$ success rates on LISA and GTSRB test sets respectively, while continuously misleading a moving camera over $95\%$ of the time in real-world scenarios. We also offer discussions about the limitations and the defense mechanism of this attack1. + +# 1. Introduction + +In the past few years, we have witnessed the great success of deep neural networks (DNNs) in a variety of computer vision tasks, such as image classification, object detection, scene segmentation and so on. However, recent studies have revealed that DNNs based models are vulnerable to adversarial examples, even though the added magnitude of perturbations is small. In safety sensitive scenar- + +ios, such as autonomous driving [18] and medical diagnosis [19], adversarial inputs would enforce a machine learning system to produce erroneous decision, leading to unexpected situations that may be potentially dangerous. + +Estimating when a machine learning model fails to work is of great concern to trustworthy AI. Accordingly, it is important to understand the level of risk of various adversarial examples to the machine learning models. There are numerous attack strategies investigated in the literature, which can be in the digital domain, where digital images corresponding to a scene are modified; or in the physical domain, where perturbations are physically added to the objects themselves [10]. + +The adversarial attacks in the physical domain receive more attention recently, since they are more practical and challenging. One popular approach for physical-world attacks is to adopt the "sticker-pasting" strategy [10], where the adversarial perturbation is printed as a sticker and then attached onto the target object, e.g., a road sign. However, this approach would suffer from a few troubles: 1) In some cases, it may be impossible to access the target object; 2) The printing of perturbations is imperfect, i.e., some values cannot be reproduced by valid colors in the real world. Some strategies emerged very recently to remedy these limitations, which explored a new type of adversarial attack—the threats of light—to achieve non-invasive attack [9, 12, 22, 28]. For instance, Duan et al. [9] propose to utilize the laser beam as adversarial perturbation directly rather than crafting adversarial perturbation from scratch, which has been demonstrated to be an effective physical-world attack to DNNs. Gnanasambandam et al. [12] propose to project calculated patterns to alter the appearance of the target objects based on a low-cost projector-camera system. Experimental results shown in [9, 12] demonstrate the effectiveness of light attacks in both digital- and physical-settings. + +A basic principle in adversarial attack is that the carefully perturbed inputs should cause the network to generate wrong decision while without introducing a visible change to humans. However, the added optical patterns in existing + +methods, both laser beam [9] and projected pattern [12], are artificial but not natural. Thus, they are still conspicuous and attention-grabbed, and can be easily noticed by humans. In this paper, we study a new type of optical adversarial examples, in which the perturbations are generated by a very common natural phenomenon, shadow, to achieve naturalistic and stealthy physical-world adversarial attack. We choose traffic sign recognition as our target task to validate the effectiveness of this attack. It is worth noting that, in the field of computer vision, many methods have been proposed to conduct shadow removal [11, 17, 33], which work from the perspective of image restoration in order to improve the accuracy of the subsequent high-level tasks [34]. We are the first work to reveal that shadow can also become a threat to harm the reliability of machine learning based vision system. It is a meaningful reminding to prevent such attacks in practical systems. + +The contributions of this paper can be highlighted as follows: + +- We propose a new light-based physical-world adversarial attack under the black-box setting via the very common natural phenomenon—shadow, which is more naturalistic and stealthy. +- We offer feasible optimization strategies to generate digitally and physically realizable adversarial examples perturbed by shadows. +- We provide thorough evaluations conducted on both simulated and real-world environments to demonstrate the effectiveness of our method. We also discuss the limitations and the defense mechanism of this attack. + +# 2. Related Work + +# 2.1. Adversarial Examples + +Adversarial examples were first discovered by Szegedy et al. [27], showing that a small perturbation can drastically change the network output while being quasi-imperceptible to humans. More interestingly, they also found the cross model generalization ability of adversarial examples, i.e., a large fraction of them will be misclassified by networks trained with different hyper-parameters or even with different architectures. This intriguing property of DNNs has greatly inspired the enthusiasm of academic research. Existing works on adversarial examples are either in the digital domain or in the physical world. + +# 2.2. Adversarial Examples in Digital Domain + +In the digital domain, adversarial perturbations are directly added to the inputs of a model, and their amplitudes are usually limited by $l_{p}$ -norm, e.g. $l_{\infty}$ -norm [13, 20], $l_{2}$ -norm and $l_{0}$ -norm [3] to ensure imperceptibility. According to adversary's knowledge, adversarial attacks can either + +be white-box, where an attacker knows all the details of a model so that the gradient can be fully used to craft a perturbation [3,13,16,20,23], or black-box, where an attacker can only query the target model and get a corresponding output without knowing its internal structure. In the black-box scenario, an attacker can take advantage of the cross model generalization ability of adversarial examples [6,7,30,31] or reconstruct the internal information of a model through multiple queries [2,4,5,14]. Further, these two strategies can be used at the same time to promote each other [32]. + +# 2.3. Adversarial Examples in Real Physical World + +Due to the variations caused by camera, a major concern is whether these highly optimized samples can pose a real threat to applications in the physical world. Kurakin et al. [16] first demonstrated the existence of physical adversarial examples. They printed out digital adversarial examples, and found that their corresponding photos taken by a mobile phone were still adversarial. However, such noise-based perturbations are not practical in the physical world, as they are hard to be captured by cameras at large distances. To make adversarial patterns more prominent, while keeping their stealthiness, a line of work hides perturbations with natural styles [8] or limit the large perturbations to a small area with specific semantics, e.g., stickers arranged in the shape of letters [10] or a pair of glasses [25]. To further improve robustness to the variations caused by camera, Athalye et al. [1] proposed Expectation Over Transformation (EOT), by which the first robust 3D adversarial example was generated. + +Recently, a new line of work explores non-invasive attacks that do not access the target object, e.g., optic-based attacks. Sayles et al. [24] illuminates the target object with a special light that varies with a high frequency to cause rolling shutter effect of the camera. Duan et al. [9] disturb the classifier by generating a laser beam in front of the target object. Gnanasambandam et al. [12] project their calculated adversarial patterns to the target object by a projector. Instead of the optical phenomena produced by these sophisticated artificial devices, in this work, we turn to explore a common natural phenomenon—shadow. + +# 3. Approach + +In this section, we present our method for learning an adversarial object by casting shadow to achieve successful attack. We first describe the representation of shadow. + +# 3.1. Problem Formulation + +Given an input image $x \in \mathbb{R}^d$ with the class label $y \in [1, \dots, k]$ , a DNN based classifier $f: \mathbb{R}^d \to \mathbb{R}^k$ is trained to derive the predicted label $\widetilde{y}$ : + +$$ +\widetilde {y} \triangleq \arg \max _ {i} f _ {i} (x) \tag {1} +$$ + +![](images/4da8995474a5955f51bf401b9dfa366d7ec3caa6c12169b10f911e9cf98590d1.jpg) +a) Shadows in the real world. + +![](images/0babd1726ef63e834dd1e6ca6abfae07091db4314d08ea9aaadf4724210754ae.jpg) +b) Our simulated shadows. +Figure 1. Comparison of our simulated shadows and real-world shadows on traffic signs from LISA [21] and GTSRB [26] datasets. + +where $f_{i}(x)$ is the confidence of the $i$ -th class. The goal of our proposed method is to cast a specific shadow onto the target object to produce adversarial example $x_{adv}$ , which causes the machine learning system to produce misclassification: + +$$ +\arg \max _ {i} f _ {i} (x) \neq \arg \max _ {i} f _ {i} \left(x _ {a d v}\right) \tag {2} +$$ + +Meanwhile, it should guarantee that the perturbation imposed on $x_{adv}$ is imperceptible enough so that $x_{adv}$ is stealthy for humans. + +# 3.2. Shadow Perturbation Modeling + +To generate the adversarial example by shadow, two factors should be carefully considered: the location of shadow and the value of shadow. + +Shadow Location. For the location of shadow, we propose to find an appropriate polygon $\mathcal{P}_{\mathcal{V}}$ to simulate the shadow region, which is determined by a set of vertices $\mathcal{V} = \{(m_1,n_1),(m_2,n_2),\dots,(m_s,n_s)\}$ . Given $\mathcal{M}$ as the mask to locate the target object, the shadow region in the target object can be defined as $\mathcal{M} \cap \mathcal{P}_{\mathcal{V}}$ . Note that, although $\mathcal{P}_{\mathcal{V}}$ can be any valid polygon, based on the experimental experience shown in Sec. 4, the simplest polygon—triangles—are sufficient to produce successful adversarial examples. We can exploit more complex polygon to achieve higher attack success rate, however, the shadow would look unnatural and it becomes more difficult to implement in the real world. Therefore, in practice, $\mathcal{P}_{\mathcal{V}}$ is simply set to be a triangle. Thus, the optimization location parameters in our method is the corresponding vertices coordinates $\mathcal{V} = \{(m_1,n_1),(m_2,n_2),(m_3,n_3)\}$ . + +Shadow Value. To perform a successful physical-word attack, a main concern is the non-negligible gap between the digital and the physical domains. A widely used technique + +to tackle this problem is Expectation Over Transformation (EOT) [1], which produces robust physical-world objects that remain adversarial when captured over a wide range of transformations, including distances, angles, exposures, etc. + +In addition to the variations caused by camera, in our context, another key factor should be considered is the relationship of pixel values between shadow and non-shadow areas in the real world scenario, since we need to simulate shadows in digital images when generating adversarial examples. However, the exact formula of this relationship is obscure. To simplify this problem, following the assumption in the field of shadow removal [17], we regard that shadows only affect the illumination component and leave other ones remain unchanged. Accordingly, we transform images from RGB space to LAB space, and only consider the $L$ channel which is a correlate of lightness. Our statistical results on SBU Shadow dataset [29] confirmed this assumption by indicating that the mean ratio of pixel values of channels $L$ , $A$ and $B$ in shadow areas to that in nonshadow areas are 0.43, 0.99 and 0.90 respectively, and the corresponding standard deviations of channels $A$ and $B$ are as low as 0.05 and $0.07^2$ . + +Based on the above analysis, we can generate shadow perturbation cast in an image by multiplying the corresponding $L$ channel in LAB color space with a coefficient $k^3$ . Specifically, given a clean image $x$ in RGB color space, we first convert $x$ to LAB color space: + +$$ +L A B (x) = L A B \left(\left[ R _ {x} G _ {x} B _ {x} \right]\right) = \left[ L _ {x} A _ {x} B _ {x} \right]. +$$ + +Then given a polygon $\mathcal{P}_{\mathcal{V}}$ and a mask $\mathcal{M}$ , the value of pixel $(i,j)$ in the shadow image $x_{adv}$ can be calculated as follows: + +$$ +\begin{array}{l} L A B ^ {i j} \left(x _ {a d v}\right) = \left[ L _ {x _ {a d v}} ^ {i j} A _ {x _ {a d v}} ^ {i j} B _ {x _ {a d v}} ^ {i j} \right] \\ = \left\{ \begin{array}{l l} L A B ^ {i j} (x) \cdot [ k 1 1 ] ^ {T} & (i, j) \in \mathcal {P} _ {\mathcal {V}} \cap \mathcal {M} \\ L A B ^ {i j} (x) \cdot [ 1 1 1 ] ^ {T} & (i, j) \notin \mathcal {P} _ {\mathcal {V}} \cap \mathcal {M} \end{array} \right.. \\ \end{array} +$$ + +Finally, we convert $x_{adv}$ back to RGB color space. For simplicity, we denote the above adversarial example generation process as: + +$$ +x _ {a d v} = \mathcal {S} (x, \mathcal {P} _ {\mathcal {V}}, \mathcal {M}, k) \tag {3} +$$ + +In Fig. 1, we show some instances of our simulated shadows on traffic signs, as well as some real-world shadows for comparison. + +In practice, however, the form of shadow is the result of complex physical process. The coefficient $k$ can be varied due to numerous factors, including light sources, scene geometry, materials of the target object, and the imaging quality of the camera, etc. The distribution of $k$ in SBU Shadow + +![](images/eabb0a0bb2f31ec6fa56c042d242dbda48eb0938cfb3ea6c29c55b38af88b802.jpg) +Figure 2. The distribution of coefficient $k$ . + +dataset is shown in Fig. 2. Accordingly, in our scheme, before generating an adversarial example, we first cast a random shadow on the target object to measure the coefficient $k$ . Further, by leveraging EOT, the impact of the mismatch of $k$ can be minimized. + +# 3.3. Shadow Attack in Digital Domain + +In this subsection, we introduce in detail the generation process of adversarial examples using simulated shadows in the digital domain. + +The aim of our proposed attack method is to find vertices coordinates $\mathcal{V} = \{(m_1, n_1), (m_2, n_2), (m_3, n_3)\}$ of the triangle, which is used to simulate the shadow area, to make the resultant shadow image $x_{adv}$ being misclassified by the target model $f$ . In this work, we consider the more practical and challenging black-box attack scenario, where we can only access to the input (images) and the output (confidence scores $f(\cdot)$ ) of a targeted DNN, without knowing the detailed network structure and parameters. To this end, we formulate the optimization objective as minimizing the confidence score on true label: + +$$ +\underset {\mathcal {V}} {\arg \min } f _ {t r u e} \left(\mathcal {S} (x, \mathcal {P} _ {\mathcal {V}}, \mathcal {M}, k)\right), \text {s . t .} \widetilde {y} _ {a d v} \neq y _ {t r u e} \tag {4} +$$ + +where $\widetilde{y}_{adv} = \arg \max_{i}f_{i}(x_{adv})$ . We want to find the best set of coordinates $\mathcal{V}^*$ to minimize $f_{true}(x_{adv})$ so as to produce misclassification. + +In black-box scenarios, a popular approach is to use zeroth order optimization (ZOO) [5] to estimate the gradients of the targeted DNN. However, we observe severe gradient exploding and vanishing effect in the practical implementation of ZOO, which is probably due to: 1) the coordinate values in $\mathcal{V}$ are discrete, 2) the judgement on whether a coordinate locates within $\mathcal{P}_{\mathcal{V}} \cap \mathcal{M}$ is a boolean function, making gradients unreliable. + +Instead, in our method, we turn to exploit the particle swarm optimization (PSO) strategy [15], which stems from + +the study on how bird flocks search for food. Based on the cooperation and information sharing between individuals in a population, a valid solution can be found quickly without the help of gradients. Specifically, in PSO, we maintain a population of particles, each of which represents a candidate solution of Eq. (4) and has its own speed of movement in the solution space. In each iteration, all the particles adjust their speeds and positions according to the current individual optima and the global optimum shared by the whole population, and finally update every optimum. During this process, a cost function is needed to evaluate the quality of each candidate solution, which is the confidence score $f_{true}(\cdot)$ in our context. The algorithm terminates as long as $\widetilde{y}_{adv} \neq y_{true}$ or the maximum number of iterations is reached. To further increase the success rate, we adopt the $n$ -random-restarts strategy, which means that when the attack fails we can reinitialize and rerun the PSO at most $n - 1$ times. + +# 3.4. Shadow Attack in Real Physical-World + +To generate robust adversarial examples in the real physical-world, we adopt the following two strategies for enhancement: + +Expectation Over Transformation. EOT [1] is a powerful tool for dealing with the domain shift between the digital and the physical domains. To implement EOT, we start by defining a distribution of transformation $\mathcal{T}$ to simulate domain shift. Each instance of $\mathcal{T}$ is a combination of a set of random image transformations including down sampling, brightness adjustment, perspective transformation, motion blur. More importantly, the possible mismatch of shadow coefficient $k$ is also considered in $\mathcal{T}$ by setting a random $k$ . Next, rather than optimizing $\mathcal{V}$ for a single image, we instead minimize the expectation of $f_{true}(\cdot)$ over the set of transformed images, i.e., + +$$ +\underset {\mathcal {V}} {\arg \min } \mathbb {E} _ {t \sim \mathcal {T}} [ f _ {t r u e} (t (x _ {a d v})) ], \text {s . t .} \widetilde {y} _ {a d v} \neq y _ {t r u e}. \tag {5} +$$ + +In practice, we approximate the expectation in Eq. (5) by the mean of 10 transformed samples together with the original sample. + +Prediction stabilization. According to Eykholt et al. [10], any successful physical perturbation must cause targeted misclassification in a range of distances and angles to avoid attack failure by performing simple majority voting. However, due to the relatively small perturbation space, it is difficult to achieve targeted misclassification by shadows. Instead, we first optimize Eq. (5) such that the classifier should output a wrong decision $\widetilde{y}_w$ . Then, we stabilize this prediction by rerunning PSO while conducting the following optimization: + +$$ +\underset {\mathcal {V}} {\arg \max } \mathbb {E} _ {t \sim \mathcal {T}} [ f _ {w} (t (x _ {a d v})) ], \text {s . t .} \widetilde {y} _ {a d v} = \widetilde {y} _ {w}. \tag {6} +$$ + +Table 1. Success rates of the proposed Shadow Attack with different shadow coefficient $k$ on LISA and GTSRB test sets. The column in bold refers to the performances when $k$ takes the mean of $k$ in SBU Shadow dataset, which is 0.43. + +
ModelShadow Coefficient k
0.200.250.300.350.400.430.450.500.550.600.650.70
LISA-CNN100.00100.0099.7399.1899.0598.2397.9596.0493.1888.8183.0872.71
GTSRB-CNN97.3796.3595.1493.4591.3690.4788.9787.1584.2580.3673.7666.73
+ +Table 2. Average number of queries at the time when the attack succeeds with different shadow coefficient $k$ on LISA and GTSRB test sets. The column in bold refers to the performances when $k$ takes the mean of $k$ in SBU Shadow dataset, which is 0.43. + +
ModelShadow Coefficient k
0.200.250.300.350.400.430.450.500.550.600.650.70
LISA-CNN26.627.738.471.883.491.2100.6137.0169.2195.9306.7293.4
GTSRB-CNN98.393.7112.8129.0128.4126.8136.9155.9188.3232.0294.2343.4
+ +Experiments in Sec. 4.3 demonstrate that our algorithm can achieve similar performance with targeted attacks in terms of the stability of predictions. + +# 4. Experiments + +# 4.1. Datasets and Models + +We choose road sign classification as our target task. Following Eykholt et al. [10], we evaluate the performance of our algorithm on the same datasets and model architectures. One dataset is LISA [21], which consists of 47 different US road sign classes. To avoid the effect of long-tailed distribution, only the top 16 classes with the largest number of samples are tested. The other dataset is GTSRB [26], which consists of 43 different German road sign classes. Note that there are some images in both datasets that are captured under very dark condition or already in shadows. In view of this, we remove images whose average pixel value of L-channel in the area of traffic sign is less than 120. + +# 4.2. Evaluation in Digital Domain + +In the digital domain, we attack every image in the test sets of LISA and GTSRB with simulated shadow. We measure the performance of our algorithm by attack success rate, which is defined as the ratio of the number of samples that successfully cause misclassification to the number of all samples in the test set. As shown in Fig. 2, the shadow value $k$ can be varied in a wide range in the real world. Therefore, we repeat the experiment with several different values of $k$ ranging from 0.2 to 0.7, and the results are shown in Tab. 1. It can be found that, when $k$ is set to 0.43, which is the mean of shadow values in the SBU Shadow dataset [29], our success rates on LISA and GTSRB test sets are $98.23\%$ and $90.47\%$ respectively. When $k > 0.7$ , the successful rates are relatively low, because the shadows are weak and the perturbed images are close to the clean ones. + +In the black-box scenario, to keep stealthy, another important concern is how many queries should be performed. We investigate this point in Tab. 2, from which it can be found that our method can get a valid adversarial example with only dozens or hundreds of queries. + +# 4.3. Evaluation in Physical Domain + +In the physical domain, to simulate real-world application scenarios, we first cast the specific shadow onto our target traffic sign and then record a video with a camera moving towards the sign. Next, we measure the performance of our attack by the percentage of misclassified frames in this video. By experiments, we demonstrate that our method can consistently carry out effective attacks not only outdoors in the daytime using sunlight to generate shadows, but also at night or indoors by leveraging artificial light source to generate shadows. + +Outdoor Environment. We take the US speed limit 25 sign as an example for outdoor test in the daytime. As shown in Fig. 3, we generate the shadow by a cardboard. We record a video with 220 frames to simulate a self-driving car coming from far to near. For each frame, we first manually draw the bounding-box of the traffic sign and then follow the crop-resize-then-classify pipeline for classification. The results show that, our attack achieves $100.00\%$ misclassification rate, while $95.91\%$ of the frames are misclassified as speed limit 35. This implies that the performance of our untargeted attack is comparable to that of targeted attacks in term of the stability of predictions, making the voting algorithm fail to be an effective defense. Fig. 3 shows some frames at equal intervals of time as well as their predictions. + +Indoor Environment. One limitation of our attack is that it is difficult to produce obvious shadows at night without sunlight or indoors with poor lighting. In this case, we use a flashlight to generate artificial light, which achieves comparable effect to sunlight. Our indoor test is conducted + +![](images/3300419226178d65633ad9e3b27ee22d1fd7fcbc51a197ec8bfc0c051831f021.jpg) +Predict: Speed Limit 35 + +![](images/e9decaa96d0f923bb2cc9439301187a3c8eaee8c34351b7348f0137af5c33d95.jpg) +Predict: Speed Limit 35 + +![](images/2bc49526a94146069e81a1adf58dc83c158275b3626b7aa86618a3c46bf34a3d.jpg) +Predict: Speed Limit 35 + +![](images/7d028ed0eb8a7a4ad9847c9d8fe6c6806b21b67758a325da2479022bb4bf999c.jpg) +Predict: Speed Limit 35 + +![](images/03a21c19b8a3ddc6c6042242653f2e0c0a3f26f42ab6ef2e51aebadcb7f951b7.jpg) +Confidence: $31.63\%$ +Predict: Speed Limit 35 +Confidence: $47.08\%$ +Figure 3. Examples of frames in the video of our outdoor experiment and the corresponding classification results. + +![](images/d3d4e26b6fda8f28342f13f971224139fa010b640b0786100fdecd96a661e4b4.jpg) +Confidence: $53.26\%$ +Predict: Speed Limit 35 +Confidence: $29.67\%$ + +![](images/06daee134990a76981cf64bdee4708152ffe57924fbd1d92a7418ed7b7fa8381.jpg) +Confidence: $61.43\%$ +Predict: Speed Limit 35 +Confidence: $26.84\%$ + +![](images/2eaae391f8bbc782dbf46f7e0a9bd3d7e9583b79015c1bdf64c24013cfb10c3e.jpg) +Confidence: $31.37\%$ +Predict: Speed Limit 35 +Confidence: $54.97\%$ + +Table 3. Experimental results of our indoor test, where error rate refers to the percentage of misclassified frames in each video and stability refers to the percentage of frames predicted as the primary error class. + +
Ground truthPredictError rateStability
Speed limit 25Speed limit 35100%88%
Speed limit 30Speed limit 35100%93%
Speed limit 35Speed limit 3095%71%
Speed limit 45Signal Ahead100%76%
+ +in a dark stairwell, as illustrated in Fig. 4. The traffic signs are placed on the platform in the middle of two floors and the flashlight is fixed on the upper floor while ensuring that the light can be cast onto the traffic signs. We take four US speed limit signs from LISA [21] as examples for indoor test. For each sign, we record a video when walking from the lower floor to the upper floor. The videos include 100 frames. Tab. 3 offers the misclassification rate of each video, which demonstrates that our attack is also effective indoors. Fig. 4 provides some example frames in the test of the speed limit 45 sign, in which their predictions are also given. It can be found our attack is successful for all. + +# 4.4. Scheduled Attack + +Once the cardboard is fixed, the generated shadow will move over time due to the angle change of sunlight, which inspires us that our method can be used to conduct an interesting scheduled attack. Scheduled attack means that, due to the movement of the sun, we can control our shadow perturbation to be harmless in most of the time but to be adversarial at a certain time, e.g. the peak traffic hour in the morning. + +To carry out a scheduled attack, we just need to fix the cardboard as done in Sec. 4.3 at a specific time of a day + +in advance, and then the adversarial effect would be generated at the same time the future days if there is no significant change of the weather. Furthermore, after applying the strategies mentioned in Sec. 3.4 to enhance robustness, our attack can maintain successful for a period of time, rather than only effective at a certain moment. + +To test the scheduled attack, we simulate it on digital images. We first place our targeted traffic sign image on the XOZ plane of a three-dimensional coordinate system. Next, we calculate the solar elevation angle and the solar azimuth angle by using our scheduled time, longitude and latitude. Based on this, as long as we set the distance to the traffic sign in the Y-axis direction, we can further get the coordinates of each vertex of the cardboard. By fixing these coordinates, we can figure out the positions of shadows on the XOZ plane at any time. In this way, we simulate the dynamic changes of shadows over time. + +We choose eight German speed limit signs from GTSRB [26] as test examples for our experiment. The longitude and latitude are set to 0 and 45 respectively. The traffic signs face south, i.e., the Y-axis points to the south. The distances from cardboard to traffic signs in the Y-axis direction are set to one meter. For each sign, we set 8:30 in the morning as the scheduled time, and we generate images with shadow every second from 8:25 to 8:35, from which we can observe how the classifier's predictions change over time. We show an instance of our simulated scheduled attack in Fig. 5. As shown in Fig. 6, we achieve the goal of scheduled attacks on all eight speed limit signs. The duration of successful attack ranges from dozens of seconds to several minutes. + +# 4.5. Ablation study + +About the number of edges of $\mathcal{P}_{\nu}$ . Theoretically, $\mathcal{P}_{\nu}$ can be any valid polygon. However, when the number of edges is relatively large, the shadow would look unnatural, + +![](images/66b9ea2d2cdc5a5cd7598374bfebb14eaa180b906a6de6d0f3ff0d1ce2415013.jpg) +Frame 1: Signal Ahead +Frame 20: Pedestrian Crossing + +![](images/444f586b63122c862d2001158bba2d140a97f65d23a7253890b4036f26bd81f2.jpg) +Frame 40: Signal Ahead + +![](images/df9dd31ebf8db60c78e6aaaf887f264e464e567dbdc0f0fcde54c56c31d8f57b.jpg) +Frame 60: Signal Ahead +Frame 80: Pedestrian Crossing + +![](images/6e6ae2f222844af2561e26b1a07f1d76dc364b4ec4856def055a880e2d4b9e06.jpg) + +![](images/d0676765bc02475cbc7c3911cabbb62dfa81a6c3d8d6b8f3c7d3c9d5bc1a97c0.jpg) +Frame 100: Signal Ahead + +![](images/cdb544856c1ab1d3a0ec0ae5fafbb022ac8e83227e06b8cc225a1636485acbd1.jpg) +Figure 4. Examples of frames in a video of our indoor experiment and the corresponding classification results. + +Time: 8:26:00 AM + +Predict: Speed Limit 30 Confidence: $91.17\%$ + +![](images/6c5a63dad4abd72d93f30485668f70dea013736a7b3d50b907f57c429d5380c9.jpg) + +Time: 8:28:30 AM + +Predict: Speed Limit 80 Confidence: $87.87\%$ + +![](images/f68a4166e413b8ffb1405b7a628209d67ad5c1cd66d3c51e020365289d6ed18a.jpg) + +Time: 8:30:52 AM + +Predict: Speed Limit 20 Confidence: $47.20\%$ + +![](images/745a2a94a8d8ff01d741883fe4bcde094c64c3ff4d38f279c4cfd988004ed680.jpg) + +![](images/178e8e321a49143ff1f2c02a06f974b135641ff5be80f21ff18aaf5ac320be03.jpg) + +![](images/a886505b4322ea161930ac199a21f7afb00dddf2beb670503a09c4ac7619f6c4.jpg) + +Time: 8:27:00 AM + +Predict: Speed Limit 30 Confidence: $90.81\%$ + +Time: 8:29:00 AM + +Predict: Speed Limit 80 Confidence: $62.67\%$ + +Time: 8:32:00 AM + +Predict: Speed Limit 30 Confidence: $22.69\%$ + +![](images/efae1eb70538b8e7d5cad432933f7f9edf27032194bad2669a10d5c8ad3b2267.jpg) + +![](images/478c52636f3fee9dd96fd66fd84159b286b6e2cb4b88bb88e961b1bbe732a181.jpg) + +![](images/a69ae6021cbc8d9843d125a424a6696695b71001a4a0a6df470bd70e0c6ddc4f.jpg) +Figure 5. Our simulated scheduled attack. Our scheduled time is 8:30 in the morning, and the target class is speed limit 80. We show how the predictions change as the shadow moves on the German speed limit 30 sign. The predictions before 8:28:07 am and after 8:30:52 am are correct, while the predictions from 8:28:07 am to 8:30:06 am are speed limit 80 and the predictions from 8:30:07 am to 8:30:52 am are speed limit 20. + +Time: 8:28:07 AM + +Predict: Speed Limit 80 Confidence: $41.87\%$ + +Time: 8:29:30 AM + +Predict: Speed Limit 80 Confidence: $53.97\%$ + +Time: 8:34:00 AM + +Predict: Speed Limit 30 Confidence: $91.34\%$ + +Table 4. Performances of the proposed Shadow Attack with different number of edges of polygon $\mathcal{P}_{\nu}$ . + +
ModelNumber of edges
3579
LISA-CNN97.9598.9199.4599.59
GTSRB-CNN90.8093.7296.8397.59
+ +which goes against the requirement of stealthiness. Moreover, a polygon with too many edges leads to more computational overhead and it is not easy to implement in the real world. So in practice, we choose to attack the target object by a simple polygon area. Indeed, as shown in Tab. 4, the + +Table 5. ablation study of $n$ -random-starts strategy. + +
ModelNumber of restarts
151050100
LISA-CNN95.9198.3698.5099.0599.18
GTSRB-CNN87.7690.7491.7692.8193.22
+ +simplest polygon—triangles—are sufficient to produce successful adversarial examples. The performance loss caused by the reduction in the number of edges is also acceptable. + +About $n$ -random-restarts strategy. We test the effectiveness of $n$ -random-restarts by setting $n$ to 1, 5, 10, 50, and 100 respectively. As shown in Tab. 5, compared with + +![](images/35430b137cdf1a5b7e1a04fdaf12501da9e59bbf515b7e50c3898db201efbc2e.jpg) +Figure 6. The test result of our scheduled attack on 8 German speed limit signs. The green and red areas represent correct and incorrect classifications respectively. + +Table 6. Performance comparison of models with and without robustness training, where accuracy denotes the clean accuracy in LISA and GTSRB test sets, robustness denotes the probability that our attack fails (1 - attack success rate), and queries denotes the average number of queries at the time when our attack succeeds. All the data are obtained when $k = 0.43$ . + +
ModelAccuracyRobustnessQueries
LISA-CNN99.631.7391.24
GTSRB-CNN99.009.53126.75
LISA-CNNrob99.5640.93849.51
GTSRB-CNNrob98.9125.57464.52
+ +$n = 1$ , by setting $n = 5$ we can effectively improve the success rate. However, when $n$ is greater than 5, there are only marginal improvements in performance by increasing $n$ , demonstrating the effectiveness of PSO. To balance the success rate and computational overhead, we set $n = 5$ in practice. + +# 4.6. How to Defend against the Shadow Attack? + +In the above subsections, we demonstrate that the shadow perturbations is able to pose a security threat to the traffic or other security-critical scenarios. We discuss the defense mechanism against this type of attack as follows. + +One of the most effective defense strategies against adversarial examples is adversarial training (AT) [20], which improves model robustness by using newly generated adversarial examples as training samples in each epoch. In our context, to implement AT, we need to apply the algorithm described in Sec. 3.3 to each training sample in an + +epoch, which however is a particularly time-consuming process. In order to make training faster, in each epoch we only add a random shadow to each training sample (the coordinate values in $\mathcal{V}$ and the coefficient $k$ are random variables), instead of the worst case shadow. We expect that such a training method can reduce the model's sensitivity to shadows, thereby improving the robustness to our attack. We retrain the models in this way, which are denoted as LISA-CNN $_{rob}$ and GTSRB-CNN $_{rob}$ . To verify the effectiveness of the modified adversarial training, we perform attack on the retrained models in the digital domain. The results summarized in Tab. 6 demonstrate that this defense can improve the model robustness and the difficulty of the attack significantly at the expense of slightly decreased accuracy on clean samples. + +# 5. Limitation + +One limitation of our attack is the requirement of a strong single light source. In the environment with poor lighting condition, our method is difficult to produce significant shadow perturbations, i.e., $k$ would be large, which result in little difference between the attacked images and the clean ones. As shown in Tab. 1 and Tab. 2, a large $k$ leads to a low success rate and more queries. To remedy this problem, we can achieve the adversarial effect through a stronger artificial light as shown in Sec. 4.3. For the scenarios with multiple light sources, it is also difficult for our method to produce effective shadow perturbations. + +Another limitation is that we cannot explicitly conduct targeted attacks, which is probably due to the perturbation directions produced by shadows are relatively single. However, as shown in our outdoor experiment, we are able to achieve comparable results to that of targeted attacks in term of the stability of predictions. + +# 6. Conclusion + +In this paper, we present a new optics-based adversarial attack strategy, which utilizes the very common natural phenomenon, shadow, to produce harmful perturbations on the targets. Experimental results demonstrate this attack can be successfully applied in both digital- and physical-settings. Our work reveals that shadows can be dangerous, which is able to mislead the machine learning based vision system to produce erroneous decision. + +As a new type of attack, there surely would be some drawbacks or limitations. We will work on making it more practical in future research. + +# 7. Acknowledgement + +This work was supported by National Natural Science Foundation of China under Grants 61922027, 6207115 and 61932022. + +# References + +[1] Anish Athalye, Logan Engstrom, Andrew Ilyas, and Kevin Kwok. Synthesizing robust adversarial examples. In International conference on machine learning, pages 284-293. 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Mitra $^{2,3}$ Dani Lischinski $^{4}$ Daniel Cohen-Or $^{1,5}$ Hui Huang $^{1*}$ + +1Shenzhen University 2University College London 3Adobe Research 4Hebrew University of Jerusalem 5Tel Aviv University + +# Abstract + +We present ShapeFormer, a transformer-based network that produces a distribution of object completions, conditioned on incomplete, and possibly noisy, point clouds. The resultant distribution can then be sampled to generate likely completions, each exhibiting plausible shape details while being faithful to the input. + +To facilitate the use of transformers for 3D, we introduce a compact 3D representation, vector quantized deep implicit function (VQDIF), that utilizes spatial sparsity to represent a close approximation of a 3D shape by a short sequence of discrete variables. Experiments demonstrate that ShapeFormer outperforms prior art for shape completion from ambiguous partial inputs in terms of both completion quality and diversity. We also show that our approach effectively handles a variety of shape types, incomplete patterns, and real-world scans. + +# 1. Introduction + +Shapes are typically acquired with cameras that probe and sample surfaces. The process relies on line of sight and, at best, can obtain partial information from the visible parts of objects. Hence, sampling complex real-world geometry is inevitably imperfect, resulting in varying sampling densities and missing parts. This problem of surface completion has been extensively investigated over multiple decades [5]. The central challenge is to compensate for incomplete data by inspecting non-local hints in the observed data to infer missing parts using various forms of priors. + +Recently, deep implicit function (DIF) has emerged as an effective representation for learning high-quality surface completion. To learn shape priors, earlier DIFs [13, 41, 48] encode each shape using a single global latent vector. Combining a global code with region-specific local latent codes [14, 15, 22, 27, 35, 50] can faithfully preserve geometric details of the input in the completion. However, when presented with ambiguous partial input, for which multiple + +![](images/58e059257199d91e66c5da8452d6c40c187901a8f04e962c2f133cfadf4a11fc.jpg) +Figure 1. ShapeFormer predicts multiple completions for a real-world scan of a sports car (left column), a chair with missing parts (middle column), and a partial point cloud of human lower legs (right column). The input point clouds are superimposed with the generated shapes to emphasize the faithfulness of the completion to the input point cloud. + +plausible completions are possible (see Fig. 1), the deterministic nature of local DIF usually fails to produce meaningful completions for unseen regions. A viable alternative is to combine generative models to handle the input uncer- + +tainty. However, for representations that contain enormous statistical redundancy, as in the case of current local methods, such combination [57] excessively allocates model capacity towards perceptually irrelevant details [21, 25]. + +We present ShapeFormer, a transformer-based autoregressive model that learns a distribution over possible shape completions. We use local codes to form a sequence of discrete, vector quantized features, greatly reducing the representation size while keeping the underlying structure. Applying transformer-based generative models toward such sequences of discrete variables have been shown to be effective for generative pretraining [3, 11], generation [23, 53] and completion [64] in image domain. + +However, directly deploying transformers to 3D feature grids leads to a sequence length cubic in the feature resolution. Since transformers have an innate quadratic complexity on sequence length, only using overly coarse feature resolution, while feasible, can barely represent meaningful shapes. To mitigate the complexity, we first introduce Vector Quantized Deep Implicit Functions (VQDIF), a novel 3D representation that is both compact and structured, that can represent complex 3D shapes with acceptable accuracy, while being rather small in size. The core idea is to sparsely encode shapes as sequences of discrete 2-tuples, each representing both the position and content of a non-empty local feature. These sequences can be decoded to deep implicit functions from which high-quality surfaces can subsequently be extracted. Due to the sparse nature of 3D shapes, such encoding reduces the sequence length from cubic to quadratic in the feature resolution, thus enabling effective combination with generative models. + +ShapeFormer completes shapes by generating complete sequences, conditioned on the sequence for partial observation. It is trained by sequentially predicting the conditional distribution of both location and content over the next element. Unlike image completion [64], where the model is trained with the BERT [3, 20] objective to only predict for unseen regions, in the 3D shape completion setting, the input features may also come from both noisy and incomplete observations, and keeping them intact necessarily yields noisy results. Hence, in order to generate whole complete sequences from scratch while being faithful to the partial observations, we adapt the auto-regressive objective and prepend the partial sequence to the complete one to achieve conditioning. This strategy has been proved effective for conditional synthesis for both text [39] and images [23]. + +We demonstrate the ability of ShapeFormer to produce diverse high-quality completions for ambiguous partial observations of various shape types, including CAD models and human bodies, and of various incomplete sources such as real-world scans with missing parts. In summary, our contributions include: (i) a novel DIF representation based on sequences of discrete variables that compactly + +represents satisfactory approximations of 3D shapes; (ii) a transformer-based autoregressive model that uses our new representation to predict multiple high-quality completed shapes conditioned on the partial input; and (iii) state-of-the-art results for multi-modal shape completion in terms of completion quality and diversity. The FPD score on PartNet is improved by at most 1.7 compared with prior multi-modal method cGAN [67]. + +# 2. Related Work + +Shape reconstruction and completion. 3D reconstruction is a longstanding ill-posed problem in computer vision and graphics. Traditional methods can produce faithful reconstruction from complete input such as point cloud [5], or images [26]. Recently, neural network-based methods have demonstrated an impressive performance toward reconstruction from partial input [30], where the unseen regions are completed with the help of data priors. They can be classified according to their output representation, such as voxels, meshes, point clouds, and deep implicit functions. Since voxels can be processed or generated easily through 3D convolutions thanks to their regularity, they are commonly used in earlier works [17, 19, 31, 56]. However, since their cubic complexity toward resolution, the predicted shapes are either too coarse or too heavy in size for later applications. While meshes are more data-efficient, due to the difficulty of handling mesh topology, mesh-based methods have to either use shape template [38, 54, 65], limiting to a single topology, or produce self-intersecting meshes [29]. Point clouds, in contrast, do not have such a problem and are popularly used lately for generation [1, 24] and completion [59, 68, 69, 71]. However, point clouds need to be non-trivially post-processed using classical methods [6, 34, 36, 37] to recover surfaces due to their sparse nature. Recent works that represent shapes as deep implicit functions have been shown to be effective for high-quality 3D reconstruction [13, 41, 48]. By leveraging local priors, follow-up works [15, 22, 27, 40, 50] can further improve the fidelity of geometric details. However, most current methods are not effective toward ambiguous input due to their deterministic nature. Other methods handle such input by leveraging generative models. They learn the conditional distribution of complete shapes represented as either a single global code [2, 67], which, due to their lack of spatial structure, leads to completions misaligned with the input, or raw point cloud [73], which, due to its statistical redundancy, is only effective for completing simple shapes with a limited number of points. In this paper, we show how building generative models upon our new compact, structured representation enables multi-modal high-quality reconstruction for complex shapes. + +![](images/64c978f29b71f81692cd27b2111595873ba586610c26b4c8e357552a73ffd863.jpg) +Figure 2. Overview of our shape completion approach. Given a partial point cloud $\mathcal{P}$ , possibly from a depth image, as input, our VQDIF encoder first converts it to a sparse feature sequence $\mathbf{z}_{0\dots K - 1}$ , replacing them with the indices of their nearest neighbor $\mathbf{e}_j$ in a learned dictionary $\mathcal{D}$ , forming a sequence of discrete 2-tuples consisting of the coordinate (pink) and the quantized feature index (blue). We refer to this partial sequence as $\mathcal{S}_{\mathcal{P}}$ (drawn with dashed lines). The ShapeFormer then takes $\mathcal{S}_{\mathcal{P}}$ as input and models the conditional distribution $p(S_{\mathcal{C}}|S_{\mathcal{P}})$ . Autoregressive sampling yields a probable complete sequence $\mathcal{S}_{\mathcal{C}}$ . Finally, the VQDIF decoder converts the sequence $\mathcal{S}_{\mathcal{C}}$ to a deep implicit function, from which the surface reconstruction $\mathcal{M}$ can be extracted. To show the faithfulness of our reconstructions, we super-impose the input point cloud on them. Please see the supplementary material for more architectural details. + +Autoregressive models and Transformers. Autoregressive models are generative models that aim to model distributions of high dimensional data by factoring the joint probability distribution to a series of conditional distributions via the chain rule [4]. Using neural networks to parameterize the conditional distribution has been proved to be effective [28, 60] in general, and more specifically to image generation [12, 47, 62]. Transformers [63], known for their ability to model long-range dependencies through self-attention, have shown the power of autoregressive models in natural languages [8, 51], image generation [11, 49]. Contrary to deterministic masked auto-encoders [32], Transformers can produce diverse image completions [64] that are sharp in masked regions by adopting the BERT [20] training objective. In the 3D domain, autoregressive models have been used to learn the distribution of point clouds [57, 66] and meshes [44]. However, these models can only generate small point clouds or meshes restricted to 1024 vertices due to the lack of efficient representation. In contrast, by eliminating statistical redundancy, a compressed discrete representation enables generative models to focus on data dependencies at a more salient level [53, 61] and recently allows high-resolution image synthesis [23, 52]. Follow-up works utilize data sparsity to obtain even more compact representations [21, 45]. We explore this direction in the context of surface completion. Concurrently with our work, AutoSDF [42] trains Transformers to complete and generation shapes with dense grid. And Point-BERT [70] adopts generative training for downstream tasks like classification. + +# 3. Method + +We model the shape completion problem as mapping a partial point cloud $\mathcal{P} \in \mathbb{R}^{N \times 3}$ to a complete, watertight mesh $\mathcal{M}$ which matches the cloud. Since this is an ill-posed problem, we seek to estimate the probabilistic distribution of such mesh $p(\mathcal{M}|\mathcal{P})$ utilizing the power of Transformers. Instead of working directly on point clouds, meshes, or feature grids, we approximate shapes as short discrete sequences (see Sec. 3.1) to greatly reduce both the number of variables and the variable bit size, which enables Transformers to complete complex 3D shapes (see Sec. 3.2). + +With such compact representation, the conditional distribution becomes $p(S_{\mathcal{C}}|S_{\mathcal{P}})$ , where $S_{\mathcal{P}}$ and $S_{\mathcal{C}}$ are the sequence encoding of the partial point cloud and the complete shape, respectively. Once such distribution is modeled, we can sample multiple complete sequences $S_{\mathcal{C}}$ , from which different surface reconstructions $\mathcal{M}$ can be obtained through decoding. This process is illustrated in Fig. 2. + +# 3.1. Compact sequence encoding for 3D shapes + +We propose VQDIF, whose goal is to approximate 3D shapes with a shape dictionary, with each entry describing a particular type of local shape part inside a cell of volumetric grid $G$ with resolution $R$ . With such a dictionary, shapes can be encoded as short sequences of entry indices, describing the local shapes inside all non-empty grid cells, enabling transformers to efficiently model the global dependencies. + +We design an auto-encoder architecture to achieve this. The encoder $E$ first maps the input point cloud to a 64 resolution feature grid with local-pooled PointNet and then downsample it to resolution $R$ . Unlike the previous strategy for image synthesis [23], the encoder parameters are + +carefully set to have the least receptive field, reducing the number of non-empty features to the number of sparse voxels of the voxelized input point cloud $\mathcal{P}$ at resolution $R$ . Then these non-empty features are flattened to a sequence of length $K$ in row-major order. Since these features are sparse, we record their locations with their flattened index $\{c_i\}_{i=0}^{K-1}$ . Other orderings are also possible, but for generation they are not as effective as row-major order [23]. + +Following the idea of neural discrete representation learning [61], we compress the bit size of the feature sequence $\{\mathbf{z}_i\}_{i = 0}^{K - 1}$ through vector quantization, that is, clamping it to its nearest entry in a dictionary $\mathcal{D}$ of $V$ embeddings $\{\mathbf{e}_j\}_{j = 0}^V$ and we save the indices of these entries: + +$$ +v _ {i} = \operatorname {a r g m i n} _ {j \in [ 0, V)} \| \mathbf {z} _ {i} - \mathbf {e} _ {j} \|. \tag {1} +$$ + +Thus, we get a compact sequence of discrete 2-tuples representing the 3D shape $S = \{(c_i, v_i)\}_{i=0}^{K-1}$ . Finally, the decoder projects this sequence back to a feature grid and, through a 3D-Unet [18], decodes it to a local deep implicit function $f$ [50], whose iso-surface is the reconstruction $\mathcal{M}$ . + +Training. We train the VQDIF by simultaneously minimizing the reconstruction loss and updating the dictionary using exponential moving averages [61], where dictionary embeddings are gradually pulled toward the encoded features. We also adopt commitment loss $\mathcal{L}_{\mathrm{commit}}$ [61] to encourage encoded features $\mathbf{z}_i$ to stay close to their nearest entry $\mathbf{e}_{v_i}$ in the dictionary, with index $v_{i}$ , thus keeping the range of the embeddings bounded. We define the loss as, + +$$ +\mathcal {L} _ {\text {c o m m i t}} = \frac {1}{K} \sum_ {i = 0} ^ {K - 1} \left(\mathbf {z} _ {i} - \operatorname {s g} \left[ \mathbf {e} _ {v _ {i}} \right]\right) ^ {2}, \tag {2} +$$ + +where sg stands for stop gradient operator which prevents the embedding being affected by this loss. + +The full training objective for VQDIF is the combination of reconstruction loss of $\mathcal{L}_{\mathrm{commit}}$ with weighting factor $\beta$ : + +$$ +\mathcal {L} _ {\mathrm {v q D I F}} = \frac {1}{T} \sum_ {i = 0} ^ {T - 1} \operatorname {B C E} \left(f \left(\mathbf {x} _ {i}\right), o _ {i}\right) + \beta \mathcal {L} _ {\text {c o m m i t}}. \tag {3} +$$ + +Here, $T$ is the size of the target set and BCE is the binary cross-entropy loss which measures the discrepancy between the predicted and the ground truth occupancy $o_i$ at target point $\mathbf{x}_i$ . During training, we select the target set $\mathcal{T}_x = \{\mathbf{x}_{i=0}^{T-1}\}$ and its occupancy values $\mathcal{T}_o = \{o_{i=0}^{T-1}\}$ in a similar fashion to prior work [41]. + +# 3.2. Sequence generation for shape completion + +We autoregressively model the distribution $p(S_{\mathcal{C}}|S_{\mathcal{P}})$ , by predicting the distribution of the next element conditioned + +![](images/9dc1f1cdcb57a579fcbcc3d8712af972107893149954a7333a1485e6cd3e2886.jpg) +Figure 3. The architecture of the ShapeFormer. The partial sequence $\mathcal{S}_{\mathcal{P}}$ (dashed boxes) and the complete one $S_{\mathcal{C}}$ (solid boxes) both appended with an end token are concatenated before sending their locations, $c_{i}$ (pink) and values $v_{i}$ (blue), to a Coordinate Transformer to predict the next location $c_{i + 1}$ . The Value Transformer takes both $c_{i + 1}$ and the former Transformer's output embedding to predict the next value $v_{i + 1}$ . + +on the previous elements. We also factor out the tuple distribution for each element: $p(c_{i}, v_{i}) = p(c_{i})p(v_{i}|c_{i})$ . The final factored sequence distribution is as follows: + +$$ +\begin{array}{l} p \left(\mathcal {S} _ {\mathcal {C}} \mid \mathcal {S} _ {\mathcal {P}}; \theta\right) = \prod_ {i = 0} ^ {K - 1} p _ {c _ {i}} \cdot p _ {v _ {i}} \\ p _ {c _ {i}} = p \left(c _ {i} \mid \mathbf {c} _ {< i}, \mathbf {v} _ {< i}, \mathcal {S} _ {\mathcal {P}}; \theta\right) \\ p _ {v _ {i}} = p \left(v _ {i} \mid \mathbf {c} _ {\leq i}, \mathbf {v} _ {< i}, \mathcal {S} _ {\mathcal {P}}; \theta\right). \\ \end{array} +$$ + +Here, $\theta$ indicates model parameters and $p_{c_i}$ and $p_{v_i}$ are the distributions of the coordinate and the index value of the $i$ -th element of $\mathcal{S}_{\mathcal{C}}$ , conditioned on previously generated elements and the partial sequence $\mathcal{S}_{\mathcal{P}}$ . Note that $p_{v_i}$ is also conditioned on the current coordinate $c_i$ . + +Different approaches have been applied to build a transformer model that can predict tuple sequences. Instead of flattening them [57], which in our case doubles the sequence length, we stack two decoder-only transformers to predict the $p_{c_i}$ and $p_{v_i}$ respectively in a similar way to prior works [21, 45, 66], as illustrated in Fig. 3. Unlike in the image completion case [64], where the partial sequence is strictly a part of the complete sequence so that only the missing regions need to be completed. For our case, however, due to the noise or incompleteness of local observations, we would like to predict complete sequences from scratch to fix such data deficiencies. And thanks to the autoregressive structure of the decoder-only transformer, we can achieve conditioning by simply prepending $S_{\mathcal{P}}$ before $S_{\mathcal{C}}$ to generate complete sequences that are in coordination with the partial one. We also append an additional end token to both sequences to help learning. + +Training and inference. The training objective of Shape + +![](images/1520187b222739ad8ef545fa39c68cd836af087d10dfab6ee33c4a181388bb29.jpg) + +![](images/e972062cce8e9028fc3aca7a8a1b50c112204a424de37b21fa822dc2e0c01835.jpg) +Input +VQDF-only + +![](images/f347ef4a79fc38ae3f1e77774043b163e358371e0ac9fbf63a4d1897ecaad0fb.jpg) + +![](images/fa781cee9764618d2d4e190004c2168921dfaec8dbc056f53fea01663bb83490.jpg) +OccNet +Ours-1 + +![](images/6806c88cd18528ff51b8751467fb91d73af2abc9e35cb43b1bf9409af2755724.jpg) + +![](images/7eb87958325bc72ceb1efaecc8660ec3cc12d6e2172b37e5085b35a9c3ac51b9.jpg) +ConvONet +Ours-2 + +![](images/6ab42a4dc99991dc337901c2d8bd5bdd99fca2814c16da7fba66ae9a1551ca54.jpg) + +![](images/6bb182fbeca72060c3f4ab578b11b4078186bc3058dd851b1dfef767e4ee0574.jpg) +IF-Net +Ours-3 + +![](images/1982ba27ef24d79bf7ad0a879149f8259e2c05a672125fa1be18e41a06e03c19.jpg) + +![](images/4db4d3cc80304524a19db18aba418940f7e2e8d1d6ce190ac2bc5f8a0e2aa20e.jpg) +PoinTr +Ours-4 + +![](images/ba86d013478b87c7b599c8904a0c1309a619b45d77468ba432a914eebe24282f.jpg) + +![](images/611ef2b002e673650cef1f93099949d55a36a7b08a258a7a919dddca4ed842a6.jpg) +cGAN-1 +Ours-5 + +![](images/317e254d66b1703941a84198f34ed522809368019f7a63e7d7d8dc9d6a8c176d.jpg) + +![](images/a638b0e7d02a15206050a3f6bb88179935335f376d43490b3919f2ea92065b0d.jpg) +CGAN-2 +Ours-6 + +![](images/843c9caded4eeddd2e41d9debc7169e11b412d72077148c88be6015cd69ee8ef.jpg) + +![](images/399b6016b59345d7c2c63ae80a877f068fb972f0f62399fca6e63e462427e9d5.jpg) +Input +VQDIF-only +Figure 4. Visual comparison with prior shape completion methods on the ShapeNet dataset. Our method can better handle ambiguous scans and produce completions that are more faithful on both observed and unseen regions. More examples are in the supplementary material. + +![](images/ac041e4b806b2ca7d3ea2bb2ec2186f12fad3e5dcf2c199f71cdb4ae22404a22.jpg) + +![](images/26549dc18b4536e9edd738f98b3c5588d84fc65433e9a3b7182da1768475b4c8.jpg) +OccNet +Ours-1 + +![](images/fc640575fe933e14ed22dc880f52581a803491172495a6a75aeb205d5d272f37.jpg) +ConvONet + +![](images/5ccc24907d67908911545b6682dc6b04b6f7a2c53cdd7da36bd4865b2df3d46d.jpg) +Ours-2 + +![](images/b542b01aeb5cc1913643a292fb69ebce142ea88653dda04b1db7d4c9ab7410c7.jpg) + +![](images/b766cee250f30e39fdaffee8b696a5f4e808827b3e0bd0977a302fc97acf8804.jpg) +IF-Net +Ours-3 + +![](images/723460a3e46c2c5029fd63476fc1f4d9de04f02d3f2c69671f8c978ba3b1830e.jpg) +PoinTr + +![](images/1d2726199bbd46bb3d03bec03a6aee60ec5316909527833760dc1619d90bd670.jpg) +Ours-4 + +![](images/6054a0109a52bde4e51dd1481eee3f1d35742bf3d234877ad9f05b62e281a107.jpg) + +![](images/6552f6b38dd15f9b2ccc8027b40d06b9fa896b804cf6bd91fde358d6c4b9e1c1.jpg) +cGAN-1 +Ours-5 + +![](images/af85710cc59808cbf734528e4799969b281f359651cb49faa6c764e795227195.jpg) +CGAN-2 + +![](images/a2dd78f60fd22a42a2d22a9a807df3b9b3c24d70742fc414b49a5c9a146bb0b5.jpg) +Ours-6 + +Former is to maximize the log-likelihood given both $S_{\mathcal{C}}$ and $S_{\mathcal{P}}$ : $\mathcal{L}_{\mathrm{ShapeFormer}} = -\log p(S_{\mathcal{C}}|S_{\mathcal{P}};\theta)$ . After the model is trained, ShapeFormer performs shape completion by sequentially sampling the next element of the complete sequence until an end token ([END]) is encountered. Given the partial sequence, we alternatively sample the new coordinate and value index using top-p sampling [33], where only a few top choices, for which the sum of probabilities exceeds a threshold $p_n$ , are kept. Also, we mask out the invalid choices for coordinate to guarantee monotonicity. + +# 4. Results and Evaluation + +In this section, we demonstrate our method outperforms prior arts for shape completion from ambiguous scans and part-level incompleteness (Sec. 4.1). Then we show our approach can effectively handle a variety of shape types, out-of-distribution shapes, and real-world scans from the Redwood dataset [16] (Sec. 4.2). Lastly, we show our VQDIF representation has a significantly smaller size compared with prior DIFs while achieving similar accuracy (Sec. 4.3). + +
SCAN AMBIGUITYLOWHIGH
MethodCD↓F1↑FPD↓CD↓F1↑FPD↓
OccNet [41]1.4863.20.342.7950.43.12
ConvONet [50]0.8172.90.233.1460.42.85
IF-Net [15]0.7973.80.2518.451.53.66
PoinTr [69]0.8070.10.233.1159.33.29
cGAN [67]1.3362.11.363.4959.32.55
Ours0.7470.30.244.7260.51.45
Ours*0.7371.40.224.6960.71.83
VQDIF-only0.7973.80.253.0760.33.14
+ +Table 1. Quantitative results on ShapeNet with different scan ambiguity. Ours: top-p=0.4 sampling, Ours*: top-p=0 sampling. + +Throughout all these experiments, we use feature resolution $R = 16$ for VQDIF and set its loss balancing factor $\beta = 0.01$ . We also set the vocabulary of the dictionary $\mathcal{D}$ to be $V = 4096$ . We use 20 and 4 blocks for Coordinate and Value Transformers, respectively. All of these blocks have 16 heads self-attention, and the embedding dimension is 1024. We find that a maximum sequence length of 812 + +![](images/788377a1692deb1c7f9e63eaacf0f7f1989192565bf380d39b652e4e126c2799.jpg) +Figure 5. Visual comparison for multi-modal shape completion of Table, Chair, and Lamp categories on PartNet. We can produce diverse completions that better align with the input. + +is enough for all of our experiments. We set the default probability factor $p = 0.4$ for sampling. Further implementation details such as architecture and training statistics are provided in the supplementary. + +# 4.1. Shape completion results + +Data. We consider two datasets: 1) ShapeNet [9] for testing on partial scan and 2) PartNet [43] for testing on part-level incompleteness; we follow the same setting as in cGAN [67]. For ShapeNet, following prior works [13, 15, 41, 50], we use 13 classes of the ShapeNet with train/val/test split from 3D-R2N2 [17]. The data are processed and sampled similarly to IMNet [13] and we create partial input for training via random virtual scanning. For evaluation, we first measure the ambiguity score of a partial point cloud $\mathcal{P}$ to its complete counterpart $\mathcal{C}$ as the mean ratio of the distance of each point $x \in \mathcal{C}$ with its nearest neighbor in $\mathcal{P}$ to its distance toward furthest neighbor in $\mathcal{C}$ . We uniformly sample 70 viewpoints on a sphere for each shape. Then we create two setups for the dataset according to ambiguity. The high scan ambiguity setup selects scans with the top half ambiguity score and vice versa. More details about this score are provided in the supplementary material. + +Metric. For the low ambiguity setting, we use Chamfer $L_{2}$ Distance (CD) and F-score%1 (F1) [58] to measure how accurate the completion is; this is similar to the previous setup [50]. And to evaluate completion quality for high ambiguity setting, we follow prior work [55] to use pre-trained PointNet [10] classifier as a feature extractor to compute the Fréchet Point Cloud Distance (FPD) between the set of completion results and ground truth shapes. Additionally, for the PartNet dataset, we follow cGAN [67] and use Uni + +
MethodMMD ↓TMD ↑UHD ↓FPD ↓
cGAN [67]1.983.053.392.95
SInv. [72]2.140.622.323.45
Ours1.323.960.981.22
+ +Table 2. Quantitative comparison for multi-modal completion on PartNet between our method and prior works. The metrics are averaged across all three categories (Table, Chair, Lamp) and are scaled by $10^{3}$ , $10^{2}$ , $10^{2}$ , $10^{1}$ respectively. + +directional Hausdorff Distance (UHD) to measure faithfulness toward input, Total Mutual Difference (TMD) to measure diversity, and Minimal Matching Distance (MMD) [1]. + +Baselines. We compare our model with a global DIF method OccNet [41], two local DIF methods ConvONet [50] and IF-Net [15], PoinTr [69], which adopts Transformers without autoregressive learning, and multimodal completion method cGAN [67]. We also compare our VQDIF-only model to illustrate the necessity of ShapeFormer. We train these methods for shape completion in our dataset setting with their official implementation. + +Results on ShapeNet. As shown in Fig. 4, methods incorporating structured local features can better preserve the input details than those that only operate on global features (OccNet [41], cGAN [67]) And deterministic methods tend to produce averaged shape since they are unable to handle multi-modality. Notice that PoinTr [69] also utilizes the power of Transformers, but they can not alleviate this problem by adopting Transformers without generative modeling. This phenomenon is more apparent for the chair example, + +![](images/e7e51afe225a03146b2f6ed9f7de743c1c59e25fa226e8672edf94775736c591.jpg) +RGBD + +![](images/bb97a6803723e030ad4d789be1b947c7678ba071340221bfdbad68c925d20c60.jpg) +Input + +![](images/ebb11803da746dd1293590cf2295c93ffd067880a8d6f8a09bf6d00309184478.jpg) +Completions + +![](images/8f5235319b454c877e45867688d9d2bbf2a9d37449281dbf6a92a90d38a37233.jpg) + +![](images/ce2f2e20ef7e4f8e11be39403e045c9f0d0b61c97f10633d603cd361814b5d4d.jpg) + +![](images/eafb588047e8fed7065ba514b48a7b3d138b0839771a022f1a68e12fdf109a50.jpg) + +![](images/32c4d8763f3c5c0600e39c16fa2ea6bacd301bee052046668f67e171eb33b5a8.jpg) + +![](images/3326ec6b334ef1e58a0b13ff0b4fc033666f6a3fe0a1a06fc3cf8c074c382112.jpg) + +![](images/bec21ae7d4da3fb244d46156777b43f64e8d5ea28d4676e359751ede0b19641f.jpg) + +![](images/96c7b77c85329744c139263e5d9364cc3881860b4d348ad108505773a52cf122.jpg) + +![](images/7e759e1040d0bfa670ed1c0afd1d80c0874fe53a6f8506f2046f4dc16a81deb7.jpg) + +![](images/b4f0e177640510f9a8370af81a29a3afae55009d63f0a460f3c3443df4964113.jpg) + +![](images/d50505f25b96f269a05f2fcee86d8746d785656a1d402588a272a4189ee38e75.jpg) + +![](images/5805208521b4f7936966d5ee781f55d2b49eef01dfa519fb7ab416351ee25d2f.jpg) + +![](images/c4dcbca24b5f3108e76f45cc71e646147791bc29c2e3c13a2d670981fb5093bf.jpg) + +![](images/0433c2997578b11aea29ef63d4e9216913ce4c89dd45883e0d5d5fb0f0e58582.jpg) +Figure 6. Shape completion results on real-world depth scan from Redwood dataset. ShapeFormer takes partial point clouds converted from depth images and produces multiple possible completions whose variation depends on the uncertainty of viewpoints. + +![](images/852f46cd0e3b33f0cce9166c8670be00b78b74d0b51f4e8b266338bdcdd246c6.jpg) + +![](images/3596b48a332c5590fe0e0da028fe536a45023589fb6b1c207b6e712c418ee262.jpg) + +![](images/dd0ca41acb45b96d7416183c86aff7e68a6eb795156ae52958e3fc5b8343879d.jpg) + +![](images/673ca12e3bed6ca9b0567fcb7560e182e8fe7e00da267c32e898613159464ab1.jpg) +Figure 8. Given partial human body parts (left column), our method generates complete human bodies with different poses (along the rows) and the variety depends on the ambiguity. + +![](images/945c7ac86de8e6af6f828c3bb1d20646f29de282ad1d943b644f3c8bbd57159e.jpg) +Scan + +![](images/c3fe6327c8db4743e1031f504d1053b8333b5bde033498c3a19a4e7658f6bf9d.jpg) + +![](images/e087a599225130c59c16e26f0793e6103526024aac91fcd259f32e0f36fc1cdf.jpg) +Completions + +![](images/6db5b72a74af9483179bb461dd472726c897acaa6bffc2e0167e7a64409e35d9.jpg) + +![](images/dd25c6b83a11b5d0f532446904760787b9f90d4239e3b81cb480873025560446.jpg) + +![](images/9df8667395050985a0b4b4784c2d43e44cc76f9a069a957e7c83c37316779372.jpg) +Figure 7. Shape completion results on out-of-distribution shapes. Given a scan of an unseen type of shape, ShapeFormer can produce multiple reasonable completions by generalizing the knowledge learned in the training set. + +![](images/51357960b22bca4653dd7ec0b85f6fa4d0b6e155182f143111c353d452a76343.jpg) + +![](images/f90aca01992abab06f2fab94a45874021f4e304c77f962df300d106ecafd0fc1.jpg) + +![](images/33b9132713dc790b421f08ee5f04f36085f883a4f2e6bc075ea20a74b8690bf6.jpg) + +![](images/a6d5f9c77600b697ee596fe861903129395b48aff4e915bd2be92e5a2881f1e7.jpg) + +which has higher ambiguity. Our VQDIF-only model also fails to produce good completion in this case. Based on VQDIF, our ShapeFormer resolves ambiguity by factoring the estimation into a distribution, with each sampled shape sharp and plausible. In contrast, the multi-modal method cGAN [67] is unable to produce high-quality shapes due to their unstructured representation. Further, we generate one completion per input with top-p sampling for quantitative evaluation. As shown in Tab. 1, our method has a much better FPD for high ambiguity scans. Notice CD is not reliable when ambiguity is high since it often treats plausible completions as significant errors. For low ambiguity scans, our method is also competitive toward previous state-of-the-art completion methods in terms of accuracy. + +Results on PartNet. We compare our model with cGAN and ShapeInversion [72] on PartNet. The latter method achieves multiple completions through GAN inversion. The quantitative and qualitative comparisons are shown in Tab. 2 and Fig. 5, respectively. Thanks to our structured represent + +![](images/91fe1f7ff7c822667cf8c1b551f70b89dc2bb55cbbd8963eae03f6797fd1fb2c.jpg) + +tation, we achieve much better faithfulness (UHD) and can generate more varied (TMD) high-quality shapes (MMD and FPD) than these GAN-based methods. + +# 4.2. More results + +Results on real scans. We further investigate how our model pre-trained on ShapeNet can be applied to scans of real objects. We test our model on partial point clouds converted from RGBD scans of the Redwood 3D Scans dataset [16]. Figure 6 shows the results for a sofa and a table, both of them have two scans from different views. Notice that our model sensitively captures the uncertainty of a scan, producing a distribution of completions that are faithful to the scan and plausible in unobserved regions. We also show results for a sports car in Fig. 2. + +Results on out-of-distribution objects. We further evaluate ShapeFormer's generalization by testing scans of unseen types of shapes on our trained model of Sec. 4.1. We pick the novel shapes from the "Famous" dataset collected by Erler et al. [22] which includes many famous geometries for testing, such as the "Utah teapot," and apply virtual scan to get the partial point cloud. Fig. 7 demonstrates our ShapeFormer can grasp general concepts such as symmetry or hollow and filled. Even the model is only trained on the 13 ShapeNet categories, without ever seeing any cups or teapot, it can still successfully produce multiple reasonable completions from the partial scan. Moreover, in the second row, we see the completions of a one-side scan of a cup contain two distinct features: the cups might be solid or empty. These examples show the ShapeFormer's potential for general-purpose shape completion, where once we have it trained, we can apply it for all types of shapes. + +Results on human shapes. In addition to CAD models, we qualitatively evaluate our completion results on scans of hu + +
Occ.CONet.IF.Ours8Ours16Ours32
CD3.560.980.431.900.980.55
F168.289.097.877.588.196.4
len.1323128357217889
+ +Table 3. Auto-encoding results for objects in ShapeNet. len. stands for sequence length of the flattened representation. + +![](images/1f257a564b289731f42cedbedaa9ee68464847646a1f3134dfcb7fcca0e5b437.jpg) +Figure 9. The relation between representation size and reconstruction accuracy. With higher feature resolution, our VQDIF achieves satisfactory accuracy while keeping a rather small byte size. + +man shapes (D-FAUST dataset [7]) using the same setting as Niemeyer et al. [46]. Human shapes are very challenging due to their thin structures and the wide variety of poses. To simulate part level incompleteness, we randomly select a point from the complete cloud and only keep neighboring points within a ball of a fixed radius as partial input. Fig. 8 shows examples of our results. We can see that our completions keep the pose of the observed body parts and generate various possible poses for the unobserved body parts. + +# 4.3. Surface reconstruction with VQDIF + +Our final experiment evaluates the representation size and reconstruction accuracy of VQDIF. We compare VQDIF of different feature resolutions (Ours $_8$ , Ours $_{16}$ , Ours $_{32}$ ) with OccNet, ConvONet, IF-Net, which are retrained to auto-encode the complete shape with their released implementations. As shown in Fig. 9, Ours $_{32}$ achieves similar accuracy to the local implicit approach IF-Net while being significantly smaller in size thanks to the sparse and discrete VQDIF features. The minimum receptive field of our encoder keeps the feature as local as possible, which greatly reduces the feature amount. Then the multi-dimensional feature vectors are quantized and can be referred to using a single integer index, which further reduces the size. The accuracy loss is only salient for lower feature resolution, as seen in the w/o quant. comparison, where we train VQDIF without vector quantization. These together allow transformers to effectively model the distri + +![](images/fcf27a428c9d1fd43227812df61006b08d93a8c1da17cdc62c37167ef4f756a4.jpg) +Figure 10. Results for auto-encoding complete shapes. Our VQDIF in different feature resolutions achieves better or similar results compared to the prior DIF methods. + +bution of shapes. We adopt $\mathrm{Ours}_{16}$ for ShapeFormer since it only has an average length of 217 (see Tab. 3) and its accuracy is already comparable with ConvONet (see Fig. 10). + +# 5. Conclusions + +We have presented ShapeFormer, a transformer-based architecture that learns a conditional distribution of completions, from which multiple plausible completed shapes can be sampled. By explicitly modeling the underlying distribution, our method produces sharp output instead of regressing to the mean producing a blurry result. To facilitate generative learning for 3D shape, we propose a new 3D representation VQDIF that can significantly compress the shapes into short sequences of sparse, discrete local features, which in turn enables producing better results, both in terms of quality and diversity, than previous methods. + +The major factor limiting our method to be applied in fields like robotics is the sampling speed, which is currently 20 seconds per generated complete shape. In the future, we would also like to explore utilizing a more efficient attention mechanism to allow Transformers to learn VQDIF with smaller size, producing even higher quality completions. Moreover, the current method is generic, leveraging advances in language models. More research is required to include geometric or physical reasoning in the process to better deal with ambiguities. + +Acknowledgements. We thank the reviews for their comments. We thank Ziyu Wan, Xuelin Chen and Jiahui Lyu for discussions. This work was supported in parts by NSFC (62161146005, U21B2023, U2001206), GD Talent Program (2019JC05X328), GD Science and Technology Program (2020A0505100064), DEGP Key Project (2018KZDXM058, 2020SFKC059), Shenzhen Science and Technology Program (RCJC20200714114435012, JCYJ20210324120213036), Royal Society (NAF-R1-180099), ISF (3441/21, 2492/20) and Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ). + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas J. Guibas. Learning representations and generative models for 3D point clouds. In International conference on machine learning, 2017. 2, 6 +[2] Himanshu Arora, Saurabh Mishra, Shichong Peng, Ke Li, and Ali Mahdavi-Amiri. Multimodal shape completion via imle. arXiv preprint arXiv:2106.16237, 2021. 2 +[3] Hangbo Bao, Li Dong, and Furu Wei. Beit: Bert pre-training of image transformers, 2021. 2 +[4] Yoshua Bengio and Samy Bengio. 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Existing shape from polarization (SfP) works mainly focus on estimating the normal of a single object rather than complex scenes in the wild. A key barrier to high-quality scene-level SfP is the lack of real-world SfP data in complex scenes. Hence, we contribute the first real-world scene-level SfP dataset with paired input polarization images and ground-truth normal maps. Then we propose a learning-based framework with a multi-head self-attention module and viewing encoding, which is designed to handle increasing polarization ambiguities caused by complex materials and non-orthographic projection in scene-level SfP. Our trained model can be generalized to far-field outdoor scenes as the relationship between polarized light and surface normals is not affected by distance. Experimental results demonstrate that our approach significantly outperforms existing SfP models on two datasets. Our dataset and source code will be publicly available at https://github.com/ChenyangLEI/sfp-wild. + +# 1. Introduction + +Accurate surface normal estimation in the wild can provide valuable information about a scene's geometry and can be used in various computer vision tasks, including segmentation [19], 3D reconstruction [26], and many others [22, 33]. Therefore, normal estimation is an important task studied for a long time. However, estimating high-quality normals in the wild is still an open problem. Various techniques such as photometric stereo [9, 10] can produce high-frequency normals, but most of them only provide short-range object-level normal maps. Active depth sensors can be another approach to obtaining normals from depth maps, but the corresponding depth maps are often sparse (LiDAR) or noisy (time-of-flight, structured light) so they can not estimate normals reliably. Also, the depth range of active sensors is limited. + +![](images/03b31e5b8cf197f1d07e886162d3184e879ea6104689bcd21b3b65c43131e9ed.jpg) + +![](images/4b723ca562ea46827ac3e4916751dd7237e6f5146a68cbddecaeb45c0ff483dc.jpg) + +![](images/dddbdabc2307e802db5307f13eeeca0ec3b2e6aa43949f5d93c1743dc45bb0c1.jpg) + +![](images/8bb55ff4e1d57ad6e37e2fdfa4707b363dc5cb223a23756f5f6c809fd038c59e.jpg) + +![](images/3bc9cd496692e50f7e2b8d295da1597bca6e44374944b9e644375d3b7d55763b.jpg) + +![](images/d7e16751d4e2b5a6b4250d92746cbb21f801da0155c54ae82256711592aae4cb.jpg) + +![](images/7fc6e7c8a9999ae89956bba2fc92c882f538e8236c62e53bf74552cfb54b1ce5.jpg) + +![](images/8697b25d89af2759f566021279655052cb51e062b6005e53b6b9e9c40563941e.jpg) + +![](images/9cab96e962c6786366b3752379378d6004c52249ee8e1b33677291f6bc46666c.jpg) +Input $I_{un}$ + +![](images/36c181d98c0200a366c68acf0d125bc09cdf42cafb3c9423cf3fd750f1c2ab74.jpg) +Input $\phi$ + +![](images/76b2e15cd12abd37e44811d8b9257b663adddf514c01fe98b56a72d4e9e834f0.jpg) +Without pol. + +![](images/e5a4a4a5282b7423ba8a51468cbfd60768f0ffefcc565fd54c75010acd8fbd28.jpg) +With pol. +Figure 1. Our method can estimate dense scene-level surface normals from a single polarization image. Polarization can provide effective cues for obtaining more accurate results. In the first row, polarization provides geometry cues for our model so that it is not fooled by objects in the printed image on a wall. In the second and third rows, polarization provides guidance for planes with different surface normals even when their materials are quite similar. $I_{un}$ : unpolarized image; $\phi$ : angle of polarization. + +In this work, we are interested in estimating surface normal from a single polarization image for complex scenes in the wild. Since the polarization of light changes differently when the light interacts with the surfaces of different shapes and materials (governed by the Fresnel equations [12]), the polarization images can provide dense surface orientation cues from the polarized light perceived at each pixel. Also, compared with the active sensors and object-level normal estimation techniques (e.g., photometric stereo), the polarization camera is a passive sensor that is not constrained to a specific depth range. Thus polarization images are promising data sources for accurate normal estimation in the wild. + +However, estimating normals from a polarization image for complex scenes (scene-level SfP) is challenging. To the best of our knowledge, no existing SfP work focuses on complex scenes, and several challenges are yet to be solved. Firstly, polarization contains ambiguities from unknown information such as object materials and reflection + +types [12]. Object-level SfP methods approach these ambiguities by utilizing various cues (e.g., shading [44]) or making restrictive assumptions (e.g., known albedo [35]), which are unfeasible for multiple-object scenes because of the variabilities of material properties and complexities of reflections. Secondly, while some works [4, 29] demonstrate the potential of combining convolutional neural networks and polarization cues in estimating normals for unknown materials, there are only object-level [4] or synthetic data [29] for training, which are not sufficient for scene-level SfP. Finally, scene-level SfP brings up another challenge. The viewing direction influences the measured polarization information. Previous object-level SfP approaches ignore the impact of viewing direction since they assume orthographic projection by placing objects at the center of an image, which does not hold for scene-level SfP. + +To solve the challenge of lacking real-world scene-level polarization data, we construct the first real-world scene-level SfP dataset that contains diverse complex scenes. Building such a new dataset is necessary because the existing DeepSfP dataset [4] only contains a single object per image and the dataset by Kondo et al. [29] is synthetic and not publicly available. + +Due to the challenges of scene-level SfP, the performances of previous learning-based SfP works [4,29] are not satisfactory when they are trained on our scene-level data. To improve the performance of scene-level SfP in the wild, we adopt three novel designs in our model. First, we introduce multi-head self-attention [45] in a convolutional neural network (CNN) for SfP. Multi-head self-attention utilizes the global context of an image, which helps the CNN resolve the local ambiguities in polarization cues. Second, to handle non-orthographic projection for scene-level SfP, the neural network must be aware of the viewing direction of each pixel since the convolution operation is translation invariant. We thus propose a simple but critical technique that improves the performance of SfP methods on scene-level data: providing per-pixel viewing encoding to the neural network. Finally, as an additional contribution, we design a novel polarization representation, which is effective and considerably more efficient than the representations in prior work [4]. + +We compare our approach with various state-of-the-art methods. Experimental results show that our model can generate a high-quality normal map from a single polarization image (Fig. 1) and can generalize beyond the depth range of the training data. In summary, our contributions are as follows. + +- We construct the first real-world SfP dataset containing paired input polarization images and ground-truth normal maps in complex scenes. +- Our proposed shape-from-polarization approach is the + +first one trained on complex real-world scene-level data and also the best-performing one for normal estimation from polarization in the wild. + +- Technically, we introduce three novel designs to scene-level SfP: viewing encoding that can handle the challenge of non-orthographic projection in scene-level SfP, a dedicated network architecture that adopts multi-head self-attention for SfP, and a practical polarization representation that is effective and efficient. + +# 2. Related Work + +Shape from polarization. The polarization of light changes when the light interacts with a surface, which can be described by the Fresnel equations using the geometry and materials of objects [12]. Shape from polarization (SfP) works [2, 38, 42] utilize this effect to estimate the surface normal of objects. Since the polarization state is affected by various factors simultaneously, early SfP methods usually enforce assumptions of reflection types and materials to constrain the problem. For example, Rahmann et al. [42] assume pure specular reflection and some works [1, 38] assume pure diffuse reflection. + +Various cues and techniques have been explored to resolve the ambiguities in this problem. Atkinson et al. [3] use shading from two views. Baek et al. [5] perform joint optimization of appearance, normals, and refractive index. A coarse depth map from a depth sensor [25], two-view stereo [21, 56], reciprocal image pairs [16], or multi-view stereo [13, 37], can also be served to disambiguate the problem. For single-view SfP, some methods combine photometric stereo [1] or shading information [35, 44] with SfP. Also, some works try to solve this problem under specific illumination conditions (e.g., front-flash illumination [15] and sunlight under the clear sky [23]). Unlike these works, our approach aims to estimate surface normal in the wild without specific assumptions or additional tools. + +Deep learning is proven effective in solving the ambiguities of object-level SfP. Ba et al. [4] collect a real-world object-level dataset and train a CNN to obtain normals from polarization, significantly outperforming physics-based SfP. Instead of collecting real-world data, Kondo et al. [29] create a synthetic dataset of polarization images with a new polarimetric BRDF model. However, these approaches have not studied complex scenes in the wild due to the lack of real-world scene-level data. To address this issue, we propose the first real-world scene-level SfP dataset. Besides, we also notice existing frameworks [4, 29] cannot achieve satisfactory results on our dataset due to the challenges that emerge in scene-level SfP, and we propose effective solutions to these challenges. + +Surface normals from an RGB image. Even though RGB data does not directly contain geometry cues for objects + +![](images/89aa7394be17eb0b99b20f987b0b727fb1867c8459d2f65f2123e7b3318acfbb.jpg) +Polarization image + +![](images/80f79235cb38797c4c810702e5c30e0f1ecda5f6c384443fa7a6887b4c8a35ef.jpg) +Polarization angle + +![](images/4f1944a9bb5ca6de6280fbb3bc7cbf4e94cc1361c3e2c7e136ee4e3d0409ad7f.jpg) +XTC [51] +Figure 2. The importance of polarization. Note that polarization conveys the underlying physical shape while RGB-based methods [17, 51] are distracted by the semantics in a printed picture attached to a wall. + +![](images/aa29966d0541432faa9050dc6c657341e1ed155c817f8c5f1f69e16083213eef.jpg) +Do et al. [17] + +![](images/944c558ad4ac685b9bf521d698e7344dbd9e5d7acb7c9ea8a1446640d87e0cfe.jpg) +Ours w/o polarization + +![](images/6440c127afeeb839d2ff3d8bba86ecf69309e4342862b325a5312bea71036852.jpg) +Ours w/ polarization + +such as polarization data, estimating the surface normal from a single RGB image is feasible, especially with the advent of deep learning. The related works [6,7,31,48,52] train a neural network using a large amount of RGB-surface normal paired data, including real-world indoor dataset [43] or synthetic dataset [14]. However, without the guidance of physics-based cues, these learning-based approaches mainly rely on semantic cues in the image, which leads to performance degradation when they are applied to data out of the training distribution (e.g., from indoor to outdoor data [11] and from gravity-aligned to tilted images [17]). + +Some approaches attempt to utilize the relevance between surface normals and other information (e.g., depth, semantic information and shading). It has been shown that better surface normal estimation can be achieved by simultaneously estimating geometric information, such as depth [40, 41], local principal axes [22], Manhattan label map [47], planes and edges [46]. Eigen and Fergus [18] and Zhang et al. [53] jointly predict depth, normals, and semantics, exploiting affinity between these three modalities. Zamir et al. [51] consider the consistency of normals and other attributes, such as shading, depth, occlusion, and curvature. Surface normal estimation is also an essential element in inverse rendering, which aims to recover normals, reflectance, and illumination from one image [8, 33, 50] or multiple images [27, 54]. However, according to our experiments, these approaches mainly depend on the semantic information of images for normal estimation. As a comparison, our method can better recover the physical geometry with the polarization cues, as shown in Fig. 2. + +# 3. SPW Dataset + +We construct the SPW (Shape from Polarization in the Wild) dataset, the first real-world dataset that contains scene-level ground-truth surface normals for polarization images in the wild. Table 1 provides a comparison between SPW and prior SfP datasets. The only existing realworld SfP dataset is DeepSfP [4]; however, it only provides ground-truth normals on masked objects. Kondo et al. [29] built a big SfP dataset, but it is synthetic and not publicly available. + +
DatasetLevelCollectionSizeResolutionPublic
DeepSfP [4]ObjectReal-world2631224×1024✓
Kondo [29]SceneSynthetic44305256×192×
OursSceneReal-world5221224×1024✓
+ +Table 1. Comparison among different datasets. DeepSfP [4] is real-world but focuses on object-level, Konda et al. [29] has a big dataset size, but it is synthetic and not publicly available. Ours is the first real-world scene-level SfP dataset. + +Our dataset consists of 522 sets of images from 110 different scenes containing diverse object materials and lighting conditions, and each scene includes 3-7 sets of images with different depths and viewing directions. A polarization image and the corresponding normal map are provided in each set. In addition to these image sets with ground truth normals, we also capture a separate set of images in outdoor scenes. Since most depth sensors cannot easily acquire dense depth for faraway scene content, these images are used for perceptual evaluation only, to assess generalization beyond the depth range of the training data. + +Fig. 3 shows our data preparation pipeline. The pipeline can be divided into the following four parts. + +a) Devices. Since there is no existing polarization-depth camera, we need to choose a depth sensor to capture dense scene-level depth. We notice that most LiDAR cannot produce dense point clouds efficiently, and the 360-degree rotating device used in [4] can only reconstruct small objects. Hence, we use a ToF sensor (Azure Kinect) to capture scene-level depth, and this depth sensor's resolution is $640 \times 576$ . For polarization, we use a PHX050S-P polarization camera that can capture four polarization images with polarizer angles of $0^{\circ}, 45^{\circ}, 90^{\circ}, 135^{\circ}$ in a single shot, and the resolution of this polarization camera is $1224 \times 1024$ . We fix the two sensors with a custom mount to make sure the camera pose between the depth sensor and polarization camera is the same in each capture, as shown in Fig. 3(a). +b) Depth-polarization alignment. We obtain the intrinsic and the initial extrinsic parameters between the polarization and depth sensor from stereo calibration. We then use + +![](images/d8e31aee531542761b604256308e381f74fb276f3748309f47fbfc290afc475f.jpg) +(a) Capture setup + +![](images/11237493a70640a4263be1e163ddec272e402ca66ed9275e018feb1bfbb0b276.jpg) +(b) Polarization image + +![](images/cbb559d545220b5b8216d2ee728c9cee4f644ea306401ed5f30c4b21cfd45920.jpg) +(c) Depth map +Figure 3. Our capture setup (a) fixes a polarization camera (red arrow) and a depth sensor (black arrow) with a custom mount. The polarization camera captures polarization images (b), and the depth sensor collects scene-level depth (c). We use PCA-based normal estimation to obtain normal maps from the depth data, as shown in (d) and (e). (d) uses a single depth map, and (e) uses a median-denoised depth map. Post-processing the denoised normal map in (e) yields the final normal map shown in (f), there we exclude normals in areas where the depth sensor returns the inaccurate or sparse depth (e.g., dark region). + +![](images/dc8625b662e0a7699570358933ae97b03e59d413ba75d1b967898703c17b3ef9.jpg) +(d) Coarse normal + +![](images/12f113d58f542984ee0005d5237bf995b05242f5ef772b618893687bcea78e37.jpg) +(e) Denoised normal + +![](images/f3a9b42739ccedcd5b3f03c903fca6897a26293f067c014eab5c7c259e6fbcee.jpg) +(f) Final normal + +coordinate descent to improve depth-polarization alignment further. Specifically, we optimize the extrinsic parameters with fixed intrinsic parameters to minimize the projection error between the reprojected RGB image and the polarization image. The optimized extrinsic parameters are used to produce polarization-aligned depth. + +c) Depth denoising. Since surface normals computed from a single polarization-aligned depth map are noisy, we capture 50 depth images with a stationary setup and compute the median at each pixel to reduce noise in the depth map. Finally, we generate a point cloud from the denoised depth map and calculate the surface normals from the aligned point cloud using Principal Component Analysis (PCA) from the Open3D library [55]. As shown in Fig. 3(d,e), denoising the depth map yields much cleaner normals. +d) Post-processing. Even though we get high-quality normals by the above steps, we further improve the quality by excluding normals in areas where the depth sensor returns inaccurate values, such as dark and occluded regions. We also exclude normals on thin structures where the depth sensor only captures very sparse point clouds, such as chair legs or wires. The final normals are shown in Fig. 3(f). + +# 4. Method + +In this paper, we consider linear polarization. A polarization camera can measure the intensity of light $\mathbf{I}^{\phi_{pol}}$ passing a polarizer [12, 56], which is determined by the polarizer angle $\phi_{pol}$ and the polarization of the light: + +$$ +\mathbf {I} ^ {\phi_ {p o l}} = \mathbf {I} _ {u n} \left\{1 + \rho \cos \left(2 \phi - 2 \phi_ {p o l}\right) \right\}, \tag {1} +$$ + +where $\phi$ is the angle of polarization (AoP), $\rho$ is the degree of polarization (DoP), $\mathbf{I}_{un}$ is the unpolarized intensity of light. $\phi, \rho,$ and $\mathbf{I}_{un}$ can be computed from images with different polarizer angles by [30, 32]. + +Degree of polarization (DoP) $\rho$ contains cues for the viewing angle $\theta_{\mathbf{v}}$ between surface normal $\mathbf{n}$ and viewing direction $\mathbf{v}$ . Specifically, the DoP $\rho$ is decided by the viewing angle $\theta_{\mathbf{v}}$ , the refractive index $\eta$ of the object and reflec + +tion type $r$ (specular or diffuse reflection). More details are provided in the supplement. + +Angle of polarization (AoP) $\phi$ is the projection of the polarization direction $\mathbf{d}$ on the image plane. In terms of physical properties, $\mathbf{d}$ is always parallel or perpendicular to the incidence plane, which is defined by surface normal $\mathbf{n}$ and viewing direction $\mathbf{v}$ . There are two ambiguities for the polarization angle: $\pi$ -ambiguity and diffuse/specular-ambiguity. The $\pi$ -ambiguity is because $\phi$ is from 0 to $\pi$ and there is no difference between $\phi$ and $\phi + \pi$ (Eq. 1). The reflection type causes the diffuse/specular-ambiguity: the polarization direction is parallel or perpendicular to the incidence plane respectively for diffuse/specular dominant reflection. + +# 4.1. Overview + +Fig. 4 provides an overview of our approach. The raw polarization image $\mathbf{I} \in \mathbb{R}^{H \times W \times 4}$ consists of four polarization images $\mathbf{I}^{\phi_{pol}} \in \mathbb{R}^{H \times W \times 1}$ under four polarizer angles $\phi_{pol} \in \{0, \pi/4, \pi/2, 3\pi/4\}$ . We firstly compute a polarization representation $\mathbf{P}$ for normal estimation (Sec. 4.2). Then, to handle the perspective projection for scene-level SfP, we provide the viewing encoding $\mathbf{V}$ as an extra input (Sec. 4.3). At last, we predict the normal $\hat{\mathbf{n}}$ from all the provided information with our designed architecture (Sec. 4.4). + +# 4.2. Polarization representation + +Having a proper polarization representation $\mathbf{P}$ as the input to a neural network can effectively improve the performance of SfP [4, 29]. Kondo et al. [29] directly compute AoP $\phi$ , DoP $\rho$ and $I_{un}$ as the polarization representation. DeepSfP [4] calculates possible SfP solutions under the assumption of orthographic projection: + +$$ +\mathbf {n} = (\sin \theta \cos \alpha , \sin \theta \sin \alpha , \cos \theta) ^ {\intercal}, \tag {2} +$$ + +where $\theta$ and $\alpha$ are the zenith angle and azimuth angle computed from DoP $\rho$ and AoP $\phi$ , respectively. While it is effective, computing their polarization representation is quite time-consuming, as reported in their paper [4]. + +![](images/199dfb19623795a4c1fbd59bb52f5378b70d1d1f97273cfffbfc2fc9afee6e1f.jpg) +Figure 4. An overview of our approach. The input to our network includes three parts: (1) Polarization images $\mathbf{I}^0, \mathbf{I}^{\pi/4}, \mathbf{I}^{\pi/2}, \mathbf{I}^{3\pi/4}$ . (2) The polarization representation $\mathbf{I}_{un}$ , $\phi_e$ , and $\rho$ computed from polarization images. (3) The viewing encoding $\mathbf{V}$ is vital to handle the perspective projection for scene-level SfP. The concatenated inputs are fed into the neural network to output an estimated normal $\hat{\mathbf{n}}$ . + +We propose a new polarization representation $\mathbf{P}$ that is efficient and more effective compared with existing polarization representations [4, 29], as shown in our experiments (Table 4). $\mathbf{P} \in \mathbb{R}^{H \times W \times 4}$ consists of $\mathbf{I}_{un}, \phi_e, \rho$ , where $\phi_e$ is the encoded AoP: + +$$ +\phi_ {e} = (\cos 2 \phi , \sin 2 \phi). \tag {3} +$$ + +The encoded AoP $\phi_e$ is designed to address a weakness of raw AoP $\phi$ . For example, given two polarization angles $0^\circ$ and $179^\circ$ , the distance between them should be $1^\circ$ in physics for polarization. However, in the calculated $\phi$ space, the difference is $179^\circ$ . Encoding helps solve the weakness of raw AoP representation since there is no difference between $\phi$ and $\phi + \pi$ in the encoding space. + +We input the DoP $\rho$ as cues for solving specular/diffuse ambiguity since the DoP $\rho$ is usually large when specular reflection dominates. This strategy improves the performance but does not fully resolve the specular/diffuse ambiguity. + +Importance of polarization. Polarization contains useful cues about physical 3D information of objects based on real-world reflection. Thus, utilizing polarization can improve the fidelity of estimated normals, especially for areas with rare or wrong semantic information. Fig. 2 shows an example about the advantage of polarization: given an image printed on a flat sheet of paper, the RGB-based baselines are distracted by the content of the image and fail to predict correct normals for the physical content of the scene (i.e., the flat paper). Polarization provides an alternative modality that can convey the true shape of objects in the scene. Hence, the polarization can give a robust cue to distinguish that the wall (paper) is exactly flat. + +# 4.3. Viewing encoding + +We introduce the viewing encoding $\mathbf{V}$ to account for non-orthographic projection in scene-level SfP, which con + +![](images/129f704cc9dfdb29e5b7d54255ebb588e5a0c0de3dff0fbce34408ef3bbe54ed.jpg) +Figure 5. An analysis of our proposed viewing encoding $\mathbf{V}$ . The polarization representation is affected by spatial-varying viewing directions in scene-level SfP. Enforcing the viewing encoding $\mathbf{V}$ can effectively calibrate the impact of viewing direction on the polarization representation. + +![](images/914fb0f1022bb68742533c947ca7ac55917d73864508359f5492c08662e8b035.jpg) + +![](images/825c71a73063ef42da976b41213d7c910b9902238de9b43841b872e1591fddd8.jpg) + +![](images/eb87cd903604c1f038c9f58115ffd5204e57516af37b80581d3e083a614e865b.jpg) + +tains the viewing direction cues for every pixel of the polarization representation. Previous object-level SfP approaches [3, 4] assume viewing directions are $(0,0,1)^{\mathrm{T}}$ for all pixels (i.e., orthographic projection) since an object is always put at the image center. However, the viewing direction is spatially varying in scene-level SfP, and the polarization representation is heavily influenced by the viewing direction. As shown in Fig. 5, for pixels with the same material and surface normal, their polarization representations are quite different. Also, since the CNN is translation-invariant, it is hard for CNN to know the viewing direction without explicitly providing it to the CNN. We thus propose to input the viewing encoding to the CNN. + +A direct representation of viewing encoding is the viewing direction, which is computed from the intrinsic parameters of the polarization camera. If the intrinsic parameters of the camera are not available, we can also use the 2D coordinate $(u,v)$ of each pixel and normalize it to $[-1,1]$ as input [34]. Fig. 5 presents an example for the effectiveness of our viewing encoding. + +Discussion. Note that our viewing encoding is different from the positional encoding used in NeRF [36] or transformers [45]. Our design is inspired by the fact that per + +
MethodTaskAngular Error ↓Accuracy ↑
MeanMedianRMSE11.25°22.5°30.0°
Miyazaki et al. [38]Physics-based SfP55.3455.1960.352.610.418.8
Mahmoud et al. [35]Physics-based SfP52.1451.9356.972.711.621.0
Smith et al. [44]Physics-based SfP50.4247.1755.5311.024.733.2
DeepSFP† [4]Learning-based SfP28.4324.9033.1718.848.362.3
Kondo et al.† [29]Learning-based SfP28.5925.4133.5417.547.162.6
OursLearning-based SfP17.8614.2022.7244.676.385.2
+ +Table 2. Quantitative evaluation on the SPW dataset. Our approach outperforms all baselines by a large margin on all evaluation metrics. †: our implementation. + +
MethodMean Angular Error↓
Miyazaki et al. [38]43.94
Mahmoud et al. [35]51.79
Smith et al. [44]45.39
DeepSfP [4]18.52
Ours14.68
+ +Table 3. Quantitative evaluation on the DeepSfP dataset [4]. Our approach obtains the best score. The results of other baselines are collected from the official results in DeepSfP [4]. + +pixel viewing directions influence polarization. Besides, viewing encoding yields better performance than the positional encoding in our experiments. + +# 4.4. Network architecture and training + +To handle the ambiguities that exist in polarization cues, we introduce multi-head self-attention [45] to SfP for utilizing the global context information. As shown in Fig. 4, the self-attention block is added in the bottleneck of an Encoder-Decoder architecture [39]. Different from similar architectures that combine CNN encoder with transformer [24, 49], we remove the linear projection layer since the CNN encoder already extracts the embeddings. Besides, similar to position embedding of transformer [24, 49], our viewing encoding can provide the position information to self-attention, and we thus remove the position embedding. Finally, we add instance normalization to the encoder since we notice it helps convergence. + +We adopt a cosine similarity loss [4] for training. We implement our model in PyTorch. The model is trained for 1000 epochs with batch size 16 on four Nvidia Tesla V100 GPUs, each with 16 GB memory. We use the Adam optimizer [28] with initial learning rate 1e-4 and we adopt a cosine decay scheduler for the learning rate. The learning rate is linearly scaled with the batch size. We crop images to $512 \times 512$ patches in each iteration for data augmentation. + +# 5. Experiments + +# 5.1. Experimental setup + +Evaluation metrics. Following previous surface normal estimation works [6, 48], we adopt six widely used metrics. The first three are Mean, Median, and RMSE (lower is better $\downarrow$ ), which are the mean, median, and RMSE of angular errors. The last three are $11.25^{\circ}$ , $22.5^{\circ}$ , and $30.0^{\circ}$ (higher is better $\uparrow$ ), and each shows the percentage of pixels within a specific angular error. + +Datasets. We use two datasets in the experiments. + +- DeepSfP [4]. DeepSfP is the only publicly available SfP dataset that contains real-world ground-truth surface normals. There is only one object in each image, but the surface normal is high-quality. We use the train/test split provided in the original paper [4]. +- SPW. We use our SPW dataset, presented in Sec. 3. We use 403 and 119 images for training and evaluation, respectively. Train and test sets do not include the images from the same scene to avoid overfitting. We also use the far-field data for perceptual evaluation, randomly divided based on scenes (instead of images). + +# 5.2. Comparison to SfP baselines + +Our approach is compared with three physics-based SfP methods (Miyazaki et al. [38], Mahmoud et al. [35], and Smith et al. [44]) and two learning-based SfP methods (DeepSfP [4] and Kondo et al. [29]). The source code and results of DeepSfP [4] and Konda et al. [29] are not available. We reimplement these two approaches and retrain their models on our SPW dataset. + +Table 2 presents the quantitative results of all the methods on our SPW dataset. Our approach outperforms all baselines by a large margin on all metrics. + +Fig. 6 provides a qualitative comparison on images from the SPW dataset. Our estimated surface normal maps are more accurate. Besides, Our approach can produce high-quality normals while other methods do not. + +![](images/7fd23775571a9ed6a3f1b75ba33a013e0b2529f7e256aa63af5e8ad9fd87299a.jpg) +Input $\mathbf{I}_{un}$ + +![](images/80d67213ca282c13cf3fe89b370230942d1abf681e3069b99c6fbfec58fecceb.jpg) +Input $\phi$ + +![](images/aa2cba318a51344c207b73b03f263fba102eee673b46faa996edee55ba735bab.jpg) +Miyazaki [38] + +![](images/43d4e784a4d66f767c058bac02293b9eb61d3dbd5a7c46a46e81e88b6d2ff2ec.jpg) +Smith et al. [44] + +![](images/38294fd8b15027586cb059575d22a2762da69508feed3d1d4a7924019740426e.jpg) +DeepSfP [4] + +![](images/3eb3034257c644a21698646c4d950dae108706074675107cd23580c1b5ebd9de.jpg) +Kondo et al. [29] + +![](images/b3e499bf28ad22ceb1f12817ed20bdf7761df879a51c6cb35c0bc0709f40a5ad.jpg) +Ours + +![](images/c6bcf0d28a3859d8d8d6ce33f3f37e4354b1119b5a73772bc491f8a366a92627.jpg) +Ground truth + +Table 3 presents the quantitative results on the public DeepSfP dataset [4], in which we also achieve the best performance. Our approach reduces the mean angular error by $20\%$ compared to the second-best result reported by DeepSfP [4]. + +For physics-based SfP [35, 38, 44], since the assumptions of these methods do not hold in the wild, the quantitative accuracy of these approaches is low on the SPW dataset. They cannot obtain satisfying performance on the DeepSfP dataset, either. For example, Mahmoud et al. [35] assume a distant light source, which is not common in the real world (e.g., multiple light sources can exist in a room). As for the learning-based SfP methods [4, 29], our approach is the best-performing one and we analyze the designs (i.e., polarization representation, viewing encoding and architectures) that contribute to our model in Sec. 5.4. + +# 5.3. Generalization to outdoor scenes + +Although our model is trained on near-field depth estimated by a Kinect camera, it can generalize to outdoor scenes with distances far beyond the Kinect depth range. This is illustrated qualitatively in Fig. 7. Quantitative results are not provided due to the lack of ground-truth normals in this regime. This generalization is possible because the relationship between polarized light and surface normals is not affected by distance. Thus our model that learns to estimate normals from near-field polarization data can generalize to outdoor scenes. + +# 5.4. Controlled experiments + +# 5.4.1 Polarization representation + +The experiments are conducted on both DeepSfP dataset [4] and SPW dataset. We remove the polarization information or replace our proposed polarization representation with other representations as input to our model. Table 4 provides the quantitative results of various polarization representations. Utilizing our polarization representation reduces the mean angular error by $9^{\circ}$ . Besides, we obtain the lowest + +![](images/7fce3f0a4842a4a6b93cbb82f8bdd81f230f089b58ef227245cdcae0a23f7aff.jpg) +Figure 6. Qualitative comparison between our approach and other shape from polarization methods baselines [4, 29, 38, 44] on the SPW dataset [4]. + +![](images/b8aad74a5ad6d39455c4761a48c3533143fa3046870c428e241f9a5287d17440.jpg) +Figure 7. Our results on outdoor scenes. Although our model is trained on near-field content, it appears to successfully generalize to large-scale outdoor scenes. + +![](images/7f759cc775395d6da462502ae21462f3928fc87537b3ac3f1c916ea078adfcbe.jpg) + +![](images/705d44984544ddf1fa28daa8fe2ba736b5162bda930eb6c0855e9783ac3f8392.jpg) + +![](images/32eeaadc4db0b60074112cb98517df71f135ea60ca5e4542cfa770e3bd5441fb.jpg) + +![](images/50ab9e8338d1b7f22e98207f75a21c5f537af86403a82531f5f8b2d967779ebf.jpg) + +
Polarization representation PMean SPWAngular Error↓ DeepSfP [4]Time(s)
Without polarization27.5219.140.000
Raw polarization21.7714.890.000
P from Kondo et al. [29]18.2615.440.203
P from DeepSfP [4]18.0514.821.514
P from our approach17.8614.680.281
+ +Table 4. Controlled experiments for polarization representations on SPW and DeepSfP [4] datasets. Please check Sec. 4.2 for the details of various representations. We test the preprocessing time of a raw image with resolution $1024 \times 1224$ using a single thread on Intel Xeon Gold CPU with $2.30\mathrm{GHz}$ frequency. + +MAE on both datasets and the running time of our representation is much shorter than DeepSfP [4]. + +# 5.4.2 Viewing encoding + +Since the DeepSfP dataset is not designed for scene-level SfP, we only conduct the controlled experiments on the + +
Viewing encodingAngular Error ↓Accuracy ↑
MeanMedianRMSE11.25°22.5°30.0°
Ours without V22.1218.0027.0332.266.977.8
Ours with Vp20.3116.0225.6840.471.080.5
Ours with Vc18.4414.6223.4643.776.184.8
Ours with V17.8614.2022.7244.676.385.2
+ +![](images/e585534a09d5fd96f1e74d1c75cf80c448b228c16c8671a1192cdbeb89535ebd.jpg) +Figure 8. An analysis of the viewing encoding. We calculate the mean angular error (MAE) for each pixel on the test set. We notice that the improvement brought by viewing encoding increases with the distance to the image center. We believe this is because the impact of non-orthographic projection is more severe in the corners of images. + +SPW dataset. For each model, we remove the viewing encoding from the input or use different types of viewing encoding. In Table 5, using viewing encoding improves our model in all the metrics effectively by a large margin. The model that uses raw viewing directions achieves the best performance. The model that uses positional encoding of NeRF [36] also improves the performance but is not as good as ours. When the images in a dataset are captured with the same intrinsic parameters, using normalized coordinates as viewing encoding also obtains satisfying performance. We further analyze the impact of viewing encoding in Fig. 5 and Fig. 8. + +# 5.4.3 Network architectures + +We study different network architectures in this section. In addition to networks of previous SfP methods (DeepSfP [4] and Kondo et al. [29]), we also compare with two RGB- + +Table 5. Controlled experiments for the viewing encoding on the SPW dataset. Previous learning-based SfP methods [4,29] do not input any viewing encoding. In addition to our viewing encoding $\mathbf{V}$ , we also try to use the positional encoding of NeRF [36] $\mathbf{V}_p$ and normalized coordinates $\mathbf{V}_c$ as the viewing encoding. + +
NetworkAngular Error ↓Accuracy ↑
MeanMedianRMSE11.25°22.5°30.0°
Kondo et al.† [29]26.4322.6931.8023.854.167.6
DeepSfP† [4]24.9720.8330.1325.658.470.9
U-Net [39]26.3522.4531.9725.454.567.6
DORN [20]20.1615.6025.4739.871.381.1
TransDepth [49]22.0517.4627.7733.066.677.9
Ours without IN20.7416.6325.9838.569.379.0
Ours without SA21.0816.5426.6236.168.579.3
Ours17.8614.2022.7244.676.385.2
+ +Table 6. Controlled experiments for network architectures on the SPW dataset. We retrain Kondo et al. [29], DeepSfP [4] and other networks with the same representation as ours (e.g. viewing encoding and our novel polarization representation) for fair comparison. SA: self-attention. IN: instance normalization. †: our implementation. + +based normal estimation methods: TransDepth [21] and DORN [20]. For all the experiments, we provide the same polarization representation and viewing encoding to these compared network architectures. Table 6 presents the quantitative results of different architectures. Our architecture obtains the best performance. Besides, removing self-attention or replacing instance normalization with batch normalization leads to performance degradation. + +# 6. Conclusion + +We present the first approach dedicated to scene-level surface normal estimation from a single polarization image in the wild. The accuracy of our model is demonstrated on SPW, the first scene-level dataset for real-world SfP. By introducing the viewing encoding, a self-attention module and a novel polarization representation to SfP, our model substantially outperforms prior work on both SPW and the object-level DeepSfP dataset. In addition, our model can generalize from near-field scenes (used during training) to far-field outdoor scenes. This is possible because the polarization sensor is based on passive sensing, so our trained model is expected to generalize to distant scenes. We hope our work including the proposed SPW dataset and our technical designs can contribute to high-quality normal estimation, especially shape from polarization. + +Limitations. One of the limitations of our work is the lack of quantitative evaluation in outdoor scenes. 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Our method realizes passive, texture independent, far range, and dark scene applicability, which can broaden the depth sensing subjects. A key observation is that thermal radiation is attenuated by the air and is wavelength dependent. By modeling the wavelength-dependent attenuation by the air and building a multispectral LWIR measurement system, we can jointly estimate the depth, temperature, and emissivity of the target. We analytically show the capability of the thermal radiation cue and show the effectiveness of the method in real-world scenes using an imaging system with a few bandpass filters. + +# 1. Introduction + +Depth sensing is an important technology, as shown by its wide range of applications. Depth sensing techniques refer to physics-based cues used to recover the scene depth, known as "shape from X." Historically, a great number of cues such as triangulation/disparity [23], time-of-flight [21], polarization [46], shading [25], silhouettes [9], focus/defocus [44], and texture [60] have been proposed. These "X" cues play an important role in depth sensing in various scenarios. However, existing depth sensing techniques require either clear visibility of the texture or an active light source to illuminate the surface, and there is no approach to passively measure depth in dark environments. + +In this paper, we propose an unprecedented depth sensing modality that can be used in dark and passive scenarios. As a key to achieving this property, we use the attenuation of long wavelength infrared (LWIR) radiation through the air. As all objects emit thermal radiation according to their temperature, we can see the objects without any active light sources. Besides, since the attenuation of LWIR is much + +![](images/e08e4818cec5ed9fc70bdda4fca34cb689ec3c3eb1815e49b7ffa650f014df83.jpg) +Figure 1. Overview of the shape from thermal radiation. Our method jointly estimates the depth, temperature, and emissivity images from multi-spectral LWIR images. A key observation is that thermal radiation from the target object is attenuated through the air and is wavelength dependent. + +larger than that of visible light and the amount of attenuation decays exponentially with respect to the depth, it is possible to recover the depth. + +Because the observed intensity depends on both the object's temperature and the attenuation, we have to separate these factors. Fortunately, attenuation through the air is wavelength dependent. Thus, we use multi-spectral observation in the LWIR range to jointly estimate the depth and temperature of the target object as shown in Fig. 1. + +This paper focuses on the possibility of depth sensing by only using passive thermal radiation. The contributions of this study are twofold. + +- We propose a novel cue for "shape from X" techniques. The shape from thermal radiation uses the attenuation of thermal radiation by the air. This is new to computer vision and computational imaging areas and broadens the field of research. +- To the best of our knowledge, the proposed method is the first attempt to realize passive, texture-less, far range, and can be used for dark scenes. This property proves that air absorption cues in LWIR are useful for depth sensing. + +# 2. Related Work + +Three-dimensional imaging Three-dimensional (3D) imaging has been studied over the decades and remains an active research topic in the computer vision area. Here, we briefly review the existing shape from X approaches. + +Triangulation-based approaches use the disparity between two viewing/lighting positions. They include stereo cameras [6, 45, 52, 54, 65], multi-view stereo [17, 23, 59], structure from motion [57], and structured light [11, 19, 37, 49, 67]. Stereo reconstruction using thermal cameras is also proposed [38, 56]. The accuracy of triangulation depends on the baseline; hence, it is not suitable for far-range imaging. + +Time-of-flight [21] is also a major 3D imaging technique and known as the principle of Lidar and the time-of-flight camera. They use a pulse or periodically modulated light and measure the round-trip time of light. It is effective for texture-less targets; however, either strong active illumination or a point scanning mechanism is required. + +Monocular depth estimation methods that use deep learning [14, 35, 66] estimate the scene depth from a single RGB image. This approach is up-to-scale and easy to deceive using, for example, a printed photo placed in front of the camera. Recently, to mitigate this problem, physics-based assistance for monocular depth estimation is proposed [7, 10, 20, 42, 53, 62]. Another extension of learning-based depth estimation is to use thermal imaging to apply dark and night environments [29, 33], which are pure learning-based. + +Depth from focus/defocus [24, 44, 63] is another well-known approach of monocular depth estimation, which recovers the depth from the amount of blur. These methods require textures on the target to measure the focus and are not applied for dark scenes. + +Photometric information is a rich cue for 3D imaging. Several methods, for example, shape-from-shading [64], photometric stereo [1, 50, 61], shape from polarization [5, 40, 46], shape from water absorption [2, 3, 30], light falloff stereo [32], and attenuation by fog or haze [31, 43] have been proposed. Although these methods can recover a high-quality shape, an active or pre-calibrated light source is required. + +Table 1 shows a comparison of major depth sensing approaches. Our method first uses multi-spectral LWIR observations to estimate scene depths based on air absorption of thermal radiation. Our approach is fundamentally passive, texture independent, and very far range depth sensing. One of the advantages of the approach is that it is fully passive and applicable to a dark scene. + +Computational thermal imaging The unique property of thermal radiation is very useful for computer vision and computational imaging problems. For example, the polarization cue of thermal radiation is used to resolve the ambi + +
MethodDark sceneFar rangeTexture independence
Time-of-flightLight sourceNoYes
LidarLight sourceYesYes
Structured lightLight sourceBaselineYes
Multi-cameraNoBaselineNo
Focus/DefocusNoNoNo
OursYesYesYes
+ +Table 1. Comparison of depth sensing approaches. Fundamental features are compared. Our method is adaptable to a dark scene, capable of sensing a far-range target, and texture independent. + +guity of shape from polarization [39]. The transient feature of the thermal heating and cooling cycle is also used for material classification [51]. LWIR observation is useful for computational imaging problems, such as non-line-of-sight imaging [28, 34] and lensless imaging [47]. Our method falls into this computational thermal imaging category as a new 3D imaging. + +The properties of thermal radiation have also been used for 3D sensing problems. Tanaka et al. [55] illuminated an object from various positions and recovered the surface normal of various materials using the shape-from-shading approach. Erdozain et al. [15] developed an LWIR projector and applied structured light algorithms. The shape of transparent and metallic objects can be measured using triangulation by scanning the heating point [4, 8, 16] because the objects are opaque in the LWIR region. Although these approaches are effective in active illumination scenarios, our method is the first attempt at passive LWIR 3D imaging. + +Thermography The study of thermography has focused on the accurate measurement of temperature [12, 58]. Because thermal radiation through the air is attenuated according to its distance from the target object, the temperature of a distant object must be corrected by atmosphere transmittance databases [13, 18], the application of a simplified model [36], or displaying a reference target with known temperature or known size as a guide. We contrarily use the air absorption of LWIR for depth estimation. Although our goal is depth estimation, the temperature of the object can be also estimated at the same time. This can be an advantage over conventional thermography because the correct temperature is measured even when the target depth is unknown. + +Spectral information in the LWIR region is useful for some applications. While thermography requires the user to set the emissivity of the object or assumes uniform emissivity, two-color or ratio thermography recovers both emissivity and temperature using two bands [27] in LWIR. Spectral information in the LWIR region is also used for gas detection [48]. Our method uses multi-bands in LWIR for depth sensing because air absorption of LWIR depends on the wavelength. + +# 3. LWIR Light Transport + +We start from a brief review of thermal radiation theory and temperature measurement. After that, we build an imaging model using the attenuation by the air. + +Thermal radiation theory [26] Planck's law explains the spectral radiant exitance (emittance) $M_{e}$ of a black body at the absolute temperature $T$ as + +$$ +M _ {e} (\lambda ; T) = \frac {2 \pi h c ^ {2}}{\lambda^ {5}} \frac {1}{e ^ {h c / \lambda k T} - 1}, \tag {1} +$$ + +where $\lambda$ is the wavelength of light, $c$ is the speed of light, $h$ is the Planck constant $^1$ , and $k$ is the Boltzmann constant $^2$ . + +As most objects are not black bodies, their radiation $E$ is less than that of a black body: + +$$ +E (\lambda ; \epsilon , T) = \epsilon M _ {e} (\lambda ; T), \tag {2} +$$ + +where $\epsilon$ is the emissivity, which is object dependent. + +Thermography [58] A thermographic camera is designed to measure the intensity of thermal radiation. A typical sensor measures the intensity of LWIR (typically, 8-14 $\mu$ m) as + +$$ +E (\epsilon , T) = \int_ {\lambda_ {1}} ^ {\lambda_ {2}} E (\lambda ; \epsilon , T) d \lambda , \tag {3} +$$ + +where $E$ is the intensity of the radiated LWIR light. As almost all radiation energy is within this integration range, the temperature $T$ can be obtained using the Stefan-Boltzmann law, in theory. In practice, the correspondence between the intensity $E$ and temperature $T$ is calibrated using a black body in the factory. Thermal cameras assume that the emissivity is known: they either use a constant value or have a dialog that can be used to select the target's material to adjust the emissivity. + +# 3.1. Imaging model + +The air is an attenuating medium and some LWIR light is absorbed through the air as it travels from the target to the camera [58]. Using the Lambert-Beer law, the transmission of the medium is expressed as + +$$ +i _ {\text {o u t}} (\lambda) = \exp (- \sigma_ {\text {a i r}} (\lambda) d) i _ {\text {i n}} (\lambda), \tag {4} +$$ + +where $i_{\mathrm{in}}$ and $i_{\mathrm{out}}$ are the input and transmitted intensity of light, respectively, $\sigma_{\mathrm{air}}$ is the extinction coefficient of the medium, and $d$ is the thickness of the medium. Thermal cameras either cancel this attenuation by allowing the user to manually input the depth of interest or simply ignore it. We contrarily take this into account to estimate the depth of the target. + +Based on Eqs. (1), (2), and (4), the observed intensity $I$ at wavelength $\lambda$ is expressed as + +$$ +I (\lambda) = R _ {v} (\lambda) \exp (- \sigma_ {\text {a i r}} (\lambda) d) \epsilon M _ {e} (\lambda ; T), \tag {5} +$$ + +where $R_{v}(\lambda)$ is the sensitivity that associates the energy density with the observed intensity. The sensitivity $R_{v}(\lambda)$ depends on the imaging system (e.g., image sensor, lens, and spectral filter) and is known by calibration beforehand. We aim to recover the depth $d$ with additional unknowns, emissivity $\epsilon$ and temperature $T$ , from the observation $I(\lambda)$ . + +# 4. Depth from Multi-spectral LWIR Measurements + +Equation (5) has three unknown variables: $T$ , $\epsilon$ , and $d$ . These variables cannot be obtained using only a single observation. This means that we cannot identify whether the target object is far away or the radiation from the target is low. + +We address this problem using multi-spectral LWIR observations to estimate the variables, as shown in Fig. 1. A key idea is to use the wavelength dependence of the extinction coefficient of the air. Because spectral radiance follows Planck's law and the attenuation by the air is wavelength dependent, we can separate the effect of the depth and the amount of radiation from the target. + +# 4.1. Assumptions + +Before explaining our proposed method, we clarify the assumptions of the scene. These assumptions are reasonable as they are also assumed in thermography and the coverage of the material is very wide. + +- As the major attenuating medium is water and carbon dioxide [36], the attenuating spectrum of the air $\sigma_{\mathrm{air}}(\lambda)$ is known. It can be measured in advance, as well as being obtained from databases of extinction coefficients of the air [13, 18]. +- The target object is a gray body, that is, the emissivity of the target is not wavelength-dependent in LWIR. Only a few materials, such as metal, do not satisfy this assumption. +- The target object does not reflect LWIR light from any other heat source. + +# 4.2. Proposed method + +Suppose that we obtain two measurements using different wavelengths: $I(\lambda_{i})$ and $I(\lambda_{j})$ . By dividing one measurement by another, we cancel out the emissivity $\epsilon$ : + +$$ +\begin{array}{l} \hat {I} _ {i, j} = \frac {I (\lambda_ {i})}{I (\lambda_ {j})} \\ = \frac {R _ {v} (\lambda_ {i}) \exp (- \sigma_ {\mathrm {a i r}} (\lambda_ {i}) d) M _ {e} (\lambda_ {i} ; T)}{R _ {v} (\lambda_ {j}) \exp (- \sigma_ {\mathrm {a i r}} (\lambda_ {j}) d) M _ {e} (\lambda_ {j} ; T)}, \tag {6} \\ \end{array} +$$ + +![](images/98d544f9e9d8cb5c641d09d606230469c3d39b732b71e9bd8ee56bd22bbed5ec.jpg) +Figure 2. A plot of the solution space. The two lines represent the different combinations of filters. The intersection is the estimate of the temperature and depth. + +where $\hat{I}_{i,j}$ is the divided ratio image. By transforming the expression, we can represent the depth $d$ as + +$$ +d _ {i, j} (T) = \frac {1}{\sigma_ {\mathrm {a i r}} (\lambda_ {j}) - \sigma_ {\mathrm {a i r}} (\lambda_ {i})} \ln \left(\frac {R _ {v} (\lambda_ {j}) M _ {e} (\lambda_ {j} ; T)}{R _ {v} (\lambda_ {i}) M _ {e} (\lambda_ {i} ; T)} \hat {I} _ {i, j}\right). \tag {7} +$$ + +This equation describes a curved line as the solution space of $T$ and $d$ as shown in Fig. 2, because $\sigma_{\mathrm{air}}$ and $R_v$ are known and $M_e$ is calculable using Eq. (1). As we have multiple wavelength observations with sufficiently different amounts of air absorption, for example, $\lambda_i$ , $\lambda_j$ , and $\lambda_k$ , Eq. (7) also represents another set of wavelengths. For example, we have two solution spaces of depth $d$ and temperature $T$ that use three wavelength combinations, and the crossing point of these curves is a unique solution. We can find the temperature $T$ and depth $d$ that satisfies the following equation: + +$$ +d _ {i, j} (T) = d _ {i, k} (T). \tag {8} +$$ + +Optionally, we can estimate the emissivity $\epsilon$ by substituting the estimated depth $d$ and temperature $T$ into Eq. (5). + +Effect of broad bandpass filters In the above discussion, we implicitly assume that the measurement is implemented using an ideal filter, whose response function is a delta function. If a bandpass filter of broader bandwidth is used, we have to integrate the imaging model with respect to the wavelength; therefore, Eq. (5) becomes + +$$ +I _ {s} (\lambda_ {i}) = \int_ {0} ^ {\infty} f _ {i} (\lambda) R _ {v} (\lambda) \exp (- \sigma_ {\text {a i r}} (\lambda) d) \epsilon M _ {e} (\lambda ; T) d \lambda , \tag {9} +$$ + +where $f_{i}$ is the spectral response of the bandpass filter. + +Although this model is no longer the Lambert-Beer model, the observation is still monotonically decreasing with respect to the depth, and the magnitude of attenuation varies depending on the filter. Therefore, it is possible to estimate the depth numerically. In our environment, we found that the observation using a filter of a sufficiently narrow + +![](images/9df2a5f6a37a8cc5be2b50d757de2dd9bc07a94dd65b1e1229b20618ae2abda2.jpg) +(a) w/o filter + +![](images/b8d14353b8fc63d2c57b890766e27b2c97c7933aa3e3dc08b65508e7e66d684d.jpg) +(b) w/ filter + +![](images/2b1b9470ce02f2c86052b9dcb8459420b86f34f49e2380817d9cff10c1e83834.jpg) +(c) Reference image + +![](images/2d4115359a455e5127a17c001d5de6c7246c3fa0e2dc1a6d8d1a08f5bbe2f2b7.jpg) +(d) Difference +Figure 3. Example of the unique noise in LWIR images. (a) Without filter: a clear image can be obtained. (b) With filter: as the radiation from the camera is reflected by the optics, the image becomes unclear (narcissus effect). (c) Reference image of the shutter plane in front of the optics. (d) Subtraction of (c) from (b): image remains noisy because of $1/f$ noise. (e) Result using the external shutter: unwanted effects are canceled and a clear image is obtained. + +![](images/89cde748cb568c6cdad1f0afd445accbdd6fbd175afa6f4064e56b8993f67394.jpg) +(e) Proposed + +bandwidth can be approximated using Eq. (5); hence, we do not use the extended imaging model. + +Optimization As the method above is naive and sensitive to noise, the estimated values can be physically incorrect values, such as a negative depth. Therefore, we adopt an optimization technique to regulate scene parameters. We formulate the optimization problem as + +$$ +\hat {d}, \hat {\epsilon}, \hat {T} = \underset {d, \epsilon , T} {\operatorname {a r g m i n}} \sum_ {i} ^ {N} \| I (\lambda_ {i}) - I ^ {\prime} (\lambda_ {i}: d, \epsilon , T) \| _ {2} ^ {2} \tag {10} +$$ + +$$ +\begin{array}{l} \text {s . t .} 0 \leq \epsilon \leq 1, d \geq 0, T \geq 0, \end{array} +$$ + +where $N$ is the number of observations and $I'$ is a rendered image using Eq. (5). We initialize all parameters using the naive result obtained using Eq. (8) and estimated using constrained gradient descent. + +# 5. Unique Noise Characteristics of the LWIR Camera + +As an LWIR camera is very different from an RGB camera, several issues exist that do not appear in traditional imaging. In this section, we introduce two unique effects in LWIR imaging and explain how to deal with them. + +# 5.1. Narcissus effect + +In LWIR observation, radiation from the camera body is reflected by the surface of the optics, including lens and + +filters. This is known as the narcissus effect [58]. Figure 3(b) shows an example of the narcissus effect. This effect is generally canceled using the non-uniformity correction (NUC) [58] function in the camera. NUC is calibrated to cancel the camera's radiation in the factory. Because it is calibrated for the built-in optics, it does not work well if another optic is added to the system. Therefore, we have to perform this correction for each filter explicitly. + +To cancel the narcissus effect, we require an image with a black body plane with the known temperature immediately in front of the optics. By subtracting two images (i.e. scene and reference) captured through a filter, we can obtain only the filter transmitted component. We can obtain pure transmitted component $I(\lambda_{i})$ by subtracting the scene and reference images: + +$$ +I \left(\lambda_ {i}\right) = I _ {s} \left(\lambda_ {i}\right) - I _ {r} \left(\lambda_ {i}\right), \tag {11} +$$ + +where $I_{s}$ and $I_{r}$ are the observed images with the narcissus effect of the scene and reference, respectively. Fig. 3(d) shows an example of canceling the narcissus effect by simply subtracting Fig. 3(c) from Fig. 3(b). + +# 5.2. $1 / f$ noise + +Another unique noise characteristic of an LWIR camera is $1/f$ noise. In particular, this noise dominates the total noise of the microbolometer sensor [22, 41]. $1/f$ noise is a low-frequency fluctuation; hence, it strongly appears when images taken at long intervals are processed. For example, averaging multiple images does not improve the signal-to-noise ratio (SNR) but degrades the image, which is completely different from RGB imaging. Considering the processing of NUC, this noise is very noticeable, as shown in Fig. 3(d), because there is a very long interval between the two images. + +# 5.3. Noise mitigation using an external shutter + +To mitigate both the narcissus effect and $1/f$ noise, we propose to use an external shutter in front of the optics. The shutter is operated open and closed, alternately, and we obtain a total of $M$ pairs of a scene and reference images. Then, we suppress the narcissus effect by taking a subtraction of each pair. Note that the $1/f$ noise is ignorable each of them is captured in a short time. Finally, we suppress the $1/f$ noise by taking the average of them. This corresponds to locking-in high frequency signals. Fig. 3(e) shows the result of noise reduction using $M = 10$ pairs. + +# 6. Depth Resolution Analysis + +Before conducting the experiment, we confirmed the feasibility of our method in terms of depth resolution. The depth resolution depends on the sensitivity of the sensor, in addition to the temperature and depth of the object. To analyze the depth resolution, we first explain a standard sensor + +noise measure for LWIR cameras known as the noise equivalent temperature difference (NETD). NETD represents the minimum temperature that changes the intensity at the same level of system noise and is typically provided as a camera specification. + +Definition of NETD [58] We consider the area of the detector $A_{d}$ , the f-number of the imaging lens $F$ , and the spectral sensitivity of the sensor $R_{v}(\lambda)$ . The power of LWIR that irradiates to the detector is represented as + +$$ +P (\lambda) = \frac {A _ {d}}{4 F ^ {2}} M _ {e} (\lambda ; T). \tag {12} +$$ + +Assuming that the LWIR camera captures the intensity from $\lambda_{1}$ to $\lambda_{2}$ , the sensor output voltage is represented as + +$$ +V _ {s} = \int_ {\lambda_ {1}} ^ {\lambda_ {2}} R _ {v} (\lambda) P (\lambda) d \lambda . \tag {13} +$$ + +The change in $V_{s}$ when the temperature changes by $\Delta T$ is represented as + +$$ +\Delta V _ {s} = \frac {\partial V _ {s}}{\partial T} \Delta T. \tag {14} +$$ + +As the microbolometer sensor has almost flat spectral sensitivity, Eq. (14) is typically simplified as + +$$ +\Delta V _ {s} = \frac {A _ {d} R _ {v}}{4 F ^ {2}} \frac {\partial \int_ {\lambda_ {1}} ^ {\lambda_ {2}} M _ {e} (\lambda ; T) d \lambda}{\partial T} \Delta T. \tag {15} +$$ + +The change in the output voltage when the temperature changes by $1\mathrm{K}$ is expressed as + +$$ +V _ {t} = \frac {\Delta V _ {s}}{\Delta T}. \tag {16} +$$ + +The temperature change when the voltages of the output and noise are balanced (i.e., NETD) is defined as + +$$ +\begin{array}{l} \mathrm {N E T D} \triangleq \frac {V _ {n}}{V _ {t}} (17) \\ = \frac {4 F ^ {2} V _ {n}}{A _ {d} R _ {v}} \frac {1}{\frac {\partial \int_ {\lambda_ {1}} ^ {\lambda_ {2}} M _ {e} (\lambda ; T) d \lambda}{\partial T}}, (18) \\ \end{array} +$$ + +where $V_{n}$ is the root mean square noise voltage. The first factor represents the sensor characteristics and the second factor is numerically obtainable. + +Definition of noise equivalent depth difference (NEDD) We extend the discussion to the depth resolution of our method. Considering the air absorption into the model, the power of LWIR that reaches the camera is rewritten as + +$$ +P (\lambda) = \frac {A _ {d}}{4 F ^ {2}} e ^ {- \sigma_ {\mathrm {a i r}} d} M _ {e} (\lambda ; T). \tag {19} +$$ + +Equation (13) also holds for this model. We define the NEDD analogously to NETD. The change in $V_{s}$ when the depth of the target changes by $\Delta d$ is represented as + +$$ +\Delta V _ {s} = \frac {\partial V _ {s}}{\partial d} \Delta d. \tag {20} +$$ + +NEDD is defined as + +$$ +\mathrm {N E D D} \triangleq \frac {V _ {n}}{V _ {d}}, \tag {21} +$$ + +where $V_{d}$ is the change of the output voltage caused by $1\mathrm{m}$ depth change defined as + +$$ +V _ {d} = \frac {\Delta V _ {s}}{\Delta d}. \tag {22} +$$ + +Based on the flat sensitivity of the microbolometer sensor, Eq. (21) is expanded as + +$$ +\mathrm {N E D D} = \frac {4 F ^ {2} V _ {n}}{A _ {d} R _ {v}} \frac {1}{\underbrace {\partial \int_ {\lambda_ {1}} ^ {\lambda_ {2}} e ^ {- \sigma_ {\mathrm {a i r}} d} M _ {e} (\lambda ; T) d \lambda} _ {\partial d}}. \tag {23} +$$ + +The second factor of this equation can be also numerically obtained. Substituting Eq. (18) into Eq. (23), the NEDD can be expressed using the NETD measure as + +$$ +\mathrm {N E D D} = \frac {\frac {\partial \int_ {\lambda_ {1}} ^ {\lambda_ {2}} M _ {e} (\lambda ; T) d \lambda}{\partial T}}{\frac {\partial \int_ {\lambda_ {1}} ^ {\lambda_ {2}} e ^ {- \sigma_ {\text {a i r}} d} M _ {e} (\lambda ; T) d \lambda}{\partial d}} \mathrm {N E T D}. \tag {24} +$$ + +NEDD using bandpass filters The SNR becomes worse when bandpass filters are placed in front of the camera as they block a large amount of energy. The voltage of the sensor output with a bandpass filter is represented as + +$$ +V _ {f} = \int_ {\lambda_ {1}} ^ {\lambda_ {2}} f (\lambda) R _ {v} (\lambda) P (\lambda) d \lambda , \tag {25} +$$ + +where $f(\lambda)$ is the spectral transmittance of the bandpass filter. Following the NEDD definition, the NEDD using the filter is expressed as + +$$ +\begin{array}{l} \mathrm {N E D D} _ {f} = \frac {V _ {n}}{V _ {d} ^ {\prime}} (26) \\ = \frac {4 F ^ {2} V _ {n}}{A _ {d} R _ {v}} \frac {1}{\frac {\partial \int_ {\lambda_ {1}} ^ {\lambda_ {2}} e ^ {- \sigma_ {\mathrm {a i r}} d} M _ {e} (\lambda ; T) f (\lambda) d \lambda}{\partial d}}, (27) \\ \end{array} +$$ + +where + +$$ +V _ {d} ^ {\prime} = \frac {\Delta V _ {f}}{\Delta d}. \tag {28} +$$ + +Similar to the above specific example, the NEDD of any bandpass filter observations can be numerically calculated. + +![](images/87e91299ca5ea5a5a72abd8a365695a92eb8976aae832aa74ac58f985524ffbc.jpg) +Figure 4. A theoretical plot of the observable depth difference of our measuring system. Each observation has an NEDD of less than approximately $1.5\mathrm{m}$ , which determines the total depth resolution of the method. + +Specific example A typical LWIR sensor records the intensity from $8\mu \mathrm{m}$ to $14\mu \mathrm{m}$ . The value of the numerator of the first factor in Eq. (24) at $300\mathrm{K}$ in this bandwidth is + +$$ +\frac {\partial \int_ {8 \mu \mathrm {m}} ^ {1 4 \mu \mathrm {m}} M _ {e} (\lambda ; 3 0 0 \mathrm {K}) d \lambda}{\partial T} \approx 2. 1 2 3. \tag {29} +$$ + +Assuming the target depth is at $20\mathrm{m}$ and $\sigma_{\mathrm{air}} = 0.008\mathrm{m}^{-1}$ the denominator is, + +$$ +\frac {\partial \int_ {8 \mu \mathrm {m}} ^ {1 4 \mu \mathrm {m}} e ^ {- \sigma_ {\mathrm {a i r}} d} M _ {e} (\lambda ; 3 0 0 \mathrm {K}) d \lambda}{\partial d} \approx 0. 9 3 9. \tag {30} +$$ + +If the NETD of the camera is $40\mathrm{mK}$ $(= 0.04\mathrm{K})$ , the NEDD of a bare LWIR sensor is calculated by Eq. (24) as, + +$$ +\mathrm {N E D D} = \frac {2 . 1 2 3}{0 . 9 3 9} \mathrm {N E T D} = 0. 0 9 0 \mathrm {m}. \tag {31} +$$ + +For a bandpass filter of the center wavelength (CWL) $10.400\mu \mathrm{m}$ and full width at half maximum (FWHM) $737\mathrm{nm}$ , + +$$ +\frac {\partial \int_ {\lambda_ {1}} ^ {\lambda_ {2}} e ^ {- \sigma_ {\mathrm {a i r}} d} M _ {e} (\lambda ; 3 0 0 \mathrm {K}) f (\lambda) d \lambda}{\partial d} \approx 0. 0 8 8. \tag {32} +$$ + +The NEDD with the bandpass filter is calculated as $\mathrm{NEDD}_{10\mu \mathrm{m}} = \frac{2.123}{0.088} 0.04 = 0.965\mathrm{~m}$ . This demonstrates that it is feasible to use the NEDD for large-scale scenes. Figure 4 shows the plot of NEDD of our system with the target temperature at $300\mathrm{K}$ . The feasibility of our method is confirmed by this analysis. + +# 7. Real-world Experiments + +We build a multi-spectral LWIR imaging system and evaluate the effectiveness of our proposed method in real-world experiments. + +![](images/0956cd2e49694ff4c6406947ad9393dc0997630074ede277fd1058bda627cfd7.jpg) +LWIR camera & Filter wheel +Peltier device Black body &Cooling fan spray +(a) Imaging system + +![](images/3a8b64041ce97a5aa6c10f1cf5bb91893584b05c802f13c1b9e4c40daff86d1d.jpg) +(b) Spectral response +Figure 6. Experiment for measuring the extinction coefficients. (a) Experimental setup. (b) Measured values attenuated by the air. Dashed lines represent the fit curve of the Lambert-Beer law for each filter. + +# 7.1. Imaging system and calibration + +Multi-spectral LWIR imaging system Our multispectral LWIR imaging system is shown in Fig. 5(a). The system consists of a thermal imaging camera (FLIR Boson 640, NETD = 40 mK) and a filter wheel with three narrow bandpass filters. We select three filters with the best NEDD values in our laboratory (8 μm (CWL 8.248 μm, FWHM 452 nm), 9 μm (CWL 9.127 μm, FWHM 545 nm), and 10 μm (CWL 10.400 μm, FWHM 737 nm)). The spectral response ratio of each filter is shown in Fig. 5(b). These filters are automatically changed using the filter wheel. An external shutter in front of the camera removes the narcissus effect and reduces $1/f$ noise. The shutter is sprayed with black body paint. To obtain a strong signal, the shutter is cooled using a Peltier device. + +Calibration In the calibration step, we obtain the sensitivity $R_{v}$ and extinction coefficients $\sigma_{\mathrm{air}}$ of all wavelengths. We use a black body furnace, whose surface temperature is controllable. Fig. 6(a) shows the experimental setup. By placing the black body at $0\mathrm{m}$ , $R_{v}$ can be obtained directly. By placing the black body at several known depths, and fitting the Lambert-Beer law to the measured value, we can obtain the extinction coefficients at each wavelength. We set the temperature of the black body at $80^{\circ}\mathrm{C}$ . The fitting result is illustrated in Fig. 6(b) and the calculated extinction coefficients are shown in Table 2. The fitted result shows that the extinction coefficients are different at each wavelength. + +![](images/1a357c52a89bff0dfc8761fb73e1adf825ad9dc9fce880b38e1169afd6ad2845.jpg) + +![](images/6049e97671a7e8f677a9c518f21517c6de9d9c766a1a8da8d96960ce37bb4e82.jpg) +(a) Experimental set up +(b) Attenuation + +Table 2. Fitting results for the extinction coefficients. + +
wavelength8 μm9 μm10 μm
σair(λ)0.00787m-10.00436m-10.00346m-1
+ +![](images/bfef1c175dd4de698f4c40128cd41a44077548c6c80ff717e313377b7d7738b8.jpg) +Figure 5. Imaging system and profiles of each filter. (a) The multispectral imaging system consists of an LWIR camera, filter wheel with three bandpass filters, and external shutter. The external shutter is painted with black body spray and kept at low temperature using a Peltier device. (b) The response ratio of the bare LWIR sensor with the lens and transmittance of each filter. +Depth to the black body from the camera [m] +Figure 7. Results for the black body. Temperature is set to $50^{\circ}\mathrm{C}$ (left column) and $90^{\circ}\mathrm{C}$ (right column). Estimated depth, temperature, and emissivity are shown. Root mean squared error (RMSE) is calculated for each result. In the case of $90^{\circ}\mathrm{C}$ , in particular, we demonstrate the clear effectiveness of our method. + +![](images/9e7a964624f9d7cbbf16e299935006cef48c21e9e5c0c468f263fde5ba8d0adf.jpg) + +ly from the camera [m] + +# 7.2. Results + +Black body target We first evaluate the method using a black body target, whose emissivity is almost 1. we set the temperature of the black body to $50^{\circ}\mathrm{C}$ and $90^{\circ}\mathrm{C}$ , and placed it at several distances from the camera. Figure 7 + +![](images/65f50ce399ee7248edd8de2110a1a64fdef16fe09472207009330e4b366f2f45.jpg) +Figure 8. Result for some practical targets. Top: the photo of the target object with its ground truth of the depth. Middle: the thermal image (w/o filter). Bottom: the estimated depth. Red rectangles are the zoom up of the target region. + +shows the results for the estimated depth, temperature, and emissivity. Regardless of the target temperature, the target depth is estimated well with respect to the target depth. The temperature and emissivity are estimated at the correct values. The result for $50^{\circ}\mathrm{C}$ is slightly noisier than that for $90^{\circ}\mathrm{C}$ because the SNR depends on the target temperature. This demonstrated that our method works better as the temperature is higher. + +Our proposed method also has an advantage in the scenario of long range temperature measurement. When the target is measured at a long distance with conventional thermography, the result becomes lower than its actual temperature due to the attenuation. Compared with conventional thermography, the temperature is flat with respect to the depth as shown in the middle row of Fig. 7. + +Practical scenes Figure 8 shows the applicability of our method to real-world objects. The target objects are a pot, oven, clothes iron, electric griddle, and motorcycle. The temperatures of the objects are approximately between $80^{\circ}\mathrm{C}$ and $120^{\circ}\mathrm{C}$ . In the two-pot scene, the depths of the pots are estimated as $3\mathrm{m}$ and $8\mathrm{m}$ , which shows that our method distinguishes the depth difference. In the motorcycle scene, although it is very difficult to measure the depth using ordinary passive approaches because the scene is very dark, our method estimates the depth of the motorcycle as $15\mathrm{m}$ . All objects are estimated well considering approximately $0.7\mathrm{m}$ NEDD of our system as shown in the analysis. + +# 8. Conclusion + +We propose a novel and unique approach for fully passive, texture-less, and far-range depth sensing using an LWIR camera. We demonstrate that the attenuation of thermal radiation is a cue for the scene depth. We build a multispectral LWIR measurement system and demonstrated the effectiveness of our proposed method in real-world experiments. + +As this is the first attempt at passive LWIR depth sensing, there are many open challenges to applying it at an industrial level. A major problem to be solved is the low SNR of the LWIR measurement, which makes it difficult to measure low-temperature objects. On the other hand, considering the recent advancement of the LWIR sensor, we believe the measurable temperature will reach air temperature in the future. + +Another interesting future direction is the combination of our method with learning-based approaches. 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Previous adversarial attacks on 3D point cloud recognition have often been criticized for their noticeable point outliers, since they just involve an "implicit constrain" like global distance loss in the time-consuming optimization to limit the generated noise. While point cloud is a highly structured data format, it is hard to constrain its perturbation with a simple loss or metric properly. In this paper, we propose a novel Point-Cloud Sensitivity Map to boost both the efficiency and imperceptibility of point perturbations. This map reveals the vulnerability of point cloud recognition models when encountering shape-invariant adversarial noises. These noises are designed along the shape surface with an "explicit constrain" instead of extra distance loss. Specifically, we first apply a reversible coordinate transformation on each point of the point cloud input, to reduce one degree of point freedom and limit its movement on the tangent plane. Then we calculate the best attacking direction with the gradients of the transformed point cloud obtained on the white-box model. Finally we assign each point with a non-negative score to construct the sensitivity map, which benefits both white-box adversarial invisibility and black-box query-efficiency extended in our work. Extensive evaluations prove that our method can achieve the superior performance on various point cloud recognition models, with its satisfying adversarial imperceptibility and strong resistance to different point cloud defense settings. Our code is available at: https://github.com/shikiw/SI-Adv. + +# 1. Introduction + +Deep Neural Networks (DNNs) have contributed a lot to various computer vision tasks with their highly praised performances. However, recent works prove that DNNs are + +![](images/6e89129c9e436046dae6b4013c071f0bb049fcb854bb6c9aba31780ca9244dd5.jpg) +(a) Clean PC + +![](images/a8512645f8b789ae6d228246f6c21dc86bed970be4631f190ea5b1a0fdc6777f.jpg) +(b) Previous Adv + +![](images/d440c2ad69e27a63d0df63572979a8622fe6a12a9f0f97863648496d2cfba05c.jpg) +(c) Our Adv +Figure 1. The point-cloud shape surface of clean (left), previous adversarial perturbations (middle) and our perturbation (right). + +vulnerable to adversarial examples [11, 25], which are generated by adding imperceptible perturbations on clean inputs to mislead the prediction of deep learning models. Numerous algorithms have been proposed to implement different kinds of adversarial attacks [4, 8, 11, 13, 25]. In addition to 2D images, the research scope of adversarial attacks has been gradually extended to 3D point clouds. As one of the most popular data representations captured by 3D sensors like LiDAR, point clouds are widely used in a variety of 3D computer vision applications, such as autopilot [42] and autonomous driving [20]. Similar with image recognition models, recent works [3, 22, 24, 28, 30, 38, 40] show that point-cloud models are also susceptible to adversarial perturbations. But unfortunately, existing 3D adversarial attacks either generate the noticeable point perturbation or focus on the white-box case, leading to the poor performance on well-defended models or unseen black-box models. + +The motivation for delving into black-box attacks on point cloud recognition is quite clear. On the one hand, both industry and academia have attached increasing importance on evaluating the robustness of point cloud models, especially for some security-critical applications like autonomous driving. But usually, they can not release the details of the model or algorithms to robustness testers due to the protection agreement of trade secrets. Therefore, testers can only conduct black-box attacks to reach the demand of robustness evaluation, which requires the more efficient + +![](images/bada21c3e0d0c3e8c77ab1ea827cd9cd5e4968e18db5d3e8bbae2b9a8dd47d91.jpg) + +![](images/7054cfccadd7d0e3d7dd3f6d9e95e954d5c52cd5a3debb9031cdc63dbdea8801.jpg) +(a) PointNet++ +Figure 2. Visualization results of the point-cloud sensitivity maps obtained from different 3D recognition models. + +![](images/44c8fa4f62219eca8710d07c3c7e854fa5465280b85f3d5c6bb8ab445d202695.jpg) +(b) DGCNN + +![](images/0879d4c77262afb1e884ced0dd86e897a149c5bfcb4c7e6074c8aa88659ac20c.jpg) +(c) CurveNet + +black-box attack method. On the other hand, black-box attacks are obviously more practical but challenging compared with white-box attacks, since the attacker can hardly access to the target model in many realistic scenarios. Considering these points, in this paper we adopt a novel shape-invariant perspective to rethink the adversarial imperceptibility and black-box efficiency of adversarial point clouds, based on the following two crucial observations. + +First, we mathematically analyze the vulnerability of a white-box point cloud recognition model by defining the novel point-cloud sensitivity map. This map is constructed by a non-negative score set, where each score measures the variance of the recognition confidence when the corresponding point encounters the imperceptible perturbation. To realize such imperceptibility, we intuitively design the point perturbation along the certified optimal direction on the the tangent plane, assuming this slight point shift does not change the shape surface of the point cloud. Each point cloud input can obtain its unique sensitivity map on the white-box model, where all points can be ranked in a descending order according to their scores. Through iteratively perturbing the top ranked $30\%$ points, we find that the white-box recognition accuracy can be degraded over $40\%$ on different models, which demonstrates the existing of shape-invariant white-box attacks. + +Second, we discover that these top ranked points obtained from the same point cloud input are similar across different recognition models. As visualized in Figure 2, the positions of top ranked points almost overlap with each other to a large extent when scored by different 3D classifiers. To support this finding more concretely, we look into the 1024-point data samples on the commonly used point-cloud dataset ModelNet40 [31] and compare the top ranked points for different recognition models, i.e., PointNet [5], PointNet++ [21], DGCNN [29] and CurveNet [34]. It shows that the top ranked $30\%$ points of each point cloud have $75.8\%$ overlapped between every two models on average and $40.3\%$ overlapped among every three of them, which are much more than $30\%$ and $9\%$ obtained by random sampling respectively. Inspired by this internal commonality, we can estimate the top ranked points for the un + +seen black-box model with a white-box surrogate model to improve the black-box attack ability. + +Motivated by the above two observations, our paper further proposes the first query-based black-box attack algorithm on point cloud recognition. Through inheriting the ranked sensitivity map prior from white-box surrogate model $\mathcal{H}_w$ to black-box target model $\mathcal{H}_b$ , we limit the point movement on the shape surface as shown in Figure 1. To boost the query efficiency, we combine each point with its certified best direction as a point-wise basis. Only one basis is perturbed during each query step according to the sensitivity ranking, in the light of SimBA [14] and LeBA [36]. Experiments on ModelNet40 [31] and ShapeNetPart [37] show that our method achieve the superior performance on various 3D recognition models, which highlights the meaning of the proposed point-cloud sensitivity map. + +To summarize, our contributions are three-fold as below. + +- We propose the point-cloud sensitivity map, for evaluating the variance of recognition confidence when each point encounters the shape-invariant perturbation. +- Guided by the sensitivity map, we propose the strong shape-invariant white-box attack and the first query-based black-box attack on point cloud recognition. +- Experiments show the efficiency of our attack on various recognition models with the high imperceptibility and the low query cost under black-box settings. + +# 2. Related Work + +# 2.1. Point Cloud Recognition + +A point cloud is a sparse and unordered point set sampled from object surfaces by 3D sensors. Thanks to the development of deep learning, various methods [5,12,21,29,34,35] have been proposed to process 3D point clouds. One of the pioneering works is PointNet [5], which directly applies multi-layer perceptron to learn point features and aggregates them with a max-pooling module in an effective way. And its variant, called PointNet++ [21], is a improved hierarchical neural network for better abstracting local features, including single-scale (SSG) and multi-scale (MSG) designs. By exploiting point structures with neighborhood graphs, DGCNN [29] is another typical work using convolutional networks. In this paper, we mainly evaluate our black-box attack on six representative recognition models. + +# 2.2. Existing 3D Adversarial Attacks and Defenses + +Current 3D adversarial attack methods can be roughly divided into three categories: point-shifting based [15, 28, 30, 32, 40], point-adding based [33] and point-dropping based [38]. Following previous works w.r.t. adversarial attacks on 2D images, a variety of point-shifting based methods either + +utilize the gradient descent or solve an optimization problem like C&W [4] to perturb point sets and deceive target classifiers. As for point-adding and point-dropping based approaches, they depend on changing the number of input points to realize attacks. For instance, Zheng et al. propose saliency map [39] to drop out critical points of the input and get model fooled successfully. Corresponding to attacks, defense methods based on point-cloud preprocessing [41], adversarial training [17, 23], gather-vector [7] or provable defense [18] have been seriously under-researched. + +Since there is still lack of the study on 3D query-based black-box adversarial attack, we delve into this topic based on the proposed sensitivity map in this paper. + +# 2.3. Query-based Black-box Adversarial Attacks + +Traditional query-based black-box attacks on 2D images can be divided into two categories: decision-based [2,9] and score-based [1,6,14,27,36]. Both of them mainly rely on the limited times of queries to the unseen black-box model to achieve attacks, without any inner model information or gradient guidance. The different things is that, score-based methods utilize the output confidence score, while decision-based methods need the output label from the query feedback. In our work, we extend the score-based black-box attack to 3D point-cloud recognition, which is a seriously under-researched field for adversarial attack. + +# 3. Preliminaries + +# 3.1. Point Cloud Sensitivity Maps + +For a point cloud $\mathcal{P}$ that consists of total $N$ points, we can define it as a set of vectors $\{\pmb{p}_i\}_{i=1}^N$ where $\pmb{p}_i \in \mathbb{R}^3$ denotes the 3D coordinates of each point. Also, there exists $k$ nearest neighbors $\mathcal{N}_{\pmb{p}_i}$ for each point $\pmb{p}_i = (p_{i1}, p_{i2}, p_{i3})$ , which can help us simulate its normal vector by calculating the $3 \times 3$ positive semi-definite matrix [16] formulated as + +$$ +\mathcal {C} _ {\boldsymbol {p} _ {i}} = \sum_ {\boldsymbol {q} \in \mathcal {N} _ {\boldsymbol {p} _ {i}}} (\boldsymbol {q} - \boldsymbol {p} _ {i}) \otimes (\boldsymbol {q} - \boldsymbol {p} _ {i}), \tag {1} +$$ + +where $\otimes$ denotes the outer product operation. Note that the normal vector $\pmb{n}_i = (n_{i1}, n_{i2}, n_{i3})$ of $\pmb{p}_i$ can be acquired by solving the eigen-decomposition on matrix $\mathcal{C}_{\pmb{p}_i}$ and choosing the last unit eigen-vector. + +Once both the shape surface point $\pmb{p}_i$ and its normal vector $\pmb{n}_i$ are determined in the original coordinate system, the corresponding plane that is tangent to the shape surface is also uniquely determined, so called tangent plane $\Omega_i$ . Since the normal vector $\pmb{n}_i$ is perpendicular to $\Omega_i$ , the coordinates of any position $\pmb{m} = (m_1, m_2, m_3)$ on the tangent plane can be easily represented with the following equation: + +$$ +\left(\boldsymbol {m} - \boldsymbol {p} _ {i}\right) \cdot \boldsymbol {n} _ {i} = \sum_ {j = 1} ^ {3} \left(m _ {j} - p _ {i j}\right) n _ {i j} = 0 \tag {2} +$$ + +where $\cdot$ denotes the inner product operation. As illustrated in Figure 3(a), we assume that this tangent plane $\Omega_{i}$ intersects with the coordinate axes (i.e., $x$ axis, $y$ axis and $z$ axis) of the original coordinate system at position $A$ , $B$ and $C$ . Combined with Eq.(2), we obtain these three positions as + +$$ +\boldsymbol {A} \left(\frac {\boldsymbol {p} _ {i} \cdot \boldsymbol {n} _ {i}}{n _ {i 1}}, 0, 0\right), \boldsymbol {B} \left(0, \frac {\boldsymbol {p} _ {i} \cdot \boldsymbol {n} _ {i}}{n _ {i 2}}, 0\right), \boldsymbol {C} \left(0, 0, \frac {\boldsymbol {p} _ {i} \cdot \boldsymbol {n} _ {i}}{n _ {i 3}}\right). (3) +$$ + +Obviously, $O$ -ABC forms a right angle triangular pyramid since the three axes $x$ , $y$ and $z$ are orthogonal with each other, where $O$ denotes the coordinate origin. As clarified in Figure 3(b), we suppose the projection of origin $O$ on the tangent plane $\Omega_i$ as $O'$ . Note that $OO' \perp \Omega_i$ and $BA \in \Omega_i$ , thus we can get $OO' \perp BA$ . Likewise, we can also get $OC \perp BA$ . Based on these two vertical relationships, we can obtain $BA \perp COO'$ where $COO'$ means the plane determined by $C$ , $O$ and $O'$ . Since $CO' \in COO'$ , we finally obtain $CO' \perp BA$ , which is the fundamental point for us to introduce the following coordinate transformation. + +To limit the movement of $p_i$ on the tangent plane $\Omega_i$ with only two variables, we reduce its one degree of freedom (DoF). Intuitively, we consider to leverage a transformed coordinate system to represent this shape surface point, based on the orthogonality among $OO'$ , $CO'$ and $BA$ . Specifically, we assume the direction denoted by $\overrightarrow{BA}$ as the transformed axis $x'$ , the direction denoted by $\overrightarrow{CO'}$ as the transformed axis $y'$ and the direction denoted by $\overrightarrow{O'O}$ as the transformed axis $z'$ . As shown in Figure 3(c), the origin of the newly constructed rectangular coordinate system becomes $O'$ , with the transformed coordinates of $p_i$ as $p_i' = (p_{i1}', p_{i2}', p_{i3}')$ . In this way, the surface point can be constrained on the tangent plane when we assign the coordinate value on axis $z'$ as zero. Therefore, the problem is simplified as formulating the transformation applied for converting the original coordinate system $O - xyz$ to the transformed coordinate system $O' - x'y'z'$ . + +Theorem 1. Assume $f_{i}:\mathbb{R}^{3}\mapsto \mathbb{R}^{3}$ is the transformation for converting the original coordinate system $O$ -xyz to the new coordinate system $O^{\prime} - x^{\prime}y^{\prime}z^{\prime}$ . Then $f_{i}$ is reversibly composited by rotation transformation $f_{ir}$ and translation transformation $f_{it}$ , and new $3\times 1$ coordinates $\pmb{p}_i^\prime$ can be converted with original $3\times 1$ coordinates $\pmb{p}_i$ as + +$$ +\boldsymbol {p} _ {i} ^ {\prime} = \boldsymbol {R} _ {i} \left(\boldsymbol {p} _ {i} + \boldsymbol {T} _ {i}\right), \quad \boldsymbol {p} _ {i} = \boldsymbol {R} _ {i} ^ {\top} \boldsymbol {p} _ {i} ^ {\prime} - \boldsymbol {T} _ {i}, \tag {4} +$$ + +where $\mathbf{R}_i$ and $\mathbf{T}_i$ is the rotation transformation matrix and the translation transformation matrix respectively, i.e., + +$$ +\pmb {R} _ {i} = \left( \begin{array}{c c c} \frac {n _ {i 2}}{\sqrt {1 - n _ {i 3} ^ {2}}} & \frac {- n _ {i 1}}{\sqrt {1 - n _ {i 3} ^ {2}}} & 0 \\ \frac {n _ {i 1} n _ {i 3}}{\sqrt {1 - n _ {i 3} ^ {2}}} & \frac {n _ {i 2} n _ {i 3}}{\sqrt {1 - n _ {i 3} ^ {2}}} & - \sqrt {1 - n _ {i 3} ^ {2}} \\ n _ {i 1} & n _ {i 2} & n _ {i 3} \end{array} \right), \qquad (5) +$$ + +![](images/0d1bdcafe0bd52776f7b2f0512f0153c0d66f338de41bd66ec256d5b9064e289.jpg) +(a) Build Tangent Plane + +![](images/17334f728f3d38c83fb44c5b5d3444538e65ae677b869f1331807e50e938bf4c.jpg) +(b) Define New Coordinate Basis + +![](images/b8d2718c16181d5ea6bbebfc3115d83e1a39aaf62b4458dbbe6df44aeb995aa2.jpg) +(c) Construct New Coordinate System +Figure 3. Schematic diagram of the newly constructed coordinate system for our reversible coordinate transformation. + +$$ +\boldsymbol {T} _ {i} = \left(\boldsymbol {p} _ {i} \cdot \boldsymbol {n} _ {i}\right) \boldsymbol {n} _ {i}, \tag {6} +$$ + +including a boundary case when $|n_{i3}| \to 1$ that is + +$$ +\lim _ {| n _ {i 3} | \rightarrow 1} \boldsymbol {R} _ {i} = \left(\begin{array}{c c c}1 / \sqrt {2}&- 1 / \sqrt {2}&0\\n _ {i 3} / \sqrt {2}&n _ {i 3} / \sqrt {2}&0\\0&0&n _ {i 3}\end{array}\right). \tag {7} +$$ + +Proof. The proof is given in supplementary mater + +The above transformation facilitates the convenience of the sensitivity map computation. Given a white-box point cloud recognition model $\mathcal{H}_w$ and the point cloud input $\mathcal{P}$ , we first apply the reversible transformation elaborated in Eq.(4) on original coordinates of each point, i.e., $\forall \pmb{p}_i\in \mathcal{P}$ + +$$ +\mathcal {P} ^ {\prime} = \left\{\boldsymbol {R} _ {i} \left(\boldsymbol {p} _ {i} + \boldsymbol {T} _ {i}\right) \right\} _ {i = 1} ^ {N}, \quad \mathcal {P} = \left\{\boldsymbol {R} _ {i} ^ {\top} \boldsymbol {p} _ {i} ^ {\prime} - \boldsymbol {T} _ {i} \right\} _ {i = 1} ^ {N}, \tag {8} +$$ + +then we implement the model inference for $\mathcal{P}$ and compute the max-margin logit loss proposed in C&W [4], i.e., + +$$ +\mathcal {L} (\mathcal {P}, t; \theta_ {w}) = \max \left(\left[ \mathcal {H} _ {w} (\mathcal {P}) \right] _ {t} - \max _ {j \neq t} \left[ \mathcal {H} _ {w} (\mathcal {P}) \right] _ {j}, 0\right), \tag {9} +$$ + +where $t$ is the ground-truth label of point cloud $\mathcal{P}$ and $\theta_w$ is the model parameter of white-box model $\mathcal{H}_w$ . And $[\mathcal{H}_w(\mathcal{P})]_j$ is the probability logit score on class $j$ . Since the transformation in Eq.(8) is differentiable, we can easily obtain the gradient map of $\mathcal{P}'$ by back propagation, + +$$ +\mathcal {G} = \left\{\boldsymbol {g} _ {i} \right\} _ {i = 1} ^ {N} = \nabla_ {\mathcal {P} ^ {\prime}} \mathcal {L} = \frac {\partial \mathcal {L} (\mathcal {P} , t ; \theta_ {w})}{\partial \mathcal {P} ^ {\prime}}, \tag {10} +$$ + +where $\pmb{g}_i = (g_{i1}, g_{i2}, g_{i3}) = \left(\frac{\partial\mathcal{L}}{\partial x'}, \frac{\partial\mathcal{L}}{\partial y'}, \frac{\partial\mathcal{L}}{\partial z'}\right)$ denotes the gradients of loss $\mathcal{L}$ to transformed point coordinates $\pmb{p}_i'$ . + +With the guidance of gradient map for the transformed point clouds, the shape-invariant point cloud sensitivity can be defined as: For each point $\pmb{p}_i \in \mathcal{P}$ , we define its sensitivity on white-box model $\mathcal{H}_w$ as the maximal variation rate of the logit loss $\mathcal{L}$ when perturbing $\pmb{p}_i$ along any direction on the tangent plane $\Omega_i$ . Through assigning the last element $p_{i3}'$ of $\pmb{p}_i'$ as a constant zero and ignoring $g_{i3}$ in the gradients + +$g_{i}$ , we can limit the point on its tangent plane and measure the aforementioned variation with $g_{i} = (g_{i1}, g_{i2}, 0)$ . So the remaining problem is how to find the direction that achieves the maximal variation on the logit loss $\mathcal{L}$ . + +Theorem 2. Given the function $\mathcal{L}$ and the freedom-reduced ternary variable $\pmb{p}^{\prime} = (x^{\prime},y^{\prime},0)$ initialized as $(p_{i1}^{\prime},p_{i2}^{\prime},0)$ , the variation rate of $\mathcal{L}$ is upper bounded at $\sqrt{g_{i1}^{2} + g_{i2}^{2}}$ . + +Proof. We ignore the constant zero item and shift the variable in the spherical coordinate system where the point is presented as $(x', y', 0) = (p_{i1}' + r\cos \theta, p_{i2}' + r\sin \theta, 0)$ , where $\theta$ is the angle between the perturbing direction and the positive half axis of $x'$ . Hence $r$ can be presented as $r = \sqrt{(x' - p_{i1}')^2 + (y' - p_{i2}')^2}$ . Based on this, the variation of $\mathcal{L}$ can be regarded as $\nabla_r\mathcal{L}$ , upper bounded by + +$$ +\begin{array}{l} \frac {\partial \mathcal {L}}{\partial r} = \frac {\partial \mathcal {L}}{\partial x ^ {\prime}} \frac {\partial x ^ {\prime}}{\partial r} + \frac {\partial \mathcal {L}}{\partial y ^ {\prime}} \frac {\partial y ^ {\prime}}{\partial r} = g _ {i 1} \cos \theta + g _ {i 2} \sin \theta (11) \\ \leq \sqrt {\left(g _ {i 1} ^ {2} + g _ {i 2} ^ {2}\right) \left(\cos^ {2} \theta + \sin^ {2} \theta\right)} = \sqrt {g _ {i 1} ^ {2} + g _ {i 2} ^ {2}}, (12) \\ \end{array} +$$ + +where we leverage Cauchy Inequality and the equal condition of maximum is when angle $\theta = \arctan (g_{i2} / g_{i1})$ . + +Therefore, when we use $\theta$ to represent the perturbing direction on the tangent plane, the sensitivity score of each point can be determined by the maximal variation rate solved above. Hereby, the sensitivity map of $\mathcal{P}$ is defined as + +$$ +\mathcal {S} = \left\{\boldsymbol {s} _ {i} \right\} _ {i = 1} ^ {N}, \quad \text {s u b j e c t t o :} \boldsymbol {s} _ {i} = \sqrt {g _ {i 1} ^ {2} + g _ {i 2} ^ {2}} \tag {13} +$$ + +# 3.2. Shape-invariant White-box Attack + +With the same definition on point cloud $\mathcal{P} \in \mathbb{R}^{N \times 3}$ , white-box model $\mathcal{H}_w$ and gradient map $\mathcal{G} = \{(g_{i1}, g_{i2}, 0)\}_{i=1}^N$ , the shape-invariant coordinate transformation denoted in Eq.(8) are applied in our white-box attack. Specifically, we first perform gradient-based optimization on the transformed point cloud $\mathcal{P}'$ with white-box model $\mathcal{H}_w$ to generate the transformed adversarial point cloud $\tilde{\mathcal{P}}'$ . Then we apply the inverse transform mentioned + +in Eq.(8) to get adversarial point cloud $\tilde{\mathcal{P}}$ . Inspired by IFGSM [13], we implement the adversarial example generation in an iterative style, where rotation matrix gather $\mathcal{R} = \{\pmb{R}_i\}_{i=1}^N$ and translation matrix gather $\mathcal{T} = \{\pmb{T}_i\}_{i=1}^N$ are iteratively updated in each step $t$ to inherit the shape invariance. To simplify the formulation, we first define the following mappings: + +$$ +F _ {t} (\mathcal {P}) = \mathcal {R} _ {t} (\mathcal {P} + \mathcal {T} _ {t}), \quad F _ {t} ^ {\prime} (\mathcal {P} ^ {\prime}) = \mathcal {R} _ {t} ^ {\top} \mathcal {P} ^ {\prime} - \mathcal {T} _ {t}, \tag {14} +$$ + +where $\mathcal{R}^{\top} = \{\pmb{R}_i^{\top}\}_{i=1}^{N}$ . Then in each step $t$ , our untargeted adversarial example generation can be formulated as + +$$ +\tilde {\mathcal {P}} _ {t + 1} ^ {\prime} = \tilde {\mathcal {P}} _ {t} ^ {\prime} - \beta \cdot \frac {\nabla_ {\tilde {\mathcal {P}} ^ {\prime}} \mathcal {L} \left(F _ {t} ^ {\prime} \left(\tilde {\mathcal {P}} _ {t} ^ {\prime}\right) , t ; \theta_ {w}\right)}{\| \nabla_ {\tilde {\mathcal {P}} ^ {\prime}} \mathcal {L} \left(F _ {t} ^ {\prime} \left(\tilde {\mathcal {P}} _ {t} ^ {\prime}\right) , t ; \theta_ {w}\right) \|}, \tag {15} +$$ + +$$ +\tilde {\mathcal {P}} _ {t + 1} = \operatorname {C l i p} \left(F _ {t} ^ {\prime} \left(\tilde {\mathcal {P}} _ {t + 1} ^ {\prime}\right)\right), \tag {16} +$$ + +$$ +\tilde {\mathcal {P}} _ {t + 1} ^ {\prime} = F _ {t + 1} (\tilde {\mathcal {P}} _ {t + 1}), \tag {17} +$$ + +where $\beta$ means the step size and $Clip$ means the $l_{\infty}$ -norm constraint. When the generation is completed, the adversarial point cloud $\tilde{\mathcal{P}}$ can fool $\mathcal{H}_w$ with satisfying visual quality. + +Algorithm 1: Shape-invariant Query-based Attack +Input: point-cloud input $(\mathcal{P},l)$ , black-box model $\mathcal{H}_b$ , surrogate model $\mathcal{H}_w$ and step size $\epsilon$ Output: adversarial point cloud $\hat{\mathcal{P}}$ +1 Initialize the perturbation $\delta = 0$ +2 Initialize the prediction pool $\mathbf{p}_c = [\mathcal{H}_b(\mathcal{P})]_c$ +3 Transform $\mathcal{P}$ to $\mathcal{P}'$ AttackDefensePointNet [5]DGCNN [29]CurveNet [34]ASR↑ (%)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)ASR↑ (%)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)ASR↑ (%)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)I-FGM [13]-100.06.963.041.1799.516.852.392.02100.015.612.8910.77MI-FGM [8]-99.535.994.161.3195.9120.104.992.1499.0119.175.1010.88PGD [19]-100.07.003.051.1799.416.772.402.02100.015.322.8610.783d-Adv [32]-99.93.252.114.94100.010.122.4618.73100.07.483.51116.24AdvPC [15]-99.816.573.432.9098.814.351.488.1099.918.362.7864.76Ours-99.82.152.041.3299.96.331.273.87100.06.251.9921.53 + +![](images/0e225af5f85d09cd724f1f110ccdf5b5ca0c74fb9bee20544ad69b9f4acd5d6b.jpg) +Figure 4. Attack success rate (curve) and successfully attacked sample numbers (histogram) when perturbing different number of input points on PACov, the step size is unified as 0.03. + +we uniformly sample 1,024 points from the surface of each object and rescale them into a unit cube, as done by Qi et al. [5]. Besides, several kinds of data augmentation such as random point-dropping and rotation are applied to preprocess all of point clouds in the training set. + +Applied Models. Our approach is evaluated on six categories of the most popular 3D recognition models, i.e., PointNet [5], PointNet++ (MSG) [21], DGCNN [29], PA-Conv [35], SimpleView [12] and CurveNet [34]. In the manuscript, we mainly report the experimental results on ModelNet40 [31], in which we choose DGCNN [29] as the surrogate model for black-box attack evaluation. The results on ShapeNetPart [37] or with PointNet [5] as the surrogate model can be found in supplementary materials. + +Evaluation Metrics. To verify the imperceptibility of the generated adversarial point clouds, we compute $l_{2}$ -norm distance, Chamfer distance (CD) [10] and Hausdorff distance (HD) [26] between the original point cloud and the adversarial output to measure the modification caused by attack methods. To investigate the attack performance quantitatively, attack success rate (ASR) is further defined as the ratio of perturbed examples that are incorrectly classified by the black-box model. Besides, both query numbers and time cost are used for measuring the algorithm efficiency. + +Table 1. Quantitative comparison between our white-box shape-invariant attack and existing white-box attacks in terms of attack success rate (ASR), Chamfer distance (CD), Hausdorff distance (HD) and average time budget for each adversarial point cloud generation (A.T), where CD is multiplied by $10^{4}$ and HD is multiplied by $10^{2}$ for better comparison. + +
Defense3d-Adv [32]AdvPC [15]GeoA3[30]Ours
-99.999.8100.099.8
SOR [41]12.033.669.697.4
DUP-Net [41]12.329.073.795.8
AT [19]94.878.699.690.0
+ +Table 2. Attack success rate (ASR) results of different white-box point cloud attacks on PointNet equipped with various defenses. + +# 4.2. Efficiency of Sensitivity Maps + +We first conduct the experiment to verify the theoretical validity of the proposed point-cloud sensitivity map. In practice, we follow different orders to perturb each single point of the point cloud input on PACConv [35], where the perturbation direction is along the shape surface and the step size is unified as 0.03. Here "Pert-Descent" means following the descending order of sensitivity maps, and "Pert-Ascent" means following the ascending order by contrast. We also validate the attack performance on the random order denoted by "Pert-Rand". As indicated in Figure 4, the recognition accuracy gets much more degradation in "Pert-Descent", proving the effectiveness brought by the proposed sensitivity map and its descending score ranking. + +# 4.3. White-box Performance + +Comparison with Existing Methods. We comprehensively compare our shape-invariant white-box attack with different baselines (i.e., regular gradient-based $l_{2}$ attack including I-FGM [13], MI-FGM [8] and PGD [19]); optimization-based point cloud attack including 3d-Adv [32], AdvPC [15] and GeoA3 [30]. Specifically, our method are implemented with the step size 0.007 for 50 iterations. All adversarial examples are equally constrained by the $l_{\infty}$ -norm ball (radius is 0.16). To unify the verification, all baselines adopt the untargeted mode under the same setting. We conduct the comparison on a same RTX 3090Ti GPU in terms of attack success rate (ASR), Chamfer distance (CD), Hausdorff Distance (HD) and average time cost (A.T). The + +![](images/31f85fd875847dbe29799f62b0c4d7433a56a7830ce3f03e1e42cdfe58ac3fcf.jpg) +Figure 5. Black-box performance when applying different attack step size, in terms of attack success rate (ASR), query cost, $l_{2}$ -norm distance and Chamfer distance results between adversarial point clouds and originals. + +![](images/9e1580846c137bdf14bacb852d3136fc62579d6a1b8305b1f40dd039f5c3f08c.jpg) + +![](images/5c71452f86798a391d043f33c78aa34336cc29006264e20fd4ded6963690feec.jpg) + +![](images/70aae53cbb94c58205888b0051d963bd546ba92ad4145fe3901c06ecd38f1bcd.jpg) + +
AttackPointNet++ [21]PAConv [35]CurveNet [34]
ASR↑ (%)A.Q↓ (times)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)ASR↑ (%)A.Q↓ (times)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)ASR↑ (%)A.Q↓ (times)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)
SimBA [14]94.9683.83.054.80112.04100.073.24.514.930.36100.0114.54.674.9313.51
SimBA+ [36]95.5603.43.418.2199.57100.067.45.029.580.36100.098.95.299.7612.94
Ours95.8417.02.664.4476.81100.053.93.894.580.3199.981.53.974.598.77
+ +Table 3. Quantitative comparison between our black-box shape-invariant attack and different black-box attacks with unified step size 0.32 on attack success rate (ASR), average query cost (A.Q), Chamfer distance (CD), Hausdorff distance (HD) and average time budget (A.T). + +
DefensePAConv [35]SimpleView [12]PointNet [5]
ASR↑ (%)A.Q↓ (times)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)ASR↑ (%)A.Q↓ (times)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)ASR↑ (%)A.Q↓ (times)CD↓ (10-4)HD↓ (10-2)A.T↓ (s)
-100.053.93.894.580.31100.0101.67.384.770.5499.929.92.394.310.14
Drop (30%)75.4651.61.684.123.2651.11090.62.204.256.0296.9150.91.844.260.47
Drop (50%)84.4466.11.213.712.1863.7850.01.493.774.9493.6260.11.704.200.78
SOR [41]49.21187.62.453.347.8293.3576.09.733.773.9689.7638.99.114.202.33
+ +Table 4. Resistance of our black-box attack on defended point cloud models. "Drop (30%)" means randomly dropping ${30}\%$ of input points. + +results listed in Table 1 show that our method takes the least geometry distance cost to achieve nearly $100\%$ ASR and the lower time budget compared to regular gradient-based attacks. It is consistent with our intuition of better inhering the shape invariance from original point clouds during adversarial example generation. + +Resistance to Defenses. To verify the attack performance when facing the well-defended point cloud recognition models, we conduct the experiments on defense methods including standard PGD-based adversarial training (AT), point cloud statistical outlier removal SOR [41] and DUP-Net [41]. Trough comparing to three point cloud attack methods in Table 2, we find that our method outperforms the baselines a lot on outlier removal based defenses, which further proves the proposed shape-invariant perturbations are mainly along the shape surface with fewer outliers. + +# 4.4. Black-box Performance + +Efficiency on Different Black-box Models. We compare the proposed shape-invariant query-based attack with two related black-box attack algorithms as baselines: SimBA + +[14] and SimBA+ [36]. SimBA [14] is one of the most famous query-based black-box adversarial attacks that works well in fooling image recognition models, which randomly searches perturbation direction in the whole orthonormal space to perturb each basis. Fortunately, we can regard all $N \times 3$ dimensions as the orthonormal bases for SimBA implementation on point clouds. SimBA+ [36] further improve SimBA by narrowing the perturbation searching space with the gradient prior obtained on a pretrained surrogate model. But different from image recognition, there are little overlap among pure gradient maps computed on different point cloud models, due to their diverse designs for point feature extraction. So the pure gradient prior only brings limited improvement for SimBA++ on unseen point cloud models. As results shown in Figure 5 and Table 3, our attack achieves comparable ASR, fewer queries and less point modification than baselines on unseen black-box models. In other words, the proposed point-cloud sensitivity map can well depict the internal vulnerability of point cloud recognition models, making the perturbation searching more concrete while maintaining the shape invariance. + +![](images/88a2692b8ed43039926c676503321734167f3a9ec43526b196890e027c11e54c.jpg) +Cee + +![](images/dc6d5843b24fdd7c5395c3c988bcb4bcc7100505ba6ca72162419fa1665b4ca2.jpg) + +![](images/841759ac6df2b7fec5d22a66d4030c45193ecf70862a491d223804161b46dad9.jpg) + +![](images/5fc8564e19641cdfc236510d940d2455740932abe86584bd3f3806903dadd229.jpg) + +![](images/8310cd9f556242bebb84959162304041c8fab2db4a0887b80312b2d951665ff0.jpg) + +![](images/27718de3e9a1d6ce0c009be0f9c3bbe9b1041f9f80649e10a8f4466135272532.jpg) + +![](images/785c19f659ba6e6f49042eed52b8e39d28d83e17e38e2f794f72b8fe061d0ed4.jpg) + +![](images/1e61a9fce07b6e125367fd9cef25fcee1f8292edea3fb7485f450823c20c2c0e.jpg) +F + +![](images/16f653c0e1855b1526293cf0cf1f6c8c490861ed265499b7b5a9ebd6d6880ac5.jpg) + +![](images/45b5229b34047668cfa6d2573b24225153756a5672c73c71549997a43ac24d3a.jpg) + +![](images/a01494c8d5b80207a1e2c22e9275e3737651c52c6602ff4fe9fb9ceb8af97708.jpg) + +![](images/58f21ea7cff982335d0494e43b313d7885e3afd470167d55d1f34500f4288327.jpg) + +![](images/bf771cabf04eb9fdcdd22752bc03f28c2e8f998246f377d2b10d6bc57cad3b8f.jpg) + +![](images/5ef83366eb01125f2d36da4141320893e14f721d826fc50fe514c77ebf768511.jpg) + +![](images/c8630c0d889f7daa37121318f07f58f81ffb87040750018d7d8a6c42c35409d6.jpg) +Owrs + +![](images/2b46ac62fbc541917249c407e3829603a3cc6b88d3293b10503e91960731a89d.jpg) + +![](images/16d79530e38f4921e8e40e11065397e3559968ad0cc023b19e5414787c82bf95.jpg) + +![](images/5ac666e16078f6f8445956917f83800eaafb71d355e0f382b43770991a72374d.jpg) + +![](images/334145586ab0060047806f07dbcb0024783c5466ba96eaf4696d868bfc7263d5.jpg) + +![](images/b969bb6762324172f04bfe273d524607da0251565ad1e9fb8b2e3687606acbcc.jpg) + +![](images/2a037c003c4e9ffd8e5d6037fcda2867a1f87d75cafd455f4a7fabce196f888c.jpg) + +![](images/7c69e1e608214fa184ae4afb56b4c6ab55fa0be82da4239a9f0c974d0d1d4123.jpg) +Ours + +![](images/87b0e3af486152fa7ade0c4c6efc57ee6b184636e941cb4bdec2407aaceb14c9.jpg) +Figure 6. Visualization of clean/adversarial point clouds generated by I-FGM and ours method. + +![](images/8d0bfc0add96e49aa949c2aa296b3f1a890d39760c4f2c52a0ebaf8747a7f1a6.jpg) + +![](images/573200a6ba885d3dd0e39f2711f91b2cbaea7e24a185809e6d96efc548d34682.jpg) + +![](images/4e980bf0398983bda2aeaf8f4cc9a7885525a9e6d9052db035d27669f489fd3f.jpg) + +![](images/e0fc426a024fc7e1f5961c79ae147fe1aea44c2ba0c8e90796add886ee58bf66.jpg) + +![](images/856041d4ff0e332ec66f5cd792206a3853a219958ee161ba00002b8f8f133e91.jpg) + +Different Step Size $\epsilon$ . The attack step size is a crucial and configurable parameter for query-based attack performance. Accordingly, we conduct the evaluation on a variety of step size $\epsilon$ from 0.08 to 0.32. In Figure 5, it can be easily found that the needed queries decreases rapidly under nearly $100\%$ ASR as the step size gets larger. While it significantly strengthens the attack efficacy, the higher $l_{2}$ -norm distance and Chamfer distance indicate more visual quality it has to sacrifice. + +Resistance to Defenses. To investigate the robustness of our shape-invariant black-box attack against different kinds of adversarial defenses, we conduct the experiments on three kinds of defense methods: random point-dropping and input preprocessing based defense SRS [41]. As shown in Table 4, for PACnv [35], SimpleView [12] and PointNet [5], the ASR on point dropout just degrades up to $36.3\%$ although the needed queries become more. It is worth noted that our method performs even better on PACnv and SimpleView when the dropout defense get enhanced from $30\%$ to $50\%$ . Empirically, we attribute it to the larger natural accuracy degradation of these models when dropped points are increasing. Overall, our black-box shape-invariant attack has the considerable resistance to these defenses. + +# 4.5. Qualitative Results + +We further visualize the adversarial point clouds and provide the results in Figure 6. Since our perturbation is almost + +along the shape surface, we can hardly find any outliers on the generated adversarial point clouds. Notably, our attack is proved to be more threatening with its well-inherited shape invariance and satisfying attack imperceptibility. + +# 5. Conclusion + +In this paper, we propose Point-Cloud Sensitivity Map by calculating the variation rate of recognition confidence when adding the explicitly constrained shape-invariant perturbation on each point, to reveal the vulnerability of point cloud recognition models when encountering the slight perturbation. With the guidance of this map, we further propose Shape-invariant Adversarial Point Clouds to improve the attack imperceptibility and extend the white-box attack to the black-box case. To the best of authors' knowledge, it is the first query-based black-box attack on point cloud recognition. Experiments show the effectiveness and practicality of our method with its superior shape invariance. + +# 6. Acknowledgement + +This work was supported in part by the Natural Science Foundation of China under Grant U20B2047, 62072421, 62002334, and 62121002, Exploration Fund Project of University of Science and Technology of China under Grant YD3480002001, and by Fundamental Research Funds for the Central Universities under Grant WK2100000011. + +# References + +[1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: A query-efficient black-box adversarial attack via random search. In European Conference on Computer Vision (ECCV), 2020. 3 +[2] Wieland Brendel, Jonas Rauber, and Matthias Bethge. Decision-based adversarial attacks: Reliable attacks against black-box machine learning models. 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Differentiable architecture search (DARTS) acquires the optimal architectures by optimizing the architecture parameters with gradient descent, which significantly reduces the search cost. However, the magnitude of architecture parameters updated by gradient descent fails to reveal the actual operation importance to the task performance and therefore harms the effectiveness of obtained architectures. By contrast, we propose to evaluate the direct influence of operations on validation accuracy. To deal with the complex relationships between supernet components, we leverage Shapley value to quantify their marginal contributions by considering all possible combinations. Specifically, we iteratively optimize the supernet weights and update the architecture parameters by evaluating operation contributions via Shapley value, so that the optimal architectures are derived by selecting the operations that contribute significantly to the tasks. Since the exact computation of Shapley value is NP-hard, the Monte-Carlo sampling based algorithm with early truncation is employed for efficient approximation, and the momentum update mechanism is adopted to alleviate fluctuation of the sampling process. Extensive experiments on various datasets and various search spaces show that our Shapley-NAS outperforms the state-of-the-art methods by a considerable margin with light search cost. The code is available at https://github.com/Euphoria16/Shapley-NAS.git. + +# 1. Introduction + +Neural architecture search (NAS) has attracted great interest in deep learning since it discovers the optimal architecture from a large search space of network components according to task performance and hardware config + +urations. Pioneering works applied reinforcement learning [48], evolutionary algorithms [30, 38], and Bayesian optimization [22] for the architecture search, but the large computational overhead prohibits practical deployment of NAS algorithms. Therefore, it is desirable to design highly efficient search strategies without performance degradation. + +To reduce the search cost of architecture search, several efficient search strategies have been presented including one-shot NAS [29], network transformation [3], and architecture optimization [26]. Among these approaches, one-shot NAS preserves the optimal sub-networks from the over-parameterized supernet with weight sharing, which prevents the time-consuming exhaustive training for model evaluation. In particular, DARTS [23] converted the discrete operation selection into continuous mixing weights learning and iteratively optimized the architecture parameters and supernet weights by gradient descent with significantly reduced search cost. However, the magnitude of architecture parameters in DARTS cannot reflect the actual operation importance in general [36, 42, 47]. That is, the operation with the largest parameter magnitude does not necessarily result in the highest validation accuracy, which degrades the performance of derived architectures. + +In this paper, we present a Shapley-NAS method to evaluate the operation contribution via the Shapley value of supernet components for neural architecture search. Instead of relying on the magnitude of architecture parameters updated by gradient descent, we consider their practical influences on task performance and propose to directly evaluate their contributions to the validation accuracy. Moreover, we observe that the operations in the supernet are related to each other: combinations of operations might have different joint influences on performance compared with their separate ones. In order to deal with such complex relationships, we leverage Shapley value [31, 32], an important solution to attribute contributions to players in cooperative game theory. Fig. 1 shows the differences between our Shapley-NAS and existing DARTS methods. Shapley value directly measures the contributions of operations according to the vali + +![](images/24dc6c157e2094cae8e5a6910d9f380df72c0e3e3f6fd786a161caffa9510eeb.jpg) +Figure 1. The comparison between DARTS and our Shapley-NAS. (a) DARTS constructs a weight-sharing supernet that consists of all candidate operations. The architecture parameters are optimized by gradient descent, which fails to reflect the importance of operations [36, 42, 47]. (b) The proposed Shapley-NAS method directly evaluates the marginal contribution of operations to the task performance, according to the validation accuracy difference of all possible operation subsets and their counterparts without the given operation. + +dation accuracy difference. Meanwhile, it considers all possible combinations and quantifies the average marginal contribution to handle complex relationships between individual elements. Benefiting from these, Shapley value is effective for obtaining operation importance that is highly correlated with task performance. Since computing the exact Shapley value is NP-hard, we employ the Monte-Carlo sampling with early truncation for operation permutation set sampling to approximate it efficiently. Finally, we optimize the supernet weights and update the architecture parameters iteratively, where the momentum update mechanism is adopted to alleviate the fluctuation caused by the sampling process. We empirically demonstrate that the obtained Shapley value has a higher correlation with task performance compared with DARTS. We conducted extensive experiments on different datasets across various search spaces, where our Shapley-NAS outperforms the state-of-the-art architecture search methods. We achieve an error rate of $2.43\%$ on CIFAR-10 [19] on the search space of DARTS and obtain the top-1 accuracy of $23.9\%$ on ImageNet [9] under the mobile setting. Furthermore, our Shapley-NAS acquires the optimal architectures on CIFAR-10 and CIFAR-100 and near-optimal solutions on ImageNet-16-120 of the NAS-Bench-201 benchmark [11]. + +# 2. Related Work + +Differentiable NAS: Differentiable architecture search (DARTS) was first proposed by Liu et al. [23] with the goal of reducing the heavy search cost in NAS. They apply a continuous relaxation to the graphical architecture representation, thus enabling efficient gradient descent to solve the bi-level optimization objective for architecture search. PC-DARTS [40] further proposed to only search the partially-connected operations by leveraging the redundancy in net- + +work space to further reduce the memory overhead. Despite the computation efficiency of DARTS, several works have challenged its generalizability [8,20,39,42] and stability [6,7,36,43,44]. In order to reduce the bias of DARTS for operation selection, SNAS [39] and GDAS [10] introduced stochasticity into the supernet training and adopted the differentiable Gumbel-Softmax trick [17] for gradient estimation. SGAS [20] greedily chose and pruned the candidate operations based on edge importance, selection certainty, and selection stability to alleviate the performance gap between the search and evaluation phase. RobustDARTS [43] found that the stability of DARTS is highly correlated with dominant eigenvalue of the Hessian of validation loss with respect to the architecture parameters. Therefore, they performed early stop regularization according to the largest eigenvalue to avoid poor generation. SmoothDARTS [6] further smoothed the loss landscape via perturbation-based regularization. However, recent studies [36, 42, 47] have demonstrated the magnitude of architecture parameters in the DARTS framework fails to reveal the actual operation importance, which greatly degrades the performance of architectures derived from the search phase. + +Shapley value: Shapley value has been well studied in the cooperative game theory as a fair contribution distribution method [31, 32]. Recently, Shapley value has been adopted in explainable machine learning to discover the importance of different elements, which can be divided into three groups: explaining feature importance [1, 24, 25, 28, 33], model component importance [2, 13, 37], and data importance [18, 41]. For the first regard, Ancona et al. [1] conducted an axiomatic comparison to show the advantage of the Shapley value over the attribution methods for feature map explanation in deep networks. SHAP [25] presented the additive feature attribution based on the Shapley value of features to acquire higher consistency with hu + +man intuition. For model component importance explanation, ShapNets [37] leveraged the Shapley transform that transforms the input into Shapley representations so that the network prediction can be explained during the forward pass. Neuron Shapley [13] identified the most important filters in neural networks and demonstrated potential applications to improve the accuracy, fairness, and robustness of the model prediction. Moreover, Ghorbani et al. [12] quantified the contribution of individual data points which effectively identified the outliers and corrupted data. Since computing the exact Shapley value is NP-hard, Monte-Carlo sampling [12,13], perturbation-based approximation [1], influence function, and many others were presented for efficient estimation of Shapley value. In this paper, we extend the Shapley value to operation importance evaluation in the DARTS framework, so that the optimal architectures are derived by selecting the operations that contribute significantly to the performance. + +# 3. Approach + +In this section, we first briefly introduce differentiable architecture search (DARTS), which suffers from degenerate architectures due to the mismatch between the architecture parameters and operation importance. Then we propose to directly evaluate the influence of operations on the task performance and introduce Shapley value to quantify their relative contributions at the presence of complex relationships between different operations. We also present the Monte-Carlo sampling algorithm with early truncation for efficient approximation of Shapley value. Finally, we propose Shapley-based architecture search (Shapley-NAS) which can effectively identify the optimal architectures with the most important operations from the large search space. + +# 3.1. Preliminaries + +The differentiable architecture search (DARTS) is one of the most popular solutions to identify effective architectures, as it largely reduces the search cost by relaxing the architecture search to continuous mixture weights learning. Following prior works [22, 30, 49], DARTS searches for the best cell structure and constructs the supernet by repetitions of normal and reduction cells. Each cell is represented by a directed acyclic graph (DAG) with $\mathcal{N}$ nodes and $\mathcal{E}$ edges, where each node $x^{(i)}$ defines a latent representation and each edge $(i,j)$ is associated with an operation $o^{(i,j)}$ . The core idea of DARTS is to apply continuous relaxation to the search space to perform the gradient-based search. Concretely, the intermediate node is computed as a softmax mixture of candidate operations: + +$$ +\bar {o} ^ {(i, j)} \left(x ^ {(i)}\right) = \sum_ {o \in \mathcal {O}} \frac {\exp \left(\alpha_ {o} ^ {(i , j)}\right)}{\sum_ {o ^ {\prime} \in \mathcal {O}} \exp \left(\alpha_ {o ^ {\prime}} ^ {(i , j)}\right)} o \left(x ^ {(i)}\right), \tag {1} +$$ + +where $\mathcal{O}$ is the set of all candidate operations and $\alpha_{o}^{(i,j)}$ denotes the mixing weight of operation $o^{(i,j)}$ to construct the supernet. With such relaxation, the architecture search can be performed by jointly optimizing the network weight $w$ and architecture parameters $\alpha$ in a differentiable manner with the following bi-level objective: + +$$ +\min _ {\alpha} \mathcal {L} _ {v a l} \left(w ^ {*}, \alpha\right) \quad \text {s . t .} \quad w ^ {*} = \arg \min _ {w} \mathcal {L} _ {t r a i n} (w, \alpha). \tag {2} +$$ + +During the search stage, the weight-sharing supernet containing all these candidate operations is optimized by gradient descent. At the end of the search stage, the final architecture is derived by selecting the operation with the largest architecture parameter $\alpha$ on every edge across all operation choices, $o^{(i,j)} = \arg \max_{o\in \mathcal{O}}\alpha_o^{(i,j)}$ . + +# 3.2. Operation Importance Evaluation + +The magnitude-based architecture selection process in DARTS relies on an important assumption that the magnitude of architecture parameters represents the operation importance. In other words, it supposes that operations with low magnitude of $\alpha$ result in weak feature representations and thus have little contribution to the network performance. However, recent studies [36,42,47] have shown that the value of architecture parameters does not necessarily reflect the actual operation contribution. In many cases, the operation with the largest $\alpha$ does not result in the highest validation accuracy. Therefore, selecting the best operations based on values of $\alpha$ may lead to significant performance degradation at the evaluation phase. + +To solve this problem, we propose to perform the architecture search by identifying operations that contribute the most to the validation accuracy. [36] performs a similar evaluation of operation contribution by removing the target operation from the supernet while keeping all other operations to obtain the performance drop. However, we observe that the operations in the supernet are not independent of each other. To demonstrate the underlying relationships between operations on different edges, we remove only one operation separately on the 4th edge and the 5th edge from the supernet pretrained on the NAS-Bench-201 space, and re-evaluate the supernet accuracy. As shown in Fig. 2a, removing the skip_connect operation on the 4th edge and the conv_3x3 on the 5th edge leads to the most dramatic performance drop. However, we find the impacts of combinations of the two edges differ from the simple accumulation of their separate influence. We remove one operation for both edges simultaneously and enumerate all candidate operation combinations to show the results. As Fig. 2b illustrates, removing conv_3x3 on the 4th edge and conv_1x1 on the 5th edge results in the most significant degradation, while removing the combination of skip_connect and conv_3x3 only lead to $3.88\%$ performance drop. + +![](images/350f641d13b54fa0c62b84f7da0d437b71f235525ecb7b31389e7b18bfe6b807.jpg) + +![](images/8fc700b400fcdd0ac17541e52dd0c733b731902e0766032d049833c7dab49030.jpg) +(a) Removing one operation on each edge +Figure 2. The performance drop caused by (a) removing the target operation on the 4th and 5th edge separately (b) removing one operation on both edges at the same time and enumerating all combinations. + +![](images/63bdb888febc09016954e7d4fb6cf3c941849f691cab686883e783c82133e1e3.jpg) +(b) Removing one operation on both edges at the same time + +This observation reveals the complex relationships between different operations on different edges: some operations can collaborate with each other and thus have a significant joint contribution to the supernet performance. To deal with such relationships, we leverage Shapley value [31, 32], an important solution from cooperative game theory, to evaluate the individual contribution. Specifically, the differentiable architecture search process can be uniquely mapped into a cooperative game, providing a practical scheme to quantify the operation contribution based on Shapley value. In a cooperative game, $N$ players associate with each other, and a value function $V$ maps each subset of players $S \subseteq N$ to a real value $V(S)$ , which represents the expected payoff the players can obtain by cooperation. In differentiable NAS, the supernet is composed of several layers with identical cell structures, and each cell has $|\mathcal{E}|$ edges each with $|\mathcal{O}|$ operations. Therefore, a set of individual operations, $N = \mathcal{O} \times \mathcal{E} = \{o^{(i,j)}\}_{o \in \mathcal{O}, (i,j) \in \mathcal{E}}$ , can be modeled as players in the cooperative game, where all players work together towards the supernet's performance $V(N)$ . Shapley value is utilized to distribute the total performance gains $V(N)$ to each player in $N$ . In our problem, for operation $o^{(i,j)}$ , its Shapley value $\phi_o^{(i,j)}$ can be computed as: + +$$ +\phi_ {o} ^ {(i, j)} (V) = \frac {1}{| N |} \sum_ {S \subseteq N \backslash \{o ^ {(i, j)} \}} \frac {V \left(S \cup \left\{o ^ {(i , j)} \right\}\right) - V (S)}{\binom {| N | - 1} {| S |}} \tag {3} +$$ + +The Shapley value represents the average marginal contribution of the operation to the network performance, which is obtained by evaluating the performance difference between all operation subsets and their counterparts without the given operation. Here we use the validation accuracy as the value function $V$ to measure the network performance. It has been proved that the formulation of Shapley value in Eq. (3) makes it the only method to quantify individual contributions that uniquely satisfies the following properties [32], which we interpret according to our problem: + +Efficiency The performance of the entire supernet is the sum of contributions of individual operations, i.e. $\sum_{o^{(i,j)}\in N}\phi_o^{(i,j)} = V(N)$ + +Null Player If the operation has no impact on the performance when added to or removed from any subsets of the supernet, then its contribution is zero. That is, if $V(S) = V(S \cup \{o^{(i,j)}\})$ for any operation subset $S \subseteq N \setminus \{o^{(i,j)}\}$ , we can derive $\phi_o^{(i,j)} = 0$ . For example, the zero operation in the search space of DARTS has no impact on the final performance and thus has zero contribution. + +Symmetry If two different operations could be exchanged without affecting the performance, they should be assigned with equal contributions. For any operation subset $S \subseteq N \setminus \{o^{(i,j)}, o^{\prime(k,l)}\}$ , $V(S \cup \{o^{(i,j)}\}) = V(S \cup \{o^{\prime(k,l)}\})$ , then we have $\phi_o^{(i,j)} = \phi_{o'}^{(k,l)}$ . + +# 3.3. Shapley Value Approximation + +Although Shapley value can be considered as a desirable attribution metric for quantifying the contribution of operations, directly computing Shapley value from Eq. (3) requires $2^{|\mathcal{O}| \times |\mathcal{E}|}$ network evaluations caused by enumerating all possible subsets. Therefore, the exact computation of Shapley value becomes expensive since $|\mathcal{O}| \times |\mathcal{E}|$ in the common search space is usually large. To efficiently estimate the Shapley value, we present an approximate method based on Monte-Carlo sampling [5]. Specifically, the Shapley value of operation $o^{(i,j)}$ (denoted as $o$ for simplicity) is equivalent to estimating the mean of a random variable, which can be written as: + +$$ +\phi_ {o} (V) = \frac {1}{N !} \sum_ {R \in \pi (N)} [ V (P r e _ {o} (R) \cup \{o \}) - V (P r e _ {o} (R)) ] \tag {4} +$$ + +where $\pi(N)$ denotes the set of permutations of all elements in $N$ , and $Pre_{o}(R)$ is the set of predecessors of $o$ in a given permutation $R \in \pi(N)$ . Based on Eq. (4), we can get an unbiased approximation of every operation's Shapley value by sampling permutations of operation set $N$ . Notably, the Monte-Carlo estimation reduces the exponential calculation complexity to polynomial-time $M \times (|\mathcal{O}| \times |\mathcal{E}|)$ , where $M$ is the number of samples. Although this sampling-based estimation requires repetitions of accuracy evaluation on the validation set, it only includes the forward process through the supernet with no need for back-propagation, thus enabling efficient approximation of Shapley value. + +Moreover, we find when the number of operations in $Pre_{o}(R)$ becomes too small, the task performance degrades dramatically and yields unstable sampling results. Therefore, to reduce the fluctuation of Shapley value estimation, we utilize the early truncation technique during the Monte-Carlo sampling procedure. Specifically, when the masked out operations lead to an extreme performance drop exceeding a pre-defined threshold $\eta$ , we break off the current sam + +pling. This early truncation technique also reduces nearly half of computation cost, which makes the overall computational overheads comparable with gradient-based architecture parameter optimization in DARTS. + +# 3.4. Shapley-based Architecture Search + +We leverage the Shapley value of operations to guide the architecture search to find the best solutions as it reveals the actual operation contribution to performance. Fig. 1 shows the difference between our Shapley-NAS and conventional differential NAS. Instead of updating the architecture parameters by gradient descent, we utilize the Shapley value to represent the relative strength of operations. Specifically, the search objective should be modified as follows: + +$$ +\alpha \propto \phi \left(\mathcal {L} _ {\text {v a l}} \left(w ^ {*}, \alpha\right)\right) \quad \text {s . t .} \quad w ^ {*} = \arg \min _ {w} \mathcal {L} _ {\text {t r a i n}} (w, \alpha). \tag {5} +$$ + +Since solving the above problem exactly is impractical, we optimize this objective via an approximate way. We update $\alpha$ according to the Shapley value estimated by the algorithm presented in Sec. 3.3: + +$$ +\boldsymbol {\alpha} _ {t} = \boldsymbol {\alpha} _ {t - 1} + \epsilon \cdot \frac {\boldsymbol {s} _ {t}}{\left| \left| \boldsymbol {s} _ {t} \right| \right| _ {2}} \tag {6} +$$ + +where $\alpha_{t}$ means the architecture parameter at the $t$ -th step during the optimization, $s_t$ represents the accumulated Shapley value in the $t_{th}$ step, $||\cdot ||_2$ is the $L_{2}$ norm and $\epsilon$ is the step size. We iteratively optimize $\boldsymbol{w}_{t}$ by descending $\nabla L_{train}(\boldsymbol{w}_{t - 1},\boldsymbol{\alpha}_{t - 1})$ and update architecture parameters $\alpha$ until convergence. To reduce undesired fluctuation in updating caused by random sampling, we introduce the momentum into the iteration to stabilize the optimization: + +$$ +\boldsymbol {s} _ {t} = \mu \cdot \boldsymbol {s} _ {t - 1} + (1 - \mu) \cdot \frac {\phi \left(A c c _ {v a l} \left(\boldsymbol {w} _ {t - 1} , \boldsymbol {\alpha} _ {t - 1}\right)\right)}{\left| \left| \phi \left(A c c _ {v a l} \left(\boldsymbol {w} _ {t - 1} , \boldsymbol {\alpha} _ {t - 1}\right)\right) \right| \right| _ {2}} \tag {7} +$$ + +where $\mu$ is the momentum coefficient that balances the accumulated Shapley value and the current sampling result, $Acc_{val}$ is the validation accuracy used as value function, and $\boldsymbol{w}_{t-1}$ is the supernet weights at $(t-1)$ step. After the search stage, we derive the final architecture by selecting the operation with the largest contribution on each edge. + +# 4. Experiments + +In this part, we conducted extensive experiments to evaluate our method on the DARTS search space with CIFAR10 [19] and ImageNet [9] for image classification, as well as on a widely used NAS benchmark dataset, NAS-Bench201 [11]. We first introduce the datasets and implementation details of our Shapley-NAS. In the following ablation study, we analyzed the effectiveness of the proposed Shapley value evaluation, as well as the influence of hyperparameters on task performance and search cost. We compare our + +Shapley-NAS with the state-of-the-art methods with respect to the accuracy, model complexity, and search cost. Finally, we empirically demonstrated the effectiveness of Monte-Carlo sampling estimation, as well as the high correlation between obtained Shapley value and task performance. + +# 4.1. Datasets and Implementation Details + +CIFAR-10: For the CNN search space on CIFAR-10, we employed the same operation space $\mathcal{O}$ as DARTS and set the initial channel number as 16. We utilized the partial connection strategy in PC-DARTS [40] to reduce memory overhead and increase batch size. We trained the supernet for 50 epochs (the first 15 epochs for warm-up) with a batch size of 256. The training set of CIFAR-10 was divided into two parts with equal size, one for optimizing network weights and the other for evaluating Shapley value. We set the number of samples $M$ to be 10 in the Monte-Carlo sampling and the early truncation threshold $\eta$ to be 0.5. The momentum coefficient $\mu$ and step size $\epsilon$ were assigned to 0.8 and 0.1 respectively. At the evaluation phase, We simply followed the DARTS experimental settings for fair comparison and retrained the network from scratch for 600 epochs. + +ImageNet: ImageNet contains about 1.2 million training and 50K validation images from 1000 categories, which is much more challenging than CIFAR-10. We randomly sampled $10\%$ and $2.5\%$ images from the entire 1.3M training set of ImageNet for training network weights and estimating Shapley value respectively. The supernet was trained for 50 epochs with batch size 1024 and the architecture parameters remained frozen in the first 25 epochs. The other hyper-parameters were the same with CIFAR-10. At the evaluation stage, we trained the network from scratch for 250 epochs by an SGD optimizer with a linearly decayed learning rate initialized as 0.5, a momentum of 0.9, and a weight decay of $3 \times 10^{-5}$ . + +NAS-Bench-201: NAS-Bench-201 is a popular benchmark to analyze NAS algorithms, as it provides performance of all candidate architectures which can be directly obtained by querying. In the search space of NAS-Bench-201, the operation set $\mathcal{O}$ has 5 elements and each cell contains 4 nodes, leading to a total search space of 15,625 architectures. NAS-Bench-201 supports three datasets, CIFAR-10, CIFAR-100, and ImageNet-16-120, and more details about the datasets can be found in their paper [11]. Specifically, we acquired the task-specific performance by directly searching on the evaluation dataset, and obtained the mean and standard deviation for the best architecture from 4 independent runs with different random seeds. + +# 4.2. Ablation Study + +Effectiveness of Shapley value evaluation: To verify the effectiveness of Shapley-NAS, we conducted experiments on 4 simplified search spaces S1-S4 proposed by + +Table 1. The test error(%) of different search algorithms on S1-S4. DARTS+Shapley denotes the combination of DARTS and Shapley value evaluation, and * means freezing $\alpha$ during the search. + +
DatasetMethodS1S2S3S4
C10DARTS3.844.853.347.20
DARTS+Shapley3.112.922.583.45
DARTS+Shapley*2.952.842.672.94
Shapley-NAS2.822.552.422.63
C100DARTS29.4626.0528.9022.85
DARTS+Shapley28.2124.5123.6722.78
DARTS+Shapley*25.2424.6622.3922.15
Shapley-NAS23.6022.7721.9221.53
SVHNDARTS4.583.533.413.05
DARTS+Shapley2.592.722.832.65
DARTS+Shapley*2.882.642.492.58
Shapley-NAS2.362.432.342.41
+ +[43] on CIFAR-10, CIFAR100, and SVHN. We first combined the proposed Shapley value evaluation method with DARTS (denoted as DARTS+Shapley in Tab. 1, by only applying Shapley value evaluation at the final discretization step, i.e. selecting operations based on their Shapley values instead of $\alpha$ . Moreover, we also tested the performance under the same setting but keeping $\alpha$ frozen, denoted as DARTS+Shapley*. As shown in Tab. 1, DARTS achieves competitive results with the proposed Shapley evaluation method, even when $\alpha$ is not optimized in the training. Notably, our Shapley-NAS still outperforms DARTS+Shapley and DARTS+Shapley*, since taking Shapley value into the supernet optimization can further alleviate the problem caused by gradient-based NAS methods. + +Influence of samples times $M$ and early truncation threshold $\eta$ : We also explored the influence of sampling times $M$ and early truncation threshold $\eta$ in the Monte-Carlo sampling algorithm. The values of sampling times $M$ and early truncation threshold $\eta$ are significant for accurate Shapley value estimation, which also affect the overall search cost. Fig. 3 shows the test error (\%) and search cost (GPU days) on CIFAR-10 with various $M$ and $\eta$ . Reducing the number of samples results in lower search cost while degrading the performance since the sampling is not enough to make an accurate estimation. However, the estimation accuracy with samples larger than 10 is not sensitive to the number of samples, and we choose $M = 10$ for search efficiency. Meanwhile, medium $\eta$ also achieves the best accuracy-complexity trade-off as it mitigates the fluctuation of sampling and reduces the search cost. + +Impact of momentum coefficient $\mu$ and step size $\epsilon$ : To investigate the influence of momentum coefficient $\mu$ and step size $\epsilon$ on test accuracy, we implemented the architecture parameter assignment with different $\mu$ and $\epsilon$ . The test error range and model parameter cost are demonstrated in Tab. 2, where medium $\epsilon$ outperforms other values. Small step sizes fail to achieve the optimal distribution when reaching the maximum update iterations, and large step sizes make the supernet optimization hard to converge. + +![](images/a9f528c122f35ffcca1841112598eea7a715c769bf40fdc5727a63d6e57793fc.jpg) +(a) Varying number of samples $M$ + +![](images/8fc01197568b6a589d570a74f98d3fe520abb3a249ade3fceeaeb9db784898df.jpg) +(b) Varying early truncation threshold $\eta$ +Figure 3. The test error $(\%)$ and search cost (GPU days) of the proposed method on CIFAR-10 with (a) different number of samples and (b) various thresholds of early truncation in the Monte-Carlo sampling for Shapley value estimation. + +With the increase of $\mu$ , the training stabilization becomes enforced, where $\mu$ with 0.8 achieves the best accuracy. + +# 4.3. Comparison with the State-of-the-art NAS Methods + +Tab. 3 shows the performance of Shapley-NAS on CIFAR-10 compared with the state-of-the-art NAS methods. Our Shapley-NAS achieves an average test error of $2.47\%$ while only using 0.3 GPU days, significantly surpassing the DARTS baseline in both search cost and accuracy. The test error of the best single run in our experiments is $2.43\%$ , ranking top amongst popular NAS methods. Although ProxylessNAS [4] achieves a lower test error of $2.08\%$ , it performs architecture search on a different space with heavy search cost. The low variance of the experimental results also demonstrates the stability of the proposed search method. + +The comparison results on ImageNet with other methods are demonstrated in Tab. 4. We follow the mobile setting in [23] for ImageNet, where the number of multiply-add operations (" $\times+$ " ) is restricted to be less than 600M. We trained the best-found architecture on CIFAR-10 to evaluate its transferability to ImageNet and obtained a competitive result with $24.3\% / 7.3\%$ top-1/5 test error, verifying the generalization ability of our Shapley-NAS. We also evaluated the optimal architecture directly searched on ImageNet and obtain a top-1/5 test error of $23.9\% / 7.2\%$ , which outperforms all other NAS methods with light search cost. Notably, despite the outstanding performance of DrNAS, it has a number of multiply-add operations much over 600M. By contrast, out Shapley-NAS never violates the mobile setting while achieving competitive results. + +For NAS-Bench-201, our Shapley-NAS achieves outstanding performance with $94.37\%$ , $73.51\%$ , and $46.85\%$ test accuracy on CIFAR-10, CIFAR-100, and ImageNet-16-120 respectively, as shown in Tab. 5. Notably, we obtain the global optimal architectures on CIFAR-10 and CIFAR-100, which indicates that the proposed method can identify im + +Table 2. The test error (%) and parameter storage cost (M) of the final architectures w.r.t. different values of momentum coefficient $\mu$ and different assignments of step size $\epsilon$ . + +
step size εμ = 0.2μ = 0.5μ = 0.8μ = 0.9
Test Error(%)Params(M)Test Error(%)Params(M)Test Error(%)Params(M)Test Error(%)Params(M)
0.012.89 ± 0.214.02.87 ± 0.163.72.67 ± 0.063.52.74 ± 0.113.8
0.052.85 ± 0.183.62.79 ± 0.123.42.55 ± 0.073.22.68 ± 0.073.5
0.12.82 ± 0.113.72.66 ± 0.103.32.47 ± 0.043.42.61 ± 0.064.1
0.52.92 ± 0.193.52.84 ± 0.134.22.71 ± 0.123.82.83 ± 0.153.9
+ +Table 3. Comparison with state-of-the-art image classifiers on CIFAR-10. Means and standard deviations of our Shapley-NAS are obtained by repeated experiments with 4 random seeds. + +
ArchitectureTest Error (%)Params (M)Search Cost (GPU days)
DenseNet-BC [16]3.4625.6-
NASNet-A [49]2.653.32000
AmoebaNet-A [30]3.34 ± 0.063.23150
AmoebaNet-B [30]2.55 ± 0.052.83150
PNAS [22]3.41 ± 0.093.2225
ENAS [29]2.894.60.5
NAONet [26]3.533.10.4
RandomNAS [21]2.85 ± 0.084.32.7
DARTS (1st order) [23]3.00 ± 0.143.30.4
DARTS (2nd order) [23]2.76 ± 0.093.31.0
SNAS(moderate) [39]2.85 ± 0.022.81.5
GDAS [10]2.933.40.3
BayesNAS [46]2.81 ± 0.043.40.2
ProxylessNAS [4]2.085.74.0
P-DARTS [8]2.503.40.3
PC-DARTS [40]2.57 ± 0.073.60.1
SGAS (Cri 1. avg) [20]2.66 ± 0.243.70.25
SDARTS-RS [6]2.61 ± 0.023.40.4
DrNAS [7]2.54 ± 0.034.00.4
DARTS+PT [36]2.61 ± 0.083.00.8
Shapley-NAS(avg.)2.47 ± 0.043.40.3
Shapley-NAS(best)2.433.60.3
+ +Table 4. Comparison with state-of-the-art image classifiers on ImageNet under the mobile setting [23]. $\dagger$ indicates the results obtained by searching on ImageNet, otherwise on CIFAR-10. + +
ArchitectureTest Error (%)Params (M)×+ (M)Search Cost (GPU days)
Inception-v1 [34]30.16.61448-
MobileNet [15]29.44.2569-
ShuffleNet 2× (v1) [45]26.4~ 5524-
ShuffleNet 2× (v2) [27]25.1~ 5591-
NASNet-A [49]26.05.35642000
AmoebaNet-C [30]24.36.45703150
PNAS [22]25.85.1588225
MnasNet-92 [35]25.24.4388-
DARTS (2nd) [23]26.74.75741.0
SNAS (mild) [39]27.34.35221.5
GDAS [10]26.05.35450.3
BayesNAS [46]26.53.9-0.2
ProxylessNAS (GPU) [4]†24.97.14658.3
P-DARTS [8]24.44.95570.3
PC-DARTS [40]25.15.35860.1
PC-DARTS [40]†24.25.35823.8
SGAS (Cri 1. best) [20]24.25.35850.25
SDARTS-ADV [6]25.66.1-0.4
DrNAS [7]†24.25.26443.9
DARTS+PT [36]†25.54.75383.4
Shapley-NAS24.35.15660.3
Shapley-NAS†23.95.45824.2
+ +important operations and derive the best architecture from the large search space. On the ImageNet-16-120 dataset, we + +![](images/2dbbb767d73d0790c3a5a4dd1f3fec2f35768a3a5c88e5509213d2e4847887c9.jpg) +(a) Normal cell + +![](images/432d7d610911a7f277a5cc68ad2834ecfa76af85ba31e4467763d719c288689a.jpg) +(b) Reduction cell +Figure 4. The evolution of architecture parameters $\alpha$ by estimating Shapley value based on Monte-Carlo Sampling. (a) The curves of $\alpha$ on the first edge of the normal cell. (b) The curves of $\alpha$ on the first edge of the reduction cell. + +also acquire a near-optimal solution, which outperforms the state-of-the-art algorithms, again verifying the effectiveness of our Shapley-NAS. + +# 5. Performance Analysis + +Shapley value estimation by Monte-Carlo Sampling: To verify the effectiveness of Monte-Carlo Sampling for Shapley value approximation, we plot the architecture parameters evolution on the first edge of normal and reduction cells in Fig. 4. Note that the curves of the first 15 epochs for warm-up are not presented. As Fig. 4a shows, although the max_pool_3x3 operation is larger than all other operations at the start, the operation sep_conv_5x5 finally becomes the strongest operation since it has the most contribution to the supernet along with the training process. While in Fig. 4b, the operation sep_conv_3x3 becomes dominant after several epochs, while other operations gradually converge to be very weak. The supernet gradually converges to the final derived architecture using the proposed estimation. Moreover, the architecture parameters are differentiated to make the arg max selection more reliable. + +Correlation between Shapley value and task performance: We investigate the correlation between Shapley value of operations and real task performance on NAS-Bench-201. After the search phase, we sample 200 discrete architectures from the search space and compute their corresponding operation strength by averaging the magnitude of architecture parameters. Then we plot the test accuracy obtained by directly querying along with the computed operation strength of DARTS and our Shapley-NAS. We use the Kendall Tau coefficient to measure the correlation, and the results on CIFAR-10, CIFAR-100, and + +Table 5. Comparison results with state-of-the-art NAS methods on NAS-Bench-201. † denotes the results are obtained by searching on CIFAR-10, otherwise by directly searching on the evaluation dataset. + +
MethodCIFAR-10CIFAR-100ImageNet-16-120
validationtestvalidationtestvalidationtest
ResNet [14]90.8393.9770.4270.8644.5343.63
Random (baseline)90.93 ± 0.3693.70 ± 0.3670.60 ± 1.3770.65 ± 1.3842.92 ± 2.0042.96 ± 2.15
RSPS [21]84.16 ± 1.6987.66 ± 1.6945.78 ± 6.3346.60 ± 6.5731.09 ± 5.6530.78 ± 6.12
REINFORCE [49]†91.09 ± 0.3793.85 ± 0.3771.61 ± 1.1271.71 ± 1.0945.05 ± 1.0245.24 ± 1.18
ENAS [29]39.77 ± 0.0054.30 ± 0.0010.23 ± 0.1210.62 ± 0.2716.43 ± 0.0016.32 ± 0.00
DARTS [23]†39.77 ± 0.0054.30 ± 0.0015.03 ± 0.0015.61 ± 0.0016.43 ± 0.0016.32 ± 0.00
DARTS [23]39.77 ± 0.0054.30 ± 0.0038.57 ± 0.0038.97 ± 0.0018.87 ± 0.0018.41 ± 0.00
SNAS [39]90.10 ± 1.0492.77 ± 0.8369.69 ± 2.3969.34 ± 1.9842.84 ± 1.7943.16 ± 2.64
GDAS [10]90.01 ± 0.4693.23 ± 0.2324.05 ± 8.1224.20 ± 8.0840.66 ± 0.0041.02 ± 0.00
PC-DARTS [40]89.96 ± 0.1593.41 ± 0.3067.12 ± 0.3967.48 ± 0.8940.83 ± 0.0841.31 ± 0.22
iDARTS [44]†89.96 ± 0.6093.58 ± 0.3270.57 ± 0.2470.83 ± 0.4840.38 ± 0.5940.89 ± 0.68
DrNAS [7]91.55 ± 0.0094.36 ± 0.0073.49 ± 0.0073.51 ± 0.0046.37 ± 0.0046.34 ± 0.00
Shapley-NAS91.61 ± 0.0094.37 ± 0.0073.49 ± 0.0073.51 ± 0.0046.57 ± 0.0846.85 ± 0.12
optimal91.6194.3773.4973.5146.7747.31
+ +![](images/8ed319bad095f710348ab843e3ea69726a7fb65c5b64a47cc8825adcfc1013e4.jpg) +(a) CIFAR-10 + +![](images/3c5096312ee010906915f90ebd798c108f37e676fc8e751058ebcd71f23a2cb8.jpg) +(b) CIFAR-100 +Figure 5. Correlation between operation strength and test accuracy of 200 sampled architectures using DARTS and our Shapley NAS on NAS-Bench-201. The average operation strength is obtained by the magnitude of corresponding architecture parameters in the supernet, and $\tau$ is the Kendall Tau coefficient that measures the correlation. + +![](images/9a80a7cdda4d8d1286739211f179a04938e8bd2a99c21f3d1fc0b63170aade06.jpg) +(c) ImageNet-16-120 + +ImageNet-16-120 are shown in Fig. 5. The Shapley value of operations has a higher correlation with the test accuracy $(\tau = 0.526, 0.474, 0.357$ respectively), while the magnitude of $\alpha$ in DARTS is almost entirely uncorrelated with the final task performance. It indicates the effectiveness of Shapley value to help us discover optimal architectures with superior performance during the evaluation phase. + +# 6. Conclusion and Discussion + +In this paper, we have presented Shapley-NAS, a Shapley value based operation contribution evaluation method for neural architecture search. Since the architecture parameters updated by gradient descent in DARTS cannot reveal the actual operation importance in general, we propose to directly evaluate the marginal contribution of operations on accuracy via Shapley value. Specifically, the Shapley value of operations can be efficiently approximated by Monte-Carlo sampling based algorithm with early truncation, thus enabling the optimization of the supernet whose architecture parameters are directly updated with the operation contribution. Shapley-NAS achieves state-of-the-art performance on CIFAR-10, ImageNet, and NAS-Bench + +201 benchmarks, which proves its effectiveness to identify the optimal architectures with the most important operations in neural architecture search. + +Limitations: The exact computation of Shapley value is expensive on common search space since it needs exponential times of evaluations, and the resulting heavy search burdens would limit the practical applications for task-specific network deployment. Therefore, to evaluate operation contribution during the architecture search, we utilize the Monte-Carlo sampling method which gives an unbiased approximation of Shapley value. Despite being computationally efficient, it might not be as accurate as the exact computation via enumerating all possible subsets. + +# Acknowledgements + +This work was supported in part by the National Key Research and Development Program of China under Grant 2017YFA0700802, in part by the National Natural Science Foundation of China under Grant 62125603 and Grant U1813218, in part by a grant from the Beijing Academy of Artificial Intelligence (BAAI), and in part by a grant from the Institute for Guo Qiang, Tsinghua University. + +# References + +[1] Marco Ancona, Cengiz Oztireli, and Markus Gross. Explaining deep neural networks with a polynomial time algorithm for shapley value approximation. In ICML, pages 272-281, 2019. 2, 3 +[2] Marco Ancona, Cengiz Öztireli, and Markus Gross. Shapley value as principled metric for structured network pruning. arXiv preprint arXiv:2006.01795, 2020. 2 +[3] Han Cai, Tianyao Chen, Weinan Zhang, Yong Yu, and Jun Wang. 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For practical use, an ideal post-processing refinement scheme are required to be accurate, generic and efficient. However, most of existing approaches propose pixel-wise refinement, which either introduce a massive computation cost or design specifically for different backbone models. Contour-based models are efficient and generic to be incorporated with any existing segmentation methods, but they often generate over-smoothed contour and tend to fail on corner areas. In this paper, we propose an efficient contour-based boundary refinement approach, named SharpContour, to tackle the segmentation of boundary area. We design a novel contour evolution process together with an Instance-aware Point Classifier. Our method deforms the contour iteratively by updating offsets in a discrete manner. Differing from existing contour evolution methods, SharpContour estimates each offset more independently so that it predicts much sharper and accurate contours. Notably, our method is generic to seamlessly work with diverse existing models with a small computational cost. Experiments show that SharpContour achieves competitive gains whilst preserving high efficiency. + +# 1. Introduction + +Instance segmentation is a fundamental topic in computer vision which plays an important role in scene understanding [45], intelligent robots [36], clinical analysis [6, 46] and autonomous driving [10, 14]. The mainstream of instance segmentation approaches follow the design of detection-then-segmentation framework like Mask R-CNN [13] and achieve promising performance. However, high fidelity segmentation of fine details especially in the + +![](images/66c5df6832b6aea09ec37ac7909218842b80dc08bb42bc344189b1a8326ea368.jpg) +(A) + +![](images/24a90bb5f8eeb12aab2742929174cdf20d2f35877523f2d0b3d726f01635bc6f.jpg) + +![](images/02270a613812003e30c6d2bb60b176d7ab763fa599e7982722cff77431094bf1.jpg) +(C) +Figure 1. Instance segmentation with SharpContour. Top: A is the coarse mask predicted by Mask R-CNN and B is the refinement result of SharpContour. Bottom: C is the coarse contour generated by DANCE and D is the refinement result of SharpContour. In the corner areas, SharpContour yields significant improvements. + +![](images/f25f6d0941f52d9905649a4eef01e38c8356fa152087a87788d83110572c9672.jpg) +(B) + +![](images/f73048eb569cfc8b5e10d1d133a4ec8fc250e787e30eaaaf0c0479beb9eca5a2.jpg) +(D) + +boundary area remains extremely challenging. + +To address this issue, the refinement of boundaries is raised as a new topic in recent years. A novel evaluation metric called Boundary AP [7] and a number of approaches [8, 18, 33, 42] are proposed. Boundary AP [7] focuses on the accuracy of the object boundary region thus can better reflect boundary refinement. As for the approaches, refinement can be generally recognized as a post-processing operation which is expected to meet three basic requirements: accurate, efficient and generic. It is worth mentioning that "generic" is also a significant factor. However, existing top-performing refinement methods mainly focus on accuracy and lacks consideration of other two factors which are actually important in the practical application scenarios. For example, Boundary Patch Refinement method [33] proposed to additionally process patches along boundaries after the instance segmentation model, resulting in massive computational cost. RefineMask [42] designed a new architecture built upon Mask-RCNN [13] to refine the quality of instance mask with fine-grained features. Though the computational cost is not extremely expensive, this method is + +too specific to be applied to other types of instance segmentation models. It is intrinsically hard for the pixel-wise refinement methods to achieve the three requirements at once, since the dense pixel maps usually bring excessive computation cost. + +Another group of trending segmentation approaches proposed contour-based segmentation methods [1,3,23,27,29, 38, 39] which directly process and generate sparse points along the boundaries. They are advantageous on efficiency and naturally generic to be appended after mask-based algorithms since it is straightforward to extract a contour from a mask. Thus, an interesting question can be raised up: "Is it possible to use contour-based methods to address the boundary refinement problem?" + +However, existing contour-based methods, like DANCE [26] and DeepSnake [10], tend to produce over-smoothed contours especially on the sharp turner areas (as shown in Fig. 1) so that their performances on boundary areas is still lagging behind. We figure out the major reason which leads to the oversmoothing problem is that all the vertices on the contour are tied together by their feature learning strategies (e.g. circular convolutions [10]) and the smoothness regularization in their contour evolution process. As a result, a slight offset on one vertex will cause a wide chain reaction on all vertices of the contour. To address this, we elaborate a drastically different contour evolution process that estimates the deformation offsets independently for each vertex. Based on this, we propose an accurate, efficient and generic refinement approach, named SharpContour, for boundary area using contour-based representation. + +Specifically, our SharpContour takes a coarse contour as input and deforms each vertex on the contour individually. To avoid artefacts caused by the involved "independence", we constrain each vertex to move along its normal direction and conduct the deformation in an iterative procedure, making the deformation stably. For the sake of balancing between efficiency and accuracy for each vertex's movement, instead of directly regressing the offset, we propose to determine the target position by performing classification on a few discrete points. Specifically, we first sample some points along the moving direction and classify them into "inner/outer" status to obtain the flipping position which indicates the boundary. The classifier plays a pivotal role in this contour evolution process. Thus, we carefully design an Instance-aware Point Classifier (IPC), which can predict "inner/outer" of a vertex with respect to different instance boundaries in the form of a probability score. There are two important factors for IPC to achieve high fidelity: 1) It is required to be instance-aware, which is essential to enable generating different results for a pixel with respect to different instances. For this purpose, the parameters of the IPC are predicted on-the-fly for each instance. 2) It should + +capture the information of the boundary details. Thus IPC takes the fine-grained feature, which is derived from the high-resolution feature map, as input to predict the vertex state. + +With IPC, we can determine how to move each vertex during the deformation. The moving distance is further defined by the object size and IPC probability score. We iteratively adjust the vertices of the predicted contour, until they match the object boundary. In this process, SharpContour avoids the high-dependency over neighbouring vertices without using any smooth term, thus overcoming the oversmoothing issue. Notably, SharpContour only introduces a handful of parameters and involves a negligible amount of points in the calculation. Therefore, our approach is considerably efficient. Experiments manifest that SharpContour can work seamlessly with various segmentation models by introducing a small computational cost and producing high-quality object boundaries. + +We validate the effectiveness of our SharpContour approach quantitatively and qualitatively on various large scale segmentation benchmarks. On COCO datasets [22], we use both AP and the Boundary AP metrics. Coupled with DANCE [26], SharpContour brings significant improvements of 1.5 AP and 3.2 Boundary AP. Coupled with the Mask R-CNN [13] and CondInst [34] as the refinement approach, our approach surpasses the baseline by a significant gain of 2.3, 2.2 AP and 3.4, 3.3 Boundary AP respectively. On Cityscapes datasets [9], SharpContour achieves 3.9 AP boost when combined with Mask R-CNN [13]. Compared with other boundary refinement models, SharpContour consistently produces high-quality boundaries with a low computational cost. Taking the output of the state-of-the-art contour refinement method, RefineMask, as initial contour, SharpContour still gains 0.5 AP and 1.1 Boundary AP. The qualitative results further demonstrate the effectiveness of our approach. + +# 2. Related Work + +Mask-based methods. The mainstream mask-based approaches can be broadly categorized into top-down and bottom-up methods. The typical top-down approaches [2, 4, 5, 8, 13, 19, 24, 34, 37, 43] follow the pipeline of Mask-RCNN [13], which detects each instance first and predicts a pixel-wise binary map for each instance. Models can be categorized into two-stage [5, 8, 24] and one-stage [2, 4, 19, 34, 37, 40] according to their pipelines. However, they usually rely on a pooling operation to extract canonical-size features from the feature maps for each instance, which loses many boundaries details. CondINST [34] removed the RoI operation and use dynamic convolution layer to generate segmentation masks, but it still losses many details around boundaries. Bottom-up approaches [11, 17, 25, 28, 32, 44] first generate semantic segmentation and then cluster pixels + +![](images/213b95dca52defa37b854936246c4e2e4c4d4d900eabf733dcc184fd5544502c.jpg) +Figure 2. Contour Evolution of SharpContour. SharpContour obtains the initial contour from coarse segmentation results and deforms the contour to achieve boundary refinement. In the deformation process, 1) SharpContour obtains the normal direction. 2) SharpContour predicts the inner/outer state of vertex to decide negative/positive normal direction of deformation. 3) SharpContour decides the step size. 4) SharpContour obtains the moving step number based upon the position of the flipping point. 5) SharpContour estimates the offsets and deforms the contour. + +into different instances. In all the pixel-wised methods, the boundary points only occupy a very small proportion (less than $1\%$ [17]) so that their accuracy is usually over compromised during the optimization. Our method avoids these drawbacks and can work together with various models to enhance their performance on boundaries. + +Boundary refinement To tackle the aforementioned limitations, various boundary refinement methods [8, 18, 20, 33, 41, 42] are proposed. Meanwhile, to evaluate the boundary performance more accurate, a novel evaluation metric Boundary AP [7] is proposed, which can solve the desensitization problem of the current evaluation metric (AP) for object boundary region. As for the approaches, BPR [33] adopts a post-processing scheme, refining predicted instance boundary patches in detail to improve mask quality. Another top-performing model, PolyTransform [20] proposes the first contour-based refinement approach which uses the results of the mask-based model as initial contour and refines the contour by Transformer network [35]. These methods achieve superior performance while introducing a large computational cost and scarifying the efficiency. Some other methods try to balance the performance enhancement and the extra computational overheads. For example, PointRend [18] only performs point-based segmentation around the boundary blurred areas to obtain high-quality mask. RefineMask [42] achieves high-quality results by introducing fine-grained features during the upsampling process to refine entire objects. However, these two methods lack of generality since they can only refine the results of specific mask-based methods. In contrast, our refinement approach can not only achieve accurate and effi + +cient refinement but also be generic to refine the results of both mask-based and contour-based models. + +Contour-based methods Neural contour-based models [15, 23, 27, 30, 38, 39] for segmentation are widely studied in recent years due to their potential advantage on efficiency. Most of them formulate the contour as polygons and propose various regression methods to estimate the coordinate of vertices on the polygons. [27, 39] propose CNN-based models which can learn high-level and expressive features for deformation. [23] proposes a contour-based model which utilizes Graph Convolution Networks (GCN) to regress the offsets of vertices on the contour. Following the pipeline of traditional Snake model [16], Deep-Snake [29] proposes a two-stage contour evolution process and designs circular convolution to exploit the features on the contour. DANCE [26] follows the pipeline of Deep-Snake [29] and introduces edge attention module and improves the matching scheme in the contour evolution process. DANCE [26] achieves state-of-the-art results for the contour-based instance segmentation methods. However, all of these regression-based contour evolution methods still suffer severe performance degradation in approximating the corners or cusps of instance. This is because their regression method needs to balance the regression error and the smoothness of the current contour and the offsets are highly dependent on each other during feature learning. Our approach elaborates a drastically different evolution method. In our deformation stage, the offset of each vertex on the polygon is estimated by discrete moving steps rather than regression. Incorporated with DANCE [26], our approach is proved to be more effective than all the existing contour + +based methods, yielding accurate and high-fidelity segmentation results even for significant challenging areas. + +# 3. Methodology + +We propose a contour refinement approach, SharpContour, which coupled with existing instance segmentation models (either mask-based or contour-based), can produce high-quality boundary segmentation results. Let $C^{(0)}: \{x_i | i = 1, \dots, N\}$ be an initial contour, which is obtained by off-the-shelf instance segmentation methods. The contour is defined by a sequence of vertices $x_i$ . SharpContour iteratively moves the vertices to approach the actual boundary of an instance. To perform the contour evolution, we design an iteration process to deform the vertices along their normal. The key challenge of the contour evolution methods is to predict the offset for each vertex accurately. In contrast to existing methods that directly regress the offsets for all the vertices at once, which is often error-prone and leads to over-smoothed contours, we propose to adjust the vertices iteratively in a discrete manner inspired by [31]. Due to the inherent challenge of directly regressing offsets, we cast this problem to be a classification-based formula. Specifically, we propose an Instance-aware Point Classifier (IPC) $\varphi(x_i)$ which predicts a state for the vertex $x_i$ indicating its relative position to the actual object boundary (i.e., inside or outside), such that we can determine whether a vertex should march along the positive or negative normal direction. Our approach greatly reduces the dependency on the offsets of neighbour vertices and allows for delicate segmentation details on complex and challenging boundary areas, such as the corner and cusps areas where the existing methods struggle. An overview of SharpContour can be found in Fig. 2. + +# 3.1. Contour Evolution + +Given a vertex $x_{i}$ which is off the object boundary, its evolution process in one iteration can be written as + +$$ +x _ {i} ^ {\prime} = x _ {i} + m s _ {i} d _ {i}, \tag {1} +$$ + +where $d_{i}$ is the moving direction, $s_{i}$ the moving step and $m$ the step number. For each vertex, $\varphi(x_{i})$ will output a scalar value in [0, 1], indicating the probability of $x_{i}$ being outside (i.e., $\varphi(x_{i}) = 1$ ) or inside (i.e., $\varphi(x_{i}) = 0$ ) the object. $\varphi(x_{i}) = 0.5$ means that IPC is not sure whether the point is inside or outside the object, implying the point is probably located on the boundary. More details of IPC will be introduced in Sec. 3.2. Next, we describe how we obtain the moving step $s_{i}$ and the step number $m$ . They together define the moving distance. + +To define the moving step, we take into account the object size (in terms of the area of the bounding box, denoted as $A$ ) and the uncertainty of the vertex state from IPC. Intuitively, if the object is larger, the step size should also be + +![](images/fbcd1cbd1c3a83f5b119181843c719456276b13752c1b8971a9d699ef7f29124.jpg) +Figure 3. Deformation of SharpContour. Value flipping indicates the position of instance boundary. SharpContour uses the position of flipping points to update the contour. + +larger, and vice versa. If the uncertainty of vertex is higher, the step size should be smaller to reach finer prediction, and vice versa. To reflect these, concretely, we define the step size as $s_i = \lambda \sqrt{A} |\varphi(x_i) - 0.5|$ , where $\lambda$ is an empirical deformation ratio which we set to 0.003 in experiments. $|\varphi(x_i) - 0.5|$ indicates the uncertainty of state of $x_i$ for IPC, the closer $\varphi(x_i)$ is to 0.5, the higher the uncertainty of state of $x_i$ for IPC, so smaller step size for $x_i$ should be assigned for accuracy. For the moving step number, ideally, we expect the vertex to progressively move towards the actual object boundary. Therefore, we move the vertex along $d_i$ step-by-step, and after each move, we examine the value of $\varphi$ on the current location. If we reach a location that $\varphi$ indicates the vertex is moved from inside to outside of the boundary or the other way around, then we stop. We call this location flipping point. The number of moves from the original location to the flipping point is then our moving step number $m$ . To avoid the vertex moving towards an improper direction too far away, we set an upper bound for the move, i.e., for each move if after $M$ steps, a flipping point is still not reached, we then set $m = M$ . + +Iteratively Evolution We perform the above evolution process for each vertex of $C^{(0)}$ to obtain an updated contour $C^{(1)}$ . We then run another evolution cycle for $C^{(1)}$ to update the vertices. We iteratively run the evolution process and generate a series of contours $\{C^{(0)}, C^{(1)}, \dots, C^{(n)}, \dots\}$ to approach actual object boundary progressively. Note that during each iteration, if a vertex reaches a flipping point, which indicates that it has reaches the object boundary, it will not participate the subsequent deformation process anymore. This further improves the efficiency of SharpContour. + +# 3.2. Instance-aware Point Classifier + +Here, we introduce our Instance-aware Point Classifier (IPC) $\varphi$ , which aims at predicting a state for a given vertex $x_{i}$ to tell its relative position to the actual object boundary. In a nutshell, IPC takes the fine-grained feature of $x_{i}$ derived from the high-resolution feature map and the relative location of $x_{i}$ to its corresponding bounding box as input to predict the probability indicating whether $x_{i}$ is located inside or outside the object. Importantly, the parameters of $\varphi$ + +are dynamically predicted for each instance on the fly, such that $\varphi$ is instance-aware, which plays an important role at inferring vertices relative location to the instance. + +Fine-grained Feature To be able to identify the subtle details for the vertex evolution, we employ the fine-grained features from the high-resolution feature map produced by the instance segmentation backbone as the input for $\varphi$ . We append a convolution layer on the high-resolution feature map to further encode feature to benefit $\varphi$ for contour refinement and reduce the dimension. Let the encoded fine-grained feature for $x_{i}$ be $f_{i}$ . We concatenate $f_{i}$ with the relative coordinates $c_{i}$ of $x_{i}$ to the instance bounding box, forming a new fine-grained location-aware feature vector $f_{i}^{c} = [f_{i}; c_{i}]$ , which serves as the input of $\varphi$ to predict the state probability. Taking Mask R-CNN as example, we utilize the highest resolution feature map from the feature pyramid network (FPN), which is $1/4$ of the image size. To decrease the parameters number of IPC and enhance the utilization of the high-resolution feature, we attach a $3 \times 3$ convolution layer to this feature map and reduce its channel from 256 to 16. From the resulting feature map, we extract the fine-grained feature for each vertex. + +Instance-aware Dynamic Parameters Only equipped with the fine-grained feature, the classifier still struggles at the determination. For example, a point with the same feature can be outside one instance but inside another instance. To deal with this problem, our classifier needs to be instance-aware and has strong ability to grasp holistic information to identify each instance. Inspired by [34], we propose to dynamically predict the parameters $\theta$ of the classifier $\varphi$ for each instance, based on the feature of each instance. This strategy can capture strong instance-aware information therefore it can discriminate the state of a vertex w.r.t different instance. For example, we incorporate a boundary controller head inspired by [34] for Mask R-CNN to obtain the dynamic parameters for each instance. The boundary controller head is a very compact and lightweight network with three fully connected layers. The output dimension of this controller head is the same with the parameter number of IPC. By sharing feature with the original mask head of Mask R-CNN, we can make better use the instance-aware feature while only introducing a small computation cost. Our IPC can therefore be written as $\varphi(x_i) = \varphi_\theta([f_i, c_i])$ . If $\varphi(x_i) > 0.5$ , $x_i$ is considered as outside the object predicting the label $\hat{y}_i$ as 1, otherwise inside the object predicting the label $\hat{y}_i$ as 0. In our implementation, IPC is simply realized an MLP with three hidden layers with the ReLU activation. The sigmoid activation applied to its output layer. Hence, the extra cost introduced by the IPC is marginal. + +# 3.3. Instance Segmentation with SharpContour + +In this section, we describe how to combine our SharpContour with different types of instance segmentation models, including mask-based models and contour-based models. In the training stage, we train the head which generates parameters of IPC by randomly sampling pixels near the ground-truth instance boundary. In the inference stage, SharpContour obtains the initial contour from the coarse segmentation results and the contour evolution process can be iterated for refinement. In general, when working with existing instance segmentation methods, the SharpContour takes three inputs: initial contour, fine-grained features and dynamic parameters. Methods to obtain these three inputs vary from different instance segmentation methods. Here we introduce how to apply SharpContour to three typical instance segmentation methods. For contour-based models such as DANCE [26], the predicted contour of their model can be used directly as the initial contour for our SharpContour. For Mask-based models such as Mask R-CNN [13] and CondInst [34], we extract the initial contour by transferring the predicted mask into contour representation. To obtain the fine-grained features, we use convolution layers to encode the feature maps of highest resolution from their backbone and use the encoded feature map to extract fine-grained features. To obtain the dynamic parameters, we tailor the boundary controller head to incorporate it with various instance segmentation models. The detailed network structure and parameters settings are provided in the supplementary. + +# 3.4. Loss Function + +We use the focal loss [21] to train the boundary controller head which generates parameters of IPC and the convolution layer which encodes the fine-grained features. Since the points sampled around ground-truth boundary for training is random, the ratio between positive and negative samples is not fixed. To compensate this, we exploit the focal loss with a dynamic coefficient $\alpha$ , which is the ratio of current positive and negative samples. The loss can be written as + +$$ +L _ {I P C} = \left\{ \begin{array}{c} - \alpha (1 - \hat {y} _ {i}) ^ {\gamma} \log (\hat {y} _ {i}), y _ {i} = 1 \\ - (1 - \alpha) (\hat {y} _ {i}) ^ {\gamma} \log (1 - \hat {y} _ {i}), y _ {i} = 0 \end{array} \right. \tag {2} +$$ + +where $\hat{y}$ denotes the predicted label, $\alpha$ is dynamically determined by the proportion of positive and negative samples in the current batch and $\gamma$ is the difficulty factor which we set to 2 in our experiments. + +After combining our SharpContour with a baseline instance segmentation model, we jointly train our SharpContour and with the coupled instance segmentation model. The overall loss function can be expressed as + +$$ +L = L _ {s} + \mu L _ {I P C}, \tag {3} +$$ + +where $L_{s}$ is the original loss of the instance segmentation model. We set the weight $\mu = 10$ in our experiments. + +![](images/ef059850090b79348ca28b9022acb233a59aa144c6d830a4d51311f34a33e69b.jpg) + +![](images/b2ed049fd14a35b629fd0dc9f7202f3d95cb7c64f9bafb9a5da005d88296ac3a.jpg) + +![](images/0102438b04663c2a7e24cd1826869294238fe8bee17dd93ae4280bcd251154a7.jpg) + +![](images/19cc07ad7143324cfd8de79d1defd7b5c71df7bfa84eb970ed3cac0a798a11f8.jpg) + +![](images/986939cc4c8d6375c3c117953ccc7a78994e1a0dfb3751a039cd237c7d3513e1.jpg) + +![](images/382087f0d07f176673995ec00833ab07f97cd24257bf31395ccbe33540c0baf6.jpg) + +![](images/54ebd0b105cb98af1a5c3b6e325fc05a147c49ab4c88cc3fbdc60bbf47becf4e.jpg) +Figure 4. Qualitative results on COCO dataset. We use SharpContour to refine the segmentation results of different models. The top line is the results of DANCE while the bottom line is the results of Mask-RCNN. For each example, the left is the result before refinement while the right is our result. As is illustrated, SharpContour can refine the segmentation results near instance boundary. + +![](images/53eed5ee81f62d3b4d71987da0628c3cd766fd238975df4f889223a9ca5b237e.jpg) + +![](images/779d3220d62426c4543e5cfe207e1cf250be3cdeca8566a24a86f51e3da1d712.jpg) + +![](images/4cfbb6fc8d8092df3ac53871ad06b46c3372ca1837ff596c6099f4a0e79829de.jpg) + +![](images/fc44f08c7eed8d208f652814f71a819b8aac3310d858d98d854b94edb188db1c.jpg) + +![](images/77fcdf619238158997ca9a4f09640ef2b4bcbd66b3bb4306e84ed070390bc915.jpg) + +![](images/0d1e0ce101248e48d4eae6098e2dc7ab9c9792c18a16a466c0c5b44614b5988f.jpg) + +![](images/a482d429e0ee5ddbd5562aab5e2b079187321e1f616908ab29df45c39e041b17.jpg) + +
APdevAPvalBoundary APAP*AP*SAP*MAP*LFPSInference time (ms/per image)
Mask R-CNN34.634.7-36.822.643.752.012.381.3
Mask R-CNN*35.535.221.237.622.844.753.817.557.1
DANCE34.634.520.2----16.560.6
CondInst35.435.721.6----17.457.5
PointRend36.836.3 (+1.1)23.5(+2.3)39.722.946.757.413.076.9 (+19.8)
RefineMask37.637.3 (+2.1)24.7(+3.5)40.924.148.858.013.076.9 (+19.8)
DANCE + SharpContour36.336.1 (+1.5)23.9(+3.7)----13.673.5
Mask R-CNN* + SharpContour37.737.5 (+2.3)24.6(+3.4)41.224.249.158.515.066.7 (+9.6)
CondInst + SharpContour37.737.9 (+2.2)24.9(+3.3)----15.464.9
RefineMask + SharpContour38.037.8 (+0.5)25.8(+1.1)41.924.349.459.112.182.6 (+5.7)
+ +Table 1. Comparisons on COCO val2017 and test-dev. $\mathrm{AP}_{dev}$ denotes the evaluation results on test - dev, and other columns denote the evaluation results on val2017. "Mask R-CNN" is a original Mask R-CNN, and "Mask R-CNN*" is the improved version in Detectron2. All methods are trained with 1x schedule using R50-FPN backbone. The FPS is measured on a single Tesla V100 GPU. SharpContour brings significant AP enhancement for DANCE, Mask R-CNN and CondInst. Moreover, SharpContour can achieve competitive performance compared with other boundary refinement approaches with the highest efficiency. + +
MethodAP\( AP_S \)\( AP_M \)\( AP_L \)
Mask R-CNN33.812.031.551.8
PointRend35.8(+2.0)---
RefineMask37.6(+3.8)14.634.058.1
Mask R-CNN + SharpContour37.7(+3.9)14.434.258.3
+ +Table 2. Results on Cityscapes validation set. The training setting for all models are same: trained on fine annotations for 64 epochs, using multi-scale training and ResNet-50 with FPN. + +# 4. Experiments + +# 4.1. Impmentation Details + +Training strategy We train the SharpContour with the DANCE, Mask R-CNN and the CondInst together to enhance the performance. For each combination model, we conduct experiments using totally the same training settings with coupled model, including training epoch, learning rate schedule, data augmentation methods, etc, to ensure fairness. We set the deformation ratio $\lambda = 0.003$ , the number of sampling points $M = 10$ and the resolution of the polygon $N = 128$ . The iteration number of evolution is set to be 3. More detailed training settings will be described in supp. + +# 4.2. Benchmarks and Metrics + +We evaluate the efficiency and the effectiveness of SharpContour on three standard benchmarks, which are Cityscapes [9] and Microsoft COCO [22]. Following the + +prior work, we use Mask AP as the evaluation metrics. To further demonstrate the effectiveness of SharpContour, we report Boundary AP on the COCO datasets. (Unless explicitly stated, AP denotes Mask AP in this paper.) + +COCO [22] is one of the most common benchmarks to evaluate the models for object detection and segmentation tasks, and we mainly report the results on COCO. Our models were trained on train2017. Following PointRend and RefineMask, we also report $\mathrm{AP^{*}}$ , which evaluates the COCO categories using LVIS annotations, since LVIS annotations have much higher quality mask. The results of $\mathrm{AP^{*}}$ are obtained by the same model trained on COCO. + +Cityscapes [9] is a large-scale dataset for pixel-level and instance-level segmentation evaluation, which provides a massive amount of video records of daytime urban street scenes from 50 cities. Cityscapes contain a rich set of annotations including 5,000 images with fine pixel-level annotations and 20,000 images with coarse annotations. It is one of the most widely used and challenging benchmarks. + +# 4.3. Comparison with the state-of-the-art + +Effectiveness for contour-based model We apply Sharp-Contour to the DANCE [26], which follows the idea of DeepSnake [29] and achieves current state-of-the-art performance for contour-based instance segmentation meth + +![](images/e9155eef6527199763bd3f62af149271074a47801a01b992dd2eb7a2ab9c4b8e.jpg) +Figure 5. Qualitative comparison results of complex contours SharpContour+MaskRCNN (Right) performs better than Refine-Mask(Left) at challenging regions. + +
Training SchemeAPAP*
joint training37.5(+2.3)41.2(+3.6)
training alone36.2(+1.0)39.8(+2.2)
+ +Table 3. Results of Different training scheme on COCO val2017. The performance is reported on "Mask R-CNN + Sharp-Contour" combination. + +
Mask R-CNNMask R-CNN+Mask R-CNN+SharpContour
AP35.235.537.5
AP*37.638.041.2
+ +Table 4. Results on COCO val2017. Mask R-CNN+ is the results of Mask R-CNN trained with SharpContour. It demonstrates that original model can get benefits from joint training, and our proposed module indeed improve the mask quality. + +ods. We conduct experiments on the COCO datasets. As is shown in the Tab. 1, SharpContour brings 1.5AP and 3.7 Boundary AP improvement. + +Effectiveness for Mask-based methods We apply SharpContour to the Mask R-CNN [13] and the CondInst [34] and complete experiments on the COCO and Cityscapes datasets. On COCO datasets, we further report the AP* measured using the higher quality LVIS [12] annotations. 1) For Mask R-CNN [13], SharpContour outperforms baseline model 2.3AP, 3.4 Boundary AP and 3.6AP* on COCO datasets (Tab. 1) and yields 3.9AP enhancement on CityScapes datasets(Tab. 2). 2) For CondInst [34], SharpContour achieves an improvement of 2.2AP and 3.3 Boundary AP on the COCO [22] datasets. Besides, 'RefineMask + SharpContour' combination in Tab. 1 represents: we directly run 'Mask R-CNN + SharpContour' model on the contour simply extracted from the output mask of RefineMask, it still gains 0.5AP and 1.1 Boundary AP improvement. SharpContour gains larger improvements on Cityscapes compared with COCO. The probable reason is that the classes of Cityscapes is much less than COCO, which leads to a better IPC. This further proves the effectiveness of SharpContour. + +Efficiency We compare the efficiency with other boundary refinement methods, including PointRend [18] and RefineMask [42], on the COCO and Cityscapes dataset. For fairness, 1) These methods are built on Mask R-CNN. 2) All the methods adopt ResNet-50 with FPN as the backbone, 3) All the models are trained for the same epochs. As is shown in Tab. 1, 2, comparing with PointRend [18] and RefineMask [42], SharpContour achieves better performance with higher efficiency. Notably, PointRend [18] and RefineMask [42] incorporate their methods after Mask R-CNN and introduce additional inference time of $19.8\mathrm{ms}$ . Compared with them, our SharpContour only introduces infer + +ence time of 9.6ms, half of theirs, but brings more gains. + +Qualitative Comparison Fig. 4 shows the qualitative results of SharpContour on the COCO datasets. We use SharpContour to refine two models: DANCE (top line) and Mask R-CNN (bottom line). For each instance in these figures, the left one is the result without the SharpContour while the right one is the result with the SharpContour. As is illustrated, the SharpContour can ameliorate the contour near instance boundary since it can extract extra information in vertex neighbourhood so that achieve high-fidelity and accurate results for diverse instances. More results can be found in the supplementary materials. Fig.5 shows qualitative comparison results between RefineMask and SharpContour+MaskRCNN. SharpContour can deal with objects with complex contour and perform better at challenging regions (e.g., thin structure region). + +# 4.4. Ablation Study + +We conduct ablation experiments to analyze the proposed SharpContour on the COCO datasets. We explore the influence of different choices of SharpContour. + +Training Scheme To demonstrate the effectiveness of SharpContour in advance, we also adopt the training scheme which freezes all parameters of the instance segmentation models and only trains the SharpContour independently. Specifically, we only train the boundary controller head (Sec. 3.2) used to generate parameters of the IPC and the convolution layer (Sec. 3.2) used to generate fine-grained feature. As shown in Tab. 3, SharpContour can still refine the instance segmentation results of these models by adopting such training scheme. + +Effectiveness for feature extraction SharpContour shares the backbone with the instance segmentation model to refine. We explore what effects such training strategy casts to the feature extraction process of the backbone. We examine the instance segmentation accuracy of the model w/o training with the SharpContour. As illustrated in Tab. 4, Training with SharpContour can actually enhance the performance of the instance segmentation models, which indicates that SharpContour can ameliorate feature extraction process. + +Effects of dynamic step size The output probability of the IPC indicates the uncertainty of inner/outer state. We argue that such uncertainty can be used to better control the moving distance in contour evolution process. We conduct ablation experiments w/o such dynamic step size on COCO datasets. As reported in Tab. 5, the dynamic step size yields $0.5\mathrm{AP}$ and $0.9\mathrm{AP}^*$ enhancements. Moreover, we notice that dynamic step size can also stable the inference process. + +Larger models, longer training We train SharpContour together with Mask-RCNN using different backbones, including ResNet-101 with FPN and ResNeXt-101 with FPN, with longer 3x schedule. In the Tab. 6, SharpContour consistently improves the performance of baseline model. + +
adaptive stepAPAP*
w37.541.2
w/o37.0(-0.5)40.3(-0.9)
+ +Table 5. Effectiveness of adaptive step on COCO val2017. When combining Mask R-CNN with our SharpContour, the adaptive step strategy can bring significant 0.5AP and 0.9AP* improvements, which can also stable the inference process. + +
backboneAPAP*
Mask R-CNNR50-FPN37.239.5
Mask R-CNN + SharpContourR50-FPN39.3(+2.1)43.1(+3.6)
Mask R-CNN.R101-FPN38.641.4
Mask R-CNN + SharpContourR101-FPN40.8(+2.2)45.2(+3.8)
Mask R-CNN.X101-FPN39.542.1
Mask R-CNN + SharpContourX101-FPN41.8(+2.3)46.0(+3.9)
+ +Table 6. Larger models and longer 3x schedule. Even with a stronger backbone (ResNet-101) and a longer training schedule (3x), a consistent improvement brought by SharpContour is achieved as well. AP* is COCO mask AP evaluated using the higher-quality LVIS annotations. + +
λAPvalMAPvalFPSNAPvalFPS
0.001537.1536.815.412837.515.0
0.00337.51037.515.025637.814.6
0.00636.61537.214.734838.014.2
2037.114.351238.013.7
+ +Table 7. $\mathrm{AP}_{val}$ and FPS for different parameters of sampling strategy on COCO val2017 datasets. The parameters selected achieve the balance of accuracy and efficiency. + +
Combined Methodn=1n=2n=3n=4
DANCE35.235.736.136.2
Mask R-CNN36.637.137.537.7
CondInst36.937.437.938.0
+ +Table 8. Results of different iteration numbers of Evolution Process. It can be seen that the Iterative Evolution can consistently boost the performance, as well as preserve stability on the COCO val2017 datasets. As the number of iterations increases, the improved performance of each iteration continues to decrease, indicating the convergence of contour. + +
Reg.1Reg. 2SharpContour
AP36.1(+0.9)36.2(+1.0)37.5(+2.3)
+ +Table 9. Results of Regression-based model Both regression-based designs can only slightly enhance the AP. + +Different parameters of Contour Evolution process There are three main parameters in the design of the points sampling strategy, which are the deformation ratio $\lambda$ , the number of sampling points $M$ and the resolution of the polygon $N$ . In final version, we set $\lambda = 0.003$ , $M = 10$ and $N = 128$ . In this ablation study, we conduct control experiments for each one of these parameters (preserving the other two parameters the same with the final version) and the results of three evolution iterations are in Tab. 7. + +For $\lambda$ , a) a larger deformation ratio causes performance degradation with more iterations, which is due to the fast deformation; b) a smaller deformation ratio requires more iterations for convergence. From these two experiments, we can see that our final choice achieves the best performance. + +For $M$ , a) a larger number of points will increase the inference time; b) a smaller number of points will decrease the running time but require more iterations for better performance; c) if the number of points becomes very large, the + +performance will decrease as more iterations are performed. This is because the polygon deforms too fast so that errors tend to appear in the result. + +For $N$ , it shows that denser sampling on the polygon contributes to minor performance improvements, while greatly increasing the inference time. We use 128-resolution in the final model for a better trade-off between accuracy and efficiency. + +Different number of Stacked Contour Evolution Process To comprehensively evaluate the effectiveness of the SharpContour, we explore the performance of different iterations of the Contour Evolution Process. The results are reported in Table. 8. As is shown, if stacking the contour evolution process of SharpContour more times, a stable enhancement of accuracy is validated for our methods. + +Regression-based Baselines We have explored two regression-based designs before adopting current discretization design: 1) regressing offset vectors (Reg.1); 2) regressing the distance along the normal direction (Reg.2), where the proposed instance-aware feature is also used. We adopted the Mask-RCNN as the basic framework and carried out experiments on COCO datasets. As is shown in Tab. 9, both regression-based designs can only slightly enhance the AP comparing with the SharpContour. + +# 5. Conclusion + +We propose a novel contour-based refinement approach called SharpContour to improve the boundary quality of instance segmentation. The existing mask-based refinement methods are lack of efficiency or generality and contour-based approaches prone to generate over-smoothed contours around sharp corners. We address all of their limitations by designing a new contour evolution method and an Instance-aware Points Classifier. In contrast to the previous approaches, our approach shows superior accuracy in a considerable efficient fashion and can refine both mask-based and contour-based methods. We extensively evaluate the qualitative and quantitative performance of SharpContour on two large-scale public benchmarks for instance segmentation. It achieves significant improvement on all benchmarks when incorporated with different models. + +Acknowledgement The work was supported in part by the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone, National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, and by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104. This work was also supported by NSFC-62172348, 61902334, Shenzhen General Project (JCYJ20190814112007258) and Shenzhen Sustainable Development Project(KCXFZ20201221173008022). We thank the ITSO in CUHKSZ for their High-Performance Computing Services. + +# References + +[1] David Acuna, Huan Ling, Amlan Kar, and Sanja Fidler. Efficient interactive annotation of segmentation datasets with polygon-rnn++. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pages 859-868, 2018. 2 +[2] Daniel Bolya, Chong Zhou, Fanyi Xiao, and Yong Jae Lee. Yolact: Real-time instance segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9157-9166, 2019. 2 +[3] Lluis Castrejon, Kaustav Kundu, Raquel Urtasun, and Sanja Fidler. Annotating object instances with a polygon-rnn. 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Existing methods use pre-trained query-agnostic visual backbones to extract visual feature maps independently without considering the query information. We argue that the visual features extracted from the visual backbones and the features really needed for multimodal reasoning are inconsistent. One reason is that there are differences between pretraining tasks and visual grounding. Moreover, since the backbones are query-agnostic, it is difficult to completely avoid the inconsistency issue by training the visual backbone end-to-end in the visual grounding framework. In this paper, we propose a Query-modulated Refinement Network (QRNet) to address the inconsistent issue by adjusting intermediate features in the visual backbone with a novel Query-aware Dynamic Attention (QD-ATT) mechanism and query-aware multiscale fusion. The QD-ATT can dynamically compute query-dependent visual attention at the spatial and channel levels of the feature maps produced by the visual backbone. We apply the QRNet to an end-to-end visual grounding framework. Extensive experiments show that the proposed method outperforms state-of-the-art methods on five widely used datasets. Our code is available at https://github.com/LukeForeverYoung/QRNet. + +# 1. Introduction + +Visual grounding [25, 32, 36, 59], i.e., localizing the referent object in an image according to the given natural language query, is a fundamental component of multi- + +![](images/c30ca0fd4af7346efea60b5cf439295a0139a78cd2778a85a58952add34ffd9e.jpg) +(a) Previous end-to-end framework + +![](images/8c4672c0ba81e60bd57a067873f14aec5f541ca415adbcbb0b48089c2d3d6b67.jpg) +(b) Our QRNet-based framework +Figure 1. (a) A typical end-to-end visual grounding framework that uses two individual encoders to extract visual and textual features for cross-modal interaction. (b) Our visual grounding framework based on a Query-modulated Refinement Network (QRNet). + +modal reasoning system. Compared with conventional object detection methods [38, 39] which can only recognize the restricted categories contained in the training data, visual grounding has the advantage of detecting novel combinations of categories and attributes expressed in free-form text. In recent years, it has attracted much attention in the field of computer vision and machine learning due to its potential applications in many downstream tasks, such as visual question answering [15, 50, 63], visually-grounded language navigation [2, 47] and image captioning [1, 8, 57]. + +The early methods of visual grounding focus on extending the popularly used one-stage and two-stage object detection architectures. One-stage methods [11, 23, 54, 56] use a pre-trained fully convolutional network (e.g. DarkNet53 [38], ResNet [20]) to directly extract pixel-level feature maps and leverage manually-defined dense anchors to return the most likely candidate for the query text. These methods are easy and efficient for learning or inference, but they cannot perform well on complex queries that have various objects and relations. Two-stage methods [52, 53, 58] use an off-the-shelf detector (e.g. Faster R-CNN [39]) to extract the region proposals and return the one that best matches the query text using the modality-shared representations. These methods always have better performance than the one-stage ones by introducing more complicated multimodal fusion and reasoning mechanisms [33, 52, 53]. However, the complicated fusion modules cannot be jointly learned with the detectors, which may limit their ability in multimodal reasoning. More recently, Transformer [46] has been applied in visual grounding [11, 24] to conduct the multimodal reasoning more succinctly based on pixel-level feature maps without region proposals or dense anchors. + +Although existing visual grounding methods, especially the Transformer-based methods [11, 24], have achieved promising results, we argue that they do not pay enough attention to the visual backbone which plays a crucial role in effective multimodal reasoning. Since the visual backbone determines whether all integral visual content in the image is successfully extracted for matching the query text. Currently, the most widely used backbones are the CNN model (e.g., ResNet [20]) pre-trained for image classification on ImageNet and the detector (e.g., Faster R-CNN [39] and Mask R-CNN [19]) pre-trained for general object detection of close-set categories. Therefore, the difference between the visual grounding task and the pre-training task of the backbones may lead to an inconsistency between the visual features produced by the backbones and the ones really needed for the multimodal reasoning. As shown in Figure 1(a), the pre-trained visual backbone extracts general purported visual features sensitive to regions that may contain the objects of pre-defined categories. Whereas, the visual grounding requires the backbone to localize a different object referred to by the query. A straightforward way to alleviate the inconsistency is learning the visual grounding model in an end-to-end form as in [11]. However, it still cannot completely avoid the inconsistency because the backbone is query-agnostic. In other words, given the same image, the query-agnostic backbone will always output the same feature map no matter what the query sentences are. + +In this paper, we propose a Query-modulated Refinement Network (QRNet) to address the inconsistency issue. As shown in Figure 1(b), the proposed QRNet can produce query-consistent features by adjusting the feature + +maps of the visual backbone with the guidance of the query text, which benefits the cross-modal alignment between the query and the relevant region to make a correct prediction. The QRNet is designed based on Swin-Transformer [31] and a novel Query-aware Dynamic Attention (QD-ATT), which can help the QRNet extract query-refined visual feature maps from the visual backbone and fuse the multiscale features with the query guidance. The QD-ATT dynamically computes textual-dependent visual attentions at the spatial and channel level of the feature maps produced by the visual backbone. The spatial and channel attentions are further multiplied with the original feature maps to obtain query-refined hierarchical visual feature maps. To comprehensively consider the fine-grained visual features of the candidate regions at different scales, we aggregate the query-refined visual feature maps obtained at different stages of the QRNet by a query-aware multiscale fusion scheme. + +We instantiate the proposed QRNet by building a flexible visual grounding framework based on the recently proposed TransVG [11]. We adopt the same multi-layer visua-linguistic transformer as in [11] to perform intra- and inter-modal reasoning based on the output token sequence of the QRNet. The complete pipeline significantly outperforms existing methods, e.g., TransVG [11] (3.75% on Refer-ItGame and 2.85% on Flickr30K Entities). Note that the proposed QD-ATT can be easily applied to other pre-trained visual backbones, e.g., ResNet [20]. + +The main contributions of this paper are three-fold: + +- We propose a query-modulated refinement network to address the inconsistency issue caused by the pretrained visual backbone through adjusting the visual feature maps with the guidance of query text. +- We propose a novel query-aware dynamic attention mechanism, which can dynamically compute query-dependent spatial and channel attentions for refining visual features. +- We build a flexible visual grounding framework based on the query-modulated refinement network and demonstrate that it achieves significantly better performance than existing methods on five widely used public datasets. + +# 2. Related Work + +# 2.1. Visual Grounding + +The visual grounding methods can be categorized into two-stage methods and one-stage methods. + +Two-stage methods divide the visual grounding process into two steps: generation and ranking. Specifically, a module such as selective search [44], region proposal network [39], or pre-trained detector [16, 17, 39] is firstly used + +to generate proposals that contain objects. Then a multimodal ranking network will measure the similarity between the query sentence and proposals and select the best matching result. Early works [22, 32, 41] only consider sentence-region level similarity. Yu et al. [58] decompose the query sentence and image into three modular components related to the subject, location, and relationship to model fine-grained similarity. Several studies [4, 33, 52, 53] incorporate graph learning to better model cross-modal alignment. The more related work to ours is Ref-NMS [7], which uses the query feature to guide the Non-Maximum Suppression on region proposals to increase the recall of critical objects. However, Ref-NMS [7] can only be integrated into two-stage methods. Moreover, it cannot affect the visual backbone in feature extraction and proposal generation. + +One-stage methods extract visual feature maps that maintain the spatial structure and perform cross-modal interaction at pixel level. The fused feature maps are further used to predict bounding boxes. Yang et al. [55] use a Darknet [38] to extract feature maps and broadcast the query embedding to each spatial location. Several recent works [26, 54, 56] regard multimodal interaction as a multistep reasoning process to better understand the input query. Huang et al. [23] extract landmark features with the guidance of a linguistic description. The more recent work TransVG [11] incorporates DETR encoder to extract visual features and proposes a transformer-based visual grounding framework. Kamath et al. [24] model the visual grounding as a modulated detection task and propose a novel framework MDETR derived from the DETR detector. + +# 2.2. Transformer-based Visual Backbones + +Dosovitskiy et al. [13] propose to extract image features by applying a pure Transformer architecture on image patches. This method is called Vision Transformer (ViT) and achieves excellent results compared to state-of-the-art convolutional networks. Touvron et al. [43] introduce improved training strategies to train a data-efficient ViT. Yuan et al. [60] propose a Tokens-to-Token transformation to obtain a global representation and a deep-narrow structure to improve the efficiency. Some recent works [9, 18] modify the ViT architecture for better performance. Liu et al. [31] present a novel hierarchical ViT called Swin Transformer. It computes the representation with shifted windowing scheme to allow for cross-window connection. Due to the fixed window size, the architecture has linear computational complexity with respect to image size. + +# 2.3. Multimodal Interaction + +In early studies, multimodal systems use simple interaction methods such as concatenation, element-wise product, summation, and multilayer perception to learn the interaction [5, 61]. Fukui et al. [14] introduce a compact bilin + +ear pooling to learn a more complex interaction. Arevalo et al. [3] present a gated unit that can learn to decide how modalities influence the activation. [34, 35] use the cross-attention mechanism to enable dense, bi-directional interactions between the visual and textual modalities. De Vries et al. [10] introduce Conditional Batch Normalization at channel-level to modulate visual feature maps by a linguistic embedding. Vaezi Joze et al. [45] use squeeze and excitation operations to fuse the multimodal features and recalibrate the channel-wise visual features. There are also methods [3, 5, 10, 45, 61] that only perform interaction at channel-level. However, spatial-level information is also important to some downstream tasks, e.g., visual grounding and visual commonsense reasoning. Other methods [14, 34, 35] maintain the spatial structure to perform interaction but have a high computational cost. + +# 3. Approach + +# 3.1. Architecture + +In this section, we first formulate the visual grounding task and then present the architecture of the adopted framework. + +Visual grounding task aims at grounding a query onto a region of an image. The query refers to an object in the image and can be a sentence or a phrase. It can be formulated as: given an image $I$ and a query $q$ , the model needs to predict a bounding box $\mathbf{b} = \{x, y, w, h\}$ which exactly contains the target object expressed by the query. + +As shown in Figure 2 (a), our framework is designed based on a typical end-to-end visual grounding architecture TransVG [11]1. Given an image and a query sentence, there is a linguistic backbone, typically a pre-trained BERT model, extracting a sequence of 1D feature $\mathbf{T} \in \mathbb{R}^{D_l \times N_l}$ . For the visual backbone, we adopt a new Query-modulated Refinement Network (described in Section 3.2) to extract a flattened sequence of visual feature $\mathbf{V} \in \mathbb{R}^{D_v \times N_v}$ . The major difference between the proposed Query-modulated Refinement Network and existing visual backbones is that we take the contextual textual feature from the linguistic backbone to guide the feature extraction and multiscale fusion with the help of Query-aware Dynamic Attention (described in Section 3.2.1). Two projection layers map the visual and linguistic features into the same feature space $\mathbb{R}^D$ . The projected visual and linguistic features are denoted by $\mathbf{p}_v \in \mathbb{R}^{D \times N_v}$ and $\mathbf{p}_l \in \mathbb{R}^{D \times N_l}$ . Then $\mathbf{p}_v$ and $\mathbf{p}_l$ are concatenated by inserting a learnable embedding (i.e., a [REG] token) at the beginning of the concatenated sequence. The joint sequence is formulated as: + +$$ +\boldsymbol {X} = \left[ \mathbf {p} _ {r}, \underbrace {\mathbf {p} _ {v} ^ {1} , \mathbf {p} _ {v} ^ {2} , \cdots , \mathbf {p} _ {v} ^ {N _ {v}}} _ {\text {v i s u a l t o k e n s} \boldsymbol {p} _ {v}}, \underbrace {\mathbf {p} _ {l} ^ {c} , \mathbf {p} _ {l} ^ {1} , \cdots , \mathbf {p} _ {l} ^ {N _ {l}}} _ {\text {l i n g u i s t i c t o k e n s} \boldsymbol {p} _ {l}} \right], \tag {1} +$$ + +![](images/9146a1b8b7041ee469ca81429189464367512eec3eb6370e865af9fb3519c70d.jpg) +Figure 2. (a) The QRNet-based visual grounding framework used in this paper. (b) An overview of our Query-modulated Refinement Network. (c) Illustration of Query-aware Dynamic Attention. + +where $\mathbf{p}_r$ is the learnable embedding of [REG] token. $\mathbf{p}_l^c$ is the [CLS] token's representation which is regarded as the contextual textual feature. + +Next, a multi-layer visual-linguistic transformer is applied to perform intra- and inter-modal reasoning on the joint sequence. Finally, a prediction head takes the output representation of the [REG] token to predict the bounding box coordinates $\mathbf{b}$ . The smooth L1 loss [16] and giou loss [40] are used to train the framework. The training objective can be formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s m o o t h} - l 1} (\mathbf {b}, \hat {\mathbf {b}}) + \mathcal {L} _ {\text {g i o u}} (\mathbf {b}, \hat {\mathbf {b}}), \tag {2} +$$ + +where $\hat{\mathbf{b}}$ is the ground-truth box. + +# 3.2. Query-modulated Refinement Network + +In this section, we introduce the proposed visual backbone of Query-modulated Refinement Network (QRNet). An overview of the network is shown in Figure 2 (b). The network consists of two phases: (1) Query-refined Feature Extraction for extracting query-refined visual feature maps with a hierarchical structure, (2) Query-aware Multiscale Fusion for fusing the extracted feature maps at different scales with the guidance of the query feature. The two phases both rely on a novel Query-aware Dynamic Attention (QD-ATT), which dynamically computes textual-dependent visual attentions at spatial and channel levels, to enable to compute features with query guidance. In the following, we will first introduce the implementation of the Query-aware Dynamic Attention. Then we detail the Query-refined Feature Extraction and Multiscale Fusion. + +# 3.2.1 Query-aware Dynamic Attention + +Now, we will describe the details of our Query-aware Dynamic Attention (shown in Fig. 2(c)). We first introduce + +the dynamic linear layer, which learns a linear transformation that can be applied to the visual features to compute the query-aware attentions. Different from the conventional trainable linear layer, the parameters of the dynamic linear layer are generated dynamically based on textual features. Next, we will illustrate how to use the dynamic linear layer to compute query-aware channel and spatial attentions and obtain the query-consistent visual features. A pseudo-code is presented in the Appendix for better comprehension. + +Dynamic Linear Layer. Existing visual backbones use modules with static parameters to compute the visual feature maps, where feeding in the same image will output the same feature maps. However, in visual grounding, different queries for a single image may reveal different semantic information and intentions, which require different visual features. We present a dynamic linear layer which can leverage the contextual textual feature $\mathbf{p}_l^c\in \mathbb{R}^{D_l}$ to guide the mapping from an given input vector $\mathbf{z}_{in}\in \mathbb{R}^{D^{in}}$ to the output $\mathbf{z}_{out}\in \mathbb{R}^{D^{out}}$ . The dynamic linear layer is formalized as follow: + +$$ +\mathbf {z} _ {\text {o u t}} = \operatorname {D y L i n e a r} _ {\mathcal {M} _ {l}} \left(\mathbf {z} _ {i n}\right) = \mathbf {W} _ {l} ^ {\mathrm {T}} \mathbf {z} _ {i n} + \mathbf {b} _ {l} \tag {3} +$$ + +where $\mathcal{M}_l = \{\mathbf{W}_l,\mathbf{b}_l\}$ $\mathbf{W}_l\in \mathbb{R}^{D^{in}\times D^{out}}$ $\mathbf{b}_l\in \mathbb{R}^{D^{out}}$ $D^{in}$ and $D^{out}$ are the dimensions of input and output, respectively. + +We use a plain linear layer to generate the $\mathcal{M}_l$ . The generator is denoted by $\mathcal{M}_l' = \Psi(\mathbf{p}_l^c)$ , where $\mathcal{M}_l' \in \mathbb{R}^{(D^{in} + 1)*D^{out}}$ . In detail, we predict a $(D^{in} + 1)*D^{out}$ vector which can be reshaped to $\mathcal{M}_l$ . However, it is easy to find that the number of parameters in the generator, i.e., $D_l * ((D^{in} + 1)*D^{out})$ , is too large. Such large-scale parameters will slow down the speed of the network and make it easier to be overfitting. Inspired by matrix factorization, we consider decomposing the $\mathcal{M}_l$ into two factors + +$\mathbf{U} \in \mathbb{R}^{(D^{in} + 1) \times K}$ and $\mathbf{S} \in \mathbb{R}^{K \times D^{out}}$ , where $\mathbf{U}$ is a matrix generated from $\mathbf{p}_l^c$ , $\mathbf{S}$ is a static learnable matrix, $K$ is a hyper-parameter denoting the factor dimension. The factor generator $\{\mathbf{W}_l, \mathbf{b}_l\} = \Psi^*(\mathbf{p}_l^c)$ can be formulated as follows: + +$$ +\mathbf {U} = \operatorname {R e s h a p e} \left(\mathbf {W} _ {g} ^ {\intercal} \mathbf {p} _ {l} ^ {c} + \mathbf {b} _ {g}\right), +$$ + +$$ +\mathcal {M} _ {l} = \mathbf {U S}, \tag {4} +$$ + +$$ +\{\mathbf {W} _ {l}, \mathbf {b} _ {l} \} = \operatorname {S p l i t} (\mathcal {M} _ {l}), +$$ + +where $\mathbf{W}_g\in \mathbb{R}^{D_l\times (D^{in} + 1)*K}$ and $\mathbf{b}_g\in \mathbb{R}^{(D^{in} + 1)*K}$ are trainable parameters of the factor generator. The parameter matrix $\mathcal{M}_l$ of the dynamic linear layer can be reconstructed by multiplying $\mathbf{U}$ and $\mathbf{S}$ . The $\mathbf{W}_l$ and $\mathbf{b}_l$ can be split from the matrix $\mathcal{M}_l$ along the first dimension. Finally, we reformulate the dynamic linear layer as follows: + +$$ +\mathbf {z} _ {\text {o u t}} = \operatorname {D y L i n e a r} _ {\mathcal {M} _ {l}} \left(\mathbf {z} _ {i n}\right) = \operatorname {D y L i n e a r} _ {\Psi^ {*} \left(\mathbf {p} _ {l} ^ {c}\right)} \left(\mathbf {z} _ {i n}\right). \tag {5} +$$ + +Unless otherwise specified, we use DyLinear $(\mathbf{z}_{in})$ to represent a dynamic linear layer with $\mathbf{p}_l^c$ for simplify. And the different dynamic linear layers do not share parameters. When the input is a multidimensional tensor, the dynamic linear layer transforms the input at the last dimension. + +Channel and Spatial Attention. As explained above, the pre-trained visual backbone is sensitive to all the objects it learned in the pre-training task. However, only the object which is referred to by the query text is useful. Besides, the features useful for the bounding box prediction highly depend on the semantics contained in the query sentence (e.g. entities, descriptions of attributes, and relationships). In other words, the importance of each channel or each region of the feature map should change dynamically according to the query sentence. Inspired by Convolutional Block Attention Module [51], we consider inferring channel and spatial attentions, i.e., $\mathbf{A}^{cl}$ and $\mathbf{A}^{sl}$ , along the separate dimensions of the feature map to obtain adaptively refined features for a better cross-modal alignment. + +Specifically, for a given visual feature map $\mathbf{F} \in \mathbb{R}^{H \times W \times D_v}$ , we first aggregate its spatial information by average and maximum pooling and produce $\mathbf{F}_{max}^c$ , $\mathbf{F}_{mean}^c \in \mathbb{R}^{1 \times 1 \times D_v}$ . Then, a dynamic multilayer perception consisting of two dynamic linear layers with a ReLU activation in the middle is built to process the pooled features. The output dimension is the same as the input dimension. To reduce the number of parameters, we set the dimension of multilayer perception's hidden states as $D_v / r$ , where $r = 16$ is a reduction ratio. By feeding the $\mathbf{F}_{max}^c$ and $\mathbf{F}_{mean}^c$ to the dynamic multilayer perception, a Sigmoid function is applied to the summation of the two output features. The channel + +attention map $\mathbf{A}^{cl}$ can be captured as follow: + +$$ +\mathbf {F} _ {m e a n} ^ {c l} = \mathrm {D y L i n e a r} _ {1} (\mathrm {R e L U} (\mathrm {D y L i n e a r} _ {2} (\mathbf {F} _ {m e a n} ^ {c})) +$$ + +$$ +\mathbf {F} _ {\text {m a x}} ^ {c l} = \operatorname {D y L i n e a r} _ {1} (\operatorname {R e L U} (\operatorname {D y L i n e a r} _ {2} \left(\mathbf {F} _ {\text {m a x}} ^ {c}\right)) \tag {6} +$$ + +$$ +\mathbf {A} ^ {c l} = \operatorname {S i g m o i d} \left(\mathbf {F} _ {m e a n} ^ {c l} + \mathbf {F} _ {m a x} ^ {c l}\right). +$$ + +We perform element-wise multiplication between $\mathbf{F}$ and $\mathbf{A}^{cl}$ to form the channel-wise refined visual feature, where the $\mathbf{A}^{cl}$ is broadcast along the spatial dimension: + +$$ +\mathbf {F} ^ {\prime} = \mathbf {A} ^ {c l} \otimes \mathbf {F}. \tag {7} +$$ + +To generate a spatial attention map, instead of squeezing the channel dimension, we leverage another dynamic linear layer to reduce the channel dimension to learn areas of interest to the query and apply an activation function Sigmoid to generate the attention map. In short, the computing process is formulated as follows: + +$$ +\mathbf {A} ^ {s l} = \operatorname {S i g m o i d} \left(\operatorname {D y L i n e a r} _ {3} \left(\mathbf {F} ^ {\prime}\right)\right) \tag {8} +$$ + +$$ +\mathbf {F} ^ {\prime \prime} = \mathbf {A} ^ {s l} \otimes \mathbf {F} ^ {\prime} +$$ + +where $\mathbf{A}^{sl}\in \mathbb{R}^{H\times W\times 1}$ is the spatial attention map and $\mathbf{F}^{\prime \prime}$ is the spatially refined visual feature and also the output of our Query-aware Dynamic Attention. + +# 3.2.2 Query-refined Feature Extraction + +To extract refined feature maps with the guidance of the query feature, we extend the Swin-Transformer $^2$ to a modulated visual feature extractor. As shown in Figure 2 (b), for a given image $I \in \mathbb{R}^{H \times W \times 3}$ , a patch partition operation is firstly adopted to embed $I$ to $\mathbf{F}_0 \in \mathbb{R}^{\frac{H}{4} \times \frac{W}{4} \times C}$ , where $C$ is the embed dimension. Then $\mathbf{F}_0$ is fed into four cascaded stages, where each stage consists of multiple Swin-Transformer blocks and a QD-ATT module. In this work, we take the [CLS] representation of the input query sentence from BERT [12] as the contextual query representation $\mathbf{p}_l^c$ to compute the query-aware dynamic attention. The $k$ -th stage receives the visual feature map $\mathbf{F}_{k-1}^*$ (or $\mathbf{F}_0$ if $k = 1$ ) obtained in the previous stage and generates a transformed feature map $\mathbf{F}_k$ through the Swin-Transformer blocks. Then, the QD-ATT module takes the transformed feature $\mathbf{F}_k$ and produces a query-aware feature $\mathbf{F}_k^*$ that will be further used in the next stage. The output of the query-refined feature extractor is a list of hierarchical features $[\mathbf{F}_1^*, \mathbf{F}_2^*, \mathbf{F}_3^*, \mathbf{F}_4^*]$ . + +# 3.2.3 Query-aware Multiscale Fusion + +Multiscale features are beneficial to detecting objects at different scales [6]. However, because visual grounding requires fine-grained interaction after visual backbone (e.g. + +Cross Attention), high-resolution features will dramatically increase the computation. Therefore, previous works always use the low-resolution features or fuse the multiscale features in a query-agnostic manner, which will lose scale information or incorporate noise. Thanks to the hierarchical structure of the modulated Swin-Transformer, we can obtain multiscale features. We fuse the features obtained from different stages with the help of Query-aware Dynamic Attention mechanism and pooling operation. We flatten and concatenate the low-resolution features as the output token sequence of the backbone. Specifically, except for the first stage, each stage reduces the resolution of the feature map by a patch merging operator. In other words, the resolutions of the output feature maps at four stages are $\frac{H}{4} \times \frac{W}{4}$ , $\frac{H}{8} \times \frac{W}{8}$ , $\frac{H}{16} \times \frac{W}{16}$ and $\frac{H}{32} \times \frac{W}{32}$ , respectively. Besides, the patch merging operator fuses the patch features into the channel which doubles the channel dimension. Thus the channel dimensions of the output at the four stages are $C$ , $2C$ , $4C$ and $8C$ , respectively. Next, we will introduce how to efficiently fuse these multiscale features with the guidance of the query text. + +As shown in Figure 2 (b), we propose to fuse the output features at different stages with the help of QD-ATT. Specifically, we first use four $1 \times 1$ convolutional layers to unify the channel dimensions to $D$ . To filter out noisy signals in the feature maps, we build QD-ATT modules for the feature maps $\{\mathbf{F}_k^* | k = 1, 2, 3\}$ of the first three stages. From $\mathbf{F}_k^*$ , the QD-ATT module produces a weighted feature map with the same size as the input. We apply a $2 \times 2$ mean pooling with stride=2 to reduce the resolution to be the same as the next feature map $\mathbf{F}_{k+1}^*$ and compute the average of them to obtain $\bar{\mathbf{F}}_{k+1}^*$ . Finally, the last feature map $\bar{\mathbf{F}}_4^*$ contains features of interest to the query from all scales. To detect very large objects, we also apply a $2 \times 2$ max pooling to obtain a $\frac{H}{64} \times \frac{W}{64}$ feature map $\bar{\mathbf{F}}_5^*$ . We flatten and concatenate the $\bar{\mathbf{F}}_4^*$ and $\bar{\mathbf{F}}_5^*$ as the output token sequence $\mathbf{V}$ . + +# 4. Experiments + +# 4.1. Datasets and Evaluation + +We evaluate our method on phrase grounding dataset Flickr30K Entities[36] and referring expression grounding datasets RefCOCO[59], RefCOCO+[59], RefCOCOg[32] and ReferItGame[25]. The details and statistics are summarized in Appendix. In phrase grounding the queries are phrases and in referring expression grounding, they are referring expressions corresponding to the referred objects. We follow the same metric used in [11]. Specifically, a prediction is right if the IoU between the grounding-truth box and the predicted bounding box is larger than 0.5. + +# 4.2. Implementation Details + +The QRNet is built based on Swin-Transformer, i.e., Swin-S pre-trained with Mask-RCNN on MSCOCO [27] $^3$ . We use $\mathrm{BERT}_{\mathrm{base}}$ (uncased) for linguistic feature extraction. We set the intermediate dimension $D = 256$ and the factor dimension $K = 30$ . We follow the TransVG [11] to process the input images and sentences. We also follow the training setting used in TransVG, which uses a AdamW optimizer with weight decay $10^{-4}$ , sets the batch size to 64 and the dropout ratio to 0.1 for FFN in Transformer. The learning rate is set to $10^{-5}$ for pre-trained parameters and $10^{-4}$ for other parameters. The parameters without pretraining are randomly initialized with Xavier. We train our model for 160 epochs. The learning rate is multiplied by a factor of 0.1 at epoch 40 for Flickr30K Entities and at epoch 60 for other datasets. We also follow the commonly used data augmentation strategies in [26, 54, 55]. + +# 4.3.Quantitative Results + +We show the comparison results on ReferItGame and Flickr30k Entities in Table 1. The ReferItGame collects queries by a cooperative game, requiring one player to write a referring expression for a specified object. The other one needs to click on the correct object. Queries in Flickr30k Entities are phrases in the caption. We observe that the proposed QRNet outperforms previous works. We replace the visual branch of TransVG with Swin-Transformer and denote it by TransVG(Swin) to explore the impact of backbone. The performance is similar to the original TransVG, indicating that the accuracy gains are not from Swin-Transformer. + +We also present the accuracy comparison with state-of-the-art methods on ReferCOCO, ReferCOCO+, and ReferCOCOg in Table 2. In ReferCOCO and ReferCOCO+ datasets, referred objects are people in "testA" and could be common objects in "testB". The expressions in ReferCOCOg are much longer than the ones in other datasets. Note that TransVG uses a ResNet-101 and a DETR encoder split from a pre-trained DETR framework. Its backbone is more powerful than a single ResNet-101. + +We observe that our QRNet greatly outperforms all two-stage and one-stage state-of-the-art methods. On RefCOCO and RefCOCO+ datasets, our method gains $1.84\% \sim 2.52\%$ absolute improvement in "testA" and $2.51\% \sim 4.32\%$ in "testB". When the referred objects are arbitrary, the inconsistent issue will be more serious, and our modulated backbone can better filter irrelevant objects and correct the representation with textual guidance. In the RefCOCOg test split, we notice that ISRL [42] performs better than TransVG [11]. It models the visual grounding as a Markov + +
ModuleBackboneReferItGame testFlickr30K test
Two-stage
VC [62]VGG1631.13-
MAttNet [58]ResNet-10129.04-
Similarity net [48]ResNet-10134.5450.89
LCMCG [30]ResNet-101-76.74
DIGN [33]VGG-1665.1578.73
One-stage
FAOA [55]DarkNet-5360.6768.71
RCCF [26]DLA-3463.79-
ReSC-Large [54]DarkNet-5364.6069.28
SAFF [56]DarkNet-5366.0170.71
TransVG [11]ResNet-10170.7379.10
TransVG (Swin)Swin-S70.8678.18
QRNet (ours)Swin-S74.6181.95
+ +Table 1. The performance comparisons (Acc@0.5) on ReferItGame and Flickr30K Entities. + +decision process that handles long expressions iterative by filtering out irrelevant areas. However, the limited action space makes it easy to converge to a local optimum. Our model does not modify the Visual-Linguistic Transformer in the TransVG and only provides query-consistent visual features. The performance is greatly improved, which demonstrates that our query-aware refinement is more effective to model the representation for visual grounding. + +# 4.4. Ablation Study + +We conduct ablation studies on ReferItGame and Flickr30k to reveal the effectiveness of the proposed QR-Net. + +We first study the effectiveness of QD-ATT in query-refined feature extraction and query-aware multiscale fusion. As shown in Table 3, we use a checkmark to denote enabling QD-ATT in the corresponding module, and a cross mark to denote disabling QD-ATT and passing the feature without modification. When disabling QD-ATT in multiscale fusion, the performance is dropped by $2.52\%$ in ReferItGame-test and $0.79\%$ in Flickr30k-test, respectively. When disabling QD-ATT in query-refined feature extraction, the performance is dropped by $3.22\%$ and $1.51\%$ . When completely disabling QD-ATT, the performance is dropped by $3.75\%$ and $3.77\%$ . We find that QD-ATT is more important in query-refined feature extraction than in multiscale fusion. We also notice that, when compared with completely disabling QD-ATT, only enabling QD-ATT in multiscale fusion gains little improvement because the features from the transformer are still noise and query-inconsistent. + +We further study the effectiveness of spatial attention and + +![](images/49f5d0e1320a6a5ee5c9aa90a351604171d5050b80c9cb90ee88fe79cf2eeb7a.jpg) +Figure 3. Visualization of activation maps from the backbone of our QRNet and other popular models. Red: the predicted box. White: the ground-truth box. + +channel attention in the QD-ATT. Spatial attention can filter out irrelevant areas. And channel attention can redistribute the importance of the features to fit different query sentences. The results shown in the Table 4 demonstrate that spatial and channel attention are both effective. + +# 4.5. Qualitative Results + +We show the qualitative comparison between our QRNet and three popular methods in Figure 3. The feature maps are extract from the backbone of each model. We can see that previous methods are sensitive to many query-unrelated areas, which may lead to wrong predictions, e.g., the results of TransVG and ReSC for the queries of "glass upper righ" and "light blue tall board", and the result of Swin-S for the query of "upper left cake". In contrast, our QRNet generates query-consistent features and makes more accurate predictions. More results can be found in the supplementary. + +# 5. Online Deployment + +Previous experimental results have proven the advantages of our proposed QRNet, so we deploy it in a real-world online environment to test its practical performance. Specifically, we apply QRNet to enhance the search engine in Pailitao at Alibaba and perform A/B testing to evaluate the impact of our model. Details can be found in supplementary materials. We observe that QRNet decreases the no click rate by $1.47\%$ and improves the number of transactions by $2.20\%$ over the baseline. More specifically, the decrease of no click rate implies that QRNet can generate more accurate target boxes so that users are more likely to click. The improvement of the number of transactions means that the clicked item is exactly the users want to purchase, which also reveals the great performance of QRNet. + +
ModelsBackboneRefCOCORefCOCO+RefCOCOg
valtestAtestBvaltestAtestBval-gval-utest-u
Two-stage
VC [62]VGG16-73.3367.44-58.4053.1862.30--
MAttNet [58]ResNet-10176.6581.1469.9965.3371.6256.02-66.5867.27
Ref-NMS [7]ResNet-10178.8282.7173.9466.9571.2958.40-68.8968.67
LGRANs [49]VGG16-76.6066.40-64.0053.4061.78--
RvG-Tree [21]ResNet-10175.0678.6169.8563.5167.4556.66-66.9566.51
CM-Att-Erase [29]ResNet-10178.3583.1471.3268.0973.6558.0368.67--
NMTree [28]ResNet-10176.4181.2170.0966.4672.0257.5264.6265.8766.44
One-stage
FAOA [55]DarkNet-5372.5474.3568.5056.8160.2349.6056.1261.3360.36
RCCF [26]DLA-34-81.0671.85-70.3556.32--65.73
ReSC-Large [54]DarkNet-5377.6380.4572.3063.5968.3656.8163.1267.3067.20
SAFF [56]DarkNet-5379.2681.0976.5564.4368.4658.43-68.9468.91
HFRN [37]ResNet-10179.7683.1275.5166.8072.5359.09-69.7169.08
ISRL [42]ResNet-101-74.2768.10-71.0558.25--70.05
LBYL-Net [23]DarkNet-5379.6782.9174.1568.6473.3859.4962.70--
TransVG [11]ResNet-10181.0282.7278.3564.8270.7056.9467.0268.6767.73
TransVG (Swin)Swin-S82.3384.0179.8364.9470.1956.4767.8169.3468.99
QRNet (ours)Swin-S84.0185.8582.3472.9476.1763.8171.8973.0372.52
+ +Table 2. The performance comparisons (Acc@0.5) on ReferCOCO, ReferCOCO+, and ReferCOCOg. The results of previous best two-stage and one-stage methods are highlighted with underlines. We highlight our results in bold. The results demonstrate that our method outperforms all state-of-the-art one-stage and two-stage methods. + +
ModelsFeature ExtractionMultiscale FusionReferIt GameFlickr30k
valtestvaltest
QRNet✓✓76.8474.6180.8381.95
(a)✓X74.3172.0980.0981.16
(b)X✓73.6371.3979.3580.44
(c)XX73.2570.8677.1778.18
+ +Table 3. Ablation studies of QD-ATT in two phases of QRNet. + +
ModelsChannel AttentionSpatial AttentionReferIt GameFlickr30k
valtestvaltest
QRNet✓✓76.8474.6180.8381.95
(d)✓X74.3572.0280.2281.35
(e)X✓74.4171.8080.6781.55
+ +Table 4. Ablation studies of different attentions in QD-ATT. + +# 6. Conclusion + +In this paper, we argue that pre-trained visual backbones cannot produce visual features that are consistent with the requirement of visual grounding. To overcome the weak + +nesses, we propose a Query-modulated Refinement Network (QRNet) to adjust the visual feature maps with the guidance of query text. The QRNet is designed based on a novel Query-aware Dynamic Attention mechanism, which can dynamically compute query-dependent spatial and channel attentions for refining visual features. Extensive experiments indicate that the improved framework significantly outperforms the state-of-the-art methods. The proposed QRNet exhibits vast potential to improve multimodal reasoning. In future work, we plan to improve the fine-grained interaction ability of QRNet and discard the post-interaction modules to simplify the existing end-to-end visual grounding frameworks. + +Acknowledgement We thank Zenghui Sun, Quan Zheng and Weilin Huang at Alibaba Group for their help on online deployment and the anonymous reviewers for their valuable suggestions. This work was supported by the National Innovation 2030 Major S&T Project of China (No.2020AAA0104200 & 2020AAA0104205), the Science and Technology Commission of Shanghai Municipality (No. 19511120200 & 21511100100 & 18DZ2270800), the Open Fund of PDL, and Alibaba Group through Alibaba Research Intern Program. + +# References + +[1] Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. Bottom-up and top-down attention for image captioning and visual question answering. 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However, most transformer-based captioning methods ever overlook two kinds of elusive confounders: the visual confounder and the linguistic confounder, which generally lead to harmful bias, induce the spurious correlations during training, and degrade the model generalization. In this paper, we first use Structural Causal Models (SCMs) to show how two confounders damage the image captioning. Then we apply the backdoor adjustment to propose a novel causal inference based image captioning (CIC) framework, which consists of an interventional object detector (IOD) and an interventional transformer decoder (ITD) to jointly confront both confounders. In the encoding stage, the IOD is able to disentangle the region-based visual features by deconfounding the visual confounder. In the decoding stage, the ITD introduces causal intervention into the transformer decoder and deconfounds the visual and linguistic confounders simultaneously. Two modules collaborate with each other to alleviate the spurious correlations caused by the unobserved confounders. When tested on MSCOCO, our proposal significantly outperforms the state-of-the-art encoder-decoder models on Karpathy split and online test split. Code is published in https://github.com/CUMTGG/CIIC. + +# 1. Introduction + +Image captioning aims to automatically understand the semantic information of an image and generate its accurate description. Inspired by neural machine translation [36], the encoder-decoder architecture has been widely adopted by most conventional image captioning models [2, 10, 39, 41], in which a deep convolutional neural network (CNN) serves + +
Cake +ForkGT1: A white plate covered in cake and a fork.
GT2: A slice of cake sitting on a plate next to a fork.
GT3: A piece of white cake on a plate has a fork.
Cake +ForkGT1: The remains of a piece of cake and a fork.
GT2: A tasty looking piece of cake with a fork next to it.
GT3: Two forks on a plate of cake.
+ +(a) + +
CakeGT: A bowl with a piece of cake in it next to a spoon.
Sta +SpoonTransformer: A piece of cake on a plate with a fork.
CIIC: A piece of cake on a plate with a spoon.
+ +(b) + +Figure 1. The example about the spurious correlation in image captioning. (a) Examples of the visual confounder (the visual feature of cake) and linguistic confounder (the word embedding of "cake") in the MSCOCO training dataset when generating the word "fork", where "GT1", "GT2" and "GT3" denote three ground truth captions of each image chosen from the dataset. (b) Some captions generated by the original Transformer [37] and CIIC. The generated correct and incorrect words are colored by blue and red, respectively. "GT" means the ground truth caption. + +as the encoder to extract visual features from the input image, and a recurrent neural network (RNN) is used as the decoder to generate the corresponding caption. Based on this architecture, a large number of improvements have been made by recent works, which mainly focus on two-fold: (i) Optimizing the visual representations of the input image [2,15,18,42], and (ii) enhancing the architectural modeling capabilities for inter-modal and intra-modal interactions [8,28]. + +In the aspect of visual representation, most captioning models apply a well-trained detector, e.g., Faster R-CNN [33], to extract visual features. Nevertheless, these models neglected the problem of entangled visual features in the visual feature extraction stage. As shown in Figure 1a, the features of a region of the fork extracted by Faster R- + +CNN tend to be its surrounding cake-like features since forks and cake co-occur too many times, i.e., the feature representations of forks are severely affected by the visual feature of cake. In this case, the visual feature of the cake is actually one visual confounder, which builds a "short-cut path" [11] that leads to the spurious correlations between object features and target categories, e.g., the learned cake-like features correspond to the class label of the fork. Consequently, it is critical to disentangle the visual features in the stage of visual representation to alleviate the spurious correlation between the cake region and the word "fork". + +In the aspect of model structure improvement, transformer-based models [13, 15, 17, 23, 27] have obtained the superior performance over the CNN-RNN based captioning methods. However, most transformer-based captioning models may still learn dataset bias caused by the hidden confounders. As shown in Figure 1a, when there are more forks than spoons co-occur with cake, due to both the visual confounder (i.e., the visual feature of cake) and linguistic confounder (i.e., the word embedding of "cake"), the traditional captioning models tend to learn the spurious correlation between the cake region and the word "fork" during training. Thus, as shown in Figure 1b, the original transformer usually generates the incorrect word "fork" instead of the correct word "spoon" for the test image. + +Recently, Yang et al. [44] analyzed the spurious correlation between the visual features and captions by causal graph and proposed a deconfounded image captioning (DIC) framework to tackle the confounders. But they still have two limitations: (i) In their causal graph, the whole dataset is considered as the confounder and hard to be stratified. Thus, the complex front-door adjustment is utilized to deconfound it by introducing an additional mediator. (ii) DIC focuses on deconfounding the decoder while neglecting the confounded visual features in the encoder, leading to limited performance improvements. + +To solve these problems, we first divide the confounder of the existing causal graph into two classes: visual confounder and linguistic confounder. Based on the detailed causal graph, we propose a novel causal inference based image captioning (CIIC) framework, which mainly consists of two components: an interventional object detector (IOD) and an interventional Transformer decoder (ITD) to jointly confront two kinds of confounders. Specifically, the IOD incorporates causal inference into Faster R-CNN [33] to cope with the visual confounder, aiming to obtain the disentangled region-based representations. The ITD implements causal intervention in the Transformer decoder by deconfounding both the visual and linguistic confounder simultaneously. As shown in Figure 1b, CIIC can effectively eliminate the spurious correlations caused by the visual and linguistic confounders and generate the correct word "spoon". + +Our contributions can be summarized as follows: + +- We decompose the confounder into the visual and linguistic confounders and show a more detailed causal graph for the transformer-based image captioning system, which can be easily deconfounded by the backdoor adjustment, instead of the more complex front-door adjustment. +- We propose an IOD to disentangle the region-based features in the encoder and design a novel ITD by deconfounding the causal graph, which can effectively eliminate the spurious correlations caused by both visual and linguistic confounders. +- We implement our transformer-based CIIC framework to facilitate the unbiased captioning generation and extensively evaluate our approach on the MSCOCO benchmark [24]. CIIC achieves a new state-of-the-art performance compared to previous transformer-based captioning approaches. + +# 2. Related Work + +# 2.1. Image Captioning + +The mainstream image captioning methods generally follow the encoder-decoder paradigm [2, 12, 39, 41, 50], where image features extracted by a CNN are fed into a recurrent net (often based on LSTM units) to generate the corresponding sentence. Since RNN-based models are limited by their sequential nature, the convolutional language model has been explored to replace conventional RNNs as well [3]. Different from the local operator essence of convolution, new transformer-based captioning models, based on the fully-attentive paradigm, have recently been proposed and achieved quite promising results [9, 13, 17, 25]. For example, spatial relationships between region features [13,15] and relative geometry features between grids [27] were explicitly incorporated with geometric attention to enhance visual representations. Li et al. [23] introduced Entangled Attention that exploits visual and semantic information simultaneously. Pan et al. [28] applied Bilinear Pooling to encode region-level and image-level features. Despite great progress made on the basis of fully-attentive paradigms, how to cope with dataset biases caused by the visual and linguistic confounders in image captioning is still largely under-explored. + +# 2.2. Causal Inference + +Recently, some researchers have incorporated causal inference into deep learning models in the computer vision community [6,26,32,47,49,51]. These efforts make it possible to endow DNNs with the abilities to learn the causal effects, which significantly advance the performances of many CV and NLP models, including image classification [4, 26], image semantic segmentation [47], visual feature representation [40], visual dialog [32], image captioning + +![](images/72b6b5569e2090b800f903158a07b2c854319beefb840c089d1b878f80585709.jpg) +Figure 2. Illustration of the CIIC framework for image captioning. The RoI features are first disentangled by the interventional object detector, which are then combined with the bottom-up features of Faster R-CNN as inputs of the transformer encoder. In the decoder of CIIC, we propose a causal intervention module to confront both the visual and linguistic confounders for word prediction. The notation “ $L \times$ ” denotes that the block in the dotted box is stacked with $L$ times. Our CIIC is able to effectively eliminate the spurious correlations that occurred in both the visual feature representation and caption generation to get more grounded image captions. + +![](images/510d7410c63ae0090a96d58f556d2ea23e0fa9b9d4ef55d199c0bbe8a7f66c73.jpg) +Figure 3. The causal intervention $P(Y|do(X))$ in object detection. The backdoor path $X \leftarrow Z \rightarrow Y$ is blocked by cutting off $Z \rightarrow X$ , i.e., the backdoor adjustment, which is able to effectively deconfound the unobserved confounder as a fundamental causal inference technique [30]. + +![](images/ae4445d6263b1e2fad4ee23301bb8da6b9f90b3027b152cab39720d6e33741eb.jpg) + +[44] and dialogue generation [51]. For example, Wang et al. [40] presented Visual Commonsense Region-based Convolutional Neural Network (VC R-CNN) to boost the performance of visual feature representation learning, in which causal intervention, instead of the conventional likelihood, is used to predict the contextual objects of a region. Yang et al. built a Deconfounded Image Captioning (DIC) framework [44] and a causal attention mechanism [45] respectively to cope with the confounders. However, these models still lack a detailed analysis of the confounders in both visual and linguistic domains. Consequently, we present the IOD to directly disentangle the visual features of the RoI proposals. The IOD incorporates causal intervention into self-predictor instead of the more complicated context predictor in VC R-CNN. As a result, the IOD can extract the + +visual features from both single-object and multi-object images. Compared with the works by Yang et al. [44, 45], we devise the more detailed causal graphs for the transformer-based image captioning system and propose the ITD to simultaneously eliminate the spurious correlations caused by both the visual and linguistic confounders. + +# 3.CIIC + +As illustrated in Figure 2, CIIC is composed of a transformer encoder and a transformer decoder, in which causal inference is introduced into the visual representation step and sentence generation step, respectively. + +# 3.1. Interventional Object Detector + +Causal Intervention in Object Detection. In the causal graph [6,26], a variable is defined as the confounder if such variable is a common cause for the other two variables. As illustrated in Figure 3a, we formulate the causalities among the region-based visual features $X$ , the visual confounder $Z$ of an image, and class labels $Y$ based on SCM [6], where the direct edges represent the causalities between the two variables. On one hand, we denote the causal effect of $Z$ on $X$ as $Z \rightarrow X$ since the extracted visual features are inevitably affected by the visual contexts from the real world when the classifier of Faster R-CNN is trained. On the other + +![](images/86fd2ce84bddf12fd539a6352fea82f1f0726a23e719952e3f3a2d6bd9e2623c.jpg) +Figure 4. The architecture of our interventional object detector, where Faster R-CNN is used as the visual backbone [33] to extract visual features from regions of interest (RoIs). Subsequently, the extracted RoI feature is utilized to predict the class probability output $y^{C}$ and the bounding box $y^{B}$ , respectively. Depending on the class probability output $y^{C}$ and the confounder dictionary $Z$ , we perform causal intervention based on the do calculus to accurately predict the final object class label $y^{I}$ . + +hand, we have the causal effect $Z \rightarrow Y$ because the visual contexts also affect the classifier's probability outputs. Hence, in the case of dataset bias, Faster R-CNN tends to learn some spurious correlation between $X$ and $Y$ caused by $Z$ , i.e., overexploiting the co-occurrence between the visual contexts and class labels to learn biased visual representations of image regions. + +As shown in Figure 3a, conventional object detectors, such as Faster R-CNN, essentially use the likelihood $P(Y|X)$ as the training objective of classifier, which is usually affected by the confounder $Z$ and gives rise to the spurious correlations. To see this, we formulate $P(Y|X)$ as: + +$$ +P (Y | X) = \sum_ {z} P (Y | X, Z = z) P (Z = z | X), \tag {1} +$$ + +where the confounder $Z$ generally brings about the observational bias via $P(z|X)$ . For instance, when $P(z = \text{cake}|X = \text{fork})$ is large while $P(z = \text{spoon}|X = \text{fork})$ is small. According to Eq. (1), $P(Y = l_{\text{fork}}|X = \text{fork}, z = \text{cake})$ , where $l_{\text{fork}}$ denotes the class label of fork, plays a more important role than $P(Y = l_{\text{fork}}|X = \text{fork}, z = \text{spoon})$ in estimating $P(Y|X)$ . Thus, the classifier learns the correlation between the visual features of cake and the class label of fork by mistake, i.e., the learned RoI features of one fork are actually its surrounding cake-like visual features. + +Motivated by the recent success of applying causal inference in deep learning [6, 26, 32, 47], we introduce causal intervention $P(Y|do(X))$ into object detection to block the backdoor path $X \gets Z \to Y$ , where the do calculus $\mathbf{d}\mathbf{o}(\bullet)$ plays a role of cutting off $Z \to X$ . As shown in Figure 3b, the backdoor adjustment is exploited to achieve $P(Y|do(X))$ as follows [40]: + +$$ +P (Y | d o (X)) = \sum_ {z} P (Y | X, Z = z) P (Z = z). \tag {2} +$$ + +In Eq. (2), $P(Y|do(X))$ forces $X$ to fairly "borrow" each $z$ in the confounder set and "put" them together for the + +prediction of $Y$ . In this way, the classifier removes the confounding effect and learns the true causality from $X$ to $Y$ , leading to the visual representations of high quality. However, Eq. (2) requires expensive sampling to estimate $P(Y|do(X))$ when applying it to a deep object detection network, which will make training time prohibitive. Fortunately, by applying the Normalized Weighted Geometric Mean (NWGM) approximation [40, 41], Eq. (2) can be approximated as: + +$$ +\begin{array}{l} P (Y | d o (X = x)) \\ \approx P \left(Y | c o n c a t \left(x, \frac {1}{n} \sum_ {i = 1} ^ {n} P \left(y _ {i} ^ {c} \mid x\right) z _ {i}\right)\right), \tag {3} \\ \end{array} +$$ + +where $\text{concat}(\cdot)$ denotes vector concatenation, $y_{i}^{c}$ is the $i$ -th class label and $P(y_{i}^{c}|x)$ is the pre-trained classifier's probability output that $x$ belongs to class $y_{i}^{c}$ . Note that we approximate the confounder in Eq. (2) to a predefined confounder dictionary $Z = [z_{1}, z_{2}, \dots, z_{n}]$ , where $n$ is the class number and $z_{i} \in \mathbb{R}^{d}$ denotes the average RoI feature of the $i$ -th class pretrained by Faster R-CNN. + +IOD Architecture. In Figure 4, we propose a novel IOD network to extract the disentangled visual features, where Faster R-CNN [33] is used as the visual backbone. In IOD, we use the same bounding box regressor as Faster R-CNN to specify each RoI on the feature map. As shown in Figure 4, the RoI feature $x$ is then fed into two parallel branches to predict the class probability output $y^{C}$ and bounding box $y^{B}$ , respectively. Finally, based on the RoI feature $x$ , the class probability output $y^{C}$ , and the predefined confounder dictionary $Z$ , we make the do calculus to implement the interventional class predictor and output the final object class label $y^{I}$ , namely, the IOD applies Eq. (3) as the new classification objective to replace the classifier of Faster R-CNN. In this way, the RoI feature $x$ can be effectively disentangled and subsequently adopted to facilitate the Transformer decoder to generate the unbiased caption. + +# 3.2. Transformer Encoder with Multi-view Visual Representation + +Now we are ready to utilize the IOD to extract the disentangled object features (called the IOD features) from any RoI proposal. Considering the bottom-up visual features obtained by the Up-Down approach [2] have the discriminative ability of different object attributes, we integrate the IOD features with the bottom-up features extracted from the same image to facilitate the visual representation of the CIIC model. Since the bottom-up and IOD features are unaligned, we introduce a multi-view transformer encoder, namely, Unaligned Feature Transformer (UFT) encoder, to adapt them. + +As illustrated in Figure 2, the UFT encoder takes the unaligned visual features as inputs and performs the alignment and fusion operations simultaneously. Assume that + +![](images/a8e8ee96a598b7c6a6b423859dcfd97dbadd4755aee4b5839fb33cba7273047d.jpg) +(a) Confounded + +![](images/1fca0604e3f1ec539449ade49d56f0474a05f5b7fc6142f8778f786c8f5b852a.jpg) +(b) Deconfounded +Figure 5. The causal intervention $P(W|do(V), do(h_1))$ in image captioning. Aiming at capturing the true causal effect: $V \rightarrow W$ , we block the backdoor path $V \leftarrow h_1 \leftarrow D_2 \rightarrow W$ and $V \leftarrow D_1 \rightarrow W$ by cutting off $D_2 \rightarrow h_1$ and $D_1 \rightarrow V$ simultaneously. + +the extracted bottom-up features and IOD features from an image can be respectively denoted as $X_{F}\in \mathbb{R}^{m\times d_{1}}$ and $X_{I}\in \mathbb{R}^{n\times d_{2}}$ , where $m\neq n$ and $d_1\neq d_2$ . Two linear layers are utilized to transform $X_{F}$ and $X_{I}$ into a common $d$ -dimensional space, denoted as $\bar{X}_F$ and $\bar{X}_I$ , respectively. Subsequently, we choose $\bar{X}_F$ as the features of the primary view and exploit it to learn the cross-attention over $\bar{X}_I$ : + +$$ +\tilde {X} _ {I} = \text {M u l t i H e a d} \left(\bar {X} _ {F}, \bar {X} _ {I}, \bar {X} _ {I}\right), \tag {4} +$$ + +where MultiHead $(\cdot)$ denotes the multi-head attention function of standard transformer, and $\tilde{X}_I \in \mathbb{R}^{m \times d}$ is the attended features over $\bar{X}_I$ . Accordingly, we model the multi-head self-attention within $\bar{X}_F$ as follows: + +$$ +\tilde {X} _ {F} = \text {M u l t i H e a d} \left(\bar {X} _ {F}, \bar {X} _ {F}, \bar {X} _ {F}\right). \tag {5} +$$ + +Note that $\tilde{X}_I$ has the same shape as $\tilde{X}_F$ and $\bar{X}_F$ , we encapsulate them by the AddNorm operator as follows: + +$$ +\mathcal {F} = \text {L a y e r N o r m} \left(\bar {X} _ {F} + \tilde {X} _ {F} + \tilde {X} _ {I}\right), \tag {6} +$$ + +where $LayerNorm(\cdot)$ denotes layer normalization [37]. Finally, the fused features $\mathcal{F}$ are fed into the FFN module to generate the encoding results of UFT. Noticeably, the UFT encoder is actually stacked in depth to generate more abstract and discriminative visual features for decoding, we omit them for a concise expression. + +# 3.3. Interventional Transformer Decoder + +To alleviate the spurious correlations between attended visual features and their corresponding words, we build a novel Transformer-based decoder architecture, which incorporates a causal intervention module into each Transformer decoder layer to cope with both the visual and linguistic confounders in image captioning. + +Causal Intervention in Image Captioning. We first formulate the causalities among the attended visual features $V$ , visual context $D_{1}$ , linguistic context $D_{2}$ , attended word features over the partially generated sentence $h_{1}$ , fused feature $h_{2}$ and predicted word $W$ with an SCM, as illustrated in Figure 5a. Concretely, the causal effect $V \rightarrow W$ denotes that the attended visual features cause the generation of their corresponding words. The causal effect of $D_{1}$ on $V$ stands for $D_{1} \rightarrow V$ because the attended visual features are severely affected by some frequently appearing visual con + +texts when one captioner is trained, while the causal effect $D_{1} \rightarrow W$ means that the visual contexts directly affect the frequency of some related words in the captions. In addition, $D_{2} \rightarrow h_{1} \rightarrow V$ denotes that the attended word features, affected by the linguistic contexts, are used to guide the attended visual features via multi-head cross-attention. $h_{1} \rightarrow h_{2}, V \rightarrow h_{2}$ and $h_{2} \rightarrow W$ indicate that the decoder integrates the visual features with linguistic features and utilizes the fused feature $h_{2}$ to infer the next word $W$ . Thus, when we use the observational likelihood $P(W|V, h_{1})$ as the training target, the captioner is likely to learn some spurious correlation between $V$ and $W$ due to the confounders $D_{1}$ and $D_{2}$ . To describe the principle of causal intervention in image captioning, we formulate $P(W|V, h_{1})$ as: + +$$ +\begin{array}{l} P (W | V, h _ {1}) = \sum_ {d _ {2}} P \left(d _ {2} \mid h _ {1}\right). \tag {7} \\ \sum_ {d _ {1}} P (W | V, h _ {1}, d _ {1}, d _ {2}) P (d _ {1} | V), \\ \end{array} +$$ + +where the confounders $D_{1}$ and $D_{2}$ generally introduces the observational biases via $P(d_{1}|V)$ and $P(d_{2}|h_{1})$ . Similar to the IOD, we substitute causal intervention $P(W|do(V),do(h_1))$ for the conventional training objective of image captioning, aiming at removing the causal effects of $D_{1}$ on $V$ and $D_{2}$ on $h_1$ , as shown in Figure 5b. Thus, the two backdoor paths: $V\gets D_1\to W$ and $h_1\gets D_2\to W$ are blocked and the spurious correlations are eliminated. Suppose that the confounders $D_{1}$ and $D_{2}$ can be stratified respectively, $P(W|do(V),do(h_1))$ can be calculated based on the backdoor adjustment as follows [6,26]: + +$$ +\begin{array}{l} P \left(W | d o (V), d o \left(h _ {1}\right)\right) \\ = \sum_ {d _ {2}} P (d _ {2}) \sum_ {d _ {1}} P (W | V, h _ {1}, d _ {1}, d _ {2}) P (d _ {1}). \tag {8} \\ \end{array} +$$ + +Consequently, based on the interventional probability in Eq. (8), the image captioner is forced to learn the true causal effect: $V \rightarrow W$ rather than the spurious correlations caused by the visual confounder $D_{1}$ and linguistic confounder $D_{2}$ . + +Likewise, we build the approximate visual confounder dictionary $\mathbb{D}_1$ and linguistic confounder dictionary $\mathbb{D}_2$ since both $D_{1}$ and $D_{2}$ are unobserved and beyond objects in image captioning. On the one hand, we construct the visual matrix $V_{r} \in \mathbb{R}^{c \times d_{v}}$ by setting each entry as the average RoI feature of objects in each class, where $c$ denotes the class size and $d_{v}$ is the dimensionality of each RoI feature. On the other hand, a set of $d_{e}$ -dimensional word embeddings $W_{e} \in \mathbb{R}^{N \times d_{e}}$ from a pre-defined word vocabulary are utilized to build a semantic space. Then, the captioner is trained to learn two linear projections $P_{v} \in \mathbb{R}^{d_{v} \times d}$ and $P_{w} \in \mathbb{R}^{d_{e} \times d}$ to respectively transform $V_{r}$ and $W_{e}$ into $\mathbb{D}_1$ and $\mathbb{D}_2$ , i.e., $\mathbb{D}_1 = V_r P_v$ , $\mathbb{D}_2 = W_e P_w$ . Thus, Eq. (8) can be computed by utilizing the NWGM approximation [40, 41] as follows: + +$$ +\begin{array}{l} P (W | d o (V), d o \left(h _ {1}\right)) \\ \approx \operatorname {S o f t m a x} \left\{g \left(h _ {2}, \mathbb {E} _ {D _ {1}} [ D _ {1} ], \mathbb {E} _ {D _ {2}} [ D _ {2} ]\right) \right\}, \tag {9} \\ \end{array} +$$ + +where $g(\cdot)$ represents an FC layer, $\mathbb{E}_{D_1}[D_1] \approx$ softmax $(\mathbb{D}_1h_2)\mathbb{D}_1$ and $\mathbb{E}_{D_2}[D_2] \approx$ softmax $(\mathbb{D}_2h_2)\mathbb{D}_2$ . Similar to DIC [44], we set $D_{1}$ and $D_{2}$ to be conditioned on the fused feature $h_2$ to increase the representation power of ITD. + +Transformer Decoder Architecture. The flowchart of the Transformer decoder architecture is shown in Figure 2. Similar to the Transformer encoder, the decoder consists of $L$ identical decoder layers stacked in sequence. Unlike the original Transformer decoder, our proposal inserts a CI module after the FFN module. Specifically, by means of the visual dictionary $\mathbb{D}_1$ and linguistic dictionary $\mathbb{D}_2$ , the CI module integrates the fused feature $h_2$ with the expectations of both the visual confounder $D_1$ and linguistic confounder $D_2$ to predict the next word, i.e., it actually implements causal intervention by the backdoor adjustment according to Eq. (9). The output of the last decoder layer is subsequently projected into an $N$ -dimensional space by a linear embedding layer, where $N$ is the vocabulary size. Finally, a softmax operation is adopted to predict a probability over words in the vocabulary. + +# 3.4. Training Details + +Following the same training strategies in [2, 10], our model is first pre-trained with the word-level cross entropy (XE) loss: + +$$ +\begin{array}{l} L _ {X E} (\theta) \\ = - \sum_ {t = 1} ^ {T} \log \left(p _ {\theta} \left(w _ {t} ^ {*} \mid d o (V), d o \left(h _ {1}\right), w _ {1: t - 1} ^ {*}\right)\right), \tag {10} \\ \end{array} +$$ + +where $\theta$ denotes the parameters of CIIC, $w_{1:T}^{*}$ is the target ground truth sequence. + +After that, the model is optimized for the nondifferentiable metric via Reinforcement Learning (RL). In practice, we adopt a variant of the Self-Critic Sequence Training (SCST) [34] on sequences sampled by beam search. The target is to minimize the following negative expected score: + +$$ +L _ {R L} (\theta) = - \mathbb {E} _ {w _ {1: T} \sim p _ {\theta}} \left[ r \left(w _ {1: T}\right) \right], \tag {11} +$$ + +where the reward $r(\cdot)$ denotes the CIDEr-D score. + +In the testing stage, we use beam search to generate the sentence word-by-word and obtain the sequence with the largest probability among those in the last beam. + +# 4. Experiments + +# 4.1. Experimental Setup + +MS COCO Dataset [24]. This popular benchmark dataset contains 123,287 images and each of them equipped with 5 manually annotated sentences. In the experiments, We adopt two popular splits: the Karpathy split [20] and the online test split. + +Evaluation Metrics. To evaluate the performance of different captioning methods, we utilize the full set of the stan- + +dard evaluation metrics, including BLEU [29], METEOR [5], ROUGR [7], CIDEr [38], and SPICE [1]. Besides, we employ two metrics: $\mathrm{CHAIR}_s$ and $\mathrm{CHAIR}_i$ [35] to measure the object bias degree of the generated captions. + +Implementation Details. To represent the image features, we first train the proposed IOD on the MSCOCO dataset to extract the 1024 dimensional IOD features of the top-100 objects with the highest confidence scores. Then, we use the pre-trained Up-Down model [2] to extract the 2048 dimensional bottom-up features of the detected objects. Finally, we linearly project both features to the 512 dimensional vectors and fed them into the UFT encoder. To represent the words, we respectively utilize one-hot vectors and pretrained GloVe word embeddings [31] in the experiments. Both of them are linearly projected to the 512 dimensional input vectors of ITD. To represent word positions inside the sentence, we sum the input vectors and their sinusoidal positional encodings [36] before the first decoding layer. + +Following the same settings in [37], we convert all sentences to lowercase, delete the punctuation characters and tokenize each caption. We construct a new vocabulary by selecting the words which appear more than 5 times. In addition, we use 8 attentive heads in both the encoder and decoder of CIIC. The latent dimensionality in each head is set to $d_h = d / h = 64$ , where the latent dimensionality $d$ is 512. We train our CIIC on one Nvidia 3080 GPU with a batch size of 10 images for 220K iterations. For fair comparisons, we employ ResNet-101 as the backbone for both the image feature extraction and encoding. + +In the training stage, we employ the Adam optimizer [21] with a batch size of 10 and 20000 warmup steps. Our models are first trained for 30 epochs based on the XE loss and then optimized with the SCST approach [34] for additional 30 epochs with a beam size of 5. The learning rate is set to $5 \times 10^{-6}$ . During the inference stage, the beam search [36] is also adopted with a beam size of 3. + +# 4.2. Ablation Studies + +We carry out extensive experiments to investigate the impacts of different modules on captioning performance. + +Comparing Methods. Base: We denote the original Transformer captioning model with the bottom-up features as Base. Base+GloVe: We incorporate the GloVe embedding [31] into Base to represent the words. Base+ITD: We introduce the ITD module into the decoder of Base. + +Base+ITD+GloVe: Compared with Base+ITD, we further integrate the GloVe embedding with Base. Base+UFT: We exploit the UFT to improve the visual representation ability of Base. Base+UFT+GloVe: Compared with Base+UFT, we replace the one-hot embeddings by the GloVe embeddings for the generated words. CIIC $_{\mathcal{O}}$ and CIIC $_{\mathcal{G}}$ : The subscripts “ $\mathcal{O}$ ” and “ $\mathcal{G}$ ” represent that our CIIC is implemented with the one-hot word vectors and GloVe word em + +Table 1. Ablation experiments. All the models are trained with the XE loss. B@1, B@4, M, R, C, S, CHs and CHi are short for BLEU-1, BLEU-4, METEOR, ROUGE-L, CIDEr, SPICE, CHAIR $_s$ and CHAIR $_i$ scores. “ $\downarrow$ ” and “ $\uparrow$ ” denote the lower the better and the higher the better, respectively. + +
ModelB@1↑B@4↑M↑R↑C↑S↑CHs↓CHi↓
Base75.935.528.056.5114.121.08.46.3
Base+GloVe76.336.228.256.8115.921.37.96.0
Base+ITD76.136.228.156.7116.021.27.76.0
Base+ITD+GloVe76.536.528.457.0117.121.36.95.4
Base+UFT77.036.728.457.1117.521.55.83.9
Base+UFT+GloVe77.136.928.157.0117.921.35.93.9
CIICO77.337.028.357.4118.321.35.63.9
CIICG77.537.328.557.4119.021.55.33.6
+ +beddings, respectively. + +Results and Analysis. Table 1 shows the ablation experiments on different encoding and decoding modules with the number of attention blocks $L = 6$ . From Table 1, we can observe that GloVe and CI schemas respectively bring an improvement over Base. When they are both employed, the performance can be further enhanced, which indicates that both of them are beneficial. The performance of Base+UFT and Base+UFT+GloVe is superior to that of Base+GloVe+CI, which confirms the effectiveness of the extracted IOD features. After respectively incorporating the CI module into Base+UFT and Base+UFT+GloVe, the performance of both CIIC $_{\mathcal{O}}$ and CIIC $_{\mathcal{G}}$ can be further significantly boosted (from 117.5 CIDEr to 118.3 CIDEr and from 117.9 CIDEr to 119.0 CIDEr, respectively), which further confirms the utility of deconfounding the visual and linguistic confounders in the sentence generation. + +# 4.3. Quantitative Analysis + +Results on the Karpathy Test Splits. In Table 2, we compare our CIIC with the SOTA models on the offline COCO Karpathy test split, including SCST [34], Up-Down [2], RFNet [19], GCN-LSTM [46], SGAE [42], ORT [15], AoANet [16], $\mathcal{M}^2$ Transformer [8], Transformer+CATT [45] and X-Transformer [28]. SCST applies the RL-based reward, which is widely used in the following methods. Up-Down and RFNet utilize the visual attention mechanism. GCN-LSTM and SGAE employ scene graphs and graph convolution networks. ORT incorporates geometry information into the transformer. AoANet exploits the relevance of attention results via a gate guided by the context. $\mathcal{M}^2$ Transformer proposes a fully-connected architecture between the encoder and decoder layers. Transformer+CATT incorporates a novel causal attention into the Transformer architecture. X-Transformer applies Bilinear Pooling to the attention module of Transformer. + +For fair comparisons, we conduct experiments to compare our proposed CIIC with the transformer-based methods on the same ResNext101 region-based features. From Ta + +ble 2, we can observe that $\mathbf{C}\mathbf{I}\mathbf{C}_{\mathcal{O}}$ achieves the best BLEU-1, BLEU-4 and ROUGE-L scores in comparison with the other SOTA methods. Particularly, it is even comparable to X-Transformer which is trained on 4 P40 GPUs ( $4 \times 24 = 96\mathrm{G}$ )1. $\mathbf{C}\mathbf{I}\mathbf{C}_{\mathcal{G}}$ surpasses other SOTA methods significantly in terms of BLEU-1, BLEU-4, CIDEr, ROUGE-L, while being competitive on METEOR and slightly worse on SPICE with respect to X-Transformer. + +Table 2. Experimental results of different models on the MSCOCO "Karpathy" test split. + +
ModelB@1B@4MRCS
SCST [34]-34.226.755.7114.0-
Up-Down [2]79.836.327.756.9120.121.4
RFNet [19]79.136.527.757.3121.921.2
GCN-LSTM [46]80.538.228.558.3127.622.0
SGAE [42]80.838.428.458.6127.822.1
ORT [15]80.538.628.758.4128.322.6
AoANet [16]80.238.929.258.8129.822.4
M2Transformer [8]80.839.129.258.6131.222.6
Transformer+CATT [45]-39.429.358.9131.722.8
X-Transformer [28]80.939.729.559.1132.823.4
CIICO81.440.229.359.2132.623.2
CIICG81.740.229.559.4133.123.2
+ +Table 3. Performance comparison with the SOTA methods in the setting of single model on the online MS-COCO test server, where c5/c40 means employing 5/40 ground-truth captions for testing. + +
ModelB@4MRC
c5c40c5c40c5c40c5c40
Up-Down [2]36.968.527.636.757.172.4117.9120.5
CAVP [48]37.969.028.137.058.273.1121.6123.8
SGAE [42]37.868.728.137.058.273.1122.7125.5
CNM [43]37.968.428.136.958.372.9123.0125.3
VSUA [12]37.468.328.237.157.972.8123.1125.5
AOA-DICv1.0 [44]38.870.528.838.258.673.9126.2128.4
Transformer+CATT [45]38.870.628.938.258.773.9126.3128.8
CIICO38.570.028.938.458.473.8126.3129.2
CIICG38.570.129.138.458.674.0126.4129.2
+ +Table 4. The bias analysis of different models on MSCOCO Karpathy split. + +
ModelB@4↑M↑R↑C↑CHs↓CHi ↓
Up-Down [2]36.327.756.9120.113.78.9
Transformer38.428.658.4128.612.18.1
UD-DICv1.0 [44]39.028.858.8128.810.16.5
Transformer+CATT [45]39.429.358.9131.79.76.5
CIICG40.229.359.2132.68.25.0
CIICG40.229.559.4133.17.74.5
+ +Results on the Official Test Server. Table 3 reports the performance of different models on the online COCO test + +![](images/784d4ac6dac599774ee8dcada0d399c6d8341cbeab9e8c357968bcea14118f4a.jpg) + +![](images/f79f1bd88de0b754e94ff70c5c8d1c0e36531390925d347848a1614a883617c6.jpg) +Figure 6. The t-SNE visualization [22] of some object features extracted by Faster R-CNN (left) and IOD (right). + +![](images/e0251f8fc2811cad102ccb5713c0a2a4dd39fcb5832bff7ff1e03249e4bbed93.jpg) + +![](images/2f74cc5c749a1cb39b79a1703dc394a9d3fc5a6718767f9945545115f307bbb1.jpg) +Figure 7. Some generated captions by CIIC and the Transformer baseline in the case of gender, object and action biases. The green contexts denote the linguistic confounders which may induce biases. The correct and incorrect words are colored by blue and red, respectively. + +server. For a fair comparison, we still train CIIC and competitive models in the same single model setting on the official test split. Compared with the top-performing approaches on the leaderboard, we can see that our single models still achieve the superior performance against the competitive methods. Particularly, $\mathbf{CIIC}_{\mathcal{G}}$ can achieve a new state-of-the-art score of 126.4 on CIDEr (C5) and 129.2 on CIDEr (C40). + +Analysis of the Biases. To confirm whether the proposed CIIC model can mitigate the dataset bias or not, we further evaluate the bias degree of the generated captions in Table 4. From Table 4, we can see that after performing causal intervention in object detection and image captioning, CIIC achieves the lowest CHs and CHi, which indicates that CIIC can generate the least biased captions. Meanwhile, we can see that CIIC obtains the best results in terms of BLEU-4, METEOR, ROUGE-L and CIDEr, which can further demonstrates that our CIIC model generates the more grounded captions in the case of dataset bias. Compared with Table 1, it can be found that CHs and CHi of + +both $\mathbf{C}\mathbf{I}\mathbf{C}_{\mathcal{O}}$ and $\mathbf{C}\mathbf{I}\mathbf{C}_{\mathcal{G}}$ also increase with the increase of the CIDEr scores. This is due to the fact that the widely-adopted SCST optimization may cause biases in order to improve the CIDEr score [35]. + +# 4.4. Qualitative Analysis + +Finally, we qualitatively evaluate the performance of our method. Figure 6 visualizes some visual features of MSCOCO images extracted by Faster R-CNN (left) and the proposed IOD (right). We can see that our IOD can learn the more discriminative feature representations compared to Faster R-CNN. For example, cake and fork features as well as person and ski features are entangled in red box when the conventional likelihood $P(Y|X)$ (left) is used. After causal intervention $P(Y|do(X))$ (right), they are clearly disentangled, implying that the IOD actually deconfounds the visual confounder while extracting the visual features. Figure 7 shows some captions of test images generated by CIIC and the Transformer baseline. Intuitively, CIIC is able to produce more grounded and less biased captions compared with the Transformer baseline. For example, our model effectively alleviates the spurious correlation between the boy feature and the word "cake" caused by both the visual and linguistic confounders. Besides, our CIIC can also alleviate gender and action biases, which indicates that our CIIC is able to effectively deconfound both the visual and linguistic confounders and further validates the effectiveness of our method. + +# 5. Conclusion + +In this paper, we present CIIC, a novel Transformer-based architecture for image captioning from the causal perspective, which seamlessly incorporates causal intervention into both object detection and captioning generation to jointly alleviate the confounding effect. On one hand, the proposed IOD effectively disentangles the visual features and facilitates the deconfounding of image captioning. On the other hand, the proposed ITD implements causal intervention to tackle the visual and linguistic confounders simultaneously during the generation of sentences. Experimental results have demonstrated that our method can significantly outperform the state-of-the-art image captioners in the single-model configuration on the MS-COCO dataset. The limitations of our method are given in the supplementary material. + +# Acknowledgement + +This work is supported by the National Natural Science Foundation of China (No.61403394, No.62172417 and No.62106268), and the High-Level Talent Program for Innovation and Entrepreneurship (Shuang Chuang Doctor) of Jiangsu Province (JSSCBS20211220). + +# References + +[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Spice: Semantic propositional image caption evaluation. In Adaptive Behavior, pages 382-398, 2016. 6 +[2] Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. Bottom-up and top-down attention for image captioning and visual question answering. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6077-6086, 2018. 1, 2, 4, 6, 7, 12 +[3] Jyoti Aneja, Aditya Deshpande, and Alexander G. Schwing. Convolutional image captioning. 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This comes with major limitations. For example, it is problematic for a model conditioned on an image to generate a specific motion trajectory desired by the user since there is no means to provide motion information. Conversely, language information can describe the desired motion, while not precisely defining the content of the video. This work presents a multimodal video generation framework that benefits from text and images provided jointly or separately. We leverage the recent progress in quantized representations for videos and apply a bidirectional transformer with multiple modalities as inputs to predict a discrete video representation. To improve video quality and consistency, we propose a new video token trained with self-learning and an improved mask-prediction algorithm for sampling video tokens. We introduce text augmentation to improve the robustness of the textual representation and diversity of generated videos. Our framework can incorporate various visual modalities, such as segmentation masks, drawings, and partially occluded images. It can generate much longer sequences than the one used for training. In addition, our model can extract visual information as suggested by the text prompt, e.g., "an object in image one is moving northeast", and generate corresponding videos. We run evaluations on three public datasets and a newly collected dataset labeled with facial attributes, achieving state-of-the-art generation results on all four1. + +# 1. Introduction + +Generic video synthesis methods generate videos by sampling from a random distribution [56, 57]. To get more control over the generated content, conditional video synthesis works utilize input signals, such as images [9, 19], text or language [7, 30], and action classes [62]. This enables synthesized videos containing the desired objects as + +specified by visual information or desired actions as specified by textual information. + +Existing works on conditional video generation use only one of the possible control signals as inputs [8, 30]. This limits the flexibility and quality of the generative process. For example, given a screenplay we could potentially generate several movies, depending on the decisions of the director, set designer, and visual effect artist. In a similar way, a video generation model conditioned with a text prompt should be primed with different visual inputs. Additionally, a generative video model conditioned on a given image should be able to learn to generate various plausible videos, which can be defined from various natural language instructions. For example, to generate object-centric videos with objects moving [70], the motion can be easily defined through a text prompt, e.g., "moving in a zig-zag way," while the objects can be defined by visual inputs. Thus, an interesting yet challenging question arises: Can we learn a video generation model that can support such behavior? + +We tackle the question in this work and propose a new video synthesis model supporting diverse, multimodal conditioning signals. Our method consists of two phases. The first phase obtains discrete representations from images. We employ an autoencoder with a quantized bottleneck, inspired by the recent success of two-stage image generation using quantized feature representations [21,38,47,76]. The second phase learns to generate video representations that are conditioned on the input modalities, which can then be decoded into videos using the decoder from the first stage. We leverage a bidirectional transformer, i.e., BERT [17], trained with a masked sequence modeling task, that uses tokens from multimodal samples and predicts the latent representation for videos. Building such a framework requires solving several challenging problems. First, video consistency is a common problem among video generation methods. Second, it is necessary to ensure that the correct textual information is learned. Third, training a transformer for image synthesis is computationally demanding [12], an issue that is even more severe in the time domain, as a longer sequence of tokens needs to be learned. To solve these challenges, we propose the following contributions: + +- We introduce a bidirectional transformer with several new techniques to improve video generation: For training, we propose the video token VID, which is trained via self-learning and video attention, to model temporal consistency; For inference, we improve mask-predict to generate videos with improved quality. +- We introduce text augmentation, including text dropout and pretrained language models for extracting textual embeddings, to generate diverse videos that are correlated with the provided text. +- We explore long sequence synthesis with the transformer model to generate sequences with lengths that are much longer than the one used for training (Fig. 5). + +We name our framework MMVID and show that a MultiModal VIDeo generator can enable various applications. The user can show what to generate using visual modalities and tell how to generate with language. We explore two settings for multimodal video generation. The first involves independent multimodality, such that there is no relationship between textual and visual controls (Fig. 3a and Fig. 4). The second one targets dependent multimodal generation, where we use text to obtain certain attributes from given visual controls (Fig. 3b and Fig. 4). The latter case allows for more potential applications, in which language is not able to accurately describe certain image content that the user seeks to generate, but images can efficiently define such content. We also show our model can use diverse visual information, including segmentation masks, drawings, and partially observed images (Fig. 4). + +To validate our approach extensively, we conduct experiments on four datasets. In addition to three public datasets, we collect a new dataset, named Multimodal VoxCeleb, that includes 19,522 videos from VoxCeleb [37] with 36 manually labeled facial attributes. + +# 2. Related Works + +Video Generation. For simplicity, previous works on video generation can be categorized into unconditional and conditional generation, where most of them apply similar training strategies: adversarial training with image and video discriminators [14, 24, 50]. Research on unconditional video generation studies how to synthesize diverse videos with input latent content or motion noise [1, 28, 49, 57, 62, 66, 75]. Recent efforts in this direction have achieved high resolution and high quality generation results for images and videos [14, 29, 56]. On the other hand, conditional video generation utilizes given visual or textual information for video synthesis [9, 19, 39, 48, 54, 64, 67]. For example, the task of video prediction uses the provided first image or a few images to generate a sequence of frames [3-6, 11, 15, 16, 26, 60, 61, 63]. Similarly, text-to-video generation applies the conditional signal from text, captions, or natural + +language descriptions [31, 36, 40]. TFGAN [7] proposes a multi-scale text-filter conditioning scheme for discriminators. TiVGAN [30] proposes to generate a single image from text and synthesizes consecutive frames through further stages. In this work, we study conditional video synthesis. However, we differ from existing methods since we address a more challenging problem: multimodal video generation. Instead of using a single modality, such as textual guidance, we show how multiple modalities can be input within a single framework for video generation. With multimodal controls, i.e., textual and visual inputs, we further enhance two settings for video generation: independent and dependent multimodal inputs, in which various applications can be developed. + +Transformers for Video Generation. Transformer-based networks have shown promising and often superior performance not only in natural languages processing tasks [10, 43, 59], but also in computer vision related efforts [12, 20, 27, 41, 42]. Recent works provide promising results on conditional image generation [13, 21], text-to-image generation [18, 45], video generation [44, 68, 70, 72], and text-to-video synthesis [69] using transformers. Unlike existing transformer-based video generation works that focus on autoregressive training, we apply a non-autoregressive generation pipeline with a bidirectional transformer [22, 23, 25, 35, 65]. Our work is inspired by M6-UFC [76], which utilizes the non-autoregressive training for multimodal image generation and produces more diverse image generation with higher quality. Building upon M6-UFC, we further introduce training techniques for multimodal video synthesis. + +# 3. Methods + +Our framework for multimodal video generation is a two-stage image generation method. It uses discrete feature representations [21, 38, 47, 76]. During the first stage we train an autoencoder (with encoder $E$ and decoder $D$ ) that has the same architecture as the one from VQGAN [21] to obtain a quantized representation for images. Given a real video clip defined as $\mathbf{v} = \{\mathbf{x}_1, \mathbf{x}_2, \dots, \mathbf{x}_T\}$ with $\mathbf{x}_t \in \mathbb{R}^{H \times W \times 3}$ , we get a quantized representation of the video defined as $\mathbf{z} = \{\mathbf{z}_1, \mathbf{z}_2, \dots, \mathbf{z}_T\}$ , where $\mathbf{z}_t = q(E(\mathbf{x}_t)) \in \mathbb{N}_1^{h \times w}$ . $q(\cdot)$ denotes the quantization operation and $\mathbb{N}_1$ indicates a set of positive integers. + +During the second stage we learn a bidirectional transformer for modeling the correlation between multimodal controls and the learned vector quantization representation of a video. Specifically, we concatenate the tokens from the multimodal inputs and the target video as a sequence to train the transformer. Tensors obtained from an image and video must be vectorized for concatenation. We do so using the reshape operation (Reshape). Therefore, we have a video tensor $\mathbf{z}$ reshaped into a single-index tensor as $\mathrm{Reshape}(\mathbf{z}) = [z^{(1)},\dots ,z^{(hwT)}]$ . For simplicity + +![](images/c4dddc13664d773eeb37d380aa964e446c46bc5def785e041f648b35e7b738ce.jpg) +Figure 1. Pipeline for training and inference. (a) Data quantization. (b) Model training. Within the BERT module, the green and blue triangles indicate the attention scopes of [REL] and [VID], respectively. (c) Video extrapolation. For simplicity, each step represents a full mask-predict process instead of a single forward pass of the transformer. (d) Video interpolation. + +![](images/1a31eb5182494bfb54efd34826a67a8f9b6f267240109df421b6712414cb84fd.jpg) + +![](images/1db59fb337f920f05593df5ef02598afd2b85789c8e7b966f46492f3f53e6d39.jpg) + +of notation, we define $\mathbf{z} \equiv \mathrm{Reshape}(\mathbf{z})$ . To train the non-autogressive transformer (BERT) on video tokens, we employ three tasks: Masked Sequence Modeling (MSM), RELevance estimation (REL), and VIDEo consistency estimation (VID). During inference, samples are generated via an iterative algorithm based on mask-predict [23], which is simulated by the MSM task during training. The REL and VID tasks regularize the model to synthesize videos that are relevant to the multimodal signals and are temporally consistent. In the following two sections we present each task. + +# 3.1. Masked Sequence Modeling with Relevance + +Masked Sequence Modeling. The MSM task is similar to a conditional masked language model [23]. It is essential for the non-autoregressive model to learn bidirectional representations and enables parallel generation (mask-predict). Inspired by M6-UFC [76] and VIMPAC [55], we consider five masking strategies: (I) i.i.d. masking, i.e., randomly masking video tokens according to a Bernoulli distribution; (II) masking all tokens; (III) block masking [55], which masks continuous tokens inside spatio-temporal blocks; (IV) the negation of block masking, which preserves the spatio-temporal block and masks the rest of the tokens; (V) randomly keeping some frames (optional). Strategies I and II are designed to simulate mask-predict sampling (the strategy chosen most of the time). Strategy II helps the model learn to generate from a fully masked sequence in the first step of mask-predict. Strategies III - V can be used as Preservation Control (PC) for preservation tasks, which enable the use of partial images as input (Figs. 3a, 4) and per + +forming long sequence generation (Fig. 5). The MSM task minimizes the softmax cross-entropy loss $\mathcal{L}_{\mathrm{MSM}}$ as follows: + +$$ +\mathcal {L} _ {\mathrm {M S M}} = - \frac {1}{| \mathcal {M} |} \sum_ {i \in \mathcal {M}} \log P \left(z ^ {(i)} \mid \mathbf {z} ^ {m}, \mathbf {c}\right), \tag {1} +$$ + +where $\mathcal{M}$ is the masking indices, $\mathbf{z}^m$ is the masked sequence, and $\mathbf{c}$ denotes the control sequence. + +Relevance Estimation. To encourage the transformer to learn the correlation between multimodal inputs and target videos, we prepend a special token REL that is similar to the one used in M6-UFC [76] to the whole sequence, and learn a binary classifier to classify positive and negative sequences. The positive sequence is the same as the sequence used in the MSM task so that we can reuse the same transformer in the forward pass. The negative sequence is constructed by swapping the condition signals along the batch dimension. This swapping does not guarantee constructing strictly negative samples. Nevertheless, we still find it is good enough to make the model learn relevance in practice. The loss function $\mathcal{L}_{\mathrm{REL}}$ for the relevance task is given by: + +$$ +\mathcal {L} _ {\mathrm {R E L}} = - \log P \left(1 | \mathbf {z} ^ {m}, \mathbf {c}\right) - \log P \left(0 | \mathbf {z} ^ {m}, \bar {\mathbf {c}}\right), \tag {2} +$$ + +where $\bar{\mathbf{c}}$ denotes the swapped control sequence. + +# 3.2. Video Consistency Estimation + +To further regularize the model to generate temporally consistent videos, we introduce the video consistency estimation task. Similar to REL, we use a special token VID to classify positive and negative sequences. + +Video Attention. The VID task focuses on video token sequences. Thus, we place the VID token between the control and target sequences. We apply a mask to BERT to blind the scope of the VID token from the control signals so it only calculates attention from the tokens of the target videos. The positive sequence is the same one used in MSM and REL tasks. The negative sequence is obtained by performing negative augmentation on videos to construct samples that do not have temporally consistent motion or content. + +Negative Video Augmentation. We employ four strategies to augment negative video sequences: (I) frame swapping – a random frame is replaced by using a frame from another video; (II) frame shuffling – frames within a sequence are shuffled; (III) color jittering – randomly changing the color of one frame; (IV) affine transform – randomly applying an affine transformation on one frame. All augmentations are performed in image space. With $\bar{\mathbf{z}}$ denoting the video sequence after augmentation, the loss $\mathcal{L}_{\mathrm{VID}}$ for the VID task is: + +$$ +\mathcal {L} _ {\mathrm {V I D}} = - \log P \left(1 | \mathbf {z} ^ {m}, \mathbf {c}\right) - \log P \left(0 | \overline {{\mathbf {z}}} ^ {m}, \mathbf {c}\right). \tag {3} +$$ + +Overall, the full objective is $\mathcal{L} = \lambda_{\mathrm{MSM}}\mathcal{L}_{\mathrm{MSM}} + \lambda_{\mathrm{REL}}\mathcal{L}_{\mathrm{REL}} + \lambda_{\mathrm{VID}}\mathcal{L}_{\mathrm{VID}}$ , where $\lambda$ s balances the losses. + +# 3.3. Improved Mask-Predict for Video Generation + +We employ mask-predict [23] during inference, which iteratively remarks and repredicts low-confidence tokens by starting from a fully-masked sequence. We chose it because it can be used with our bidirectional transformer, as the length of the target sequence is fixed. In addition, mask predict provides several benefits. First, it allows efficient parallel sampling of tokens in a sequence. Second, the unrolling iterations from mask-predict enable direct optimization on synthesized samples, which can reduce exposure bias [46]. Third, information comes from both directions, which makes the generated videos more consistent. + +We build our sampling algorithm based on the original mask-predict [23] with two improvements: (I) noise-annealing multinomial sampling, i.e., adding noise during remasking; (II) a new scheme for mask annealing, i.e., using a piecewise linear annealing scheme to prevent the generated motion from being washed out after too many steps of mask-predict. We also apply a beam search from M6UFC [76]. In Alg. 1, the transformer (BERT) takes input tokens $\mathbf{z}_{in}$ and outputs score $s$ and the logits $\tilde{\mathbf{p}}$ for all target tokens. At each mask-predict iteration, we sample tokens with SampleToken that returns a predicted token $\mathbf{z}_{out}$ and a vector $\mathbf{y}$ containing its probabilities (unnormized). SampleToken also accepts a scalar $\sigma$ that indicates the noise level to be added during the token sampling process. SampleMask $(\mathbf{y},\mathbf{m},N - n)$ remacks $n$ tokens from a total of $N$ tokens according to the multinomial defined by the normalized $\mathbf{y}$ , while ensuring tokens with $\mathbf{m} = 1$ are always preserved. $\mathbf{z}_{\phi}$ denotes the fully-masked + +sequence. The functions SampleToken, SampleMask and the schedules of $n^{(i)}$ and $\sigma^{(i)}$ are shown in Appendix. + +Algorithm 1 Improved Mask-Predict for Video Generation +Require: Initial PC mask $\mathbf{m}_{\mathrm{PC}}$ and initial token $\mathbf{z}_{in}$ +1: $\tilde{\mathbf{p}},s\gets \mathrm{BERT}(\mathbf{z}_{in})$ +2: $\mathbf{z}_{out},\mathbf{y}\gets$ SampleToken $(\tilde{\mathbf{p}},\sigma^{(1)})$ +3: $\mathbf{z}_{out}\gets \mathbf{m}_{\mathrm{PC}}\odot \mathbf{z}_{in} + (1 - \mathbf{m}_{\mathrm{PC}})\odot \mathbf{z}_{out}$ ▷PC +4: for $i\in \{2,\dots,L\}$ do ▷main loop +5: for $b\in \{1,\dots,B\}$ do ▷beam search +6: $\mathbf{m}^b\gets$ SampleMask(y, mPC, $N - n^{(i)}$ ） +7: $\mathbf{z}_{in}^{b}\gets \mathbf{m}^{b}\odot \mathbf{z}_{out} + (1 - \mathbf{m}^{b})\odot \mathbf{z}_{\phi}$ ▷remask +8: $\tilde{\mathbf{p}}^b,s^b\gets \mathrm{BERT}(\mathbf{z}_{in}^b)$ ▷repredict +9: end for +10: $b^{*}\gets$ arg maxb(sb) +11: $\mathbf{z}_{out},\mathbf{y}\gets$ SampleToken $(\tilde{\mathbf{p}}^{b^{*}},\sigma^{(i)})$ +12: end for +13: return $\mathbf{z}_{out}$ + +# 3.4. Text Augmentation + +We study two augmentation methods. First, we randomly drop sentences from the input text to avoid memorizing certain word combinations. Second, we apply a fixed pretrained language model, i.e., RoBERTa [33], rather than learning text token embeddings in a lookup table from scratch, to let the model be more robust for input textual information. The features of text tokens are obtained from an additional multilayer perceptron (MLP) appended after the language model that matches the vector dimension with BERT. The features are converted to a weighted sum to get the final embedding of the input text. With the language model, the video generation framework is more robust for out-of-distribution text prompts. When using the tokenizer from an existing work [42], we observed that it might not properly handle synonyms without a common root (Fig. 6). + +# 3.5. Long Sequence Generation + +Due to the inherent preservation control mechanism during training (strategy V in the MSM task), we can generate sequences with many more frames than the model is trained with via interpolation or extrapolation. Interpolation is conducted by generating the intermediate frames between given frames. As illustrated by Fig. 1 (d), we place $\mathbf{z}_1$ and $\mathbf{z}_2$ at the positions of frames 1 and 3 to serve as preservation controls, i.e., they are kept the same during mask-predict iterations, and we can interpolate a frame between them. Extrapolation is similar to interpolation, except we condition the model on previous frames to generate the next frames. As illustrated in Fig. 1 (c), this process can be iterated a number of times to generate longer videos. + +# 4. Experiments + +Datasets. We show experiments on the following datasets. + +- Shapes is proposed by TFGAN [8] for text-to-video generation. Each video shows one object (a geometric shape with specified color and size) displayed in a textured moving background. The motion of an object is described by a text and the background is moving in a random way. There are 30K videos with size $64 \times 64$ . +- MUG [2] contains 52 actors performing 6 different facial expressions. We also provide gender labels for the actors. For a fair comparison, we obtain text descriptions by following TiVGAN [30]. We run experiments on 1039 videos with resolution $128 \times 128$ . +- iPER [32] consists of 206 videos of 30 subjects wearing different clothes performing an A-pose and random actions. Experiments are conducted with size $128 \times 128$ . +- Multimodal VoxCeleb is a new dataset for multimodal video generation. We first obtain 19,522 videos from VoxCeleb [37] after performing pre-processing [53]. Second, we manually label 36 facial attributes described in CelebA [34] for each video. Third, we use a probabilistic context-free grammar to generate language descriptions [71]. Finally, we run APDrawingGAN [73] to get artistic portrait drawings and utilize face-parsing [74] to produce segmentation masks. + +Baseline Methods. We run TFGAN [8] on Shapes, MUG, and Multimodal VoxCeleb datasets for comparison of text-to-video synthesis. We also compare our approach with TiVGAN [30] on MUG. Additionally, we unify the autoregressive transformer of DALL-E [45] and the autoencoder from VQGAN (the same one used in our method) in a multimodal video generative model. We name the strong baseline as AutoRegressive Transformer for Video generation (ART-V) and compare it with our bidirectional transformer for predicting video tokens. We train ART-V with the next-token-prediction objective on concatenated token sequences obtained from input controls and target videos. + +Evaluation Metrics. We follow the metrics from existing works on Shapes and MUG to get a fair comparison. Specifically, we compute classification accuracy on Shapes and MUG and Inception Score (IS) [52] on MUG. On Multimodal VoxCeleb and iPER datasets, we report Fréchet Video Distances (FVD) [58] that is computed from 2048 samples, and Precision-Recall Distribution (PRD) ( $F_{8}$ and $F_{1/8}$ ) for diversity [51]. We further perform human evaluation using Amazon Mechanical Turk to verify the quality and diversity of synthesized videos. + +# 4.1. Text-to-Video Generation + +Shapes. We report the classification accuracy in Tab. 1 (top four rows) for the Shapes dataset. ART-V and MMVID are + +A woman is making a surprise face. + +![](images/64183c6eee3f0bec84589db731286d792a1a9fe49f7e4b2527056de9b917c6ed.jpg) +(a) Samples on MUG. ART-V and our method can generate sharp and temporally consistent videos while frames produced by TFGAN are blurry. + +Figure 2. Text-to-video generation results for different methods. Sample frames are shown at several time steps $(t)$ . Conditioned text is provided at the top with light blue background. +![](images/38f2f980b280ee1d1888c44062b5696dee99f6eff45fa0e6d3bc0988c3d0d59a.jpg) +A female is wearing lipstick. This person has wavy hair and blond hair. She has high cheekbones, arched eyebrows and rosy cheeks. She has heavy makeup. She is young. +(b) Samples on Multimodal VoxCeleb. Frame generated by ART-V at $t = 1$ is sharp and clear, but are blurry at later steps such as $t = 5$ and 8. + +Table 1. Classification accuracy $(\%)$ on the Shapes dataset for video generation. Our method achieves the best performance. + +
ConditionMethodsShapeColorSizeMotionDirAvg
Text OnlyTFGAN [8]80.22100.0084.3399.9099.9592.88
ART-V95.0798.6897.7192.7296.0496.04
MMVID (Ours)95.5699.7197.9597.8099.6198.12
MultimodalART-V92.8297.1797.3189.5593.9994.17
MMVID (Ours)98.1999.7698.8399.4699.9599.24
+ +trained for 100K iterations. Compared with TFGAN [8], our model achieves significantly higher classification accuracy for Shape, Size, and Average (Avg) categories. Compared with ART-V, we perform better in all the categories. Note that our method has slightly lower accuracy on Color, Motion, and Direction (Dir) than TFGAN. The reason might be the VQGAN introduces errors in reconstruction, since the background is diverse and moving, and it needs to encode these small translations by only $4 \times 4$ codes. Note that to have a fair comparison, we do not apply text augmentation when performing comparison with other works. MUG. We follow the experimental setup in TiVGAN [30] + +Table 2. Inception Score (IS) and classification accuracy $(\%)$ on MUG for video generation. We mark $*$ to IS values reported in TiVGAN. Our model achieves highest accuracy and IS. + +
ConditionMethodsGender (%) ↑Expression (%) ↑IS ↑
Text OnlyTGAN [49]--*4.63
MoCoGAN [57]--*4.92
TGANs-C [40]--*4.65
TiVGAN [30]--*5.34
TFGAN [8]99.22100.005.53
ART-V93.4699.125.72
MMVID (Ours)99.90100.005.94
MultimodalART-V89.1698.545.59
MMVID (Ours)98.14100.005.85
+ +Table 3. Evaluation metrics for text-to-video generation on iPER and Multimodal VoxCeleb datasets. + +
DatasetMethodsHuman (%) ↑FVD ↓\( F_8 \uparrow \)\( F_{1/8} \uparrow \)
iPERART-V-277.6040.9360.806
MMVID (Ours)-209.1270.9440.924
Multimodal VoxCelebART-V46.070.9520.9460.940
MMVID (Ours)54.059.4640.9650.961
+ +for experiments on the MUG expression dataset. We train models with a temporal step size of 8 due to the memory limit of GPU. Note TiVGAN is trained with a step size of 4 and generates 16-frame videos, while our model generates 8-frame videos in a single forward. We also train a 3D ConvNet as described in TiVGAN to evaluate the Inception Score and perform classification on Gender and Expression. Results are shown in Fig. 2a and Tab. 2 (top 8 rows). Our model achieves the best performance. + +iPER. We show the results of the dataset in Tab. 3 (top 3 rows), demonstrating the advantages of our method. Long sequence generation results are shown in Fig. 5. + +Multimodal VoxCeleb. We train ART-V and our model at a spatial resolution of $128 \times 128$ and a temporal step of 4 to generate 8 frames. Our method shows better results than ART-V on all the metrics, as shown in Tab. 3 (bottom two rows). We notice ART-V can also generate video samples with good visual quality and are aligned well with the text descriptions. However, ART-V often produces samples that are not temporally consistent. For example, as shown in Fig. 2b, the frame generated by ART-V at $t = 1$ is sharp and clear, but frames at $t = 5$ or $t = 8$ are blurry. The reason might be the exposure bias in autoregressive models becomes more obvious as the sequence length is long, i.e., an 8-frame video at resolution $128 \times 128$ has 512 tokens. Thanks to bidirectional information during training and inference, our MMVID is able to produce temporally consistent videos. + +# 4.2. Multimodal Video Generation + +Multimodal conditions can evolved in two cases: independent and dependent, and we show experiments on both. + +A large green square is moving in a diagonal path in the northeast direction. + +![](images/f3cfc7f683ecd9fd4ca7ed7d33f79ab61851e35c1ed72cd84b442cc637785890.jpg) + +(a) Independent multimodal control. The text description specifies the size, color, and shape of the object, and its motion. The visual control is a partially observed image with its center masked out (shown as white), which provides control for the background. ART-V can generate correct object and motion, but suffers from incorporating consistent visual inputs such that the background is not temporal consistent. + +An object with color in image one, shape in image two, background in image three is moving in a diagonal path in the southwest direction. + +![](images/5adb5e36070179c6293523ca412e06ea1b52ec12886b0c0fcdffcd7bf2428990.jpg) +Figure 3. Multimodal generation results on Shapes with textual (at top) and visual (first column(s)) modalities. Sample frames are shown at several time step $(t)$ . + +(b) Dependent multimodal controls. The text description specifies from which image to extract color, shape, and background. + +Independent Multimodal Controls. This setting is similar to conventional conditional video generation, except the condition is changed to multimodal controls. We conduct experiments on Shapes and MUG datasets with the input condition as the combination of text and image. The bottom two rows in Tab. 1 and Tab. 2 demonstrate the advantages of our method over ART-V on all metrics. Additionally, we provide generated samples in Fig. 3a, where only a partial image is given as the visual condition. As can be seen, ART-V cannot satisfy the visual constraint well and the generated video is not consistent. The quality degradation for multimodal video synthesis of ART-V can also be verified in Tab. 1 as it shows lower classification accuracy than text-only generation, while our method is able to generate high quality videos for different condition signals. + +We also conduct extensive experiments of video generation under various combinations of textual and image controls on Multimodal VoxCeleb, as shown in Fig. 4. We apply three different image controls, including segmentation mask (Fig. 4 row (a) - (b)), drawing (Fig. 4 row (c) - (d)), and partial image (Fig. 4 row (d) - (f)). In Fig. 4 row (b), our + +# Text Control + +This man has mustache, straight hair and beard. He has arched eyebrows. He wears eyeglasses and goatee. + +![](images/a20519023946dfcda1378f5dc60d5fb92a458b4613a3c91d9318efc400053cf2.jpg) + +A person with draw in image one and mask in image two is talking. + +A person with mask in image two and appearance in image one is talking. + +She has high cheekbones, pale skin and arched eyebrows. She has big lips, straight hair and heavy makeup. She has rosy cheeks and blond hair. She is young. She wears lipstick. + +... blond black hair ... + +He has pointy nose, black hair and double chin. He has straight hair, arched eyebrows and big nose. This man is chubby. + +A person with appearance in image one and motion in the following frames is talking. + +# Image / Video Control + +![](images/6042ab3e4dbea7e532c4234ce2bfe37ecb1c08a59aca05ada9ff5dd08137d653.jpg) +IC1 + +![](images/1ffbd0ef7a562384891b9e2a941aaff5ae822774d81ff8b97c238fb797a391be.jpg) +IC1 + +![](images/3455b1d8dbaad5237823d7994a53c9a4fa7445e70d83be36b2309a3ab22cd564.jpg) + +![](images/f4ded54968e032de07b3526f49117def53f6ed76f46d6c0bc43f3da4cdc81e3e.jpg) + +![](images/de7ac6329db2b271224e18625c48962ac5e8800ec399bbd64b1dd14279bf346f.jpg) +IC1 +IC1 + +![](images/9740425b010e0383562b115e4c55f0c5c038e051059545429b620b86cd4b0f4d.jpg) +IC1 + +![](images/9ce391afc9f1777ab62b3680eb82ed174baa492e38853210134434157bdb8076.jpg) +IC1 + +![](images/aa3550485e35efecaf5f3956b0ef1d36a3d25365343378d41cb46abe6cebc7d0.jpg) +IC1 + +![](images/98fd816e536b93da19c03474e08c0f6ea0342a9ade466c6be01aca6a79c556f3.jpg) +IC2 + +![](images/071e9617267c23a3848e8b02cf451f0d36641559ec72cae9d49092f7ffef70d3.jpg) +IC2 + +![](images/59123347a7157a2dd1b42a91adaaa121590a9afe4ee435a9b93f2008714089e5.jpg) +VC1 +Figure 4. Independent and Dependent multimodel video generation on Multimodal VoxCeleb with textual control (TC), image control (IC), and video control (VC). Row $(a) - (b)$ : TC + IC (segmentation mask); Row $(c)$ : TC (null) + IC (drawing); Row $(d) - (e)$ : dependent TC + IC; Row $(f) - (h)$ : TC + IC (partial image) and the TC of (g) is obtained from the TC of (f) by replacing "blond" with "black"; Row $(i)$ : dependent TC + VC and the VC includes content and motion information. + +# Generated Video + +![](images/af84084e490dc093a633d1dd4543894ec9ce16990cdcdffd95996e32576e2462.jpg) + +![](images/f205efeb9e475d88c6e5a41e1685c24b685eb50fdef3ac725c877633b4bf9c7b.jpg) + +![](images/70efbf0598b167c04e1fd986c05cdead352df6a437782bfb4291cf7269ad3b0e.jpg) + +![](images/b293f80878ac8c981ff1f1513b3f447d67872b4780298141a10a48467c9f59fe.jpg) +(a) + +![](images/7546539970d606fb41cd05eaa96ba41f1c7edcac282b2e1f2e4fd2d585c28c75.jpg) + +![](images/062b2e6c441fbdbb9f8b8e1db77d73cda8a43fbd85b2d91ab8b90b5bdc4a1d1b.jpg) + +![](images/0065b309131c4b6a4fe7ae6c661a9f1f4a0ec982f3f73166a94b927de843ccaf.jpg) + +![](images/ed729ac8be3ddd7cc1303e079fcb146d4aeaca6401a3d4f08e0b62e499ddc19e.jpg) + +![](images/12565eccebb52263652779fb3a67ac4e400ff3f618a63cdadce574dc401551fc.jpg) + +![](images/11af131b7fcb9e752d976246cbd824b8fbb9f9b247d04a4757ea378c576d00ab.jpg) + +![](images/6676a25094405000b934a30312aa1efcdccab1797c919f4424ab84f348077490.jpg) + +![](images/789226e219b40aa698121648efdb0f26ae0cacd88ff6e84572162bf0f6baa0ed.jpg) +(c) + +![](images/a1e241bf78d8046c3007d957a239643b8da8169d823091c1c1dbb0ecef5989a3.jpg) + +![](images/f4611e1e5b5fccfbe46012ea1d77588ecf48d1ce08ee5795b44910d82f740d5b.jpg) + +![](images/2ec815b811295cb29b443b798fd09174cc599d5bf721ac0626007e3fb73a90f6.jpg) + +![](images/a93c2714d0e0b4775fa4ff98b7ca0f5b7b379b5feeee3fb36656dadf2067d55e.jpg) +(d) + +![](images/a53547ceab8bd8e71c45058b3c1cda529821f7581becabd2dc59f6e1ce74a3ce.jpg) + +![](images/5a3bb74feb0f84a3e0522677e9a28c8193faef467e0dd36896e5629b6d025c20.jpg) + +![](images/3202e9d1a2cc6df590ce43c4d3c31411d5b8f65c6bbb7ed94220ca11654ead3c.jpg) + +![](images/111dc189a5f576b82185148fa6b3cd133853ce3cb5c4657d66b703f889454a5a.jpg) + +![](images/15f2601219d3d032cb80dd6f27ca420371d14ad1fbd92f995778870133f3c270.jpg) + +![](images/012cae0f70d250fe9330099be8a851dab7b0b488aa2bcb55658721bc0ea507a6.jpg) + +![](images/ac58feb497f8f554896ad2829eb21f17a5a1b3f0fb641abed2593c76c294a35e.jpg) + +![](images/b0afb6fa6494e212ddf6ad04cf63793645562aa1977f0db565d58ca8984c50ad.jpg) +(f) + +![](images/9b13a733db5a17f56c32aec25c07931f49ebb6af046d15f645e1c946ae4f6d1f.jpg) + +![](images/19d20f488b01a17c8b7e7b392406a413633bac8281c1189d46dc3db102fd7bbc.jpg) + +![](images/5231fd786dde76238c0bd9f9c794d52985327f79846672cded9089cab58afe31.jpg) + +![](images/92621dfa8299ec868ed8cd49f8e95af9a4ad1cbb05d33b10c3740a4aa61f3bd6.jpg) +(g) + +![](images/854eb7161e023ac72349e317bbd48f14d819fd40a78fa3e18d15a393b9eb70de.jpg) + +![](images/0a38d926abace309865e96ed0fa7ae1d59ee271f09d83c2f79104c65bf1a213d.jpg) + +![](images/91ff77c161bdb05768bc4b8db90982cc1fe29f876b7b0b1f3428e584b47e1fae.jpg) + +![](images/e3a63c52160204aa206eb14224cdf211db6deb12b62ab9a39710e3771537e541.jpg) +(h) + +![](images/3fd70946d3437974632ac716509c900feb4f6adb5ee74eb68de33adbc3b48fcd.jpg) +$t = 1$ + +![](images/c43a5d262712149e67614b70aba270b484ade85c900028ef44207df6839fb3e3.jpg) +$t = 3$ + +![](images/e3c5f2ca69cc76a74177aefad5234327826a0fe40e086b42aa1b30e329b152f7.jpg) +$t = 5$ + +![](images/c0734ccf67536ada40c1bc0e7345a4ccde582cb7339238ffc3951fe5f325c7ca.jpg) +$t = 7$ + +method can synthesize frames with eyeglasses even though eyeglasses are not shown in segmentation mask. In Fig. 4 row (f) - (g), we show that using the same image control while replacing the "blond" with "black" in the text description, we can generate frames with similar content except the hair color is changed. Such examples demonstrate that our method has a good understanding of multimodal controls. + +Dependent Multimodal Controls. Furthermore, we intro- + +duce a novel task for multimodal video generation where textual and visual controls are dependent, such that the actual control signals are guided by the textual description. For example, Fig. 3b illustrates how the text informs from which image the model should query color, shape, and background information. More synthesized examples on Multimodal VoxCeleb are given in Fig. 4. For Fig. 4 row (d) - (e), our model learns to combine detailed facial features + +![](images/3ad293db56bfe3b8ecb62d044c09eb4fcfc7df6c70e1935d6505a99c424868eb.jpg) +Figure 5. Extrapolation and Interpolation. Row (a) - (b): long sequence generation via extrapolation. Row (c): interpolating a real sequence. Frames in dotted red boxes are fixed as preservation control. Textual controls for each row are: (a) "Person 024 dressed in 2 is performing random pose, normal speed"; (b) "Person 024 dressed in 1 is performing A-posed, normal speed"; and (c) "Person 028 dressed in 2 is performing A-posed, normal speed." + +from drawing or image and coarse features (i.e., pose) from mask. For Fig. 4 row (i), our method successfully retargets the subject with an appearance from the given image control (IC1) and generates frames with the motion specified by consecutive images that provide motion control (VC1). + +Table 4. Analysis on Shapes for video augmentation strategies. + +
Video AugmentationAccuracy (%)
SwapShuffleColorAffineShapeColorSizeMotionDirAvg
XXXX90.4389.0795.6192.4899.1393.34
✓XXX91.0289.8493.7591.0298.0592.73
X✓XX88.2889.4594.5388.2898.4491.80
XX✓X91.8091.0294.5393.3698.8393.91
XXX✓90.6290.6295.3189.8498.8393.05
✓✓✓✓93.3688.2895.7093.7599.6194.14
+ +# 4.3. Long Sequence Generation and Ablation + +Long Sequence Generation. Our approach enables temporal extrapolation of videos. We show samples of video extrapolation and interpolation in Fig. 5. Samples from Fig. 5 row (a) - (b) are generated by being iteratively conditioned on previous 6 frames to generate the following 2 frames. Fig. 5 row (c) shows an example of synthesizing one frame by interpolating two consecutive real frames. + +Analysis on VID Task. We perform analysis for different VID strategies on the Shapes dataset. Tab. 4 shows that the highest average accuracy is achieved when all augmentation is used (sampled uniformly). Also note that accuracy for color is the highest when we only apply color augmentation. Analysis on Language Embedding. Analysis of using a pretrained language model is shown in Fig. 6. The method with a language model ( $w/$ RoBERTa) is more robust to various text inputs than the one without it ( $w/o$ RoBERTa). + +# 5. Limitation and Conclusion + +This paper targets a new problem, which is video generation using multimodal inputs. To tackle the problem, we utilize a two-stage video generation framework that includes + +![](images/e400669a1482105885e52bf3422e9d4869fe2ed12ce9343d19290ccaf531189b.jpg) +Figure 6. Analysis on language embedding. Samples are generated with out-of-distribution textual inputs. We reword the original text (strikethrough) with equivalent descriptions (italic) that do not exist in the training. We show the first frames from the generated sequences for each method. Frames generated using the pretrained language model ( $w/\text{RoBERTa}$ ) is more correlated with text inputs. + +an autoencoder for quantized representation of images and videos and a non-autoregressive transformer for predicting video tokens from multimodal input signals. 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These models, however, usually designate the similar receptive fields of each token feature within each layer. Such a constraint inevitably limits the ability of each self-attention layer in capturing multi-scale features, thereby leading to performance degradation in handling images with multiple objects of different scales. To address this issue, we propose a novel and generic strategy, termed shunted self-attention (SSA), that allows ViTs to model the attentions at hybrid scales per attention layer. The key idea of SSA is to inject heterogeneous receptive field sizes into tokens: before computing the self-attention matrix, it selectively merges tokens to represent larger object features while keeping certain tokens to preserve fine-grained features. This novel merging scheme enables the self-attention to learn relationships between objects with different sizes, and simultaneously reduces the token numbers and the computational cost. Extensive experiments across various tasks demonstrate the superiority of SSA. Specifically, the SSA-based transformer achieve $84.0\%$ Top-1 accuracy and outperforms the state-of-the-art Focal Transformer on ImageNet with only half of the model size and computation cost, and surpasses Focal Transformer by 1.3 mAP on COCO and 2.9 mIOU on ADE20K under similar parameter and computation cost. Code has been released at https://github.com/OliverRensu/Shunted-Transformer. + +# 1. Introduction + +The recent Vision Transformer (ViT) models [7] have demonstrated superior performance across various computer vision tasks, e.g., classification [6], object detec + +![](images/ed149d145729e54b64a6f5cd36bc73acf845424a163cc095264656dc7a5964f4.jpg) +Figure 1. Top-1 accuracy on ImageNet of recent SOTA CNN and transformer models. Our proposed Shunted Transformer outperforms all the baselines including the recent SOTA focal transformer (base size). Notably, it achieves competitive accuracy to DeiT-S with $2 \times$ smaller model size. + +tion [8, 13], semantic segmentation [4, 36] and video action recognition [15, 22]. Different from convolutional neural networks focusing on local modeling, ViTs partition the input image into a sequence of patches (tokens) and progressively update the token features via global self-attention. The self-attention can effectively model long-range dependencies of the tokens and progressively expand sizes of their receptive fields via aggregating information from other tokens, which accounts largely for the success of ViTs. + +However, the self-attention mechanism also brings the cost of expensive memory consumption that is quadratic w.r.t. the number of input tokens. Thus, state-of-the-art Transformer models have resorted to various down-sampling strategies to reduce the feature size and the memory consumption. For example, the approach of [7] conducts a $16 \times 16$ down-sampling projection at the first layer, and computes the self-attention at the resulted coarse-grained and single-scale feature maps; the incurred fea + +![](images/85515a03a76ea632addc35d74d9196c5aa39adf298fdcf9cff09970c31747ab4.jpg) +(a) ViT + +![](images/716aad53cc18c0600d5d76e4ebce66970a7b7f45f41a2ac768250eb41563d8ac.jpg) +(b)PVT + +![](images/d0d45a48a5fa4085ec44cc7dc17b21d6fbe67e1f17ed416f5d512d22723198f9.jpg) +(c) Ours +Figure 2. Comparison of different attention mechanisms in Vision Transformer (ViT), Pyramid Vision Transformer (PVT), and our SSA with the same feature map size. The number of circles represents the number of tokens involved in the self-attention computation, and reflects the computation cost. The size of the circle indicates the receptive field size of the corresponding token. Unlike ViT and PVT, our method adaptively merges circles on large objects for enhancing computation efficiency, and accounts for objects of different scales simultaneously, e.g., cyan for large sofa, purple for middle size window and orange for small size fan and bottle. + +ture information loss, therefore, inevitably downgrades the model performance. Other approaches strive to compute self-attention at high-resolution features and reduce the cost by merging tokens with spatial reduction on tokens [25, 26, 29]. Nevertheless, these approaches tend to merge too many tokens within one self-attention layer, thereby resulting in a mixture of tokens from small objects and background noise. Such behavior, in turn, makes the model less effective in capturing small objects. + +Besides, prior Transformer models have largely overlooked the multi-scale nature of scene objects within on attention layer, making them brittle to in-the-wild scenarios that involves objects of distinct sizes. Such incompetence is, technically, attributed to the their underlying attention mechanism: existing methods rely on only static receptive fields of the tokens and uniform information granularity within one attention layer, and are therefore incapable of capturing features at different scales simultaneously. + +To address this limitation, we introduce a novel and generic self-attention scheme, termed shunted self-attention (SSA), which explicitly allows the self-attention heads within the same layer to respectively account for coarse-grained and fine-grained features. Unlike prior methods that merge too many tokens or fail in capturing small objects, SSA effectively models objects of various scales simultaneously at different attention heads within the same layer, lending itself to favorable computational efficiency alongside the competence to preserve fine-grained details. + +We show in Figure 2 a qualitative comparison between vanilla self-attention (from ViT), down-sampling aided attention (from PVT), and the proposed SSA. When different attentions are applied to features maps of the same + +![](images/e45d9740ec7354959feda499aa0727af251b1915175a7c98501b164112d11318.jpg) +Image +Figure 3. The attention map of PVT and our model. PVT attends to only large objects like sofa and bed, while our model, by contrast, precisely captures the small objects like lights alongside large ones. + +![](images/12c9853db3a30b7c7d1046201dee4445a7ac9aaf17278dd141437b19e3fefcd3.jpg) +PVT + +![](images/ef680358be7c455632abb5235965da15fbfe5b8e54c7f0eaff2f9da6c30e72c1.jpg) +Ours + +size, ViT captures fine-grained small objects yet with an extremely heavy computational cost (Figure 2(a)); PVT reduces the computation cost but its attention is limited only to coarse-grained larger objects (Figure 2(b)). By contrast, the proposed SSA maintains a light computational load yet simultaneously accounts for hybrid-scale attention (Figure 2(c)). Effectively, SSA precisely attends to not only coarse-grained large objects (e.g., sofa) but also fine-grained small objects (e.g., bottle and fan), even some of those located at the corners, which are unfortunately missed by PVT. We also show visual comparisons of attention maps in Figure 3, to highlight the learned scale-adaptive attention of SSA. + +The multi-scale attentive mechanism of SSA is achieved via splitting multiple attention heads into several groups. Each group accounts for a dedicated attention granularity. For the fine-grained groups, SSA learns to aggregate few tokens and preserves more local details. For the remaining coarse-grained head groups, SSA learns to aggregate a large amount of tokens and thus reduces computation cost while preserving the ability of capturing large objects. The multi-grained groups jointly learn multi-granularity information, making the model able to effectively model multi-scale objects. + +As depicted in Figure 1, we demonstrate the performance of our Shunted Transformer model obtained from stacking multiple SSA-based blocks. On ImageNet, our Shunted Transformer outperforms the state of the art, Focal Transformers [29], while halving the model size. When scaling down to tiny sizes, Shunted Transformer achieves performance similar to that of DeiT-Small [20], yet with only $50\%$ parameters. For object detection, instance segmentation, and semantic segmentation, Shunted Transformer consistently outperforms Focal Transformer on COCO and ADE20K with a similar model size. + +In sum, our contribution are listed as follows. + +- We propose the Shunted Self-Attention (SSA) which unifies multi-scale feature extractions within one self-attention layer via multi-scale token aggregation. Our SSA adaptively merges tokens on large objects for + +computation efficiency and preserves the tokens for small objects. + +- Based on SSA, we build our Shunted Transformer, which is able to capture multi-scale objects especially small and remote isolated objects efficiently. +- We evaluate our proposed Shunted Transformer on various studies including classification, object detection, and segmentation. Experimental results demonstrate that our Shunted Transformer consistently outperform previous Vision Transformers under similar model sizes. + +# 2. Related Work + +# 2.1. Self-Attention in CNNs + +The receptive field of a convolution layer is usually small and fixed. Although dilated convolution [30] enlarge the receptive filed and deformable convolution allows some offsets [5] for the kernel, it is hard for them to be adaptive and flexible to extend to the whole feature maps. Inspired by the self-attention [21] layer of transformers pioneered in the NLP field, some works introduce self-attention or non-local blocks [27] to augment convolutional neural networks in the computer vision field. Such attentions always apply in the deep layers, where the size of feature map is small and preprocessed by multiple convolution layers. Therefore, they do not incur too much additional computation cost but bring limited performance improvements. + +# 2.2. Vision Transformer + +Vision Transformer (ViT) [7] models directly apply self-attention in very shadow layers to build a convolution-free neural network model. Since the seminal ViT model, many follow-up works are developed to improve the model's classification performance [17, 20] via more complex data augmentation or knowledge distillation. Because the computational complexity of self-attention is quadratic w.r.t. the number of tokens, it is hard for them to directly apply on large number of tokens. Therefore, these ViT models usually partition the image into non-overlapped and largesize patches (tokens). But such partitioning is too coarse and loses much fine-grained information. To preserve fine-grained features, + +these models usually down-sample the feature maps and operate on low-resolution features. This compromise however impedes their deployment in dense-prediction tasks like segmentation and detection. + +# 2.3. Efficient ViT Variants + +To make the self-attention attention applicable on large-size feature maps, recent works develop two solution strategies [2, 14, 25, 26, 29] to reduce the computation cost: (1) + +![](images/b457fedb0be8d5f212aa04c182cebfcc892616dc2d49b064571ee02c408e1903.jpg) +Figure 4. Comparing our shunted self-attention with self attention in ViT, Swin, PVT. ViT applies self-attention globally on small-size feature maps. Swin Transformer applies local self-attention on large-size feature maps within small regions. PVT fuses the key and value with a large stride. Differently, our shunted self-attention conducts multi-scale token aggregation for obtaining key and value of various sizes. + +split the features maps into regions and perform local self-attention within the region or (2) merge tokens to reduce the number of tokens. The representative work of local attention is the Swin Transformer [14] that splits feature maps into non-overlap squared regions and do the self-attention locally. However, to model global dependencies via self-attention, these local attention needs to shift the windows over the image or stack a lot of layers for obtaining a global receptive field. Regarding the strategy of token merging, PVT (Pyramid Vision Transformer) [26] designs a spatial-reduction attention to merge tokens of key and query. However, PVT and similar models tend to merge too many tokens in such spatial-reduction. This makes the fine-grained information of small objects mixed with the background and hurts model's performance. Therefore, we propose the shunted self-attention that can simultaneously preserve coarse- and fine-grained details while maintaining a global dependency modeling over the image tokens. + +# 3. Method + +The overall architecture of our proposed Shunted Transformer is illustrated in Figure 5. It is built upon the novel shunted self-attention (SSA) blocks. There are two main differences between our SSA blocks and the traditional self-attention blocks in ViT: 1) SSA introduces a shunted attention mechanism for each self-attention layer to capture multi-granularity information and better model objects with different sizes, especially the small objects; 2) it enhances the capability of extracting local information in the pointwise feed-forward layer by augmenting the cross-token interaction. Besides, our Shunted Transformer deploys a new patch embedding method for obtaining better input feature + +![](images/28c9bbff468c23e5c44faef06fb5bf51755af9dacacb2ce7d5b412c6ab94336b.jpg) +Figure 5. Left: the overall architecture of our Shunted Transformer. Right: details of our Shunted Self-Attention block. + +maps for the first attention block. In the following, we elaborate on these novelties one by one. + +# 3.1. Shunted Transformer Block + +In the $i$ -th stage of the proposed Shunted Transformer, there are $L_{i}$ transformer blocks. Each transformer block contains a self-attention layer and a feed-forward layer. To reduce the computation cost when processing high-resolution feature maps, PVT [26] introduces spatial-reduction attention (SRA) to replace the original multi-head self-attention (MSA). However, SRA tends to merge too many tokens within one self-attention layer and only provides token features at a single scale. These limitations impede the capability of the models in capturing multiscale objects especially the small-size ones. Therefore, we introduce our shunted self-attention with learning multi-granularity within one self-attention layer in parallel. + +# 3.1.1 Shunted Self-Attention + +The input sequence $F \in \mathbb{R}^{h \times w \times c}$ are projected into query $(Q)$ , key $(K)$ and value $(V)$ tensors at first. Then the multi-head self-attention adopts $H$ independent attention heads to compute self-attention in parallel. To reduce the computation cost, we follow the PVT [26] and reduce the length of $K$ and $V$ instead of splitting $\{Q, K, V\}$ into regions as in Swin Transformer [14]. + +As show in Figure 4, our SSA is different from the SRA of PVT in that the length of $K$ , $V$ is not identical across the attention heads of the same self-attention layer. Instead, the length varies in different heads for capturing different granularity information. This gives the multi-scale token aggregation (MTA). Specifically, the keys $K$ and values $V$ are down-sampled to different sizes for different heads indexed by $i$ : + +$$ +Q _ {i} = X W _ {i} ^ {Q}, +$$ + +$$ +K _ {i}, V _ {i} = M T A (X, r _ {i}) W _ {i} ^ {K}, M T A (X, r _ {i}) W _ {i} ^ {V}, \tag {1} +$$ + +$$ +V _ {i} = V _ {i} + L E (V _ {i}). +$$ + +Here the $\mathrm{MAT}(\cdot ;r_i)$ is the multi-scale token aggregation layer in the $i$ -th head with the down-sampling rate of + +$r_i$ . In practice, we take a convolution layer with kernel size and stride of $r_i$ to implement the down-sampling. $W_{i}^{Q}, W_{i}^{K}, W_{i}^{V}$ are the parameters of the linear projection in the $i$ -th head. There are variant $r_i$ in one layer across the attention heads. Therefore, the key and value can capture different scales in a self-attention. $LE(\cdot)$ is the local enhancing component of MTA for value $V$ by a depth-wise convolution. Comparing with the spatial-reduction [26], more fine-grained and low-level details are preserved. + +Then the shunted self-attention is calculated by: + +$$ +h _ {i} = \operatorname {S o f t m a x} \left(\frac {Q _ {i} K _ {i} ^ {\top}}{\sqrt {d _ {h}}}\right) V _ {i} \tag {2} +$$ + +where $d_h$ is the dimension. Thanks to multi-scale key and value, our shunted self-attention is more powerful in capturing multi-scale objects. The computation cost reduction may depend on the value of $r$ , therefore, we can well define the model and $r$ to trade-off the computation cost and model performance. When $r$ grows large, more tokens in $K, V$ are merged and the length of $K, V$ is shorter, therefore, the computation cost is low but it still preserve the ability of capturing large objects. In contrast, when $r$ becomes small, more details are preserved but brings more computation cost. Integrating various $r$ in one self-attention layer enables it to capture multi-granularity features. + +# 3.1.2 Detail-specific Feedforward Layers + +In the traditional feed forward layer, the fully connected layer are point-wise and no cross token information can be learnt. Here, we aim at complementing local information by specifying the details in the feedforward layer. As shown in Figure 6, we complement the local details in the feed forward layer by adding our data specific layer between the two fully connected layer in the feed forward layer: + +$$ +x ^ {\prime} = F C (x; \theta_ {1}), +$$ + +$$ +x ^ {\prime \prime} = F C (\sigma \left(x ^ {\prime} + D S \left(x ^ {\prime}; \theta\right)\right); \theta_ {2}), \tag {3} +$$ + +where $DS(\cdot; \theta)$ is the detail specific layer with parameters $\theta$ , implemented by a depth-wise convolution in practice. + +
Output SizeLayer NameShunted-TinyShunted-SmallShunted-BaseShunted-L
Stage156x56Transformer Blockr_i=\begin{cases}4 & i<\frac{head}{2}\\8 & i\geq\frac{head}{2}\\C_1=64, head=2,N_1=1\end{cases}r_i=\begin{cases}4 & i<\frac{head}{2}\\8 & i\geq\frac{head}{2}\\C_1=64, head=2,N_1=2\end{cases}r_i=\begin{cases}4 & i<\frac{head}{2}\\8 & i\geq\frac{head}{2}\\C_1=64, head=2,N_1=3\end{cases}r_i=\begin{cases}4 & i<\frac{head}{2}\\8 & i\geq\frac{head}{2}\\C_1=64, head=2,N_1=4\end{cases}
Stage228x28Transformer Blockr_i=\begin{cases}2 & i<\frac{head}{2}\\4 & i\geq\frac{head}{2}\\C_2=128, head=4,N_1=2\end{cases}r_i=\begin{cases}2 & i<\frac{head}{2}\\4 & i\geq\frac{head}{2}\\C_2=128, head=4,N_1=4\end{cases}r_i=\begin{cases}2 & i<\frac{head}{2}\\4 & i\geq\frac{head}{2}\\C_2=128, head=4,N_1=4\end{cases}r_i=\begin{cases}2 & i<\frac{head}{2}\\4 & i\geq\frac{head}{2}\\C_2=128, head^4,N_1=8\end{cases}
Stage314x14Transformer Blockr_i=\begin{cases}1 & i<\frac{head}{2}\\2 & i\geq\frac{head}{2}\\C_3=256, head=8,N_1=4\end{cases}r_i=\begin{cases}1 & i<\frac{head}{2}\\2 & i\geq\frac{head}{2}\\C_3=256, head=8,N_1=12\end{cases}r_i=\begin{cases}1 & i<\frac{head}{2}\\2 & i\geq\frac{head}{2}\\C_3=256, head=8,N_1=24\end{cases}r_i=\begin{cases}1 & i<\frac{head}{2}\\2 & i\geq\frac{head}{2}\\C_3=320, head=10,N_1=32\end{cases}
Stage47x7Transformer Blockr=1 +C_4=512, head=16, N_1=1r=1 +C_4=512, head=16, N_1=1r=1 +C_4=512, head=16, N_1=2r=1 +C_4=768, head=24, N_1=2
+ +Table 1. Model variants for our Shunted Transformer. $C$ and $N$ represent the dimension and number of blocks. head indicates the number of heads. + +![](images/fd7d357369d0fd71f7dc52550ee0408cefacc3efaa79deb3079b2b31703d926e.jpg) +Figure 6. Comparing the feed-forward layer in ViT (left), PVT (right), and our detail-specific feedforward layer. We complement fine-grained cross-token details in the feed-forward layer. + +# 3.2. Patch Embedding + +Transformer is firstly designed for handling sequential data. How to map the image to sequence is important for the model's performance. ViT directly splits the input image into $16 \times 16$ non-overlap patches. A recent study [23] finds using convolution in the patch embedding provides a higher-quality token sequence and helps transformer "see better" than a conventional large-stride non-overlapping patch embedding. Therefore, some works [14, 26] conduct overlapped patch embedding like using a $7 \times 7$ convolution. + +In our model, we take different convolution layers with overlapping based on the model size. We take a $7 \times 7$ convolution layer with stride of 2 and zero padding as the first layer in the patch embedding, and add extra $3 \times 3$ convolution layer with stride of 1 depending on the model size. Finally, a non-overlapping projection layer with stride of 2 to generate the input sequence with size of $\frac{H}{4} \times \frac{W}{4}$ . + +# 3.3. Architecture Details and Variants + +Given an input image with size of $H \times W \times 3$ , we adopt the above patch embedding scheme for obtaining more informative token sequence with the length of $\frac{H}{4} \times \frac{W}{4}$ + +and the token dimension of $C$ . Following previous designs [2, 14, 26, 29], there are four stages in our model and each stage contains several Shunted Transformer blocks. In each stage, each block outputs the feature maps of the same size. We take a convolution layer with stride 2 (Linear embedding) to connect different stages and the size of the feature maps will be halved before feeding into the next stage, but the dimension will be doubled. Therefore, we have four feature maps $F_{1}, F_{2}, F_{3}, F_{4}$ of the output of each stage and the size of $F_{i}$ is $\frac{H}{2^{i+1}} \times \frac{W}{2^{i+1}} \times (C \times 2^{i-1})$ . + +We propose three kinds of different configurations of our model for fair comparison under similar parameters and computation costs. As show in Table 1, head and the $N_{i}$ indicate the number of heads in one block and the number of blocks in one stage. The variants only comes from the number of layers in different stage. Specifically, the number of head in each block is set 2,4,8,16. The convolution in the patch embedding range from 1 to 3. + +# 4. Experiments + +To evaluate the effectiveness of our Shunted Transformer, we apply our model on ImageNet-1K [6] classification, COCO [13] object detection and instance segmentation, ADE20K [36] semantic segmentation. Besides, we evaluate effects of different components of our model via ablation studies. + +# 4.1. Image Classification on ImageNet-1K + +We first evaluate our model and compare it with recent SOTA CNN and transformer based models on ImageNet-1K. For fair comparison, we follow the same training strategies of DeiT [20] and PVT [26]. Specifically, we take AdamW as the optimizer with the weight decay of 0.05. The whole training epochs are 300 with the input size of $224 \times 224$ , and the batch size is 1024. The learning rate is set to $1 \times 10^{-3}$ following cosine learning rate decay. The data + +
ModelParams (M)Image SizeFLOPs (G)Top1 (%)
ResNet-18 [12]11.722421.869.8
Reg-1.6G [16]11.222421.678.0
DeiT-T [20]5.722421.372.2
PVT-T [26]13.222421.975.1
PVTv2-b1 [25]13.122422.178.7
Shunted-T11.522422.179.8
ResNet-50 [12]25.022424.176.2
Reg-4G [16]20.622424.079.4
Efficient-B4 [19]1938024.282.9
DeiT-S [20]22.122424.679.9
T2T-14 [31]22.022425.281.5
DeepViT-S [37]27.022426.282.3
ViL-S [34]24.622424.982.0
TNT-S [11]23.822425.281.3
CViT-15 [1]27.422425.681.5
PVT-S [26]24.522423.879.8
Swin-T [14]28.322424.581.2
Twin-S [2]2422422.981.7
Focal-T [29]29.122424.982.2
PVTv2-b2 [25]25.422424.082.0
Shunted-S22.422424.982.9
Shunted-S22.438424.984.3
ResNet-101 [12]45.022427.977.4
ViT-B [7]86.6224217.677.9
DeiT-B [20]86.6224217.581.8
Swin-S [14]49.622428.783.1
Swin-B [14]87.8224215.483.4
PVT-M [26]44.222426.781.2
PVT-L [26]61.422429.881.7
Focal-S [29]51.122429.183.5
Focal-B [29]89.8224216.083.8
Shunted-B39.622428.184.0
Shunted-L81.2224214.984.6
DeiT-B [20]86.6384255.483.1
Swin-B [14]87.8384247.084.2
Shunted-B39.6384227.285.5
Shunted-L81.2384248.485.8
+ +Table 2. Comparison of different backbones on ImageNet-1K classification. + +augmentations and regularization methods follow DeiT [20] including random cropping, random flipping, label smoothing [18], Mixup [33], CutMix [32] and random erasing [35]. + +As shown in Table 2, by comparing with other CNN backbones under similar parameters and computation cost, our model is the first transformer based model that achieves comparable results with EfficientNet which uses much larger input resolution. Notably, although RegNet and EfficientNet come from neural architecture search, our manually designed Transformer still outperform them. + +We then compare our model with Transformer backbones. Our tiny model achieves similar performance with + +Transformer baseline (DeiT-S) but only requires half of parameters $(22\mathrm{M}\rightarrow 11\mathrm{M})$ and computation cost $(4.6\mathrm{G}\rightarrow 2.1\mathrm{G}$ FLOPs). When our model size grows similar to DeiT-S, it outperforms by $3\%$ . Comparing with the very recent SOTA models like Swin and Twin, our model consistently outperform them. Specifically, our small-size model outperforms the existing state-of-the-art, Focal Transformer Tiny by $0.7\%$ , while reducing the model size by $20\%$ . When model size grows large, our base model achieves state-of-the-art performance with only half of parameters and computation cost comparing with Focal Transformer. + +We further fine-tune our model 30 epochs on the size of $384 \times 384$ , and whether the model size is small or base, our model shows more superiority over Swin Transformer. + +# 4.2. Object Detection and Instance Segmentation + +We evaluate the models for object detection and instance segmentation on COCO 2017 [13]. We take our proposed Shunted Transformer as backbone and plug it into Mask R-CNN. We compare it with other SOTA backbones including ResNet, Swin Transformer, Pyramid Vision Transformer, Twin and Focal Transformer. We follow the same settings of Swin: pretraining on ImageNet-1K and fine-tuning on COCO. In the fine-tuning stage, we take two training schedules: $1 \times$ with 12 epochs and $3 \times$ with 36 epochs. In $1 \times$ schedule, the shorter side of the input image will be resize to 800 while keeping the longer side no more than 1333. In $3 \times$ schedule, we take multi-scale training strategy of resizing the shorter size between 480 to 800. We take AdamW with weight decay of 0.05 as the optimizer. The batch size is 16 and initial learning rate is $10^{-4}$ . + +In Table 3, we take Mask-RCNN for object detection and report the bbox mAP $(AP^b)$ of different CNN and Transformer backbones. Under comparable parameters, our model outperforms previous SOTA with a significant gap. For object detection, with $1\times$ schedule, our tiny model achieves 9.1 points improvements over ResNet-50, and 2.3 points over Focal Transformer with only $85\%$ model size. Moreover, with $3\times$ schedule and multi-scale training, our backbone still concisely outperforms CNN backbones over 7.7 and Transformer backbone over 1.6 points on average. We find similar results in instance segmentation. We report the mask mAP $(AP^m)$ in Table 3. Our model achieves 8.1 points higher than ResNet-50 and 1.5 points higher than Focal Transformer in $1\times$ schedule and in $3\times$ schedule. Our model achieves these superior performances at a smaller model size, clearly demonstrating the benefits of its shunted attention for learning multi-granularity tokens and effectiveness in handling presence of multi-scale visual objects. + +We also report the results of RetinaNet in the Table 4. With the least parameters, our model outperforms all the previous ones in both $1 \times$ and $3 \times$ schedule. Comparing with PVT, our model brings improvements on all small, medium + +
BackboneParams (M)Mask R-CNN 1× scheduleMask R-CNN 3× schedule + MS
\(AP^b\)\(AP_{50}^b\)\(AP_{75}^b\)\(AP^m\)\(AP_{50}^m\)\(AP_{75}^m\)\(AP^b\)\(AP_{50}^b\)\(AP_{75}^b\)\(AP^m\)\(AP_{50}^m\)\(AP_{75}^m\)
Res50 [12]4438.058.641.434.455.136.741.061.744.937.158.440.1
PVT-S [26]4440.462.943.837.860.140.343.065.346.939.962.542.8
Swin-T [14]4842.264.646.239.161.642.046.068.250.241.665.144.8
TwinP-S [2]4442.965.847.140.062.742.946.869.351.842.666.346.0
Twin-S [2]4443.466.047.340.363.243.446.869.251.242.666.345.8
Focal-T [29]4944.867.749.241.064.744.247.269.451.942.766.545.9
Shunted-S4247.168.852.142.565.845.749.170.653.843.967.847.5
Res101 [12]6340.461.144.236.457.738.842.863.247.138.560.141.3
PVT-M [26]6442.064.445.639.061.642.144.266.048.240.563.143.5
Swin-S [14]6944.866.648.940.963.444.248.570.253.543.367.346.6
Swin-B [14]10746.9--42.3--48.569.853.243.466.846.9
TwinP-B [2]6444.666.748.940.963.844.247.970.152.543.267.246.3
Twin-B [2]7645.267.649.341.564.544.848.069.552.743.066.846.6
Focal-S [29]7147.469.851.942.866.646.148.870.553.643.867.747.2
Shunted-B5948.069.853.343.266.946.850.170.954.145.268.048.0
+ +Table 3. Object detection and instance segmentation with Mask R-CNN on COCO. Only $3 \times$ schedule has the multi-scale training. All backbone are pretrained on ImageNet-1K. + +
BackboneParams (M)RetinaNet 1× scheduleRetinaNet 3× schedule + MS
APbAP50AP75APSAPMAPLAPbAP50AP75APSAPMAPL
Res50 [12]37.736.355.338.619.340.048.839.058.441.822.442.851.6
PVT-S [26]34.240.461.343.025.042.955.742.262.745.026.245.257.2
ViL-S [26]35.741.662.544.124.944.656.242.963.845.627.846.456.3
Swin-T [14]38.542.063.044.726.645.855.745.065.948.429.748.958.1
Focal-T [29]39.443.765.246.728.647.456.945.566.348.831.249.258.7
PVTv2-b2* [25]35.144.665.647.627.448.858.6------
Shunted-S32.145.465.949.228.749.360.046.466.750.431.051.060.8
+ +Table 4. Object detection with RetinaNet on COCO. Only $3 \times$ schedule has the multi-scale training. All backbone are pretrained on ImageNet-1K. * indicate that methods have not been peer reviewed. + +and large size objects which shows the strong power of capturing multi-scale objects in our shunted self-Attention. + +# 4.3. Semantic Segmentation on ADE20K + +We evaluate the performance of our model for semantic segmentation on the ADE20K [36] dataset. There are 20,210 images for training, 2,000 images for validation and 3,352 images for testing with 150 fine-grained semantic categories. We report the mIOU with and without multi-scale testing. We take UperNet and Semantic FPN as the main frameworks and take different architectures as backbones. We follow the defaults settings of Focal Transformer and mmsegmentation [3]. For UperNet, we take AdamW with weight decay of 0.01 as the optimizer for 160K iterations. The learning rate is $6 \times 10^{-5}$ with 1500 iteration warmup at the beginning of training and linear learning rate decay. The augmentations include random flipping, random scaling and random photo-metric distortion. The input size is $512 \times 512$ in training, and single scale and multi-scale (MS) test. For SemanticFPN, we take AdamW with weight decay of 0.0001 as the optimizer and the learning rate is also + +0.0001 for 80K iterations. + +The results are reported in Table 5. Our Shunted Transformer outperforms previous state-of-the-art with a large margin and less parameters for all the frameworks. Specifically, when using semantic FPN, our model outperforms the Swin Transformer by $6.7\mathrm{mIOU}$ , with $20\%$ model size reduction. When the framework is UpperNet, our Shunted Transformer is $3.1\%$ and $2.9\%$ higher than focal transformer. The results of segmentation show the superiority of our Shunted Transformer. + +We also take SegFormer [28] as the framework and compare our backbone with the MiT in the SegFormer. The results are reported in Table 6. With less parameters, our method achieve $1.8\mathrm{mIoU}$ improvements over SegFormer. + +# 4.4. Ablation Studies + +Patch Embedding Many recent works [9, 10, 24] study the function of the image to token mapping, i.e. the patch embedding head. They find well-designed head provide better input sequence for the transformer models. We evaluate the impact of our patch embedding with non-overlap head in + +
BackboneSemantic FPN 80kUpernet 160K
Param (M)FLOPs (G)mIOU (%)Param (M)FLOPs (G)mIOU (%)MS mIOU (%)
ResNet-50 [12]28.518336.7----
Swin-T [14]31.918241.559.994544.545.8
PVT-S [26]28.211639.8----
TwinsP-S [2]28.416244.354.691946.247.5
Twin-S [2]28.314443.254.490146.247.1
Focal-T [29]---6299845.847.0
Shunted-S26.118348.25294048.949.9
+ +Table 5. Comparison of the segmentation performance of different backbones in Semantic FPN and UpperNet framework on ADE20K. + +
BackboneParams(M)FLOPs (G)mIoU
MiT-B227.562.446.5
Ours25.170.348.3
+ +ViT, overlap head in Swin and PVT. The results are shown in Table 7. With more complex head like overlapping or our patch embedding, the computation cost and model size only slightly grow, but the performance improves relatively significant. Specifically, with limited additional parameters, from the traditional non-overlap head or the overlap head to patch embedding, the model achieves $1.4\%$ and $0.3\%$ performance gain respectively. + +Table 6. Comparison of different backbone in Segformer framework on Ade20K. + +
Patch EmbeddingParams (M)FLOPs (G)Top-1 (%)
Non-Overlap22.34.481.5
Overlap22.44.582.6
Ours22.44.982.9
+ +Token Aggregation Function We propose a new token aggregation function to merge tokens for multi-scale objects and keeping the global and local information simultaneously. From Table 8, our novel token aggregation function has similar computation with the convolutional spatial-reduction but gain more improvements. + +Table 7. Top-1 accuracy on ImageNet of different patch embedding heads. Our patch embedding requires slightly more computation cost, but the performance improvement is significant. + +
AggregationParams(M)FLOPs (G)Top-1 (%)
Linear18.54.582.1
Convolution22.44.982.6
Ours22.44.982.9
+ +Detail-specific Feed-Forward In the Feed-Forward layer [20], all the operation is point-wise and no cross + +token operations exist, therefore, complement the cross token and local information will significantly improves the learning ability of the feed-forward layer. In Table 9, we compare our new detail-specific feed-forward layer, traditional feed-forward layer [20] and convolutional feed-forward layer [25] in ViT and our model. The detail-specific feed-Forward consistently brings performance gain over the traditional feedforward layer which indicate the utility of complementing the local details in the feedforward layer. + +Table 8. Top-1 accuracy on ImageNet of different token aggregation functions. + +
LayersBackboneTop-1 (%)
FeedforwardViT79.8
Conv-FeedforwardViT80.5
Detail Specific FeedforwardViT80.7
FeedforwardShunted82.6
Conv-FeedforwardShunted82.7
Detail Specific FeedforwardShunted82.9
+ +Table 9. With similar parameter numbers and FLOPs, Detail-specific feedForward layers provide higher top-1 accuracy on ImageNet than the traditional feedforward ones. + +# 5. Conclusion + +In this paper, we present a novel Shunted Self-Attention (SSA) scheme to explicitly account for multiscale features. In contrast to prior works that focus on only static feature maps in one attention layer, we maintain various-scale feature maps that attend to multi-scale objects within one self-attention layer. Extensive experiments show the effectiveness of our model as a backbone for various downstream tasks. Specifically, the proposed model outperforms prior Transformers, and achieves state-of-the-art results on classification, detection, and segmentation tasks. + +# Acknowledgement + +This work is supported by NUS Faculty Research Committee Grant (WBS: A-0009440-00-00) and NRF Centre for Advanced Robotics Technology Innovation (CARTIN). + +# References + +[1] Chun-Fu Chen, Quanfu Fan, and Rameswar Panda. Crossvit: Cross-attention multi-scale vision transformer for image classification. arXiv preprint arXiv:2103.14899, 2021. 6 +[2] Xiangxiang Chu, Zhi Tian, Yuqing Wang, Bo Zhang, Haibing Ren, Xiaolin Wei, Huaxia Xia, and Chunhua Shen. Twins: Revisiting the design of spatial attention in vision transformers. In NeurIPS, 2021. 3, 5, 6, 7, 8 +[3] MMSegmentation Contributors. 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Since the same state may be various in the visual appearance while entangled with different objects, CZSL is still a challenging task. Some methods recognize state and object with two trained classifiers, ignoring the impact of the interaction between object and state; the other methods try to learn the joint representation of the state-object compositions, leading to the domain gap between seen and unseen composition sets. In this paper, we propose a novel Siamese Contrastive Embedding Network (SCEN)1 for unseen composition recognition. Considering the entanglement between state and object, we embed the visual feature into a Siamese Contrastive Space to capture prototypes of them separately, alleviating the interaction between state and object. In addition, we design a State Transition Module (STM) to increase the diversity of training compositions, improving the robustness of the recognition model. Extensive experiments indicate that our method significantly outperforms the state-of-the-art approaches on three challenging benchmark datasets, including the recent proposed C-QGA dataset. + +# 1. Introduction + +Humans possess the ability to compose their knowledge of known entities to generalize to novel concepts inherently. Given words, such as green horse, people can combine the known state green with the known object horse immediately, although they have never seen the inexistent stuff. To equip an AI system the similar ability, Compositional Zero-Shot Learning (CZSL) [20] is proposed, which aims to recognize unseen compositions composed of a set of seen states and objects. In CZSL setting, each composition comprises two components, namely, state and object, where the compositions of train and test sets are disjoint. + +![](images/0cefe8e670e2f61d9c66bd6956258f7bf60aa30ee4daaff5d1ea24f0678d03ce.jpg) +Figure 1. The overall concept of our method. We aim to separately extract discriminative prototypes of state and object based on establishing state and object specific databases, which can generalize to represent corresponding properties. + +In order to infer unknown concepts such as green horse, CZSL aims to understand the meaning of state green and object horse after trained on other compositional concepts that separately contain green or horse, e.g., green grasses and young horse. The challenge of the task lies in the interaction degree between state and object that we cannot quantify, which gives rise to varying contextuality within different state-object combinations. For instance, we can not equate the state old in old car and that in old tiger, since they are fundamentally distinct in visual presentations, which greatly hinders the recognition of novel compositions. + +Existing mainstream methods [17, 20, 26] focus on converting such problem into a general supervised recognition task by training two classifiers for state and object, respectively. They aim to directly predict state and object from the original visual features, ignoring their entanglement. Based on this problem, classifiers cannot capture discriminative state and object features, which potentially limits the recognition accuracy. In addition, other methods [23, 24] aim to learn a common embedding space where the compositions as well as visual features can be projected to narrow the distance between them, such as Euclidean distance. However, these methods, only regarding compositions as enti + +ties, neglect the domain gap between training and testing compositions, which can be simply confused by similar images from unseen compositions (e.g., young cat and young tiger). Therefore, it is vital to excavate the discriminative prototypes of state and object to separate the interaction between them and consider the domain transfer between training and testing samples. + +To address the problem mentioned above, we propose a Siamese Contrastive Embedding Network (SCEN) for recognizing novel compositions in this paper, aiming to excavate discriminative prototypes of state and object, respectively, as shown in Fig. 1. To be specific, we first project the visual features into state/object-based contrastive spaces to gain the prototypes of state and object. Then, to excavate the discriminative prototypes by contrastive constraints, we set up specific databases named State-constant and Object-constant databases as positive samples. Besides, a shared irrelevant database is built up as a negative sample set, which is embedded into two contrastive spaces. Benefiting from this learning paradigm, our proposed model can successfully excavate discriminative prototypes to represent the corresponding component. In addition, considering that the distribution between seen and unseen compositions is discrepant, we present a State Transition Module (STM), which generates the virtual but reasonable samples to augment the diversity of training data. In this way, the domain gap between seen and unseen composition sets can be mitigated effectively. + +To sum up, our main contributions are as follows: + +- We propose a novel Siamese Contrastive Embedding Network (SCEN) to excavate prototypes of state and object for successfully recognizing both seen and unseen compositions. +- We present a State Transition Module (STM) to produce virtual samples and augment the diversity of training compositions, guiding the model to generalize to those compositions not existing in the training process, and alleviating the issue of model migration performance. +- Comprehensive experimental results on three benchmark datasets demonstrate the effectiveness of our proposed approach, which outperforms the state-of-the-art CZSL methods. + +# 2. Related Work + +Compositional Zero-Shot Learning. The goal of Com- compositional Zero-Shot Learning [7, 17, 19, 20, 23, 26, 30] is to learn the compositionality of objects and their states from the training data and is tasked with the generalization to an unseen combination of these primitives. Compared + +with typical Zero-Shot Learning [15, 16, 29] that utilizes inherent semantic descriptions or attributed vectors to recognize unseen instances, CZSL exploits transferable knowledge by two compositional parts as image labels: objects and states. There are two mainstream methods in this direction. The first mainstream approach is inspired by [2, 11], which learns a single classifier for recognition and a transformation module [20]. In addition, [23] models each state as a linear transformation of objects. [32] aims to learn disentangled and compositional primitives hierarchically. [17] models objects to be symmetric under attribute transformations. Other methods try to learn the joint representation of the state-object compositions [1, 26, 28]. They aim to learn a modular network to rewire the new compositions conditioned on each composition [26, 28]. Recently, GCN [22] is proposed to utilize a causal graph to establish the relationship between state and object reasonably. However, these methods ignore the interaction between state and objects that brings a negative influence for compositions recognition. + +As for [1], the author argues to tackle the CZSL problems through a causal graph where the latent features of primitives are independent from each other. However, it also neglects the discriminant analysis of state and object, which cannot excavate discriminative primitives for classification. In addition, there still exists a domain gap between seen and unseen compositions, although they are made up of the same states and objects, which potentially limits the performance of the model. + +Contrastive Learning. Inspired by noise contrastive estimation [8, 21, 34], contrastive learning has attracted much attention which leads to major advances in self-supervised representation learning. An efficient way to get better contrastive learning is to employ large numbers of negative examples and design more semantically meaningful augmentations to create different view of images. SimCLR [4] implements two data augmentation paths and a learnable non-linear transformation to train an encoder with a large batch by pulling the features embedding from the same images. Momentum Contrast (MoCo) [9] is presented which enables building a large and consistent dictionary on-the-fly and transfers well to downstream tasks. Aiming at improving generalization in real domains, a contrastive synthetic-to-real generalization model [5] is proposed to prevent overfitting to the synthetic domain by leveraging the pre-trained ImageNet knowledge. More recently, supervised contrastive learning [13] is proposed to extend the self-supervised batch contrastive approach to the fully supervised setting which can effectively leverage label information. + +Based on the effectiveness of Contrastive Learning, the differences between this study and existing works are given below. First, we propose a Siamese Contrastive Embedding + +![](images/68322567c509d45999a48e99ea9cdbefa84977a401184ca338c0850a6462aa1b.jpg) +Figure 2. The framework of our SCEN method. The proposed method consists of State-Specific Encoder $E_{s}$ , Object-Specific Encoder $E_{o}$ , and a State Transition Module (STM). The prototypes of state $h_{s}$ and object $h_{o}$ are separately encoded from Specific Encoders. Prototypes are trained conditioned on two different contrastive embedding spaces, where the anchor and negative samples are shared. In addition, STM aims to generate virtual samples with the help of the adversarial loss function, which diversifies and rationalizes the states of objects effectively. Along with the increasing of the realistic samples, Specific Encoders gradually gain the ability to extract discriminative prototypes that can be generalized to novel compositions. + +Network (SCEN) to excavate the discriminative prototypes of state and object, respectively. Besides, we present a State Transition Module (STM) to produce a virtual composition in training to improve the generalization of the proposed model. Second, we construct two contrastive spaces and utilize contrastive constraints to enforce the prototypes of state and object to be discriminative and generalized. + +# 3. Approach + +The goal of CZSL is to recognize the novel compositional samples whose labels are composed of a state (e.g., old) and an object (e.g., tiger). This is particularly challenging since various states significantly change the visual appearance of an object, which hinders the performance of the classifiers. + +We propose a novel formulation to tackle the problem, namely Siamese Contrastive Embedding Network (SCEN), which constructs two independent embedding spaces and utilizes contrastive losses to guide corresponding feature extractors to excavate discriminative prototypes of state and object separately. The overview of our approach is shown in Fig. 3. + +# 3.1. Problem Definition + +In CZSL setting, each image consists of two primitive concepts. i.e., a state and an object. Given $\mathcal{A}$ and $\mathcal{O}$ as two sets of states and objects, we can compose a set of state-object pairs, i.e., $\mathcal{C} = \mathcal{A} \times \mathcal{O} = \{(a,o) \mid a \in \mathcal{A}, o \in \mathcal{O}\}$ . Besides, we denote training set as $\mathcal{D}_{tr} = \{(i,c) \mid i \in \mathcal{I}^s, c \in \mathcal{C}^s\}$ , where $\mathcal{I}^s$ is the image set known in training, and $\mathcal{C}^s$ is a subset of $\mathcal{C}$ containing the corresponding + +labels. In the traditional Zero-Shot Learning setting, training and testing label are disjoint, i.e., $\mathcal{C}^s \cap \mathcal{C}^u = \emptyset$ , where $\mathcal{C}^s$ , $\mathcal{C}^u$ are two subsets of $\mathcal{C}$ seen/unseen in training. In this case, the model only needs to predict the compositions drawn from $\mathcal{C}^u$ in testing [20]. In this paper, we follow the setting of Generalized ZSL [31] where testing samples can be drawn from either seen or unseen compositions, i.e., $\mathcal{C}^s \cup \mathcal{C}^u$ , which is more challenging on account of the larger prediction space and the dominant bias to seen compositions [26]. To sum up, CZSL aims to learn a mapping function $\mathcal{I} \to \mathcal{C}^s \cup \mathcal{C}^u$ that is trained on $\{\mathcal{I}^s, \mathcal{C}^s\}$ , in which $\mathcal{C}$ is composed of two primitive concepts drawn from $\mathcal{A}$ and $\mathcal{O}$ . + +# 3.2. Siamese Contrastive Embedding Network + +Due to the entanglement between state and object into an image that influences the final classification, we design a Siamese Contrastive Embedding Network (SCEN) to better materialize the discriminative prototypes of state and object, which can effectively improve the accuracy of recognition models. The overall architecture is illustrated in Fig. 2. The SCEN is composed of a feature extractor $FC$ , a State-Specific Encoder $E_{s}$ , a Object-Specific Encoder $E_{o}$ , and a State Transition Module (STM). + +Specific database. Let us consider a training sample, such as sliced apple in Fig. 1. As we all know, from our training set, that object apple comes in various states such as caramelized and state sliced also does not just modify a single object, e.g., sliced banana. Therefore, these sample points with overlapping information might have potential relationships. Based on this idea, we set up three specific databases $D_{s}$ , $D_{o}$ , and $D_{ir}$ to excavate discriminative state + +![](images/83b5fef15f4133786781324b906e6d8057525901dd7323fde9c4a986573c6507.jpg) +Figure 3. The framework of our State Transition Module (STM). The proposed module aims to improve the generalization of State-Specific Encoder $E_{s}$ and Object-Specific Encoder $E_{o}$ . To be specific, the Generator $G$ takes the state $h_{s}$ and object $h_{o}$ vectors as input and generates virtual samples, which is the input of Discriminator $D$ . Although we do not gain the label for generated samples, we can utilize $E_{s}$ and $E_{o}$ to re-encode them and set classification losses as constraints. + +and object factors, respectively. $D_{s}$ is the set of compositions consisting of constant state and various objects, named State-constant database, while the Object-constant database $D_{o}$ is defined as the set of compositions made up of various states and a constant object. In addition, $D_{ir}$ is the set of compositions formed from various states and objects, which are both different from the state and object of input instances. For instance, given an image as input which consists of a state $\hat{a}$ and an object $\hat{o}$ , i.e., $x = (\hat{a},\hat{o})\in \mathcal{I}^s$ , the $D_{o}$ is denoted as: + +$$ +\mathcal {D} _ {o} = \left\{\left(a, o\right) \mid o = \hat {o}, (a, o) \in \mathcal {C} ^ {s} \right\}. \tag {1} +$$ + +Analogously, the State-specific database $D_{s}$ is denoted as: + +$$ +\mathcal {D} _ {s} = \left\{\left(a, o\right) \mid a = \hat {a}, (a, o) \in \mathcal {C} ^ {s} \right\}. \tag {2} +$$ + +And the irrelevant database $D_{ir}$ is denoted as: + +$$ +\mathcal {D} _ {i r} = \left\{\left(a, o\right) \mid a \neq \hat {a}, o \neq \hat {o}, (a, o) \in \mathcal {C} ^ {s} \right\}. \tag {3} +$$ + +Siamese Contrastive Space. Based on sets of specific databases being set up, the visual feature $\pmb{x}$ , extracted by the feature extractor $FC$ , are separately projected into two independent contrastive embedding spaces to extract prototypes of state $h_s$ and object $h_o$ : + +$$ +h _ {s} = E _ {s} (\boldsymbol {x}), +$$ + +$$ +h _ {o} = E _ {o} (\boldsymbol {x}). \tag {4} +$$ + +We hope that $h_s$ and $h_o$ contain information that is separately sensitive to classifiers for compositions recognition. Therefore, we aim to utilize contrastive learning as a constraint condition to extract discriminative prototypes of state and object. However, a general contrastive loss simultaneously cannot extract their discriminative representations due to their interaction. Based on this problem, we define state-based contrastive loss $\mathcal{L}_{scl}$ and object-based contrastive loss + +$\mathcal{L}_{ocl}$ as constraints to enforce the model to extract discriminative primitives. + +To be specific, we set $h_s$ as an anchor in the state-based contrastive space. Meanwhile, $h_s^{ss}$ selected from $D_s$ is set as a positive point while $k$ negative samples selected from the $D_{ir}$ are denoted as $\{h_{s_1}^{ir},\dots,h_{s_k}^{ir}\}$ . We aim to decrease the distance between the anchor $h_s$ and the positive instance $h_s^{ss}$ , increasing the distance between $h_s$ and each negative point $h_{s_i}^{ir}$ to extract discriminative prototype of state. Therefore, the state-specific loss function $\mathcal{L}_{scl}$ in the state-based contrastive space can be calculated as follows: + +$$ +\mathcal {L} _ {s c l} = - \log \frac {\exp \left(\left(h _ {s}\right) ^ {\top} h _ {s} ^ {s s} / \tau_ {s}\right)}{\exp \left(\left(h _ {s}\right) ^ {\top} h _ {s} ^ {s s} / \tau_ {s}\right) + \sum_ {i = 1} ^ {K} \exp \left(\left(h _ {s}\right) ^ {\top} h _ {s _ {i}} ^ {i r} / \tau_ {s}\right)}, \tag {5} +$$ + +where $\tau_{s} > 0$ is the temperature parameter for the contrastive embedding and $K$ is the number of negative samples. It is obvious that the larger $K$ we set, the longer time the training process cost. The larger number of negative samples encourages State-Specific Encoders $E_{s}$ to excavate a more representative state prototype, which can be generalized to novel compositions. + +As a Siamese Contrastive Embedding space, similar to the state-based contrastive space, we denote $h_{o}$ embedded from the same input visual features as an anchor in the object-based contrastive space, and $\{h_{o_1}^{ir},\dots,h_{o_k}^{ir}\}$ as negative points embedded from irrelevant database $D_{ir}$ . Therefore, the object-specific loss function $\mathcal{L}_{ocl}$ can be defined in the object contrastive space as: + +$$ +\mathcal {L} _ {o c l} = - \log \frac {\exp \left(\left(h _ {o}\right) ^ {\top} h _ {o} ^ {o s} / \tau_ {o}\right)}{\exp \left(\left(h _ {o}\right) ^ {\top} h _ {o} ^ {o s} / \tau_ {o}\right) + \sum_ {j = 1} ^ {K} \exp \left(\left(h _ {o}\right) ^ {\top} h _ {o _ {j}} ^ {i r} / \tau_ {o}\right)}, \tag {6} +$$ + +where $\tau_{o} > 0$ is the temperature parameter for the con + +trastive embedding and $K$ is the number of negative samples. + +Considering that the prototypes of state and object should be optimized in the same direction, we share irrelevant samples for two contrastive spaces $\{h_{o_1}^{ir},\dots,h_{o_k}^{ir}\}$ as negative points, which effectively avoids the problem of unbalanced optimization between $E_{s}$ and $E_{o}$ . + +Finally, we introduce classification losses to guide classifiers to recognize prototypes of state and object, respectively, which is formulated as: + +$$ +\mathcal {L} _ {c l s} = C _ {a} \left(h _ {s}, a\right) + C _ {o} \left(h _ {o}, o\right), \tag {7} +$$ + +where $C_a$ and $C_o$ are both fully connected layers with the cross-entropy loss trained to classify state and object respectively. The prototypes of state and object can be further preserved in the composition with the supervision of classification losses. + +Thus, the total loss function in Siamese Contrastive Space $\mathcal{L}_{cts}$ can be formulated as: + +$$ +\mathcal {L} _ {c t s} = \mathcal {L} _ {s c l} + \mathcal {L} _ {o c l} + \mathcal {L} _ {c l s}. \tag {8} +$$ + +State Transition Module. In order to enforce the SCEN to be generalized to novel samples that do not appear in the training stage, we aim to produce virtual samples to augment the diversity of training compositions, alleviating the domain gap between training and testing data. Therefore, we propose a State Transition Module (STM), which consists of a State-Specific encoder $E_{s}$ , a Object-Specific encoder $E_{o}$ , a Generator $G$ and a Discriminator $D$ [6]. The architecture is shown in Fig. 3. + +Let us consider two objects, namely apple and banana. As is known to all, from our training set, that apple can be ripe while banana can be caramelized since there appears at least one image in training. However, there exists caramelized apple and ripe banana compositions in the testing set while the training set does not. Therefore, we can conclude that the object has the possibility of forming a new combination with various states. Based on this discovery, we aim to utilize the Generator $G$ to produce virtual compositions with the input of various states and a given object. However, such generation with the random combination can produce many irrational compositions, which will actually widen the domain gap between seen and unseen data. For instance, cored banana and squished apple do not appear in the testing set or even exist in reality. Thus, we design a Discriminator $D$ to distinguish whether a composition is composed by the generator $G$ . + +In particular, the Generator $G$ takes as input the prototype of an object $h_{o}$ and another state $\tilde{h}_{s}$ to generate virtual compositions that never appear in training. Then, the Discriminator $D$ takes the real samples $x_{a,o}$ as input and determines which are produced by the Generator $G$ . $G$ and $D$ + +can be optimized by the following adversarial objective: + +$$ +\begin{array}{l} \max _ {D} \min _ {G, E _ {s}, E _ {o}} V (G, D) = \mathbb {E} _ {s, o} (\log D (x _ {a, o})) + \\ \mathbb {E} _ {h _ {\bar {s}}, h _ {o}} \left(\log \left(1 - D \left(G \left(h _ {\bar {s}}, h _ {o}\right)\right)\right)\right), \tag {9} \\ \end{array} +$$ + +where $G(h_{\bar{s}}, h_o) = \hat{x}_{\bar{s},o}$ . $G$ tries to minimize $V(G, D)$ while $D$ tries to maximize it. + +The goal of improving the $E_{s}$ and $E_{o}$ performance is to be generalized to novel compositions in testing, but the generated samples do not have labels as supervision. Thus, we re-encode the generated samples to extract prototypes of state and object again, and design a re-classification loss to constrain them, which is formulated as follows: + +$$ +\mathcal {L} _ {\text {c l s} _ {r e}} = C _ {a} \left(E _ {s} \left(G \left(h _ {\tilde {s}}, h _ {o}\right), \tilde {a}\right) + C _ {o} \left(E _ {o} \left(G \left(h _ {\tilde {s}}, h _ {o}\right)\right), o\right). \right. \tag {10} +$$ + +The total loss function of State Transition Module $\mathcal{L}_{stm}$ is formulated as follows: + +$$ +\mathcal {L} _ {s t m} = \max _ {D} \min _ {G, E _ {s}, E _ {o}} V (G, D) + \mathcal {L} _ {c l s _ {r e}}. \tag {11} +$$ + +Eventually, the final loss of our proposed framework is formulated as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \alpha \mathcal {L} _ {\text {c t s}} + \beta \mathcal {L} _ {\text {s t m}}, \tag {12} +$$ + +where $\alpha$ and $\beta$ are the weighting coefficients to balance the influence of each loss function, respectively. + +# 3.3. Inference + +In the training stage, the model is trained to estimate the likelihood $p(I = i \mid A = a, O = o)$ for image $i$ conditioned on state $s$ and object $o$ . The inference takes place in both $\mathcal{C}^s$ and $\mathcal{C}^u$ . In the inference, model embeds an image as $x$ and extract prototypes of state and object, i.e., $h_a$ and $h_s$ with trained $E_s$ and $E_o$ , respectively. Then the state and object of the most similar prototypes are taken as the prediction. The inference rule can be parameterized as: + +$$ +c _ {t} = \left(a _ {t}, o _ {t}\right) = \underset {(a, o) \in \mathcal {C}} {\arg \max } p (i \mid E _ {s} (\boldsymbol {x}), E _ {o} (\boldsymbol {x})). \tag {13} +$$ + +# 4. Experiment + +In this section, all datasets and evaluation protocols are introduced concretely. Then, we present the implementation details and the comparison of experimental results with other state-of-the-art methods. Eventually, ablation studies prove the effectiveness of the method we proposed. + +# 4.1. Experimental Setup + +Datasets. Our proposed method is evaluated on three CZSL benchmark datasets, i.e., MIT-States [12], UT-Zappos [33], and C-GQA [22]. + +MIT-States contains 53753 images, e.g., young cat and rusty bike, with 115 states and 245 objects in total. MIT-States has 1962 available compositions where 1262 state-object pairs are seen in the training stage, leaving 700 pairs unseen. UT-Zappos contains 50025 images of shoes, e.g., Cotton Sandals and Suede Slippers, with 16 states and 12 objects. In UT-Zappos, there are 116 state-object pairs, 83 pairs of which are used for training, while the other 33 pairs are unseen in training. As for C-GQA dataset, it contains over 9500 compositions that make it most extensive dataset for CZSL. The detailed information of each dataset is summarized in Tab. 1. + +Evaluation Metrics. We evaluate the performance according to prediction accuracy for recognizing seen and unseen compositions. Following the setting of [26], we compute the accuracy in two situations: 1) Seen, testing only on seen compositions; 2) Unseen, testing only on unseen compositions. Based on these, we can compute Harmonic Mean HM of the two metrics, which balances the performance between seen and unseen accuracies. Eventually, we compute 4) Area Under the Curve (AUC) to quantify the overall performance of both seen and unseen accuracy at different operating points with respect to the bias. Following [3, 26], we utilize a calibration bias to trade off between the prediction scores of seen and unseen pairs. As the calibration bias varies, we can draw a seen-unseen accuracy curve where the AUC metric can be computed. + +Implementation Details. For each image, we extract a 1024 dimensional visual feature vector using ResNet-18 [10] pre-trained on the ImageNet dataset [27]. We separately extract a 300-dimensional feature vectors for both states and objects with $E_{s}$ and $E_{o}$ , which is implemented with two fully-connected layers and ReLU activation. Our model is implemented with PyTorch [25] and optimized by ADAM optimizer [14] on an NVIDIA GTX 1080Ti GPU. In addition, we set the learning rate as 0.00004, batch size as 128, and the number of negative samples $K$ as 10. For the MIT-States dataset, the training time is approximately 3 hours for 800 epochs. For the UT-Zappos dataset, it takes around 1 hour for 500 epochs in training. As for C-GQA, it spends around 4 hours for 1000 epochs in training. + +# 4.2. Comparison with State-of-the-Arts + +We compare our experiments with the state-of-the-art in Tab. 2 and show that our Siamese Contrastive Embedding Network (SCEN) outperforms all previous methods in three benchmark datasets, which includes recent proposed C-GQA dataset [22]. Our detailed observations are as follows. + +Generalized CZSL performance. For the CZSL task, our SCEN achieves a test AUC of $5.3\%$ , which achieves the best result on MIT-States. In addition, our method significantly boosts the state-of-the-art harmonic mean, i.e., + +17.2% to 18.4%. When it refers to state and object prediction accuracy, we can observe an improvement from 27.9% to 28.2% for states and 31.8% to 32.2% for objects. + +Similar observations are confirmed on UT-Zappos, in which we can achieve a superior improvement on state-of-the-arts with an AUC of $32.0\%$ compared to $28.7\%$ from Compcos. In addition, our proposed model performs the best harmonic mean $47.8\%$ and improves around $4.5\%$ compared with the Compcos. + +Finally, on the recent proposed splits of the C-GQA dataset, which is shown in Tab. 3, we also achieve the best test AUC of $5.5\%$ . Since C-GQA is a large number of compositions (over 9.3k concepts), which is more complex than MIT-States and UT-Zappos for recognition. The state and the object accuracies of our method are $28.1\%$ and $32.8\%$ , which are both higher than state-of-the-arts. In addition, our best seen and unseen accuracies $(28.9\%$ and $25.4\%)$ also achieve the best results on this new dataset. + +According to the significant improvement on three challenging datasets, we can conclude that our proposed Siamese Contrastive Embedding Network (SCEN) can not only effectively extract discriminative prototypes of state and object, but also improve the robust of the model for unseen compositions recognition. + +# 4.3. Ablation Study + +We now make an ablation study to evaluate the effectiveness of the Siamese Contrastive Embedding Network. We take a single classification model as a base model, which trains two classifiers to recognize states and objects separately. Meanwhile, we train three variants by adding Siamese Contrastive space, adding State Transition Module (STM), or adding both of them, which is denoted as base model, base model + $\mathcal{L}_{cts}$ , and base model + $\mathcal{L}_{cts} + \mathcal{L}_{stm}$ , respectively. According to the showing experiment of each setting as shown in Tab. 4, every variant tends to be more superior performance than the base model. The combination of two variants we proposed achieves the best improvement, which demonstrates that different components promote each other and work together to improve the performance of SCEN significantly. In addition, the result of the base model with $\mathcal{L}_{cts}$ proves that our proposed model successfully excavates discriminative prototypes of states and objects, which is better for compositions recognition. Meanwhile, the significant improvement after adding $\mathcal{L}_{stm}$ indicates the necessity of the proposed State Transition Module, which can effectively alleviate the domain gap between training and testing data. Finally, the result of the base model with adding $\mathcal{L}_{cts}$ and $\mathcal{L}_{stm}$ achieves the best, which shows that they improve the performance of the model together, not affected by each other. + +
DatasetsoTrainingValidationTest
csicscuicscui
MIT-States [12]115245126230k30030010k40040013k
UT-Zappos [33]16128323k15153k18183000
C-GQA [22]453870696326k117313687k102210475k
+ +Table 1. Datasets used in our experiments and their statistics. We use three datasets to benchmark our method against the baseline states. states $s$ , objects $o$ , seen compositions $c_{s}$ , unseen compositions $c_{u}$ , images $i$ . + +
MethodMIT-StatesUT-Zappos
AUCBestAUCBest
ValTestHMSeenUnseensoValTestHMSeenUnseenso
AttOp [23]2.51.69.914.317.421.123.621.525.940.859.854.238.969.6
LE+ [20]3.02.010.715.020.123.526.326.425.741.053.061.941.269.2
TMN [26]3.52.913.020.220.123.326.536.829.345.058.760.040.869.9
SymNet [17]4.33.016.124.425.226.328.325.923.939.253.357.940.571.2
CGE [22]6.85.117.228.725.327.932.038.726.441.256.863.645.073.9
CompCos [18]5.94.516.425.324.627.931.838.628.743.159.862.544.773.5
Ours7.25.318.429.925.228.232.240.232.047.863.563.147.375.6
+ +Table 2. The state-of-the-art comparisons on UT-Zappos and MIT-States. $U$ and $S$ are the accuracies tested on unseen classes and seen classes in CZSL, respectively. $H$ is the harmonic mean value of $U$ and $S$ . The best results are marked in bold. + +
MethodAUCC-GQA
ValTestHMBestso
AttOp [23]2.51.69.914.317.421.123.6
LE+ [20]3.02.010.715.020.123.526.3
TMN [26]3.52.913.020.220.123.326.5
SymNet [17]4.33.016.124.425.226.328.3
CGE [22]6.85.117.228.725.327.932.0
CompCos [18]5.94.516.425.324.627.931.8
Ours6.95.517.528.925.428.132.8
+ +Table 3. The state-of-the-art comparisons on recent proposed C-GQA dataset. + +# 4.4. Qualitative Results + +We show some qualitative results for the novel compositions with top-3 predictions in Fig. 4. The first three columns present some examples where the top prediction matches the label. For MIT-States and UT-Zappos datasets, we notice that the remaining two answers of the model can fundamentally capture at least one factor, which proves that the superior performance of our method. As for more complex C-GQA dataset, our model can give the correct answer in top-3 predictions, which shows the robustness of our proposed framework. + +Meanwhile, the model can predict more combinations of unseen compositions, rather than being limited to that of seen compositions, which effectively alleviate the domain gap between seen and unseen samples. + +In addition, the last two columns show the wrong prediction. For instance, in column 4 and row 2, the image of + +the Slippers is misclassified as Sandals or Boost. This is because there exists a large number of training compositions so that the negative sample dataset may not contain the entire negative samples, such as Sandals and Boost, thus the model does not pay more attention to these pairs that are not included in $D_{ir}$ . Besides, limited by the compositional class accuracy dependent on the number of groups associated with an object in the label space, the model may only focus on the state of the object in a certain aspect and ignore the state of the object labeled by the tag. For example, in column 4, row 1 the image of the cat consists of texture and age both present in the label space of the dataset and the output of the model. However the label for this image only contains its age. + +# 4.5. Hyper-Parameter Analysis. + +We perform an experiment to demonstrate the effect of the weighting co-efficients $\alpha$ and $\beta$ for the loss functions $\mathcal{L}_{cts}$ and $\mathcal{L}_{stm}$ in our proposed model. As is shown in Fig. 5 and Fig. 6. With the different $\alpha$ and $\beta$ setting, the Harmonic Mean HM and AUC have a certain degree of change, which indicates that $\mathcal{L}_{cts}$ and $\mathcal{L}_{stm}$ dominate the performance of the entire model. Based on this situation, we set and fix $\alpha = 0.1$ , changing the value of $\beta$ to observe the performance on different datasets. Finally, on MIT-States, UT-Zappos, and C-GQA datasets, we set $\beta = 0.5$ , $\beta = 0.1$ , and $\beta = 0.1$ , which can achieve the best results, respectively. + +
MethodMIT-StatesUT-Zappos
AUCBestAUCBest
ValTestHMSeenUnseensoValTestHMSeenUseenso
Base2.51.69.914.317.421.123.621.525.940.859.854.238.969.6
+Lcts5.84.316.525.324.727.931.632.626.444.260.061.242.571.3
+Lstm4.83.913.322.521.927.630.234.628.543.959.861.146.972.1
Lcts+Lstm7.25.318.429.225.228.232.239.029.747.863.362.547.374.4
+ +Table 4. Ablation studies for Compositional Zero-Shot Learning on MIT-States and UT-Zappos datasets. + +![](images/3c1a0a4ac0e33df1de3af31f7ede707cc6b41e05263c70550f6859ef69d9550d.jpg) +Figure 4. Qualitative results. We show the top-3 predictions of our proposed model for some instances. From the first three columns, we can observe that all predictions of the model indicate it can categorize accurately. However, the model is only incentivized when it matches the label. The task of CZSL is a multi-label one, and future datasets need to account for this. The last two columns show some examples of suboptimal labels and wrong predictions. + +![](images/79d669ee4cb9fad2c8ae54a6ae422164d402a2143805125095ff275db70cd0ab.jpg) +Figure 5. The influence of the weighting coefficient $\beta$ for $H$ value. + +![](images/3fcfebf3ecc7248a46757307a3800506be0467fb2c0cb8a6098b310795b72e4f.jpg) +Figure 6. The influence of the weighting coefficient $\beta$ for AUC. + +# 5. Conclusion + +In this paper, we propose a novel Siamese Contrastive Embedding Network (SCEN) to excavate discriminative prototypes of state and object for the CZSL task. We firstly project the visual feature into two contrastive spaces, where + +we set up state-constant and object-constant databases. Meanwhile, we design state-specific and object-specific loss functions as constraints, forcing them to contain discriminative corresponding information. In addition, we design a State Transition Module (STM) to produce virtual but rational compositions that never appear in training, which effectively augment the diversity of training data. The proposed module can provide a robust model that can excavate prototypes for seen samples and be generalized to novel compositions, where linear softmax classifiers can be trained to recognize compositions from both seen and unseen instances. The comparison and ablation study experiments demonstrate that our proposed CZSL framework has achieved state-of-the-arts on three challenging datasets. + +# 6. Acknowledgements + +Our work was supported in part by the National Key R&D Program of China under Grant 2017YFE0104100, in part by the National Natural Science Foundation of China under Grant 62132016, Grant 62171343, and Grant 62071361, in part by Key Research and Development Program of Shaanxi under Grant 2021ZDLGY01-03, and in part by the Fundamental Research Funds for the Central Universities ZDRC2102. + +# References + +[1] Yuval Atzmon, Felix Kreuk, Uri Shalit, and Gal Chechik. A causal view of compositional zero-shot recognition. arXiv preprint arXiv:2006.14610, 2020. 2 +[2] Irving Biederman. Recognition-by-components: a theory of human image understanding. Psychological review, 94(2):115, 1987. 2 +[3] Wei-Lun Chao, Soravit Changpinyo, Boqing Gong, and Fei Sha. 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