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+# SeeThroughNet: Resurrection of Auxiliary Loss by Preserving Class Probability Information
+
+Dasol Han\*, Jaewook Yoo\*, Dokwan Oh†
+
+Samsung Advanced Institute of Technology
+
+{dasol.han,jaewook.yoo,dokwan.oh}@samsung.com
+
+# Abstract
+
+Auxiliary loss is additional loss besides the main branch loss to help optimize the learning process of neural networks. 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.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Cityscapes (mIoU %)</td><td colspan="3">PASCAL VOC (mIoU %)</td><td colspan="3">PASCAL Context (mIoU %)</td><td colspan="3">NYU-V2 (mIoU %)</td></tr><tr><td>Baseline</td><td>w/ CPP</td><td>Gain</td><td>Baseline</td><td>w/ CPP</td><td>Gain</td><td>Baseline</td><td>w/ CPP</td><td>Gain</td><td>Baseline</td><td>w/ CPP</td><td>Gain</td></tr><tr><td>OCRNet [48]</td><td>81.17</td><td>81.79</td><td>+0.62</td><td>77.43</td><td>78.43</td><td>+1.00</td><td>45.96</td><td>46.72</td><td>+0.76</td><td>58.09</td><td>58.59</td><td>+0.50</td></tr><tr><td>DeepLabV3+ [5]</td><td>79.77</td><td>81.07</td><td>+1.30</td><td>78.35</td><td>79.89</td><td>+1.54</td><td>45.69</td><td>48.23</td><td>+2.54</td><td>54.66</td><td>55.71</td><td>+1.05</td></tr><tr><td>UPerNet [46]</td><td>79.13</td><td>79.59</td><td>+0.46</td><td>76.32</td><td>78.95</td><td>+2.63</td><td>44.13</td><td>46.89</td><td>+2.76</td><td>53.60</td><td>55.22</td><td>+1.62</td></tr><tr><td>DMNet [14]</td><td>78.15</td><td>79.69</td><td>+1.54</td><td>78.19</td><td>78.94</td><td>+0.75</td><td>45.36</td><td>47.95</td><td>+2.59</td><td>54.08</td><td>55.07</td><td>+0.99</td></tr><tr><td>CCNet [17]</td><td>77.47</td><td>79.64</td><td>+2.17</td><td>76.90</td><td>79.51</td><td>+2.61</td><td>43.76</td><td>46.24</td><td>+2.48</td><td>53.63</td><td>54.10</td><td>+0.47</td></tr><tr><td>PSPNet [53]</td><td>78.34</td><td>79.85</td><td>+1.51</td><td>77.44</td><td>79.56</td><td>+2.12</td><td>45.11</td><td>47.77</td><td>+2.66</td><td>54.51</td><td>55.14</td><td>+0.63</td></tr><tr><td>ANN [56]</td><td>78.31</td><td>78.93</td><td>+0.62</td><td>77.45</td><td>78.59</td><td>+1.14</td><td>44.42</td><td>47.19</td><td>+2.77</td><td>54.50</td><td>55.44</td><td>+0.94</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="3" colspan="2">Method</td><td colspan="18">Class IoU (%)</td><td></td></tr><tr><td colspan="11">Non-Instance</td><td colspan="7">Instance</td><td></td></tr><tr><td>road</td><td>swalk</td><td>build</td><td>wall</td><td>fence</td><td>pole</td><td>thight</td><td>fistern</td><td>veg</td><td>terrain</td><td>sky</td><td>person</td><td>rider</td><td>car</td><td>truck</td><td>bus</td><td>train</td><td>moc</td><td>bicycle</td></tr><tr><td rowspan="4">OCRNet [48]</td><td>Base</td><td>98.3</td><td>85.7</td><td>93.6</td><td>58.1</td><td>65.5</td><td>71.7</td><td>76.3</td><td>83.4</td><td>93.2</td><td>63.8</td><td>95.6</td><td>85.1</td><td>67.5</td><td>95.8</td><td>79.5</td><td>91.2</td><td>86.3</td><td>70.9</td><td>80.7</td></tr><tr><td>CPP</td><td>98.5</td><td>87.2</td><td>93.7</td><td>59.4</td><td>65.3</td><td>72.4</td><td>76.8</td><td>83.6</td><td>93.2</td><td>64.3</td><td>95.6</td><td>84.7</td><td>66.5</td><td>96.1</td><td>86.2</td><td>92.5</td><td>87.1</td><td>70.2</td><td>80.8</td></tr><tr><td>Diff.</td><td>0.2</td><td>1.5</td><td>0.1</td><td>1.3</td><td>-0.2</td><td>0.7</td><td>0.5</td><td>0.2</td><td>0.0</td><td>0.5</td><td>0.0</td><td>-0.4</td><td>-1.0</td><td>0.3</td><td>6.7</td><td>1.3</td><td>0.8</td><td>-0.7</td><td>0.1</td></tr><tr><td>Diff. Avg.</td><td></td><td></td><td></td><td></td><td></td><td>0.44</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.89</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">DeepLabV3+ [5]</td><td>Base</td><td>98.4</td><td>86.5</td><td>93.1</td><td>53.2</td><td>62.0</td><td>70.0</td><td>75.3</td><td>81.9</td><td>92.9</td><td>63.4</td><td>95.2</td><td>84.4</td><td>67.4</td><td>95.4</td><td>79.8</td><td>90.2</td><td>77.2</td><td>69.1</td><td>80.1</td></tr><tr><td>CPP</td><td>98.4</td><td>86.3</td><td>93.2</td><td>51.4</td><td>63.3</td><td>70.0</td><td>75.6</td><td>82.0</td><td>93.0</td><td>64.0</td><td>95.4</td><td>84.8</td><td>67.6</td><td>96.1</td><td>87.0</td><td>92.6</td><td>87.1</td><td>72.0</td><td>80.7</td></tr><tr><td>Diff.</td><td>0.0</td><td>-0.2</td><td>0.1</td><td>-1.8</td><td>1.3</td><td>0.0</td><td>0.3</td><td>0.1</td><td>0.1</td><td>0.6</td><td>0.2</td><td>0.4</td><td>0.2</td><td>0.7</td><td>7.2</td><td>2.4</td><td>9.9</td><td>2.9</td><td>0.6</td></tr><tr><td>Diff. Avg.</td><td></td><td></td><td></td><td></td><td></td><td>0.06</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.04</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">PSPNet [53]</td><td>Base</td><td>98.2</td><td>85.2</td><td>92.9</td><td>54.4</td><td>61.7</td><td>67.1</td><td>73.5</td><td>80.2</td><td>92.6</td><td>62.7</td><td>95.0</td><td>82.9</td><td>65.6</td><td>95.2</td><td>74.7</td><td>88.3</td><td>74.5</td><td>64.6</td><td>79.2</td></tr><tr><td>CPP</td><td>98.2</td><td>85.6</td><td>93.0</td><td>54.2</td><td>61.3</td><td>66.9</td><td>73.8</td><td>80.7</td><td>92.8</td><td>65.3</td><td>95.1</td><td>83.3</td><td>65.2</td><td>95.7</td><td>84.7</td><td>90.4</td><td>83.4</td><td>68.1</td><td>79.7</td></tr><tr><td>Diff.</td><td>0.0</td><td>0.4</td><td>0.1</td><td>-0.2</td><td>-0.4</td><td>-0.2</td><td>0.3</td><td>0.5</td><td>0.2</td><td>2.6</td><td>0.1</td><td>0.4</td><td>-0.4</td><td>0.5</td><td>10.0</td><td>2.1</td><td>8.9</td><td>3.5</td><td>0.5</td></tr><tr><td>Diff. Avg.</td><td></td><td></td><td></td><td></td><td></td><td>0.31</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.19</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">UPerNet [46]</td><td>Base</td><td>98.3</td><td>85.9</td><td>92.8</td><td>50.9</td><td>60.8</td><td>68.7</td><td>74.5</td><td>80.3</td><td>92.7</td><td>61.9</td><td>95.2</td><td>83.6</td><td>64.6</td><td>95.6</td><td>79.2</td><td>90.1</td><td>81.7</td><td>67.3</td><td>79.5</td></tr><tr><td>CPP</td><td>98.3</td><td>86.3</td><td>92.8</td><td>51.3</td><td>59.8</td><td>68.1</td><td>73.7</td><td>80.7</td><td>92.8</td><td>63.0</td><td>94.9</td><td>83.4</td><td>65.0</td><td>95.6</td><td>83.7</td><td>90.7</td><td>81.3</td><td>71.3</td><td>79.6</td></tr><tr><td>Diff.</td><td>0.0</td><td>0.4</td><td>0.0</td><td>0.4</td><td>-1.0</td><td>-0.6</td><td>-0.8</td><td>0.4</td><td>0.1</td><td>1.1</td><td>-0.3</td><td>-0.2</td><td>0.4</td><td>0.0</td><td>4.5</td><td>0.6</td><td>-0.4</td><td>4.0</td><td>0.1</td></tr><tr><td>Diff. Avg.</td><td></td><td></td><td></td><td></td><td></td><td>-0.03</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.13</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">CCNet [17]</td><td>Base</td><td>98.3</td><td>85.9</td><td>92.6</td><td>51.1</td><td>57.9</td><td>66.8</td><td>72.2</td><td>80.1</td><td>92.4</td><td>63.2</td><td>95.0</td><td>82.9</td><td>66.5</td><td>95.0</td><td>70.4</td><td>86.2</td><td>70.6</td><td>66.3</td><td>78.6</td></tr><tr><td>CPP</td><td>98.3</td><td>86.6</td><td>92.9</td><td>52.1</td><td>60.3</td><td>66.8</td><td>73.8</td><td>80.2</td><td>92.6</td><td>63.6</td><td>95.1</td><td>83.9</td><td>67.2</td><td>95.8</td><td>83.7</td><td>91.9</td><td>81.4</td><td>67.5</td><td>79.4</td></tr><tr><td>Diff.</td><td>0.0</td><td>0.7</td><td>0.3</td><td>1.0</td><td>2.4</td><td>0.0</td><td>1.6</td><td>0.1</td><td>0.2</td><td>0.4</td><td>0.1</td><td>1.0</td><td>0.7</td><td>0.8</td><td>13.3</td><td>5.7</td><td>10.8</td><td>1.2</td><td>0.8</td></tr><tr><td>Diff. Avg.</td><td></td><td></td><td></td><td></td><td></td><td>0.62</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.29</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">DMNet [14]</td><td>Base</td><td>98.3</td><td>85.8</td><td>92.9</td><td>51.1</td><td>59.3</td><td>67.1</td><td>73.8</td><td>80.6</td><td>92.6</td><td>63.0</td><td>94.9</td><td>83.3</td><td>65.1</td><td>95.6</td><td>75.5</td><td>87.0</td><td>72.3</td><td>67.7</td><td>79.4</td></tr><tr><td>CPP</td><td>98.3</td><td>85.8</td><td>92.9</td><td>52.6</td><td>60.3</td><td>66.8</td><td>73.7</td><td>80.9</td><td>92.7</td><td>64.0</td><td>94.9</td><td>83.6</td><td>64.5</td><td>95.9</td><td>85.2</td><td>91.5</td><td>83.6</td><td>67.3</td><td>79.7</td></tr><tr><td>Diff.</td><td>0.0</td><td>0.0</td><td>0.0</td><td>1.5</td><td>1.0</td><td>-0.3</td><td>-0.1</td><td>0.3</td><td>0.1</td><td>1.0</td><td>0.0</td><td>0.3</td><td>-0.6</td><td>0.3</td><td>9.7</td><td>4.5</td><td>11.3</td><td>-0.4</td><td>0.3</td></tr><tr><td>Diff. Avg.</td><td></td><td></td><td></td><td></td><td></td><td>0.32</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.18</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">ANN [56]</td><td>Base</td><td>98.1</td><td>84.9</td><td>92.7</td><td>53.3</td><td>60.1</td><td>66.8</td><td>72.9</td><td>80.0</td><td>92.5</td><td>62.4</td><td>95.1</td><td>82.9</td><td>63.8</td><td>95.6</td><td>80.3</td><td>87.2</td><td>72.3</td><td>68.2</td><td>79.0</td></tr><tr><td>CPP</td><td>98.2</td><td>85.1</td><td>92.8</td><td>53.4</td><td>59.2</td><td>67.2</td><td>73.4</td><td>81.3</td><td>92.5</td><td>62.3</td><td>94.8</td><td>83.3</td><td>64.4</td><td>95.6</td><td>81.8</td><td>90.6</td><td>77.8</td><td>66.9</td><td>79.3</td></tr><tr><td>Diff.</td><td>0.1</td><td>0.2</td><td>0.1</td><td>0.1</td><td>-0.9</td><td>0.4</td><td>0.5</td><td>1.3</td><td>0.0</td><td>-0.1</td><td>-0.3</td><td>0.4</td><td>0.6</td><td>0.0</td><td>1.5</td><td>3.4</td><td>5.5</td><td>-1.3</td><td>0.3</td></tr><tr><td>Diff. Avg.</td><td></td><td></td><td></td><td></td><td></td><td>0.13</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.30</td><td></td><td></td><td></td><td></td></tr></table>
+
+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.  
+
+<table><tr><td>Class</td><td>road</td><td>swalk</td><td>build</td><td>wall</td><td>fence</td><td>pole</td><td>light</td><td>tsign</td><td>veg</td><td>terrain</td><td>sky</td><td>person</td><td>rider</td><td>car</td><td>truck</td><td>bus</td><td>train</td><td>mecy</td><td>bicycle</td></tr><tr><td>Counts</td><td>2934</td><td>2811</td><td>2934</td><td>970</td><td>1296</td><td>2949</td><td>1658</td><td>2808</td><td>2891</td><td>1654</td><td>2686</td><td>2343</td><td>1023</td><td>2832</td><td>359</td><td>274</td><td>142</td><td>513</td><td>1646</td></tr></table>
+
+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.
+
+<table><tr><td>CPP pooling</td><td>MS Attention</td><td>IOU (%)</td><td>Gain</td></tr><tr><td></td><td></td><td>84.06</td><td></td></tr><tr><td>✓</td><td></td><td>84.69</td><td>0.63</td></tr><tr><td></td><td>✓</td><td>84.37</td><td>0.31</td></tr><tr><td>✓</td><td>✓</td><td>85.29</td><td>1.23</td></tr></table>
+
+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).
+
+<table><tr><td>Model</td><td>Pre-trained</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_s \)</td><td>\( AP_m \)</td><td>\( AP_l \)</td></tr><tr><td rowspan="3">Mask-RCNN [15]</td><td>ImageNet(En.frozen)</td><td>41.0(36.6)</td><td>65.8(65.6)</td><td>18.7(16.8)</td><td>39.9(37.1)</td><td>60.6(53.8)</td></tr><tr><td>SeeTh. w/o CPP(En.frozen)</td><td>44.6(42.1)</td><td>69.1(69.7)</td><td>20.2(21.9)</td><td>42.7(40.9)</td><td>64.3(59.0)</td></tr><tr><td>SeeTh. w/ CPP(En.frozen)</td><td>45.9(46.1)</td><td>71.3(75.1)</td><td>22.3(32.3)</td><td>43.9(47.0)</td><td>65.3(61.8)</td></tr><tr><td rowspan="3">FCOS [42]</td><td>ImageNet(En.frozen)</td><td>37.7(32.4)</td><td>62.4(59.6)</td><td>15.2(13.8)</td><td>35.2(31.1)</td><td>55.9(49.8)</td></tr><tr><td>SeeTh. w/o CPP(En.frozen)</td><td>42.3(39.2)</td><td>67.7(66.1)</td><td>19.7(19.8)</td><td>41.8(38.2)</td><td>59.8(53.9)</td></tr><tr><td>SeeTh. w/ CPP(En.frozen)</td><td>44.2(43.8)</td><td>70.7(72.3)</td><td>20.7(22.0)</td><td>43.4(44.2)</td><td>61.8(58.1)</td></tr><tr><td rowspan="3">Faster-RCNN [31]</td><td>ImageNet(En.frozen)</td><td>39.4(34.0)</td><td>64.7(62.1)</td><td>17.5(16.5)</td><td>39.3(34.5)</td><td>58.1(49.6)</td></tr><tr><td>SeeTh. w/o CPP(En.frozen)</td><td>43.4(39.7)</td><td>68.4(69.0)</td><td>20.3(20.1)</td><td>41.2(39.4)</td><td>63.0(55.3)</td></tr><tr><td>SeeTh. w/ CPP(En.frozen)</td><td>44.7(44.8)</td><td>71.6(75.7)</td><td>22.4(31.5)</td><td>43.4(45.9)</td><td>61.7(58.4)</td></tr></table>
+
+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.  
+
+<table><tr><td>Method</td><td>Map.</td><td>road</td><td>swalk</td><td>built</td><td>wall</td><td>fence</td><td>pole</td><td>high</td><td>plain</td><td>veg</td><td>ferrier</td><td>sky</td><td>person</td><td>rider</td><td>car</td><td>fruex</td><td>bus</td><td>train</td><td>mecyc</td><td>bicycle</td></tr><tr><td>PSPNet [53]</td><td>No</td><td>98.68</td><td>86.92</td><td>93.46</td><td>58.38</td><td>63.67</td><td>67.67</td><td>76.12</td><td>80.47</td><td>93.63</td><td>72.20</td><td>95.29</td><td>86.83</td><td>71.91</td><td>96.21</td><td>77.69</td><td>91.51</td><td>83.64</td><td>70.80</td><td>77.53</td></tr><tr><td>DeepLabv3+ [5]</td><td>No</td><td>98.69</td><td>87.04</td><td>93.91</td><td>59.47</td><td>63.73</td><td>71.39</td><td>78.16</td><td>82.15</td><td>93.96</td><td>73.03</td><td>95.84</td><td>87.95</td><td>73.26</td><td>96.40</td><td>78.02</td><td>90.91</td><td>83.90</td><td>73.83</td><td>78.87</td></tr><tr><td>OCRNet [48]</td><td>Yes</td><td>98.82</td><td>88.29</td><td>94.26</td><td>66.88</td><td>66.69</td><td>73.28</td><td>80.21</td><td>83.04</td><td>94.20</td><td>74.10</td><td>95.97</td><td>88.50</td><td>75.78</td><td>96.51</td><td>78.51</td><td>91.78</td><td>90.12</td><td>73.40</td><td>79.31</td></tr><tr><td>DecoupleSegNet [23]</td><td>Yes</td><td>98.79</td><td>87.78</td><td>94.37</td><td>66.07</td><td>64.77</td><td>72.32</td><td>78.79</td><td>82.61</td><td>94.20</td><td>73.97</td><td>96.12</td><td>88.67</td><td>75.88</td><td>96.58</td><td>80.19</td><td>93.78</td><td>91.55</td><td>74.32</td><td>79.53</td></tr><tr><td>SegFix [50]</td><td>Yes</td><td>98.88</td><td>88.33</td><td>94.39</td><td>67.97</td><td>67.82</td><td>73.59</td><td>80.60</td><td>83.92</td><td>94.35</td><td>74.45</td><td>96.06</td><td>89.21</td><td>75.85</td><td>96.83</td><td>83.62</td><td>94.17</td><td>91.28</td><td>74.02</td><td>80.09</td></tr><tr><td>Panoptic Deeplab [7]</td><td>Yes</td><td>98.84</td><td>88.40</td><td>94.44</td><td>64.31</td><td>68.34</td><td>75.32</td><td>81.04</td><td>84.19</td><td>94.19</td><td>73.73</td><td>96.09</td><td>89.69</td><td>78.64</td><td>96.73</td><td>82.19</td><td>93.69</td><td>90.16</td><td>76.40</td><td>79.80</td></tr><tr><td>HMSA [41]</td><td>Yes</td><td>98.97</td><td>89.38</td><td>94.90</td><td>71.83</td><td>68.38</td><td>75.85</td><td>82.18</td><td>85.27</td><td>94.49</td><td>74.97</td><td>96.30</td><td>90.14</td><td>79.71</td><td>96.96</td><td>82.58</td><td>94.60</td><td>87.80</td><td>77.15</td><td>81.70</td></tr><tr><td>InverseForm [3]</td><td>Yes</td><td>98.60</td><td>89.45</td><td>94.61</td><td>71.80</td><td>69.24</td><td>75.84</td><td>82.38</td><td>85.53</td><td>94.32</td><td>75.00</td><td>95.83</td><td>90.17</td><td>79.78</td><td>96.92</td><td>84.45</td><td>95.58</td><td>88.65</td><td>76.68</td><td>81.76</td></tr><tr><td>SeeThroughNet (Ours)</td><td>Yes</td><td>98.94</td><td>89.09</td><td>95.04</td><td>73.76</td><td>71.35</td><td>76.10</td><td>82.41</td><td>85.13</td><td>94.52</td><td>75.26</td><td>96.25</td><td>90.06</td><td>79.63</td><td>97.04</td><td>84.25</td><td>95.07</td><td>92.68</td><td>77.85</td><td>81.76</td></tr></table>
+
+![](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. This shows the possibility that the proposed method could also be effective for object detection tasks. The SeeThroughNet shows state-of-the-art results on the Cityscapes benchmarks. We expect our proposed method to potentially boost the auxiliary loss use to any segmentation models enhancing the performance.
+
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+# Segment and Complete: Defending Object Detectors against Adversarial Patch Attacks with Robust Patch Detection
+
+Jiang Liu<sup>1</sup>, Alexander Levine<sup>2</sup>, Chun Pong Lau<sup>1</sup>, Rama Chellappa<sup>1</sup>, Soheil Feizi<sup>2</sup>  
+<sup>1</sup>Johns Hopkins University, <sup>2</sup>University 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.  
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Method</td><td rowspan="2">Clean</td><td colspan="3">Non-adaptive Attack</td><td colspan="3">Adaptive Attack</td></tr><tr><td>75×75</td><td>100×100</td><td>125×125</td><td>75×75</td><td>100×100</td><td>125×125</td></tr><tr><td rowspan="6">COCO</td><td>Undefended</td><td>49.0</td><td>19.8±1.0</td><td>14.4±0.6</td><td>9.9±0.5</td><td>19.8±1.0</td><td>14.4±0.6</td><td>9.9±0.5</td></tr><tr><td>AT [30]</td><td>40.2</td><td>23.5±0.7</td><td>18.6±0.8</td><td>13.9±0.3</td><td>23.5±0.7</td><td>18.6±0.8</td><td>13.9±0.3</td></tr><tr><td>JPEG [13]</td><td>45.6</td><td>39.7±0.3</td><td>37.2±0.3</td><td>33.3±0.4</td><td>22.8±0.9</td><td>18.0±0.8</td><td>13.4±0.7</td></tr><tr><td>Spatial Smoothing [48]</td><td>46.0</td><td>40.4±0.6</td><td>38.1±0.6</td><td>34.3±0.1</td><td>23.2±0.7</td><td>17.5±1.0</td><td>13.5±0.6</td></tr><tr><td>LGS [33]</td><td>42.7</td><td>36.8±0.1</td><td>35.2±0.6</td><td>32.8±0.9</td><td>20.8±0.7</td><td>15.9±0.5</td><td>12.2±0.9</td></tr><tr><td>SAC (Ours)</td><td>49.0</td><td>45.7±0.3</td><td>45.0±0.6</td><td>40.7±1.0</td><td>43.6±0.9</td><td>44.0±0.3</td><td>39.2±0.7</td></tr><tr><td rowspan="2">Dataset</td><td rowspan="2">Method</td><td rowspan="2">Clean</td><td colspan="3">Non-adaptive Attack</td><td colspan="3">Adaptive Attack</td></tr><tr><td>50×50</td><td>75×75</td><td>100×100</td><td>50×50</td><td>75×75</td><td>100×100</td></tr><tr><td rowspan="6">xView</td><td>Undefended</td><td>27.2</td><td>8.4±1.6</td><td>7.1±0.4</td><td>5.3±1.1</td><td>8.4±1.6</td><td>7.1±0.4</td><td>5.3±1.1</td></tr><tr><td>AT [30]</td><td>22.2</td><td>12.1±0.4</td><td>8.6±0.1</td><td>7.2±0.7</td><td>12.1±0.4</td><td>8.6±0.1</td><td>7.15±0.7</td></tr><tr><td>JPEG [13]</td><td>23.3</td><td>19.3±0.4</td><td>17.8±1.0</td><td>15.9±0.4</td><td>11.2±0.3</td><td>9.5±1.0</td><td>8.3±0.3</td></tr><tr><td>Spatial Smoothing [48]</td><td>21.8</td><td>16.2±0.7</td><td>14.2±1.1</td><td>12.4±0.8</td><td>11.0±0.7</td><td>7.9±0.6</td><td>6.5±0.2</td></tr><tr><td>LGS [33]</td><td>19.1</td><td>11.9±0.5</td><td>10.9±0.3</td><td>9.8±0.5</td><td>8.2±0.8</td><td>6.5±0.4</td><td>5.4±0.5</td></tr><tr><td>SAC (Ours)</td><td>27.2</td><td>25.3±0.3</td><td>23.6±1.2</td><td>23.2±0.3</td><td>24.4±0.8</td><td>23.0±0.9</td><td>22.1±0.6</td></tr></table>
+
+![](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.  
+
+<table><tr><td></td><td>Attack</td><td>Method</td><td>75×75</td><td>100×100</td><td>125×125</td></tr><tr><td rowspan="4">COCO</td><td rowspan="2">DPatch [29]</td><td>Undefended</td><td>33.6±0.8</td><td>29.1±0.6</td><td>25.0±1.7</td></tr><tr><td>SAC (Ours)</td><td>45.3±0.3</td><td>44.1±0.6</td><td>42.1±0.8</td></tr><tr><td rowspan="2">MIM [12]</td><td>Undefended</td><td>20.1±1.2</td><td>14.2±0.8</td><td>10.5±0.2</td></tr><tr><td>SAC (Ours)</td><td>42.2±0.9</td><td>43.5±1.0</td><td>40.0±0.2</td></tr><tr><td></td><td>Attack</td><td>Method</td><td>50×50</td><td>75×75</td><td>100×100</td></tr><tr><td rowspan="4">xView</td><td rowspan="2">DPatch [29]</td><td>Undefended</td><td>16.0±0.5</td><td>13.4±0.9</td><td>11.1±0.9</td></tr><tr><td>SAC (Ours)</td><td>25.3±0.5</td><td>22.7±1.1</td><td>21.8±0.5</td></tr><tr><td rowspan="2">MIM [12]</td><td>Undefended</td><td>8.3±0.4</td><td>7.3±0.8</td><td>6.5±1.5</td></tr><tr><td>SAC (Ours)</td><td>24.7±0.7</td><td>23.0±0.9</td><td>22.1±0.6</td></tr></table>
+
+Table 3. mAP (%) under adaptive attacks of ablated models.  
+
+<table><tr><td></td><td>Method</td><td>75×75</td><td>100×100</td><td>125×125</td></tr><tr><td rowspan="4">COCO</td><td>Undefended</td><td>19.8±1.0</td><td>14.4±0.6</td><td>9.9±0.5</td></tr><tr><td>PS</td><td>23.3±0.7</td><td>18.7±0.3</td><td>13.1±0.3</td></tr><tr><td>+ self AT</td><td>41.5±0.2</td><td>40.5±0.6</td><td>36.6±0.1</td></tr><tr><td>+ SC</td><td>43.6±0.9</td><td>44.0±0.3</td><td>39.2±0.7</td></tr><tr><td></td><td>Method</td><td>50×50</td><td>75×75</td><td>100×100</td></tr><tr><td rowspan="4">xView</td><td>Undefended</td><td>8.4±1.6</td><td>7.1±0.4</td><td>5.3±1.1</td></tr><tr><td>PS</td><td>16.8±0.6</td><td>13.6±0.4</td><td>11.1±0.3</td></tr><tr><td>+ self AT</td><td>20.6±0.4</td><td>17.6±0.5</td><td>15.4±0.6</td></tr><tr><td>+ SC</td><td>24.4±0.8</td><td>23.0±0.9</td><td>22.1±0.6</td></tr></table>
+
+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 dataset<sup>1</sup>, 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. Instead of masking out the patches, one can potentially impair or reconstruct the content within the patches, which can be the future direction of this work.
+
+Acknowledgment This work was supported by the DARPA GARD Program HR001119S0026-GARD-FP-052.
+
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+# Segment-Fusion: Hierarchical Context Fusion for Robust 3D Semantic Segmentation
+
+Anirud Thyagharajan<sup>1</sup>, Benjamin Ummenhofer<sup>2</sup>, Prashant Laddha<sup>1</sup>, Om Ji Omer<sup>1</sup>, Sreenivas Subramoney<sup>1</sup>  
+{<sup>1</sup>Processor Architecture Research Lab India, <sup>2</sup>Autonomous 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.  
+
+<table><tr><td>Model</td><td>wall</td><td>floor</td><td>cabinet</td><td>bed</td><td>chair</td><td>sofa</td><td>table</td><td>door</td><td>window</td><td>bookshelf</td><td>picture</td><td>counter</td><td>desk</td><td>curtain</td><td>fridge</td><td>shower</td><td>toilet</td><td>sink</td><td>bathroom</td><td>furniture</td><td>mean</td></tr><tr><td>SparseConvNet</td><td>82.9</td><td>95</td><td>64.4</td><td>76.9</td><td>79.5</td><td>64.4</td><td>55.4</td><td>57.7</td><td>54.1</td><td>78.6</td><td>27.6</td><td>39.5</td><td>54.1</td><td>65.6</td><td>66.6</td><td>79.4</td><td>92.7</td><td>71</td><td>78.1</td><td>48</td><td>66.6</td></tr><tr><td>SparseConvNet + SF</td><td>85.4</td><td>97.3</td><td>67</td><td>79.9</td><td>86</td><td>75.7</td><td>60</td><td>60.5</td><td>61.4</td><td>79.6</td><td>28.1</td><td>44.8</td><td>61.9</td><td>79.7</td><td>70.5</td><td>88.7</td><td>95.7</td><td>79</td><td>85.9</td><td>51.3</td><td>71.9</td></tr><tr><td>PointConv</td><td>72.6</td><td>94.2</td><td>51.8</td><td>64</td><td>77.4</td><td>70</td><td>51.2</td><td>37.1</td><td>54</td><td>61</td><td>20.6</td><td>40</td><td>46.1</td><td>57.3</td><td>55.9</td><td>58.2</td><td>87.8</td><td>56.1</td><td>70</td><td>38.9</td><td>58.2</td></tr><tr><td>PointConv + SF</td><td>75.9</td><td>96.8</td><td>57</td><td>66.5</td><td>79.9</td><td>73.1</td><td>54.1</td><td>40.5</td><td>55.9</td><td>63.5</td><td>21.4</td><td>45.3</td><td>48.7</td><td>60.5</td><td>59.9</td><td>62</td><td>92.8</td><td>62.7</td><td>81.7</td><td>41.4</td><td>62.0</td></tr><tr><td>MinkNet42</td><td>83.9</td><td>95.4</td><td>71.1</td><td>82.4</td><td>84.5</td><td>76.1</td><td>66</td><td>59</td><td>66.8</td><td>80</td><td>19.7</td><td>50.5</td><td>59.4</td><td>82.1</td><td>19.7</td><td>89.1</td><td>88.7</td><td>72.8</td><td>91.2</td><td>54.5</td><td>72.4</td></tr><tr><td>MinkNet42 + SF</td><td>85.6</td><td>97.5</td><td>72.5</td><td>83.2</td><td>86.3</td><td>77.4</td><td>67.4</td><td>63</td><td>67.7</td><td>81.2</td><td>22</td><td>54.2</td><td>59.3</td><td>82.9</td><td>22</td><td>93.4</td><td>92.6</td><td>77.6</td><td>97.4</td><td>56.1</td><td>74.7</td></tr><tr><td>VMNet</td><td>85.9</td><td>95.4</td><td>74.5</td><td>82.1</td><td>84.2</td><td>81.9</td><td>61.8</td><td>62.3</td><td>71.6</td><td>83.9</td><td>24</td><td>49.6</td><td>61.4</td><td>88.4</td><td>74.7</td><td>90.3</td><td>93.1</td><td>78.1</td><td>81.8</td><td>58</td><td>74.2</td></tr><tr><td>VMNet + SF</td><td>88.3</td><td>97.5</td><td>77.2</td><td>83.3</td><td>85.7</td><td>83.8</td><td>62.5</td><td>67.1</td><td>72.6</td><td>84.9</td><td>28</td><td>55.1</td><td>61.6</td><td>89.9</td><td>77.1</td><td>93.6</td><td>96.9</td><td>85.2</td><td>85.4</td><td>59.2</td><td>76.7</td></tr></table>
+
+$$
+\mathcal {L} _ {\text {f u s e}} = \frac {1}{| \mathcal {E} _ {\text {f u s e}} |} \sum_ {e _ {i j} \in \mathcal {E} _ {\text {f u s e}}} H \left(d \left(\bar {\mathbf {F}} _ {i}, \bar {\mathbf {F}} _ {j}\right) - \Delta_ {V}\right) \tag {9}
+$$
+
+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-
+
+Net<sup>1</sup> and S3DIS datasets<sup>1</sup> 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  
+
+<table><tr><td>Model</td><td>clutter</td><td>beam</td><td>board</td><td>bookcase</td><td>ceiling</td><td>chair</td><td>column</td><td>door</td><td>floor</td><td>sofa</td><td>table</td><td>wall</td><td>window</td><td>mean</td></tr><tr><td>MinkNet18</td><td>51.4</td><td>0.0</td><td>66.5</td><td>67.4</td><td>92.3</td><td>87.1</td><td>34.9</td><td>68.4</td><td>95.9</td><td>59.8</td><td>76.0</td><td>81.0</td><td>49.2</td><td>63.8</td></tr><tr><td>MinkNet18+SF</td><td>52.4</td><td>0.0</td><td>69.3</td><td>67.2</td><td>93.0</td><td>88.4</td><td>37.6</td><td>67.7</td><td>96.7</td><td>67.7</td><td>76.5</td><td>81.6</td><td>51.2</td><td>65.3</td></tr><tr><td>KPConv</td><td>54.3</td><td>0.0</td><td>60.9</td><td>72.5</td><td>92.3</td><td>89.7</td><td>20.2</td><td>73.2</td><td>96.8</td><td>70.1</td><td>77.9</td><td>80.1</td><td>52.0</td><td>64.6</td></tr><tr><td>KPConv+SF</td><td>55.2</td><td>0.0</td><td>61.8</td><td>73.3</td><td>92.4</td><td>89.5</td><td>20.7</td><td>75.6</td><td>96.9</td><td>70.0</td><td>77.9</td><td>80.7</td><td>53.4</td><td>65.2</td></tr><tr><td>ASIS</td><td>41.5</td><td>0.0</td><td>52.5</td><td>0.0</td><td>89.6</td><td>1.4</td><td>7.8</td><td>17.2</td><td>96.5</td><td>0.0</td><td>1.4</td><td>73.1</td><td>39.9</td><td>32.4</td></tr><tr><td>ASIS+SF</td><td>43.2</td><td>0.0</td><td>61.6</td><td>0.0</td><td>89.7</td><td>0.0</td><td>2.9</td><td>16.9</td><td>96.6</td><td>0.0</td><td>0.0</td><td>74.5</td><td>43.4</td><td>33.2</td></tr></table>
+
+![](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) ( $\mathcal{L}_{\mathrm{ins}} = \mathcal{L}_{\mathrm{instance}}$ ,  $\mathcal{L}_{\mathrm{seg}} = \mathcal{L}_{\mathrm{segment}}$ )  
+
+<table><tr><td>Model</td><td>Base</td><td>Base + J-GSV</td><td>Base + SF(Lins)</td><td>Base + SF(Lins+Lseg)</td></tr><tr><td>SparseConvNet</td><td>67.1</td><td>70.4</td><td>69.7</td><td>71.5</td></tr><tr><td>PointConv</td><td>58.3</td><td>61.5</td><td>61.4</td><td>63.6</td></tr><tr><td>MinkNet42</td><td>72.4</td><td>74.6</td><td>73.11</td><td>75.2</td></tr></table>
+
+![](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.
+
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+# Segment, Magnify and Reiterate: Detecting Camouflaged Objects the Hard Way
+
+Qi Jia, Shuilian Yao, Yu Liu,* Xin Fan, Risheng Liu, Zhongxuan Luo  
+International School of Information Science & Engineering, Dalian University of Technology
+
+{jiaqi, liuyu8824, xin.fan, rsliu, zxluo}@dlut.edu.cn, Shuilian.Yao@mail.dlut.edu.cn
+
+# Abstract
+
+It is challenging to accurately detect camouflaged objects from their highly similar surroundings. 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
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">COD10K-Test (2,026 images)</td><td colspan="4">CAMO-Test (250 images)</td><td colspan="4">CHAMELEON-Test (79 images)</td></tr><tr><td>\(S_{\alpha}\uparrow\)</td><td>αE↑</td><td>wF↑</td><td>M↓</td><td>\(S_{\alpha}\uparrow\)</td><td>αE↑</td><td>wF↑</td><td>M↓</td><td>\(S_{\alpha}\uparrow\)</td><td>αE↑</td><td>wF↑</td><td>M↓</td></tr><tr><td>CPD [43]</td><td>0.752</td><td>0.820</td><td>0.557</td><td>0.049</td><td>0.712</td><td>0.813</td><td>0.561</td><td>0.108</td><td>0.860</td><td>0.908</td><td>0.753</td><td>0.044</td></tr><tr><td>PraNet [9]</td><td>0.768</td><td>0.836</td><td>0.599</td><td>0.047</td><td>0.738</td><td>0.814</td><td>0.613</td><td>0.098</td><td>0.864</td><td>0.918</td><td>0.784</td><td>0.038</td></tr><tr><td>MINet-R [31]</td><td>0.759</td><td>0.832</td><td>0.580</td><td>0.045</td><td>0.749</td><td>0.835</td><td>0.635</td><td>0.090</td><td>0.844</td><td>0.919</td><td>0.746</td><td>0.040</td></tr><tr><td>SINet [8]</td><td>0.771</td><td>0.807</td><td>0.565</td><td>0.048</td><td>0.742</td><td>0.834</td><td>0.601</td><td>0.101</td><td>0.869</td><td>0.903</td><td>0.749</td><td>0.041</td></tr><tr><td>LSR [25]</td><td>0.767</td><td>0.861</td><td>0.611</td><td>0.045</td><td>0.712</td><td>0.791</td><td>0.583</td><td>0.104</td><td>0.846</td><td>0.913</td><td>0.767</td><td>0.046</td></tr><tr><td>PFNet [28]</td><td>0.800</td><td>0.868</td><td>0.660</td><td>0.040</td><td>0.782</td><td>0.852</td><td>0.695</td><td>0.085</td><td>0.882</td><td>0.942</td><td>0.810</td><td>0.033</td></tr><tr><td>C2F-Net [39]</td><td>0.810</td><td>0.875</td><td>0.674</td><td>0.038</td><td>0.791</td><td>0.863</td><td>0.706</td><td>0.083</td><td>0.886</td><td>0.931</td><td>0.824</td><td>0.032</td></tr><tr><td>MGL [49]</td><td>0.811</td><td>0.865</td><td>0.666</td><td>0.037</td><td>0.775</td><td>0.847</td><td>0.673</td><td>0.088</td><td>0.893</td><td>0.923</td><td>0.813</td><td>0.030</td></tr><tr><td>SegMaR (Stage-1)</td><td>0.813</td><td>0.880</td><td>0.682</td><td>0.035</td><td>0.805</td><td>0.864</td><td>0.724</td><td>0.072</td><td>0.892</td><td>0.937</td><td>0.823</td><td>0.028</td></tr><tr><td>SegMaR (Stage-2)</td><td>0.830</td><td>0.890</td><td>0.718</td><td>0.034</td><td>0.808</td><td>0.863</td><td>0.739</td><td>0.074</td><td>0.902</td><td>0.944</td><td>0.851</td><td>0.027</td></tr><tr><td>SegMaR (Stage-3)</td><td>0.833</td><td>0.892</td><td>0.725</td><td>0.034</td><td>0.810</td><td>0.870</td><td>0.745</td><td>0.073</td><td>0.905</td><td>0.947</td><td>0.858</td><td>0.027</td></tr><tr><td>SegMaR (Stage-4)</td><td>0.833</td><td>0.895</td><td>0.724</td><td>0.033</td><td>0.815</td><td>0.872</td><td>0.742</td><td>0.071</td><td>0.906</td><td>0.954</td><td>0.860</td><td>0.025</td></tr></table>
+
+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]
+
+<table><tr><td rowspan="2">SegMaR (Stage-1)</td><td colspan="4">COD10K-Test (2,026 images)</td><td colspan="4">CAMO-Test (250 images)</td><td colspan="4">CHAMELEON-Test (76 images)</td></tr><tr><td>Sα↑</td><td>αE↑</td><td>wF↑</td><td>M↓</td><td>Sα↑</td><td>αE↑</td><td>wF↑</td><td>M↓</td><td>Sα↑</td><td>αE↑</td><td>wF↑</td><td>M↓</td></tr><tr><td>fixation</td><td>0.806</td><td>0.871</td><td>0.669</td><td>0.037</td><td>0.784</td><td>0.855</td><td>0.693</td><td>0.083</td><td>0.884</td><td>0.931</td><td>0.808</td><td>0.032</td></tr><tr><td>edge</td><td>0.809</td><td>0.882</td><td>0.679</td><td>0.036</td><td>0.796</td><td>0.863</td><td>0.712</td><td>0.075</td><td>0.890</td><td>0.944</td><td>0.822</td><td>0.030</td></tr><tr><td>binary</td><td>0.810</td><td>0.877</td><td>0.680</td><td>0.036</td><td>0.799</td><td>0.857</td><td>0.719</td><td>0.075</td><td>0.887</td><td>0.920</td><td>0.818</td><td>0.031</td></tr><tr><td>discriminative</td><td>0.813</td><td>0.880</td><td>0.682</td><td>0.035</td><td>0.805</td><td>0.864</td><td>0.724</td><td>0.072</td><td>0.892</td><td>0.937</td><td>0.823</td><td>0.028</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">SegMaR (Stage-1)</td><td colspan="4">COD10K-Test (2,026 images)</td><td colspan="4">CAMO-Test (250 images)</td><td colspan="4">CHAMELEON-Test (76 images)</td></tr><tr><td>Sα↑</td><td>αE↑</td><td>wF↑</td><td>M↓</td><td>Sα↑</td><td>αE↑</td><td>wF↑</td><td>M↓</td><td>Sα↑</td><td>αE↑</td><td>wF↑</td><td>M↓</td></tr><tr><td>without DM</td><td>0.799</td><td>0.866</td><td>0.654</td><td>0.039</td><td>0.795</td><td>0.865</td><td>0.706</td><td>0.077</td><td>0.881</td><td>0.926</td><td>0.799</td><td>0.033</td></tr><tr><td>with DM</td><td>0.813</td><td>0.880</td><td>0.682</td><td>0.035</td><td>0.805</td><td>0.864</td><td>0.724</td><td>0.072</td><td>0.892</td><td>0.937</td><td>0.823</td><td>0.028</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="3" colspan="2">Method</td><td colspan="6">COD10K(2,026 images)</td></tr><tr><td colspan="3">Small (1,084 images)</td><td colspan="3">Non-Small (924 images)</td></tr><tr><td>\( S_{\alpha} \uparrow \)</td><td>\( \alpha E \uparrow \)</td><td>\( wF \uparrow \)</td><td>\( S_{\alpha} \uparrow \)</td><td>\( \alpha E \uparrow \)</td><td>\( wF \uparrow \)</td></tr><tr><td rowspan="2" colspan="2">SINet [8]MGL [49]</td><td>0.764</td><td>0.743</td><td>0.500</td><td>0.779</td><td>0.881</td><td>0.639</td></tr><tr><td>0.796</td><td>0.823</td><td>0.598</td><td>0.832</td><td>0.911</td><td>0.743</td></tr><tr><td rowspan="4">SegMaR</td><td>stage-1</td><td>0.797</td><td>0.852</td><td>0.620</td><td>0.832</td><td>0.913</td><td>0.753</td></tr><tr><td>stage-2</td><td>0.821</td><td>0.866</td><td>0.667</td><td>0.841</td><td>0.917</td><td>0.775</td></tr><tr><td>stage-3</td><td>0.825</td><td>0.871</td><td>0.677</td><td>0.843</td><td>0.917</td><td>0.782</td></tr><tr><td>stage-4</td><td>0.825</td><td>0.868</td><td>0.677</td><td>0.842</td><td>0.921</td><td>0.779</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Stage</td><td colspan="4">COD10K-Test (2026 images)</td></tr><tr><td>Sα↑</td><td>αE↑</td><td>wF↑</td><td>M↓</td></tr><tr><td rowspan="4">SINet [8] with SegMaR framework</td><td>Stage-1</td><td>0.771</td><td>0.807</td><td>0.565</td><td>0.048</td></tr><tr><td>Stage-2</td><td>0.795</td><td>0.847</td><td>0.639</td><td>0.043</td></tr><tr><td>Stage-3</td><td>0.801</td><td>0.862</td><td>0.658</td><td>0.041</td></tr><tr><td>Stage-4</td><td>0.805</td><td>0.869</td><td>0.667</td><td>0.041</td></tr></table>
+
+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.
+
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+# Selective-Supervised Contrastive Learning with Noisy Labels
+
+Shikun Li $^{1,2}$ , Xiaobo Xia $^{3}$ , Shiming Ge $^{1,2*}$ , Tongliang Liu $^{3}$
+
+$^{1}$  Institute of Information Engineering, Chinese Academy of Sciences, China  
+$^{2}$  School of Cyber Security, University of Chinese Academy of Sciences, China  
+$^{3}$  Trustworthy Machine Learning Lab, The University of Sydney, Australia
+
+{lishikun,geshiming}@iie.ac.cn,xxia5420@uni.sydney.edu.au,tongliang.liu@sydney.edu.au
+
+# Abstract
+
+Deep networks have strong capacities of embedding data into latent representations and finishing following tasks. 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.  
+
+<table><tr><td rowspan="2">Fractiles</td><td colspan="2">CIFAR-10</td><td colspan="2">CIFAR-100</td></tr><tr><td>Sym.</td><td>Asym.</td><td>Sym.</td><td>Asym.</td></tr><tr><td>α</td><td>50%</td><td>50%</td><td>75%</td><td>25%</td></tr><tr><td>β</td><td>25%</td><td>25%</td><td>35%</td><td>0%</td></tr></table>
+
+Table 2. Weighted KNN evaluations  $(\%)$  on CIFAR-100. The best results are in bold.  
+
+<table><tr><td rowspan="2">Methods</td><td>Clean</td><td colspan="2">Symmetric</td><td colspan="2">Asymmetric</td></tr><tr><td>0%</td><td>20%</td><td>80%</td><td>10%</td><td>40%</td></tr><tr><td>Uns-CL [7]</td><td>56.23</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Sup-CL [27]</td><td>72.66</td><td>58.32</td><td>41.00</td><td>71.11</td><td>68.00</td></tr><tr><td>MOIT [41]</td><td>77.48</td><td>67.42</td><td>55.58</td><td>74.86</td><td>72.60</td></tr><tr><td>Sel-CL</td><td>77.94</td><td>75.36</td><td>62.49</td><td>76.77</td><td>72.71</td></tr></table>
+
+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.  
+
+<table><tr><td>Dataset</td><td colspan="7">CIFAR-10</td><td colspan="7">CIFAR-100</td><td></td><td></td></tr><tr><td rowspan="2">Methods/Noise rate</td><td colspan="4">Symmetric</td><td colspan="3">Asymmetric</td><td colspan="4">Symmetric</td><td colspan="3">Asymmetric</td><td></td><td></td></tr><tr><td>20%</td><td>50%</td><td>80%</td><td>90%</td><td>10%</td><td>20%</td><td>30%</td><td>40%</td><td>20%</td><td>50%</td><td>80%</td><td>90%</td><td>10%</td><td>20%</td><td>30%</td><td>40%</td></tr><tr><td>Cross-Entropy</td><td>82.7</td><td>57.9</td><td>26.1</td><td>16.8</td><td>88.8</td><td>86.1</td><td>81.7</td><td>76.0</td><td>61.8</td><td>37.3</td><td>8.8</td><td>3.5</td><td>68.1</td><td>63.6</td><td>53.3</td><td>44.5</td></tr><tr><td>Mixup [61]</td><td>92.3</td><td>77.6</td><td>46.7</td><td>43.9</td><td>93.3</td><td>88.0</td><td>83.3</td><td>77.7</td><td>66.0</td><td>46.6</td><td>17.6</td><td>8.1</td><td>72.4</td><td>65.1</td><td>57.6</td><td>48.1</td></tr><tr><td>Forward [43]</td><td>83.1</td><td>59.4</td><td>26.2</td><td>18.8</td><td>90.4</td><td>86.7</td><td>81.9</td><td>76.7</td><td>61.4</td><td>37.3</td><td>9.0</td><td>3.4</td><td>68.7</td><td>63.2</td><td>54.4</td><td>45.3</td></tr><tr><td>GCE [64]</td><td>86.6</td><td>81.9</td><td>54.6</td><td>21.2</td><td>89.5</td><td>85.6</td><td>80.6</td><td>76.0</td><td>59.2</td><td>47.8</td><td>15.8</td><td>7.2</td><td>68.0</td><td>58.6</td><td>51.4</td><td>42.9</td></tr><tr><td>P-correction [59]</td><td>92.0</td><td>88.7</td><td>76.5</td><td>58.2</td><td>93.1</td><td>92.9</td><td>92.6</td><td>91.6</td><td>68.1</td><td>56.4</td><td>20.7</td><td>8.8</td><td>76.1</td><td>68.9</td><td>59.3</td><td>48.3</td></tr><tr><td>M-correction [1]</td><td>93.8</td><td>91.9</td><td>86.6</td><td>68.7</td><td>89.6</td><td>91.8</td><td>92.2</td><td>91.2</td><td>73.4</td><td>65.4</td><td>47.6</td><td>20.5</td><td>67.1</td><td>64.5</td><td>58.6</td><td>47.4</td></tr><tr><td>DivideMix [30]</td><td>95.0</td><td>93.7</td><td>92.4</td><td>74.2</td><td>93.8</td><td>93.2</td><td>92.5</td><td>91.4</td><td>74.8</td><td>72.1</td><td>57.6</td><td>29.2</td><td>69.5</td><td>69.2</td><td>68.3</td><td>51.0</td></tr><tr><td>ELR [37]</td><td>93.8</td><td>92.6</td><td>88.0</td><td>63.3</td><td>94.4</td><td>93.3</td><td>91.5</td><td>85.3</td><td>74.5</td><td>70.2</td><td>45.2</td><td>20.5</td><td>75.8</td><td>74.8</td><td>73.6</td><td>70.0</td></tr><tr><td>GCE (Uns-CL init.) [13]</td><td>90.0</td><td>89.3</td><td>73.9</td><td>36.5</td><td>91.1</td><td>87.3</td><td>82.2</td><td>78.1</td><td>68.1</td><td>53.3</td><td>22.1</td><td>8.9</td><td>70.2</td><td>60.2</td><td>52.6</td><td>44.1</td></tr><tr><td>ELR (Uns-CL init.)</td><td>94.4</td><td>93.0</td><td>88.3</td><td>86.2</td><td>95.0</td><td>94.7</td><td>94.4</td><td>93.3</td><td>76.2</td><td>71.9</td><td>57.9</td><td>40.8</td><td>77.2</td><td>75.5</td><td>74.3</td><td>70.4</td></tr><tr><td>MOIT+ [41]</td><td>94.1</td><td>91.8</td><td>81.1</td><td>74.7</td><td>94.2</td><td>94.3</td><td>94.3</td><td>93.3</td><td>75.9</td><td>70.6</td><td>47.6</td><td>41.8</td><td>77.4</td><td>76.4</td><td>75.1</td><td>74.0</td></tr><tr><td>Sel-CL+</td><td>95.5</td><td>93.9</td><td>89.2</td><td>81.9</td><td>95.6</td><td>95.2</td><td>94.5</td><td>93.4</td><td>76.5</td><td>72.4</td><td>59.6</td><td>48.8</td><td>78.7</td><td>77.5</td><td>76.4</td><td>74.2</td></tr></table>
+
+![](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.  
+
+<table><tr><td>Sel-CL with different selected sets</td><td>CIFAR-10</td><td>CIFAR-100</td></tr><tr><td>All examples and all pairs</td><td>90.58</td><td>68.66</td></tr><tr><td>Confident examples T and pairs G&#x27;</td><td>90.64</td><td>70.25</td></tr><tr><td>Confident examples T and pairs G&#x27; ∪ G&#x27;&#x27;</td><td>92.97</td><td>72.71</td></tr><tr><td>Clean examples and associated pairs</td><td>94.21</td><td>71.45</td></tr><tr><td>Clean examples and all pairs</td><td>94.76</td><td>73.43</td></tr><tr><td>Clean examples and clean pairs</td><td>95.52</td><td>76.56</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">WebVision</td><td colspan="2">ILSVRC12</td></tr><tr><td>top-1</td><td>top-5</td><td>top-1</td><td>top-5</td></tr><tr><td>Forward [43]</td><td>61.12</td><td>82.68</td><td>57.36</td><td>82.36</td></tr><tr><td>Decoupling [40]</td><td>62.54</td><td>84.74</td><td>58.26</td><td>82.26</td></tr><tr><td>D2L [39]</td><td>62.68</td><td>84.00</td><td>57.80</td><td>81.36</td></tr><tr><td>MentorNet [26]</td><td>63.00</td><td>81.40</td><td>57.80</td><td>79.92</td></tr><tr><td>Co-teaching [16]</td><td>63.58</td><td>85.20</td><td>61.48</td><td>84.70</td></tr><tr><td>Iterative-CV [6]</td><td>65.24</td><td>85.34</td><td>61.60</td><td>84.98</td></tr><tr><td>DivideMix [30]</td><td>77.32</td><td>91.64</td><td>75.20</td><td>90.84</td></tr><tr><td>ELR [37]</td><td>76.26</td><td>91.26</td><td>68.71</td><td>87.84</td></tr><tr><td>ELR+ [37]</td><td>77.78</td><td>91.68</td><td>70.29</td><td>89.76</td></tr><tr><td>ELR (Uns-CL init.)</td><td>79.93</td><td>92.00</td><td>71.23</td><td>88.23</td></tr><tr><td>ProtoMix [31]</td><td>76.3</td><td>91.5</td><td>73.3</td><td>91.2</td></tr><tr><td>MoPro [32]</td><td>77.59</td><td>-</td><td>76.31</td><td>-</td></tr><tr><td>NGC [51]</td><td>79.16</td><td>91.84</td><td>74.44</td><td>91.04</td></tr><tr><td>Sel-CL+</td><td>79.96</td><td>92.64</td><td>76.84</td><td>93.04</td></tr></table>
+
+Table 6. Ablation study for Sel-CL and Sel-CL+ on CIFAR-100. The best results are in bold.  
+
+<table><tr><td>Methods</td><td>Sym. 20%</td><td>Asym. 40%</td></tr><tr><td>Sel-CL w/o Mixup Data Aug.</td><td>70.3/70.6</td><td>64.2/66.2</td></tr><tr><td>Sel-CL w/o MOCO Trick</td><td>73.3/74.1</td><td>69.2/71.5</td></tr><tr><td>Sel-CL w/o Selection</td><td>67.2/68.9</td><td>49.9/68.7</td></tr><tr><td>Sel-CL w/o Classifier Learning</td><td>— /69.9</td><td>— /70.2</td></tr><tr><td>Sel-CL w/o LSTM</td><td>74.5/74.9</td><td>71.8/72.5</td></tr><tr><td>Sel-CL</td><td>74.9/75.4</td><td>72.0/72.7</td></tr><tr><td>Sel-CL+ w/ Strong Data Aug.</td><td>74.5</td><td>72.7</td></tr><tr><td>Sel-CL+ w/o Retraining Cls.</td><td>76.4</td><td>73.4</td></tr><tr><td>Sel-CL+</td><td>76.5</td><td>74.2</td></tr></table>
+
+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+.  
+
+<table><tr><td>Dataset</td><td colspan="3">CIFAR-10</td><td colspan="3">CIFAR-100</td></tr><tr><td>Noise type</td><td colspan="2">Sym.</td><td>Asym.</td><td colspan="2">Sym.</td><td>Asym.</td></tr><tr><td>Noise rate</td><td>20%</td><td>90%</td><td>40%</td><td>20%</td><td>90%</td><td>40%</td></tr><tr><td>Uns-CL [7]</td><td>95.5</td><td>81.9</td><td>93.4</td><td>76.5</td><td>48.8</td><td>74.2</td></tr><tr><td>Sup-CL [27]</td><td>95.5</td><td>81.6</td><td>93.4</td><td>76.8</td><td>51.4</td><td>74.5</td></tr></table>
+
+Table 8. Comparison with using different fine-tuning methods in the test accuracy (\%). The best results are in bold.  
+
+<table><tr><td>Dataset</td><td colspan="2">CIFAR-10</td><td colspan="2">CIFAR-100</td></tr><tr><td>Noise type</td><td>Sym.</td><td>Asym.</td><td>Sym.</td><td>Asym.</td></tr><tr><td>Noise rate</td><td>20%</td><td>40%</td><td>20%</td><td>40%</td></tr><tr><td>DivideMix [30]</td><td>95.7</td><td>92.1</td><td>76.9</td><td>53.8</td></tr><tr><td>ELR+ [37]</td><td>94.6</td><td>93.0</td><td>77.5</td><td>72.2</td></tr><tr><td>DivideMix (Uns-CL init.) [65]</td><td>96.2</td><td>90.8</td><td>78.3</td><td>52.9</td></tr><tr><td>ELR+ (Uns-CL init.) [65]</td><td>94.8</td><td>94.3</td><td>77.7</td><td>72.3</td></tr><tr><td>DivideMix (Sel-CL init.)</td><td>96.3</td><td>91.6</td><td>78.7</td><td>55.2</td></tr><tr><td>ELR+ (Sel-CL init.)</td><td>95.2</td><td>94.6</td><td>77.7</td><td>72.9</td></tr></table>
+
+Table 9. Comparison with one-stage methods in the test accuracy  $(\%)$ . † denotes fine-tuning using AugMix data augmentation. The best results are in bold.  
+
+<table><tr><td>Dataset</td><td colspan="3">CIFAR-10</td><td colspan="3">CIFAR-100</td></tr><tr><td>Noise type</td><td colspan="2">Sym.</td><td>Asym.</td><td colspan="2">Sym.</td><td>Asym.</td></tr><tr><td>Noise rate</td><td>20%</td><td>90%</td><td>40%</td><td>20%</td><td>90%</td><td>40%</td></tr><tr><td>ProtoMix [31]</td><td>95.8</td><td>75.0</td><td>91.9</td><td>79.1</td><td>29.3</td><td>48.8</td></tr><tr><td>NGC [51]</td><td>95.9</td><td>80.5</td><td>90.6</td><td>79.3</td><td>29.8</td><td>-</td></tr><tr><td>Sel-CL+</td><td>95.4</td><td>67.5</td><td>92.8</td><td>76.4</td><td>35.5</td><td>74.2</td></tr><tr><td>Sel-CL+†</td><td>95.2</td><td>67.4</td><td>92.5</td><td>76.0</td><td>35.4</td><td>74.2</td></tr></table>
+
+Table 10. Comparison with different example selection strategies in the test accuracy/label precision  $(\%)$  of Sel-CL+.  
+
+<table><tr><td>Noise type</td><td colspan="2">Sym.</td><td colspan="2">Asym.</td></tr><tr><td>Noise rate</td><td>20%</td><td>90%</td><td>20%</td><td>40%</td></tr><tr><td>w pseudo-labels</td><td>76.5/99.1</td><td>48.8/62.0</td><td>77.5/97.5</td><td>74.2/92.2</td></tr><tr><td>w/o pseudo-labels</td><td>76.5/99.1</td><td>46.2/55.4</td><td>76.8/96.6</td><td>69.4/83.9</td></tr></table>
+
+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
+
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+# Self-augmented Unpaired Image Dehazing via Density and Depth Decomposition
+
+Yang Yang $^{1}$ , Chaoyue Wang $^{2}$ , Risheng Liu $^{3}$ , Lin Zhang $^{4}$ , Xiaojie Guo $^{1,\star}$ , Dacheng Tao $^{2,5}$
+
+$^{1}$ Tianjin University, Tianjin, China  $^{2}$ The University of Sydney, Sydney, Australia  $^{3}$ Dalian University of Technology, Liaoning, China  $^{4}$ Tongji University, Shanghai, China  $^{5}$ JD Explore Academy, Beijing, China
+
+yangyangcic@tju.edu.cn, chaoyue.wang@outlook.com, rsliu@dlut.edu.cn cslinzhang@tongji.edu.cn, {xj.max.quo, dacheng.tao}@gmail.com
+
+# Abstract
+
+To overcome the overfitting issue of dehazing models trained on synthetic hazy-clean image pairs, many recent methods attempted to improve models' generalization ability by training on unpaired data. 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.  
+
+<table><tr><td rowspan="2" colspan="2">Methods</td><td colspan="3">SOTS-Indoor</td><td colspan="3">SOTS-Outdoor</td><td colspan="3">I-HAZE</td><td colspan="2">Efficiency</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>CIEDE↓</td><td>PSNR↑</td><td>SSIM↑</td><td>CIEDE↓</td><td>PSNR↑</td><td>SSIM↑</td><td>CIEDE↓</td><td>Params (M)</td><td>FLOPs (GMac)</td></tr><tr><td rowspan="4">Paired</td><td>EPDN [32]</td><td>25.06</td><td>0.931</td><td>4.578</td><td>20.47</td><td>0.896</td><td>8.566</td><td>15.02</td><td>0.763</td><td>14.96</td><td>17.38</td><td>4.826</td></tr><tr><td>FFANet [31]</td><td>36.36</td><td>0.993</td><td>1.108</td><td>20.23</td><td>0.905</td><td>6.908</td><td>12.00</td><td>0.592</td><td>20.33</td><td>4.456</td><td>288.3</td></tr><tr><td>HardGAN [6]</td><td>35.45</td><td>0.991</td><td>1.269</td><td>23.33</td><td>0.937</td><td>5.348</td><td>13.82</td><td>0.720</td><td>17.54</td><td>2.546</td><td>49.18</td></tr><tr><td>PSD [5]</td><td>15.02</td><td>0.764</td><td>13.80</td><td>15.63</td><td>0.834</td><td>12.60</td><td>15.30</td><td>0.800</td><td>14.84</td><td>33.11</td><td>182.5</td></tr><tr><td rowspan="7">W/o Paired</td><td>DCP [14]</td><td>13.10</td><td>0.699</td><td>7.404</td><td>20.15</td><td>0.919</td><td>7.613</td><td>13.10</td><td>0.699</td><td>19.04</td><td>-</td><td>-</td></tr><tr><td>CycleGAN [52]</td><td>21.34</td><td>0.898</td><td>7.000</td><td>20.55</td><td>0.856</td><td>9.298</td><td>15.29</td><td>0.756</td><td>19.50</td><td>11.38</td><td>56.89</td></tr><tr><td>CycleDehaze [9]</td><td>20.11</td><td>0.854</td><td>8.761</td><td>21.31</td><td>0.899</td><td>9.481</td><td>14.69</td><td>0.751</td><td>19.05</td><td>11.38</td><td>49.16</td></tr><tr><td>DisentGAN [47]</td><td>21.51</td><td>0.899</td><td>7.294</td><td>18.45</td><td>0.831</td><td>12.24</td><td>14.48</td><td>0.675</td><td>16.52</td><td>11.48</td><td>57.46</td></tr><tr><td>YOLY [20]</td><td>15.84</td><td>0.819</td><td>12.37</td><td>14.75</td><td>0.857</td><td>15.85</td><td>14.74</td><td>0.688</td><td>15.24</td><td>32.00</td><td>-</td></tr><tr><td>RefineDNet [51]</td><td>24.36</td><td>0.939</td><td>4.305</td><td>19.84</td><td>0.853</td><td>8.481</td><td>13.60</td><td>0.660</td><td>17.08</td><td>65.80</td><td>75.41</td></tr><tr><td>Ours</td><td>25.42</td><td>0.932</td><td>3.670</td><td>25.83</td><td>0.956</td><td>4.295</td><td>15.61</td><td>0.780</td><td>14.45</td><td>10.70</td><td>2.246</td></tr></table>
+
+![](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.  
+
+<table><tr><td rowspan="2">Metrics</td><td colspan="3">SOTS-indoor</td><td colspan="3">SOTS-outdoor</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>CIEDE↓</td><td>PSNR↑</td><td>SSIM↑</td><td>CIEDE↓</td></tr><tr><td>w/o Aug</td><td>23.15</td><td>0.9126</td><td>4.975</td><td>24.08</td><td>0.9472</td><td>5.041</td></tr><tr><td>w/o PS</td><td>20.02</td><td>0.8509</td><td>7.315</td><td>22.95</td><td>0.9168</td><td>5.669</td></tr><tr><td>Ours</td><td>25.42</td><td>0.9321</td><td>3.670</td><td>25.83</td><td>0.9559</td><td>4.295</td></tr></table>
+
+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. We hope our method can innovate future works, especially for unpaired learning in low-level vision tasks.
+
+# References
+
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+[2] Bolun Cai, Xiangmin Xu, Kui Jia, Chunmei Qing, and Dacheng Tao. Dehazenet: An end-to-end system for single image haze removal. IEEE TIP, 25(11):5187-5198, 2016. 3  
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+# Self-Distillation from the Last Mini-Batch for Consistency Regularization
+
+Yiqing Shen $^{1*†}$ , Liwu Xu $^{2*}$ , Yuzhe Yang $^{2}$ , Yaqian Li $^{2‡}$ , Yandong Guo $^{2}$ $^{1}$ Shanghai Jiao Tong University,  $^{2}$ OPPO Research Institute
+
+shenyq@sjtu.edu.cn, {xuliwu, liyaqian}@oppo.com, ippllewis@gmail.com, yandong.guo@live.com
+
+# Abstract
+
+Knowledge distillation (KD) shows a bright promise as a powerful regularization strategy to boost generalization ability by leveraging learned sample-level soft targets. 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-KD<sub>self</sub>, Tf-KD<sub>reg</sub>) [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].  
+
+<table><tr><td>Characteristic</td><td>LSR</td><td>Tf-KDself</td><td>Tf-KDreg</td><td>CS-KD</td><td>PS-KD</td><td>Mr-KD</td><td>DDGSD</td><td>BYOT</td><td>Ours</td></tr><tr><td>Sample-level smoothing</td><td>×</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>No pre-trained teacher</td><td>✓</td><td>×</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>No Architecture modification</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>×</td><td>✓</td></tr><tr><td>Forward times per batch</td><td>1</td><td>2</td><td>1</td><td>2</td><td>2</td><td>≥2</td><td>2</td><td>1</td><td>1</td></tr><tr><td>Backward times per batch</td><td>1</td><td>1</td><td>1</td><td>2</td><td>1</td><td>1</td><td>2</td><td>≥2</td><td>1</td></tr><tr><td>Number of involved networks</td><td>1</td><td>2</td><td>1</td><td>1</td><td>2</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Label update frequency</td><td>-</td><td>epoch</td><td>-</td><td>-</td><td>epoch</td><td>epoch</td><td>-</td><td>-</td><td>batch</td></tr></table>
+
+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.  
+
+<table><tr><td>Dataset</td><td>Methods</td><td>Vgg-16</td><td>Vgg-19</td><td>ResNet-32</td><td>ResNet-110</td><td>WRN20-8</td><td>DenseNet-40-12</td></tr><tr><td rowspan="8">CIFAR-10</td><td>Baseline</td><td>6.03±0.22</td><td>6.04±0.10</td><td>6.54±0.10</td><td>5.21±0.24</td><td>5.47±0.08</td><td>7.09±0.28</td></tr><tr><td>LSR</td><td>5.91±0.40</td><td>6.05±0.06</td><td>6.73±0.17</td><td>5.60±0.17</td><td>4.76±0.06</td><td>7.47±0.27</td></tr><tr><td>Tf-KDself</td><td>5.92±0.15</td><td>5.91±0.01</td><td>6.32±0.01</td><td>4.92±0.08</td><td>5.33±0.13</td><td>7.03±0.14</td></tr><tr><td>Tf-KDreg</td><td>6.12±0.07</td><td>6.25±0.18</td><td>6.60±0.05</td><td>5.48±0.18</td><td>4.79±0.01</td><td>7.38±0.16</td></tr><tr><td>CS-KD</td><td>6.22±0.20</td><td>6.38±0.11</td><td>6.88±0.15</td><td>6.12±0.05</td><td>4.89±0.19</td><td>7.85±0.17</td></tr><tr><td>PS-KD</td><td>5.90±0.04</td><td>6.07±0.57</td><td>5.96±0.06</td><td>5.09±0.68</td><td>4.99±0.01</td><td>6.77±0.28</td></tr><tr><td rowspan="2">DLB</td><td>5.38±0.01</td><td>5.58±0.08</td><td>5.85±0.02</td><td>4.85±0.11</td><td>4.46±0.01</td><td>6.57±0.02</td></tr><tr><td>(0.65↑)</td><td>(0.46↑)</td><td>(0.70↑)</td><td>(0.37↑)</td><td>(1.01↑)</td><td>(0.53↑)</td></tr><tr><td rowspan="8">CIFAR-100</td><td>Baseline</td><td>26.37±0.19</td><td>27.16±0.42</td><td>28.26±0.18</td><td>23.64±0.25</td><td>22.42±0.23</td><td>28.31±0.35</td></tr><tr><td>LSR</td><td>25.81±0.02</td><td>26.75±0.45</td><td>28.21±0.13</td><td>23.32±0.16</td><td>22.17±0.01</td><td>29.07±0.01</td></tr><tr><td>Tf-KDself</td><td>25.94±0.11</td><td>27.46±0.82</td><td>26.09±0.24</td><td>27.02±0.01</td><td>21.88±0.34</td><td>28.40±0.09</td></tr><tr><td>Tf-KDreg</td><td>25.85±0.30</td><td>26.82±0.59</td><td>28.29±0.07</td><td>23.54±0.04</td><td>22.28±0.05</td><td>28.92±0.04</td></tr><tr><td>CS-KD</td><td>25.81±0.43</td><td>26.65±0.49</td><td>29.21±0.21</td><td>23.41±0.28</td><td>21.75±0.26</td><td>29.65±0.51</td></tr><tr><td>PS-KD</td><td>25.95±0.74</td><td>26.36±0.76</td><td>27.49±0.75</td><td>22.85±0.65</td><td>21.26±0.11</td><td>28.48±0.53</td></tr><tr><td rowspan="2">DLB</td><td>23.88±0.06</td><td>24.53±0.13</td><td>26.00±0.03</td><td>21.82±0.19</td><td>20.79±0.33</td><td>27.48±0.21</td></tr><tr><td>(2.50↑)</td><td>(2.63↑)</td><td>(2.26↑)</td><td>(1.83↑)</td><td>(1.63↑)</td><td>(0.83↑)</td></tr><tr><td rowspan="8">TinyImageNet</td><td>Baseline</td><td>48.83±0.33</td><td>50.02±0.12</td><td>50.38±0.38</td><td>43.20±0.56</td><td>43.72±0.28</td><td>50.94±0.56</td></tr><tr><td>LSR</td><td>47.95±0.32</td><td>48.86±0.78</td><td>52.75±0.69</td><td>42.18±0.57</td><td>43.51±0.13</td><td>51.01±0.16</td></tr><tr><td>Tf-KDself</td><td>46.76±0.10</td><td>47.25±0.06</td><td>49.48±0.16</td><td>41.31±0.01</td><td>41.13±0.11</td><td>50.78±0.01</td></tr><tr><td>Tf-KDreg</td><td>48.31±0.06</td><td>49.54±0.16</td><td>50.97±0.02</td><td>41.88±0.91</td><td>42.85±0.07</td><td>51.47±0.10</td></tr><tr><td>CS-KD</td><td>46.95±0.15</td><td>47.89±0.13</td><td>53.99±0.03</td><td>43.06±0.22</td><td>42.04±0.42</td><td>54.93±0.25</td></tr><tr><td>PS-KD</td><td>48.39±0.23</td><td>49.77±0.23</td><td>50.28±0.17</td><td>42.22±0.72</td><td>43.37±0.01</td><td>51.57±0.05</td></tr><tr><td rowspan="2">DLB</td><td>45.66±0.01</td><td>46.68±0.09</td><td>48.66±0.07</td><td>40.39±0.01</td><td>41.03±0.02</td><td>50.13±0.01</td></tr><tr><td>(3.17↑)</td><td>(3.35↑)</td><td>(1.72↑)</td><td>(2.81↑)</td><td>(2.69↑)</td><td>(0.81↑)</td></tr></table>
+
+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**.  
+
+<table><tr><td>Dataset</td><td>Methods</td><td>Vgg-16</td><td>Vgg-19</td><td>ResNet-32</td><td>ResNet-110</td><td>WRN20-8</td><td>DenseNet-40-12</td></tr><tr><td rowspan="8">C10</td><td>Baseline</td><td>6.03±0.22</td><td>6.04±0.10</td><td>6.54±0.10</td><td>5.21±0.24</td><td>5.47±0.08</td><td>7.09±0.28</td></tr><tr><td>+ DLB</td><td>5.38±0.01</td><td>5.58±0.08</td><td>5.85±0.02</td><td>4.85±0.11</td><td>4.46±0.01</td><td>6.57±0.02</td></tr><tr><td>+ CutOut</td><td>4.93±0.04</td><td>5.10±0.05</td><td>5.91±0.12</td><td>4.64±0.14</td><td>4.88±0.11</td><td>6.68±0.11</td></tr><tr><td>+ CutOut + DLB</td><td>4.48±0.03</td><td>4.46±0.40</td><td>5.18±0.05</td><td>3.78±0.09</td><td>4.12±0.09</td><td>5.54±0.04</td></tr><tr><td>+ CutMix</td><td>5.29±0.04</td><td>5.41±0.03</td><td>5.96±0.28</td><td>4.82±0.10</td><td>4.89±0.31</td><td>6.76±0.17</td></tr><tr><td>+ CutMix + DLB</td><td>5.20±0.13</td><td>5.21±0.01</td><td>5.22±0.66</td><td>4.41±0.25</td><td>4.29±0.20</td><td>5.28±0.06</td></tr><tr><td>+ DDGSD</td><td>5.65±0.14</td><td>5.79±0.08</td><td>5.96±0.04</td><td>4.77±0.04</td><td>4.72±0.13</td><td>6.83±0.21</td></tr><tr><td>+ DDGSD + DLB</td><td>5.31±0.07</td><td>5.52±0.05</td><td>5.75±0.25</td><td>4.45±0.59</td><td>4.14±0.03</td><td>5.74±0.23</td></tr><tr><td rowspan="8">C100</td><td>Baseline</td><td>26.37±0.19</td><td>27.16±0.42</td><td>28.26±0.18</td><td>23.64±0.25</td><td>22.42±0.23</td><td>28.31±0.35</td></tr><tr><td>+ DLB</td><td>23.88±0.06</td><td>24.53±0.13</td><td>26.00±0.03</td><td>21.82±0.19</td><td>20.79±0.33</td><td>27.48±0.21</td></tr><tr><td>+ CutOut</td><td>25.76±0.16</td><td>26.19±0.69</td><td>27.72±0.02</td><td>22.09±0.18</td><td>21.14±0.37</td><td>28.58±0.47</td></tr><tr><td>+ CutOut + DLB</td><td>23.02±0.08</td><td>23.62±0.17</td><td>25.93±0.28</td><td>20.27±0.33</td><td>20.30±0.01</td><td>27.04±0.43</td></tr><tr><td>+ CutMix</td><td>24.07±1.02</td><td>25.67±0.04</td><td>27.31±0.42</td><td>21.42±0.1</td><td>20.57±0.27</td><td>28.27±0.42</td></tr><tr><td>+ CutMix + DLB</td><td>23.48±0.29</td><td>24.06±0.01</td><td>25.77±0.64</td><td>20.93±0.04</td><td>20.10±0.11</td><td>26.82±0.12</td></tr><tr><td>+ DDGSD</td><td>24.36±0.04</td><td>24.69±0.01</td><td>26.32±0.23</td><td>22.55±0.17</td><td>20.83±0.08</td><td>27.69±0.32</td></tr><tr><td>+ DDGSD + DLB</td><td>23.81±0.11</td><td>24.20±0.28</td><td>25.98±0.04</td><td>21.18±0.42</td><td>20.28±0.01</td><td>27.25±0.28</td></tr></table>
+
+![](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.  
+
+<table><tr><td>Networks</td><td>Baseline</td><td>loss in (4) removed</td><td>All settings</td></tr><tr><td>Vgg-16</td><td>26.37±0.19</td><td>25.45±0.13</td><td>23.88±0.06</td></tr><tr><td>Vgg-19</td><td>27.16±0.42</td><td>25.73±0.28</td><td>24.53±0.13</td></tr><tr><td>ResNet-32</td><td>28.26±0.18</td><td>28.01±0.02</td><td>26.00±0.03</td></tr><tr><td>ResNet-110</td><td>23.64±0.25</td><td>22.65±0.23</td><td>21.82±0.19</td></tr><tr><td>WRN20-8</td><td>22.42±0.23</td><td>21.18±0.01</td><td>20.79±0.33</td></tr><tr><td>DenseNet-40-12</td><td>28.31±0.35</td><td>28.30±0.24</td><td>27.48±0.21</td></tr></table>
+
+# 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. Additionally, as our method depends on the knowledge transmission between soft labels, in this paper, we focus primarily on classification, which yields another future direction in the extension to other tasks e.g. semantic segmentation, object detection.
+
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+# SelfD: Self-Learning Large-Scale Driving Policies From the Web
+
+Jimuyang Zhang Ruizhao Zhu Eshed Ohn-Bar Boston University
+
+{zhangjim, rzhu, eohnbar}@bu.edu
+
+![](images/e227c8120026ac4f43144b51cbf050905f732c97bc8adf37289da06142e352cc.jpg)  
+Figure 1. 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.  
+
+<table><tr><td>Models</td><td>Command</td><td>Speed</td><td>ADE (meters)</td></tr><tr><td>CIL Baseline [13]</td><td>✓</td><td>✓</td><td>1.86</td></tr><tr><td rowspan="4">BEV Planner</td><td rowspan="3">✓</td><td></td><td>4.77</td></tr><tr><td></td><td>4.64</td></tr><tr><td>✓</td><td>1.33</td></tr><tr><td>✓</td><td>✓</td><td>1.14</td></tr></table>
+
+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).  
+
+<table><tr><td rowspan="2" colspan="2">Method</td><td colspan="3">nS-Singapore</td><td colspan="3">Argoverse</td><td colspan="2">Waymo</td></tr><tr><td>ADE</td><td>FDE</td><td>Coll. (%)</td><td>ADE</td><td>FDE</td><td>Coll. (%)</td><td>ADE</td><td>FDE</td></tr><tr><td colspan="2">BEV Planner (nS-Boston)</td><td>1.14</td><td>2.16</td><td>9.50</td><td>1.07</td><td>2.16</td><td>16.50</td><td>2.17</td><td>3.87</td></tr><tr><td rowspan="4">Pre-Trained (YouTube)</td><td>SelfD (VO)</td><td>4.63</td><td>8.07</td><td>12.91</td><td>4.35</td><td>7.54</td><td>31.87</td><td>5.16</td><td>9.02</td></tr><tr><td>SelfD (w/o What If)</td><td>1.32</td><td>2.45</td><td>10.02</td><td>1.27</td><td>2.46</td><td>13.92</td><td>2.43</td><td>4.28</td></tr><tr><td>SelfD (What If-Prior)</td><td>1.19</td><td>2.40</td><td>10.01</td><td>1.12</td><td>2.34</td><td>16.51</td><td>2.10</td><td>3.94</td></tr><tr><td>SelfD (What If-Uniform)</td><td>1.19</td><td>2.28</td><td>10.10</td><td>1.13</td><td>2.28</td><td>15.70</td><td>2.24</td><td>4.01</td></tr><tr><td rowspan="5">Fine-Tuned (YouTube &amp; nS-Boston)</td><td>FixMatch [63]</td><td>1.18</td><td>2.22</td><td>12.02</td><td>1.10</td><td>2.24</td><td>15.20</td><td>2.18</td><td>3.88</td></tr><tr><td>SelfD (VO)</td><td>1.09</td><td>2.09</td><td>9.33</td><td>1.03</td><td>2.11</td><td>17.52</td><td>2.01</td><td>3.62</td></tr><tr><td>SelfD (w/o What If)</td><td>1.18</td><td>2.23</td><td>9.34</td><td>1.09</td><td>2.18</td><td>16.26</td><td>2.03</td><td>3.62</td></tr><tr><td>SelfD (What If-Prior)</td><td>1.09</td><td>2.10</td><td>9.47</td><td>1.00</td><td>2.06</td><td>15.71</td><td>2.10</td><td>3.73</td></tr><tr><td>SelfD (What If-Uniform)</td><td>1.00</td><td>1.93</td><td>9.30</td><td>0.99</td><td>2.05</td><td>14.20</td><td>1.65</td><td>3.02</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">nS-Singapore Night</td><td colspan="2">Argoverse Rainy</td><td colspan="2">Argoverse Night</td><td colspan="2">Waymo Rainy</td><td colspan="2">Waymo Night</td></tr><tr><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td></tr><tr><td>BEV Planner (nS-Boston)</td><td>1.67</td><td>3.05</td><td>0.81</td><td>1.71</td><td>0.78</td><td>1.61</td><td>0.70</td><td>1.28</td><td>1.81</td><td>3.25</td></tr><tr><td>SelfD (Pre-Trained)</td><td>1.73</td><td>3.17</td><td>0.84</td><td>1.85</td><td>0.94</td><td>1.94</td><td>0.77</td><td>1.42</td><td>1.96</td><td>3.55</td></tr><tr><td>SelfD (Fine-Tuned)</td><td>1.28</td><td>2.42</td><td>0.79</td><td>1.71</td><td>0.91</td><td>1.80</td><td>0.67</td><td>1.32</td><td>1.53</td><td>2.80</td></tr></table>
+
+Table 4. Impact of Initial Training Dataset. We analyze the impact of different datasets for training the initial BEV planner model.  
+
+<table><tr><td rowspan="2">Initial Dataset</td><td rowspan="2">Method</td><td colspan="2">nS-Singapore</td></tr><tr><td>ADE</td><td>FDE</td></tr><tr><td rowspan="3">Argoverse</td><td>BEV Planner</td><td>1.42</td><td>2.58</td></tr><tr><td>SelfD (w/o FT)</td><td>1.38</td><td>2.52</td></tr><tr><td>SelfD (w/ FT)</td><td>1.18</td><td>2.23</td></tr><tr><td rowspan="3">Waymo</td><td>BEV Planner</td><td>1.08</td><td>2.03</td></tr><tr><td>SelfD (w/o FT)</td><td>1.13</td><td>2.14</td></tr><tr><td>SelfD (w/ FT)</td><td>0.91</td><td>1.81</td></tr></table>
+
+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  $10\mathrm{km}$ .  
+
+<table><tr><td>Method</td><td>ADE ↓</td><td>FDE ↓</td><td>SR (%) ↑</td><td>RC (%) ↑</td><td>Coll. ↓</td></tr><tr><td>CIL Baseline [13]</td><td>0.57</td><td>1.30</td><td>16</td><td>66.88</td><td>10.71</td></tr><tr><td>BEV Planner</td><td>0.66</td><td>1.32</td><td>12</td><td>65.66</td><td>11.33</td></tr><tr><td>SelfD (Town 1)</td><td>0.56</td><td>1.30</td><td>25</td><td>71.84</td><td>11.51</td></tr><tr><td>SelfD (Town 1 &amp; 2)</td><td>0.55</td><td>1.24</td><td>26</td><td>74.50</td><td>5.18</td></tr></table>
+
+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. Finally, beyond complex 3D navigation, it would be interesting to explore the applicability of our proposed training framework for learning various embodied tasks from unlabeled web data.
+
+Acknowledgments: We thank the Red Hat Collaboratory and the BU Center for Information and Systems Engineering for research awards.
+
+# References
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