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Adaptive 3D Convolution Selection for Efficient Video Recognition + +Hengduo Li $^{1}$ Zuxuan Wu $^{2*}$ Abhinav Shrivastava $^{1}$ Larry S. Davis $^{1}$ + +$^{1}$ University of Maryland $^{2}$ Fudan University + +{hdli, abhinav, lsd}@cs.umd.edu zxwu@fudan.edu.cn + +# Abstract + +3D convolutional networks are prevalent for video recognition. While achieving excellent recognition performance on standard benchmarks, they operate on a sequence of frames with 3D convolutions and thus are computationally demanding. Exploiting large variations among different videos, we introduce Ada3D, a conditional computation framework that learns instance-specific 3D usage policies to determine frames and convolution layers to be used in a 3D network. These policies are derived with a two-head lightweight selection network conditioned on each input video clip. Then, only frames and convolutions that are selected by the selection network are used in the 3D model to generate predictions. The selection network is optimized with policy gradient methods to maximize a reward that encourages making correct predictions with limited computation. We conduct experiments on three video recognition benchmarks and demonstrate that our method achieves similar accuracies to state-of-the-art 3D models while requiring $20\% - 50\%$ less computation across different datasets. We also show that learned policies are transferable and Ada3D is compatible to different backbones and modern clip selection approaches. Our qualitative analysis indicates that our method allocates fewer 3D convolutions and frames for "static" inputs, yet uses more for motion-intensive clips. + +# 1. Introduction + +Videos are expected to make up a staggering $82\%$ of Internet traffic by 2022 [1], which demands approaches that can understand video content like actions and events accurately and efficiently. Key to video recognition is temporal modeling to capture relationships among different frames. Towards this goal, extensive studies have been conducted with 3D convolutional networks by extending 2D convolutions over time [33, 4, 35, 34, 9, 8, 45]. While of + +![](images/f8564f8eef28b1993b2b24d2a04eeec18f442efaa23609246320b668545f55d9.jpg) +Figure 1: A conceptual overview of our approach. Ada3D learns to adaptively keep/discard 3D convolutional layers and frames conditioned on input clips for efficient video recognition. Fewer 3D convolutions and frames are kept for clips that contain discriminative static cues and contextual information, while more are used for motion-intensive clips, in pursuit of a reduced overall computational cost without sacrificing recognition accuracy. Black mask indicates the frame is discarded. + +fering excellent recognition accuracy on standard benchmarks [4, 13, 16], 3D models are often computationally expensive due to the costly convolution operations along the temporal axis on a large number of stacked frames. For example, at the clip-level ${}^{1}$ ,a standard ResNet50 [14] model only requires 4.1 GFLOPs (giga floating-point operations) to compute predictions for a single image, while a SlowFast network [9] with the same ResNet50 backbone needs 16 times more computation (65.7 GFLOPs). Furthermore, the computational cost linearly grows with the number of clips uniformly sampled through the entire sequence for video-level prediction aggregation. + +But are 3D convolutions really important for recognizing different types of videos? Do we really need them through- + +out the network? Is it necessary to perform 3D convolution on a fixed number of stacked frames for all different samples? Intuitively, 3D convolutions are critical for capturing changing patterns among inputs. However, due to large intra-class and inter-class variations, some videos are relatively more "static" than others, for which using a computationally expensive 3D model on redundant inputs might be unnecessary. This paper seeks to develop a computationally efficient framework for video recognition by learning how many frames to use and whether to use 3D convolutions in 3D networks. This is an orthogonal yet complementary direction to existing work on fast video recognition, which either designs lightweight 3D architectures [35, 44, 8, 34] or develops clip selection schemes to use fewer clips for classification [43, 20, 12, 41, 48]. + +With this in mind, we introduce Ada3D, an end-to-end framework that learns adaptive 3D convolution usage conditioned on each input clip sample for efficient video recognition. For each clip, deriving a dynamic inference strategy entails (1) learning how many frames are used as inputs to the 3D network; (2) conditioned on these selected frames, determining how many 3D convolutional layers are activated; (3) and most importantly, making correct predictions while only using a small number of input frames and 3D convolutions. By doing so, Ada3D allocates more computational resources to videos with complicated motion patterns while performing economical inference for "easy static" videos, enabling efficient video classification while maintaining reliable classification accuracy. While appealing, learning whether to keep/discard input frames and 3D convolutions is a non-trivial task, as it requires making binary decisions that are non-differentiable. + +To this end, Ada3D is built upon a reinforcement learning framework [32]. In particular, given a video clip, Ada3D trains a two-head selection network to produce a frame usage policy and a convolution usage policy, indicating which frames in the input stack and which 3D convolutions in the network should be kept or discarded, respectively. Then, conditioned on the derived policies, dynamic inference is performed on a pretrained 3D network with selected frames and 3D convolutions for fast recognition. The selection network is optimized with policy gradient methods [32] to maximize a reward function that is carefully designed to incentivize using as few computational resources as possible while making correct predictions. We further jointly finetune the selection network with the 3D network such that the 3D model is able to adapt to the adaptive inference paradigm. It worth noting that the selection network is designed to be lightweight so that its computational overhead is negligible. + +We conduct extensive experiments to evaluate Ada3D on ActivityNet [16], FCVID [19], Mini-Kinetics-200 [44, 4], and demonstrate that Ada3D is able to save $20\%$ to $50\%$ + +computation on different datasets while maintaining similar recognition performance compared with baselines. We show policies learned on Mini-Kinetics-200 can be further transferred to the full Kinetics dataset [4]. In addition, we show the approach is compatible with different 3D models and it is also complementary to other clip-level selection methods [20, 43, 41, 12, 48]. We also demonstrate qualitatively that our method learns to allocate fewer 3D convolutions and frames for clips that are relatively more static, while applying more computation to motion-intensive clips. + +# 2. Related Work + +Deep neural networks for video recognition. Existing work typically designs video recognition architectures by equipping state-of-the-art 2D models with the ability for temporal modeling, and can be roughly categorized into two directions. In particular, the first applies 2D models on a per-frame basis and then model temporal relationships across frames by aggregating features along the temporal axis with operations such as pooling [38, 31, 10], recurrent networks [6, 47, 23], and using inputs with explicit temporal information such as optical flow [31, 10, 38]. The other [4, 33, 29, 35, 9, 8] directly transforms 2D models into 3D models with 3D convolutions applied on stacked RGB frames (clips). While achieving state-of-the-art performance on various benchmarks [4, 16, 13], 3D models are computationally expensive, limiting their deployment in real-world applications with limited resources. Our work aims to reduce the computational cost of 3D models by learning instance-specific 3D policies using fewer frames and 3D convolutions in a 3D model conditioned on inputs while making correct predictions at the same time. + +Efficient video recognition. Extensive studies have been conducted on designing efficient network architectures for video recognition [50, 5, 35, 8, 49, 24, 34]. Recent advances in efficient 2D ConvNets, e.g. group convolution [17, 30], have been explored in 3D models [5, 35, 34]. In addition, some lightweight temporal aggregation operations are introduced to speed up inference such as a relational module in TRN [49] and a shift module in TSM [24]. More recently, X3D [8] expands a tiny model across several dimensions for a good efficiency/accuracy trade-off. However, all these approaches use a fixed input sampling scheme (i.e., number of frames and frame rate) and compute predictions with a "one-size-fits-all" model for all inputs clips, regardless of the large temporal variations among them. In contrast, we learn dynamic frame usage policies and convolution usage policies conditioned on input clips, in pursuit of computational efficiency without sacrificing accuracy. It is worth pointing out that our method is model-agnostic, and can be used in tandem with these efficient networks. + +Adaptive computation. Many adaptive computation + +![](images/ca3e6586c05967ad27dbceba9fb8c072f2f3754d6b7075f6ca5a66100c534cd2.jpg) +Figure 2: An overview of our approach. Given an input clip, the selection network produces features for each frame in the clip, which are further aggregated uniformly to derive a frame usage policy and a convolution usage policy simultaneously. These policies activate a subset of frames and 3D convolutions in the 3D network for inference. Then, conditioned on the prediction, two rewards are computed to evaluate the frame and convolution policy, respectively. See texts for more details. + +(a.k.a, conditional computation) methods have been developed in the image domain, achieving reduced computation by dynamically selecting channels [2, 25], skipping layers [42, 11, 40, 37], performing early exiting with auxiliary structures [22, 18, 3, 46], adaptively switching input resolutions [27, 36, 46], etc. There are also a few recent studies exploring adaptive computation for videos. These approaches adaptively select salient clips for faster inference with one [43] or more [41] agents to aggregate video-level predictions. Compressed video [20] and audio [12, 20] are also utilized for further improvement in clip selection. More recently, a dynamic resolution selection strategy is introduced in [26]. + +Our method is closely related yet orthogonal to these approaches. They focus on selecting informative clips throughout the entire sequence to achieve fast inference, aiming to improve the widely used uniform sampling baseline for video recognition. For each selected clip, the same amount of computational resource is used. In contrast, we allocate computation conditioned on the complexity of the input video clip. This can be considered as dynamic routing in a network and is complementary to those clip-selection methods (as will be shown empirically) [43, 12, 20], which are a form of routing across different time steps in videos. + +# 3. Approach + +Ada3D reduces the computational cost of 3D networks by learning instance-specific 3D usage policies that encourage using fewer computational resources, in the forms of frames and 3D convolutions, while producing accurate pre + +dictions. To this end, we first revisit popular 3D networks used for temporal modeling in Sec. 3.1, and then elaborate different components of Ada3D in Sec. 3.2 + +# 3.1. 3D Networks for Video Recognition + +Operating on stacked RGB frames, 3D video models typically extend state-of-the-art 2D networks by replacing a number of 2D convolutions with 3D convolutions for temporal modeling over time. Formally, taking as inputs an input clip $\mathcal{V}$ with $T$ frames $\{v_{1}, v_{2}, \dots, v_{T}\}$ , 3D models obtain final predictions through a stack of 2D $(k_{1 \times d \times d})$ and 3D $(k_{t \times d \times d})$ convolutional layers, where $t$ denotes the temporal extent of 3D convolutional filters which is typically set to 3 and 5 in practice, and $d$ denotes the spatial height and width. In common instantiations of 3D video models [33, 35, 4, 44, 9, 8], 3D convolutions are inserted into the building blocks of 2D networks, and these 3D blocks are organized based on heuristics such as using them in early [44, 35] or late [9, 44, 45] stages of the network, if not applied in all stages [4, 8, 35, 33]. Note that state-of-the-art frameworks usually perform temporal convolutions in a non-degenerate form [9, 8], i.e., taking in $T$ frames and outputting $T$ convolved frames. While achieving state-of-the-art recognition performance, 3D video models are often computationally expensive since a number of costly 3D convolutions are applied on a sequence of stacked frames. + +# 3.2. Ada3D: Adaptive 3D Convolution Selection + +Ada3D learns 3D convolution usage policies conditioned on input video clips to reduce the computational cost of 3D + +models. We achieve this with a lightweight selection network that is trained to determine which frames to use as inputs to a pretrained 3D model and which convolution layers to activate in the network for those selected frames. This involves making binary decisions that are non-differentiable, and thus not applicable for supervised frameworks. Instead, we formulate learning the selection network as Markov Decision Process (MDP) [28]. We define the state space of the MDP as the input video clip; actions in the model involve keeping/discarding frames and 3D convolutions in 3D networks. The reward balances between recognition accuracy and computation. The MDP is single-step: a video clip is observed, actions are taken, and a reward is computed—this can also be considered as a contextual bandit [21]. + +More formally, given an input clip $\mathcal{V}$ of length $T$ and a 3D ResNet video classifier $\mathbf{F}$ with $K$ 3D convolution stages $^2$ , the selection network $f_{p}$ , parameterized by $\mathbf{w}$ , computes features for each frame in the input clip; these features are then aggregated as inputs to two parallel branches, outputting two vectors $\mathbf{m} \in \mathbb{R}^T$ and $\mathbf{n} \in \mathbb{R}^K$ : + +$$ +\mathbf {m}, \mathbf {n} = \operatorname {s i g m o i d} \left(f _ {p} (\mathcal {V}; \mathbf {w})\right). \tag {1} +$$ + +Here, each entry in $\mathbf{m}$ and $\mathbf{n}$ is normalized to be in the range $[0,1]$ with the sigmoid $(x) = \frac{1}{1 + \exp(-x)}$ function, indicating the likelihood of keeping the corresponding frame and 3D convolution stage2. + +We then define a frame usage policy $\pi^f$ and a convolution usage policy $\pi^c$ with a $T$ -dimensional and a $K$ -dimensional Bernoulli distribution, respectively: + +$$ +\pi^ {f} (\mathbf {u} \mid \mathcal {V}) = \prod_ {t = 1} ^ {T} \mathbf {m} _ {t} ^ {\mathbf {u} _ {t}} \left(1 - \mathbf {m} _ {t}\right) ^ {1 - \mathbf {u} _ {t}} \tag {2} +$$ + +$$ +\pi^ {c} (\mathbf {v} \mid \mathcal {V}) = \prod_ {k = 1} ^ {K} \mathbf {n} _ {k} ^ {\mathbf {v} _ {k}} (1 - \mathbf {n} _ {k}) ^ {1 - \mathbf {v} _ {k}}. \tag {3} +$$ + +where $\mathbf{u} \in \{0,1\}^T$ and $\mathbf{v} \in \{0,1\}^K$ are actions based on $\mathbf{m}$ and $\mathbf{n}$ , and $\mathbf{u}_t = 1$ indicates the $t$ -th frame in $\mathcal{V}$ is used; similarly $\mathbf{v}_k = 1$ means the $k$ -th 3D convolution stage in the 3D model is activated. Zero entries in $\mathbf{u}$ and $\mathbf{v}$ represent inactive frames and convolutions, respectively. During training, $\mathbf{u}$ and $\mathbf{v}$ are produced by sampling from the corresponding policy, and a greedy approach is used at test time. + +Given these actions, a subset $\mathcal{V}'$ of the full clip $\mathcal{V}$ is formed based on $\mathbf{u}$ . Similarly, according to $\mathbf{v}$ , certain 3D convolution layers are changed to 2D by taking only the center channel of its 3D convolutional filter along the temporal axis, i.e., the slicing operation $k_{t\times d\times d}[\left\lfloor \frac{t}{2}\right\rfloor ,\dots ,]$ in PyTorch style. Then, conditioned on $\mathcal{V}'$ , we run a forward pass with the 3D network where certain 3D convolutions are degraded, and a prediction is then computed. To encourage + +correct predictions with limited computation, we evaluate these actions with a reward function: + +$$ +R (\mathbf {x}) = \left\{ \begin{array}{l l} 1 - \mathcal {O} (\mathbf {x}) & \text {f o r c o r r e c t p r e d i c t i o n} \\ - \gamma & \text {e l s e} \end{array} \right. \tag {4} +$$ + +where $\mathcal{O}(\mathbf{x})$ represents the normalized computational cost of the action and $\mathbf{x}\in \{\mathbf{u},\mathbf{v}\}$ . Based on Eqn. 4, we compute two rewards for frame actions and convolution actions respectively, encouraging using as little computation as possible when making correct predictions while penalizing incorrect predictions with a negative reward, i.e., $-\gamma$ . Note that $\gamma$ also balances the speed-accuracy trade-off with different values. While we instantiate $\mathcal{O}(\mathbf{u})$ and $\mathcal{O}(\mathbf{v})$ as $(\frac{||\mathbf{u}||_0}{T})$ and $(\frac{||\mathbf{v}||_0}{K})^2$ —the normalized usage of the number of frames and 3D convolutions—there are also other options such as FLOPs [26, 15]. The selection network is then optimized to maximize the expected reward: + +$$ +\max _ {\mathbf {w}} \mathcal {L} = \mathbb {E} _ {\mathbf {u} \sim \pi_ {f}, \mathbf {v} \sim \pi_ {c}} [ R (\mathbf {u}) + R (\mathbf {v}) ]. \tag {5} +$$ + +We use policy gradient methods [32] to learn the parameters $\mathbf{w}$ for the selection network and the expected gradient can be derived as: + +$$ +\begin{array}{l} \nabla_ {\mathbf {w}} \mathcal {L} = \mathbb {E} \left[ R (\mathbf {u}) \nabla_ {\mathbf {w}} \log \pi^ {f} (\mathbf {u} \mid \mathcal {V}) \right. \\ + R (\mathbf {v}) \nabla_ {\mathbf {w}} \log \pi^ {c} (\mathbf {v} | \mathcal {V}) ]. \tag {6} \\ \end{array} +$$ + +Eqn. 6 can be estimated with many samples at a time, and thus we use samples in mini-batches to compute the expected gradient and then Eqn. 6 is approximated by: + +$$ +\begin{array}{l} \nabla_ {\mathbf {w}} \mathcal {L} \approx \frac {1}{B} \sum_ {i = 1} ^ {B} \left[ R (\mathbf {u} _ {i}) \nabla_ {\mathbf {w}} \log \pi^ {f} (\mathbf {u} _ {i} \mid \mathcal {V} _ {i}) \right. \\ + R \left(\mathbf {v} _ {i}\right) \nabla_ {\mathbf {w}} \log \pi^ {c} \left(\mathbf {v} _ {i} \mid \mathcal {V} _ {i}\right) ], \tag {7} \\ \end{array} +$$ + +where $B$ is the total number of samples in the mini-batch. The gradient is then propagated back to train the policy network with SGD. We further reduce variance by adding a baseline function to the reward [32]. + +So far we have only trained the selection network while keeping the pretrained video model fixed. The selection network is able to learn decent policies that use fewer frames and 3D convolutions while maintaining prediction accuracies. However, input distributions to the 3D model are no longer the same as those used to train the original network, where all frames and 3D convolutions are used. As a result, the 3D model is not equipped with the ability to deal with inputs with varying number of frames and 3D convolutions that are adaptively turned on/off. To remedy this, we further jointly fine-tune the 3D model with the selection network such that it is able to accustomed to such adaptive inference paradigm. The objective function then becomes: + +$$ +\min _ {\mathbf {w}, \boldsymbol {\theta}} - \sum_ {j = 1} \mathbf {y} ^ {j} \log \left(\mathbf {F} (\mathcal {V}; \boldsymbol {\theta}) ^ {j}\right) - \mathcal {L} (\mathbf {w}) \tag {8} +$$ + +Algorithm 1: Training algorithm of our approach. +Input: An input video clip $\mathcal{V}$ , the number of epochs of for training the selection network $E_{1}$ , the number of epochs of joint fine-tuning $E_{2}$ +1 Obtain a pretrained video classifier F +2 Randomly initialize selection network w +3 for e $\leftarrow 0$ to $E_{1}$ do +4 $\mathbf{m},\mathbf{n} = \mathrm{sigmoid}(f_p(\mathcal{V};\mathbf{w}))$ +5 $\mathbf{u},\mathbf{v}\sim \pi_{\mathbf{w}}(\mathbf{u}|\mathcal{V}),\pi_{\mathbf{w}}(\mathbf{v}|\mathcal{V})$ // Eqn. 3 +6 $p = \mathbf{F}(\mathcal{V}|\mathbf{u},\mathbf{v})$ // Apply actions on F and forward +7 $R = R(\mathbf{u}) + R(\mathbf{v})$ // Eqn. 4 +8 $\mathbf{w} = \mathbf{w} - \nabla \mathbf{w}\mathcal{L}$ // Eqn. 6 +9 end +10 for e $\leftarrow 0$ to $E_{2}$ do +11 Repeat Line 4-7 +12 $\mathbf{w} = \mathbf{w} - \nabla \mathbf{w}\mathcal{L}$ // Eqn. 6 +13 $\theta = \mathbf{w} - \nabla \theta \mathcal{L}_{cls}$ // Eqn. 8 +14 end + +where $\theta$ denotes the weights of the 3D network $\mathbf{F}$ and the first term is the cross-entropy loss for an input clip $\mathcal{V}$ with one-hot label $\mathbf{y}$ for classification training. Algorithm 1 summarizes algorithm of Ada3D. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets and evaluation metrics. We evaluate our approach on three video recognition datasets: ActivityNet (ACTIVITYNET) [16], Fudan-Columbia Video Datasets (FCVID) [19] and Mini-Kinetics-200 (MINI-KINETICS) [44]. ACTIVITYNET contains around $20K$ Youtube videos of 200 action classes, with an average duration of 117 seconds. We use the latest version 1.3 and its official split with 10,024 training videos, 4,926 validation videos and 5,044 testing videos. We report results on the validation set as the labels of testing videos are not publicly available. FCVID consists of 91,223 Youtube videos belonging to 239 categories, with an average duration of 167 seconds. The official split is adopted with a training set of 45,611 videos and a testing set of 45,612 videos. MINI-KINETICS is a publicly released subset of KINETICS [4] initially introduced in [44], consisting of 200 classes with the most training samples in Kinetics; 400 and 25 videos are sampled from each action class for training and validation, forming a training set with 80,000 videos and a validation set with 5,000 videos. Here we use the identical samples as [44]. To demonstrate the transferability of the selection network, we experiment with the Kinetics full set, which contains 240K training videos and 20K validation videos. + +Following official instructions, we report mean aver + +age precision (mAP) on ACTIVITYNET and FCVID. For MINI-KINETICS and KINETICS, we report Top-1 accuracy. + +Network architectures. We use an I3D [4] with a backbone of ResNet-50 [14] as the 3D video model if not mentioned otherwise, due to its popularity and competitive recognition performance across various benchmarks [4, 13, 16]. Our implementation follows [7], where 3D convolutions are factorized spatially and temporally in a similar way as $\mathrm{R}(2 + 1)$ -D [35], which is already a more efficient architecture than original I3D. In addition, we also experiment with the Slowonly model introduced in [9] to demonstrate the compatibility of our approach with more recent networks. + +We use a lightweight architecture for the selection network with negligible computational overhead. Specifically, we use MobileNetV2 [30] as the backbone of the selection network. The inputs to the network are downsampled to $112 \times 112$ per frame, and it only requires 0.08 GFLOPs to compute features for each frame. + +Implementation details. All 3D networks are fine-tuned from models provided by [7], which are pre-trained on Kinetics. We fine-tune 3D models for 40 epochs on FCVID and ACTIVITYNET and 20 epochs on MINI-KINETICS, with a cosine learning rate schedule starting at 0.01 and a batch size of 64. The MobileNetV2 backbone of the selection network is also pre-trained on these datasets with the same schedules to speed up convergence. We first fix the pretrained 3D models and train the selection network for 40 epochs with a learning rate of 0.0001 and a batch size of 256. Finally, the whole pipeline is jointly fine-tuned for 60 epochs with the same learning rate described above. SGD with momentum 0.9 is used for optimization. We use 8 GPUs for all experiments. + +Regarding network inputs during training, we follow [9, 8] by randomly sampling a clip with 8/16 frames using a temporal stride of 8 (sampling rate) from a given video. For the spatial domain, $224 \times 224$ pixels are randomly cropped from the sampled clip during training. For inference, we follow the common practice [9, 8, 39] and uniformly sample 10 clips with a spatial size of $256 \times 256$ from a testing video. Video-level prediction is obtained by averaging the clip-level predictions. + +# 4.2. Main Results + +We compare our proposed method with various baselines under different input settings (8/16 frames per clip) and report results in Table 1. The baselines we use include: + +- Random: Based on the frame usage and convolution usage produced by Ada3D, we generate random policies that use a similar amount of computational resources compared to Ada3D. +- Random $FT$ : The 3D model is further jointly fine-tuned with the random policies. + +
FCVIDACTIVITYNETMINI-KINETICS
mAPGFLOPs#3D#FramemAPGFLOPs#3D#FrameAccGFLOPs#3D#Frame
8-frame per clip
Upper82.158.65.08.082.658.65.08.079.058.65.08.0
Random78.136.12.25.879.242.93.06.674.042.22.06.9
Random FT80.736.12.25.881.142.93.06.677.441.51.96.8
Ours81.935.62.25.782.642.23.16.678.942.41.96.9
16-frame per clip
Upper84.4117.35.016.084.4117.35.016.079.6117.35.016.0
Random79.263.22.110.380.473.33.011.275.275.82.911.8
Random FT82.065.32.110.682.871.33.011.178.278.02.912.0
Ours84.366.62.110.784.070.13.011.179.273.82.911.8
+ +Table 1: Recognition performance and computational cost of our method vs. baselines. Two input settings are experimented, i.e. 8-frame setting (Top) and 16-frame setting (Bottom). #3D and #Frame denote the number of 3D convolutions and frames usage per input clip respectively, averaged over the entire test set. See texts for more details. + +- Upper: The original pretrained 3D model with all 3D convolutions and all frames used, which can be viewed as a performance "upperbound" of our method. + +As shown in Table 1, under the 8-frame input setting, Ada3D obtains an mAP (accuracy for MINI-KINETICS) of $81.9\%$ , $82.6\%$ and $78.9\%$ , requiring an average of 35.6, 42.2 and 42.4 GFLOPs per clip on FCVID, ACTIVITYNET, MINI-KINETICS respectively. Ada3D achieves comparable recognition performance but brings $40\%$ , $28\%$ and $27\%$ computational savings. This confirms that Ada3D is able to learn effective 3D convolution and frame usage policies by saving computational resources and preserving accuracies at the same time across different datasets. Similar patterns are also observed under the 16-frame input setting for all three datasets. + +Using similar computational resources, Ada3D improves the Random baseline by $3.5\%$ to $5\%$ mAP/accuracy on three datasets. Ada3D also outperforms Random FT by $1\%$ to $2.5\%$ . These results verify that Ada3D produces adaptive polices and allocates computational resources on a per-input basis to maintain recognition performance. It is worth noting that there are slightly differences in computational savings on different datasets. This results from the fact that video categories in these datasets are different. For example, FCVID contains some classes of static objects and scenes like "bridge" and "temple", and thus we observe more computational savings than ACTIVITYNET and MINI-KINETICS, which are more activity-focused; on MINI-KINETICS, where categories are motion-intensive, more computational resources are needed compared to FCVID and ACTIVITYNET. + +Recognition with varying computational budgets. As discussed in Section 3.2, the choice of $\gamma$ in Eqn. 4 adjusts + +the amount of penalty on policies that produce incorrect predictions, and thus it controls the speed/accuracy trade-off. Here we report recognition accuracies of Ada3D under different computational budgets. As demonstrated in Fig. 3, our method is able to cover a wide range of speed/accuracy trade-offs and consistently outperforms Random $FT$ with different computational budgets. For example, on ACTIVITYNET, Ada3D obtains an mAP of $82.6\%$ , $81.9\%$ and $80.9\%$ with an average of 42.2, 30.1 and 24.4 GFLOPs per clip respectively, while Random $FT$ obtains $81.1\%$ , $80.7\%$ and $79.8\%$ with 42.9, 32.6 and 25.4 GFLOPS per clip on average. Same patterns are also observed on FCVID. + +Extension to clip selection. As mentioned in Sec. 2, our method is orthogonal and thus could be complementary to the line of clip selection methods [41, 43, 20, 12] for efficient video recognition. We validate our hypothesis by combining our method with AdaFrame [43]. Specifically, we use Ada3D as the backbone of AdaFrame to dynamically allocate computational resources conditioned on each input clip, as opposed to the original AdaFrame that uses the + +![](images/8c96e49697093d97de86ee808a42ffddf79c270691322968f35d0e6fd82eb1e9.jpg) +Figure 3: Recognition performance under different computational budgets controlled by $\gamma$ . + +
Van → AdaVan → AdaVan → Ada
#Clip3.0 → 2.95.0 → 4.210.0 → 7.4
mAP77.8 → 78.180.3 → 80.581.9 → 82.0
+ +same amount of computation with a fixed backbone for all clips. Following [43], we train three variants of AdaFrame which operates on 3, 5, and 10 clips for different computational budgets. As demonstrated in Table 2, extending our approach with adaptive clip selection further decreases the computational cost while producing comparable performance with the Upper. For example, it reduces the number of clips sampled from each testing video from 10 to 7.4 and obtains an mAP of $82.0\%$ that is on par with Upper $(82.1\%)$ . Additionally, we believe our method is also complementary to other clip selection methods leveraging multi-modal inputs such as audio [20, 12], as well as adaptive spatial resolution modulating methods [26, 36, 46]. + +Table 2: Extension to clip-level selection. Combining Ada3D with AdaFrame [43] offers computational savings for video-level aggregation. #Clip denotes number of clips used per testing video; Van (Vanilla) and Ada denote our method without and with AdaFrame, respectively. + +
MethodAccGFLOPs#3D#Frame
Upper73.158.65.08.0
Ours72.843.72.36.9
+ +Transferring learned policies. We now analyze whether the policies learned by our method can be transferred to novel action categories. To this end, we take the selection network trained on MINI-KINETICS and fine-tune a pretrained I3D model with a ResNet-50 as its backbone on full Kinetics. We keep the weights of the selection network fixed during fine-tuning. Details of training and testing are the same as joint fine-tuning as described in Sec. 4.1. As shown in Table 3, policies learned on MINI-KINETICS can reduce the overall computational cost of the fine-tuned video model by $25\%$ on Kinetics with negligible difference in recognition accuracy compared to the Upper baseline, indicating that our method learns strategies that are transferable to unseen classes and videos. It is worth noting that the I3D baseline we use obtains superior recognition performance on Kinetics that is higher than [4, 44] and competitive compared to results reported in [39] using 32 frames per input clip. + +Compatibility with different 3D architectures. Next, we evaluate the compatibility of our approach with different 3D + +networks. We use a more efficient 3D network architecture recently introduced in [9] termed as Slowonly and evaluate our approach. In particular, it only uses 3D convolutions in the 4-th and 5-th stage of a ResNet50, resulting in competitive recognition performance with less computational cost. As shown in Table 4, our method still obtains $20\%$ to $40\%$ savings in GFLOPs with similar recognition performance, indicating Ada3D is compatible with different 3D models. Our method by design is model-agnostic, for which we believe it could be complementary to recent work on designing efficient 3D models such as X3D [8] as well. + +Table 3: Transferring learned policies. We fine-tune a Kinetics pretrained model on Kinetics full training set, with policies learned on Mini-Kinetics, and evaluate on Kinetics validation set. + +
MethodmAPGFLOPs#3D#Frame
Upper82.654.52.08.0
Ours82.442.11.36.6
Upper83.5109.12.016.0
Ours83.461.81.49.5
+ +Table 4: Results on FCVID [19] using Slowonly [9] architecture as 3D model. Top: 8-frame input setting. Bottom: 16-frame input setting. + +Qualitative analysis. In addition to the quantitative results presented above, we also qualitatively analyze our method. In particular, we observe that our method produces policies with fewer 3D convolutions and frames for input clips that are more "static", while uses more for motion-intensive instances. As shown in Fig. 4, a smaller number of 3D convolutions and frames are applied on clips with discriminative static cue. For instance, the presence of "bass" and "book binder" for class "playing bass guitar" and "book binding" suffice to produce correct predictions, and the scene of a "court" serves as a strong contextual signal for "hurling". On the other hand, for motion-intensive action classes and instances, especially those related to human movement such as "breakdancing", "somersaulting" and "Tai Chi", more computational resources are allocated by our method to capture finer temporal relationships among frames. + +# 4.3. Discussion + +Impact of joint finetuning. Recall that we first train the selection network with the 3D model fixed and then jointly fine-tune both of them. Here we analyze the performance of our method without the first selection network training stage (Tr) or the joint fine-tuning stage (FT). For faster evaluation, we uniformly sample 3 clips from each test video. Results are shown in Table 5. + +As can be seen, joint fine-tuning is crucial to further improve the recognition performance (75.9 vs. 77.8). This indicates that fine-tuning the video model together with learned policies indeed helps the 3D model to adapt to the adaptive inference paradigm brought by the selection network. It is worth noting that skipping the first training + +![](images/7dd56a30ca9dd0ce5de66adbf1b5b97953e0b9b17726f4839afd24a480fa78d1.jpg) +3D usage: 2 Frame usage: 3 + +![](images/bad9ebba1eb4bb0b3352c90bcb8071013025d5d8e6d00a486f01f9dad7204fd8.jpg) + +![](images/a5858538636b3de301076cb1623e6147c5e7152135dd55debdd771ad6cec5587.jpg) +Barbequing + +![](images/67d3ad8b4d2c9401608832842dd47d9d8f8c27708277ba4c0ab3fb286b3f80b4.jpg) +3D usage: 1 Frame usage: 4 + +![](images/fe5f4989999f12fe293cafbf7905037954fd38d484369263cc46f87f3c0eb4b9.jpg) + +![](images/d0074e99cf789517ea451d28ad9662347e8c1d47e87ea3befbac1d44b895ee8a.jpg) + +![](images/6f5aa07936d523f5f1c1b63f8086ae56f9eecda66e5cfe343b7a7deab07b7dba.jpg) +Playing Bass Guitar + +![](images/dc6d62ca01e5a212ed9bc52c17efcbbb46358ab22057ce8343ab23edda7a68da.jpg) +3D usage: 2 Frame usage: 4 +Frame usage + +![](images/9cbf7a54aba0b32ee9b4567c1c5121ef6ae18a0222c038d75e0180aaff297bf9.jpg) + +![](images/04c50e30abc44ad57752951a3ac571e186a58cbd1d491992fc79b3f7b97a9a6a.jpg) + +![](images/863d6c6a11b4fd0431f74a6b981ab0e1b4f1af6ccb017f64732b88c4c25f7043.jpg) +Hurling +Book Binding + +![](images/22972114fb1418ad8f9cbd82e17cb322250093b2d8747570a161300ce3bdc8a6.jpg) +3D usage: 2 Frame usage: 3 + +![](images/c91d0f3516b29df4773d31f5032fae9aa1b944c4f7f2f47329fb3067bc21d39e.jpg) +Figure 4: Qualitative results. Black mask indicates the frame is discarded. Left: Fewer 3D convolutions and frames are used for action classes and instances that are more "static", i.e. containing discriminative static cue and contextual information. +Right: For motion-intensive instances, more computation is allocated for probing finer temporal information. + +![](images/5c33f2421b261ddcc606d80d0662b657c50d497b282791ddfa1fc8fad59b1a91.jpg) + +![](images/ea05efd91de110b0623a1a9a965a4d9bb6537da0c780de240869130f86e09862.jpg) + +![](images/c9dcd4a65508aba91ff0f0c4f0c70202327fe932f33dfb30dc6e4d81722261ea.jpg) +Dancing macarena + +![](images/8639448f23775316426f9e045ba13e8b075d277feb13eb75204bc05845498581.jpg) +3D usage: 4 Frame usage: 8 + +![](images/7fff2c4c01d713faf90869f1c3fbdb70f463492f610e19447c3d558644fe2c17.jpg) +Capoeira + +![](images/12880544a2c5c0686e13d91235d42b6c6f0d634584f9daa675c16744b582b3f0.jpg) +3D usage: 4 Frame usage: 7 + +![](images/0dc09ef4655ac806bc2ccd548023445d036bb71de88bea50443f6aa69b4f2672.jpg) +Somersaulting + +![](images/056578ac35073f9def8401ed3ff583665ea98eeadd12e4b9bef29a7f3e14ffbb.jpg) +3D usage: 5 Frame usage: 8 + +![](images/c8ad22994e94c7e647b168696c53c748e9901cb80d12cb4881a06c7ac80d3cef.jpg) +Tai Chi + +![](images/9884eeb5ef69b0501d94812b6e9dee8814dce2c06fc0627bb583140d95ba2ebf.jpg) +3D usage: 4 Frame usage: 8 + +
FCVIDACTIVITYNET
Tr FTmAPGFLOPsmAPGFLOPs
Upper78.158.676.458.6
72.336.171.142.9
✓75.934.774.338.1
✓76.534.975.137.6
✓77.835.676.142.2
+ +stage (i.e., directly training the selection network with the 3D model jointly) leads to a lower recognition performance (76.5 vs. 77.8). We posit the reason is that adding another objective (the classification loss) while training the selection network from random initialization further increases the instability of network learning under such a reinforcement learning setting; and thus the selection network converges to sub-optimal policies. + +Table 5: Ablation on the effectiveness of two training stages. + +
FCVIDACTIVITYNET
3D FramemAPGFLOPsmAPGFLOPs
Upper78.158.676.458.6
75.535.674.342.3
✓76.835.375.341.1
✓76.335.574.843.5
✓77.835.676.142.2
+ +Table 6: Ablation on the usefulness of 3D convolution usage and frame usage policies. + +Contributions of convolution and frame usage policies. To demonstrate the effectiveness of 3D convolution usage and frame usage policies learned by the two-head selection + +network, we conduct experiments to analyze contributions of the two components. In particular, we replace each/both components with randomly generated policies similar to Random FT. Here we use 3-clip testing as well. As shown in Table 6, applying either 3D or frame usage policy improves recognition performance under the same computational budget, while using both achieves the best performance with $1\%$ improvement over the single-component settings, indicating the double-head architecture can learn to produce policies cooperatively. + +# 5. Conclusion + +We presented Ada3D, a framework that learns to derive adaptive 3D convolution and frame usage policies—determining which 3D convolutions in a pretrained 3D video model and which frames in the input clip to use on a per-input basis—for efficient video recognition. In particular, a two-head selection network is trained with policy gradient methods to produce these policies, reducing overall computational cost while maintaining recognition performance. Extensive experimental results on three large-scale video recognition datasets indicate that Ada3D achieves $20\% -50\%$ computational savings on state-of-the-art 3D video models while achieving similar accuracies. We further demonstrate Ada3D is compatible with different backbones of 3D model and other clip selection methods, and qualitatively show that more computational resource is allocated on motion-intensive instances but less on static ones by Ada3D. + +Acknowledgement This work is supported by IARPA via Department of Interior/Interior Business Center (DOI/IBC) contract number D17PC00345. + +# References + +[1] The state of online video for 2020. https://www.forbes.com/sites/tjmccue/2020/02/05/looking-deep-into-the-state-of-online-video-for-2020/.1 +[2] Babak Ehteshami Bejnordi, Tijmen Blankevoort, and Max Welling. Batch-shaping for learning conditional channel gated networks. In ICLR, 2020. 3 +[3] Tolga Bolukbasi, Joseph Wang, Ofer Dekel, and Venkatesh Saligrama. Adaptive neural networks for fast test-time prediction. In ICML, 2017. 3 +[4] Joao Carreira and Andrew Zisserman. Quo vadis, action recognition? a new model and the kinetics dataset. In CVPR, 2017. 1, 2, 3, 5, 7 +[5] Yunpeng Chen, Yannis Kalantidis, Jianshu Li, Shuicheng Yan, and Jiashi Feng. Multi-fiber networks for video recognition. In ECCV, 2018. 2 +[6] Jeffrey Donahue, Lisa Anne Hendricks, Sergio Guadarrama, Marcus Rohrbach, Subhashini Venugopalan, Kate Saenko, and Trevor Darrell. Long-term recurrent convolutional networks for visual recognition and description. In CVPR, 2015. 2 +[7] Haoqi Fan, Yanghao Li, Bo Xiong, Wan-Yen Lo, and Christoph Feichtenhofer. Pyslowfast. https://github.com/facebookresearch/slowfast, 2020.5 +[8] Christoph Feichtenhofer. X3d: Expanding architectures for efficient video recognition. In CVPR, 2020. 1, 2, 3, 5, 7 +[9] Christoph Feichtenhofer, Haoqi Fan, Jitendra Malik, and Kaiming He. Slowfast networks for video recognition. In ICCV, 2019. 1, 2, 3, 5, 7 +[10] Christoph Feichtenhofer, Axel Pinz, and Andrew Zisserman. Convolutional two-stream network fusion for video action recognition. In CVPR, 2016. 2 +[11] Michael Figurnov, Maxwell D Collins, Yukun Zhu, Li Zhang, Jonathan Huang, Dmitry Vetrov, and Ruslan Salakhutdinov. Spatially adaptive computation time for residual networks. In CVPR, 2017. 3 +[12] Ruohan Gao, Tae-Hyun Oh, Kristen Grauman, and Lorenzo Torresani. Listen to look: Action recognition by previewing audio. In CVPR, 2020. 2, 3, 6, 7 +[13] Raghav Goyal, Samira Ebrahimi Kahou, Vincent Michalski, Joanna Materzynska, Susanne Westphal, Heuna Kim, Valentin Haenel, Ingo Fruend, Peter Yianilos, Moritz Mueller-Freitag, et al. The" something something" video database for learning and evaluating visual common sense. In ICCV, 2017. 1, 2, 5 +[14] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, 2016. 1, 5 +[15] Yihui He, Ji Lin, Zhijian Liu, Hanrui Wang, Li-Jia Li, and Song Han. Amc: Automl for model compression and acceleration on mobile devices. In ECCV, 2018. 4 +[16] Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, and Juan Carlos Niebles. Activitynet: A large-scale video benchmark for human activity understanding. In CVPR, 2015. 1, 2, 5 + +[17] Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andretto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861, 2017. 2 +[18] Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens van der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. In ICLR, 2018. 3 +[19] Y.-G. Jiang, Z. Wu, J. Wang, X. Xue, and S.-F. Chang. Exploiting feature and class relationships in video categorization with regularized deep neural networks. IEEE TPAMI, 2018. 2, 5, 7 +[20] Bruno Korbar, Du Tran, and Lorenzo Torresani. Scsampler: Sampling salient clips from video for efficient action recognition. In ICCV, 2019. 2, 3, 6, 7 +[21] John Langford and Tong Zhang. The epoch-greedy algorithm for multi-armed bandits with side information. In NIPS, 2008. 4 +[22] Hao Li, Hong Zhang, Xiaojuan Qi, Ruigang Yang, and Gao Huang. Improved techniques for training adaptive deep networks. In ICCV, 2019. 3 +[23] Zhenyang Li, Kirill Gavrilyuk, Efstratios Gavves, Mihir Jain, and Cees GM Snoek. Videolstm convolves, attends and flows for action recognition. CVIU, 2018. 2 +[24] Ji Lin, Chuang Gan, and Song Han. Tsm: Temporal shift module for efficient video understanding. In ICCV, 2019. 2 +[25] Ji Lin, Yongming Rao, Jiwen Lu, and Jie Zhou. Runtime neural pruning. In NIPS, 2017. 3 +[26] Yue Meng, Chung-Ching Lin, Rameswar Panda, Prasanna Sattigeri, Leonid Karlinsky, Aude Oliva, Kate Saenko, and Rogerio Feris. Ar-net: Adaptive frame resolution for efficient action recognition. In ECCV, 2020. 3, 4, 7 +[27] Maharay Najibi, Bharat Singh, and Larry S Davis. Autofocus: Efficient multi-scale inference. In ICCV, 2019. 3 +[28] Martin L Puterman. Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons, 2014. 4 +[29] Zhaofan Qiu, Ting Yao, and Tao Mei. Learning spatiotemporal representation with pseudo-3d residual networks. In ICCV, 2017. 2 +[30] Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zh-moginov, and Liang-Chieh Chen. Mobilenetv2: Inverted residuals and linear bottlenecks. In CVPR, 2018. 2, 5 +[31] Karen Simonyan and Andrew Zisserman. Two-stream convolutional networks for action recognition in videos. In NIPS, 2014. 2 +[32] Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction. MIT press Cambridge, 1998. 2, 4 +[33] Du Tran, Lubomir D Bourdev, Rob Fergus, Lorenzo Torresani, and Manohar Paluri. C3d: Generic features for video analysis. In ICCV, 2015. 1, 2, 3 +[34] Du Tran, Heng Wang, Lorenzo Torresani, and Matt Feiszli. Video classification with channel-separated convolutional networks. In ICCV, 2019. 1, 2 +[35] Du Tran, Heng Wang, Lorenzo Torresani, Jamie Ray, Yann LeCun, and Manohar Paluri. A closer look at spatiotemporal + +convolutions for action recognition. In CVPR, 2018. 1, 2, 3, 5 +[36] Burak Uzkent and Stefano Ermon. Learning when and where to zoom with deep reinforcement learning. In CVPR, 2020. 3, 7 +[37] Andreas Veit and Serge Belongie. Convolutional networks with adaptive inference graphs. In ECCV, 2018. 3 +[38] Limin Wang, Yuanjun Xiong, Zhe Wang, Yu Qiao, Dahua Lin, Xiaou Tang, and Luc Van Gool. Temporal segment networks for action recognition in videos. IEEE TPAMI. 2 +[39] Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. In CVPR, 2018. 5, 7 +[40] Xin Wang, Fisher Yu, Zi-Yi Dou, Trevor Darrell, and Joseph E Gonzalez. Skipnet: Learning dynamic routing in convolutional networks. In ECCV, 2018. 3 +[41] Wenhao Wu, Dongliang He, Xiao Tan, Shifeng Chen, and Shilei Wen. Multi-agent reinforcement learning based frame sampling for effective untrimmed video recognition. In ICCV, 2019. 2, 3, 6 +[42] Zuxuan Wu, Tushar Nagarajan, Abhishek Kumar, Steven Rennie, Larry S Davis, Kristen Grauman, and Rogerio Feris. Blockdrop: Dynamic inference paths in residual networks. In CVPR, 2018. 3 +[43] Zuxuan Wu, Caiming Xiong, Chih-Yao Ma, Richard Socher, and Larry S Davis. Adaframe: Adaptive frame selection for fast video recognition. In CVPR, 2019. 2, 3, 6, 7 +[44] Saining Xie, Chen Sun, Jonathan Huang, Zhuowen Tu, and Kevin Murphy. Rethinking spatiotemporal feature learning: Speed-accuracy trade-offs in video classification. In ECCV, 2018. 2, 3, 5, 7 +[45] Ceyuan Yang, Yinghao Xu, Jianping Shi, Bo Dai, and Bolei Zhou. Temporal pyramid network for action recognition. In CVPR, 2020. 1, 3 +[46] Le Yang, Yizeng Han, Xi Chen, Shiji Song, Jifeng Dai, and Gao Huang. Resolution adaptive networks for efficient inference. In CVPR, 2020. 3, 7 +[47] Joe Yue-Hei Ng, Matthew Hausknecht, Sudheendra Vijayanarasimhan, Oriol Vinyals, Rajat Monga, and George Toderici. Beyond short snippets: Deep networks for video classification. In CVPR, 2015. 2 +[48] Yin-Dong Zheng, Zhaoyang Liu, Tong Lu, and Limin Wang. Dynamic sampling networks for efficient action recognition in videos. IEEE TIP, 2020. 2 +[49] Bolei Zhou, Alex Andonian, Aude Oliva, and Antonio Torralba. Temporal relational reasoning in videos. In ECCV, 2018. 2 +[50] Mohammadreza Zolfaghari, Kamaljeet Singh, and Thomas Brox. Eco: Efficient convolutional network for online video understanding. 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This involves categorizing, segmenting and reasoning of visual affordance. Relevant studies in 2D and 2.5D image domains have been made previously, however, a truly functional understanding of object affordance requires learning and prediction in the 3D physical domain, which is still absent in the community. In this work, we present a 3D AffordanceNet dataset, a benchmark of 23k shapes from 23 semantic object categories, annotated with 18 visual affordance categories. Based on this dataset, we provide three benchmarking tasks for evaluating visual affordance understanding, including full-shape, partial-view and rotation-invariant affordance estimations. Three state-of-the-art point cloud deep learning networks are evaluated on all tasks. In addition we also investigate a semi-supervised learning setup to explore the possibility to benefit from unlabeled data. Comprehensive results on our contributed dataset show the promise of visual affordance understanding as a valuable yet challenging benchmark. + +# 1. Introduction + +The concept of affordance was first defined as what the environment offers the animal, introduced by [6]. Affordance understanding is concerned with the interactions between human and environment. For instance, human can sit on the chair, grasp a cup or lift a bag. Being able to understand the affordance of objects is crucial for robots to operate in dynamic and complex environments [8]. Many applications are supported by affordance understanding including, anticipating and predicting future actions[12, 10, 13], recognizing agent's activities[21, 4, 26], providing valid functionality of the objects[7], understanding social scene situations[2] and understanding the hidden values of the + +![](images/b5a77164b113d30d14295f8c8875a3b8a6020addaecac9a705df9f1069f5ea86.jpg) + +![](images/4a328e4662ba7f79020b3321c3a3d75d3c7d65cc00b3a5a67920f744c0751c0d.jpg) + +![](images/e3e38142a812b8e25b6e109535dd4074cc6d9f3a45dd5c67f49d6d8f6f052ff7.jpg) +Pour + +![](images/94ce0e44c56ef8a75d0e4643ea1923d27a630691b3f27d3bf2e41cba4d9cb204.jpg) +Grasp + +![](images/c4cf1ad8293c0006ef4bb948e539e30e67a3ae1af8195a6302c31d264898047c.jpg) +Figure 1. The 3D AffordanceNet dataset. The mesh was first annotated with affordance keypoints. Then we densely sample points and obtain the ground truth data via label propagation. + +![](images/ff211ddbd15d656bfc40a0a7121c4bef5ad6757aaa763a4fc15376672071ae4d.jpg) +Grasp + +![](images/96078f55f3f36a4d08f259003445e8d90d3477cf368218e8d2510156a6a23bb3.jpg) + +![](images/6bfcad16be47d4788bf77ea6752cb6f1c3805dcb324d438f6e4599403a4bca15.jpg) +Wrap-Grasp + +![](images/3c2e38c3880159374033cabf622004ab666283600856764bc3379e9923267f7e.jpg) + +![](images/ac011410bd074116c65b06723277bf240bd511731b70deb45b18e162472acffa.jpg) +Contain +Stab + +![](images/e2377f8b101a9dd562e10f5dbb75ebfe9071cae8d49478f347be44429d121d94.jpg) +Lift + +objects[33]. Tasks including affordance categorization, reasoning, semantic labeling, activity recognition, etc. are defined as specific instantiations of affordance understanding [8]. Among all these we find semantic labeling [22, 33] is of the most importance because the ability to localize the position of possible affordance is highly desired by robotic research. We refer semantic labeling as affordance estimation throughout this paper. + +The most important and proper modality for affordance understanding is through visual sensors [8]. Visual affordance understanding has been extensively studied recently with computer vision techniques. Many algorithms are built upon deep neural networks [19, 3, 23] thus require large labeled affordance dataset for benchmarking. Relevant datasets are developed for these purposes with data collected from 2D (RGB) sensors [32, 24, 22] or 2.5D (RGBD) sensors [18, 19, 23]. Nevertheless, we believe that the affordance understanding requires learning in the 3D domain which conveys the geometric properties. For example, the affordance of grasp is highly correlated with vertical structure with small perimeter and sittable is correlated with flat surface. Unfortunately, such detailed geometry is not captured by the existing 2D datasets while the 2.5 ones [19, 23] are often captured with small depth variation and do not carry enough geometric information. + +To encourage research into visual affordance understanding in more realistic scenarios, a benchmark on real 3D dataset is highly desired. Therefore, we are inspired by PartNet[17], a recently proposed dataset containing the fine-grained part hierarchy information of 3D shapes based on the large-scale 3D CAD model dataset ShapeNet[1] and 3D Warehouse. Although PartNet mentioned affordance as potential application, there is still no benchmark purposely established for affordance yet. More importantly, we discover, via user annotations, that the human perceived affordance often do not fully overlap with the individual parts specified in PartNet dataset. For example, In the first row of Fig. 1, the Pour, Wrap-Grasp and Contain affordance from Mug do not perfectly match any part indicated by the colored image on the 1st column. Therefore, we believe it is necessary to provide a new set of affordance labels on the PartNet dataset. + +Creating 3D visual affordance benchmark is challenging due to the subjective definition. We take into account the affordance definitions from existing research on visual affordance learning in 2D and 2.5D domains [8] and select possible interactions that one can take with 3D shapes from PartNet. Finally, 18 types of affordance were formally defined over 23 semantic objects. Additional challenge associated with annotation on 3D model is the scalability issue. In order to provide highly quality annotation on such a large scale, we use label propagation method to propagate affordance sparsely labeled on individual points. Eventually, we obtain point-wise probabilistic score of affordance for each individual shape in PartNet. We name the new benchmark 3D AffordanceNet to reflect the focus on visual affordance on 3D point cloud data. + +3D AffordanceNet enables benchmarking a diverse set of tasks, in particular, we put forward full-shape, partial-view and rotation-invariant affordance estimations. Three state-of-the-art point cloud deep learning networks are evaluated on all tasks. We also propose a semi-supervised affordance estimation method to take the advantage of large amount of unlabeled data for affordance estimation. + +In summary, we make the following contributions: + +- We introduce 3D AffordanceNet, consisting of 56307 well-defined affordance information annotations for 22949 shapes covering 18 affordance classes and 23 semantic object categories. To the best of our knowledge, this is the first large-scale dataset with well-defined probabilistic affordance score annotations; +- We propose three affordance learning tasks which are supported by 3D AffodanceNet to demonstrate the value of annotated data: full-shape affordance estimation, partial-view affordance estimation and rotation-invariant affordance estimation. + +- We benchmark three baseline methods for proposed affordance learning tasks and further propose a semi-supervised affordance estimation method to take advantage of unlabeled data for affordance estimation. + +# 2. Related Work + +Affordance refers to the possible action an agent could make to interact with the environment [6]. Examples include a cup can afford 'pouring', a bed is 'sittable' and 'layable', etc. Affordance understanding is the core function in developing autonomous systems. In particular, the visual affordance understanding is the most promising way due to the rich information carried by visual sensors. We mainly review the recent development in visual affordance dataset and approaches, a detailed review can be found in [8]. Recent advances in visual affordance are mostly demonstrated on affordance recognition [7, 3], detection [3, 18] and segmentation [3, 18]. Beyond the low-level visual tasks, there is substantial attention on-the-rise paid to affordance reasoning, affordance-based activity recognition and social affordances. In this work we are interested in providing a benchmark for affordance segmentation, a.k.a. prediction, due to the clear definition and high demand in robotic applications. + +To benchmark visual affordance segmentation, UMD [18], CAD120 [23] and IIT-AFF [19] are respectively developed recently. All datasets feature affordance segmentation on RGBD images covering from 10-20 objects, 6-9 affordance types and $3\mathrm{k} - 10\mathrm{k}$ labelled images. In particular, IAF-IIT and CAD120 capture complex scenes while UMD mainly focuses on well-controlled scenes. Nevertheless, none of these datasets carry the rich geometric properties of objects that robotic application would expect and only a single view-point is present. As a result, these datasets no longer pose challenges to modern computer vision techniques. + +With the easy access to 3D point cloud data, e.g. collected from LiDAR and SFM, and potential application in robotics, atunomous driving, etc., there is a recent surge in research towards 3D point cloud. ShapeNet [1] collected 3D CAD models from open-sourced 3D repositories, with more than 3,000,000 models and 3,135 object categories. It was further developed by [29] for shape part segmentation. Partially motivated by affordance understanding, the subsequent PartNet dataset [17] was proposed with 26k objects, featuring fine-grained semantic segmentation task. Hierarchical segmentation was also addressed by a recursive part decomposition [31]. Though affordance is briefly mentioned as the motivation for creating above 3D shape datasets, to the best of our knowledge, there is no existing dataset which explicitly addresses the task of visual affordance prediction. The only known attempt on 3D shape functionality understanding [9] is still limited to a few types + +![](images/aed12d453bf31a6250996b74474a71dff15ac7a48330dc935af4cfb4d38c14c5.jpg) +Figure 2. The annotation workflow. The blue arrows indicate the annotation procedures, the green arrows refer to the corresponding 3D GUI actions. The annotators are first asked to determine the supported affordance classes and then select the functional points. The annotators need to confirm whether the adjacent parts support the same affordances. + +of objects and did not make connection to the well-studied visual affordance understanding in 2D image domains. In contrast, we created a new benchmark for visual affordance estimation on 3D point cloud. The affordance types are selectively inherited from a summary of existing works and annotations are made on 3D point cloud data directly. + +# 3. Dataset Construction + +We present 3D AffordanceNet as a dataset for affordance estimation 3D point cloud. To construct this dataset, we first define a set of affordance types by referring to the existing visual affordance works [8]. Raw 3D shape data are collected from the shapes in PartNet [17] which covers common object types in typical indoor scenes. A question-answering 3D GUI is developed to collect raw point-wise annotation on mesh shapes. In total, we hired 42 professional annotators for annotations, the average annotation time per shape is 2 minutes and each shape is annotated by 3 annotators. Finally, label propagation is employed to obtain probabilistic ground-truth for the shape point cloud. + +# 3.1. Affordance Type + +We refer to [8] for a full review of affordance types adopted in visual affordance research. From the full list of possible affordances, we select those suitable for 3D objects present in PartNet [17] and remove the irrelevant ones, e.g. 'reachable' and 'carryable'. Overall, we filter out 18 categories of affordances, namely 'grasp', 'lift', 'contain', 'open', 'lay', 'sit', 'support', 'wrap-grasp', 'pour', 'display', 'push', 'pull', 'listen', 'wear', 'press', 'cut', 'stab', and 'move'. Then, we associate the affordance types to each category of object in PartNet according to its attributes and functionality that it can afford to interact with human or robot. For example, a chair is 'sitable' but not 'layable', a table can afford 'support' but not 'contain', etc. The affordances of each category are shown in Tab. 2. The annotators are allowed to freely determine where the affordance locates on the object, e.g. 'grasp' of bag can be annotated at its handle, webbing or straps. Notice that we allow the annotators to select the supported affordance for each shape, + +thus some shapes may not have all affordances defined for its own shape category. + +# 3.2. Annotation Interface + +We created a web-based 3D GUI to collect raw annotations. The process of annotation is designed to be a question-answering workflow as illustrated in Fig. 2. A user is given one shape at a time visualized in 3D. Each individual parts are colored according to the pre-defined color map in PartNet dataset [17]. Annotators are allowed to freely rotate, translate and change the scale of the shape using mouse, which allow the annotators to observe the shape from more angles. After observation, annotators are first asked to determine the supported affordances by choosing from a list ('What affordances does this shape support?'). Considering that some annotators may not understand the affordances, we provide the explanation of each affordance on the interface. Annotators are then asked to select keypoints that support the specified affordance ('What points on the shape support the affordance?'). At least 3 keypoints will be labeled by one annotator for each affordance. Annotators will also decide whether the selected affordance will propagate beyond the part which the labeled keypoint sits on. If yes, annotators are asked to select eligible parts that the affordance can propagate to, otherwise, more annotations will be made on the same part until enough keypoints are collected. + +The questions that the annotation interface proposes for each affordance directly determine how the annotators perceive the affordances. Therefore, we define questions carefully tailored for each affordance. Some questions are shown in Tab. 1. A complete list of affordance question is given in the supplementary material. + +# 3.3. Ground-Truth Construction + +After obtaining affordance keypoints, we propagate labels to all points on the shape to create ground-truth for downstream learning tasks. We first record the coordinates of the selected keypoints. We then propagate the labels to $N$ points densely sampled on the shape mesh surface, note + +
AffordanceObjectQuestion
LayBedIf you were to lie on this bed, which points would you lie on the bed?
GraspEarphoneIf you want to grab this earphone, where will your palm position be?
LiftBagIf you want to lift this bag, at which points are your finger most likely to carry the bag?
SitChairIf you were sitting on this chair, on which points would you sit?
MoveTableIf you want to move this table, at which points on this table will you exert your strength?
OpenTrash CanIf you want to open the lid of this trash can, from which points on the trash can you open it?
PourBottleSuppose there is water in the bottle, and you want to pour the water out of the bottle. From which points on the bottle will the water flow out?
PressLaptopIf you want to press keys on a computer keyboard, which points on the keyboard would you press?
ContainMicrowaveIf you put something in the microwave, at which points in the microwave would you put the object?
SupportTableIf you want to put something on the table, at which points on the table would you put the object?
+ +![](images/a3f9d85cf36af5c5e37c3fc1eeb4116cd67cf8a770bc30027fba3a3a6afb113c.jpg) +Figure 3. The example of annotated data. Different affordances are shown in different colors, points annotated with multiple affordances are colored by the affordance that has the highest scores. The brighter the color, the higher the score. + +that we only propagate on the parts that support the specific affordance that are recorded during user annotation. Formally, we construct a kNN graph on sampled points where the adjacency matrix $\mathbf{A}$ writes as, + +$$ +a _ {i j} = \left\{ \begin{array}{c c} \| \mathbf {v} _ {i} - \mathbf {v} _ {j} \| _ {2}, & \mathbf {v} _ {j} \in N N _ {k} (\mathbf {v} _ {i}) \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {1} +$$ + +where $\mathbf{v}$ is the $xyz$ spatial coordinate of point and $NN_{k}$ denotes the set of $k$ nearest neighbors. The adjacency matrix is symmetrized by $\mathbf{W} = 1 / 2(\mathbf{A} + \mathbf{A}^{\top})$ . Then we normalize the adjacency matrix by $\widetilde{\mathbf{W}} = \mathbf{D}^{-0.5}\mathbf{W}\mathbf{D}^{-0.5}$ . where $\mathbf{D}$ is the degree matrix. Finally the scores $\mathbf{S}$ for all points is propagated by the closed-form solution $\mathbf{S} = (\mathbf{I} - \alpha \widetilde{\mathbf{W}}^{-1})\mathbf{Y}$ . where $\mathbf{Y} \in \{0,1\}^{N \times 18}$ is the one-hot label vector and 1 indicates positive label. $\alpha$ is a hyper-parameter controlling the decreasing speed of $\mathbf{S}$ , we empirically set $\alpha$ to 0.998 throughout the experiments. Finally we linearly normalize $\mathbf{S}$ to the range between 0 and 1 so that it is a probabilistic score. Example shapes with propagated affordance ground-truth are shown in Fig. 3. + +# 3.4. Statistics + +The final dataset provides well-defined visual affordance score map annotations for 22949 shapes from 23 shape categories with at most 5 affordance types defined for each category. From the perspective of affordance categories, 3D AffodanceNet contains 56307 affordance annotations from 18 affordance classes. It is worth noting that due to the multi-label nature, each point could be labeled with multiple affordances. More details of the dataset are presented in Tab. 2 and Tab. 3. + +Table 1. Some examples of the proposed questions for affordance annotation. + +
ObjectAffordanceNum
Baggrasp, lift, contain, open125
Bedlay, sit, support181
Bowlcontain, wrap-grasp, pour187
Clockdisplay524
Dishwasheropen, contain166
Displaydisplay887
Dooropen, push, pull220
Earphonegrasp, listen223
Faucetgrasp, open628
Hatgrasp, wear222
Storage Furniturecontain, open2186
Keyboardpress156
Knifegrasp, cut, stab314
Laptopdisplay, press421
Microwaveopen, contain, support184
Mugcontain, pour, wrap-grasp, grasp190
Refrigeratorcontain, open185
Chairsit, support, move6113
Scissorsgrasp, cut, stab68
Tablesupport, move7990
Trash Cancontain, pour, open315
Vasecontain, pour, wrap-grasp1048
Bottlecontain, open, wrap-grasp, grasp, pour411
+ +Table 2. 3D AffordanceNet statistics. The first column shows the object category. The second column shows the defined affordance classes for each category. The third column shows the amount of each shape semantic category. + +# 4. Tasks and Benchmarks + +In this section, we benchmark three tasks to demonstrate the 3D AffodanceNet dataset, namely, full-shape, partial-view and rotation-invariant affordance estimation. The 3D AffodanceNet dataset is split into train, validation and test + +
SupportMoveSitContainOpenGraspPourDisplayWrap-Grasp
#Annot14848145406516515545062253208619141889
PressCutStabWearListenPullPushLayLift
#Annot588393393231228225225194123
+ +Table 3. The number of shapes that are positive for each category of affordance. + +sets with a ratio of $70\%$ , $10\%$ and $20\%$ , respectively according to the shape semantic category. The first experiment estimates point-wise affordance given full 3D point cloud as input. The second experiment estimates the affordance of partially visible objects observed from different viewpoints. The last experiment estimates the affordance of rotated 3D objects under two different rotation settings. We also create a semi-supervised affordance estimation benchmark to explore the opportunity of exploiting unlabeled data for affordance estimation. + +# 4.1. Full-Shape Affordance Estimation + +Given an object as 3D point cloud without knowing the affordances supported by the object, the full-shape affordance estimation task aims to estimate the supported affordance type and predict the point-wise probabilistic score of affordance. We show that state-of-the-art 3D point cloud segmentation networks predict reasonable results on 3D AffordanceNet. + +Network and Training. We evaluate three network architecture, namely PointNet++[20], DGCNN[27] and U-Net[28] for this task. To obtain the point-wise score, we utilized the segmentation branch of PointNet++ and DGCNN as shared backbones to extract features for each point, then for each affordance type, we pass the features through multiple classification heads and used a sigmoid function to obtain the posterior scores. The classification heads were set up for each affordance category individually while the backbone networks were shared. We use cross-entropy loss $L_{CE}$ for training the network as below, + +$$ +l _ {C E} = \frac {1}{N} \sum_ {i} ^ {M} \sum_ {j} ^ {N} - (1 - t _ {i j}) \log \left(1 - p _ {i j}\right) - t _ {i j} \log \left(p _ {i j}\right) \tag {2} +$$ + +where $M$ is the total number of affordance types, $N$ is the number of points within each shape, $s_{ij}$ is the ground truth score of $j$ th point of $i$ th affordance category and $p_{ij}$ is the predicted score. + +Since the points with zero score account for a relatively large proportion of the total dataset, we further propose to use dice loss [15] to mitigate the imbalance issue. The dice loss $l_{DICE}$ is defined as: + +$$ +\begin{array}{l} l _ {D I C E} = \sum_ {i} ^ {M} 1 - \frac {\sum_ {j} ^ {N} s _ {i , j} p _ {i , j} + \epsilon}{\sum_ {j} ^ {N} s _ {i , j} + p _ {i , j} + \epsilon} \tag {3} \\ - \frac {\sum_ {j} ^ {N} (1 - s _ {i , j}) (1 - p _ {i , j}) + \epsilon}{\sum_ {j} ^ {N} 2 - s _ {i , j} - p _ {i , j} + \epsilon} \\ \end{array} +$$ + +Finally the loss function is defined as $l = l_{CE} + l_{DICE}$ . We train PointNet++ and DGCNN on the 3D AffordanceNet us- + +ing the default training strategies and hyper-parameters described in respective papers[20, 27]. For Unet, we fine-tune the network initialized by the pre-trained weight provided by PointContrast[28]. + +Evaluation and Results. We evaluate four metrics for affordance estimation, including mean Average Precision (mAP) scores, mean squared error (MSE), Area Under ROC Curve (AUC) and average Intersection Over Union (aIoU). For AP, we calculate the Precision-Recall Curve and AP is calculated for each affordance. For AUC, we report the area under ROC Curve. For MSE, we calculate mean squared error of each affordance category and sum up the results from all affordance categories. For aIoU, we gradually tune up the threshold from 0 to 0.99 with 0.01 step to binarize the prediction, and the aIoU is the arithmetic average of all IoUs at each threshold. Except for the MSE, all the other metrics for each category are averaged over all shapes, a.k.a. macro-average. For each affordance category, the groundtruth map is binarized with 0.5 threshold before evaluation. The results are reported in Tab. 4 under the Full-Shape section and some qualitative examples from PointNet++ are selected and visualized in Fig. 4. + +As shown in Tab. 4, the performances of three networks are close and all achieve a relatively low aIOU score, which indicates that affordance estimation is still a challenging task. Comparing the second row of Fig. 4 to corresponding ground truth, we found that PointNet++ produces some reasonable results. For example, the estimations of grasp on a bag are successfully localized on both the handles and the webbing. However, the results of pour on a bottle fail since the network predicts the scores mainly on the lid of the bottle rather than the body edge of the bottle where is the place that the water flow out. More qualitative examples are given in the supplementary. + +Room for Performance Improvement The performances of PointNet++ and DGCNN on the tasks mentioned above are relatively weak. Hence, we evaluate the trained network on full-shape affordance estimation task over the training, validation and testing sets to investigate the room for performance improvement with results reported in Tab. 5. From the results we observe that both two networks still underfit, meaning that the proposed affordance estimation task is very challenging for existing point cloud analysis networks. + +# 4.2. Partial-View Affordance Estimation + +Although complete point clouds or meshes can provide detailed geometric information for affordance estimation, in real-world application scenarios, we can only expect partial view of 3D shapes, represented as partial point cloud. Therefore, another important task we are concerned with is to estimate the affordance from partial point cloud. + +Network and Training. To obtain partial point clouds, we follow [11] to synthesize point cloud observed from certain + +
Full-shapeAvgGraspLiftContainOpenLaySitSupportWrap.PourDisplayPushPullListenWearPressMoveCutStab
P_mAP48.043.475.156.946.663.081.152.519.046.959.320.537.941.620.431.435.341.190.9
P_AUC87.482.897.189.390.692.696.089.772.689.290.683.185.385.967.990.979.091.498.8
P_alOU19.315.741.222.220.230.038.117.54.018.225.66.512.714.06.511.28.515.240.9
P_MSE0.0590.0030.00010.0060.0030.00050.0050.0120.0020.0020.00070.00070.00020.00060.00050.00060.0210.00030.0001
D_mAP46.443.985.257.651.812.380.954.020.747.765.520.540.536.018.334.235.540.291.4
D_AUC85.582.598.789.991.650.196.190.274.689.292.185.089.786.161.991.878.991.798.7
D_alOU17.813.940.221.625.41.034.918.85.617.732.15.511.811.95.914.89.914.535.4
D_MSE0.080.0030.00010.0070.0030.00060.0060.0130.0070.0050.0020.0020.00060.0020.0020.00070.0250.00020.0001
U_mAP47.442.675.756.645.960.680.853.719.145.061.519.736.537.420.433.935.239.889.0
U_AUC86.379.894.388.888.588.295.889.772.987.190.281.484.082.970.391.679.290.898.5
U_alOU19.713.741.222.420.829.437.318.64.718.332.46.213.013.14.414.59.214.241.5
U_MSE0.0630.0030.00030.0060.0030.00060.0050.0140.0020.0020.0020.00060.00020.00070.00030.00080.0210.00020.0001
PartialAvgGraspLiftContainOpenLaySitSupportWrap.PourDisplayPushPullListenWearPressMoveCutStab
P_mAP45.743.280.641.948.552.669.845.520.047.052.524.136.542.115.330.737.843.392.6
P_AUC85.281.296.283.387.986.795.086.571.388.485.284.986.184.264.184.779.690.298.8
P_alOU16.914.445.613.221.625.231.011.23.617.819.35.711.513.42.412.46.213.537.8
P_MSE0.0620.0030.00010.0050.0030.00060.0040.0130.0020.0020.0020.00020.00010.00070.00040.00060.0250.00030.0001
D_mAP42.240.183.838.544.546.667.343.919.644.850.315.728.619.917.726.935.643.392.1
D_AUC83.780.397.080.886.882.694.687.07086.881.783.686.07564.183.078.590.099.1
D_alOU13.813.337.98.616.015.527.213.53.213.913.83.94.38.45.25.78.213.336.8
D_MSE0.0690.0050.00020.0050.0040.00060.0040.0130.0030.0020.0020.0010.0010.0020.0030.00040.0220.00040.0001
U_mAP43.040.873.241.247.644.668.945.318.545.253.219.529.638.911.129.636.739.190.8
U_AUC83.278.994.681.787.180.494.587.069.387.584.480.979.284.256.484.977.789.398.7
U_alOU16.814.738.115.021.120.833.514.44.318.920.45.38.210.91.014.79.015.935.8
U_MSE0.0650.0030.00020.0060.0030.0010.0060.0120.0030.0030.0020.00030.00020.00030.00060.00080.0220.00070.0002
Rotate zAvgGraspLiftContainOpenLaySitSupportWrap.PourDisplayPushPullListenWearPressMoveCutStab
P_mAP47.343.185.758.139.662.780.653.820.447.547.221.834.839.719.028.136.340.491.9
P_AUC87.082.097.989.586.291.195.990.174.289.487.185.487.984.367.088.580.391.598.5
P_alOU18.715.545.422.417.626.038.018.34.619.517.47.010.513.96.99.28.814.840.6
P_MSE0.060.0030.00010.0060.0030.00060.0050.0120.0020.0020.0030.0010.00030.00070.00070.00050.020.00030.0001
D_mAP44.842.282.958.245.217.378.852.420.346.758.521.645.228.516.829.635.036.490.8
D_AUC84.980.898.289.987.954.995.889.974.089.590.684.789.481.064.489.279.790.698.4
D_alOU16.113.636.119.621.21.029.218.53.413.625.35.713.611.35.713.19.713.636.3
D_MSE0.0740.0030.00010.0070.0030.00060.0070.0130.0050.0040.0020.0030.00080.0020.0020.00090.0210.00040.0001
U_mAP46.142.774.456.140.458.481.254.918.544.756.420.735.336.817.431.635.636.288.8
U_AUC86.181.295.887.585.988.495.890.272.287.687.985.187.983.263.190.078.990.398.4
U_alOU18.915.539.621.818.424.738.418.94.518.626.96.612.214.55.114.19.912.137.7
U_MSE0.060.0030.00010.0060.0030.00040.0050.0130.0020.0020.0020.00070.00020.00080.00040.00080.0210.00030.0001
Rotate SO(3)AvgGraspLiftContainOpenLaySitSupportWrap.PourDisplayPushPullListenWearPressMoveCutStab
P_mAP41.840.578.542.432.738.474.548.319.441.741.119.730.339.417.621.534.641.190.6
P_AUC83.379.093.681.181.379.693.987.471.685.483.783.184.084.264.878.278.691.099.4
P_alOU15.212.838.312.213.19.633.616.53.816.113.73.011.114.85.58.88.914.437.2
P_MSE0.0720.0030.00010.0080.0030.00070.0070.0150.0030.0030.0030.00020.00010.00060.0020.00090.0220.00060.0001
D_mAP37.337.970.737.334.29.773.946.817.640.246.819.137.46.911.822.330.941.486.4
D_AUC78.979.195.679.481.436.393.987.271.285.685.782.388.843.560.382.776.991.999.1
D_alOU12.813.632.57.813.91.035.414.44.916.419.34.511.00.003
D_MSE0.080.0040.00020.0070.0030.00060.0070.0150.0050.0040.0050.0020.00050.00040.00060.0090.0220.00070.0002
U_mAP37.937.061.238.029.834.077.449.916.439.342.614.824.735.78.620.131.836.983.3
U_AUC80.976.990.579.577.778.194.187.867.982.781.978.183.583.752.576.677.189.699.0
U_alOU12.015.38.210.810.75.435.816.22.712.715.81.04.312.31.07.37.911.935.8
U_MSE0.070.0050.00010.0080.0030.00050.0060.0130.0030.0030.0040.00020.00010.00040.00040.00080.0220.00030.0001
+ +Table 4. Affordance Estimation Results. Except for the MSE results, others are shown in percentage, the higher the scores the higher the results. Algorithm P, D and U represent PointNet++[20], DGCNN[27] and U-Net[28] respectively. The words Full-Shape, Partial, Rotate $z$ and Rotate SO(3) represent the full-shape, partial, $z/z$ and $SO(3)/SO(3)$ rotation-invariant affordance estimation, respectively. + +
mAPAUCaIOUMSELossmAPAUCaIOUMSELoss
P Train52.389.821.70.0548.75D Train51.789.121.20.0618.83
P Val48.288.019.20.0578.81D Val47.885.817.50.0758.91
P Test48.087.419.30.0598.83D Test46.485.517.80.088.93
+ +Table 5. The performances of two different networks on full-shape affordance estimation task over train, validate and test sets. P represents PointNet++ and D refers to DGCNN. + +camera viewpoints. Only points directly facing the camera will be preserved as visible points and each point is assigned a radius to create occlusion effect. In specific, because all shapes are well aligned within the $(-1,-1,-1)$ to $(1,1,1)$ cube, we set up 4 affine cameras located at $(1,1,1)$ , $(-1,-1,1)$ , $(1,-1,-1)$ , $(-1,1,-1)$ in Cartesian coordinate system, facing towards the origin. After obtaining the partial point clouds, we sample 2048 points from each viewpoint via furthest point sampling, if the number of points of the point cloud is fewer than 2048, we utilize the point cloud up-sampling method proposed in [30] to up-sample the data. We use ex + +actly the same backbone networks and training strategies described in previous sections. + +Evaluation and Results. During testing stage, we estimate the affordance on the visible partial point cloud only. The evaluation protocol follows the one described in Section 4.1. All evaluation metrics are reported in Tab. 4 with qualitative results from PointNet++ shown in Fig. 4. + +Unsurprisingly, the quantitative performances of three networks have decreased due to the loss of geometric information of partial point cloud relative to complete point cloud. Nevertheless, we still observe reasonable qualitative results even though only a partial view is observed. For instance, the network produces high prediction for move on the upside of the legs of a table despite the unseen parts of the legs. The grasp for bag, hear for earphone, sit for chair, etc., are all more-or-less correctly predicted. In contrast, the estimation for contain on storage furniture are par + +![](images/081221030ac1c33bc4dea46934233978fd6fdcf92b74431334f6424b3226ea17.jpg) +Figure 4. Qualitative results for affordance estimation. The top row shows the ground truth. The second row shows the full-shape estimated results, the third row shows the partial-view estimated result, the fourth and the bottom row show the $z/z$ and $SO(3)/SO(3)$ rotation-invariant estimated results, respectively. All results come from PointNet++. The top words indicate the semantic category of each column and the bottom words indicate the affordance category. The greener the color of the points, the higher the confidence about specific affordance types. Wrap is the abbreviation of Wrap-Grasp. + +tially missing since it predicts the scores on the top of the furniture which is not fully observed. + +# 4.3. Rotation-Invariant Affordance Estimation + +The shapes in 3D AffordanceNet are all aligned in canonical poses, however, the data observed by sensors in real world are not always in canonical poses. The difference in rotation between real data and training data will lead to a performance drop in real-world usage which inspired research into rotation equivariant network [5]. Hence, it is critical to train the algorithms to estimate affordance on rotated objects. In this section, we provide a benchmark for affordance estimation subject to two types of rotations. + +Network and Training. We used the same backbone networks, training strategies and hyper-parameters described in the Sect. 4.1. We propose two different rotation settings for experiment: $z/z$ and $SO(3)/SO(3)$ where $z/z$ means rotation is applied along $z$ axis only for both training and inference stages while $SO(3)/SO(3)$ refers to $SO(3)$ rotation, i.e. freely rotation along $x, y$ and $z$ axes. During training session, we randomly sample rotation poses between $[0,2\pi]$ for each shape in the training mini-batch on-the-fly. We train proposed methods on complete point cloud. For testing phase, we randomly sample 5 rotation poses for each shape for both rotation settings and fix the sampled rotations for testing data. + +Evaluation and Results. We calculate mAP, AUC, aIOU + +on the proposed methods. Quantitative results are presented in Tab. 4 and qualitative results are shown in the fourth and fifth rows of Fig. 4 for $z / z$ and $SO(3) / SO(3)$ settings with PointNet++ as backbone. We observe that the performances on both $z / z$ and $SO(3) / SO(3)$ settings dropped compared to canonical view experiments. In particular, for $z / z$ setting, the performance dropped around $1\%$ in all metrics for all networks as backbone. While more significant loss of performance is observed for $SO(3) / SO(3)$ setting with $5 - 10\%$ drop in all metrics. This is aligned with our expectation that $SO(3) / SO(3)$ is a much more challenging task. We further make observations from the qualitative results in Fig. 4. First, under $z / z$ rotation scheme, despite the consistent performance drop, affordance estimations are largely correct across most categories. Obvious mistakes are made in bottle and microwave where the former missed the tip which supports pour while the latter mistakenly predict the while door of microwave for open. Under the more challenging $SO(3) / SO(3)$ scheme, there is still a visually satisfying results for most shapes. The most prominent error is made on storage furniture where contain is totally missed, probably because the complex geometric structure (many concave shapes) renders contain a hard affordance to learn under arbitrary rotation. In general, we believe affordance estimation under $SO(3) / SO(3)$ a very challenging task and it deserves further investigation. + +
VATAvgGraspLiftContainOpenLaySitSupportWrap.PourDisplayPushPullListenWearPressMoveCutStab
mAP36.634.878.844.322.634.964.841.413.341.558.913.58.320.58.529.519.433.190.2
AUC78.875.895.378.479.271.292.486.756.583.789.969.074.874.151.488.862.789.399.1
aIOU11.212.720.314.24.86.416.97.75.117.630.22.51.18.43.612.82.99.524.3
MSE0.1550.0070.00010.020.0060.00070.0120.0230.0230.0070.0080.00030.00010.0020.0020.0050.0340.0040.0003
Full-ShapeAvgGraspLiftContainOpenLaySitSupportWrap.PourDisplayPushPullListenWearPressMoveCutStab
mAP34.334.577.942.318.236.562.938.811.238.953.313.47.396.724.517.435.889.5
AUC77.575.494.878.175.773.392.185.854.482.187.574.577.461.646.783.464.189.898.9
aIOU9.811.228.114.32.510.023.49.82.27.519.91.91.01.61.66.82.35.626.5
MSE0.1050.0090.00020.0130.0030.0010.0130.0210.0040.0030.0030.00020.00010.00040.0010.00080.0310.00070.0001
+ +Table 6. The Results of Semi-Supervised Affordance Estimation. All numbers are in % except for MSE. We only implement semi-supervised affordance estimation on DGCNN. The words Full-Shape and VAT represent full-shape estimation and semi-supervised affordance estimation with virtual adversarial training. Wrap. is the abbreviation of Wrap-Grasp. + +# 4.4. Semi-Supervised Affordance Estimation + +Although the label propagation procedure allows the annotators to only annotate a few keypoints on the object surface, affordance annotation still remains as an expensive and labor intensive procedure. Inspired by the recent success in semi-supervised learning (SSL) [14, 25, 16] we establish a benchmark for semi-supervised affordance estimation. We synthesize a semi-supervised setting by randomly sampling $1\%$ training data, assumed to be labeled, and the rest are assumed to be unlabeled data. The validation and testing sets are kept the same with standard benchmarks. + +Network and Training. We utilize DGCNN[27] as our backbone. During every mini-batch in the training stage, we randomly sample a equal number of labeled data $\mathbf{X}_l$ and unlabeled data $\mathbf{X}_{ul}$ . To fully exploit the unlabeled data, we employ a state-of-the-art semi-supervised learning framework, namely Virtual Adversarial Training (VAT) [16]. It encourages the consistency between the posterior of unlabeled sample and its augmentation, measured by mean square error, + +$$ +l _ {m s e} = \frac {1}{N} \sum_ {i} ^ {M} \sum_ {j} ^ {N} \left\| p _ {i, j} - \hat {p} _ {i, j} \right\| _ {2} ^ {2} \tag {4} +$$ + +where $\hat{p}_{i,j}$ is the posterior prediction for augmented sample. To best exploit the consistency power, the augmentation is obtained by first applying a one step adversarial attack, the corresponding adversarial perturbation is then added to the original point cloud to produce the augmentation. Finally, the total loss for semi-supervised affordance estimation combines both losses defined for labeled data and unlabeled data. + +$$ +l = l _ {C E} + l _ {D I C E} + l _ {m s e} ^ {l} + l _ {m s e} ^ {u} \tag {5} +$$ + +where $l_{mse}^{l}$ and $l_{mse}^{u}$ is the mean square error (MSE) calculated between labeled and unlabeled data, respectively. We compare the semi-supervised approach against a fully supervised baseline which is trained on the $1\%$ labeled data alone with cross-entropy and dice loss. We use a mini-batch of 16, 8 for labeled data and 8 for unlabeled data, and follow the same training strategies and hyper-parameters described in [16]. We train a full-shape affordance estimation method based on DGCNN only on the labelled data following the description in Sect. 4.1. + +Evaluation and Results We evaluated the methods following the metrics described in Sect. 4.1 with results reported in Tab. 6. Comparing the performance of semi-supervised affordance estimation to the full-shape one, we found that semi-supervised affordance estimation outperforms the fully supervised baseline on all three metrics. Specifically, the gains for some affordance categories (e.g. open) that have low metrics on full-shape affordance estimation are high, which indicates that unlabeled data can provide useful information for affordance learning. In conclusion, we believe that exploiting unlabeled data to improve the performance has practical value and should receive more attention in the future. + +# 5. Conclusion + +In this work, we proposed 3D AffordanceNet, a 3D point cloud benchmark consisting of 22949 shapes from 23 semantic object categories, annotated with 56307 affordance annotations and covering 18 visual affordance categories. Based on this dataset, we define three individual affordance estimation tasks and benchmarked three state-of-the-art point cloud deep learning networks. The results suggested future research is required to achieve better performance on difficult affordance categories and under SO(3) rotation. Furthermore, we proposed a semi-supervised affordance estimation method to take advantage of large amount of unlabeled data. The proposed dataset encourages the community to focus on affordance estimation research. + +Acknowledgement This work was supported in part by the National Natural Science Foundation of China (Grant No.: 61771201, 61902131), the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant No.: 2017ZT07X183), and the Guangdong R&D key project of China (Grant No.: 2019B010155001). Xun Xu acknowledges the A*STAR Career Development Award (CDA) Funding for providing financial support (Grant No. 202D8243). + +# References + +[1] Angel X Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al. Shapenet: + +An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015. +[2] Ching-Yao Chuang, Jiaman Li, Antonio Torralba, and Sanja Fidler. Learning to act properly: Predicting and explaining affordances from images. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018. +[3] Thanh-Toan Do, Anh Nguyen, and Ian Reid. Affordancenet: An end-to-end deep learning approach for object affordance detection. In IEEE International Conference on Robotics and Automation, 2018. +[4] Jay Earley. An efficient context-free parsing algorithm. Communications of the ACM, 1970. +[5] Carlos Esteves, Christine Allen-Blanchette, Ameesh Makadia, and Kostas Daniilidis. Learning so (3) equivariant representations with spherical cnns. In Proceedings of the European Conference on Computer Vision, 2018. +[6] J Gibson James. The ecological approach to visual perception, 1979. +[7] Helmut Grabner, Juergen Gall, and Luc Van Gool. What makes a chair a chair? In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2011. +[8] Mohammed Hassanin, Salman Khan, and Murat Tahtali. Visual affordance and function understanding: A survey. arXiv preprint arXiv:1807.06775, 2018. +[9] Ruizhen Hu, Oliver van Kaick, Bojian Wu, Hui Huang, Ariel Shamir, and Hao Zhang. Learning how objects function via co-analysis of interactions. ACM Transactions on Graphics, 2016. +[10] Ashesh Jain, Amir R Zamir, Silvio Savarese, and Ashutosh Saxena. Structural-rnn: Deep learning on spatio-temporal graphs. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016. +[11] Sagi Katz, Ayellet Tal, and Ronen Basri. Direct visibility of point sets. In ACM Special Interest Group on GRAPHics and Interactive Techniques 2007 papers. 2007. +[12] Hema Swetha Koppula, Rudhir Gupta, and Ashutosh Saxena. Learning human activities and object affordances from rgb-d videos. The International Journal of Robotics Research, 2013. +[13] Hema S Koppula and Ashutosh Saxena. Anticipating human activities using object affordances for reactive robotic response. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015. +[14] Samuli Laine and Timo Aila. Temporal ensembling for semi-supervised learning. International Conference on Learning Representations, 2017. +[15] Fausto Milletari, Nassir Navab, and Seyed-Ahmad Ahmadi. V-net: Fully convolutional neural networks for volumetric medical image segmentation. In 2016 fourth international conference on 3D vision, 2016. +[16] Takeru Miyato, Shin-ichi Maeda, Masanori Koyama, and Shin Ishii. Virtual adversarial training: a regularization method for supervised and semi-supervised learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2018. +[17] Kaichun Mo, Shilin Zhu, Angel X Chang, Li Yi, Subarna Tripathi, Leonidas J Guibas, and Hao Su. Partnet: A large-scale benchmark for fine-grained and hierarchical part-level + +3d object understanding. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019. +[18] Austin Myers, Ching L Teo, Cornelia Fermüller, and Yiannis Aloimonos. Affordance detection of tool parts from geometric features. In IEEE International Conference on Robotics and Automation, 2015. +[19] Anh Nguyen, Dimitrios Kanoulas, Darwin G Caldwell, and Nikos G Tsagarakis. Object-based affordances detection with convolutional neural networks and dense conditional random fields. In IEEE/RSJ International Conference on Intelligent Robots and Systems, 2017. +[20] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. In Advances in neural information processing systems, 2017. +[21] Siyuan Qi, Siyuan Huang, Ping Wei, and Song-Chun Zhu. Predicting human activities using stochastic grammar. In Proceedings of the IEEE International Conference on Computer Vision, 2017. +[22] Anirban Roy and Sinisa Todorovic. A multi-scale cnn for affordance segmentation in rgb images. In Proceedings of the European Conference on Computer Vision, 2016. +[23] Johann Sawatzky, Abhilash Srikantha, and Juergen Gall. Weakly supervised affordance detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017. +[24] Hyun Oh Song, Mario Fritz, Daniel Goehring, and Trevor Darrell. Learning to detect visual grasp affordance. IEEE Transactions on Automation Science and Engineering, 2015. +[25] Antti Tarvainen and Harri Valpola. Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results. In Advances in neural information processing systems, 2017. +[26] Tuan-Hung Vu, Catherine Olsson, Ivan Laptev, Aude Oliva, and Josef Sivic. Predicting actions from static scenes. In Proceedings of the European Conference on Computer Vision, 2014. +[27] Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E Sarma, Michael M Bronstein, and Justin M Solomon. Dynamic graph cnn for learning on point clouds. ACM Transactions on Graphics, 2019. +[28] Saining Xie, Jiatao Gu, Demi Guo, Charles R Qi, Leonidas Guibas, and Or Litany. Pointcontrast: Unsupervised pretraining for 3d point cloud understanding. In Proceedings of the European Conference on Computer Vision, 2020. +[29] Li Yi, Vladimir G Kim, Duygu Ceylan, I-Chao Shen, Mengyan Yan, Hao Su, Cewu Lu, Qixing Huang, Alla Sheffer, and Leonidas Guibas. A scalable active framework for region annotation in 3d shape collections. ACM Transactions on Graphics, 2016. +[30] Wang Yifan, Shihao Wu, Hui Huang, Daniel Cohen-Or, and Olga Sorkine-Hornung. Patch-based progressive 3d point set upsampling. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019. +[31] Fenggen Yu, Kun Liu, Yan Zhang, Chenyang Zhu, and Kai Xu. Partnet: A recursive part decomposition network for + +fine-grained and hierarchical shape segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019. +[32] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ade20k dataset. International Journal of Computer Vision, 2019. +[33] Yixin Zhu, Yibiao Zhao, and Song Chun Zhu. Understanding tools: Task-oriented object modeling, learning and recognition. 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However, reconstructing a 3D caricature from a 2D caricature image remains a challenging task, mostly due to the lack of data. We propose to fill this gap by introducing 3DCaricShop, the first large-scale 3D caricature dataset that contains 2000 high-quality diversified 3D caricatures manually crafted by professional artists. 3DCaricShop also provides rich annotations including a paired 2D caricature image, camera parameters and 3D facial landmarks. To demonstrate the advantage of 3DCaricShop, we present a novel baseline approach for single-view 3D caricature reconstruction. To ensure a faithful reconstruction with plausible face deformations, we propose to connect the good ends of the detail-rich implicit functions and the parametric mesh representations. In particular, we first register a template mesh to the output of the implicit generator and iteratively project the registration result onto a pre-trained PCA space to resolve artifacts and self-intersections. To deal with the large deformation during non-rigid registration, we propose a novel view-collaborative graph convolution network (VC-GCN) to extract key points from the implicit mesh for accurate alignment. Our method is able to generate high-fidelity 3D caricature in a pre-defined mesh topology that is animation-ready. Extensive experiments have been conducted on 3DCaricShop to verify the significance of the database and the effectiveness of the proposed method. We will release 3DCaricShop upon publication. + +# 1. Introduction + +A caricature is a vivid art form of depicting persons by abstracting or exaggerating the peculiarities of the facial features. As a way to convey humor or sarcasm, caricatures + +![](images/f13fdb0cb8b2c06096c73fc050b27dd793f915e7e36ae805e754a02ad6860bdd.jpg) +Figure 1: Left: the proposed 3DCaricShop, a large-scale repository of 3D caricatures that are manually crafted by professional artists. It's richly annotated with 2D caricature images, camera parameters, and 3D facial landmarks. Right: the proposed baseline method that sets the new state of the art in single-view 3D caricature reconstruction. + +![](images/e656b4e07e916411305595c4dee4b99a3fd1db8debc2157ab13aae3589c52583.jpg) + +are widely used in entertainment, social events, electronic games and a variety of artistic creations. While 2D caricatures have gained popularity in comic graphics, there exist many scenarios, including cartoon character creation, game avatar customization, custom-made 3D printing, etc., that the 3D face caricatures remain the mainstream representations. However, creating a high-quality 3D caricature is a labor-intensive and time-consuming task even for a skilled artist. Thereby, generating expressive 3D face caricatures from a minimal input, such as a single image, is a highly-demanding but also challenging task. + +Most of the prior works mainly focus on 2D caricature generation [6, 33, 16], while research on reconstructing 3D caricatures from 2D caricature images remains vary rare. Wu et al. [39] propose the first work that creates 3D caricature from 2D caricature images using an optimization based approach. They formulate caricature generation as a problem of deforming the standard 3D face. In particular, they + +build a intrinsic deformation space based on the exaggerated morphable models of standard faces [25]. The deformation coefficients are then optimized to reduce the landmark fitting errors. Recently, in their follow-up work [42], they employ CNN to automate the task of 2D facial landmark prediction and deformation regression. However, previous works [32, 18] have shown that the traditional 3D morphable models (3DMM) of normal faces have very limited expressiveness in modeling the intricate facial deformations in reality. Thereby, the deformation space based on a synthetically exaggerated 3DMM, as proposed in [39, 42], is far from sufficient to capture realistic 3D caricatures, which are even more diversified and complex than normal faces. + +The key to tackling the above problem is a high-quality 3D caricature dataset created by artists that can provide realistic shape priors for both learning-based and optimization-based approaches. However, there exist two challenges in constructing such a dataset. First, the 3D models crafted by artists are not topologically consistent, making it infeasible to many downstream applications, including blend-shape creation, face animation, 3D landmark localization, etc. Secondly, the manually created meshes are typically not aligned with the corresponding images. While many face reconstruction techniques require an accurate registration, such misalignment makes the dataset inapplicable to projection-based applications such as landmark fitting, texture restoration and manipulation, etc. + +In this work, we introduce 3DCaricShop, a large-scale 3D caricature dataset that simultaneously addresses the above issues. First of all, 3DCaricShop contains 2,000 highly diversified and high-quality 3D caricature models manually crafted by professional artists. It is constructed by requesting artists to create 3D caricatures according to 2,000 manually selected caricature images from Web-Caricature [15], that span a wide range of shape exaggerations and texturing styles. Compared to the synthetic datasets [13, 42], 3DCaricShop can provide shape priors for 3D caricatures with much higher fidelity. Secondly, all the 3D models in 3DCaricShop have been re-topologized to a consistent mesh topology that paves the way to a number of future applications, including learning a parametric shape space, batch geometry processing, etc. Thirdly, we provide accurate 3D face landmarks in 3DCaricShop, which facilitates the use of landmark fitting technique that is widely adopted in the state-of-the-art face reconstruction approaches. Last but not least, 3DCaricShop offers a paired 2D caricature image and the camera parameters that are used for mesh alignment. This enables a wide range of techniques, such as differentiable rendering, landmark fitting, etc., that rely on 2D-to-3D consistency. + +To further exploit the power of 3DCaricShop, we propose a novel baseline approach to infer 3D caricatures from a single caricature image. While the methods based on deep + +implicit functions [14, 24] have shown promising capability of modeling objects with arbitrary topologies, it is prone to artifacts and self-intersections when applied to reconstruct 3D caricatures, which typically contain many extreme distortions. Though approaches using parametric mesh model can ensure a generation of plausible 3D face, they struggle to produce realistic faces with accurate geometry. We advocate to connect the good ends of both worlds by transferring the high-fidelity geometry learnt from the implicit reconstruction to a template mesh with a reasonable topology. To enable a faithful transfer, we propose a novel view-collaborative graph convolution network (VC-GCN) to extract key points from the implicit mesh for accurate mesh alignment. To strike a balance between accuracy and robustness, we iteratively project the registered template mesh onto a pre-trained PCA space using 3DCaricShop to avoid overfitting to outliers. Our approach is able to generate high-quality 3D caricatures in a pre-defined mesh topology that is animation-ready. + +We have conducted extensive benchmarking and ablation analysis on the proposed dataset. Experimental results show that the proposed approach trained on 3DCaricShop sets new state of the art on the task of single-view 3D caricature reconstruction from caricature images. + +# 2. Related Work + +Single-view Reconstruction Single-view reconstruction (SVR) is a classic task in computer vision. Existing methods could be classified as reconstruction for general objects [11, 36, 24] and for objects in specific categories[5, 3, 43]. It is an ill-posed problem due to the ambiguous nature. In tradition, strong priors are introduced to constrain the space of solutions. Shape-from-Shading (SfS) [26] is a kind of physical based prior on the relation between illumination and shape, which recovers the detailed shape in photos. However, it fails to analyze artists works because of the stylized shading effect. Most recently, with the success of deep learning architectures and the release of large-scale 3D shape datasets such as ShapeNet [7], learning based approaches have achieved great progress, by learning the shape priors directly from the huge datasets. According to the used 3D representations, these methods can be divided into voxel-based [20, 8, 30], point-based [27, 28], mesh-based [36, 23], and implicit-function-based frameworks [21, 31]. Among these methods, PIFu [31], an algorithm based on implicit functions, has been applied on the reconstruction of human body and achieves impressive results. In this paper, we employ PIFu to create the 3D mesh for each single caricature image. + +Single-view Face Modeling A closely-related task is photo-realistic face reconstruction. Two mainstream methodologies are developed to handle this problem, i.e. + +parametric based [5, 34, 10] and shape-from-shading based [29, 35] methods, and remarkable results have been achieved. However, both methods could not apply on our task directly. Parametric methods suffer from the large diversity of geometry shapes in caricature cases. For SfS algorithms, the underlying physical model could not capture various painting styles of artists. + +3D Caricature Generation Following the parametric based methods of normal face reconstruction, researchers further introduce deformation to enlarge the capability of representation [19, 39, 42]. In [19], a semi-supervised manifold regularization method is proposed to learn a regressive model for mapping from 2D real faces to the enlarged training set with 3D caricatures. Wu et al. [39] formulate the 3D caricature generation as a problem of deformation from the standard 3D face. By introducing local deformation gradients, they build an intrinsic deformation representation with the capability of extrapolation. With the deformation representation, they construct an optimization framework to create caricature model guided by the landmark constraint. Following [39], Zhang et al. [42] employ CNN to learn the deformation parameters of the intrinsic deformation representations. However, due to the lack of 3D caricature data, their works are still far from satisfaction. + +3D Face datasets 3D face datasets are of great value in face reconstruction tasks. In general, they could be categorized into synthetic and real captured datasets. For normal face, existing 3D datasets, including FaceWareHouse [5] and Facescape [40], are built from scanned 3D data, hence widely used in normal face tasks. They focus on the high accuracy and photo reality of the meshes. However, they could not be applied directly on caricature reconstruction. Researchers [39, 42] tried to perform deformation on real 3D face models to construct synthetic exaggerated data. Although some reasonable results are achieved, they still suffer from the lack of diversity. To tackle this problem, we propose 3DCaricShop, which is the first 3D caricature dataset built by artists, composed pairs of caricature images and meshes. Based on the dataset, 3D caricature shape could be learned in a model-free manner. We further propose a baseline method to reconstruct 3D mesh with uniform topology from single caricature image. + +# 3. Dataset + +We construct a dataset which contains 2,000 imagedomain pairs in total. All of the 3D models are annotated with 3D facial landmarks and poses w.r.t images. More details are introduced in the following aspects. + +3D Model Collection WebCaricature [15] is the largest-to-date dataset of 2D caricatures. It contains around 6,000 caricature images with diverse identities, geometry, and textural styles. We first selected 2,000 images from them, fur + +![](images/f820d8327b86290351f4e6388d17046aec16a63c0f46e4cfabb9fa7a6f024322.jpg) +Figure 2: Sample caricature images and crafted 3D meshes in 3DCaricShop. Images with diverse identities, geometry, and textural styles are collected. + +ther making them as diverse as possible. Then we recruited 4 paid expert Zbrush artists to create models according to images. The modeling is required to be matched with the image as much as possible, in projection manner. The contour lines for matching include edges of silhouette, lips, eyes, nose and ears. It takes around 40 minutes for each model on average, and around 40 days are cost in total. Several image-model pairs sampled from our dataset are shown in Fig. 2. Each model consists of $300\mathrm{k}\sim 700\mathrm{k}$ vertices. + +Meshing Unification To support building parametric space for our 3D caricature dataset, we unify the mesh topology for all models in two steps: 1) We first manually annotate 44 3D landmarks (see details in Fig. 3) for each model; 2) The method of Non-rigid ICP [1, 9] is applied to register a pre-defined template mesh to each model, guided by the 3D landmarks. Due to the inherent difficulty to specify vertices on a 3D mesh, the landmark annotation is performed on 3 rendered views of the 3D shape. As described in [4], these 2D landmarks can be easily transformed into their corresponding 3D positions. The template mesh we use is from FaceWareHouse [5] that consists of 11,551 vertices. This procedure is illustrated by an example in Fig. 3. + +Pose Annotation 3D pose estimation from a single image is the premise of our reconstruction method (see Sec. 4.1). It usually requires pose information supervision of the 3D face w.r.t the image. 3DCaricShop also provides accurate pose labels for each mesh that annotated by artists manually. + +Analysis of the dataset We quantitatively analyze our dataset by comparing the shape variations with two normal face datasets (FaceWarehouse (FWH) and FaceScape), as well as one synthetic caricature dataset, FaceWarehouse with deformation (Aug. FWH). We measure the shape variation using global and part variance. In particular, the variance is computed between the models and their correspond + +![](images/c4c918f409e865f2131ae7b04f8c9a1fda6be3446457bff341b3dbb9d1b17291.jpg) +(a) + +![](images/4c33a63e84f85a93f83414e3846bbde3cb1171d7e191f6e3c9f5decf135bdbf1.jpg) +left + +![](images/cb5e9db1b36c2e395bb7651d00a835408883d1a588b152fcfc3710587b2c6582.jpg) + +![](images/57f1ac68b54ed82870c251cbf705c699f6119c2bbc564a95a4f2f2c89b4a4da1.jpg) + +![](images/e51ff5078916edbd11793e712dfcb32d5a79867ed319cae4dae21dea22e89229.jpg) +(c) +Figure 3: The process of 3D landmark annotation. A raw mesh (a) is rendered from the front, left and right view. Then 2D landmarks (b) are manually annotated for each view image. 3D landmarks are obtained by projecting the mesh into a specific view and searching for the closest point on surface (d). Guiding by corresponding 3D landmarks, the template mesh (e) is deformed into the shape of the raw mesh (d), to generate mesh with correct topology (c). + +![](images/3569f880e24d1fd1761ad84ec5589cc951adc69715342d4c9c16e0a6f2cbc402.jpg) +front (b) +(d) + +![](images/09006fd235bf177a4c510a6e9edc2b0d31f4ce16fcd5faeb94b63028db9a6a63.jpg) +(e) + +ing mean shape of each dataset in terms of per-vertex displacement. The results are presented in Table 1. The shape diversity of our dataset is richer than the normal ones. For most of the face regions, 3DCaricShop has larger shape variance than Aug. FWH. + +
DatasetGlobalEyeNoseMouthEarCheekFace
FWH3.410.710.612.604.411.433.40
FaceScape2.170.360.152.635.571.242.27
Aug. FWH5.061.986.292.079.385.265.10
Ours8.264.683.0410.909.028.276.95
+ +Table 1: Shape variance comparisons of 3D face datasets. + +# 4. Methodology + +Overview In this section, we introduce the proposed baseline method. Given an input caricature image $\mathbf{I}$ , the task is to generate the corresponding 3D mesh $\mathbf{M}$ . With the topologically uniform 3D meshes in 3DCaricShop, a straight forward way to tackle the task is to construct a PCA basis using the 3D Morphable Model algorithm [2] to build the caricature face space. However, such a space could not handle the large variation in our data. To capture the diversity of geometry in caricature, we employ Pixel-aligned Implicit Function (PIFu) [31] to generate the 3D shape $\mathbf{M}_{\mathrm{I}}$ from $\mathbf{I}$ . Although the implicit function models the variation in targets, it could not ensure a uniform topology for the predictions. To achieve that, we register a template mesh $\mathbf{M}_{\mathrm{t}}$ to $\mathbf{M}_{\mathrm{I}}$ using non-rigid registration (NICP) [1]. Then the output of NICP is projected onto the pre-constructed PCA space, to alleviate deformation artifacts, such as self-intersections. We denote the output of NICP as $\mathbf{M}_{\mathbf{N}}$ and + +that of PCA as $\mathbf{M}_{\mathbf{P}}$ . Considering the large difference between the template and target meshes, a sparse 3D landmark is needed in the stage of NICP. We propose a novel view-collaborative graph convolution network (VC-GCN) to predict key points $\mathbf{k}$ from the implicit mesh, where $\mathbf{k} \in \mathbb{R}^{44}$ . + +# 4.1. The Baseline Approach + +Parametric Modeling Our parametric model space is built with standard 3D Morphable Model (3DMM) [2] algorithm. Given $p$ caricature models with uniform topology and $N$ vertices on each mesh, principal component analysis (PCA) is performed on the shape matrix $\mathbf{S}_M \in \mathbb{R}^{3N \times p}$ , which is formed by stacking the 3D coordinates of the $N \times p$ vertices. The generated $d$ eigen-vectors are employed as the shape basis $\mathbf{S}_i$ , $i = 1, 2, \dots, d$ , where $d$ is a hyper-parameter. The mean vector $\overline{\mathbf{S}}$ represents the mean shape in the mesh set. With this 3DMM, a novel caricature model $\mathbf{S}_N$ could be represented as follows: $\mathbf{S_N} = \overline{\mathbf{S}} + \sum_{i=1}^d a_i \mathbf{S}_i$ , where $\mathbf{a} = [a_1 \cdots a_d]^T$ is the vector of shape coefficients. + +Implicit Reconstruction To capture the diversity of geometric variation, we adopt Pixel-aligned Implicit Function (PIFu) [31] to reconstruct the underlying 3D shape from images. PIFu performs 3D reconstruction by estimating the occupancy of a dense 3D shape, which determines whether a point in 3D space is inside the model or not. Given a RGB image $\mathbf{I}$ , its normal maps from the front view $\mathbf{F}$ and back view $\mathbf{B}$ are generated to strengthen the local details, by using a pixel2pixel-hd network [37]. Then the implicit binary function $f(\mathbf{X},\mathbf{I},\mathbf{F},\mathbf{B})$ could be written as: + +$$ +f (\mathbf {X}, \mathbf {I}, \mathbf {F}, \mathbf {B}) = \left\{ \begin{array}{l l} 1, & \text {i f} \mathbf {X} \text {i s i n s i d e t h e m e s h s u r f a c e ,} \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {1} +$$ + +where $\mathbf{X}$ is a given 3D location in the continuous camera space. This function is modeled by a neural network. The loss function for training is formulated as: + +$$ +\mathcal {L} = \frac {1}{n} \sum_ {i = 1} ^ {n} \left| f \left(\mathbf {X} _ {i}, \mathbf {I} _ {i}, \mathbf {F} _ {i}, \mathbf {B} _ {i}\right) - f ^ {*} \left(\mathbf {X} _ {i}\right) \right| ^ {2}, \tag {2} +$$ + +where $f^{*}(\mathbf{X}_{i})$ is the ground-truth occupancy. + +3D Landmark Detection for Registration The output meshes $\mathbf{M}_{\mathbf{I}}$ of the implicit function are not topologically uniform. In order to unify the topology, we adopt non-rigid registration[1] to deform a template $\mathbf{M}_{\mathbf{t}}$ into the shape of $\mathbf{M}_{\mathbf{I}}$ . As shown in [1], without landmarks the cost function of registration could run into a local minimum, where the template is collapsed onto a point on the target surface. Thus it is important to introduce the 3D landmarks of both meshes to guide the deformation. We design a novel framework to detect 3D landmarks for $\mathbf{M}_{\mathbf{I}}$ . In short, we propose + +![](images/34c7a5da3bd414a89c053ca90da199c86baaf2f4739e1c1fdf424d98769d7858.jpg) +Figure 4: Pipeline of our framework. A detail-rich mesh is generated by implicit reconstruction from 2D caricature and the corresponding normal maps. Based on this mesh, 3D landmarks of the mesh are detected to guide the non-rigid registration, which deforms a template mesh to the target one. + +to perform detection on the rendered views of $\mathbf{M_I}$ to leverage the effectiveness of image-based CNN techniques. The process would be detailed in 4.2. + +Landmark-guided Registration Since the huge difference between $\mathbf{M}_{\mathrm{t}}$ and $\mathbf{M}_{\mathrm{I}}$ , the deformation is likely to generate artifacts, such as self-intersection. To resolve this problem, we iteratively perform NICP and PCA projection to obtain $\mathbf{M}_{\mathrm{N}}$ and $\mathbf{M}_{\mathrm{P}}$ . After projection, we obtain a deformed template which is closer to $\mathbf{M}_{\mathrm{I}}$ in shape. Fig. 4 illustrates the process of the progressive deformation. + +# 4.2. View-collaborative 3D Landmark Detection + +In this section, we discuss more details about how to detect 3D landmarks from $\mathbf{M}_{\mathbf{I}}$ , which is the key to supporting the procedure of landmark-guided registration. A straightforward way for this detection is directly applying point-based CNN (e.g., SparseConv [17]) to estimate landmarkware heatmap on mesh vertices. However, due to the inherent difficulty to conduct CNN on a mesh, this approach tends to produce inaccurate results. We thus propose to perform detection on the rendered views of $\mathbf{M}_{\mathbf{I}}$ to leverage the effectiveness of image-based CNN techniques. Coarse locations of the 3D landmarks can be obtained from detected 2D landmarks on those views. More importantly, a stack of View-Collaborative GCN block (VC-GCN) is novelly designed to aggregate and enhance information from multiple views for accurate 3D landmarks locations. As illustrated in Fig. 5, single view graph features (local features) are first extracted for initialization. Then, these local features are enhanced in a progressive manner by continually fusing global information into each view. The final local features are aggregated into the global graph feature for 3D landmark prediction. + +Initialization Stage In this part, more details about local feature initialization are introduced. Given 2D images rendered from 3 views $\{\mathrm{front},\mathrm{left},\mathrm{right}\}$ $\{(f,l,r)\}$ for simplicity), we first utilize a 2D landmark detector [12] to estimate the 2D landmarks $\hat{\mathbf{P}}^v\in \mathbb{R}^{k^v\times 2}$ , where $k^v$ denotes the key point number under the view $v\in \{f,l,r\}$ . Next, 3d land + +marks on the mesh are located using the projection matrix of each view. We use the above landmarks which exist in all local views to build local graphs. After that, to enrich the information of each graph node, we extract features from the feature maps generated by the landmark detector for each node, according to their 2D coordinates. Eventually, the initial local view features $\mathbf{F}_{init}^{v}\in \mathbb{R}^{k^{v}\times (C + 3)}$ for VC-GCN can be produced by concatenating the 3D landmark locations $\mathbf{L}^v$ with related node features under each view $v$ , where $C$ is the image feature dimension. + +View-Collaborative GCN In order to provide global information for each view, we aggregate 3 local features into a global graph feature. Then the global feature is fused into each view to enhance the local view feature. This procedure is performed by a View-Collaborative GCN block. In each VC-GCN block, local features are first sent into several GCN layers for better representations. The layer-wise operation in GCN is defined as: + +$$ +\mathbf {F} _ {\ell + 1} ^ {v} = \sigma \left(\mathbf {D} ^ {v - \frac {1}{2}} \mathbf {A} ^ {v} \mathbf {D} ^ {v - \frac {1}{2}} \mathbf {F} _ {\ell} ^ {v} \mathbf {W} _ {\ell} ^ {v}\right) \tag {3} +$$ + +where $\mathbf{A}^v$ is the adjacency matrix with self-loops, $\mathbf{D}^v$ is its diagonal node degree matrix to normalize $\mathbf{A}^v$ , $\mathbf{F}_\ell^v$ represents the local feature in layer $\ell \in \{0,1,\dots,\ell'\}$ under the view $v$ , $\mathbf{W}_{\ell}$ is a trainable parameter matrix for linear projection, and $\sigma(\cdot)$ represents the non-linear activation operation. Then the obtained local features are combined into a global graph feature. For each node in the 3D landmark, its feature can be drawn from the local feature of the corresponding node under one view. Note that for the node that shared in different views, its feature is set as the average of multiple local features. The combined global graph feature is then strengthened through several GCN layers, with same operations as in Equation 3. Hence, the process of feature aggregation now can be formulated as following: + +$$ +\begin{array}{l} \mathbf {F} _ {\ell^ {\prime}} ^ {v} = \operatorname {G C N} ^ {v} \left(\mathbf {F} _ {0} ^ {v}\right), v = f, l, r; \\ \mathbf {F} _ {\ell^ {\prime}} ^ {g} = \operatorname {G C N} ^ {g} \left(f _ {\text {c o m b}} \left(\mathbf {F} _ {\ell^ {\prime}} ^ {f}, \mathbf {F} _ {\ell^ {\prime}} ^ {l}, \mathbf {F} _ {\ell^ {\prime}} ^ {r}\right)\right). \tag {4} \\ \end{array} +$$ + +where $f_{\mathrm{comb}}(\cdot)$ denotes the combination operation, $\mathbf{F}_{\ell}^{g}$ is the strengthened global features. Note that the input $\mathbf{F}_0^v$ is set + +![](images/5a4d57d2f52919c1bd7eca0c854048d980da9c3eca0861988e892aeeb133f19a.jpg) +Figure 5: The pipeline of View-collaborative 3D landmark Detection. The initial 3D landmarks are obtained by exploiting the predicted 2D landmarks from 3 rendering views. A novel cascaded VC-GCN blocks is used to fuse the features form each view and sends the aggregated features into a GCN head layer for 3D displacement decoding. + +as the initial local view feature $\mathbf{F}_{init}^{v}$ in the first VC-GCN block, and is set as the prior output features in subsequent blocks. + +In the second step, strengthened global features are fused into local features of each view in a non-local manner [38], so that global information can guide the model to learn more representative local features. The enhanced local features $\mathbf{F}_{\mathrm{enh}}^v$ of the view $v$ can be obtained as following, where the non-local fusion operation is denoted as $f_{\mathrm{n - loc}}$ : + +$$ +\mathbf {F} _ {\mathrm {e n h}} ^ {v} = f _ {\mathrm {n - l o c}} \left(\mathbf {F} _ {\ell^ {\prime}} ^ {g}, \mathbf {F} _ {\ell^ {\prime}} ^ {v}\right), v = f, l, r. \tag {5} +$$ + +More details about the non-local fusion operation are described in the supplementary materials. + +It usually takes numerous glimpses to adjust key points to construct a 3D face, even for an expert artist. Thus, several VC-GCN blocks are stacked to progressively enhance local features. In the connection of two blocks, the enhanced local features $\mathbf{F}_{\mathrm{enh}}^v$ from the former block are taken as the input $\mathbf{F}_0^v$ of the later block. + +Loss Function Given the enhanced local features from the last VC-GCN block, we combine and strengthen them using GCN layers to obtain the final global graph features. Next, it is multiplied by a GCN head layer to get the 3D landmark estimation $\hat{\mathbf{L}}^g\in \mathbb{R}^{N\times 3}$ . The predicted 3D landmarks are supervised by 3D and 2D landmark ground truth simultaneously, which leads to more accurate prediction. We now formulate the loss function for the view-collaborative 3D landmark detection training as following: + +$$ +\begin{array}{l} \mathcal {L} = \sum_ {i \in \Omega , v} \left(\mathcal {L} _ {\text {d e t e c t}} \left(\hat {\mathbf {P}} _ {i} ^ {v}, \mathbf {P} _ {i} ^ {v}\right) \right. \\ + \mathcal {L} _ {\mathrm {3 D}} \left(\hat {\mathbf {L}} _ {i} ^ {g}, \mathbf {L} _ {i} ^ {g}\right) \tag {6} \\ + \mathcal {L} _ {\mathrm {2 D}} \big (\mathbf {M} ^ {v} (\hat {\mathbf {L}} _ {i} ^ {g}), \mathbf {P} _ {i} ^ {v}) \big), \\ \end{array} +$$ + +where $\Omega$ is the training set, $i$ is the subscript indicating each training sample, $\mathcal{L}_{\mathrm{detect}}$ denotes the 2D landmark detection + +error in the initialization stage, $\mathcal{L}_{3\mathrm{D}}$ and $\mathcal{L}_{2\mathrm{D}}$ represents the 3D landmark prediction error in 2D and 3D space, respectively, and $\mathbf{M}^v$ is the projection matrix to obtain 2D landmarks from 3D landmarks under the view $v$ . Note that all loss terms are in smooth- $l_1$ form. + +# 5. Experiments + +Implementation details The proposed framework is trained on our 3DCaricShop. The dataset is separated into 1,600 for training and 400 for testing. The weights of $\mathcal{L}_{\text {detect }}$ , $\mathcal{L}_{2D}$ and $\mathcal{L}_{3D}$ are set to 0.1, 0.8 and 1.0 respectively. To train the network for learning the implicit reconstruction, a RMSProp optimizer is adopted with learning rate 0.001, and the network is pre-trained with the minibatch size 2 for 80 epochs. During the training of 2D landmark detection network, an Adam optimizer is used. The learning rate is set to 0.0001 with a cosine decay, and the mini-batch size is set to 24 for 30 epochs. After that, the whole framework is trained in an end-to-end manner with the same strategy as above. + +Results Gallery We present some typical results of the proposed framework in Fig. 6. As illustrated, our method is robust to caricature images with diverse textures. It can also recover diversified geometric features, such as the exaggerated nose in the second sample of the first row, and the sharp long chin in the third sample of the second row Fig. 6. + +# 5.1. Comparisons with the State-of-the-arts + +We qualitatively and quantitatively compare the results of our method with a variety of state-of-the-art 3D caricature reconstruction approaches on 3DCaricShop testing set, including linear parametric model (3DMM) [35, 2], depth map (DF2Net) [41], deformation representation (AliveCaric-DL) [42], and implicit function (PIFu) [31] based methods. + +![](images/7496dfa95ab00273a2e85b5dff9b725920a4a275b864158ae24910f0ccb269f7.jpg) +Figure 6: Results gallery for our framework on 3DCaricShop. The framework has the capability to reconstruct 3D shapes from caricature images with diverse texture and geometry shapes. + +Qualitative results In Fig. 7, we visualize some results of caricature reconstruction on images from 3DCaricShop. Among the parametric methods, the nonlinear deformation representation [42] based model outperforms the linear ones on fitting the exaggerated input images, but it is still not precise enough due to its limited expressiveness. Besides, other deep learning based approaches such as DF2Net and PIFu unavoidably yield artifacts like hollows and spikes. However, our method introduces the constraint of PCA parametric space into the deep model, thus can produce highly exaggerated local details upon the foundation of a plausible global shape. + +Quantitative Results Considering other methods for comparison only reconstruct the face area, we adopt average point-to-surface Euclidean distance (P2S) as the evaluation metric, which measures the unidirectional distance from the source set to the target set. The average point-to-surface Euclidean distance can be computed as: + +$$ +d _ {P 2 S} (P, S) = \frac {1}{\| P \|} \sum_ {p \in P} \min _ {p ^ {\prime} \in S} \| p - p ^ {\prime} \| _ {2} \tag {7} +$$ + +where $P$ is the vertex set of the reconstructed mesh and $S$ is the corresponding ground truth surface. Besides, due to the mismatch in orientation and scale between the generated meshes and ground truth, before calculation, Procrustes alignment is performed and scaling is estimated based on least square error. As shown in Table 2, our method achieves the smallest P2S on the 3DCaricShop. + +# 5.2. Ablation Studies + +In this section, we perform ablation studies on the proposed 3D landmark detection framework and landmark guided registration process. The results show the effectiveness and robustness of our pipeline. + +3D landmark detection We analyze five variants of our framework: 1) directly using the 3D landmarks selected from predicted 2D landmarks without subsequent refinement, denoted as 'w/o GCN refinement'; 2) utilizing voxel-based method [22] to estimate 3D heatmaps, denoted as + +
MethodsP2SMethodsP2S
3DMMhuman0.295PiFuhead0.153
3DMMcari0.104PiFuface0.126
DF2Net0.273Ourshead0.065
AliveCaric-DL0.067Oursface0.037
+ +Table 2: Quantitative evaluation on 3DCaricShop. Note that the meshes generated by our method and PiFu contain the entire head area which are the same with ground truth, whereas the other methods in our experiment only recover the frontal face, thus we provide two versions of results(i.e. head and face) on our method and PiFu for a more solid comparison. The results are averaged on test data. + +'V2V'; 3) employing a global graph to refine the 3D landmarks from the first setting, without using VC-GCN block, which denoted as 'Global only'; 4) Only using local index to gather local features from global view, rather than using non-local operations for local feature enhancement, denoted as 'w/o G2L'; 5) The basic setting, denoted as Basic. + +The metric we evaluate the results is mean per joint position error (MPJPE) which is defined as a Euclidean distance between predicted and ground truth 3D landmarks after root joint alignment. The root joint we define is the top of nose. This metric measures how accurately the root-relative 3D landmark estimation is performed. The quantitative results are listed in Table. 3. It confirm the effectiveness of each components in the design of our 3D landmark detector. + +On landmark guided registration We evaluate three kinds of registration process: 1) directly perform NICP without landmarks information; 2) perform landmark-guided NICP without PCA projection; 3) the process used in our method. The visualized results are shown in Fig. 9. As [1] suggested, without landmark information, NICP could not capture the large discrepancy between $\mathbf{M}_{\mathbf{t}}$ and $\mathbf{M}_{\mathbf{I}}$ . Besides, the deformation without PCA projection is likely to generate meshes with self-intersection. In contrast, our method could obtain meshes with higher quality, and capture enough shape information in $\mathbf{M}_{\mathbf{I}}$ . For example, the artifacts on ears in Fig. 9(d) are eliminated, while the shape + +![](images/23e19201b0bcb4fb7c670bc9c845a6e8e0bf23ddd7332eb5f4cf1d50ef2b2823.jpg) +(a) 3DMM-Human + +![](images/c60e3d9ef6e14e42122169d2a8567f942fc7b67ef26b0d356fbf9b063533fbea.jpg) +(b) 3DMM-Cari + +![](images/f8c14638f483490fc8bcf29dbce44748a4d63a14c227d70de4e1f21c3cd77213.jpg) +(c) DF2Net + +![](images/b86e1fab37ed1b5d83237aa2da40df5df515fb228103adcd7c2945ca6e4db4f3.jpg) +(d) AliveCaric-DL + +![](images/a9a85150de74b46e51a73b6fb9c45469740128a72d06e969b7513eeb97b3b27a.jpg) +(e)PIFu + +![](images/91dd7d53497fb76741281e53d85ae517b8169cca605116e8fb3444acdeda1ba2.jpg) +(f) Ground truth + +![](images/5f38efe228019de03ec24e475e8dcabceef372036d469ccb313bf0c16e66fe96.jpg) +(g) Our method + +![](images/4a83bd95a3990c030ddb42ee6c1e425f2fe82734ccd85ff33e3a0b34bb5ebd1a.jpg) +(a) +Figure 8: Ablation experiments on 3D landmark detection: (a) input; (b) ground truth; (c) pure projection; (d) global only; (e) w/o G2L; (f) ours. Our method could capture the face geometry more accurately. + +![](images/5b9baa7299cb0fd58e6621be14eec51ac1e4e9f2fcab34c150319b33cfe7405d.jpg) +(b) + +![](images/fac7f401f8e7efb8892906a7d3347162e90b67757aa589480f8da62da7d75576.jpg) +(c) + +![](images/45471e6cb9eff8e528d4cb3eb323b61aaa298fc1a50809d55305b47e9dddf0d8.jpg) +Figure 7: Qualitative results of our method compared with state-of-the-art methods, including (a) 3DMM-Human [35], (b) 3DMM-cari [2], (c) DF2Net [41], (d) AliveCaric-DL [42] and (e) PiFu [31], on 3DCaricShop. By incorporating deep models with parametric space constraint, our method (g) can reconstruct highly exaggerated geometry without distinct artifacts. +(d) + +![](images/f9bc1ac6d6bf996eed109a5797815c6bdf0d698f2335d38abf85682617092446.jpg) +(e) + +![](images/6cc924623cd7347ed4f6516cf2bc8f2898627906ca49c7883476c102f0c18264.jpg) +(f) + +
MethodsMPJPEMethodsMPJPE
w/o GCN Refinement V2V [22]0.451Global only0.373
0.407w/o G2L0.358
Basic0.291
+ +![](images/a1cd0274bc8b80481fcf27095105ff9784f0b5d1d7b65009e84d76f6e1be8584.jpg) +(a) +Figure 9: Ablation experiments on registration: (a) input; (b) GT; (c) NICP w/o landmark; (d) NICP w/o PCA projection; (e) ours. A better result is obtained with reasonable topology (e.g., the nose) by using PCA projection. + +![](images/3febda56e5649cba60a08fb4adaa812f81af73ae5aa19fa86fd549155ab6f9df.jpg) +(b) + +![](images/0c543a07015da571a5aaa5ff7d730c04212b7caff14168de7d7598ca3b821b58.jpg) +(c) + +![](images/e69378f5dc63f1d7fd876676e3ad5148c41769141e845213b12c402861d3bc79.jpg) +(d) + +![](images/1062abcf589d72389752735c7035fed57918a97e66efa30b275de4020f01f919.jpg) +(e) + +of nose is more consistent with both the groud truth mesh and the input caricature image. + +# 6. Conclusions + +We construct a new dataset and benchmark, called 3DCaricShop, for single-view 3D reconstruction from car- + +Table 3: Ablation study for 3D landmark detection. + +
MethodsP2S
Ours w/o Landmark0.074
Ours w/o PCA projection0.076
Ours0.065
+ +Table 4: Ablation study for landmark-guided registration. The similar data implies the improvement of our method concentrate on the detail structures. + +icature images. 3DCaricShop is the largest collection by far of 3D caricature models crafted by professional artists. It consists of 2,000 high-quality and diversified 3D caricatures that are richly labeled with paired 2D caricature image, camera parameters, and 3D facial landmarks. A novel baseline approach is also presented to validate the usefulness of the proposed dataset. It combines the merits of flexible implicit functions and the robust parametric mesh representation. Specifically, we transfer the details from implicit reconstruction to a template mesh with the help of VC-GCN that accurately predicts 3D landmarks for the implicit mesh. Extensive benchmarking on our dataset has been performed including a variety of popular approaches. We found that reconstructing 3D caricature from a single 2D caricature image is a highly challenging task with ample opportunity for improvement. We hope 3DCaricShop and our baseline approach could shred light on future research in this field. + +Acknowledgment +The work was supported in part by the Key Area R&D Program of Guangdong Province with grant No. 2018B030338001, by the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund, and by Guangdong Research Project No. 2017ZT07X152, the National Natural Science Foundation of China 61902334, Shenzhen Fundamental Research (General Project) JCYJ20190814112007258. + +# References + +[1] Brian Amberg, Sami Romdhani, and Thomas Vetter. Optimal step nonrigid icip algorithms for surface registration. In 2007 IEEE Conference on Computer Vision and Pattern Recognition, pages 1-8. IEEE, 2007. +[2] Volker Blanz and Thomas Vetter. A morphable model for the synthesis of 3d faces. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques, pages 187-194, 1999. +[3] Federica Bogo, Angjoo Kanazawa, Christoph Lassner, Peter Gehler, Javier Romero, and Michael J Black. Keep it smpl: Automatic estimation of 3d human pose and shape from a single image. In European Conference on Computer Vision, pages 561-578. Springer, 2016. +[4] James Booth, Anastasios Roussos, Stefanos Zafeiriou, Allan Ponniah, and David Dunaway. A 3d morphable model learnt from 10,000 faces. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5543-5552, 2016. +[5] Chen Cao, Yanlin Weng, Shun Zhou, Yiying Tong, and Kun Zhou. Facewarehouse: A 3d facial expression database for visual computing. IEEE Transactions on Visualization and Computer Graphics, 20(3):413-425, 2013. +[6] Kaidi Cao, Jing Liao, and Lu Yuan. Carigans: Unpaired photo-to-caricature translation. arXiv preprint arXiv:1811.00222, 2018. +[7] Angel X Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015. +[8] Christopher B Choy, Danfei Xu, JunYoung Gwak, Kevin Chen, and Silvio Savarese. 3d-r2n2: A unified approach for single and multi-view 3d object reconstruction. In European conference on computer vision, pages 628-644. Springer, 2016. +[9] Hang Dai, Nick Pears, William Smith, and Christian Duncan. Statistical modeling of craniofacial shape and texture. International Journal of Computer Vision, 128(2):547-571, 2020. +[10] Yu Deng, Jiaolong Yang, Sicheng Xu, Dong Chen, Yunde Jia, and Xin Tong. Accurate 3d face reconstruction with weakly-supervised learning: From single image to image set. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 0–0, 2019. +[11] Thibault Groueix, Matthew Fisher, Vladimir G Kim, Bryan C Russell, and Mathieu Aubry. A papier-mâché approach to learning 3d surface generation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 216-224, 2018. +[12] Xiaojie Guo, Siyuan Li, Jinke Yu, Jiawan Zhang, Jiayi Ma, Lin Ma, Wei Liu, and Haibin Ling. Pfld: A practical facial landmark detector. arXiv preprint arXiv:1902.10859, 2019. +[13] Xiaoguang Han, Chang Gao, and Yizhou Yu. Deepsketch2face: a deep learning based sketching system for 3d face and caricature modeling. ACM Transactions on graphics (TOG), 36(4):1-12, 2017. + +[14] Zeng Huang, Tianye Li, Weikai Chen, Yajie Zhao, Jun Xing, Chloe LeGendre, Linjie Luo, Chongyang Ma, and Hao Li. Deep volumetric video from very sparse multi-view performance capture. In Proceedings of the European Conference on Computer Vision (ECCV), pages 336-354, 2018. +[15] Jing Huo, Wenbin Li, Yinghuan Shi, Yang Gao, and Hujun Yin. Webcaricature: a benchmark for caricature recognition. arXiv preprint arXiv:1703.03230, 2017. +[16] Sunnie S. Y. Kim, Nicholas Kolkin, Jason Salavon, and Gregory Shakhnarovich. Deformable style transfer. In European Conference on Computer Vision (ECCV), 2020. +[17] Baoyuan Liu, Min Wang, Hassan Foroosh, Marshall Tappen, and Marianna Pensky. Sparse convolutional neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 806-814, 2015. +[18] Feng Liu, Luan Tran, and Xiaoming Liu. 3d face modeling from diverse raw scan data. In Proceedings of the IEEE International Conference on Computer Vision, pages 9408-9418, 2019. +[19] Junfa Liu, Yiqiang Chen, Chunyan Miao, Jinjing Xie, Charles X Ling, Xingyu Gao, and Wen Gao. Semi-supervised learning in reconstructed manifold space for 3d caricature generation. In Computer Graphics Forum, volume 28, pages 2104-2116. Wiley Online Library, 2009. +[20] Daniel Maturana and Sebastian Scherer. Voxnet: A 3d convolutional neural network for real-time object recognition. In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 922-928. IEEE. +[21] Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. Occupancy networks: Learning 3d reconstruction in function space. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4460-4470, 2019. +[22] Gyeongsik Moon, Ju Yong Chang, and Kyoung Mu Lee. V2v-posenet: Voxel-to-voxel prediction network for accurate 3d hand and human pose estimation from a single depth map. In Proceedings of the IEEE conference on computer vision and pattern Recognition, pages 5079-5088, 2018. +[23] Junyi Pan, Xiaoguang Han, Weikai Chen, Jiapeng Tang, and Kui Jia. Deep mesh reconstruction from single rgb images via topology modification networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 9964-9973, 2019. +[24] Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove. Deepsdf: Learning continuous signed distance functions for shape representation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 165-174, 2019. +[25] Pascal Paysan, Reinhard Knothe, Brian Amberg, Sami Romdhani, and Thomas Vetter. A 3d face model for pose and illumination invariant face recognition. In 2009 Sixth IEEE International Conference on Advanced Video and Signal Based Surveillance, pages 296-301. IEEE, 2009. +[26] Emmanuel Prados and Olivier Faugeras. Shape from shading. In Handbook of mathematical models in computer vision, pages 375-388. Springer, 2006. +[27] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification + +and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 652-660, 2017. +[28] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. In Advances in neural information processing systems, pages 5099-5108, 2017. +[29] Elad Richardson, Matan Sela, Roy Or-El, and Ron Kimmel. Learning detailed face reconstruction from a single image. In proceedings of the IEEE conference on computer vision and pattern recognition, pages 1259–1268, 2017. +[30] Gernot Riegler, Ali Osman Ulusoy, and Andreas Geiger. Octnet: Learning deep 3d representations at high resolutions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017. +[31] Shunsuke Saito, Zeng Huang, Ryota Natsume, Shigeo Morishima, Angjoo Kanazawa, and Hao Li. Pifu: Pixel-aligned implicit function for high-resolution clothed human digitization. In Proceedings of the IEEE International Conference on Computer Vision, pages 2304-2314, 2019. +[32] Matan Sela, Elad Richardson, and Ron Kimmel. Unrestricted facial geometry reconstruction using image-to-image translation. In Proceedings of the IEEE International Conference on Computer Vision, pages 1576-1585, 2017. +[33] Yichun Shi, Debayan Deb, and Anil K Jain. Warpgan: Automatic caricature generation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 10762-10771, 2019. +[34] Luan Tran and Xiaoming Liu. Nonlinear 3d face morphable model. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7346-7355, 2018. +[35] Anh Tuan Tran, Tal Hassner, Iacopo Masi, Eran Paz, Yuval Nirkin, and Gerard Medioni. Extreme 3d face reconstruction: Seeing through occlusions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3935-3944, 2018. +[36] Nanyang Wang, Yinda Zhang, Zhuwen Li, Yanwei Fu, Wei Liu, and Yu-Gang Jiang. Pixel2mesh: Generating 3d mesh models from single rgb images. In Proceedings of the European Conference on Computer Vision (ECCV), pages 52-67, 2018. +[37] Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. High-resolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 8798-8807, 2018. +[38] Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7794-7803, 2018. +[39] Qianyi Wu, Juyong Zhang, Yu-Kun Lai, Jianmin Zheng, and Jianfei Cai. Alive caricature from 2d to 3d. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7336-7345, 2018. +[40] Haotian Yang, Hao Zhu, Yanru Wang, Mingkai Huang, Qiu Shen, Ruigang Yang, and Xun Cao. Facescape: a large-scale high quality 3d face dataset and detailed riggable 3d face + +prediction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 601-610, 2020. +[41] Xiaoxing Zeng, Xiaojiang Peng, and Yu Qiao. Df2net: A dense-fine-finer network for detailed 3d face reconstruction. In Proceedings of the IEEE International Conference on Computer Vision, pages 2315-2324, 2019. +[42] Juyong Zhang, Hongrui Cai, Yudong Guo, and Zhuang Peng. Landmark detection and 3d face reconstruction for caricature using a nonlinear parametric model. arXiv preprint arXiv:2004.09190, 2020. +[43] Silvia Zuffi, Angjoo Kanazawa, and Michael J Black. Lions and tigers and bears: Capturing non-rigid, 3d, articulated shape from images. 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While the GFLOPs of a 3D CNN can be decreased by reducing the temporal feature resolution within the network, there is no setting that is optimal for all input clips. In this work, we therefore introduce a differentiable Similarity Guided Sampling (SGS) module, which can be plugged into any existing 3D CNN architecture. SGS empowers 3D CNNs by learning the similarity of temporal features and grouping similar features together. As a result, the temporal feature resolution is not anymore static but it varies for each input video clip. By integrating SGS as an additional layer within current 3D CNNs, we can convert them into much more efficient 3D CNNs with adaptive temporal feature resolutions (ATFR). Our evaluations show that the proposed module improves the state-of-the-art by reducing the computational cost (GFLOPs) by half while preserving or even improving the accuracy. We evaluate our module by adding it to multiple state-of-the-art 3D CNNs on various datasets such as Kinetics-600, Kinetics-400, mini-Kinetics, Something-Something V2, UCF101, and HMDB51. + +# 1. Introduction + +In recent years, there has been a tremendous progress for video processing in the light of new and complex deep learning architectures, which are based on variants of 3D Convolutional Neural Networks (CNNs) [24, 9, 7, 4, 6, 12, 8]. They are trained for a specific number of input frames, + +*Mohsen Fayyaz and Emad Bahrami equally contributed to this work. Emad Bahrami contributed to this project while he was a visiting researcher at the Computer Vision Group of the University of Bonn. + +typically between 16 to 64 frames. For classifying a longer video, they slide over the video and the outputs are then aggregated. These networks, however, are often very expensive to train and heavy to deploy for inference task. In order to reduce the inference time, [15, 20] proposed to process not all parts of a video with the same 3D CNN. While [15] trains a second network that decides for each chunk of input frames if it should be processed by the more expensive 3D CNN, [20] uses a fix scheme where a subset of the input chunks are processed by an expensive 3D CNN and the other chunks by a less expensive 3D CNN. The latter then uses an RNN to fuse the outputs of the different 3D CNNs. Although both approaches effectively reduce the GFLOPS during inference, they increase the training time since two instead of one network need to be trained. Furthermore, they do not reduce the computational cost of the 3D CNNs themselves. + +In this work, we propose an approach that makes 3D CNNs more efficient for training and inference. Our proposal is based on the observation that the computational cost of a 3D CNN depends on the temporal resolution it operates on at each stage of the network. While the temporal resolution can be different at different stages, the schemes that define how the temporal resolution is reduced is hard-coded and thus the same for all videos. However, it is impossible to define a scheme that is optimal for all videos. If the temporal resolution is too much reduced, the network is forced to discard important information for some videos. This results in a decrease of the action recognition accuracy performance. Vice versa, a high temporal resolution results in highly redundant feature maps and increases the computational time, which makes the 3D CNN highly inefficient for most videos. In this work, we therefore address the question of how a 3D CNN can dynamically adapt its computational resources in a way such that not more resources than necessary are used for each input chunk. + +In order to address this question, we propose to exploit the redundancy within temporal features such that 3D + +![](images/edd79c6454fe7bb0baddf3a817e758d3383d7fea5e506a7710593acfcada3837.jpg) +Figure 1: The difficulty of recognizing actions varies largely across videos. For videos with slow motion (top), the temporal features that are processed within a 3D CNN can be highly redundant. However, there are also very challenging videos where all features are required to understand the content (bottom). While previous 3D CNNs use fix down-sampling schemes that are independent of the input video, we propose a similarity guided sampler that groups and aggregates redundant information of temporal features into $B' \leq T$ feature maps. The core aspect is that this process adapts the internal temporal resolution to the input video such that $B'$ is small if the input features are redundant (top) and large (bottom) if most of the features are required. + +CNNs process and select the most valuable and informative temporal features for the action classification task. In contrast to previous works, we propose to dynamically adapt the temporal feature resolution within the network to the input frames such that on one hand important information is not discarded and on the other hand no computational resources are wasted for processing redundant information. To this end, we propose a Similarity Guided Sampling (SGS) mechanism that measures the similarity of temporal feature maps, groups similar feature maps together, and aggregates the grouped feature maps into a single output feature map. The similarity guided sampling is designed such that it is differentiable and number of output feature maps varies depending on the redundancy of the temporal input feature maps as shown in Fig. 1. By integrating the similarity guided sampling as an additional module within any 3D CNN, we convert the 3D CNN with fixed temporal feature resolutions into a much more efficient dynamic 3D CNN with adaptive temporal feature resolutions (ATFR). Note that this approach is complementary to [15, 20] and the two static 3D CNNs used in these works can be replaced by adaptive 3D CNNs. However, even with just a single 3D CNN with adaptive temporal feature resolutions, we already achieve a higher accuracy and lower GFLOPs performance compared to [15, 20]. + +We demonstrate the efficiency of 3D CNNs with adaptive temporal feature resolutions by integrating the similarity guided sampler into the current state-of-the-art 3D CNNs such as $\mathrm{R}(2 + 1)\mathrm{D}$ [25], I3D [3], and X3D [8]. It drastically decreases the GFLOPs by about half in aver + +age while the accuracy remains nearly the same or gain improvements. In summary, the similarity guided sampler is capable of significantly scaling down the computational cost of off-the-shelf 3D CNNs and therefore plays a crucial role for real-world video-based applications. + +# 2. Related Work + +The computer vision community has made huge progress in several challenging vision tasks by using CNNs. In recent years, there has been a tremendous progress for video processing in the light of new and complex deep learning architectures, which are based on variants of 3D CNNs [24, 9, 7, 4, 6, 12, 8]. Tran et al. [24] and Carreira et al. [3] proposed 3D versions of VGG and Inception architectures for large-scale action recognition benchmarks like Sports-1M [13] and Kinetics [14]. These methods could achieve superior performance even without using optical-flow or any other pre-extracted motion information. This is due to the capability of 3D kernels to extract temporal relations between sequential frames. Recently, methods like HATNet [5], STC [4], and DynamoNet [6] focus on exploiting spatial-temporal correlations in a more efficient way or on learning more accurate motion representations for videos. These works based on 3D CNNs, however, require huge computational resources since they process sequences of frames with an immense number of 3D convolution layers. There has been therefore a good effort to propose more efficient architectures based on 2D and 3D CNNs [18, 17, 25, 31, 34]. For instance, Lin et al. [18] introduced a temporal shift module (TSM) to enhance 2D + +ResNet CNNs for video classification. The model even runs on edge devices. In [25, 31] 2D and 3D convolutional layers are combined in different ways. SlowFast [9] has explored the resolution trade-offs across temporal, spatial, and channel access. It decreases the computation cost by employing a light pathway with a high temporal resolution for temporal information modeling and a heavy low temporal resolution pathway for spatial information modeling. In relation to this work, [8] investigates whether the light or heavy model is required and presents X3D as a family of efficient video networks. + +In order to reduce the inference time of existing networks, [29, 30, 15, 20] proposed to process not all parts of a video with the same CNN model. This line of research is built upon the idea of big-little architecture design. In the context of 2D CNNs, [29, 30] process salient frames by expensive models and use light models to process the other frames. In contrast, [15, 20] do not process single frames but process short chunks of frames with 3D CNNs. [15] trains a second lighter network that decides for each chunk of input frames if it should be processed by the more expensive 3D CNN. [20] uses a fix scheme where a subset of the input chunks are processed by an expensive 3D CNN and the other chunks by a less expensive 3D CNN. It then uses an RNN to fuse the outputs of the different 3D CNNs. Although such approaches effectively reduce the GFLOPS during inference, they increase the training time since two instead of one network need to be trained. Furthermore, they do not reduce the computational cost of the 3D CNNs themselves. + +There are various efforts on temporal action detection or finding action segments in untrimmed videos like [1, 23, 33, 28]. These works focus on localizing actions but not on improving the computational efficiency for action recognition. While these works are not related, they can benefit from our approach by integrating the proposed similarity guided sampling module into their CNNs for temporal action localization. + +# 3. Adaptive Temporal Feature Resolutions + +Current state-of-the-art 3D CNNs operate at a static temporal resolution at all levels of the network. Due to the redundancy of neighbouring frames, traditional 3D CNN methods often down-sample the temporal resolution inside the network. This helps the model to operate at a lower temporal resolution and hence reduces the computation cost. The down-sampling, however, is static which has disadvantages in two ways. First, a fixed down-sampling rate can discard important information, in particular for videos with very fast motion as it is for instance the case for ice hockey games. Second, a fixed down-sampling rate might still include many redundant temporal features that do not contribute to the classification accuracy as it is for instance the + +![](images/8587f75688c1cc91fe8ea7b98a5fd76b91c58fd663029acc27a5678d11d736c0.jpg) +Figure 2: To learn the similarity of the feature maps, we map each temporal feature map $\mathcal{I}_t$ using $f_s(\mathcal{I})$ into an $L$ -dimensional similarity space. After the mapping, $\mathcal{Z} \in \mathbb{R}^{T \times L}$ contains all of the feature maps represented as vectors in the similarity space. Afterwards, we group similar vectors by creating B similarity bins. Using the similarity bins, sampler aggregates the similar feature maps of each bin into the output feature map $\mathcal{O}_b$ . + +case for a video showing a stretching exercise. We therefore propose a module that dynamically adapts the temporal feature resolution within the network to the input video such that on one hand important information is not discarded and on the other hand no computational resources are wasted for processing redundant information. + +Fig. 1 illustrates a 3D CNN with adaptive temporal feature resolutions (ATFR). The core aspect of ATFR is to fuse redundant information from a temporal sequence of features and extract only the most relevant information in order to reduce the computational cost for processing a video. An important aspect is that this approach is not static, i.e., the amount of information that is extracted varies for each video as illustrated in Fig. 1. In order to achieve this, we propose a novel Similarity Guided Sampling (SGS) mechanism that will be described in Sec. 4. + +In principle, any 3D CNN can be converted into a CNN with adaptive temporal feature resolutions by using our SGS module. Since the module is designed to control the temporal resolution within the network for each video, it should be added to the early stages of a network in order to get the best reduction of computational cost. For $\mathrm{R}(2 + 1)\mathrm{D}$ [25], for example, we recommend to add SGS after the second ResNet block. This means that the temporal resolution is constant for all videos before SGS, but it dynamically changes after SGS. We discuss different 3D CNNs with SGS in Sec. 5.1. + +# 4. Similarity Guided Sampling + +The SGS is a differentiable module to sample spatially similar feature maps over the temporal dimension and aggregate them into one feature map. Since the number of output feature maps is usually lower than the input feature maps, i.e., $B' < T$ , redundant information is removed as il + +lustrated in Figure 2. The important aspect is that $B'$ is not constant, but it varies for each video. In this way, we do not remove any information if there is no redundancy among the input feature maps. + +This means that we need to a) learn the similarity of feature maps, b) group similar feature maps, and c) aggregate the grouped feature maps. Furthermore, all these operations need to be differentiable. We denote an input feature map for frame $t$ by $\mathcal{I}_t \in \mathbb{R}^{C \times H \times W}$ , where $C$ , $H$ , and $W$ denote the number of channels, height, and width, respectively. To learn the similarity of the feature maps, we map each feature map $\mathcal{I}_t$ into an $L$ -dimensional similarity space. This mapping $f_s(\mathcal{I}_t)$ is described in Sec. 4.1. After the mapping, $\mathcal{Z} \in \mathbb{R}^{T \times L}$ contains all feature maps in the similarity space, which are then grouped and aggregated into $B'$ feature maps. The grouping of $\mathcal{Z}_t$ is described in Sec. 4.2 and the aggregation of the grouped features in Sec. 4.3. + +# 4.1. Similarity Space + +The similarity space is a $L$ dimensional vector space where each temporal input feature map is represented by a vector $\mathcal{Z}_t$ . The mapping is performed by the similarity network $f_{s}(\mathcal{I})$ that consists of a global average pooling layer and two convolutional layers. The pooling is applied over the spatial dimension of the feature map while keeping the temporal dimension. Afterward two $1D$ convolutional layers are applied with kernel sizes of 1 and output channel sizes $C$ and $L$ , respectively. + +# 4.2. Similarity Bins + +To group similar feature maps $\mathcal{I}_t$ , we use the magnitude of each vector $\mathcal{Z}_t$ , i.e., + +$$ +\Delta_ {t} = \left| \left| \mathcal {Z} _ {t} \right| \right| \tag {1} +$$ + +and we consider two feature maps $\mathcal{I}_t$ and $\mathcal{I}_{t'}$ similar if the value of $\Delta_t$ and $\Delta_{t'}$ lie inside a similarity bin. To make the grouping very efficient and differentiable, we propose a binning approach with $B$ similarity bins. We set $B = T$ such that no information is discarded if there is no redundancy between the feature maps of all frames. For most videos, a subset of bins remain empty and will be discarded such that the remaining bins, $B'$ , will be less than $B$ as it is described in Sec. 4.3. + +We first estimate the half of the width of each similarity bin $\gamma$ , by computing the maximum magnitude $\Delta_{max}$ and dividing it by the number of the desired bins $B$ : + +$$ +\Delta_ {m a x} = \max \left(\Delta_ {1}, \dots , \Delta_ {T}\right), \quad \gamma = \frac {\Delta_ {m a x}}{2 B}. \tag {2} +$$ + +Having the width of the similarity bins, the center of each bin $\beta_{b}$ is estimated as follows: + +$$ +\beta_ {b} = (2 b - 1) \gamma \quad \forall b \in (1, \dots , B). \tag {3} +$$ + +# 4.3. Differentiable Bins Sampling + +The grouping and aggregation of all feature maps $\mathcal{I}_t$ based on the bins $B$ will be done jointly by sampling temporal feature maps which belong to the same similarity bin and add them together. We denote the aggregated feature maps for each bin $b$ by $\mathcal{O}_b \in \mathbb{R}^{C \times H \times W}$ . To make the process differentiable, we use generic differentiable sampling kernels $\Psi(.,\beta_b)$ that are defined such that a sampler only samples from the input temporal feature map $\mathcal{I}_t$ if $\Delta_t$ lies in the similarity bin $b$ . This can be written as: + +$$ +\mathcal {O} _ {b} = \sum_ {t = 1} ^ {T} \mathcal {I} _ {t} \Psi \left(\Delta_ {t}, \beta_ {b}\right). \tag {4} +$$ + +Theoretically, any differentiable sampling kernel that has defined gradients or sub-gradients with respect to $\Delta_t$ can be used. In our experiments, we evaluate two sampling kernels. The first kernel is based on the Kronecker-Delta function $\delta$ : + +$$ +\mathcal {O} _ {b} = \frac {1}{\sum_ {t = 1} ^ {T} \delta \left(\left\lfloor \frac {\left| \Delta_ {t} - \beta_ {b} \right|}{\gamma} \right\rfloor\right)} \sum_ {t = 1} ^ {T} \mathcal {I} _ {t} \delta \left(\left\lfloor \frac {\left| \Delta_ {t} - \beta_ {b} \right|}{\gamma} \right\rfloor\right). \tag {5} +$$ + +The kernel averages the feature maps that end in the same bin. As second kernel, we use a linear sampling kernel: + +$$ +\mathcal {O} _ {b} = \sum_ {t = 1} ^ {T} \mathcal {I} _ {t} \max \left(0, 1 - \frac {\left| \Delta_ {t} - \beta_ {b} \right|}{\gamma}\right). \tag {6} +$$ + +The kernel gives a higher weight to feature maps that are closer to $\beta_{b}$ and less weights to feature maps that are at the boundary of a bin. While we evaluate both kernels, we use the linear kernel by default. + +After the sampling, some bins remain empty, i.e., $\mathcal{O}_b = 0$ . We drop the empty bins and denote by $B^{\prime}$ the bins that remain. Note that $B^{\prime}$ varies for each video as illustrated in Fig. 1. In our experiments we show that the similarity guided sampling can reduce the GFLOPS of a 3D CNN by over $47\%$ in average, making 3D CNNs suitable for applications where they are computationally expensive. + +# 4.4. Backpropagation + +Using differentiable kernels for sampling, gradients can be backpropagated through both $\mathcal{O}$ and $\Delta$ , where $\Delta$ is the magnitude of the similarity vectors $\mathcal{Z}$ which are the outputs of $f_{s}(.)$ . Therefore, we can backpropagate through $f_{s}(.)$ . For the linear kernel (6), which we use if not otherwise specified, the gradient with respect to $\mathcal{I}_t$ is given by + +$$ +\frac {\partial \mathcal {O} _ {b}}{\partial \mathcal {I} _ {t}} = \max \left(0, 1 - \frac {\left| \Delta_ {t} - \beta_ {b} \right|}{\gamma}\right) \tag {7} +$$ + +and the gradient with respect to $\Delta_t$ is given by + +$$ +\frac {\partial \mathcal {O} _ {b}}{\partial \Delta_ {t}} = \mathcal {I} _ {t} \left\{ \begin{array}{l l} 0 & | \beta_ {b} - \Delta_ {t} | \geq \gamma \\ \frac {1}{\gamma} & \beta_ {b} - \gamma < \Delta_ {t} \leq \beta_ {b} \\ - \frac {1}{\gamma} & \beta_ {b} < \Delta_ {t} < \beta_ {b} + \gamma \end{array} . \right. \tag {8} +$$ + +Note that for computing the sub-gradients (8) only the kernel support region for each output bin needs to be considered. The sampling mechanism can therefore be efficiently implemented on GPUs. + +# 5. Experiments + +We evaluate our proposed method on the action recognition benchmarks Mini-Kinetics [32], Kinetics-400 [14], Kinetics-600 [2], Something-Something-V2 [11], UCF-101 [22], and HMDB-51 [16]. For these datasets, we use the standard training/testing splits and protocols provided by the datasets. For more details and the UCF-101 and HMDB-51 results please refer to the supplementary material. + +# 5.1. Implementation Details + +3D CNNs with ATFR. The similarity guided sampling (SGS) is a differentiable module that can be easily implemented in current deep learning frameworks. We have implemented our SGS module as a new layer in PyTorch which can be easily added to any 3D CNN architecture. To better evaluate the SGS, we have added it to various backbones, such as R(2+1)D [25], I3D [3], X3D [8], and a modified 3DResNet. We place our SGS layer on the second stage of the backbone models. Please refer to the supplementary material for more details. For all of the X3D based models, we follow the training, testing, and measurement setting in [8] unless mentioned otherwise. Additional details and code are available online.1 + +Training. Our models on Mini-Kinetics, Kinetics-400, and Kinetics-600 are trained from scratch using randomly initialized weights without any pre-training. However, we fine-tune on Something-Something-V2, UCF-101, and HMDB-51 with models pre-trained on Kinetics-400. We trained our models using SGD with momentum 0.9 and a weight decay of 0.0001 following the setting in [9]. For Kinetics and Mini-Kinetics, we use a half-period cosine schedule [19] with a linear warm-up strategy [10] to adapt the learning rate over 196 epochs of training. During training, we randomly sample 32 frames from a video with input stride 2. For spatial transformations, we first scale the shorter side of each frame with a random integer from the interval between 256 and 320 [26, 9, 21] then we apply a random cropping with size $224 \times 224$ to each frame. Furthermore, each frame is horizontally flipped with probability of 0.5. + +![](images/1c9753d0b4fb9f56a94c4b4c64ca739520a66be14d34c57e7ad64b137ad38c52.jpg) +Figure 3: Histogram of active bins for 3DResNet-50 + ATFR on the Mini-Kinetics validation set. The y-axis corresponds to the number of clips and the x-axis to the number of active bins $B'$ . + +Testing. We follow [26, 9] and uniformly sample 10 clips from each video for inference. The shorter side of each clip is resized to 256 and we extract 3 random crops of size $256 \times 256$ from each clip. For the final prediction, we average the softmax scores of all clips. + +Measurements. We report top-1 and top-5 accuracy. To measure the computational efficiency of our models, we report the complexity of the models in GFLOPS based on a single input video sequence of 32 frames and spatial size $224 \times 224$ for validation and $256 \times 256$ for testing. As shown in Fig. 3, 3D CNNs with ATFR adapt the temporal feature resolutions and the GFLOPs vary for different clips. For ATFR models, we therefore report the average GFLOPs. + +# 5.2. Ablation Experiments + +We first analyze different setups for our SGS module. Then, we analyze the efficiency and effect of using our SGS module in different 3D CNN models. If not otherwise specified, we use 3DResNet-18 as 3D CNNs backbones and report the results on the Mini-Kinetics validation set. + +# 5.2.1 Different Similarity Measurements + +As mentioned in Sec. 4.2, we use the magnitude of the embedding vectors as the similarity measurement to create the similarity bins. The embedding vectors are represented in an $L$ dimensional space. Instead of magnitudes, we can use other measures such as directions of the vectors. To better study this, we convert the Cartesian coordinates of the vectors to spherical coordinates. In an $L$ dimensional space, a vector is represented by 1 radial coordinate and $L - 1$ angular coordinates. To use the spherical coordinates of the vectors for creating the similarity bins, we use multidimensional bins and sampling kernels. For more details, please refer to the supplementary material. + +We report the results in Table 1. As can be seen, using the magnitudes of the vectors results in a better accuracy compared to angular coordinates or spherical coordinates. + +
SimilarityMagnitudeAngularSpherical
top169.668.568.7
top588.887.888.1
+ +Table 1: Impact of the similarity measure for 3DResNet-18 + ATFR on Mini-Kinetics with linear sampling kernel. We show top-1 and top-5 classification accuracy $(\%)$ . + +
KernelLinearKronecker
top169.668.9
top588.888.6
+ +We believe that due to the similarity of the neighbouring video frames using only magnitudes of the vectors for the similarity measurement is enough and angular or spherical coordinates add too much of complexity to the model. In all of the experiments, the number of bins $B$ is equal to 32. For the angular coordinates, we divide the angles into 4 and 8 bins $(4 \times 8)$ . For the spherical coordinates, we divide the radial coordinate into 2 and the angular coordinates into 4 and 4 bins $(2 \times 4 \times 4)$ . + +# 5.2.2 Different Sampling Kernels + +As mentioned in Sec. 4.3, we can use different differentiable sampling kernels (4). We evaluate two different sampling kernels, namely the Kronecker-Delta sampling kernel (5) and the linear sampling kernel (6). As can be seen in Table 2, the linear kernel performs better than the Kronecker-Delta kernel. The slight superiority of the linear kernel is due to the higher weighting of the temporal feature maps that are closer to the center of the bins. We use the linear kernel for the rest of the paper. + +# 5.2.3 Embedding Dimension + +As mentioned in Sec. 4.1, we map the temporal feature maps into an $L$ -dimensional similarity space. In Table 3, we quantify the effect of $L$ . The accuracy increases as $L$ increases until $L = 8$ . For $L = 16$ the dimensionality is too large and the similarity space tends to overfit. The model with $L = 1$ is a special case since it can be considered as a direct prediction of $\Delta_t$ (1) without mapping the temporal features into a similarity space $\mathcal{Z}_t$ . The results show that using a one-dimensional embedding space results in a lower accuracy, which demonstrates the benefit of the similarity space. + +# 5.2.4 Different Input Frame-rates + +It is an interesting question to ask how a 3D CNN with ATFR performs when the number of input frames or the stride changes for inference. To answer this question, we + +Table 2: Impact of the sampling kernel. + +
L14816
top167.368.469.664.7
top587.788.188.886.1
+ +Table 3: Impact of the dimensionality $L$ of the similarity space. + +
modelinput framesGFLOPstop1top5
stride
1212
SlowFast-8x8-ResNet183230.967.569.787.189.1
6461.8 (2.0)72.174.689.991.9
R(2+1)D3246.567.469.386.287.5
6493.1 (2.0)70.873.788.891.5
R(2+1)D+ATFR3232.367.469.386.487.6
6454.9 (1.7)71.473.888.690.7
3DResNet-18+ATFR3214.067.369.687.289.0
6421.1 (1.5)72.174.889.891.4
+ +Table 4: Impact of the stride and number of input frames during inference. All models are trained with 32 frames and stride 2. + +train two 3D CNNs with ATFR and two without ATFR using 32 input frames and a sampling stride of 2, which corresponds to a temporal receptive field of 64 frames. For inference, we then change the number of frames to 64 and/or the stride to 1. + +As it can be seen in Table 4, increasing the input frames from 32 to 64 improves the accuracy of all models. This improvement in accuracy is due to the increase in the temporal receptive field over the input frames while keeping the temporal input resolution. However, the computation cost of the models without ATFR increases as expected by factor 2. If ATFR is used, the increase is only by 1.7 and 1.5 for $\mathrm{R}(2 + 1)\mathrm{D} + \mathrm{ATFR}$ and 3DResNet-18+ATFR. By comparing $\mathrm{R}(2 + 1)\mathrm{D}$ with $\mathrm{R}(2 + 1)\mathrm{D} + \mathrm{ATFR}$ , we see how ATFR drastically reduces the GFLOPS from 46.5 to 32.3 for 32 frames and from 93.1 to 54.9 for 64 frames. This shows that more frames also increase the redundancy and ATFR efficiently discards this redundancy. Furthermore, it demonstrates that ATFR is robust to changes of the frame-rate and number of input frames. + +It is also interesting to compare the results for 32 frames with stride 2 to the results for 64 frames with stride 1. In both cases, the temporal receptive field is 64. We can see the efficiency of our method in adapting the temporal resolution compared to the traditional static frame-rate sampling methods, i.e., 3DResNet-18+ATFR operates on average with 21.1 GFLOPs for 64 input frames compared to SlowFast with GFLOPs of 30.9 (32) and 61.8 (64), and $\mathrm{R}(2 + 1)\mathrm{D}$ with GFLOPs of 46.5 (32) and 93.1 (64). + +# 5.2.5 Adaptive Temporal Feature Resolutions + +As shown in Fig. 3, the temporal feature resolutions vary for different clips. In order to analyze how the temporal feature resolution relates to the content of a video, we report + +
Lowest Temporal ResolutionHighest Temporal Resolution
presenting weather forecast stretching leg playing didgeridoo playing clarinet golf puttingpassing American football (in game) swimming breast stroke playing ice hockey pushing cart gymnastics tumbling
+ +Table 5: The 5 action classes with lowest and highest required adaptive temporal resolution for 3DResNet-50 + ATFR on Mini-Kinetics. + +
StageNo SGSFirst ConvRes2Res3
top177.977.878.078.0
GFLOPs1.90.91.11.3
+ +in Table 5 the 5 action classes with lowest adaptive temporal feature resolution (<12) and highest adaptive temporal feature resolution (>20). As in Fig. 3, the results are for the 3DResNet-50+ATFR on the Mini-Kinetics validation set. As it can be seen, the actions with less movements like 'presenting weather forecast' result in a low temporal resolution while actions with fast (camera) motions like 'passing American football (in game)' result in a high temporal resolution. + +# 5.2.6 SGS Placement + +To evaluate the effect of the location of our SGS module within a 3D CNN, we add it to different stages of X3D-S [8] and train it on Mini-Kinetics. As it can be seen in Table 6, adding SGS to the first stage of X3D-S drastically reduces the GFLOPs by $52.6\%$ $(2.1\times)$ while getting slightly lower accuracy. On the other hand, adding SGS after the $2^{nd}$ stage results in a $42.1\%$ reduction of GFLOPs and slightly higher accuracy. The same accuracy and growth in GFLOPs occurs when SGS is added after the $3^{rd}$ stage. + +# 5.3. Mini-Kinetics + +Mini-Kinetics is a smaller dataset compared to the full Kinetics-400 dataset [14] and consists of 200 categories. Since some videos on YouTube are not accessible, the training and validation set contain 144,132 and 9182 video clips, respectively. Table 7 shows the results on Mini-Kinetics. We add the SGS module to four 3d CNNs R(2+1)D [25], I3D [3], X3D [8], and 3DResNet. In all cases, ATFR drastically reduces the GFLOPS while the accuracy remains nearly the same. For X3D, the accuracy even increases marginally. + +# 5.4. Kinetics-400 + +We also evaluate ATFR with state-of-the-art 3D CNNs on Kinetics-400 [14], which contains $\sim 240\mathrm{k}$ training and + +Table 6: Evaluating the result of adding our SGS layer to different stages of a X3D-S network on Mini-Kinetics. + +
modelbackboneGFLOPstop1top5
Fast-S3D [32]-43.578.0-
SlowFast 8x8ResNet1840.477.593.3
SlowFast 8x8ResNet5065.779.394.2
R(2+1)DResNet50101.878.793.4
R(2+1)D+ATFRResNet5067.378.292.9
I3DResNet50148.479.394.4
I3D+ATFRResNet50105.278.893.6
X3D-S-1.977.993.4
X3D-S+ATFR-1.178.093.5
3DResNetResNet5040.879.294.6
3DResNet+ATFRResNet5023.479.394.6
+ +Table 7: Comparison with state-of-the-art methods on Mini-Kinetics. The accuracy for Fast-S3D [32] is reported with 64 frames. + +$\sim 20\mathrm{k}$ validation videos of 400 human action categories. Table 8 shows the comparison with the state-of-the-art. We add the SGS module to the state-of-the-art 3D CNNs SlowFast [9] and three versions of X3D [8]. + +As it can be seen, our SGS module drastically decreases the GFLOPs of all 3D CNNs. In contrast to Mini-Kinetics, it even improves the accuracy for all 3D CNNs. We will see that this is the case for all large datasets. For X3D-XL [8], we observe a $\sim 45\%$ reduction in GFLOPs and $0.2\%$ improvement in accuracy. We can see that X3D-XL+ATFR requires similar GFLOPs compared to X3DL [8] while providing a higher accuracy by $1.8\%$ . We can also see that X3D-XL+ATFR requires drastically less GFLOPs compared to X3D-L [8] while getting a higher accuracy by $1.1\%$ . In comparison to the computational heavy SlowFast $16\times 8,\mathrm{R}101+\mathrm{NL}$ [9], X3D-XL+ATFR gets higher top-5 and comparable top-1 accuracy while having $8.9\times$ less GFLOPs. + +Comparing the 3D CNNs with ATFR to SCSampler [15] and FASTER [20], which require to train two networks, our approach with a single adaptive 3D CNN achieves a higher accuracy and lower GFLOPs. Note that our approach is complementary to [15, 20] and the two static 3D CNNs used in these works can be replaced by adaptive 3D CNNs. Nevertheless, our approach outperforms these works already with a single 3D CNN. Fig. 4 shows the accuracy/GFLOPs trade-off for a few 3D CNNs with and without ATFR. + +# 5.5. Kinetics-600 + +We also evaluate our approach on the Kinetics-600 dataset [2]. As shown in Table 9, ATFR shows a similar performance as on Kinetics-400. Our SGS module drastically decreases the GFLOPs of all 3D CNNs while improving their accuracy. For X3D-XL[8], we observe a $\sim 47.1\%$ reduction of GFLOPs and a slight improvement in accuracy. The best model X3D-XL+ATFR achieves state-of-the-art accuracy. Note that the average GFLOPs of X3D + +![](images/80dcbc4248399acd6cdbfb0963a4c3a5c632d8eba2915c2da9c7bc072edaa7ec.jpg) +Figure 4: Accuracy vs. GFLOPs for the Kinetics-400 validation set. + +
modelGFLOPstop1top5Param
I3D*[3]108× N/A71.190.312.0M
I3D+SCSampler*[15]108×10+N/A75.1N/AN/A
Two-Stream I3D*[3]216×N/A75.792.025.0M
Two-Stream S3D-G*[32]143×N/A77.2-23.1M
TSM R50*[18]65×1074.4N/A24.3M
HATNET[5]N/A77.2N/AN/A
STC[4]N/A68.788.5N/A
Two-Stream I3D[3]216×N/A75.792.025.0M
R(2+1)D[25]152×11572.090.063.6M
Two-Stream R(2+1)D[25]304×11573.990.9127.2M
FASTER32[20]67.7×875.3N/AN/A
SlowFast8×8,R101+NL[9]116×3078.793.559.9M
SlowFast16×8,R101+NL[9]234×3079.893.959.9M
X3D-Lα[8]18.3×1076.892.56.1M
X3D-Lβ[8]24.8×3077.592.96.1M
SlowFast4×16,R50[9]36.1×3075.692.134.40M
SlowFast4×16,R50+ATFR20.8×30 (↓42%)75.892.434.40M
X3D-Sα[8]1.9×1072.990.53.79M
X3D-S+ATFRα1.0×10 (↓47%)73.591.23.79M
X3D-XLα[8]35.8×1078.493.611.09M
X3D-XL+ATFRα20×10 (↓44%)78.693.911.09M
X3D-XLβ[8]48.4×3079.193.911.09M
X3D-XL+ATFRβ26.3×30 (↓45%)79.394.111.09M
+ +Table 8: Comparison to the state-of-the-art on Kinetics-400. X3D XL+AFTR achieves the STA top5 while requiring $8.8 \times$ less GFLOPs compared to STA SlowFast $16 \times 8$ , R101 + NL. Following [8], we apply two testing strategies: $\alpha$ samples uniformly 10 clips; $\beta$ takes additionally 3 spatial crops for each sampled clip. For both setups, spatial scaling and cropping settings are as in [8]. * denotes models pretrained on ImageNet. + +XL+ATFR are even lower on Kinetics-600 compared to Kinetics-400. This shows that the additional videos of Kinetics-600 are less challenging in terms of motion, which is also reflected by the higher classification accuracy. Compared to SlowFast $16 \times 8$ , R101+NL [9], it requires about $9 \times$ less GFLOPs. + +# 5.6. Something-Something-V2 + +We finally provide results for the Something-Something V2 dataset [11]. It contains 169K training and 25K validation. + +
modelpretrainGFLOPstop1top5
Oct-I3D+NL[3]ImageNet25.6×3076.0N/A
HATNET[5]HVUN/A81.6N/A
HATNET[5]-N/A80.2N/A
I3D[3]-108× N/A71.990.1
SlowFast16×8,R101+NL[9]-234×3081.895.1
SlowFast4×16,R50[9]-36.1×3078.894.0
X3D-M[8]-6.2×3078.894.5
X3D-M+ATFR-3.3×30 (↓ 46%)79.094.9
X3D-XL[8]-48.4×3081.995.5
X3D-XL+ATFR-25.6×30 (↓ 47%)82.195.6
+ +Table 9: Comparison to the state-of-the-art on Kinetics-600. + +
modelpretrainGFLOPstop1top5
SlowFast-R50 [27]Kinetics400132.861.787.8
SlowFast-R50+ATFRKinetics40087.8 (↓ 33%)61.887.9
+ +Table 10: Results for the Something-Something-V2 dataset. + +tion videos of 174 action classes that require more temporal modeling compared to Kinetics. Following [27], we use a R50-SlowFast model pre-trained on Kinetics-400 with 64 frames for the fast pathway, speed ratio of $\alpha = 4$ , and channel ratio $\beta = 1/8$ . Similar to Kinetics, the SGS module reduces the GFLOPs by $33.9\%$ while keeping the accuracy almost the same. For more implementation details please refer to the supplementary material. + +# 6. Conclusion + +Designing computationally efficient deep 3D convolutional neural networks for understanding videos is a challenging task. In this work, we proposed a novel trainable module called Similarity Guided Sampling (SGS) to increase the efficiency of 3D CNNs for action recognition. The new SGS module selects the most informative and distinctive temporal features within a network such that as much temporal features as needed but not more than necessary are used for each input clip. By integrating SGS as an additional layer within current 3D CNNs, which use static temporal feature resolutions, we can convert them into much more efficient 3D CNNs with adaptive temporal feature resolutions (ATFR). We evaluated our approach on six action recognition datasets and integrated SGS into five different state-of-the-art 3D CNNs. The results demonstrate that SGS drastically decreases the computation cost (GFLOPS) between $33\%$ and $53\%$ without compromising accuracy. For large datasets, the accuracy even increases and the 3D CNNs with ATFR are not only very efficient, but they also achieve state-of-the-art results. + +Acknowledgement The work has been financially supported by the ERC Starting Grant ARCA (677650). + +# References + +[1] Humam Alwassel, Fabian Caba Heilbron, and Bernard Ghanem. Action search: Spotting actions in videos and its application to temporal action localization. In Proceedings of the European Conference on Computer Vision (ECCV), 2018. 3 +[2] Joao Carreira, Eric Noland, Andras Banki-Horvath, Chloe Hillier, and Andrew Zisserman. A short note about kinetics-600. arXiv, 2018. 5, 7 +[3] Joao Carreira and Andrew Zisserman. Quo vadis, action recognition? a new model and the kinetics dataset. In CVPR, 2017. 2, 5, 7, 8 +[4] Ali Diba, Mohsen Fayyaz, Vivek Sharma, M Mahdi Arzani, Rahman Yousefzadeh, Juergen Gall, and Luc Van Gool. Spatio-temporal channel correlation networks for action classification. In ECCV, 2018. 1, 2, 8 +[5] Ali Diba, Mohsen Fayyaz, Vivek Sharma, Manohar Paluri, Jürgen Gall, Rainer Stiefelhagen, and Luc Van Gool. Large scale holistic video understanding. In ECCV, 2020. 2, 8 +[6] Ali Diba, Vivek Sharma, Luc Van Gool, and Rainer Stiefelhagen. Dynamonet: Dynamic action and motion network. In Proceedings of the IEEE International Conference on Computer Vision, pages 6192-6201, 2019. 1, 2 +[7] Ali Diba, Vivek Sharma, and Luc Van Gool. Deep temporal linear encoding networks. In CVPR, 2017. 1, 2 +[8] Christoph Feichtenhofer. X3d: Expanding architectures for efficient video recognition. In CVPR, 2020. 1, 2, 3, 5, 7, 8 +[9] Christoph Feichtenhofer, Haoqi Fan, Jitendra Malik, and Kaiming He. Slowfast networks for video recognition. ICCV, 2019. 1, 2, 3, 5, 7, 8 +[10] Priya Goyal, Piotr Dollar, Ross B. Girshick, Pieter Noordhuis, Lukasz Wesolowski, Aapo Kyrola, Andrew Tulloch, Yangqing Jia, and Kaiming He. Accurate, large minibatch sgd: Training imagenet in 1 hour. ArXiv, 2017. 5 +[11] Raghav Goyal, Samira Ebrahimi Kahou, Vincent Michalski, Joanna Materzynska, Susanne Westphal, Heuna Kim, Valentin Haenel, Ingo Fruend, Peter Yianilos, Moritz Mueller-Freitag, Florian Hoppe, Christian Thurau, Ingo Bax, and Roland Memisevic. The "something something" video database for learning and evaluating visual common sense. In ICCV, 2017. 5, 8 +[12] Kensho Hara, Hirokatsu Kataoka, and Yutaka Satoh. Can spatiotemporal 3d cnns retrace the history of 2d cnns and imagenet. In CVPR, 2018. 1, 2 +[13] Andrej Karpathy, George Toderici, Sanketh Shetty, Thomas Leung, Rahul Sukthankar, and Li Fei-Fei. Large-scale video classification with convolutional neural networks. In CVPR, 2014. 2 +[14] Will Kay, Joao Carreira, Karen Simonyan, Brian Zhang, Chloe Hillier, Sudheendra Vijayanarasimhan, Fabio Viola, Tim Green, Trevor Back, Paul Natsev, et al. The kinetics human action video dataset. arXiv preprint arXiv:1705.06950, 2017. 2, 5, 7 +[15] Bruno Korbar, Du Tran, and Lorenzo Torresani. Scsampler: Sampling salient clips from video for efficient action recognition. In ICCV, 2019. 1, 2, 3, 7, 8 + +[16] Hildegard Kuehne, Hueihan Jhuang, Estibaliz Garrote, Tomaso Poggio, and Thomas Serre. Hmdb: a large video database for human motion recognition. In ICCV, 2011. 5 +[17] Myunggi Lee, Seungeui Lee, Sungjoon Son, Gyutae Park, and Nojun Kwak. Motion feature network: Fixed motion filter for action recognition. In Proceedings of the European Conference on Computer Vision (ECCV), pages 387-403, 2018. 2 +[18] Ji Lin, Chuang Gan, and Song Han. Tsm: Temporal shift module for efficient video understanding. In Proceedings of the IEEE International Conference on Computer Vision, pages 7083-7093, 2019. 2, 8 +[19] Ilya Loshchilov and Frank Hutter. Sgdr: Stochastic gradient descent with warm restarts. In *ICLR*, 2017. 5 +[20] Anshul Shah, Shlok Mishra, Ankan Bansal, Jun-Cheng Chen, Rama Chellappa, and Abhinav Shrivastava. Faster recurrent networks for efficient video classification. In AAAI, 2020. 1, 2, 3, 7, 8 +[21] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. In ICLR, 2015. 5 +[22] Khurram Soomro, Amir Roshan Zamir, and Mubarak Shah. Ucf101: A dataset of 101 human actions classes from videos in the wild. arXiv preprint arXiv:1212.0402, 2012. 5 +[23] Yu-Chuan Su and Kristen Grauman. Leaving some stones unturned: dynamic feature prioritization for activity detection in streaming video. In European Conference on Computer Vision, 2016. 3 +[24] Du Tran, Lubomir Bourdev, Rob Fergus, Lorenzo Torresani, and Manohar Paluri. Learning spatiotemporal features with 3d convolutional networks. In ICCV, 2015. 1, 2 +[25] Du Tran, Heng Wang, Lorenzo Torresani, Jamie Ray, Yann LeCun, and Manohar Paluri. A closer look at spatiotemporal convolutions for action recognition. In CVPR, 2018. 2, 3, 5, 7, 8 +[26] Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. In CVPR, 2018. 5 +[27] Chao-Yuan Wu, Ross Girshick, Kaiming He, Christoph Feichtenhofer, and Philipp Krahenbuhl. A multigrid method for efficiently training video models. In CVPR, 2020. 8 +[28] Wenhao Wu, Dongliang He, Xiao Tan, Shifeng Chen, and Shilei Wen. Multi-agent reinforcement learning based frame sampling for effective untrimmed video recognition. In Proceedings of the IEEE International Conference on Computer Vision, 2019. 3 +[29] Zuxuan Wu, Caiming Xiong, Yu-Gang Jiang, and Larry S Davis. Liteeval: A coarse-to-fine framework for resource efficient video recognition. In NeurIPS, 2019. 3 +[30] Zuxuan Wu, Caiming Xiong, Chih-Yao Ma, Richard Socher, and Larry S Davis. Adaframe: Adaptive frame selection for fast video recognition. In CVPR, 2019. 3 +[31] Saining Xie, Chen Sun, Jonathan Huang, Zhuowen Tu, and Kevin Murphy. Rethinking spatiotemporal feature learning for video understanding. In ECCV, 2018. 2, 3 +[32] Saining Xie, Chen Sun, Jonathan Huang, Zhuowen Tu, and Kevin Murphy. Rethinking spatiotemporal feature learning: Speed-accuracy trade-offs in video classification. In ECCV, 2018. 5, 7, 8 + +[33] Serena Yeung, Olga Russakovsky, Greg Mori, and Li Fei-Fei. End-to-end learning of action detection from frame glimpses in videos. In Proceedings of the IEEE conference on computer vision and pattern recognition, 2016. 3 +[34] Mohammadreza Zolfaghari, Kamaljeet Singh, and Thomas Brox. Eco: Efficient convolutional network for online video understanding. 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Previous work focuses on developing segmentation or classification methods only for certain mass types. Differential diagnosis of all mass types is clinically highly desirable [20] but has not been investigated using an automated image understanding approach. + +We exploit the feasibility to distinguish pancreatic ductal adenocarcinoma (PDAC) from the nine other nonPDAC masses using multi-phase CT imaging. Both image appearance and the 3D organ-mass geometry relationship are critical. We propose a holistic segmentation-mesh-classification network (SMCN) to provide patient-level diagnosis, by fully utilizing the geometry and location information, which is accomplished by combining the anatomical structure and the semantic detection-by-segmentation network. SMCN learns the pancreas and mass segmentation task and builds an anatomical correspondence-aware organ mesh model by progressively deforming a pancreas prototype on the raw segmentation mask (i.e., mask-to-mesh). A new graph-based residual convolutional network (GraphResNet), whose nodes fuse the information of the mesh model and feature vectors extracted from the segmentation network, is developed to produce the patient-level differential classification results. Extensive experiments on 661 patients' CT scans (five phases per patient) show that SMCN can improve the mass segmentation and detection accuracy compared to the strong baseline method nnUNet (e.g., for nonPDAC, Dice: 0.611 vs. 0.478; detection rate: $89\%$ vs. $70\%$ ), achieve similar sensitivity and specificity in differentiating PDAC and nonPDAC as expert radiologists (i.e., $94\%$ and $90\%$ ), and obtain results comparable to a multimodality test [20] that combines clinical, imaging, and molecular testing for clinical management of patients. + +# 1. Introduction + +Pancreatic cancer is the third leading cause of cancer-related deaths in the United States [7]. Furthermore, it + +![](images/570b4560a29cd928cfbb99ca75b1df051f01190442ffd2ec45053441ce3ec310.jpg) +Figure 1. Disease taxonomy of the ten types of pancreatic masses (tumors, cysts). Mass type diagnosis determines the clinical malignancy indications that lead to the proper patient risk stratification and management. The purple histogram bars represent their relative frequencies. All images are in the arterial-late CT phase. + +has the poorest prognosis among all solid malignancies, with a 5-year survival rate $\sim 10\%$ [7, 2]. Early diagnosis is crucial, as it can potentially increase the five-year survival rate to $\sim 50\%$ [5]. The clinical management of patients with pancreatic disease is based on the potential of the mass to become an invasive cancer. Unlike masses in other organs, pancreatic masses often cannot be reached precisely via needle biopsy due to the pancreas's deep location in the abdomen and the complex network of surrounding organs and vessels. Therefore, reliable imaging-based diagnosis is critical to identifying patients who truly require cancer treatment (e.g., surgery) in a timely fashion, while avoiding unnecessary iatrogenic morbidity. Developing deep learning methods to detect masses, identify ma + +lignancies, provide diagnoses and predict cancer prognosis has the potential to revolutionize pancreatic cancer imaging [4, 2, 8, 36, 27, 32, 30]. + +Multi-phase computed tomography (CT) is the first-line imaging modality for the diagnosis of pancreatic diseases. Differential diagnosis of pancreatic masses is challenging for several reasons. (1) The same type of mass may appear in different textures, shapes, contrasts, and different enhancement patterns across CT phases. (2) Pancreatic ductal adenocarcinoma (PDAC) accounts for most cases in pancreatic cancer specialized hospitals, causing a long-tail problem. (3) Masses, at times, are surrounded by inflamed tissues and thus cannot be easily identified. The pancreatic diseases in our database encompass ten types of masses (Fig. 1): PDAC, ampullary cancer (AC), bile duct cancer (DC), pancreatic neuroendocrine tumor (PNET), rare neoplasm (RARE), solid pseudopapillary tumor (SPT), chronic pancreatitis (CP), intraductal papillary mucinous neoplasm (IPMN), mucinous cystic neoplasm (MCN), and serous cystic neoplasm (SCN). To this end, we develop anatomy-aware 3D deep graph networks to automatically segment, detect, and perform differential diagnosis of the underlying diseases. + +We tackle two main problems with strong clinical indications: 1) PDAC versus nonPDAC differentiation and 2) clinical management of patients. PDAC is a unique group with the most dismal prognosis. Distinguishing PDAC from nonPDACs is always the primary question to answer. Patient management includes three recommendations: surgery, monitoring, and discharge (lower pannel in Fig. 1) [20]. Patients with malignant masses require cancer treatment (e.g., surgery). Those with potentially malignant masses require surgery if they are invasive or high-grade dysplasias, or monitoring otherwise. Those with nonmalignant masses could be safely discharged. Fine-grained classification of ten classes of masses using multi-phase CT is a very difficult long-tail problem. + +Existing automatic pancreatic mass image analysis methods [34, 36, 33, 35, 27, 32] focus on segmentation of certain types of tumors or cysts and thus cannot exploit the full-spectrum taxonomy of pancreatic mass/disease diagnoses. For pancreatic disease diagnosis, both texture and geometry cues are clinically useful. For instance, some types of masses appear at specific locations of the pancreas: AC and DC appear only at the pancreas head while MCN rarely appears at the head. Others spread over the entire pancreas, such as CP and IPMN. Additionally, some secondary signs of diseases are informative for diagnosis. Parenchymal atrophy and pseudocyst are observed in CP, causing a significant change in the shape of the pancreas. Most pancreatic cancers lead to dilatation of the pancreatic duct, with IPMN in particular abruptly modifying its caliber. + +To integrate such prior knowledge/correspondence into the model, (1) we propose a segmentation based detection network which can segment and identify pancreatic disease regions simultaneously. Our segmentation network takes multi-phase CT scans as input and outputs segmentation masks of the pancreas (as the studied organ) and mass. We also develop a weak-supervised segmentation method for cases when we have all pixel-level PDAC annotations but only nonPDAC labels. (2) A mask-to-mesh algorithm is used to build a 3D correspondence-aware mesh from the pancreas segmentation output. The geometry of the pancreas, as well as the location, shape, and distributions of the detected mass can all be captured/encoded by the mesh model. We present a mesh-based feature pooling method that extracts features from the segmentation network and preserve the anatomic structure (each vertex of the mesh has its anatomic meaning). Based on a fixed vertex index list, the pancreas can be automatically divided or parsed into four major sections: head, ventral body, dorsal body, and tail. (3) A geometry-integrated graph classification network utilizes the 3D anatomy correspondence-aware mesh based deep feature pooling to predict the pancreatic mass type. The network consists of graph-based residual convolutional blocks and an anatomy-based graph pooling layer. All the networks can be trained end-to-end via gradient-based optimization based on a loss function combining the segmentation loss, mesh vertex classification loss, and global graph classification loss. + +Our main contributions are three-fold. (1) To the best of our knowledge, this is the first work to propose a multiphase CT imaging analysis method for the full-spectrum taxonomy of pancreatic mass/disease diagnosis. (2) We are the first to integrate the 3D geometry-aware mesh model for effective pancreatic mass (tumor or cyst) imaging analysis (Sec. 3.2, Sec. 3.3), explicitly capturing the anatomy-mass integrated geometry and texture cues. (3) We have extensively evaluated our models on 661 patients (five-phase CT scans per patient). We achieve a new state-of-the-art PDAC segmentation accuracy (Dice: 0.738) and a substantially better nonPDAC segmentation (Dice: 0.611 vs. 0.478) and detection accuracy (detection rate: $89\%$ vs. $70\%$ ) compared to the strong baseline method nnUNet. Our imaging-only automated approach demonstrates comparable performance levels with (a) expert radiologists in the differentiation of PDAC versus nonPDAC who combine the analysis on clinical factors, imaging, and blood tests, and (b) a state-of-the-art machine learning-based clinical patient management system (i.e., surgery, monitoring, discharge) using the multimodality tests [20]. + +# 2. Related Work + +Deep Mesh Learning. Deep 3D reconstruction has been extensively studied in the computer vision and graph + +![](images/2cf5284697da418c7cc35b2425d7fd957bfe0ef012d5c8dec572621eb1c64bd4.jpg) +Figure 2. Flowchart of our proposed Segmentation-Mesh-Classification Network (SMCN). SMCN has three components: the pancreas-mass segmentation network, the mask-to-mesh 3D anatomy modeling, and the global mass classification network. The mesh model is the bridge between the segmentation network and the classification network, who pools the features from the segmentation network into the vertex feature vectors in the graph classification network. + +ics fields [1, 12, 22, 25], and various methods have been proposed to learn 3D shapes of organs from medical images [17, 29, 26]. The key component of mesh learning methods is the graph convolutional neural network (GCN) [15], typically used for graph-structured data processing. A liver mesh modeling method, inspired by the Pixel2Mesh algorithm [22], is proposed in [29], which simultaneously generates the mesh model and segmentation mask with improved geometry and segmentation accuracies. Voxel2Mesh [26] learns the mesh of the liver directly from 3D image volumes with a new mesh unpooling operation for better mesh reconstruction. However, all of these methods are designed specifically for organ segmentation, and it is not clear how their segmentation and mesh results could be used for diagnosis. + +Pancreatic Image Analysis. When manual segmentations of masses are available, radiomics schemes are commonly used to classify disease types [3, 6, 4]. However, heavy reliance on hand-annotated masks can make radiomics models less reproducible and scalable. To achieve automation, researchers have used detection-by-segmentation networks [35, 36, 27, 33] with U-Net as a common backbone network [18]. More recently, nnU-Net [13] (a self-adapting framework based on vanilla U-Nets) and its self-learning version have achieved competitive accuracy on PDAC segmentation [19, 23, 32]. Shape-induced information, e.g., tubular structure of dilated duct, has been exploited along with the PDAC segmentation task [16, 27, 23] to improve diagnosis. Existing studies mainly focus on PDAC [36, 27, 27, 33, 3, 24] or PNET [35], which cannot fully meet routine clinical needs on the full taxonomy of pancreatic tumor diagnosis. A comprehensive tax + +onomy for pancreatic diseases has been clinically defined to help managing/treating patients [20] where a machine learning model is built on top of clinical factors, imaging characteristics, and molecular biomarkers. These complex measurements require intensive labor costs and manual intervention, with reduced generalization and reproducibility. + +# 3. Methods + +Our segmentation-mesh-classification framework is illustrated in Fig. 2, with three main components as below. + +# 3.1. Anatomy-Mass Segmentation Network + +The inputs $X$ of the segmentation network are multi(5)-phase 3D CT scans, which are concatenated into a 4D input, $X \in R^{5 \times W \times H \times D}$ . The input $Y$ is the label/annotation including the auto-segmented pancreas (by an ensemble nnUNet [13] model trained on a public pancreas dataset [19]) and radiologist-segmented PDAC and nonPDAC masses. It is represented by the one hot encoding $Y \in R^{K \times W \times H \times D}$ . The numbers of labels $K$ can differ by task, i.e. PDAC vs. nonPDAC or patient management. Our backbone network is nnUNet. The pixel-level segmentation loss combines the cross-entropy and Dice losses: + +$$ +L _ {C E} = - \sum_ {w, h, d} \sum_ {k} ^ {K} y _ {k, w, h, d} \log (F (x) _ {k, w, h, d}), +$$ + +$$ +L _ {D C} = - 2 \sum_ {k} ^ {K} \frac {\sum_ {w , h , d} F (x) _ {k , w , h , d} y _ {k , w , h , d}}{\sum_ {w , h , d} F (x) _ {k , w , h , d} + \sum_ {w , h , d} y _ {k , w , h , d}}, +$$ + +$$ +L _ {S e g} = L _ {C E} + L _ {D C}. \tag {1} +$$ + +![](images/bc4d7673e4650118d45714a7854718e7995ef62e6b5377464c82fc58fc76f219.jpg) +(a) Epoch 0 + +![](images/ed641073f763ea5560a3d4f0e645bf451b5710748b1ab75c1477d08cc32df6ff.jpg) +(b) Epoch 20 + +![](images/e81b341d308ba6516de8f3e69b45af9b38e319d189bceda3d1a9229bad28c72b.jpg) +(c) Epoch 40 +Figure 3. The 3D mesh deformation process. The mesh is initialized as the pancreas prototype (a). Given the pancreas-mass segmentation mask (e), the geometry of the mesh is deformed gradually to fit the surface of the segmentation mask, as in (b-d). Red: the head of pancreas; Blue: the ventral body of pancreas; Yellow: the dorsal body of pancreas; Green: the tail of pancreas. + +![](images/514e023b9ba7943a201f0a341101efa500f645cf6da85c268f264e09e125179d.jpg) +(d) Epoch 60 + +![](images/c3960fed4f2ff84eeb0b21ea24bc6af4d074a449795fc8ae36c65513e4aa43ae.jpg) +(e) Segmentation + +where $F(x)$ is the softmax output of the network, $F(x) \in R^{K \times W \times H \times D}$ . + +NonPDAC labels are usually more difficult to obtain than PDAC due to their diversified appearance in a long-tail distribution. As such, we can perform the PDAC vs. nonPDAC task using only the PDAC mask annotations (when nonPDAC ones unavailable) as follows. First, we train a segmentation model on the PDAC data alone, focusing on PDAC segmentation. Next, we apply the final PDAC segmentation model to the nonPDAC data. A large portion of the nonPDAC masses are solid tumors that can possibly be misdetected as PDAC. All raw detections from the nonPDAC dataset by the PDAC segmentation model are collected as pseudo nonPDAC labels. Finally, we train a new segmentation network by using both original PDAC and pseudo nonPDAC labels. + +# 3.2. 3D Mesh-based Anatomy Representation + +Unlike existing mesh learning methods [22, 26] that are initialized by a randomized ellipsoid mesh, we encode the prior knowledge into our initial anatomy mesh by fitting it to the pancreas shape with anatomical meanings. + +Pancreas Anatomy. We first create a prototype mesh based on the average pancreas shape from the training fold. Afterwards, we place 156 vertices that are equally distributed on the surface of the prototype to build an anatomic structure. In particular, we separate them among the four anatomical regions of the pancreas, namely the pancreas head, ventral body, dorsal body and pancreas tail. The first 48 vertices belong to the pancreas head, denoted as red dots in Fig. 3. The 49-90th vertices belong to the ventral body of the pancreas, depicted by blue dots. The 91-135th vertices correspond to the dorsal body of the pancreas, shown in yellow dots. The last 21 vertices compose the tail of the pancreas, illustrated by green dots. + +Mask-to-mesh Process. The next step is to deform the mesh to pancreas mask of each patient as the target (Fig. 3-(e)). The geometry of the mesh can be deformed gradually to fit the surface of the segmentation mask, as in Fig. 3(a-d), so as to preserve the true anatomy of the pancreas. In this way, our mesh could maintain the anatomical meaning after deformation. To guide this deformation process, we define a loss function composed of three terms: point + +loss and two edge regularization terms. We define $p$ to be the vertex in the mesh and $q$ the voxels of the surface in the segmentation mask. Point loss, intuitively, measures the distance of each point to the nearest point at the surface of the segmentation. $L_{pt} = \sum_{p} \min_{q} ||p - q||_{2}^{2}$ . With the point loss, the pancreas mesh can be driven to fit the segmentation mask. Then we propose the first edge regularization term in order to preserve the geometry of the mesh: $L_{e_1} = \sum_{e} ||e - mean(e)||_2^2$ , $e = ||p - p'||_2$ , $p' \in N(p)$ where $N(p)$ is the neighboring vertices of $p$ . Next, to penalize the flying vertices (i.e. abnormal vertices randomly updated during the deformation process, resulting in structure flaws), we propose the second edge regularization loss to simply minimize the edge length: $L_{e2} = \sum_{e} e$ . Finally, the overall loss is + +$$ +L _ {m e s h f i t} = L _ {p t} + \lambda_ {1} L _ {e 1} + \lambda_ {2} L _ {e 2} \tag {2} +$$ + +Note that mesh vertices can keep their anatomic meaning even after the deformation process. The mesh fitting process can automatically parse the head, ventral body, dorsal body, and tail of the pancreas and could better preserve the anatomical-aware information in the mesh deformation. + +**Rendering.** Based on the coordinates of the mesh vertices, we divide the pancreas into zones $Z(p)$ . Each voxel of the segmented pancreas volume is defined in a zone by its nearest vertex, as shown in Fig. 2(b). The rendering method to define the zones from the each vertex includes the following steps: 1) The vertex in a 3D volume $A \in R^{W,H,D}$ is labeled by its index, i.e., the $i$ th vertex at $(w,h,d)$ is labeled as $i$ , $A_{w,h,d} = i$ . All the other voxels of $A$ are set to zero. 2) The 3D volume $A$ is dilated by one voxel as $A'$ . Each zero-voxel in $A$ with a corresponding non-zero voxel in $A'$ that belongs to the pancreas in the segmentation output $F(x)$ is substituted with the corresponding voxel in $A'$ . 3) Repeat the step 2) until all voxels have been updated. + +# 3.3. Global Mass Classification Network + +Vertex Feature Pooling. Given a deformed mesh and its representative vertex zones, we integrate them into the deep network for shape-constrained detection and segmentation. We encode the anatomical structure of the pancreas, as well as the tumor's texture and geometry into the feature vector. As such, the feature vector can be viewed as an anatomical + +![](images/2401ddbf2078da054cf89f9523912b21e212734861bb7a3b11424401f111e53a.jpg) +(b) 3D Deep Network + +![](images/2dbf4b2efa8406bf1c6f503273c1c038ebc58798766553aaea5f445fc9e8060d.jpg) + +Figure 4. Illustration of the feature vector $h_i$ for the $i$ th vertex. $x_i, y_i, z_i$ represents the location of the $i$ th vertex. $e_i$ is the average of all edge lengths $e_{ij}$ (i.e., the distance from every neighboring vertex $j$ of to $i$ ). $d_i$ denotes the shortest distance from the $i$ th vertex to the tumor surface. +![](images/fd502c530976ba9959744f573c5775f3a899a5559e63eaa606937c69849c0be1.jpg) +(c) $h_p^0: \overline{x_p} \cdot \overline{y_p} \cdot \overline{z_p} \cdot \overline{e_p} \cdot \overline{d_p}$ Local feature vector $_p$ Global feature vector + +![](images/42f7605fbac72e6c2d4031ad79116663837bbc01f822d2c72d00164a4880b1d2.jpg) + +representation of the pancreas and tumor of interest. We define $h_p^0$ as the initialized feature vector attached to vertex $p$ of the pancreas mesh, as shown in Fig. 4(a,c). The anatomical feature representation contains the vertex coordinates $(x_p, y_p, z_p)$ , the average edge length to its neighbours $e_p$ , the distance from $p$ to the nearest tumor surface point $d_p$ , and the local and global feature vectors pooled from prediction probability maps of the segmentation network. More specifically, $e_p = \sum_{p' \in N(p)} e_{pp'} / |N(p)|$ (Fig. 4(d)) and $d_p = \min_r \| p - r\|_2^2$ , where $r$ is the point at the surface of the mass (Fig. 4(e)). The zone $Z(p)$ then acts as the receptive field within which we pool the prediction probability maps of the 3D segmentation network $(F(x))$ to obtain a local feature vector, as shown in Fig. 4(b). The probability maps within the receptive field can be represented as a list of feature vectors $F(x)_{w,h,d} \in R^K$ , where $(w,h,d) \in Z(p)$ . + +In addition to Mesh-based Feature Pooling, we also perform global average pooling to get a global feature vector from the probability map of the 3D segmentation Network in Fig. 4 (b). We then concatenate the meta information, the local feature vectors of each individual vertex, and the global feature vector of the entire mesh to create the feature vector $h_p^0$ . We explicitly encode the pancreas-to-tumor geometry, the tumor's location in the pancreas, and its texture in the mesh-based anatomy representation. This improves the model's ability to learn anatomy-aware features, which will ultimately improve its performance in pancreatic mass/disease diagnosis based on the full-spectrum pancreatic disease taxonomy. + +Graph-ResNet. After obtaining feature vectors $h_i$ for each vertex, we feed them into the graph-based residual convolutional network (Graph-ResNet) which has proven to be successful in a recent deep mesh learning application [22]. We reduced the original Graph-ResNet to a smaller network containing six graph convolutional layers and shortcut connections between every two layers to perform the tumor classification task under three granularity + +levels. Each graph-based convolutional layer is defined as: + +$$ +h _ {p} ^ {l + 1} = w _ {0} h _ {p} ^ {l} + \sum_ {p ^ {\prime} \in N (p)} w _ {1} h _ {p ^ {\prime}} ^ {l} \tag {3} +$$ + +where $h_p^l$ is the feature vector attached on vertex $p$ at layer $l$ of the Graph-ResNet. $w_0$ and $w_1$ are learned parameters, with $w_1$ being shared by all edges. The graph-based convolutional layer accounts for the way in which vertices neighboring a given vertex regularize the vertex-to-neighbor exchange of information. We use two classification training losses: the vertex-level classification loss and the global classification loss. The vertex classification loss is defined as the cross-entropy loss and is applied to each vertex as + +$$ +L _ {V e r t e x} = - \sum_ {p} \sum_ {k} ^ {K} y _ {k, p} ^ {v} \log \left(G \left(h ^ {0}\right) _ {k, p}\right), \tag {4} +$$ + +where $G(h^0)$ denotes the softmax output of the graph network at every vertex. The vertex label $y^{v}$ is inferred from the labeled mask. Background voxels are labeled as 0, pancreas voxels as 1, and voxels for all mass types with labels greater than 1. The vertex $q$ is labeled using the maximum value of the voxels in its corresponding zone $Z(p)$ , $\hat{y}_p^v = \max_{(w,h,d)\in Z(p)}\hat{y}_{w,h,d}$ . $y^{v}$ is the one-hot encoding of $\hat{y}^v$ . Considering that some mass types may have blurry boundaries and the mass neighbor $Z(p)$ may also contain relevant cancer-related information, this labeling strategy and the propagation/smoothing property of the Graph-ResNet makes our approach robust to the quality of segmentation annotations or labels and increase the detection rates of masses. + +Global Mass Classification. After running Graph ResNet, we pool four features from all four pancreatic regions according to the vertex indices (1-48, 49-93, 94-135, 136-156), as shown in Fig. 2. These four global feature vectors and 156 local feature vectors are concatenated into one vector $h^{vp}$ , and fed into the final mass classification layer. The final global classification layer is a fully-connected layer. The global classification loss is the cross-entropy loss: + +$$ +L _ {G l o b a l} = - \sum_ {k} ^ {K} y _ {k} ^ {q} \log \left(H \left(h ^ {v p}\right) _ {k}\right), \tag {5} +$$ + +where $H(h^{vp})$ is the softmax output of the classification layer, and $y^g$ the patient-level mass/disease label. The overall loss function is the combination of three losses: + +$$ +L = L _ {S e g} + \eta_ {1} L _ {V e r t e x} + \eta_ {2} L _ {G l o b a l}. \tag {6} +$$ + +where $\eta$ is a hyperparameter used to balance the three loss components. $L_{Seg}$ is the pixel-level segmentation loss, and $L_{Vertex}$ is the vertex classification loss (Eq.4). All networks, namely the 3D segmentation network and the classification Graph-ResNet, can be trained end-to-end by leveraging this global loss function. + +# 4. Experiments + +Data and Preprocessing. Our dataset contains 661 patients with surgical pathology-confirmed pancreatic masses (366 PDACs, 46 ACs, 12 DCs, 35 PNETs, 13 RAREs, 32 SPTs, 43 CPs, 61 IPMNs, 7 MCNs, and 46 SCNs). Each patient has 5-phase CT scans: non-contrast (NC), arterial-early (AE), arterial-late (AL), venous (V), and delay (D). The median voxel size is $0.419 \times 0.419 \times 3\mathrm{mm}$ . The manual annotations of masses was performed by an experienced pancreatic imaging radiologist on the AL phase; CT scans from the other four phases are registered to AL by DEEDS [11]. Data augmentation is performed on-the-fly. This includes spatial transforms, Gaussian blur, and contrast shifting [13]. The hyper-parameters are set as $\lambda_{1} = 10^{-4}$ , $\lambda_{2} = 10^{-2}$ , and $\eta_{1} = \eta_{2} = 0.1$ based on preliminary experiments. All experiments are performed using nested three-fold cross-validation. In each fold, the network is trained for 1000 epochs. The best model is selected based on its performance on the validation set. It is then applied to the test set to generate the final experimental results. + +# 4.1. Evaluation on Mass Segmentation + +Quantitative Evaluation. Segmentation accuracy is measured using the Dice coefficient. Dice scores and detection rates of PDACs and nonPDACs (10 disease classes in total) are provided in Table 1. A detection is considered successful if the intersection (between the ground truth and segmentation mask) over the ground truth is $\geq 10\%$ (counted as 1); otherwise, it is considered a misdetection (counted as 0). Our SMCN network is compared to a strong baseline, 3D nnUNet [13], trained from scratch on our dataset. We find that integrating the 3D mesh-based anatomy representation into Graph-ResNet significantly improves mass segmentation and detection accuracies, especially for non-PDAC, as determined by Wilcoxon signed-ranks test (Dice: 0.611 vs. 0.478; Detection rate: $88.7\%$ vs. $69.3\%$ ). + +Qualitative Evaluation. Fig.5 illustrates the segmentation results for qualitative comparison. SMCN can guide the segmentation network by integrating geometry cues and achieve more complete segmentation results, especially for harder and relatively rare nonPDAC classes. In Fig.5, nnUNet misdetects an AC (malignant) completely because the tumor is outside of the pancreas head. Our SMCN model instead detects this AC finding. For an IPMN case (malignant potential), our model provides more complete segmentation including the clinically-critical secondary signs of pancreatic duct dilatation, than the 3D nnUNet model [13]. For SCN (benign), SMCN segments the full tumor surface. All demonstrate that our anatomy geometry-aware SMCN network produces superior segmentation results against the state-of-the-art 3D nnUNet [13], being widely used in medical imaging applications. + +PDAC Segmentation under Different CT Phases. We + +Image Label nnUNet [13] SMCN + +![](images/c2c76227e5fcc100894d913b6d3ede3ebdc232dcda94250ef78820d30392c535.jpg) +Figure 5. Examples of pancreas-mass segmentation results. Light red: pancreas. Green: surgery mass. Blue: monitoring mass. Yellow: discharge mass. + +![](images/b8943346c7c4fcf3429403d0dfb06fafba1a4a08c0bcac9056314a5d2a4fae60.jpg) +Figure 6. Examples of 3D meshes generated from pancreas segmentation under various scenarios. Top: red denotes the head of pancreas; blue the ventral body; yellow the dorsal body; and green the tail. Bottom: light red depicts the pancreas; green the surgery tumor; blue the monitoring tumor; and yellow the discharge tumor. + +compare our method to three other state-of-the-art methods of [32], DDT [23], and [27] which are applied to Venous phase. For ease of comparison, we implement/evaluate our models using only one or a few CT phases (in Table 2). The AL phase outperforms all other individual phases due to its higher voxel resolution and imaging contrast; the second best is Venous phase, widely adopted in clinical settings. The fusion/concatenation of multiple CT phases as the network's input yields better results than any single phase. The combined five phases yield the best segmentation Dice score of 0.738, which noticeably improves upon the previous state-of-the-art result of 0.709 [32]. Note that in [32] PDACs are mostly small in size and are only located at the pancreas head. In our dataset, by contrast, PDACs appear in various sizes and span the entire pancreas. The fusion of all four phases but AL as input yields better results than any single phase as well (Dice scores 0.696 vs. $0.562 \sim 0.675$ ). + +Table 1. Segmentation and detection results over the ten types of pancreatic masses. Note that in this experiment, networks are trained with four labels: background, pancreas, PDAC, and nonPDAC. micro: result for all patients; macro: average of the metrics of the ten classes. + +
MetricPDACNonPDACACCPDCIPMNMCNPNETRARESCNSPTmicromacro
nnUNet[13]Average Dice0.7340.4780.4230.5330.0010.1510.9240.5140.8490.5850.7620.6180.548
Detection rate0.9590.6930.70.7780.00.3081.00.8331.00.81.00.8380.738
SMCN(Ours)Average Dice0.7380.6110.4380.6680.0060.6020.9240.5140.8240.6660.8010.6810.618
Detection rate0.9720.8870.80.8890.01.01.01.01.00.81.00.9340.846
+ +Table 2. PDAC segmentation under different CT phases: non-contrast (N), arterial (A), arterial-early (AE), arterial-late (AL), venous (V), and delay (D). + +
MethodsCT PhasesAverage Dice
Reported from their original papers
Zhang et al. [32]N+A+V0.709
DDT [23]V0.634
Xia et al. [27]A+V0.644
OursAE0.646
OursAL0.730
OursV0.675
OursD0.562
OursN+AE+V+D0.696
OursN+AE+AL+V+D0.738
+ +# 4.2.3D Anatomy Mesh Quality Evaluation + +Qualitative results of our generated mesh model are shown in Fig. 6. Our method can effectively and accurately model the diseased pancreases under various scenarios, e.g., PDAC at the neck (Fig. 6(a)), AC at the head with pancreatic duct dilatation (Fig. 6(b)), pseudocyst at the tail (Fig. 6(c)), IPMN on the full pancreatic duct (Fig. 6(d)) and large tumor and parenchymal atrophy (Fig. 6(e)). As described in Sec. 3.2, our 3D mask-to-mesh algorithm can automatically divide the pancreas into four parts: head, ventral body, dorsal body and tail, which are color-coded as red, blue, yellow and green. The distributions of anatomic locations of 10-class pancreatic masses in our dataset are described in the supplementary material. AC and DC only appear at the head; MCN does not appear on the head; CP and IPMN appear mostly on the head; PDAC, PNET and RARE are distributed over the entire surface of the pancreas. Cystic masses (SPT, SCN and MCN) are distributed over the entire pancreas with the majority being located at the dorsal body. These observed distributions verify the prior knowledge of different masses' spatial locations and motivate our geometry-aware mass diagnosis framework. + +From the generated 3D mesh model, we can accurately measure the shape and location of the mass against the pancreas, as shown in Fig.4, at a human-readable level (156 is a suitable number for the clinical expert's perception). Our proposed mask-to-mesh algorithm and SMCN models can be generalized to other important organs with specific anatomical structures (like liver), which can potentially improve the underlying imaging-based mass diagnosis. + +Table 3. Average values of PDAC vs. nonPDAC across 3 folds. PV: pixel voting; VV: vertices voting; GC: global classification. + +
MethodsAccuracySensitivitySpecificity
Radiomics [21]0.8570.8530.868
DeepTexture [28]0.7700.8270.697
ResNet3D [9]0.7200.7880.633
SMCN w PV0.9130.9450.875
SMCN w VV0.9200.9450.891
SMCN w GC0.9270.9450.906
Expert radiologists-~0.94~0.90
+ +# 4.3. Evaluation on Mass Classification + +We validate our model for two main mass classification tasks: PDAC vs. nonPDAC and patient management. SMCN is compared to the radiomics model and 2D/3D deep classification networks. We extract 2,410 radiomics features (482 for each CT phase) using Pyradiomics package [21] from the manually-annotated masses. These features include mass characteristics of various-ordered texture and shape descriptions. Gradient Boosting Decision Tree is used as the classifier [14]. Feature importance is calculated within each phase to select the most informative features (top 30) in the training fold. To compare with deep classification models, we use automatic mass segmentation and prepare 2D/3D tumor patches/volumes from all five phases. Each 2D patch is the tumor region representing the largest size in the axial view of the 3D volume which is then resized to $256 \times 256$ following typical texture analysis practices [31]. For 3D volumes, we test with ResNet3D [9], while for 2D patches we built deep texture networks using ResNet-18 [10] as the backbone, following the model [28]. + +PDAC vs. NonPDAC. We first evaluate our method for classifying PDAC vs. nonPDAC, which is the primary clinical diagnosis task. Comparative results are provided in Table 3. Sensitivity and specificity correspond to the proportions of the correctly predicted PDACs and nonPDACs, respectively. We also conduct an ablation study on several classification strategies. Pixel voting (PV) indicates that the classification result is voted by the pixels from the segmentation masks – using an optimal volume threshold from the validation set; vertex-based voting (VV) means that the result is voted by the classified vertices of GraphResNet; Global classification (GC) is our final model. All of our SMCN variations significantly outperform both 2D/3D deep networks, thus revealing that using only the tumor's texture information to distinguish PDAC from nonPDAC + +Table 4. Classification confusion matrix of quantitative patient management and comparison our results against the clinical test [20]. + +
CompCyst [20]DischargeMonitoringSurgeryOursDischargeMonitoringSurgery
Discharge (n=53)32 (60%)14 (26%)7 (13%)(n=46)28 (61%)10 (22%)8 (17%)
Monitor (n=140)1 (1%)68 (49%)71 (51%)(n=104)11 (11%)65 (63%)27 (26%)
Surgery (n=152)0 (0%)14 (9%)138 (91%)(n=440)6 (1%)16 (4%)418 (95%)
+ +Table 5. Experimental Results for Patient Management. PV: pixel voting; VV: vertex-based voting; GC: global classification. + +
MethodsAccuracyAverage Recall
Radiomics [21]0.8540.667
DeepTexture [28]0.7430.557
ResNet3D [9]0.7370.607
SMCN w PV0.8320.735
SMCN w VV0.8390.656
SMCN w GC0.8650.746
+ +![](images/4c122d11b6887a741fcbe7159e802d3cd39fb56a4923de385ebdad20e460d536.jpg) +Figure 7. Comparison of (a) classification and (b) detection performances between fully-supervised and semi-supervised learning. The green dot depicts the performance of the mean second reader. + +![](images/e128eb49be5ec40e669ba7658f6c292adf30853e54a4157f91f32815a52b2441.jpg) + +is insufficient. Our fully automated models greatly outperform the radiomics approach (sensitivity 0.853, specificity 0.868) using manual annotations. The SMCN-w-GC configuration reports the best quantitative results with a sensitivity of 0.945 and specificity of 0.906. + +Fully-supervised or Semi-supervised Learning. As described in Sec. 3.1, we can perform the PDAC vs. non-PDAC task even when only the patient-level nonPDAC labels are available (referred as semi-supervised). A fully-supervised setting means that both PDAC and nonPDAC annotated masks are obtained. ROC curves of PDAC (positive class) vs. NonPDAC (negative class) are shown in Fig.7(A). Generally, similar classification results are achieved by the fully-supervised or semi-supervised learning method. Using only pseudo nonPDAC masks in a semi-supervised setting slightly reduces the detection rate of PDAC. Our fully-supervised method obtains sensitivity and specificity comparable to the mean second reader at a high-volume pancreatic cancer institution at $94\%$ and $90\%$ , respectively. The detection rates by different thresholds are evaluated in Fig.7(b). A segmentation result is counted as successful detection if at least the fraction $p$ of the mass is segmented ( $p$ is the cut-off). For fully-supervised learning, the best PDAC detection rate is $0.986(p > 0)$ ; the best nonPDAC sensitivity is $0.906(p\simeq 0.08)$ . Under semi-supervised learning, these numbers are $0.959(p\simeq 0.2)$ and $0.515(p > 0)$ , revealing the limitation of semi-supervised setting. + +Quantitative Patient Management. Patient management decisions fall under three categories: "Surgery", "Monitoring" and "Discharge" (Fig.1). We once again compare our methods to the Radiomics based approach, which is the current clinical standard, and conduct the ablation study on different classification strategies: PV, VV, and GC (Table 5). Our SMCN method generally outperforms the radiomics method, and the SMCN-w-GC version yields the best results. Importantly, CompCyst [20] reports real pancreatic mass patient management results leveraging clinical features, imaging characteristics, cyst fluid genetic and biochemical markers. However, it is invasive, and more expensive and time-consuming than SMCN. For a relatively fair comparison, we adhere to the same pancreatic disease taxonomy as [20], i.e., exclude AC, DC, and RARE classes. Two confusion matrices, by CompCyst [20] and SMCN, are compared side-by-side in Table 4. SMCN achieves similar or slightly improved quantitative performance via multiphase CT imaging. (1) $95\%$ of surgery patients (increased from $91\%$ by CompCyst) are correctly guided to surgery, but $1\%$ of surgery patients are misclassified as discharge patients, which is clinically undesirable. (2) The correctly recommended monitoring patients have increased to $63\%$ by SMCN from $49\%$ in [20]. The error rate for "recommend- ing surgery" has decreased significantly from $51\%$ [20] to $26\%$ . (3) The performance for discharge patients are similar between SMCN and CompCyst clinical results. We classify more patients into the surgery class ( $17\%$ vs. $13\%$ ). This is due to the fact that the distribution of our patients among all three actionable classes is more unbalanced than that in [20], and our discharge patient sub-population may be insufficient. Finally, we provide patient-level classification results for all ten pancreatic tumor classes in the supplementary material (considered as clinically less critical). + +# 5. Conclusion + +In this paper, we present a new segmentation-mesh-classification deep network (SMCN) to tackle the challenging and clinically-demanding tasks of pancreatic mass segmentation, diagnosis, and disease management. SMCN is composed of an anatomy-mass segmentation network, a mask-to-mesh 3D geometry modeling network, and a Graph-ResNet with vertex feature pooling and can be trained end-to-end. We extensively evaluate our SMCN method on the largest pancreatic multi-phase CT dataset of 661 patients, using the full taxonomy of ten types of pancreatic masses. Our experiments demonstrate the superiority of the proposed SMCN for all three pancreatic analysis tasks. + +# References + +[1] Angel X Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015. 3 +[2] Linda C Chu, Michael G Goggins, and Elliot K Fishman. Diagnosis and detection of pancreatic cancer. The Cancer Journal, 23(6):333-342, 2017. 1, 2 +[3] Linda C Chu, Seyoun Park, Satomi Kawamoto, Yan Wang, Yuyin Zhou, Wei Shen, Zhuotun Zhu, Yingda Xia, Lingxi Xie, Fengze Liu, et al. Application of deep learning to pancreatic cancer detection: Lessons learned from our initial experience. Journal of the American College of Radiology, 16(9):1338-1342, 2019. 3 +[4] Linda C Chu, Seyoun Park, Satomi Kawamoto, Alan L Yuille, Ralph H Hruban, and Elliot K Fishman. Pancreatic cancer imaging: a new look at an old problem. Current Problems in Diagnostic Radiology, 2020. 2, 3 +[5] Thierry Conroy, Pascal Hammel, Mohamed Hebbar, Meher Ben Abdelghani, Alice C Wei, Jean-Luc Raoul, Laurence Chone, Eric Francois, Pascal Artru, James J Biagi, et al. Folfirinox or gemcitabine as adjuvant therapy for pancreatic cancer. New England Journal of Medicine, 379(25):2395-2406, 2018. 1 +[6] Vipin Dalal, Joseph Carmicheal, Amaninder Dhaliwal, Maneesh Jain, Sukhwinder Kaur, and Surinder K Batra. Radiomics in stratification of pancreatic cystic lesions: Machine learning in action. Cancer Letters, 469:228-237, 2020. 3 +[7] Aaron J Grossberg, Linda C Chu, Christopher R Deig, Eliot K Fishman, William L Hwang, Anirban Maitra, Daniel L Marks, Arnav Mehta, Nima Nabavizadeh, Diane M Simeone, et al. Multidisciplinary standards of care and recent progress in pancreatic ductal adenocarcinoma. CA: A Cancer Journal for Clinicians, 70(5):375-403, 2020. 1 +[8] Arya Haj-Mirzaian, Satomi Kawamoto, Atif Zaheer, Ralph H Hruban, Elliot K Fishman, and Linda C Chu. Pitfalls in the MDCT of pancreatic cancer: strategies for minimizing errors. *Abdominal Radiology*, pages 1–22, 2020. 1, 2 +[9] Kensho Hara, Hirokatsu Kataoka, and Yutaka Satoh. Can spatiotemporal 3d cnns retrace the history of 2d cnns and imagenet? In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 6546-6555, 2018. 7, 8 +[10] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 7 +[11] MP Heinrich, M. Jenkinson, M. Brady, and JA Schnabel. Mrf-based deformable registration and ventilation estimation of lung ct. In IEEE Trans. on Medical Imaging, pages 32(7):1239-1248, 2013. 6 +[12] Qixing Huang, Hai Wang, and Vladlen Koltun. Single-view reconstruction via joint analysis of image and shape colloc + +tions. ACM Transactions on Graphics (TOG), 34(4):1-10, 2015. 3 +[13] Fabian Isensee, Jens Petersen, Andre Klein, David Zimmerer, Paul F Jaeger, Simon Kohl, Jakob Wasserthal, Gregor Koehler, Tobias Norajitra, Sebastian Wirkert, et al. nnu-net: Self-adapting framework for u-net-based medical image segmentation. arXiv preprint arXiv:1809.10486, 2020. 3, 6, 7 +[14] Guolin Ke, Qi Meng, Thomas Finley, Taifeng Wang, Wei Chen, Weidong Ma, Qiwei Ye, and Tie-Yan Liu. Lightgbm: A highly efficient gradient boosting decision tree. In Advances in Neural Information Processing Systems, pages 3146-3154, 2017. 7 +[15] Thomas N. Kipf and Max Welling. Semi-Supervised Classification with Graph Convolutional Networks. In Proceedings of the 5th International Conference on Learning Representations, ICLR '17, 2017. 3 +[16] Fengze Liu, Lingxi Xie, Yingda Xia, Elliot Fishman, and Alan Yuille. Joint shape representation and classification for detecting pdac. In International Workshop on Machine Learning in Medical Imaging, pages 212-220. Springer, 2019. 3 +[17] Tianwei Ni, Lingxi Xie, Huangjie Zheng, Elliot K Fishman, and Alan L Yuille. Elastic boundary projection for 3d medical image segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2109-2118, 2019. 3 +[18] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 234-241. Springer, 2015. 3 +[19] Amber L. Simpson, Michela Antonelli, Spyridon Bakas, Michel Bilello, Keyvan Farahani, Bram van Ginneken, Annette Kopp-Schneider, Bennett A. Landman, Geert Litjens, Bjoern H. Menze, Olaf Ronneberger, Ronald M. Summers, Patrick Bilic, Patrick Ferdinand Christ, Richard K. G. Do, Marc Gollub, Jennifer Golia-Pernicka, Stephan Heckers, William R. Jarnagin, Maureen McHugo, Sandy Napel, Eugene Vorontsov, Lena Maier-Hein, and M. Jorge Cardoso. A large annotated medical image dataset for the development and evaluation of segmentation algorithms. CoRR, abs/1902.09063, 2019. 3 +[20] Simeon Springer, David L Masica, Marco Dal Molin, Christopher Douville, Christopher J Thoburn, Bahman Af-sari, Lu Li, Joshua D Cohen, Elizabeth Thompson, Peter J Allen, et al. A multimodality test to guide the management of patients with a pancreatic cyst. Science Translational Medicine, 11(501):eaav4772, 2019. 1, 2, 3, 8 +[21] Joost JM Van Griethuysen, Andriy Fedorov, Chintan Parmar, Ahmed Hosny, Nicole Aucoin, Vivek Narayan, Regina GH Beets-Tan, Jean-Christophe Fillion-Robin, Steve Pieper, and Hugo JWL Aerts. Computational radiomics system to decode the radiographic phenotype. Cancer Research, 77(21):e104-e107, 2017. 7, 8 +[22] Nanyang Wang, Yinda Zhang, Zhuwen Li, Yanwei Fu, Wei Liu, and Yu-Gang Jiang. Pixel2mesh: Generating 3d mesh models from single rgb images. In Proceedings of the Eu + +ropean Conference on Computer Vision (ECCV), September 2018. 3, 4, 5 +[23] Yan Wang, Xu Wei, Fengze Liu, Jieneng Chen, Yuyin Zhou, Wei Shen, Elliot K Fishman, and Alan L Yuille. Deep distance transform for tubular structure segmentation in ct scans. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3833-3842, 2020. 3, 6, 7 +[24] EM Weisberg, LC Chu, and Seyoun Park. Deep lessons learned: Radiology, oncology, pathology, and computer science experts unite around artificial intelligence to strive for earlier pancreatic cancer diagnosis. 2019. 3 +[25] Chao Wen, Yinda Zhang, Zhuwen Li, and Yanwei Fu. Pixel2mesh++: Multi-view 3d mesh generation via deformation. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), October 2019. 3 +[26] U. Wickramasinghe, Edoardo Remelli, G. Knott, and P. Fua. Voxel2mesh: 3d mesh model generation from volumetric data. In MICCAI, 2020. 3, 4 +[27] Yingda Xia, Qihang Yu, Wei Shen, Yuyin Zhou, and Alan L Yuille. Detecting pancreatic adenocarcinoma in multiphase ct scans via alignment ensemble. arXiv preprint arXiv:2003.08441, 2020. 2, 3, 6, 7 +[28] Jia Xue, Hang Zhang, and Kristin Dana. Deep texture manifold for ground terrain recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 558-567, 2018. 7, 8 +[29] Jiawen Yao, Jinzheng Cai, Dong Yang, Daguang Xu, and Junzhou Huang. Integrating 3d geometry of organ for improving medical image segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 318-326. Springer, 2019. 3 +[30] Jiawen Yao, Yu Shi, Le Lu, Jing Xiao, and Ling Zhang. Deepprognosis: Preoperative prediction of pancreatic cancer survival and surgical margin via contrast-enhanced CT imaging. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 272-282. Springer, 2020. 2 +[31] Hang Zhang, Jia Xue, and Kristin Dana. Deep ten: Texture encoding network. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017. 7 +[32] Ling Zhang, Yu Shi, Jiawen Yao, Yun Bian, Kai Cao, Dakai Jin, Jing Xiao, and Le Lu. Robust pancreatic ductal adenocarcinoma segmentation with multi-institutional multi-phase partially-annotated ct scans. In International Conference on Medical Image Computing and Computer-Assisted Intervention, 2020. 2, 3, 6, 7 +[33] Yuyin Zhou, Yingwei Li, Zhishuai Zhang, Yan Wang, Angtian Wang, Elliot K Fishman, Alan L Yuille, and Seyoun Park. Hyper-pairing network for multi-phase pancreatic ductal adenocarcinoma segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 155-163. Springer, 2019. 2, 3 +[34] Yuyin Zhou, Lingxi Xie, Elliot K Fishman, and Alan L Yuille. Deep supervision for pancreatic cyst segmentation in abdominal ct scans. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 222-230. Springer, 2017. 2 + +[35] Zhuotun Zhu, Yongyi Lu, Wei Shen, Elliot K Fishman, and Alan L Yuille. Segmentation for classification of screening pancreatic neuroendocrine tumors. arXiv preprint arXiv:2004.02021, 2020. 2, 3 +[36] Zhuotun Zhu, Yingda Xia, Lingxi Xie, Elliot K Fishman, and Alan L Yuille. Multi-scale coarse-to-fine segmentation for screening pancreatic ductal adenocarcinoma. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 3-12. 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CrosCLR consists of both single-view contrastive learning (SkeletonCLR) and cross-view consistent knowledge mining (CVCKM) modules, integrated in a collaborative learning manner. It is noted that CVC-KM works in such a way that high-confidence positive/negative samples and their distributions are exchanged among views according to their embedding similarity, ensuring cross-view consistency in terms of contrastive context, i.e., similar distributions. Extensive experiments show that CrosCLR achieves remarkable action recognition results on NTU-60 and NTU-120 datasets under unsupervised settings, with observed higher-quality action representations. Our code is available at https://github.com/LinguoLi/CrosCLR. + +# 1. Introduction + +Human action recognition is an important but challenging task in computer vision research. Due to the lightweight and robust estimation algorithms [3, 56], 3D skeleton has become a popular feature representation to study human action dynamics. Many 3D action recognition works [6, 60, 17, 25, 44, 28, 16] use a fully-supervised manner and require massive labeled 3D skeleton data. However, annotating data is expensive and time-consuming, which prompts people to explore unsupervised methods [65, 26, 39, 47] on skeleton data. Some unsupervised methods exploit structure completeness within each sample based on pretext tasks, including reconstruction [9, 65], auto-regression [20, 47] and jigsaw puzzles [35, 54], but it is unsure that the designed pretext tasks generalize well for downstream tasks. Other unsupervised methods are based + +![](images/72a2a7725ea4ac6cb798b1640e0a2acd0faa6c86f9642d8ce7bcb2edb4a43d25.jpg) +Figure 1. Hand waving in joint and motion form. Two samples are from the same action class. (a) usual contrastive learning methods regard them as negative pairs. (b) in a multi-view situation, considering their similar motion patterns, they can be positive pairs. This motivates us to introduce cross-view contrastive learning for skeleton representation. + +on contrastive learning [55, 4, 11, 18], aiming to leverage the instance discrimination of samples in latent space. + +Although the above approaches improve the skeleton representation capability to some extent, it is believed that the power of unsupervised methods is by far from fully explored. On the one hand, traditional contrastive learning uses only one positive pair generated by data augmentation and even similar samples are regarded as negative samples. Despite the high similarity, the negative samples are forced away in embedding space, which is unreasonable for clustering. On the other hand, current unsupervised methods [1, 65, 20, 26, 47] have not yet explored the rich intra-supervision information provided by different skeleton modalities. Considering that it is easy to obtain skeleton data in multiple "views", e.g., joint, motion and bone, complementary information preserved in different views can assist the operation to mine positive pairs from similar negative samples. As shown in Figure 1, the same hand waving actions are different in pose (joint), but similar in motion. Usual contrastive learning methods regard them as nega + +tive pairs, keeping them away in embedding space. If such complementary information, i.e., different in joint but similar in motion, could be fully utilized and explored, the size of hidden positive pairs in joint can be boosted, enhancing training fidelity. Thus, the cross-view contrastive learning strategy takes advantage of multi-view knowledge, resulting in better-extracted skeleton features. + +To this end, we propose a Cross-view Contrastive Learning framework for Skeleton-based action Representation (CrosCLR), which exploits multi-view information for mining positive samples and pursuing cross-view consistency in unsupervised contrastive learning, enabling the model to extract more comprehensive cross-view features. First, parallel Contrastive Learning is evoked for each single-view Skeleton action Representation (SkeletonCLR), yielding multiple single-view embedding features. Second, inspired by the fact that the distance of samples in embedding space reflects the similarity of the samples in the original space, we refer to the extreme similarity of samples in one view to guide the learning process in another view, as shown in Figure 1. More specifically, Cross-View Consistent Knowledge Mining (CVC-KM) module is developed to exam the similarity of samples, and select the most similar pairs as positive ones to boost the positive set in complementary views, i.e., embedding distance/similarity (confidence score) serves as the weight of corresponding mined sample in the contrastive loss. In other words, CVC-KM conveys the most prominent knowledge from one view to others, introduces complementary pseudo-supervised constraint and promotes information sharing among views. The entire framework excavates positive pairs across views according to the distance between samples in the embedding space to promote knowledge exchange among views, so that the extracted skeleton features will contain multi-view knowledge and are more competitive for various downstream tasks. Extensive results on NTU-RGB+D [40, 27] datasets demonstrate that our method indeed boosts the 3D action representation learning benefiting from cross-view consistency. We summarize our contributions as follows: + +- We propose CrosSCLR, a cross-view contrastive learning framework for skeleton-based action representation. +- We develop Contrastive Learning for Skeleton-based action Representation (SkeletonCLR) to learn the single-view representations of skeleton data. +- We use parallel SkeletonCLR models and CVC-KM to excavate useful samples across views, enabling the model to capture more comprehensive representation unsupervisedly. +- We evaluate our model on 3D skeleton datasets, e.g., NTU-RGB+D 60/120, and achieve remarkable results under unsupervised settings. + +# 2. Related Work + +Self-Supervised Representation Learning. Self-supervised learning is to learn feature representations from numerous unlabeled data, which usually generates supervision by pretext tasks, e.g., jigsaw puzzles [35, 36, 54], colorization [63], predicting rotation [8, 59]. For sequence data, supervision can be generated by frame orders [32, 7, 21], space-time cubic puzzles [19] and prediction [51, 26], but these methods highly rely on the quality of pretext tasks. Recently, contrastive methods [37, 55, 48, 18] based on instance discrimination have been proposed for representation learning. MoCo [11] introduces a memory bank to store the embeddings of negative samples, and SimCLR [4] uses a much larger mini-batch size to compute the embeddings in real time, but they can not capture the cross-view knowledge for 3D action representation. Concurrent work CoCLR [10] leverages multi-modal information for video representation via co-training, which doesn't consider the contrastive context. Our CrosSCLR simultaneously trains models in all views by encouraging cross-view consistency, leading to more representative embeddings. + +Skeleton-based Action Recognition. To tackle skeleton-based action recognition tasks, early approaches are generally based on hand-craft features [33, 52, 49, 50]. Recent methods pay more attention to deep neural networks. For the sequence structure of skeleton data, many RNN-based methods [6, 40, 60, 45, 61] were carried out to effectively utilize the temporal feature. Since RNN suffers from gradient vanishing [14], CNN-based models [17, 22] attract researchers' attention, but they need to convert skeleton data to another form. Further, ST-GCN [57] was proposed to better model the graph structure of skeleton data. Then the attention mechanism [24, 42, 44, 64, 62] and multi-stream structure [25, 41, 42, 53] are applied to adaptively capture multi-stream features based on GCNs. We adopt the widely-used ST-GCN as the backbone to extract the skeleton features. + +Unsupervised Skeleton Representation. Many unsupervised methods [46, 29, 31, 23] were proposed to capture action representations in videos. For skeleton data, previous works [58, 1] have achieved some progress in unsupervised representation learning without deep neural networks. Recent deep learning methods [9, 65, 20, 47] are based on the structure of encoder-decoder or generative adversarial network (GAN). LongT GAN [65] proposed an auto-encoder-based GAN for sequential reconstruction and evaluated it on the action recognition tasks. P&C [47] uses a weak decoder in the encoder-decoder model, forcing the encoder to learn more discriminative features. $\mathrm{MS}^2\mathrm{L}$ [26] proposed a multi-task learning scheme for action representation learning. However, these methods highly depend on + +reconstruction or prediction, and they do not exploit the natural multi-view knowledge of skeleton data. Thus, we introduce CrosSCLR for unsupervised 3D action representation. + +# 3. CrosSCLR + +Although 3D skeleton has shown its importance in action recognition, unsupervised skeleton representation has not been well exploited recently. Since the easily-obtained "multi-view" skeleton information plays a significant role in action recognition, we expect to exploit them to mine positive samples and pursue cross-view consistency in unsupervised contrastive learning, thus giving rise to a Cross-view Contrastive Learning (CrossSCLR) framework for Skeleton-based action Representation. + +As shown in Figure 3, CrosCLR contains two key modules: 1) SkeletonCLR (Section 3.1): a contrastive learning framework to unsupervisedly learn single-view representations, and 2) CVC-KM (Section 3.2): it conveys the most prominent knowledge from one view to others, introduces complementary pseudo-supervised constraint and promotes information sharing among views. Finally, the more discriminating representations can be obtained by cooperatively training (Section 3.2). + +# 3.1. Single-View 3D Action Representation + +Contrastive learning has been widely-used due to its instance discrimination capability, especially for images [4, 11] and videos [10]. Inspired by this, we develop Skeleton-CLR to learn single-view 3D action representations, based on the recent advanced practice, MoCo [11]. + +SkeletonCLR. It is a memory-augmented contrastive learning method for skeleton representation, which considers one sample's different augments as its positive samples and other samples as negative samples. In each training step, the batch embeddings are stored in first-in-first-out memory to get rid of redundant computation, serving as negative samples for the next steps. The positive samples are embedded close to each other while the embeddings of negative samples are pushed away. As shown in Figure 2, SkeletonCLR consists of the following major components: + +- A data augmentation module $\mathcal{T}$ that randomly transforms the given skeleton sequence into different augments $x$ , $\hat{x}$ that are considered as positive pairs. For skeleton data, we adopt Shear and Crop as the augmentation strategy (see Section 3.3 and Appendix). +- Two encoders $f$ and $\hat{f}$ that embed $x$ and $\hat{x}$ into hidden space: $h = f(x; \theta)$ and $\hat{h} = \hat{f}(\hat{x}; \hat{\theta})$ , where $h, \hat{h} \in \mathbb{R}^{c_h}$ . $\hat{f}$ is the momentum updated version of $f$ : $\hat{\theta} \gets \alpha \hat{\theta} + (1 - \alpha)\theta$ , where $\alpha$ is a momentum coefficient. SkeletonCLR uses ST-GCN [57] as the backbone (Details are in Section 3.3). + +![](images/fbc3f7af909a74711c53c55aa4bf2610a6be765725e02194f1f373f072170745.jpg) +Figure 2. Architecture of single-view SkeletonCLR, which is a memory augmented contrastive learning framework. + +- A simple projector $g$ and its momentum updated version $\hat{g}$ that project the hidden vector to a lower dimension space: $z = g(h), \hat{z} = \hat{g}(\hat{h})$ , where $z, \hat{z} \in \mathbb{R}^{c_z}$ . The projector is a fully-connected (FC) layer with ReLU. +- A memory bank $\mathbf{M} = \{m_i\}_{i=1}^M$ that stores negative samples to avoid redundant computation of the embeddings. It is a first-in-first-out queue updated per iteration by $\hat{z}$ . After each inference step, $\hat{z}$ will enqueue while the earliest embedding in $\mathbf{M}$ will dequeue. During contrastive training, $\mathbf{M}$ provides numerous negative embeddings while the new calculated $\hat{z}$ is the positive embedding. +- An InfoNCE [37] loss for instance discrimination: + +$$ +\mathcal {L} = - \log \frac {\exp (z \cdot \hat {z} / \tau)}{\exp (z \cdot \hat {z} / \tau) + \sum_ {i = 1} ^ {M} \exp (z \cdot m _ {i} / \tau)} \tag {1} +$$ + +where $m_{i}\in \mathbf{M}$ $\tau$ is the temperature hyperparameter [12], and dot product $z\cdot \hat{z}$ is to compute their similarity where $z,\hat{z}$ are normalized. + +Constrained by contrastive loss $\mathcal{L}$ , the model is unsupervisedly trained to discriminate each sample in the training set. At last, we can obtain a strong encoder $f$ that is beneficial to extract single-view distinguishing representations. + +Limitations of Single-View Contrastive Learning. The above SkeletonCLR still suffers the following limitations: + +1) Embedding distribution can provide more reliable information. We expect samples from the same category are embedded closely. However, instance discrimination in SkeletonCLR uses only one positive pair and even similar samples are regarded as negative samples. It is unreasonable that the negative samples are forced away in embedding space despite their high embedding similarity. In other words, one positive pair cannot fully describe the relationships of samples, and a more reliable embedding distribution is needed, i.e., positive/negative setting plus embedding similarity. We aim to mine more representative knowledge to facilitate contrastive learning, which is also the knowledge we want to exchange across views. Thus, we introduce the contrastive context in Section 3.2. +2) Multi-view data can benefit representation learning. SkeletonCLR only relies on single-view data. As shown in Figure 1, since we don't have any annotations, different samples of the same class are inevitably embedded + +into distinct places far from each other, i.e., they distribute sparsely/irregularly, bringing much difficulty for linear classification. Considering the readily generated multi-view data of 3D skeleton (see Section 3.3), if such complementary information in Figure 1, i.e., different in joint but similar in motion, could be fully utilized and explored, the size of hidden positive pairs in joint can be boosted, enhancing training fidelity. To this end, we inject this consideration into unsupervised contrastive learning framework. + +# 3.2. Cross-View Consistent Knowledge Mining + +Motivated by the situation in Figure 1 that complementary knowledge is preserved in multiple views, we propose the Cross-View Consistent Knowledge Mining (CKC-KM), leveraging the high similarity of samples in one view to guide the learning process in another view. It excavates positive pairs across views according to the embedding similarity to promote knowledge exchange among views, then the size of hidden positive pairs in each view can be boosted and the extracted skeleton features will contain multi-view knowledge, resulting in a more regular embedding space. + +In this section, we first clarify contrastive context as the consistent knowledge across views, and then show how to mine high-confidence knowledge, and finally inject its cross-view consistency into single-view SkeletonCLR to further benefit the cross-view unsupervised representation. + +Contrastive Context as Consistent Knowledge. As discussed above, the knowledge we want to exchange across views is one sample's contrastive context, which describes this sample's relationships with others (distribution) in embedding space under the settings of contrastive learning. Notice that SkeletonCLR uses a memory bank to store necessary embeddings. Given one sample's embedding $z$ and corresponding memory bank $\mathbf{M}$ , its contrastive context is a similarity set $S$ among $z$ and $\mathbf{M}$ conditioned on specific knowledge miner $\Gamma$ that generates index set $N_{+}$ of positive samples, + +$$ +\mathcal {S} = \left\{s _ {i} \right\} _ {i \in N} = \left\{z \cdot m _ {i} \right\} _ {i \in N} \tag {2} +$$ + +$$ +\left(\mathcal {S} _ {+}, N _ {+}\right) = \Gamma (\mathcal {S}) \tag {3} +$$ + +where $S_{+} = \{s_i\}_{i\in N_{+}}$ and dot product “.” is to compute the similarity $s_i$ among embeddings $z$ and $m_i$ . $N$ is the index set of embeddings in memory bank and $N_{+}$ is the index set of positive samples selected by knowledge miner $\Gamma$ . Thus contrastive context $\mathcal{C}(\mathcal{S}|N_{+})$ consists of following two aspects: + +- Embedding Context $S$ : it is the relationship between one sample and others in embedding space, i.e., distribution; +- Contrastive Setting $N_{+}$ : it is the positive setting mined by $\Gamma$ according to the embedding similarity $S$ ; + +thus $\mathcal{C}(\mathcal{S}|N_{+}) = \{\mathcal{S}_{+},\mathcal{S}_{-}\}$ has positive context $\mathcal{S}_{+}$ and negative context $\mathcal{S}_{-}$ , where $\mathcal{S} = \mathcal{S}_{+}\cup \mathcal{S}_{-}$ . The contrastive + +context contains not only the information of the most similar samples but the detailed relationships of samples (distribution). + +In Equation (1), the embedding $z$ has positive context $S_{+} = \{z\cdot \hat{z}\}$ which does not consider any of neighbors in embedding space except for the augments. Despite the high similarity, the negative samples are forced away in embedding space, and then samples belonging to the same category are difficultly embedded into the same cluster, which is not efficient to build a "regular" embedding space for downstream classification tasks. + +High-confidence Knowledge Mining. To solve the above issue, we develop the high-confidence Knowledge Mining mechanism (KM), which selects the most similar pairs as positive ones to boost the positive sets. It shares similar high-level spirit with neighborhood embedding [13] but performs differently in an unsupervised contrastive manner. + +Specifically, it is based on the following observation in Figure 4 that after single-view contrastive learning, two embeddings most likely belong to the same category if they are embedded closely enough; on the contrary, two embeddings hardly belong to the same class if they locate extremely far from each other in embedding space. Therefore, we can facilitate contrastive learning by setting the most similar embeddings as positive to make it more clustered: + +$$ +\Gamma (\mathcal {S}) = \operatorname {T o p k} (\mathcal {S}) \tag {4} +$$ + +$$ +\mathcal {L} _ {\mathrm {K M}} = - \log \frac {\exp (z \cdot \hat {z} / \tau) + \sum_ {i \in N _ {+}} \exp (z \cdot m _ {i} / \tau)}{\exp (z \cdot \hat {z} / \tau) + \sum_ {i \in N} \exp (z \cdot m _ {i} / \tau)} \tag {5} +$$ + +where $\Gamma = \mathrm{Topk}$ is the function to select the index of top- $K$ similar embeddings and $N_{+}$ is their index set in memory bank. Compared to Equation (1), Equation (5) will leads to a more regular space by pulling close more high-confidence positive samples. Additionally, since we don't have any labels, a larger $K$ may harm the contrastive performance (see Section 4.3). + +Cross-View Consistency Learning. Considering easily-obtained multi-view skeleton data, complementary information preserved in different views can assist the operation to mine positive pairs from similar negative samples in Figure 1. Then the size of hidden positive pairs can be boosted by cross-view knowledge communication, resulting in better-extracted skeleton features. To this end, we design the cross-view consistency learning which not only mines the high-confidence positive samples from complementary view but also lets the embedding context be consistent in multiple views. Its two-view case is illustrated in Figure 3 for example. + +Specifically, samples $x^{u}$ and $x^{v}$ are generated from the same raw data $x$ by the view generation method in Section 3.3, where $u$ and $v$ indicate two types of data views. After single-view contrastive learning, two SkeletonCLR + +![](images/99a8d6f8bd5420dbd1a71480fadd0d597c7a792248b39ccbb9a786aca8bd7143.jpg) +(a) + +![](images/9308609a1612cbc7615603337339fac6dceee7b430cdee9e3ec79811d011f123.jpg) +(b) +Figure 3. (a) CrosSCLR. Given two samples $x^{u}$ , $x^{v}$ generated from the same raw data, e.g., joint and motion, SkeletonCLR models produce single-view embeddings while cross-view consistent knowledge mining (CVC-KM) exchanges multi-view complementary knowledge. (b) how $\mathcal{L}_{v\rightarrow u}$ works in embedding space. In step 1, we mine high-confidence knowledge $N_{+}^{v}$ from similarities $S^v$ to boost the positive set of view $u$ , i.e., $z^{u}$ shares $z^{v}$ 's neighbors; In step 2, we use the similarities $S^v$ to supervise the embedding distribution in view $u$ . $z^{u}$ , $z^{v}$ share similar relationships with others. Thus, two embedding spaces become similar under the constraint of $\mathcal{L}_{\mathrm{cross}}$ . + +modules obtain the embeddings $z^u, z^v$ and corresponding memory bank $\mathbf{M}^u, \mathbf{M}^v$ respectively. We can mine the high-confidence knowledge from two views by $(S_{+}^{u}, N_{+}^{u}) = \operatorname{Topk}(S^{u})$ and $(S_{+}^{v}, N_{+}^{v}) = \operatorname{Topk}(S^{v})$ , where $S_{+}^{u}, S_{+}^{v}$ are the positive context of $z^u, z^v$ respectively. + +CrossSCLR aims to learn the consistent embedding distribution in different views by encouraging the similarity of contrastive context, i.e., exchanging high-confidence knowledge across views. In Figure 3 (b), if we want to use the knowledge of view $v$ to guide view $u$ 's contrastive learning, it contains two aspects: 1) step 1: we select the most similar pairs (positive) in view $v$ as the positive sets in view $u$ , i.e., $S^u, N_+^v \to \mathcal{C}(S^u | N_+^v)$ . Thus the sample $z^u$ shares $z^v$ 's positive neighbors; 2) step 2: we use the embedding similarity $s_i^v = z^v \cdot m_i^v$ in view $v$ as the weight of corresponding embedding $m_i^u$ in view $u$ to provide the detailed relational information, i.e., $m_i^{v\rightarrow u} = s_i^v m_i^u$ . Then the similarity is computed by $z^u \cdot m^{v\rightarrow u} = s_i^v (z^u \cdot m_i^u) = s_i^u s_i^v$ and $z^u$ has embedding context $S^{v\rightarrow u} = \{z^u \cdot m_i^{v\rightarrow u}\}_{i\in N} = \{s_i^u s_i^v\}_{i\in N}$ . Finally, the overall loss is conducted as: + +$$ +\mathcal {L} _ {v \rightarrow u} = - \log \frac {\exp \left(z ^ {u} \cdot z ^ {\hat {u}} / \tau\right) + \sum_ {i \in N _ {+} ^ {v}} \exp \left(s _ {i} ^ {u} s _ {i} ^ {v}\right) / \tau)}{\exp \left(z ^ {u} \cdot z ^ {\hat {u}} / \tau\right) + \sum_ {i \in N} \exp \left(s _ {i} ^ {u} s _ {i} ^ {v}\right) / \tau}) \tag {6} +$$ + +$$ +\mathcal {L} _ {\text {c r o s s}} = \mathcal {L} _ {u \rightarrow v} + \mathcal {L} _ {v \rightarrow u} \tag {7} +$$ + +where $\mathcal{L}_{v\rightarrow u}$ means we transfer the contrastive context of $z^v$ to that of $z^{u}$ . Since $s_i^u,s_i^v$ are the embedding context of $z_{i}^{u},z_{i}^{v}$ , we call Equation (7) as cross-view contrastive context learning, which constrains the similar distribution of two views (see Section 4.3, the results of t-SNE). Compared to Equation (5), Equation (6) considers the cross-view information, cooperatively using one view's high-confidence positive samples and its distribution to instruct the other view's contrastive learning, resulting in more regular space and better extracted skeleton features. + +Learning CrosSCLR. For more views, CrosSCLR has fol + +lowing objective: + +$$ +\mathcal {L} _ {\text {c r o s s}} = \sum_ {u} ^ {U} \sum_ {v} ^ {U} \mathcal {L} _ {u \rightarrow v} \tag {8} +$$ + +where $U$ is the number of views and $v\neq u$ + +In the early training process, the model is not stable and strong enough to provide reliable cross-view knowledge without the supervision of labels. As the unreliable information may lead astray, it is not encouraged to enable cross-view communication too early. We perform two-stage training for CrosSCLR: 1) each view of the model is individually trained with Equation (1) without cross-view communication. 2) then the model can supply high-confidence knowledge, so the loss function is replaced with Equation (8), starting cross-view knowledge mining. + +# 3.3. Model Details + +View Generation of 3D Skeleton. Generally, 3D human skeleton sequence has $T$ frames with $V$ joints, and each joint has $C = 3$ coordinate feature, which can be noted as $x \in \mathbb{R}^{C \times T \times V}$ . Different from videos, the views [41, 42] of skeleton, e.g., joint, motion, bone, motion of bone, can be easily obtained, which is a natural advantage for skeleton-based representation learning. Motion is represented as the temporal displacement between frames: $x_{:,t+1,:} - x_{:,t,:}$ , and bone is the distance between two neighboring joints in the same frame: $x_{:,v_2} - x_{:,v_1}$ . For simplicity, we use three views: joint, motion and bone in experiments. + +Encoder $f$ . We adopt ST-GCN [57] as encoder, which is suitable for modeling graph-structure skeleton data by exploiting the spatial and temporal relations. After a series of ST-GCN blocks, the output feature $x_{out} \in \mathbb{R}^{c_{out} \times t_{out} \times V}$ is applied by an average pooling operation on spatial and temporal dimensions, obtaining final representation $h \in \mathbb{R}^{c_h}$ . + +# 4. Experiments + +# 4.1. Datasets + +NTU-RGB+D 60. NTU-RGB+D 60 (NTU-60) dataset [40] is a large-scale dataset of 3D joint coordinate sequences for skeleton-based action recognition, containing 56,578 skeleton sequences in 60 action categories. Each skeleton graph contains $V = 25$ body joints as nodes, and their 3D coordinates are initial features. There are two protocols [40] recommended. 1) Cross-Subject (xsub): training data and validation data are collected from different subjects. 2) Cross-View (xview): training data and validation data are collected from different camera views. + +NTU-RGB+D 120. NTU-RGB+D 120 (NTU-120) dataset [27] is an extended version of NTU-60, containing 113,945 skeleton sequences in 120 action categories. Two protocols [27] are recommended. 1) Cross-Subject (xsub): training data and validation data are collected from different subjects. 2) Cross-Setup (xset): training data and validation data are collected from different setup IDs. + +NTU-RGB+D 61-120. NTU-RGB+D 61-120 (NTU-61-120) dataset is a subset of NTU-120 dataset, containing 57,367 skeleton sequences in the last 60 action categories in NTU-120. The categories in NTU-61-120 do not intersect with those in NTU-60. This dataset is used as external dataset to evaluate the transfer capability of our method. + +# 4.2. Experimental Settings + +All the experiments are conducted on the PyTorch [38] framework. For data pre-processing, we remove the invalid frames of each skeleton sequence and then resize them to the length of 50 frames by linear interpolation. For optimization, we use SGD with momentum (0.9) and weight decay (0.0001). The mini-batch size is set to 128. + +Data Augmentation $\mathcal{T}$ . For skeleton sequence, we choose Shear [39] and Crop [43] as the augmentation strategy. + +Shear is a linear transformation on the spatial dimension. The transformation matrix is defined as: + +$$ +\mathbf {A} = \left[ \begin{array}{c c c} 1 & a _ {1 2} & a _ {1 3} \\ a _ {2 1} & 1 & a _ {2 3} \\ a _ {3 1} & a _ {3 2} & 1 \end{array} \right] \tag {9} +$$ + +where $a_{12}, a_{13}, a_{21}, a_{23}, a_{31}, a_{32}$ are shear factors randomly sampled from $[- \beta, \beta]$ . $\beta$ is the shear amplitude. The sequence $x$ is multiplied by the transformation matrix $\mathbf{A}$ on the channel dimension. Then, the human pose in 3D coordinate is inclined at a random angle. + +$Crop$ is an augmentation on the temporal dimension that symmetrically pads some frames to the sequence and then randomly crops it to the original length. The padding length is defined as $T / \gamma$ , $\gamma$ is noted as padding ratio. The padding operation uses the reflection of the original boundary. + +
MethodViewNTU-60 (%)
xsubxview
SkeletonCLRJoint68.376.4
SkeletonCLRMotion53.350.8
SkeletonCLRBone69.467.4
2s-SkeletonCLRJoint + Motion70.577.9
3s-SkeletonCLRJoint + Motion + Bone75.079.8
CrosCLRJoint72.979.9
CrosCLRMotion72.777.6
CrosCLRBone75.278.8
2s-CrosCLRJoint + Motion74.582.1
3s-CrosCLRJoint + Motion + Bone77.883.4
+ +Table 1. Comparisons of SkeletonCLR and CrosSCLR on each view and their ensembles. SkeletonCLR models are trained independently and "+" means the ensemble model. + +Unsupervised Pre-training. We generate three views of skeleton sequences, i.e., joint, motion and bone. For the encoder, we adopt ST-GCN [57], but the number of channels in each layer is reduced to $1/4$ of the original setting. For contrastive settings, we follow that in MOCOV2 [5] but reduce the size of memory bank $\mathbf{M}$ to $30k$ . For data augmentation, We set shear amplitude $\beta = 0.5$ and the padding ratio $\gamma = 6$ . The model is trained for 300 epochs with the learning rate 0.1 (multiplied by 0.1 at epoch 250). InfoNCE loss in Equation (1) is used in the first 150 epochs, and then replaced with $\mathcal{L}_{cross}$ in Equation (8) after 150-th epoch. We set $K = 1$ as the default in the knowledge mining mechanism. + +Linear Evaluation Protocol. The models are verified by linear evaluation for action recognition task, i.e., attaching the frozen encoder to a linear classifier (a fully-connected layer followed by a softmax layer), and then training the classifier supervisedly. We train models for 100 epochs with learning rate 3.0 (multiplied by 0.1 at epoch 80). + +Finetune Protocol. We append a linear classifier to the learnable encoder, and then train the whole model for the action recognition task, to compare it with fully-supervised methods. We train for 100 epochs with learning rate 0.1 (multiplied by 0.1 at epoch 80). + +# 4.3. Ablation Study + +All experiments in this section are conducted on NTU-60 dataset and follow the unsupervised pre-training and linear evaluation protocol in Section 4.2. + +Effectiveness of CrosSCLR. In Table 1, we separately pretrain SkeletonCLR and jointly pre-train CrosSCLR models on different skeleton views, e.g., joint, motion and bone. We adopt linear evaluation on each view of the models. Table 1 reports that 1) CrosSCLR improves the capability of each single SkeletonCLR model, e.g., CrosSCLR-joint (79.88) v.s SkeletonCLR-joint (76.44) on xview protocol; 2) + +![](images/4d60a38fb5ffcd81a3742714c8b7a04af8a41e94ed61e405a2c5e67672f49195.jpg) +Figure 4. The t-SNE visualization of embeddings at different epochs during pre-training. Embeddings from 10 categories are sampled and visualized with different colors. For CrosSCLR, $\mathcal{L}_{\mathrm{cross}}$ starts to be available at epoch 150, so its distribution has no difference from that of SkeletonCLR before epoch 150, shown in red boxes. More visual results are shown in Appendix. + +CrosSCLR bridges the performance gap of two views and jointly improves their accuracy, e.g., for SkeletonCLR, joint (76.44) $\nu.s$ motion (50.82) but for CrosSCLR, joint (79.88) $\nu.s$ motion (77.59); 3) CrosSCLR improves the multi-view ensemble results via cross-view training. In summary, the cross-view high-confidence knowledge does help the model extract more discriminating representations. + +Qualitative Results. We apply t-SNE [30] with fix settings to show the embedding distribution of SkeletonCLR and CrosSCLR on 150, 200, 250, 300 epochs during pretraining in Figure 4. Note that cross-view loss, Equation (8), is available only after epoch 150. From the visual results, we can draw a similar conclusion to that in Table 1. Embeddings of CrosSCLR are clustered more closely than that of SkeletonCLR, which is more discriminating. For CrosSCLR, the distributions of joint and motion are distinct at 150-th epoch but look very similar at 300-th epoch, i.e., consistent distribution. Especially, they both build a more "regular" space than SkeletonCLR, proving the effectiveness of CrosSCLR. + +Effects of Contrastive Setting top- $K$ . As hyper-parameter $K$ determines the number of mined samples, influencing the depth of knowledge exchange, we study how $K$ impacts the performance in cross-view learning. Table 2 shows that $K$ has a great influence on the performance and achieves the best result when $K = 1$ . However, a larger $K$ decreases the performance, because the not so confident information may lead the model astray in an unsupervised case. + +Contrastive Setting $N_{+}$ and Embedding Context $\mathcal{S}$ . We develop following models in Table 4 for comparison: 1) SkeletonCLR + $\mathcal{L}_{\mathrm{KM}}$ is a model with single-view knowledge mining. 2) CrosSCLR w/o. embedding context (EC) is the model only using the contrastive setting $N_{+}$ for cross-view learning, which ignores the embedding context/distribution, i.e., $S_{i}^{v} = 1, \forall i \in N$ in Equation (6). The results of SkeletonCLR + $\mathcal{L}_{\mathrm{KM}}$ show that KM improves + +
top-KNTU-60 (%)
xsubxview
070.577.4
174.582.1
373.779.9
572.479.2
773.078.6
1064.469.9
+ +Table 2. Results of pretraining 2s-CrosSCLR with various $K$ in knowledge miner $\Gamma$ + +
AugmentationNTU-60 (%)
Shear βCrop γxsubxview
0033.326.2
0.2062.767.7
0.5066.368.8
1.0062.066.8
0.5467.676.3
0.5668.376.4
0.5869.174.7
+ +Table 3. Ablation study on different data augmentations for Skeleton-CLR (joint). + +
MethodViews of Pre-trainingNTU-60 (%)
xsubxview
SkeletonCLRJoint68.376.4
SkeletonCLR + LKMJoint69.377.4
CrossSCLR w/o. ECJoint + Motion71.478.5
CrossSCLRJoint + Motion72.979.9
+ +Table 4. Ablation study on contrastive settings $N_{+}$ and embedding context (EC). The models are linear evaluated on only joint. + +the representation capability of SkeletonCLR. Additionally, CrosSCLR achieves worse performance without using embedding context (EC), proving the significance of similarity/distribution among samples. + +Effects of Augmentations. SkeletonCLR and CrosSCLR are based on contrastive learning, but the data augmentation strategy used on skeleton data is rarely explored, especially for the GCN encoder. We verify the effectiveness of data augmentation and the impact of different augmented intensities in skeleton-based contrastive learning by conducting experiments on SkeletonCLR, as shown in Table 3. It indicates the importance of data augmentation in SkeletonCLR. We choose $\beta = 0.5$ and $\gamma = 6$ as default settings according to the mean accuracy on xsub and xview protocols. + +# 4.4. Comparison + +We compare CrosSCLR with other methods under linear evaluation and finetune protocols. Since the backbone in many methods is an RNN-based model, e.g., GRU or LSTM, we additionally use LSTM (following the setting in [39]) as the encoder for a fair comparison, i.e., CrosSCLR (LSTM). + +Unsupervised Results on NTU-60. In Table 5, LongT GAN [65] adversarially trains the model by skeleton inpainting pretext task, $\mathrm{MS}^2\mathrm{L}$ [26] trains the model by multitask scheme, i.e., prediction, jiasaw puzzle and instance discrimination, AS-CAL [39] uses momentum LSTM encoder for contrastive learning with single-view skeleton sequence, P&C [47] trains a stronger encoder by weakening decoder, and SeBiReNet [34] constructs a human-like GRU + +
MethodEncoderClassifierNTU-60 (%)
xsubxview
LongT GAN [65]GRUFC39.148.1
MS2L [26]GRUGRU52.6-
AS-CAL [39]LSTMFC58.564.8
P&C [47]GRUKNN50.776.3
SeBiReNet [34]GRULSTM-79.7
3s-CrosSCLR (LSTM)LSTMFC62.869.2
3s-CrosSCLR (LSTM)LSTMLSTM70.479.9
3s-CrosSCLR‡ST-GCNFC72.880.7
3s-CrosSCLRST-GCNFC77.883.4
+ +Table 5. Unsupervised results on NTU-60. These methods are pretrained to learn encoder and then follow the linear evaluation protocol to learn the classifiers. “‡” indicates the model pre-trained on NTU-61-120. + +
MethodSupervisionNTU-120 (%)
xsubxset
Part-Aware LSTM [40]Supervised25.526.3
Soft RNN [15]Supervised36.344.9
TSRJI [2]Supervised67.962.8
ST-GCN [57]Supervised79.781.3
AS-CAL [39]Unsupervised48.649.2
3s-CrossCLR (LSTM)Unsupervised53.953.2
3s-CrossCLRUnsupervised67.966.7
+ +network to utilize view-independent and pose-independent feature. Our CrosSCLR exploits the multi-view knowledge by cross-view consistent knowledge mining. Taking a fully-connected layer (FC) as the classifier, our model outperforms other methods with the same classifier. With LSTM classifier and LSTM encoder, our model outperforms the above methods on both xsub and xview protocols. + +Results on NTU-120. As few unsupervised results are reported on NTU-120 dataset, we compare our method with unsupervised and supervised methods. As shown in Table 6, TSRJI [2] supervisedly utilizes attention LSTM, AS-CAL [39] adopts LSTM for skeleton modeling, and our method defeats the other unsupervised method and some of the supervised methods. + +Linear Classification with Fewer Labels. We follow the same protocol as that of $\mathrm{MS}^2\mathrm{L}$ [26], i.e., pre-training with all training data and then finetuning the classifier with only $1\%$ and $10\%$ randomly-selected labeled data respectively. As shown in Table 7, CrosSCLR achieves higher performance than other methods. + +Finetuned Results on NTU-60 and NTU-120. We first unsupervisedly pre-train our model and follow the finetune protocol for evaluation. For fair comparison, ST + +Table 6. Unsupervised results on NTU-120. We show and compare our method with unsupervised and supervised methods. + +
MethodLabel FractionNTU-60 (%)
xsubxview
LongT GAN [65]1%35.2-
MS²L [26]1%33.1-
3s-CrosCLR1%51.150.0
LongT GAN [65]10%62.0-
MS²L [26]10%65.2-
3s-CrosCLR10%74.477.8
+ +Table 7. Linear classification with fewer labels on NTU-60. + +
MethodNTU-60 (%)NTU-120 (%)
xsubxviewxsubxset
3s-ST-GCN* [57]85.291.477.277.1
3s-CrossCLR‡ (FT)85.692.0--
3s-CrossCLR (FT)86.292.580.580.4
+ +Table 8. Finetuned results on NTU-60 and NTU-120. ST-GCN* is the method reproduced by released code. “‡” indicates the model pre-trained on NTU-61-120. “FT” means finetune protocol. + +GCN* [57] in Table 8 has the same number of parameters as 3s-CrosSCLR (1/4 channel with three streams). It shows that the finetuned model, CrosSCLR (FT) outperforms the supervised ST-GCN on both NTU-60 and NTU-120 datasets, indicating the effectiveness of cross-view pretraining. + +Transfer Ability. We first pre-train CrosSCLR on NTU-61-120, and then transfer it to NTU-60 for linear evaluation, noted as $\mathrm{CrosSCLR}^{\ddagger}$ . The model trained under xsub protocol is transferred to the xsub protocol of NTU-60; the model trained under xset protocol is transferred to the xview protocol of NTU-60. In Table 5, it achieves better results than the other unsupervised methods, and its supervisedly finetuning result is higher than ST-GCN as shown in Table 8. + +# 5. Conclusion + +In this work, we propose a Cross-view Contrastive Learning framework for unsupervised 3D skeleton-based action representation to exploit multi-view high-confidence knowledge as complementary supervision. It integrates single-view contrastive learning with cross-view consistent knowledge mining modules which convey the contrastive settings and embedding context among views by high-confidence sample mining. Experiments show remarkable results of CrosSCLR for action recognition on NTU datasets. + +# Acknowledgement + +This work was supported by National Science Foundation of China (U20B2072, 61976137). This work was also supported by NSFC (U19B2035), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102). + +# References + +[1] Amor Ben Tanfous, Hassen Drira, and Boulbaba Ben Amor. Coding kendall's shape trajectories for 3d action recognition. In CVPR, pages 2840-2849, 2018. +[2] Carlos Caetano, François Brémond, and William Robson Schwartz. Skeleton image representation for 3d action recognition based on tree structure and reference joints. In SIB-GRAPI, pages 16-23. IEEE, 2019. +[3] Zhe Cao, Gines Hidalgo, Tomas Simon, Shih-En Wei, and Yaser Sheikh. Openpose: realtime multi-person 2d pose estimation using part affinity fields. TPAMI, 43(1):172-186, 2019. +[4] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. arXiv:2002.05709, 2020. +[5] Xinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He. Improved baselines with momentum contrastive learning. arXiv:2003.04297, 2020. +[6] Yong Du, Wei Wang, and Liang Wang. Hierarchical recurrent neural network for skeleton based action recognition. In CVPR, pages 1110-1118, 2015. +[7] Basura Fernando, Hakan Bilen, Efstratios Gavves, and Stephen Gould. Self-supervised video representation learning with odd-one-out networks. In CVPR, pages 3636-3645, 2017. +[8] Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by predicting image rotations. arXiv:1803.07728, 2018. +[9] Liang-Yan Gui, Yu-Xiong Wang, Xiaodan Liang, and José MF Moura. Adversarial geometry-aware human motion prediction. In ECCV, pages 786-803, 2018. +[10] Tengda Han, Weidi Xie, and Andrew Zisserman. Self-supervised co-training for video representation learning. NeurIPS, 33, 2020. +[11] Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. In CVPR, pages 9729-9738, 2020. +[12] Geoffrey Hinton, Oriol Vinyls, and Jeff Dean. Distilling the knowledge in a neural network. arXiv:1503.02531, 2015. +[13] Geoffrey E Hinton and Sam Roweis. Stochastic neighbor embedding. NIPS, 15:857-864, 2002. +[14] Sepp Hochreiter, Yoshua Bengio, Paolo Frasconi, Jürgen Schmidhuber, et al. Gradient flow in recurrent nets: the difficulty of learning long-term dependencies, 2001. +[15] Jian-Fang Hu, Wei-Shi Zheng, Lianyang Ma, Gang Wang, Jianhuang Lai, and Jianguo Zhang. Early action prediction by soft regression. TPAMI, 41(11):2568-2583, 2018. +[16] Will Kay, Joao Carreira, Karen Simonyan, Brian Zhang, Chloe Hillier, Sudheendra Vijayanarasimhan, Fabio Viola, Tim Green, Trevor Back, Paul Natev, et al. The kinetics human action video dataset. arXiv:1705.06950, 2017. +[17] Qiuhong Ke, Mohammed Bennamoun, Senjian An, Ferdous Sohel, and Farid Boussaid. A new representation of skeleton sequences for 3d action recognition. In CVPR, pages 3288-3297, 2017. + +[18] Prannay Khosla, Piotr Teterwak, Chen Wang, Aaron Sarna, Yonglong Tian, Phillip Isola, Aaron Maschinot, Ce Liu, and Dilip Krishnan. Supervised contrastive learning. arXiv:2004.11362, 2020. +[19] Dahun Kim, Donghyeon Cho, and In So Kweon. Self-supervised video representation learning with space-time cubic puzzles. In AAAI, volume 33, pages 8545-8552, 2019. +[20] Jogendra Nath Kundu, Maharshi Gor, Phani Krishna Uppala, and Venkatesh Babu Radhakrishnan. Unsupervised feature learning of human actions as trajectories in pose embedding manifold. In WACV, pages 1459-1467. IEEE, 2019. +[21] Hsin-Ying Lee, Jia-Bin Huang, Maneesh Singh, and Ming-Hsuan Yang. Unsupervised representation learning by sorting sequences. In ICCV, pages 667-676, 2017. +[22] Chao Li, Qiaoyong Zhong, Di Xie, and Shiliang Pu. Skeleton-based action recognition with convolutional neural networks. In ICME Workshops, pages 597-600. IEEE, 2017. +[23] Junnan Li, Yongkang Wong, Qi Zhao, and Mohan S Kankanhalli. Unsupervised learning of view-invariant action representations. In NeurIPS, pages 1254-1264, 2018. +[24] Maosen Li, Siheng Chen, Xu Chen, Ya Zhang, Yanfeng Wang, and Qi Tian. Actional-structural graph convolutional networks for skeleton-based action recognition. In CVPR, pages 3595–3603, 2019. +[25] Duohan Liang, Guoliang Fan, Guangfeng Lin, Wanjun Chen, Xiaorong Pan, and Hong Zhu. Three-stream convolutional neural network with multi-task and ensemble learning for 3d action recognition. In CVPR Workshops, 2019. +[26] Lilang Lin, Sijie Song, Wenhan Yang, and Jiaying Liu. Ms21: Multi-task self-supervised learning for skeleton based action recognition. In ACMMM, pages 2490-2498, 2020. +[27] Jun Liu, Amir Shahroudy, Mauricio Lisboa Perez, Gang Wang, Ling-Yu Duan, and Alex Kot Chichung. Ntu rgb+d 120: A large-scale benchmark for 3d human activity understanding. TPAMI, 2019. +[28] Ziyu Liu, Hongwen Zhang, Zhenghao Chen, Zhiyong Wang, and Wanli Ouyang. Disentangling and unifying graph convolutions for skeleton-based action recognition. In CVPR, pages 143-152, 2020. +[29] Zelun Luo, Boya Peng, De-An Huang, Alexandre Alahi, and Li Fei-Fei. Unsupervised learning of long-term motion dynamics for videos. In CVPR, pages 2203–2212, 2017. +[30] Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579-2605, 2008. +[31] Julieta Martinez, Michael J Black, and Javier Romero. On human motion prediction using recurrent neural networks. In CVPR, pages 2891-2900, 2017. +[32] Ishan Misra, C Lawrence Zitnick, and Martial Hebert. Shuffle and learn: unsupervised learning using temporal order verification. In ECCV, pages 527-544. Springer, 2016. +[33] Bingbing Ni, Gang Wang, and Pierre Moulin. Rgbd-hudaact: A color-depth video database for human daily activity recognition. In ICCV Workshops, pages 1147-1153. IEEE, 2011. +[34] Qiang Nie, Ziwei Liu, and Yunhui Liu. Unsupervised 3d human pose representation with viewpoint and pose disentanglement. ECCV, 2020. + +[35] Mehdi Noroozi and Paolo Favaro. Unsupervised learning of visual representations by solving jigsaw puzzles. In ECCV, pages 69-84. Springer, 2016. +[36] Mehdi Noroozi, Ananth Vinjimoor, Paolo Favaro, and Hamed Pirsiavash. Boosting self-supervised learning via knowledge transfer. In CVPR, pages 9359-9367, 2018. +[37] Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. arXiv:1807.03748, 2018. +[38] Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. NeurIPS Workshops, 2017. +[39] Haocong Rao, Shihao Xu, Xiping Hu, Jun Cheng, and Bin Hu. Augmented skeleton based contrastive action learning with momentum lstm for unsupervised action recognition. arXiv:2008.00188, 2020. +[40] Amir Shahroudy, Jun Liu, Tian-Tsong Ng, and Gang Wang. Ntu rgb+ d: A large scale dataset for 3d human activity analysis. In CVPR, pages 1010-1019, 2016. +[41] Lei Shi, Yifan Zhang, Jian Cheng, and Hanqing Lu. Skeleton-based action recognition with directed graph neural networks. In CVPR, pages 7912-7921, 2019. +[42] Lei Shi, Yifan Zhang, Jian Cheng, and Hanqing Lu. Two-stream adaptive graph convolutional networks for skeleton-based action recognition. In CVPR, pages 12026-12035, 2019. +[43] Connor Shorten and Taghi M Khoshgoftaar. A survey on image data augmentation for deep learning. Journal of Big Data, 6(1):60, 2019. +[44] Chenyang Si, Wentao Chen, Wei Wang, Liang Wang, and Tieniu Tan. An attention enhanced graph convolutional LSTM network for skeleton-based action recognition. In CVPR, pages 1227-1236, 2019. +[45] Sijie Song, Cuiling Lan, Junliang Xing, Wenjun Zeng, and Jiaying Liu. Spatio-temporal attention-based LSTM networks for 3d action recognition and detection. TIP, 27(7):3459-3471, 2018. +[46] Nitish Srivastava, Elman Mansimov, and Ruslan Salakhudinov. Unsupervised learning of video representations using lstms. In ICML, pages 843-852, 2015. +[47] Kun Su, Xiulong Liu, and Eli Shlizerman. Predict & cluster: Unsupervised skeleton based action recognition. In CVPR, pages 9631-9640, 2020. +[48] Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. arXiv:1906.05849, 2019. +[49] Raviteja Vemulapalli, Felipe Arrate, and Rama Chellappa. Human action recognition by representing 3d skeletons as points in a lie group. In CVPR, pages 588-595, 2014. +[50] Raviteja Vemulapalli and Rama Chellapa. Rolling rotations for recognizing human actions from 3d skeletal data. In CVPR, pages 4471-4479, 2016. +[51] Jiangliu Wang, Jianbo Jiao, Linchao Bao, Shengfeng He, Yunhui Liu, and Wei Liu. Self-supervised spatio-temporal representation learning for videos by predicting motion and appearance statistics. In CVPR, pages 4006-4015, 2019. + +[52] Jiang Wang, Zicheng Liu, Ying Wu, and Junsong Yuan. Mining actionlet ensemble for action recognition with depth cameras. In CVPR, pages 1290-1297. IEEE, 2012. +[53] Minsi Wang, Bingbing Ni, and Xiaokang Yang. Learning multi-view interactional skeleton graph for action recognition. TPAMI, 2020. +[54] Chen Wei, Lingxi Xie, Xutong Ren, Yingda Xia, Chi Su, Jiaying Liu, Qi Tian, and Alan L Yuille. Iterative reorganization with weak spatial constraints: Solving arbitrary jigsaw puzzles for unsupervised representation learning. In CVPR, pages 1910-1919, 2019. +[55] Zhirong Wu, Yuanjun Xiong, Stella X Yu, and Dahua Lin. Unsupervised feature learning via non-parametric instance discrimination. In CVPR, pages 3733-3742, 2018. +[56] Jingwei Xu, Zhenbo Yu, Bingbing Ni, Jiancheng Yang, Xiaokang Yang, and Wenjun Zhang. Deep kinematics analysis for monocular 3d human pose estimation. In CVPR, pages 899-908, 2020. +[57] Sijie Yan, Yuanjun Xiong, and Dahua Lin. Spatial temporal graph convolutional networks for skeleton-based action recognition. In AAAI, 2018. +[58] Mihai Zanfir, Marius Leordeanu, and Cristian Sminchisescu. The moving pose: An efficient 3d kinematics descriptor for low-latency action recognition and detection. In ICCV, pages 2752-2759, 2013. +[59] Xiaohua Zhai, Avital Oliver, Alexander Kolesnikov, and Lucas Beyer. S4l: Self-supervised semi-supervised learning. In ICCV, pages 1476-1485, 2019. +[60] Pengfei Zhang, Cuiling Lan, Junliang Xing, Wenjun Zeng, Jianru Xue, and Nanning Zheng. View adaptive recurrent neural networks for high performance human action recognition from skeleton data. In ICCV, pages 2117-2126, 2017. +[61] Pengfei Zhang, Cuiling Lan, Junliang Xing, Wenjun Zeng, Jianru Xue, and Nanning Zheng. View adaptive neural networks for high performance skeleton-based human action recognition. TPAMI, 41(8):1963-1978, 2019. +[62] Pengfei Zhang, Cuiling Lan, Wenjun Zeng, Junliang Xing, Jianru Xue, and Nanning Zheng. Semantics-guided neural networks for efficient skeleton-based human action recognition. In CVPR, pages 1112-1121, 2020. +[63] Richard Zhang, Phillip Isola, and Alexei A Efros. Colorful image colorization. In ECCV, pages 649-666. Springer, 2016. +[64] Xikun Zhang, Chang Xu, and Dacheng Tao. Context aware graph convolution for skeleton-based action recognition. In CVPR, pages 14333-14342, 2020. +[65] Nenggan Zheng, Jun Wen, Risheng Liu, Liangqu Long, Jianhua Dai, and Zhefeng Gong. Unsupervised representation learning with long-term dynamics for skeleton based action recognition. 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Guibas $^{1}$ $^{1}$ Stanford University $^{2}$ Tsinghua University $^{3}$ NVIDIA + +# Abstract + +3D object detection is an important yet demanding task that heavily relies on difficult to obtain 3D annotations. To reduce the required amount of supervision, we propose 3D IoUMatch, a novel semi-supervised method for 3D object detection applicable to both indoor and outdoor scenes. We leverage a teacher-student mutual learning framework to propagate information from the labeled to the unlabeled train set in the form of pseudo-labels. However, due to the high task complexity, we observe that the pseudo-labels suffer from significant noise and are thus not directly usable. To that end, we introduce a confidence-based filtering mechanism, inspired by FixMatch. We set confidence thresholds based upon the predicted objectness and class probability to filter low-quality pseudo-labels. While effective, we observe that these two measures do not sufficiently capture localization quality. We therefore propose to use the estimated 3D IoU as a localization metric and set category-aware self-adjusted thresholds to filter poorly localized proposals. We adopt VoteNet as our backbone detector on indoor datasets while we use PV-RCNN on the autonomous driving dataset, KITTI. Our method consistently improves state-of-the-art methods on both ScanNet and SUN-RGBD benchmarks by significant margins under all label ratios (including fully labeled setting). For example, when training using only $10\%$ labeled data on ScanNet, 3D IoUMatch achieves 7.7 absolute improvement on mAP@0.25 and 8.5 absolute improvement on mAP@0.5 upon the prior art. On KITTI, we are the first to demonstrate semi-supervised 3D object detection and our method surpasses a fully supervised baseline from $1.8\%$ to $7.6\%$ under different label ratio and categories. + +# 1. Introduction + +Object detection is a key task in 3D scene understanding. It provides a concise representation of raw sensor measurements in the form of semantically meaningful 3D bounding boxes. This low-dimensional representation can + +already serve numerous applications in autonomous driving and AR/VR, as well as in robot navigation and manipulation. As a result, in recent years there has been a surge of interest in developing improved object detection pipelines and indeed current state-of-the-art methods show impressive performance. Yet, much of their success is attributed to the availability of large datasets of 3D scenes that are carefully annotated. While rapid advances in sensor technology facilitate the collection of 3D scenes at scale, annotating them remains the main bottleneck. This calls for detection methods that can leverage both labeled and unlabeled data at train time. + +In this work, we aim to address this requirement by proposing a novel semi-supervised 3D object detection method which we dub 3DIoUMatch. As a generally applicable method, 3DIoUMatch can be applied to both indoor scene datasets, i.e. ScanNet[4] and SUN-RGBD[28], and outdoor datasets, i.e. KITTI[7]. We adopt popular point-based object detectors, VoteNet [18] and PV-RCNN [24], as our backbone object detection networks for the indoor and outdoor scenes, correspondingly. To provide supervision to the unlabeled scenes, we leverage a teacher-student mutual learning framework [29] and use the bounding box predictions from the teacher network as pseudo-labels to supervise the student network on unlabeled data. However, unlike most pseudo-label techniques that were designed for classification, in the highly complex (joint regression and classification) task of object detection, we observe that the pseudo-labels suffer from significant noise, and using them directly is suboptimal. + +Inspired by FixMatch [26], the state-of-the-art semi-supervised learning (SSL) method for 2D image classification that proposed confidence-based filtering to improve pseudo-label quality, we adopt a pseudo-label filtering mechanism for 3D object detection by setting thresholds on predicted class probabilities (and objectness scores for VoteNet), so as to filter out teacher proposals with potentially erroneous semantic labels or ones not belong to foreground. While effective, these criteria alone are not sufficient to capture localization quality, and the pseudo-labels may still have large errors in the bounding box parameters. + +To that end, we further propose to leverage estimated IoU (intersection over union) as a localization quality measure for pseudo-label filtering. IoU estimation was first proposed in the context of 2D object detection as a localization confidence in the pioneering work IoU-Net [12], where estimated IoU was proven successful in replacement of class confidence for test-time Non-Maximal Suppression (NMS). To the best of our knowledge, leveraging IoU estimation for pseudo-label filtering is a novel idea for SSL on both 2D and 3D object detection. Equipping the detectors with a 3D IoU estimation module, we are able to filter out poorly localized pseudo-labels and leverage estimated IoU for both train-time and test-time NMS. + +A key challenge when filtering based on IoU estimation is how to properly set the threshold. Unlike objectness and class confidence for which high threshold values (e.g. 0.9) work well, 3D IoU is more sensitive to small errors. Setting the threshold too high would reduce the number of pseudo-labels to very few, from which little could be learned. To balance between quality and coverage, we propose a two-stage filtering process: first, using a relatively low IoU threshold; then, an IoU-guided class-aware Lower-Half Suppression (LHS) that removes only half of the highly-overlapping boxes with low predicted IoU. Our proposed LHS thus naturally sets a threshold that is both dynamic and class-aware. Our experiments show that LHS outperforms IoU-guided NMS, which suppresses all but the top one during semi-supervised training. + +Our method consistently improves upon the previous state-of-the-art method, SESS [34], on both ScanNet and SUN-RGBD benchmarks by significant margins. When using only $10\%$ labeled data on ScanNet, 3DIoUMatch outperforms SESS by 7.7 absolute improvement on mAP@0.25 and by 8.5 absolute improvement on mAP@0.5. When using $5\%$ labeled data on SUN-RGBD, 3DIoUMatch outperforms SESS by 4.8 absolute improvement on mAP@0.25 and by 8.0 absolute improvement on mAP@0.5. On KITTI, we are the first to demonstrate semi-supervised 3D object detection work and surpass fully-supervised baseline by large margins under all label ratios. + +Our main contributions can be summarized as follows: + +1. We propose a novel semi-supervised method for 3D object detection in point clouds based on pseudo-label propagation along with a carefully designed filtering mechanism. +2. For the first time, we leverage predicted 3D IoU as a localization confidence score for pseudo-label filtering, and further propose IoU-guided Lower-Half Suppression for robust pseudo-label dedduplication. This idea is generally applicable and can be coupled to different 3D detectors on both indoor and outdoor scenes. +3. We achieve markedly improved performance over the previous state-of-the-art semi-supervised 3D object + +detection methods on the two major indoor object detection benchmarks, ScanNet and SUN-RGBD, under low label ratios and fully labeled setting. As the first semi-supervised 3D object detection work on KITTI, we also achieve significant improvements compared to fully supervised method. + +# 2. Related Works + +Semi-Supervised Learning (SSL) Many of the recent SSL methods [2, 31, 1] leverage consistency regularization, first proposed in [23, 13], which enforces the model to predict consistently across label-preserving data augmentation of different intensity. Borrowing the concept from Mean Teacher [29], the model with frozen weight can be viewed as the teacher model, otherwise student model. Some methods [2], following Mean Teacher, make the teacher model as the EMA of the student model for further regularization. Pseudo labeling [15] is another popular class of SSL method which can also be treated as a kind of consistency regularization, as one output of the unlabeled data is enforced to be consistent with the other (the pseudo-labels) by being supervised with the other. To improve the quality of pseudo-labels, FixMatch [26], a state-of-the-art SSL work on image classification, has shown that the student network can improve significantly by setting a classification confidence threshold $\tau_{cls}$ and filtering out low-confidence predictions from the teacher. With the filtered pseudo-labels, the student model only gets supervised on the unlabeled data whose pseudo-labels are kept. Another key factor to the success of these methods is strong data augmentation. It has been shown crucial to many SSL works [23, 13, 31]. Recent works [1, 26] proposed to adopt even more powerful augmentation such as RandAugment [3] and Cutout [5]. + +Semi-Supervised Object Detection Since the beginning of the deep learning era, tremendous progress has been made in 2D object detection, e.g. region-based detectors [9, 8, 22] and single-stage detectors [16, 21, 30]. Similarly in 3D object detection, a number of deep learning methods have been proposed for different 3D data modalities, e.g. RGBD-based detectors [19, 17], point-based detectors [33, 25, 14, 18], voxel-based detectors [35], point-voxel-based detectors [24], etc. + +Despite the great progress in both 2D and 3D object detection, most works focused on a fully-supervised setting. A few works [10, 6] have proposed to leverage unlabeled data or weakly-annotated data for 2D object detection. Under a standard SSL setting as we follow, CSD [11] proposed a consistency regularization method to enforce the consistency between predictions from an image and its flipped version. STAC [27] adopts a two-stage scheme for training Faster R-CNN [22]: in the first stage it pre-trains a detector with labeled data only and then predicts the pseudo labels + +![](images/8e1fcfdd105e84af007918763abefe498a946b23172a6faf28842549e5efaa60.jpg) +Figure 1. 3D IoUMatch pipeline at semi-supervised training stage. We adopt as our backbone an extended version of VoteNet with an additional 3D IoU estimation module. For SSL, we utilize a teacher-student mutual learning framework, composed of a learnable student taking strongly augmented input data and an EMA teacher taking weakly augmented input samples. On labeled data, the student network is supervisedly trained. On unlabeled data, the student network takes pseudo-labels from its EMA teacher. To improve the quality of pseudo-label, we adopt a confidence-based filtering mechanism that filters out predictions that fail to pass all thresholds on class probability, objectness, and 3D IoU. We further use IoU-guided Lower-Half Suppression to remove the duplicated predictions. Using the filtered pseudo-labels, we selectively supervise the student predictions that are around the bounding boxes in the pseudo-labels. + +for the unlabeled data; in the second stage, STAC leverages asymmetric data augmentation and the pseudo-label filtering mechanism to remove object proposals with low confidence. Note that the pseudo-labels are only generated once at the end of the first stage. + +The only prior work on semi-supervised point-based 3D object detection, is SESS [34]. SESS is built upon VoteNet [18] and adopts a two-stage training scheme. It leverages a mutual learning framework composed of an EMA teacher and a student, uses asymmetric data augmentation, and enforces three kinds of consistency losses between the teacher and student outputs. Although SESS brings noticeable improvements upon a vanilla VoteNet when using only a small portion of labeled data, we find their consistency regularization suboptimal, as it is uniformly enforced on all the student and teacher predictions. In this work, we instead propose to apply confidence-based filtering to improve the quality of pseudo-labels from the teacher predictions and we are the first (in both 2D and 3D object detection) to introduce IoU estimation for localization filtering. + +IoU Estimation IoU estimation was first proposed in a 2D object detection work IoU-Net [12], which proposed an IoU head that runs in parallel to bounding box refinement and is differentiable w.r.t. bounding box parameters. IoU-Net adds an IoU estimation head to several off-the-shelf 2D detectors and uses IoU estimation instead of classification confidence to guide NMS, which improves the performance consistently over different backbones. Thanks to its differentiability, IoU-Net can perform IoU optimization on bounding box parameters for iterative refinement, which + +further brings noticeable performance improvement. + +For 3D object detection, STD [32] follows IoU-Net to add a simple IoU estimation branch parallel with the box estimation branch and to guide NMS with IoU estimation. PV-RCNN [24] devises a similar 3D IoU estimation module and use it at IoU-guided NMS stage. These two modules, unfortunately, are not suitable for IoU optimization as the features fed to the IoU estimation branch are not differentiable w.r.t. the bounding box size. Since the original VoteNet is not equipped with an IoU module, we devise a differentiable point-cloud-based 3D IoU estimation module is simple yet effective that can support the IoU optimization. + +# 3. Method + +In this section, we describe our solution in detail. We first formulate our problem in 3.1 and then summarize the two object detection backbones, PV-RCNN and VoteNet, in 3.2. We use VoteNet as an example to illustrate our proposed 3D IoUMatch pipeline in 3.3. We further explain how we use the estimated 3D IoU for pseudo-label filtering and dedduplication in 3.4. Finally, we illustrate how we leverage the pseudo-labels for supervision in 3.5. + +# 3.1. Problem Definition + +Given a 3D point cloud representation of a scene $\pmb{x} \in \mathbb{R}^{N \times 3}$ containing a set of objects $O = \{o^{(j)}\}$ , we aim at detecting the amodal oriented 3D bounding boxes of all objects in $O$ , along with their semantic class labels. In particular, we are interested in accomplishing this task under challenging conditions of limited supervision where we have access to a (small) set of labeled scenes $\{\pmb{x}_i^l, \pmb{y}_i^l\}_{i=1}^{N_l}$ and + +a set of unlabeled scenes $\{\pmb{x}_i^u\}_{i=1}^{N_u}$ , where $N_l$ and $N_u$ are the number of labeled and unlabeled scenes, respectively. For a labeled scene $\pmb{x}$ , the label $\pmb{y}$ comprises bounding box parameters $\{\pmb{b}^{(j)}\}$ and semantic class labels $\{q^{(j)}\}$ of all ground truth objects $\{o^{(j)}\}$ . + +# 3.2. IoU-aware 3D Object Detection + +We experiment our SSL method on two 3D detectors, VoteNet [18] and PV-RCNN [24]. VoteNet is a single-stage indoor point cloud detector while PV-RCNN is a two-stage outdoor point cloud detector. They both take point clouds only for inputs and output a list of bounding boxes after Non-Maximum Suppression (NMS) for each scene, which contain the prediction of center, size, orientation and semantic class. However, their architecture are very different partly due to the great discrepancy between indoor and outdoor scenes. + +Indoor scene detector: VoteNet VoteNet [18] is built upon PointNet++ [20] backbone, and first processes the input point cloud $\{x_{i}\}_{i = 1}^{N}$ to generate a sub-sampled set of $M < N$ seed points enriched with high-dimensional features $\{[x_i;f_i]\in \mathbb{R}^{3 + C}\}_{i = 1}^M$ . Next, each seed point votes for the center of the object it belongs to, and the votes are grouped into $K$ clusters. Finally, each of the K vote clusters is aggregated to make a prediction of a 3D bounding box parameters $\pmb{b}^{(k)}$ , a corresponding objectness score $s_k = \mathrm{P}(\pmb{b}^{(k)}$ is an object), and a probability distribution $\{p_{cls}\}$ over $L$ possible semantic classes. The bounding box parameters $\pmb{b}$ are its center location $\mathbf{c}\in \mathbb{R}^3$ , scale $\mathbf{d}\in \mathbb{R}^3$ , and orientation $\theta$ around the upright axis. + +At train time, VoteNet jointly minimizes a weighted combination of the following target losses: vote coordinate regression, objectness score binary classification, box center regression, bin classification and residual regression for heading angle, scale regression, and category classification. At test time, VoteNet applies Non-Maximum Suppression (NMS) based on objectness score to remove duplicated bounding boxes. Here, we instead rely on a 3D IoU estimation module designed for VoteNet. For more details, refer to the supplementary materials. + +Outdoor scene detector: PV-RCNN PV-RCNN[24] is a high-performance and efficient LiDAR point cloud detector that deeply integrates both 3D voxel CNNs and PointNet++ style set abstraction to learn more discriminative point cloud features. Specifically, PV-RCNN first passes the 3D scene through a novel voxel set abstraction module based on sparse 3D CNN to get a set of keypoints with representative scene features. Then RoI grid pooling is then applied to the keypoints to abstract proposal-specific features into RoI grid points. The RoI grid points containing rich context information are finally used to accurately estimate bounding box parameters. + +PV-RCNN itself incorporates an IoU-estimation module + +which can predict the IoU of each bounding box and use it to guide the sorting of the boxes. + +# 3.3. 3DIOUMatch for SSL on 3D object detection + +We take VoteNet as our example and our method with PV-RCNN is similar. With the incorporation of 3D IoU module into VoteNet, we construct an IoU-aware VoteNet for SSL on 3D object detection. Our proposed solution is comprised of two training stages: a pre-training stage, where we train our IoU-aware VoteNet on the labeled data, followed by an SSL stage where the entire data is utilized by pseudo-labeling the unlabeled scenes. + +Pre-training. We start by training our IoU-aware VoteNet in a supervised manner, using the labeled set $\{\pmb{x}_i^l,\pmb{y}_i^l\}_{i = 1}^{N_l}$ . The training loss is a sum over the original VoteNet losses $L_{\mathrm{votenet}}$ and 3D IoU loss $L_{\mathrm{IoU}}$ . Once converged, we clone the network to create a pair of student and teacher networks. + +Semi-supervised training through a teacher-student framework. We follow a teacher-student mutual learning framework [29] and train our networks on both labeled $\{\pmb{x}_i^l,\pmb{y}_i^l\}_{i = 1}^{N_l}$ and unlabeled data $\{\pmb{x}_i^u\}_{i = 1}^{N_u}$ . Each training batch contains a mixture of $\{\pmb{x}_i^l\}_{i = 1}^{B_l}$ labeled samples and $\{\pmb{x}_i^u\}_{i = 1}^{B_u}$ unlabeled samples. + +For labeled samples, we supervise the student network using ground truth supervisions (as done in the pre-training stage) whereas for unlabeled samples, the student networks is supervised using pseudo-labels $\{\tilde{\pmb{y}}_i^u\}_{i = 1}^{N_u}$ generated from the teacher network. The final loss is formed as: + +$$ +L = L _ {l} \left(\left\{\boldsymbol {x} _ {i} ^ {l} \right\} _ {i = 1} ^ {N _ {l}}, \left\{\boldsymbol {y} _ {i} ^ {l} \right\} _ {i = 1} ^ {N _ {l}}\right) + \lambda_ {u} L _ {u} \left(\left\{\boldsymbol {x} _ {i} ^ {u} \right\} _ {i = 1} ^ {N _ {u}}, \left\{\tilde {\boldsymbol {y}} _ {i} ^ {u} \right\} _ {i = 1} ^ {N _ {u}}\right) +$$ + +where $\lambda_{u}$ is the unsupervised loss weight. + +To succeed in semi-supervised learning, it is crucial for the teacher network to generate high-quality pseudo-labels and maintain a reliable performance margin over the student network throughout the training. As commonly used in SSL literature, e.g. Mean Teacher [29] and SESS [34], we adopt an EMA teacher. We further leverage asymmetric data augmentation and pseudo-label filtering (see Sec.3.4). + +To be in a position of advantage, the teacher network takes input data with weak augmentation only while the student network uses stronger data augmentation. We share the same data augmentation strategy with SESS. The input point clouds to our teacher network are augmented only by random sub-sampling while the inputs to the student network further undergo a set of stochastic transformation $\mathcal{T}$ , including random flip, random rotation around the upright axis, and a random uniform scaling. + +# 3.4. Pseudo-Label Filtering and Dedduplication + +In the teacher-student framework, the performance gap between the teacher and the student is usually quite + +marginal given that these two models are just different by EMA on weight and data augmentation strength. Hence, it is not always true that the teacher prediction is more accurate than the student's on a specific training sample. On unlabeled data, the student model will only benefit from the pseudo-labels that are more accurate than its predictions. Therefore we should filter out low-quality predictions from the teacher model and only supervise the student model with the rest of the teacher model predictions. + +Jointly filtering based on class, objectness, localization confidences For VoteNet, we propose to set an objectness threshold $\tau_{obj}$ and filter out bounding box predictions with objectness score $s < \tau_{obj}$ . We further propose to set a classification confidence threshold $\tau_{cls}$ for filtering out predictions that are likely to contain a wrong class label. + +Note that none of these two confidence measures capture the accuracy of bounding box parameter predictions. We propose to predict a 3D IoU for each predicted bounding box, use the 3D IoU estimation as a localization confidence, and set a localization threshold $\tau_{\mathrm{IoU}}$ to filter out poorly localized predictions. Formally, we remove all the predictions that fail to satisfy all three confidence thresholds, i.e. $s > \tau_{obj}$ , $\max(p_{cls}) > \tau_{cls}$ , and $v > \tau_{\mathrm{IoU}}$ . + +IoU-guided lower-half suppression for dedduplication After the confidence-based filtering, there is still a lot of duplicated bounding box predictions that may introduce harmful noise to our pseudo-labels. NMS is a standard process in object detection for duplicate removal before evaluation, which takes a set of highly overlapped bounding box predictions that share the same class prediction, ranks them according to a confidence score and removes all but the top-1 prediction. STAC [27] applies class confidence based NMS to teacher predictions during pseudo-label generation. + +The default NMS used in VoteNet is based on objectness confidence. Given that objectness score doesn't capture the localization quality, a train-time IoU-guided NMS will naturally perform better (see Table.2), where we use the product of predicted IoU and predicted objectness as the ranking metric. However, using the top one selected by IoU-guided NMS can still be suboptimal, since the predicted IoU will inevitably carry some errors. We argue that different from the test time scenario, pseudo-labels do not need to be fully deduplicated. Imagine this situation: if a bounding box predicted by the student is $0.2m$ to the left of its corresponding ground truth, it is a foreground object and will get bounding box supervision in VoteNet. However, if unfortunately the pseudo-label survives after non-maximal suppression is to the right of the ground truth more than $0.1m$ , this predicted bounding box may lose supervision and be treated as a background box. This example shows that strict non-maximal suppression can lead to a smaller number of student model predictions that can receive super- + +vision. Since we cannot know the best pseudo label among a bunch of highly-overlapped ones, it's fine to be less strict. To this end, we propose a novel Lower-Half Suppression, or in short, LHS, that only discards half of the proposals with lower predicted IoU. We argue that since LHS suppresses bounding boxes sharing the same class label, this suppression can be seen as a second-step class-aware self-adjusted filtering, which sets dynamic thresholds among the overlapping bounding boxes to keep the ones with higher confidence and hence find a better balance between pseudolabel quality and the amount of supervision. We also use the product of predicted IoU and predicted objectness as the confidence metric. + +Final-step pseudo-label processing After the filtering and IoU-guided LHS, we now have high-quality predictions $\{\hat{y}_T^u\}_{k=1}^{K'}$ from the teacher network, where $K'$ is the number of bounding boxes remains. Given that the student model inputs go through a stronger augmentation including an additional geometric transformation $\mathcal{T}$ , in synchronize with the student model inputs, the bounding box parameters of the pseudo-labels need to go through the same transformation $\mathcal{T}$ , namely $\tilde{\boldsymbol{b}}^u = \mathcal{T}(\hat{\boldsymbol{b}}_T^u)$ . We further take convert the predicted class probability distribution $\hat{p}_T^u$ into semantic class label via $\tilde{q}^u = \max(\hat{p}_T^u)$ . Now we obtain the filtered pseudo-labels $\tilde{y} = \{\tilde{\boldsymbol{b}}^u, \tilde{q}^u\}_{k=1}^{K'}$ . + +# 3.5. Selective Supervision using Pseudo-Labels + +For our generated pseudo-labels, there is no guarantee that the labels can cover all the ground truth objects from $O$ due to the filtering and potentially inaccurate teacher predictions. Given the incompleteness of our filtered pseudolabels, we are relatively confident about the bounding boxes in this set but student predictions far away from all of our pseudo-labels are not necessarily negative. Our experiments show that supervising objectness on unlabeled data using the pseudo-labels seriously hurts the performance. For similar reasons, we do not supervise vote loss, which is a unique element in VoteNet and not shown in other detectors. For more analysis and experimental proof for this, we refer the readers to the supplementary materials. In this case, we will only supervise the bounding boxes in the vicinity of the pseudo bounding boxes and aim to improve their bounding box quality. More specifically, we stick to the way how VoteNet select foreground objects for bounding box parameter supervision: we supervise bounding box parameters and class for a prediction only if the vote that generates this prediction is within $0.3\mathrm{m}$ of any bounding box in the pseudo-labels. For this set of pseudo-foreground predictions, we adopt the same way that VoteNet establishes association and enforce original VoteNet losses except for objectness loss and vote loss. + +
DatasetModel5%10%20%100%
mAP @0.25mAP @0.5mAP @0.25mAP @0.5mAP @0.25mAP @0.5mAP @0.25mAP @0.5
ScanNetVoteNet27.9±0.510.8±0.636.9±1.618.2±1.046.9±1.927.5±1.257.836.0
SESS reported\\39.7±0.918.647.9±0.426.962.138.8
SESS32.0±0.714.4±0.739.5±1.819.8±1.349.6±1.129.0±1.061.339.0
Ours40.0±0.922.5±0.547.2±0.428.3±1.552.8±1.235.2±1.162.942.1
Abs. improve.+8.0+8.1+7.7+8.5+3.2+6.2+1.6+3.1
SUN-RGBDVoteNet29.9±1.510.5±0.538.9±0.817.2±1.345.7±0.622.5±0.858.033.4
SESS reported\\42.9±1.014.447.9±0.520.661.137.3
SESS34.2±2.013.1±1.042.1±1.120.9±0.347.1±0.724.5±1.260.538.1
Ours39.0±1.921.1±1.745.5±1.528.8±0.749.7±0.430.9±0.261.541.3
Abs. improve.+4.8+8.0+3.4+7.9+2.6+6.4+1.0+3.2
+ +Table 1. Comparison with VoteNet and SESS on ScanNet val set and SUN RGB-D val set under different ratios of labeled data. We report the mAP@0.25 and mAP@0.5 as mean±standard deviation across 3 runs under different random data splits. Due to the randomness of the data splits and our better pre-training protocol, SESS results provided by us are higher than those reported in the paper on mAP@0.5, and the mAP@0.25 results differ a little (the only difference is the pre-trained weights and data splits). The final improvement is the absolute improvement of our method over SESS results provided by us. Following SESS, we also report the results with $100\%$ labeled data, where we simply make a copy of the full dataset as unlabeled data and train our method. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Metrics + +Indoor Datasets: ScanNet and SUNRGB-D We evaluate our VoteNet-based 3D IoUMatch on two major indoor datasets, ScanNet [4] and SUN RGB-D [28]. ScanNet is an indoor scene dataset consisting of 1513 reconstructed meshes, among which 1201 are training samples and the rest are validation samples. SUN RGB-D contains 10335 RGB-D images of indoor scenes which are split into 5285 training samples and 5050 validation samples. For both datasets, we follow [18, 34] for pre-processing data and labels to train our method and we report mAP@0.25 (mean average precision with 3D IoU threshold 0.25) and mAP@0.5 in the following experiments. + +Outdoor Dataset: KITTI As for our PV-RCNN-based 3DIoUMatch, we use KITTI for evaluation. KITTI [7] is a very popular dataset for autonomous driving which consists of fine annotations for 3D detection. There are 7481 outdoor scenes for training and 7518 for testing, and the training samples are generally divided into a train split of 3712 samples and a validation split of 3769 samples. We follow [24] for data pre-processing and report the mAP with 40 recall positions, with a rotated IoU threshold 0.7, 0.5, 0.5 for the three classes, car, pedestrian, and cyclist, respectively. + +# 4.2. Experiments on Indoor Scene Datasets + +For experiments on indoor datasets, i.e., ScanNet and SUNRGB-D, we use IoU-aware VoteNet as our backbone detector. + +# 4.2.1 Result Comparison + +Table 1 shows the results of our method compared to SESS and VoteNet under different ratios of labeled data on ScanNet and SUN RGB-D, respectively. The results illustrate that, with our effective train-time filtering and test-time improvement leveraging IoU estimation, we are able to significantly outperform current state-of-the-art, SESS, under all labeled ratio settings. With $5\%$ labeled data, our method outperforms SESS by 8.1 and 8.0 on mAP@0.5 on ScanNet and SUN RGB-D, respectively. Note that our method gains more improvement on mAP@0.5, thanks to the high quality of pseudo labels and the IoU guidance for test-time NMS. + +# 4.2.2 Ablation Study + +Filtering and Dedduplication Mechanism. We study the effect of each component of the filtering and dedduplication mechanism. In Table 2, the second row shows the results of naive pseudo labeling, which takes all predictions from the teacher model for supervision. Expectedly the results are not satisfying, only a little higher than VoteNet. Simply applying the dual filtering of classification and objectness confidence gives significant improvement, as the filtering picks out the teacher model proposals that are very likely to be close to true objects and have the correct class. The conventional objectness-based NMS in VoteNet, however, fails to improve further, since the remaining proposals already have high objectness scores and the objectness-based NMS is not capable of picking the ones with higher localization accuracy. + +As shown in the fifth and sixth row, after we introduce IoU during train time, IoU filtering and train-time IoU + +
Obj&Cls FilterIoU FilterTrain-time SuppressionTest-time SuppressionTest-time IoU opt.ScanNet 10%SUN-RGBD 5%
mAP@0.25mAP@0.5mAP@0.25mAP@0.5
Obj-NMS38.419.832.912.5
✓Obj-NMS44.524.736.917.5
✓Obj-NMSObj-NMS44.225.237.117.4
✓✓IoU-NMSObj-NMS45.926.837.418.7
✓✓IoU-LHSObj-NMS46.526.937.918.5
✓✓IoU-LHSIoU-NMS47.028.238.820.8
✓✓IoU-LHSIoU-NMS✓47.228.339.021.1
+ +Table 2. Effects of the different components, including train-time filtering and dedduplication, and test-time improvements. + +guided NMS contribute to better performance under both settings. Our proposed IoU-guided LHS improves over IoU guided NMS on mAP@0.25, since LHS finds a better balance between quality and coverage. With better filtering and dedduplication leveraging IoU estimation during train time, we gain 2.3 and 1.7 absolute improvement over the without-IoU version on mAP@0.25 and mAP@0.5 respectively on ScanNet $10\%$ . This verifies that considering localization confidence is important for getting high-quality pseudo labels. With test-time improvements, our method gains in total 3.0 and 3.1 absolute improvement respectively. + +We set 0.9 for both classification and objectness confidence threshold following STAC [27] and investigate the effect of different IoU thresholds on ScanNet $10\%$ , as shown in Figure 2. The performance (with test-time improvements) is higher than the without-IoU baseline by large margins when $\tau_{IoU} \leq 0.5$ . Note that the performance peaks at $\tau_{IoU} = 0.25$ for $\mathrm{mAP}@0.25$ while peaking at 0.5 for $\mathrm{mAP}@0.5$ , simply because $\mathrm{mAP}@0.5$ prefers a stronger filtering on localization quality. When $\tau_{IoU} > 0.5$ , further increasing $\tau_{IoU}$ may lead to a drastic drop in pseudo-label coverage and hence is detrimental to the performance. + +Test-time IoU-guided NMS and IoU optimization. We then evaluate the improvement brought by using IoU estimations at test time. The last two rows in Table 2 shows that IoU-guided NMS and IoU optimization improves the performance further. + +# 4.2.3 Result Analysis + +In this section, we examine how our 3DIoUMatch works during training on ScanNet $10\%$ . The upper two curves in Figure 3 show that as the training goes, the performance on unlabeled data and test data increases conformably, which indicates the increasing quality of pseudo-labels. We also show how the coverage of the pseudo-labels changes on the unlabeled data over the training. Here coverage at a certain threshold simply means the class-agnostic recall, measuring the percentage of ground truth objects that can find a pseudo-label with an IoU larger than the threshold. + +![](images/19781b34a65f4636af3e3836441c2bb494aa3e154754d6602e7b2f433ac1b319.jpg) +Figure 2. 3DIOUMatch results with different IoU thresholds on ScanNet $10\%$ . + +![](images/33dcbdb6eb8bea8b718413319c9ed24420e8851b72c6595358cb64a086afe4f3.jpg) + +![](images/e997108eb4d3cff6edb1b3f81b950d240cdecaa8fee7f93a35467c486b2620e5.jpg) + +![](images/e9e7c0ee7e6f39f494190a21626c83e7b94761a3a9eb10fd5ccfa570bcea93bb.jpg) + +![](images/d7492784c31a3b7928a710a6fa9f67425611e4fb0cb0f7d6f4ce0a7241385b5e.jpg) +Figure 3. The performance improvements and pseudo-label coverage over the semi-supervised learning stage on ScanNet $10\%$ . + +![](images/2c7cf4c46185b6e1983bd6ee04e8d5f6c712b68ee7cfa321eacf6f9df401abbf.jpg) + +As we can see from the lower two curves in Figure 3: at the beginning, the coverage of the pseudo-labels is relatively low due to the strict filtering mechanism; as the semi-supervised learning goes on, the improving detection performance leads to a higher passing rate of the filter and hence a higher coverage of the pseudo-labels, which in return fuels SSL; by the end of training, the coverage at 0.25 and at 0.5 both increase by about $10\%$ . + +# 4.2.4 Implementation Details + +Training For the pre-training stage, we train with a batch size of 8 and follow the same data augmentation of + +SESS [34]. We then use those pre-trained weights to initialize the student and teacher networks. For the SSL stage, we construct each batch by taking 4 labeled samples and 8 unlabeled samples, with the same data augmentation. The weights of different loss terms are the same as VoteNet and we set $\lambda_{u} = 2$ . The student network is trained for 1000 epochs (the labeled data is traversed in one epoch), optimized by an ADAM optimizer with an initial learning rate of 0.002, and the learning rate is decayed by 0.3, 0.3, 0.1, 0.1 at the $400^{\mathrm{th}}$ , $600^{\mathrm{th}}$ , $800^{\mathrm{th}}$ and $900^{\mathrm{th}}$ epoch, respectively. The number of generated 3D proposals is 128. We use $k = 3$ , $D = 4$ for the IoU module. The three thresholds are set to be $\tau_{obj} = 0.9$ , $\tau_{cls} = 0.9$ , $\tau_{IoU} = 0.25$ . For more details, we refer the readers to the supplementary materials. + +Inference We forward the input to the student network to generate proposals. We first apply IoU optimization to refine box parameters following IoU-Net [12], followed by an IoU-guided NMS with a 3D IoU threshold of 0.25. + +# 4.3. Experiments on KITTI + +For experiments on the KITTI dataset, we adopt PV-RCNN[24] as our backbone. PV-RCNN itself comes with a 3D IoU module, allowing to use it in our semi-supervised learning pipeline without modifying its architecture. + +# 4.3.1 Results + +We evaluate our method on KITTI validation set. Table 3 demonstrates significant and consistent improvement across all categories with $1\%$ , $2\%$ , and $100\%$ labeled data, compared to supervised training only. Similar to our experiments on indoor scene datasets, here the $100\%$ labeled data setting means making a copy of the full dataset as unlabeled data and train the network using our devised semi-supervised pipeline. With $1\%$ labeled data, our method outperforms the labeled-data-only baseline by $6.6 \mathrm{mAP} @ 0.5$ on pedestrian, which is the most challenging class. + +# 4.3.2 Ablation Study + +We conduct ablation studies on KITTI with $1\%$ labeled data. Table 4 shows our improvements compared with a pseudolabel baseline and filtering based on class confidence only. The results validate the effectiveness of our IoU-based localization confidence filtering. + +# 4.3.3 Implementation Differences with VoteNet + +In KITTI, we only care about three classes, car, pedestrian, and cyclist, which differ a lot in the difficulty to detect. Instead of using LHS, we follow PV-RCNN to set different IoU thresholds for each individual class, i.e., $\tau_{car} = 0.8$ , $\tau_{ped} = \tau_{cyc} = 0.4$ . We selectively supervise the predictions that meet the foreground bar in PV-RCNN according to our + +
1%2%100%
CarPed.Cyc.CarPed.Cyc.CarPed.Cyc.
PVR.77.347.862.980.447.163.583.057.973.1
Ours80.754.467.382.054.669.584.860.274.9
+ +Table 3. 3D detection results on KITTI val set with different labeled ratios. The results are for moderate difficulty level evaluated by the mAP with 40 recall positions, with a rotated IoU threshold 0.7, 0.5, 0.5 for the three classes, respectively. + +
CarPedestrianCyclist
EasyMod.HardEasyMod.HardEasyMod.Hard
PVR.89.677.374.154.947.842.380.462.958.7
naive psd.-lb.91.178.876.158.951.345.482.665.560.8
cls. thres. only90.879.776.863.255.049.784.965.061.2
Ours91.680.778.163.354.449.586.567.362.8
+ +Table 4. Ablation study on KITTI $1\%$ labeled data. Same evaluation metric as Table 1. + +pseudo-labels. In contrast to VoteNet, PV-RCNN is a two-stage detector containing an RPN. Bounding box objectness (or foreground probability) has been predicted in the RPN and used to pick top 100 proposals to forward to the RoI head. We therefore only additionally filter according to classification confidence with the threshold $\tau_{cls} = 0.2$ . Due to the non-differentiability of the IoU module of PV-RCNN, we also do not apply IoU optimization. + +We also adopt a two-stage training scheme for our PV-RCNN-based 3D IoUMatch. We use an unlabeled weight $\lambda_{u} = 2$ and only supervise anchor classification and bounding box regression in PV-RCNN on unlabeled data. Please refer to the supplementary materials for more details. + +# 5. Conclusion + +In this paper, we propose 3D IoUMatch, a novel semi-supervised 3D object detection method leveraging IoU estimation. Built upon a teacher-student mutual learning framework, we leverage asymmetric data augmentation and pseudo-label filtering and dedduplication to facilitate the student learning from the EMA teacher. With our IoU estimation module, we make filtering and dedduplication aware of localization confidence and apply test-time IoU-guided NMS and IoU optimization, leading to further improvement. Experiment results on the ScanNet, SUN-RGBD, and KITTI datasets validate the effectiveness of our method: we achieve significant gain over the previous state-of-the-art methods and baselines under all settings. Our idea of leveraging IoU estimation for semi-supervised learning is generally applicable to different kinds of 3D object detectors and can be extended to 2D detectors as future works. + +Acknowledgement: This research is supported by a grant from the SAIL-Toyota Center for AI Research, NSF grant CHS-1528025, a Vannevar Bush Faculty fellowship, a TUM/IAS Hans Fischer Senior Fellowship, and gifts from the Adobe, Amazon AWS, and Snap corporations. + +# References + +[1] David Berthelot, Nicholas Carlini, Ekin D Cubuk, Alex Kurakin, Kihyuk Sohn, Han Zhang, and Colin Raffel. Remixmatch: Semi-supervised learning with distribution alignment and augmentation anchoring. arXiv preprint arXiv:1911.09785, 2019. +[2] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: A holistic approach to semi-supervised learning. In Advances in Neural Information Processing Systems, pages 5049-5059, 2019. +[3] Ekin D Cubuk, Barret Zoph, Jonathon Shlens, and Quoc V Le. Randaugment: Practical automated data augmentation with a reduced search space. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 702-703, 2020. +[4] Angela Dai, Angel X Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In CVPR, 2017. +[5] Terrance DeVries and Graham W Taylor. Improved regularization of convolutional neural networks with cutout. arXiv preprint arXiv:1708.04552, 2017. +[6] Jiyang Gao, Jiang Wang, Shengyang Dai, Li-Jia Li, and Ram Nevatia. Note-rcnn: Noise tolerant ensemble rcnn for semi-supervised object detection. In Proceedings of the IEEE international conference on computer vision, pages 9508–9517, 2019. +[7] Andreas Geiger, Philip Lenz, Christoph Stiller, and Raquel Urtasun. Vision meets robotics: The kitti dataset. The International Journal of Robotics Research, 32(11):1231-1237, 2013. +[8] Ross Girshick. Fast r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 1440-1448, 2015. +[9] Ross Girshick, Jeff Donahue, Trevor Darrell, and Jitendra Malik. Rich feature hierarchies for accurate object detection and semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 580-587, 2014. +[10] Judy Hoffman, Sergio Guadarrama, Eric S Tzeng, Ronghang Hu, Jeff Donahue, Ross Girshick, Trevor Darrell, and Kate Saenko. Lsda: Large scale detection through adaptation. In Advances in Neural Information Processing Systems, pages 3536-3544, 2014. +[11] Jisoo Jeong, Seungeui Lee, Jeesoo Kim, and Nojun Kwak. Consistency-based semi-supervised learning for object detection. In Advances in neural information processing systems, pages 10759-10768, 2019. +[12] Borui Jiang, Ruixuan Luo, Jiayuan Mao, Tete Xiao, and Yun-ting Jiang. Acquisition of localization confidence for accurate object detection. In Proceedings of the European Conference on Computer Vision (ECCV), pages 784–799, 2018. +[13] Samuli Laine and Timo Aila. Temporal ensembling for semi-supervised learning. arXiv preprint arXiv:1610.02242, 2016. + +[14] Alex H Lang, Sourabh Vora, Holger Caesar, Lubing Zhou, Jiong Yang, and Oscar Beijbom. Pointpillars: Fast encoders for object detection from point clouds. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 12697-12705, 2019. +[15] Dong-Hyun Lee. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. In Workshop on challenges in representation learning, ICML, volume 3, 2013. +[16] Wei Liu, Dragomir Anguelov, Dumitru Erhan, Christian Szegedy, Scott Reed, Cheng-Yang Fu, and Alexander C Berg. Ssd: Single shot multibox detector. In European conference on computer vision, pages 21-37. Springer, 2016. +[17] Charles R. Qi, Xinlei Chen, Or Litany, and Leonidas J. Guibas. Imvotenet: Boosting 3d object detection in point clouds with image votes, 2020. +[18] Charles R Qi, Or Litany, Kaiming He, and Leonidas J Guibas. Deep hough voting for 3d object detection in point clouds. In Proceedings of the IEEE International Conference on Computer Vision, pages 9277-9286, 2019. +[19] Charles R Qi, Wei Liu, Chenxia Wu, Hao Su, and Leonidas J Guibas. Frustum pointnets for 3d object detection from rgb-d data. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 918-927, 2018. +[20] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. In Advances in neural information processing systems, pages 5099-5108, 2017. +[21] Joseph Redmon, Santosh Divvala, Ross Girshick, and Ali Farhadi. You only look once: Unified, real-time object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 779-788, 2016. +[22] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. In Advances in neural information processing systems, pages 91-99, 2015. +[23] Mehdi Sajjadi, Mehran Javanmardi, and Tolga Tasdizen. Regularization with stochastic transformations and perturbations for deep semi-supervised learning. In Advances in neural information processing systems, pages 1163-1171, 2016. +[24] Shaoshuai Shi, Chaoxu Guo, Li Jiang, Zhe Wang, Jianping Shi, Xiaogang Wang, and Hongsheng Li. Pv-rcnn: Pointvoxel feature set abstraction for 3d object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10529–10538, 2020. +[25] Shaoshuai Shi, Xiaogang Wang, and Hongsheng Li. Poincaré: 3d object proposal generation and detection from point cloud. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 770-779, 2019. +[26] Kihyuk Sohn, David Berthelot, Chun-Liang Li, Zizhao Zhang, Nicholas Carlini, Ekin D Cubuk, Alex Kurakin, Han Zhang, and Colin Raffel. Fixmatch: Simplifying semi-supervised learning with consistency and confidence. arXiv preprint arXiv:2001.07685, 2020. +[27] Kihyuk Sohn, Zizhao Zhang, Chun-Liang Li, Han Zhang, Chen-Yu Lee, and Tomas Pfister. A simple semi-supervised learning framework for object detection. arXiv preprint arXiv:2005.04757, 2020. + +[28] Shuran Song, Samuel P Lichtenberg, and Jianxiong Xiao. Sun rgb-d: A rgb-d scene understanding benchmark suite. In CVPR, 2015. +[29] Antti Tarvainen and Harri Valpola. Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results. In Advances in neural information processing systems, pages 1195–1204, 2017. +[30] Zhi Tian, Chunhua Shen, Hao Chen, and Tong He. Fcos: Fully convolutional one-stage object detection. In Proceedings of the IEEE international conference on computer vision, pages 9627-9636, 2019. +[31] Qizhe Xie, Zihang Dai, Eduard Hovy, Minh-Thang Luong, and Quoc V Le. Unsupervised data augmentation for consistency training. arXiv preprint arXiv:1904.12848, 2019. +[32] Zetong Yang, Yanan Sun, Shu Liu, Xiaoyong Shen, and Jiaya Jia. Std: Sparse-to-dense 3d object detector for point cloud. In Proceedings of the IEEE International Conference on Computer Vision, pages 1951-1960, 2019. +[33] Li Yi, Wang Zhao, He Wang, Minhyuk Sung, and Leonidas J Guibas. Gspn: Generative shape proposal network for 3d instance segmentation in point cloud. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3947-3956, 2019. +[34] Na Zhao, Tat-Seng Chua, and Gim Hee Lee. Sess: Self-ensembling semi-supervised 3d object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11079–11087, 2020. +[35] Yin Zhou and Oncel Tuzel. Voxelnet: End-to-end learning for point cloud based 3d object detection. 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However, many existing methods focus on using single frames to perform 3D detection, and do not fully utilize information from multiple frames. In this paper, we present 3D-MAN: a 3D multi-frame attention network that effectively aggregates features from multiple perspectives and achieves state-of-the-art performance on Waymo Open Dataset. 3D-MAN first uses a novel fast single-frame detector to produce box proposals. The box proposals and their corresponding feature maps are then stored in a memory bank. We design a multi-view alignment and aggregation module, using attention networks, to extract and aggregate the temporal features stored in the memory bank. This effectively combines the features coming from different perspectives of the scene. We demonstrate the effectiveness of our approach on the large-scale complex Waymo Open Dataset, achieving state-of-the-art results compared to published single-frame and multi-frame methods. + +# 1. Introduction + +3D object detection is an important problem in computer vision as it is widely used in applications, such as autonomous driving and robotics. Autonomous driving platforms require precise 3D detection to build an accurate representation of the world, which is in turn used in downstream models that make critical driving decisions. + +LiDAR provides a high-resolution accurate 3D view of the world. However, at any point of time, the LiDAR sensor collects only a single perspective of the scene. It is often the case that the LiDAR points detected on an observed object correspond to only a partial view of it. Detecting these partially visible instances is an ill-posed problem because there exist multiple reasonable predictions (shown as red and blue boxes in the upper row of Figure 1). These potential ambiguous scenarios can be a bottleneck for single-frame 3D detectors (Table 1). + +![](images/9d178e82171fd84217b1cabd66f389a5dcc2f873b326ef194806c3b6fb9c081d.jpg) +Figure 1. Upper row: Potential detections given LiDAR from a single frame demonstrating ambiguity between many reasonable predictions. Lower row: After merging the points aligned across 4 frames, there is more certainty for the correct box prediction. + +
IoU threshold0.30.50.7
AP (%)94.7288.9763.27
+ +Table 1. We vary the intersection-over-union (IoU) threshold for considering a predicted box correctly matched to a ground-truth box, and measure the performance of the PointPillars model on the Waymo Open Dataset's validation set. A lower IoU threshold corresponds to allowing less accurate boxes to match. This shows that improving the box localization could significantly improve model performance. + +In the autonomous driving scenario, as the vehicle progresses, the sensors pick up multiple views of the world, making it possible to resolve the aforementioned localization ambiguity. Multiple frames across time can provide different perspectives of an observed object instance. An effective multi-frame detection method should be able to extract relevant features from each frame and aggregate them, so as to obtain a representation that combines multiple perspectives (Figure 1). Research in 3D multi-frame detection has been limited due to a lack of available datasets with well-calibrated multi-frame data. Fortunately, recently released large-scale 3D sequence datasets (NuScenes [2], Waymo Open Dataset [23]) have made such data available. + +A straight-forward approach to fusing multi-frame point + +
ModelStationary (%)Slow (%)Medium (%)Fast (%)
1-frame60.0166.6465.0271.90
4-frames62.467.3966.6877.99
8-frames63.767.9866.2972.30
+ +Table 2. Velocity breakdowns of vehicle AP metrics for PointPillars models using point concatenation. For the 8-frame model, we find that its benefits come from slow-moving vehicles. Fast-moving objects no longer benefit from a large number of frames since the LiDAR points are no longer aligned across the frames. + +clouds is to use point concatenation, which simply combines points across different frames together [2]. The combined point cloud is then used as input to a single-frame detector. This approach works well for static and slow-moving objects since the limited movement implies that the LiDAR points will be mostly aligned across the frames. However, when objects are fast-moving or when longer time horizons are considered, this approach may not be as effective since the LiDAR points are no longer aligned (Table 2). + +As an alternative to point concatenation, Fast-and-furious [14] attempts to fuse information across frames by concatenating at a feature map level. However, this still runs into the same challenge with misaligned feature maps for fast-moving objects and longer time horizons. Recent approaches [10, 34] propose using recurrent layers such as Conv-LSTM or Conv-GRU to aggregate the information across frames. It turns out that these recurrent approaches are often computationally expensive. + +Our Approach. We propose 3D-MAN: a 3D multi-frame attention network that is able to extract relevant features from past frames and aggregate them effectively. 3D-MAN has three components: (i) a fast single-frame detector, (ii) a memory bank, and (iii) a multi-view alignment and aggregation module. + +The fast single-frame detector (FSD) is an anchor-free one-stage detector with a novel learning strategy. We show that a max-pooling based non-maximum suppression (NMS) algorithm together with a novel Hungarian-matching based loss is an effective method to generate high-quality proposals at real-time speeds. These proposals and the last feature map from FSD are then fed into a memory bank. The memory bank stores both predicted proposals and feature maps in previous frames so as to maintain different perspectives for each instance across frames. + +The stored proposals and features in the memory bank are finally fused together through the multi-view alignment and aggregation module (MVAA), which produces fused multi-view features for target proposals that are used to regress bounding boxes for final predictions. MVAA has two stages: a multi-view alignment stage followed by a multi-view aggregation stage. The alignment stage works on each stored frame independently; it uses target proposals as queries into a stored frame to extract relevant fea + +tures. The aggregation stage then merges across frames for each target proposal independently. This can be viewed as a form of factorization over the attention across proposals and frames. + +We evaluate our model on large-scale Waymo Open Dataset [23]. Experimental results demonstrate that our method outperforms published state-of-the-art single-frame methods and multi-frame methods. Our primary contributions are listed below. + +# Key Contributions. + +- We propose 3D-MAN: a 3D multi-frame attention network for object detection. We demonstrate that our method achieves state-of-the-art performance on the Waymo Open Dataset [23] and provide thorough ablation studies. +- We introduce a novel training strategy for a fast single-frame detector method that uses max-pooling to perform non-maximum suppression and a variant of Hungarian matching to compute a detection loss. +- We design an efficient multi-view alignment and aggregation module to extract and aggregate relevant features from multiple frames in a memory bank. This module produces features containing information from multiple perspectives that perform well for classification and bounding box regression. + +# 2. Related Work + +3D Single-frame Object Detection. Current 3D object detectors can be categorized into three approaches: voxel-based methods, point-based methods, and their combination. First, voxel-based methods transform via voxelization a set of unordered points into a fixed-size 2D feature map, on which convolutional neural networks (CNN) can be applied to generate detection results. Traditional approaches for voxel feature extraction rely on hand-crafted statistical quantities or binary encoding [25, 29], while recent works show that machine-learned features demonstrate favorable performance [37, 12, 28, 36, 20, 26]. Second, point-based methods [32, 19, 31, 15, 33] address detection problems by directly extracting features based on the point cloud, without an explicit discretization step. Finally, recent works have combined methods from both voxel-based and point-based feature representations [18] by using the voxel-based methods to generate proposals and the point-based methods to refine them. + +2D Multi-frame Object Detection. 2D multi-frame object detection has been widely explored compared to 3D counterparts. 2D detection methods primarily focus on aligning objects in a target frame using motion and appearance + +![](images/14e7d0b2346760860f1f64d29ab47062330bb3455f3745e977da3ecd995b54c0.jpg) +Figure 2. Framework for 3D-MAN: 3D multi-frame attention network. Given the point cloud for a target frame $t$ , a fast single-frame detector first generates box proposals. These proposals (box parameters) with the feature map (last layer of the backbone network) are inserted into a memory bank that stores proposals and features for the last $n$ frames. We use a proposal feature generation module to extract proposal features for each stored frame. Each small rectangle box denotes a proposal and its associated features extracted in different frames. The multi-view alignment and aggregation module performs attention across proposal features from the memory bank, using the target frame as queries to extract features for classification and regression. "MP-NMS" and "CA" represent MaxPoolNMS and cross-attention respectively. During training, we use classification and regression losses applied to the FSD proposals ( $L_{fsd}$ ), the final outputs of the MVAA network ( $L_{mvaa}$ ), and the outputs of the alignment stage ( $L_{cv}$ , an auxiliary cross-view loss). + +features from previous frames. Relational modules with self-attention layers [9] are prevalent among these methods [6, 4, 27, 5, 21]. They usually take as input a target frame and multiple reference frames, from which proposals are generated per frame. Relation modules are applied to aggregate temporal features for more robust object detection. Most approaches use self-attention across all proposals in all previous frames. In contrast, our method factorizes the attention layer to first operate independently across frames (alignment stage), and then independently across proposals (aggregation stage). + +3D Multi-frame Object Detection. A straight-forward approach to multi-frame detection is to concatenate the points from different frames together [2]. This has been demonstrated on the NuScenes dataset (improvement of $21.9\%$ to $28.8\%$ mAP [2]), and we also observe improvements in our experiments (Table 2). However, as we increase the number of frames concatenated, the improvement diminishes since the LiDAR points are less likely to be aligned across longer time horizons (Table 2). Fast-and-furious [14] side steps aligning the points by instead concatenating the intermediate features maps. However, this approach may still result in misalignment across the feature maps for fast-moving objects and longer time horizons. Recent approaches [10, 34] show further performance improvement by applying Conv-LSTM or Conv-GRU to fuse multi-frame information. However, the use of a single memory state that gets updated creates a potential bottleneck, and the high resolution of the feature maps make these methods computa + +tionally expensive. + +# 3. 3D-MAN Framework + +The 3D-MAN framework (Figure 2) consists of 3 components: (i) a fast single-frame detector (FSD) for producing proposals given input point clouds, (ii) a memory bank to store features from different frames and (iii) a multi-view alignment and aggregation module (MVAA) for combining information across frames to generate final predictions. + +# 3.1. Fast Single-frame Detector + +Anchor-free Point Pillars. We base our single-frame detector on the PointPillars architecture [12] with dynamic voxelization [36]. We start by dividing the 3D space into equally distributed pillars which are voxels of infinite height. Each point in the point cloud is assigned to a single pillar. Each pillar is then featurized using a PointNet [17] producing a 2D feature representation for the entire scene, which is subsequently processed through a CNN backbone. Each location of the final layer of the network produces a prediction for a bounding box relative to the corresponding pillar center. We regress the location residuals, bounding box sizes, and orientation. A binning approach is used for predicting orientation which first classifies the orientation into one bin followed by regression of the residual from the corresponding bin center [16, 19]. + +Non-maximum suppression (NMS) is often used to postprocess the detections produced by the last layer of the net + +work for redundancy removal. It first outputs the highest scoring box and then suppresses all overlapping boxes with that box, repeating this process until all boxes are processed. However, the sequential nature of this algorithm makes it slow to run in practice when there is a large number of predictions. We use a variant of NMS that leverages max-pooling to speed up this process. MaxPoolNMS [35] uses the max pooling operation to find local peaks on the objectness score map. The local peaks are kept as predictions, while all other locations are suppressed. This process is fast and highly parallelizable. We find that this approach can be up to $6 \times$ faster $^1$ than regular NMS when dealing with about 200k predictions. + +Hungarian Matching. MaxPoolNMS is usually performed using the classification score as the ranking signal to indicate that one box is better than another. However, the classification score is a proxy metric: ideally, we want to have the highest scoring box to be the best localized box. The ideal score map should have a single peak which corresponds to the best localized box. We propose using the Hungarian matching algorithm [3, 22] to produce such a score map. + +Given a set of bounding box predictions and a set of ground-truth boxes, we compute the IoU score for each pair of them. By applying the Hungarian matching algorithm to this matrix $^2$ of pair-wise scores, we can obtain a single match for each ground-truth box to a predicted box that maximizes the overall matching score. For each ground-truth box, we treat the matched predicted box as positive, and all unmatched boxes as negative. In this way, the model is encouraged to predict only one positive box per ground-truth box such that the box predicted corresponds to the highest IoU-scoring box. + +It turns out that there are two challenges when using the Hungarian matching algorithm. First, the Hungarian matching algorithm is of order $O(n^{3})$ and can be slow if there are a large number of predictions. Therefore, we choose to perform the Hungarian matching based-loss only after the MaxPoolNMS step. This ensures that only a few predictions remain, and enables the matching algorithm to complete quickly. + +Second, the model can end up in a bad local minima by only predicting boxes which are far away from any ground-truth box (e.g., predicting boxes in locations where there are no points in the input point clouds). Consequently, these ground-truth boxes do not overlap at all with their matched prediction boxes. As a result, the model does not get any meaningful learning signals from these matches and is not able to converge to a good solution. To address this issue, + +![](images/1383f68bb9a206b5652f1cacbbd75c5e060de50077cfd268d5c4f51ea50ff42c.jpg) +Figure 3. Illustration of rotated ROI feature extraction [13]. We first identify key points in each proposal box and then extract features using bilinear interpolation. Averaging pooling is further used to summarize each box into a single feature vector. Note that while the figure denotes key points over $3 \times 2$ locations, we use $7 \times 7$ for vehicles and $3 \times 3$ for pedestrians. + +we post-process the matches to reassign ground-truth boxes that have no overlap with their matched prediction box. We assign them instead to their closest pillar in the feature map, which may not be one retained by MaxPoolNMS. This encourages the model to avoid invalid assignments and converge well. + +# 3.2. Memory Bank + +Memory Bank. We use a memory bank to store the proposals and feature maps extracted by the FSD for the last $n$ frames. When proposals and features from a new frame are added to the bank, those from the oldest frame are discarded. + +Proposal Feature Generation. To obtain features from multiple perspectives, we propose to generate proposal features for each stored frame in the memory bank as well as the target frame. We find that it is useful to use all stored proposals regardless of which frame the proposal comes from to extract features from every stored frame. This allows the model to increase its recall since an object may be missed by FSD in a single frame because of occlusion or partial observation. + +For each proposal, we extract its features using a rotated ROI feature extraction approach (Figure 3) [13]. Given a proposal, we identify $K \times K \times 1$ equally distributed key points with respect to the proposal box. For each key point, we compute a feature by bilinear interpolation of its value in the feature map. Finally, we use average pooling across all the $K \times K \times 1$ key points to obtain a single feature vector for the proposal. It is worth noting that this feature extraction method can be performed without correcting the entire LiDAR point cloud for ego-motion of the autonomous vehicle. This facilitates deployment in a production autonomous driving system. + +![](images/a5a1f4bc9bb650535de35495477ffee76f8a5e203497e28a897e0ebcd3bbf1b9.jpg) +Figure 4. Cross-attention network in the multi-view alignment module. $F_{s}$ and $B_{s}$ represent features and box parameters of proposals in a stored frame while $F_{t}$ and $B_{t}$ are those for the target frame. We use $s$ and $t$ to denote the indices of the stored frame and target frame respectively. $N$ and $C$ stand for the number of proposals and channels. "Box residuals" produces a pairwise $N \times N \times 7$ tensor that encodes the differences in all pairs of boxes, using the same approach that is used to compute residuals for ground-truth boxes from anchor boxes [12]. $V_{s}$ is the output of the cross-attention network, such that each input target box has one associated output feature vector with the corresponding stored frame. + +The proposal features generated for the target frame will be used next in the MVAA module as the query features for the cross-attention networks, while proposal features for stored frames will be treated as keys and values. + +# 3.3. Multi-view Alignment and Aggregation + +These proposal features are then sent to the multi-view alignment and aggregation module (MVAA) to be extracted and aggregated. The alignment module is applied independently for each stored frame (attention is across boxes, performed separately for each frame), while the aggregation module is applied independently for each box (attention is across time). One can view this as a factorized form of attention. + +Multi-view Alignment. Given a new frame's proposal, the multi-view alignment module is responsible for extracting its relevant information in each previous frame separately (Figure 2, MVAA-Alignment). To achieve this goal, the alignment stage has to figure out how to relate the identities of the proposals in the new frame to those in the stored frames. A naive approach could use nearest neighbor matching or maximum IoU overlap. However, when an instance is fast-moving or close to any other instance, there will often be ambiguity in the appropriate assignment. Furthermore, the naive approach does not learn interactions be + +tween the new proposal and other objects in previous frames that could provide contextual information. + +We propose using a cross-attention network (Figure 4) to learn how to relate the new frame proposals to those of stored frames. This network could potentially learn to align the proposal identities and also model interactions across objects. Specifically, we apply projection layers to encode the new frame proposal features $F_{t}$ as well as stored proposal features $F_{s}$ so as to compute projected queries $F_{q}$ , keys $F_{k}$ and values $F_{v}$ . These are used to compute an attention matrix. We further provide temporal and spatial information to the attention matrix through encoding the relative frame index and box residuals between all pairs of the query and stored boxes. The cross-attention network is applied between the target frame and each stored frame independently with shared parameters, generating a feature vector for each target proposal $(V_{s})$ from each stored frame. + +Cross-view Loss. The alignment stage of MVAA is designed to extract features from each stored frame that are most relevant to each target proposal. To encourage the extracted features to be a relevant representation, we employ an auxiliary loss that encourages the extracted features to contain sufficient information to predict the corresponding ground-truth bounding box associated with the target proposal. Concretely, we add separate classification and regression heads that use each extracted feature vector of the alignment stage to predict the box residuals between target proposal and its corresponding ground-truth box. + +Multi-view Aggregation. After the alignment module, each proposal in the target frame will have an associated feature for each stored frame. The multi-view aggregation layer (Figure 2, MVAA-Aggregation) is responsible for combining these features from different perspectives together to form a single feature for each proposal. Concretely, we use the new frame's proposal features as the attention query inputs, and its corresponding extracted features in previous frames as the keys and values. + +We note that the aggregation module can enable the network to be robust to newly appearing objects. If an object appears for the first time in a new frame, the model can compute an attention matrix that will only focus on the new frame and ignore the past frames since they are not relevant. + +Box Prediction Head. After MVAA, we have an updated feature for each proposal in the new frame. We regress objectness scores and box parameters from this feature representation. For the objectness score, we follow [18] and treat the IoU between proposals and their corresponding ground-truth bounding boxes as the classification target, with the sigmoid cross-entropy loss. The box parameter targets are encoded as residuals [12, 37] and trained with a smooth $L1$ loss. The same formulations are used for the cross-view + +loss. + +# 3.4. Losses + +We minimize the total loss consisting of a fast single-frame detector (FSD) loss $L_{fsd}$ , a multi-view prediction loss $L_{mvaa}$ , and a cross-view loss $L_{cv}$ with equal loss weights. + +$$ +L _ {t o t a l} = L _ {f s d} + L _ {m v a a} + L _ {c v} \tag {1} +$$ + +The same formulation for detection loss $L_{det}$ is used in these three losses. This includes a objectness loss $L_{obj}$ and a regression loss $L_{reg}$ . + +$$ +L _ {d e t} = \frac {1}{| C |} \sum_ {i \in C} L _ {o b j} + \frac {1}{| R |} \sum_ {i \in R} L _ {r e g} \tag {2} +$$ + +$C$ represents the set of locations where we predict an objectness score. For $L_{fsd}$ , this corresponds to the remaining pillars after MaxPoolNMS, while for $L_{mvaa}$ and $L_{cv}$ , this corresponds to the proposals after FSD (specifically, those that remain after MaxPoolNMS). For the objectness loss in $L_{mvaa}$ and $L_{cv}$ , we use the IoU overlap between the proposal and its assigned ground-truth as the target. For $L_{fsd}$ , the output of the Hungarian matching is used to determine positive and negative assignments for the objectness loss. + +$R$ represents the set of locations which are associated with a ground-truth box. For all losses $(L_{fsd}, L_{mvaa}$ , and $L_{cv})$ , these are the matched boxes from Hungarian matching. For the regression losses, we use a smooth- $L1$ loss as the supervision of regressing the x, y, z center location residuals, and their corresponding dimensions. For orientation, we use a binning orientation loss [16, 19]. The model is expected to predict an angle bin first, followed by a residual from the bin center. We use 12 bins for $L_{fsd}$ and 1 bin for $L_{mvaa}$ and $L_{cv}$ . + +The cross-view identity loss $L_{cv}$ is computed across all the outputs of the multi-view alignment stage, and averaged across all instances. + +# 4. Experiments + +We evaluate our method on Waymo Open Dataset [23], a large scale 3D object detection dataset. There are a total of 1150 sequences divided into 798 training, 202 validation, and 150 testing examples. Each sequence consists of about 200 frames at a frame rate of $10\mathrm{Hz}$ , where each frame includes a LiDAR point cloud and labeled 3D bounding boxes for vehicles, pedestrians, cyclists and signs. We evaluate our model and compare it with other methods using average precision (AP) and Average Precision Weighted by Heading (APH). + +# 4.1. Implementation Details + +Hyperparameters. Given the input point cloud in a target frame, we first set the detection range as $[-76.8m, 76.8m]$ for x and y axes and $[-2m, 4m]$ for the z-axis. We equally split this 3D range into [512, 512] pillars among x and y axes respectively, following PointPillars [12]. For the MaxPoolNMS applied in FSD, we use a max-pooling kernel size of [7, 7] for vehicles and [3, 3] for pedestrians, with a stride of [1, 1]. After MaxPoolNMS, a set of 128 proposals per frame are passed to the memory bank. + +Network Architectures. In our proposed FSD, we use the same backbone network illustrated in PointPillars [12]. The channel dimension $C$ of the last feature map and proposal features is 384. For encoding the frame index and relative box residuals, we apply a 2-layer perceptron (MLP) networks with $C$ output channels for the first layer, and 1 output for the second layer. These are used in the cross-attention layers of the MVAA module. In the prediction head, we first apply a 2-layer MLP network with $C$ output channels to embed the aggregated multi-view features. These embeddings are transformed with two prediction branches for classification and regression. + +Training Parameters. Our network is trained end-to-end using the ADAM [11] optimizer for a total number of 50 epochs with an initial learning rate of 0.0016 and a batch size of 32. We apply exponential decay to anneal the learning rate, starting at 5 epochs until 45 epochs. During training, we apply random flip and random rotation as our only data augmentation methods. + +Utilizing a large number of frames. We enable 3D-MAN to exploit a large number of frames by combining it with point concatenation. Our best model uses 16 frames split into 4 windows of 4 frames. The point clouds in each window are concatenated together and used as input to the FSD. Each window thus becomes an entry in the memory bank, and the model is expected to produce predictions for only the last frame. This utilizes point concatenation for when movement is small with nearby frames and MVAA for large movement across a longer time range. We provide further ablation studies with varying sizes of input frames in Section 4.3. + +# 4.2. Main Results + +Waymo Validation Set. We compare our method with published state-of-the-art single-frame and multi-frame methods on the Waymo validation set on class Vehicle (Table 3) and class Pedestrian (Table 4). We first compare the performance between our model with and without multiframe inputs (Table 3). When the model has access to 16 stored frames, the overall 3D AP (LEVEL_1) is improved by $5.50\%$ on vehicles labeled as LEVEL_1 difficulty, illus- + +
DifficultyMethod3D AP (IoU=0.7)3D APH (IoU=0.7)
Overall0-30m30-50m50m-InfOverall0-30m30-50m50m-Inf
LEVEL_1StarNet [15]55.1180.4848.6127.7454.6479.9248.1027.29
PointPillars [12]63.2784.9059.1835.7962.7284.3558.5735.16
MVF [36]62.9386.3060.0236.02----
AFDet [7]63.6987.3862.1929.27----
RCD [1]68.9587.2266.5344.5368.5286.8266.0743.97
PV-RCNN [18]70.3091.9269.2142.1769.4991.3468.5341.31
3D-MAN (Ours)69.0387.9966.5543.1568.5287.5765.9242.37
PointPillars* [12]65.4185.5861.5139.5164.8885.0260.9538.91
ConvLSTM* [10]63.6-------
3D-MAN* (Ours)74.5392.1972.7751.6674.0391.7672.1551.02
LEVEL_2StarNet [15]48.6979.6743.5720.5348.2679.1143.1120.19
PointPillars [12]55.1883.6153.0126.7354.6983.0852.4626.24
PV-RCNN [18]65.3691.5865.1336.4664.7991.0064.4935.70
3D-MAN (Ours)60.1687.1059.2732.6959.7186.6858.7132.08
PointPillars* [12]57.2884.3155.4129.7156.8183.7954.9029.24
3D-MAN* (Ours)67.6192.0067.2041.3867.1491.5766.6240.84
+ +Table 3. 3D AP and APH Results on Waymo Open Dataset validation set for class Vehicle. *Methods utilize multi-frame point clouds for detection. We report PointPillars [12] based on our own implementation, with and without point concatenation. Difficulty levels are defined in the original dataset[23]. + +
MethodLEVEL_1LEVEL_2
3D AP3D APH3D AP3D APH
StarNet [15]68.3260.8959.3252.76
PointPillars [12]68.8856.5759.9849.14
MVF [36]65.33---
3D-MAN (Ours)71.7167.7462.5859.04
+ +trating the effectiveness of our approach. + +3D-MAN outperforms the current best published method (PV-RCNN [18]) by $3.56\%$ (30-50m range) and $9.49\%$ ( $>50\mathrm{m}$ range) AP (LEVEL_1) on vehicles. At these further ranges, objects are often partially visible, where having more information from different perspectives could help. These improvements show that our model is able to effectively combine the information across multiple views to generate more accurate 3D predictions. Moreover, compared to existing multi-frame models, 3D-MAN also outperforms them by a large margin. Our method achieves a better 3D AP than the recently published Conv-LSTM method [10] by $10.93\%$ on vehicle detection. For pedestrian detection, 3D-MAN also achieves the best performance (Table 4). + +Waymo Testing Set. We also evaluate our model on Waymo testing set through a test server submission. For vehicle detection (Table 5), 3D-MAN achieves $78.71\%$ AP and 78.28 APH, outperforming RCD [1] by $6.74\%$ and $6.69\%$ respectively, which is currently the best published method among results generated by a single model (not using any ensemble methods). + +Table 4. 3D AP and APH Results on Waymo Open Dataset validation set for class Pedestrian. + +
MethodVehiclePedestrians
3D AP3D APH3D AP3D APH
SECOND [28]50.1149.63--
StarNet [15]63.5163.0367.7860.10
PointPillars [12]68.6268.0867.9655.53
SA-SSD [8]70.2469.5457.1448.82
RCD [1]71.9771.59--
3D-MAN (Ours)78.7178.2869.9765.98
+ +Table 5. 3D AP and APH Results on Waymo Open Dataset testing set for class Vehicle and Pedestrain among LEVEL-1 difficulty objects. Metric breakdowns for our model is available on the Waymo challenge leaderboard. + +
MaskCenterednessHungarian Matching
Ped. (%)64.767.170.2
Veh. (%)44.563.764.8
+ +Table 6. Mini-validation AP comparison among different ground-truth assignment strategies using FSD for both Pedestrian and Vehicle classes. + +# 4.3. Ablation Studies + +We conduct all our ablation studies only for the vehicle class, and report LEVEL_1 difficulty results based on a subset of the full validation set. We created a mini-validation set by uniformly sampling $10\%$ of the full validation set. This results in a dataset that allows us to experiment significantly faster. We note that there is a negligible performance gap between the mini-validation and full validation set: for example, our best model obtains $74.3\%$ on the mini-validation set versus $74.5\%$ on the full validation set. + +Hungarian Matching. We compare the performance of using different assignment strategies in FSD, including the mask strategy, centeredness strategy and Hungarian matching strategy (Table 6). The mask strategy [24, 30] as + +
MethodBaselineConcatRelationMVAA
AP (%)68.270.570.172.5
+ +Table 7. Mini-validation AP comparison on class Vehicle among different multi-frame fusion approaches. + +
Supervision MethodNoneCorrespondence LossCV Loss
AP (%)70.771.472.5
+ +signs interior pillars of any valid object positive and all other pillars negative. However, this can lead to a discrepancy between classification score and localization accuracy. Our experiments show that this performs the least well. Centeredness strategy [31, 24, 35] encourages pillars with closer distance to the instance center to have a higher classification score. However, the pillar in the center may not always draw the best localization prediction in point clouds: the LiDAR points often are on the surface of the vehicle and not in the interior. We find centeredness to perform better than mask, but worse than our proposed Hungarian matching approach. FSD achieves the highest AP with the Hungarian matching strategy, which validates our approach. + +Multi-frame Approaches. We compare our method to other multi-frame approaches (Table 7), including the point concatenation approach and a self-attention approach across all previously detected boxes. Multi-frame models in the comparison have 4 frames as input and are expected to predict bounding boxes for only the last frame. We also perform ego-motion pose correction to map points from the earlier frames to the pose of the last frame. + +The Baseline model is our single-frame two-stage model, which applies FSD to generate proposals with features and deploys box prediction head with an MLP network to refine these proposals. It achieves $68.2\%$ AP on Vehicle and provides a baseline to compare the multi-frame models against. + +In the Concat approach, points across all frames are combined together, and the merged point cloud is used as input to the Baseline model. This improves upon the baseline by $2.3\%$ AP. The Relation approach first extracts box proposals from multiple frames and then uses a self-attention network on all past proposals directly to produce a prediction. This performs better than the Baseline but worse than the Concat model. + +Our approach (MVAA) performs the best, outperforming the Concat approach and Relation approach by $2.0\%$ and $2.4\%$ respectively. + +Cross-view loss. We find it useful to have an auxiliary cross-view loss to encourage the model to propagate relevant features in the alignment stage of MVAA. To evaluate the effectiveness of the cross-view loss, we compare it to not having an auxiliary loss and also an alternative auxiliary + +Table 8. Mini-validation AP comparison on class Vehicle using different auxiliary losses with the MVAA alignment stage. + +
Frames147101316
AP (%)68.272.573.473.573.874.3
+ +Table 9. Mini-validation AP comparison for different number of input frames to the 3D-MAN model. All models are expected to predict only the last frame. Models with 7, 10, 13, and 16 frames use concatenated points (over windows of 4 frames) as input, with different amount of overlaps between adjacent windows. + +
ModelStationary (%)Slow (%)Medium (%)Fast (%)
4-frames69.568.667.178.3
16-frames73.270.468.979.2
+ +Table 10. Velocity breakdowns of vehicle AP metrics for 3D-MAN with varying number of input frames. + +correspondence loss. The correspondence loss encourages elements of the attention matrix (of the alignment stage in MVAA) to be close to 1 if the query proposal matches the instance of the corresponding stored proposal, and zero otherwise. We compare these approaches for the auxiliary loss (Table 8), and find that using the cross-view loss outperforms having no auxiliary loss by $1.8\%$ and using the correspondence loss by $1.1\%$ . + +Varying number of input frames. We further compare our model's performance on different number of available frames (Table 9). In order to draw a fair comparison between models with 7 through 16 frames, we fix the computation by using point concatenation over windows of 4 frames, with different degrees of overlaps between windows (similar to strides in convolution windows). We find that our model steadily improves as it has access to more input frames corresponding to longer time horizons. + +Velocity breakdowns. We also compare our model's performance across different velocity breakdowns. Recall that the baseline multi-frame PointPillars model performance degrades when using 8-frames versus 4-frames (Table 2). Conversely, our model demonstrates an improvement when we increase the number of frames from 4 to 16 (Table 10). This shows that our approach is able to benefit fast-moving vehicles. + +# 5. Conclusion + +In this paper, we present a novel 3D object detection method, 3D-MAN, which utilizes attention networks to extract and aggregate features across multiple frames. We introduce a fast single-frame detector that utilizes a Hungarian matching strategy to align the objectness score with the best localized box. We show how the outputs of the single-frame detector can be used with a memory bank and a novel multi-view alignment and aggregation module to fuse the information from multiple frames together. Our method is effective across long time horizons and obtains state-of-the-art performance on a challenging large scale dataset. + +# References + +[1] Alex Bewley, Pei Sun, Thomas Mensink, Dragomir Anguelov, and Cristian Sminchisescu. Range conditioned dilated convolutions for scale invariant 3d object detection. In CoRL, 2020. 7 +[2] Holger Caesar, Varun Bankiti, Alex H. Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. CVPR, 2020. 1, 2, 3 +[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, ECCV, 2020. 4 +[4] Yihong Chen, Yue Cao, Han Hu, and Liwei Wang. Memory enhanced global-local aggregation for video object detection. In CVPR, 2020. 3 +[5] Hanming Deng, Yang Hua, Tao Song, Zongpu Zhang, Zhengui Xue, Ruhui Ma, Neil Martin Robertson, and Haibing Guan. Object guided external memory network for video object detection. In ICCV, 2019. 3 +[6] Jiajun Deng, Yingwei Pan, Ting Yao, Wengang Zhou, Houqiang Li, and Tao Mei. Relation distillation networks for video object detection. In ICCV, 2019. 3 +[7] Runzhou Ge, Zhuangzhuang Ding, Yihan Hu, Yu Wang, Sijia Chen, Li Huang, and Yuan Li. Afdet: Anchor free one stage 3d object detection. CoRR, 2020. 7 +[8] Chenhang He, Hui Zeng, Jianqiang Huang, Xian-Sheng Hua, and Lei Zhang. Structure aware single-stage 3d object detection from point cloud. In CVPR, June 2020. 7 +[9] Han Hu, Jiayuan Gu, Zheng Zhang, Jifeng Dai, and Yichen Wei. Relation networks for object detection. In CVPR, 2018. 3 +[10] Rui Huang, Wanyue Zhang, Abhijit Kundu, Caroline Pantofaru, David A. Ross, Thomas A. Funkhouser, and Alireza Fathi. An LSTM approach to temporal 3d object detection in lidar point clouds. CoRR, 2020. 2, 3, 7 +[11] Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. *ICLR*, 2015. 6 +[12] Alex H Lang, Sourabh Vora, Holger Caesar, Lubing Zhou, Jiong Yang, and Oscar Beijbom. Pointpillars: Fast encoders for object detection from point clouds. CVPR, 2019. 2, 3, 5, 6, 7 +[13] Ming Liang*, Bin Yang*, Yun Chen, Rui Hu, and Raquel Urtasun. Multi-task multi-sensor fusion for 3d object detection. In CVPR, 2019. 4 +[14] Wenjie Luo, Bin Yang, and Raquel Urtasun. Fast and furious: Real time end-to-end 3d detection, tracking and motion forecasting with a single convolutional net. In CVPR, 2018. 2, 3 +[15] Jiquan Ngiam, Benjamin Caine, Wei Han, Brandon Yang, Yuning Chai, Pei Sun, Yin Zhou, Xi Yi, Ouais Alsharif, Patrick Nguyen, Zhifeng Chen, Jonathon Shlens, and Vijay Vasudevan. Starnet: Targeted computation for object detection in point clouds. CoRR, 2019. 2, 7 + +[16] Charles Ruizhongtai Qi, Wei Liu, Chenxia Wu, Hao Su, and Leonidas J. Guibas. Frustum pointnets for 3d object detection from RGB-D data. CVPR, 2018. 3, 6 +[17] Charles Ruizhongtai Qi, Hao Su, Kaichun Mo, and Leonidas J. Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In CVPR, 2017. 3 +[18] Shaoshuai Shi, Chaoxu Guo, Li Jiang, Zhe Wang, Jianping Shi, Xiaogang Wang, and Hongsheng Li. PV-RCNN: point-voxel feature set abstraction for 3d object detection. In CVPR, 2020. 2, 5, 7 +[19] Shaoshuai Shi, Xiaogang Wang, and Hongsheng Li. Pointr-cnn: 3d object proposal generation and detection from point cloud. In CVPR, 2019. 2, 3, 6 +[20] Shaoshuai Shi, Zhe Wang, Xiaogang Wang, and Hongsheng Li. Part-a $^2$ net: 3d part-aware and aggregation neural network for object detection from point cloud. arXiv preprint arXiv:1907.03670, 2019. 2 +[21] Mykhailo Shvets, Wei Liu, and Alexander C. Berg. Leveraging long-range temporal relationships between proposals for video object detection. In ICCV, 2019. 3 +[22] Russell Stewart, Mykhaylo Andriluka, and Andrew Y. Ng. End-to-end people detection in crowded scenes. In CVPR, 2016. 4 +[23] Pei Sun, Henrik Kretzschmar, Xerxes Dotiwalla, Aurelien Chouard, Vijaysai Patnaik, Paul Tsui, James Guo, Yin Zhou, Yuning Chai, Benjamin Caine, Vijay Vasudevan, Wei Han, Jiquan Ngiam, Hang Zhao, Aleksei Timofeev, Scott Ettinger, Maxim Krivokon, Amy Gao, Aditya Joshi, Yu Zhang, Jonathon Shlens, Zhifeng Chen, and Dragomir Anguelov. Scalability in perception for autonomous driving: Waymo open dataset. In CVPR, 2020. 1, 2, 6, 7 +[24] Zhi Tian, Chunhua Shen, Hao Chen, and Tong He. FCOS: fully convolutional one-stage object detection. ICCV, 2019. 7, 8 +[25] Dominic Zeng Wang and Ingmar Posner. Voting for voting in online point cloud object detection. In Robotics: Science and Systems XI, 2015. 2 +[26] Yue Wang, Alireza Fathi, Abhijit Kundu, David Ross, Caroline Pantofaru, Thomas Funkhouser, and Justin Solomon. Pillar-based object detection for autonomous driving. In ECCV, 2020. 2 +[27] Haiping Wu, Yuntao Chen, Naiyan Wang, and Zhao-Xiang Zhang. Sequence level semantics aggregation for video object detection. In ICCV, 2019. 3 +[28] Yan Yan, Yuxing Mao, and Bo Li. Second: Sparsely embedded convolutional detection. Sensors, 2018. 2, 7 +[29] Bin Yang, Wenjie Luo, and Raquel Urtasun. **PIXOR: real-time 3d object detection from point clouds. In CVPR, 2018.** 2 +[30] Ze Yang, Shaohui Liu, Han Hu, Liwei Wang, and Stephen Lin. Repoints: Point set representation for object detection. ICCV, 2019. 7 +[31] Zetong Yang, Yanan Sun, Shu Liu, and Jiaya Jia. 3dssd: Point-based 3d single stage object detector, 2020. 2, 8 +[32] Zetong Yang, Yanan Sun, Shu Liu, Xiaoyong Shen, and Jiaya Jia. IPOD: intensive point-based object detector for point cloud. CoRR, 2018. 2 + +[33] Zetong Yang, Yanan Sun, Shu Liu, Xiaoyong Shen, and Jiaya Jia. STD: sparse-to-dense 3d object detector for point cloud. ICCV, 2019. 2 +[34] Junbo Yin, Jianbing Shen, Chenye Guan, Dingfu Zhou, and Ruigang Yang. Lidar-based online 3d video object detection with graph-based message passing and spatiotemporal transformer attention. In CVPR, 2020. 2, 3 +[35] Xingyi Zhou, Dequan Wang, and Philipp Krahenbuhl. Objects as points. CoRR, 2019. 4, 8 +[36] Yin Zhou, Pei Sun, Yu Zhang, Dragomir Anguelov, Jiyang Gao, Tom Ouyang, James Guo, Jiquan Ngiam, and Vijay Vasudevan. End-to-end multi-view fusion for 3d object detection in lidar point clouds. In CoRL, 2019. 2, 3, 7 +[37] Yin Zhou and Oncel Tuzel. Voxelnet: End-to-end learning for point cloud based 3d object detection. 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In this paper, we propose Pointformer, a Transformer backbone designed for 3D point clouds to learn features effectively. Specifically, a Local Transformer module is employed to model interactions among points in a local region, which learns context-dependent region features at an object level. A Global Transformer is designed to learn context-aware representations at the scene level. To further capture the dependencies among multi-scale representations, we propose Local-Global Transformer to integrate local features with global features from higher resolution. In addition, we introduce an efficient coordinate refinement module to shift down-sampled points closer to object centroids, which improves object proposal generation. We use Pointformer as the backbone for state-of-the-art object detection models and demonstrate significant improvements over original models on both indoor and outdoor datasets. + +# 1. Introduction + +3D object detection in point clouds is essential for many real-world applications such as autonomous driving [10] and augmented reality [18]. Compared to images, 3D point clouds can provide detailed geometry and capture 3D structure of the scene. On the other hand, point clouds are irregular, which can not be processed by powerful deep learning models, such as convolutional neural networks directly. This poses a big challenge for effective feature learning. + +The common feature processing methods in 3D detection can be roughly categorized into three types, based on the form of point cloud representations. Voxel-based ap + +![](images/7b912ec80d5510ef46b55997482b967f3c2005d5b8ca8e480c843d9848c5d585.jpg) +Image of the scene + +![](images/2c3a8baa57569d77c93397c6f406bc87213736cffea3ca11118bfb60610064f8.jpg) +Ground truth + +![](images/210daf8b122e239a989e73d891a3827aaa581c603bb065978243bbf1f44b5e4d.jpg) +Top-50 attention + +![](images/de941c2e75a0428f75cbe827ba71c037cf198b14bf1b4df9afb6b896bd81c3ff.jpg) +Top-100 attention + +![](images/962f04a0ab8b495f3725bf93f770d98c239b3e45eaef2fc7e750de118fab33e3.jpg) +Top-200 attention +Figure 1. Attention maps directly from Pointformer block, darker blue indicates stronger attention. For the key point (star), Pointformer first focuses on the local region of the same object (the back of the chair), then spreads the attention to other regions (the legs), finally attends to points from other objects globally (other chairs), leveraging both local and global dependencies. + +proaches [28, 12, 42] gridify the irregular point clouds into regular voxels and are followed by sparse 3D convolutions to learn high dimensional features. Though effective, voxel-based approaches face the dilemma between efficiency and accuracy. Specifically, using smaller voxels gains more precision, but suffers from higher computational cost. Conversely, using larger voxels misses potential local details in the crowded voxels. + +Alternatively, point-based approaches [25], inspired by the success of PointNet [21] and its variants, consume raw points directly to learn 3D representations, which mitigates the drawback of converting point clouds to some regular structures. Leveraging learning techniques for point sets, point-based approaches avoid voxelization-induced information loss and take advantage of the sparsity in point clouds by only computing on valid data points. Nevertheless, due to the irregularity of point cloud data, point-based learning operations have to be permutation-invariant and adaptive to the input size. To achieve this, it learns simple symmetric functions (e.g. using point-wise feedforward networks with pooling functions) which highly restricts its representation power. + +![](images/0d2e25ab11a76d622e543430d0f3fdf016d7cdddda36ee5cfb80ce7312a48329.jpg) +Figure 2. The Pointformer backbone for 3D object detection in point clouds. A basic feature learning block consists of three parts: a Local Transformer to model interactions in the local region; a Local-Global Transformer to integrate local features with global information; a Global Transformer to capture context-aware representations at the scene level. + +Hybrid approaches [41, 15, 39, 24] attempt to combine both voxel-based and point-based representations. [41, 15] leverages PointNet features at the voxel level and a column of voxels (pillar) level respectively. [39, 24] deeply integrate voxel features and PointNet features at the scene level. However, the fundamental difference between the two representations could pose a limit on the effectiveness of these approaches for 3D point-cloud feature learning. + +To address the above limitations, we resort to the Transformer [30] models, which have achieved great success in the field of natural language processing. Transformer models [8] are very effective at learning context-dependent representations and capturing long range dependencies in the input sequence. Transformer and the associate self-attention mechanism not only meet the demand of permutation invariance, but also are proved to be highly expressive. Specifically, [6] proves that self-attention is at least as expressive as convolution. Currently, self-attention has been successfully applied to classification [23] and 2D object detection [2] in computer vision. However, the straightforward application of Transformer to 3D point clouds is prohibitively expensive because computation cost grows quadratically with the input size. + +To this end, we propose Pointformer, a backbone for 3D point clouds to learn features more effectively by leveraging the superiority of the Transformer models on set-structured data. As shown in Figure 2, Pointformer is a U-Net structure with multi-scale Pointformer blocks. A Pointformer block consists of Transformer-based modules that are both expressive and friendly to the 3D object detection task. First, a Local Transformer (LT) module is employed to model interactions among points in the local region, which learns context-dependent region features at an object level. Second, a coordinate refinement module is proposed to ad + +just centroids sampled from Furthest Point Sampling (FPS) which improves the quality of generated object proposals. Third, we propose Local-Global Transformer (LGT) to integrate local features with global features from higher resolution. Finally, Global Transformer (GT) module is designed to learn context-aware representations at the scene level. As illustrated in Figure 1, Pointformer can capture both local and global dependencies, thus boosting the performance of feature learning for scenes with multiple cluttered objects. + +Extensive experiments have been conducted on several detection benchmarks to verify the effectiveness of our approach. We use the proposed Pointformer as the backbone for three object detection models, CBGS [42], VoteNet [19], and PointRCNN [25], and conduct experiments on three indoor and outdoor datasets, SUN-RGBD [27], KITTI [10], and nuScenes [1] respectively. We observe significant improvements over the original models on all experiment settings, which demonstrates the effectiveness of our method. + +In summary, we make the following contributions: + +- We propose a pure transformer model, Pointformer, which serves as a highly effective feature learning backbone for 3D point clouds. Pointformer is permutation invariant, local and global context-aware. +- We show that Pointformer can be easily applied as the drop-in replacement backbone for state-of-the-art 3D object detectors for the point cloud. +- We perform extensive experiments using Pointformer as the backbone for three state-of-the-art 3D object detectors, and show significant performance gains on several benchmarks including both indoor and outdoor datasets. This demonstrates that the versatility of Pointformer as 3D object detectors are typically designed and optimized for either indoor or outdoor only. + +![](images/4b66384df764ee5f13d03da92e4722c7211e1c692d45d1baee6ddf453f6ec536.jpg) +Figure 3. Illustration of the Local Transformer. Input points are first down-sampled by FPS and generate local regions by ball query. Transformer block takes point features and coordinates as input and generate aggregated features for the local region. To further adjust the centroid points, attention maps from the last Transformer layer are adopted for coordinate refinement. As a result, points are pushed closer to the object centers instead of surfaces. + +# 2. Related Work + +Feature learning for 3D point clouds. Prior work includes feature learning on voxelized grids, direct feature learning on point clouds and the hybrid of the two. 3D sparse convolution [11] is very effective on voxel grids. For direct feature learning, PointNet [21] and PointNet++ [22] learn point-wise features and region features using feed-forward networks and simple symmetric functions (e.g. max) respectively. PCCN [33] generalizes convolution to non-grid structured data by exploiting parameterized kernel functions that span the full continuous vector space. EdgeConv [34] exchanges local neighborhood information and acts on graphs dynamically computed in each layer of the network. Hybrid methods combine both types of features at the local level [41, 15] or at the network level [39, 24]. + +Transformers in computer vision. Image GPT [3] is the first to adopt the Transformers in 2D image classification task for unsupervised pretraining. Further, ViT [9] extends this scheme to large scale supervised learning on images. For high level vision tasks, DETR [2] and Deformable DETR [43] leverage the advantages of Transformers in 2D object detection. Set Transformer [16] uses attention mechanisms to model interactions among elements in the input set. In the field of 3D vision, PAT [38] designs novel group shuffle attentions to capture long range dependencies in point clouds. To the best of our knowledge, we are the first to propose a pure Transformer model for 3D points clouds feature learning with carefully designed Transformer blocks and a positional encoding module to capture geometric and rich context information. + +3D object detection in point clouds. Detectors are designed either with point clouds as the only input [42, 41, 15, 39, 24, 25, 19, 26, 35, 40] or fusing multiple sensor modalities such as LiDAR and camera [20, 17, 31]. Their backbones are designed with the aforementioned feature learning approaches. We focus on point cloud only object detection. In this category, VoxelNet [41] divides the point cloud into voxels, followed by 3D convolutions to extract features. VoteNet [19] devises a novel 3D proposal mechanism using deep Hough voting, before H3DNet [40] makes further investigations on geometric primitives. In addition, + +MLCVNet [35] focuses more on contextual information aggregation based on VoteNet, and PointGNN [26] exploits graph learning methods in point cloud detection. We show that our novel Transformer based model, Pointformer, can be used as a drop-in replacement for voxel-based detector, CBGS [42] and point-based detectors, VoteNet [19] and PointRCNN [25]. + +# 3. Pointformer + +Feature learning for 3D point clouds needs to confront its irregular and unordered nature as well as its varying size. Prior work utilizes simple symmetric functions, e.g., pointwise feedforward networks with pooling functions [21, 22], or resorts to the techniques in graph neural networks by aggregating information from the local neighborhood [34]. However, the former is not effective in incorporating local context-dependent features beyond the capability of the simple symmetric functions; the latter focuses on the message passing between the center point and its neighbors while neglecting the feature correlations among the neighbor points. Additionally, global representations are also informative but rarely used in 3D object detection tasks. + +In this paper, we design Transformer-based modules for point set operations which not only increase the expressiveness of extracting local features, but incorporate global information into point representations as well. As shown in Figure 2, a Pointformer block mainly consists of three parts: Local Transformer (LT), Local-Global Transformer (LGT) and Global Transformer (GT). For each block, LT first receives the output from its previous block (high resolution) and extracts features for a new set with fewer elements (low resolution). Then, LGT uses the multi-scale cross-attention mechanism to integrate features from both resolutions. Lastly, GT is adopted to capture context-aware representations. As for the up-sampling block, we follow PointNet++ and adopt the feature propagation module for its simplicity. + +# 3.1. Background + +We first revisit the general formulation of the Transformer model. Let $F = \{f_{i}\}$ and $X = \{x_{i}\}$ denote a set + +of input features and their positions, where $f_{i}$ and $x_{i}$ represent the feature and position of token $i$ , respectively. Then, a Transformer block comprises of a multi-head self-attention module and feedforward network: + +$$ +q _ {i} ^ {(m)} = f _ {i} W _ {q} ^ {(m)}, k _ {i} ^ {(m)} = f _ {i} W _ {k} ^ {(m)}, v _ {i} ^ {(m)} = f _ {i} W _ {v} ^ {(m)}, \tag {1} +$$ + +$$ +y _ {i} ^ {(m)} = \sum_ {j} \sigma \left(q _ {i} ^ {(m)} k _ {j} ^ {(m)} / \sqrt {d} + \operatorname {P E} \left(x _ {i}, x _ {j}\right)\right) v _ {j} ^ {(m)}, \tag {2} +$$ + +$$ +y _ {i} = f _ {i} + \operatorname {C o n c a t} \left(y _ {i} ^ {(0)}, y _ {i} ^ {(1)}, \dots , y _ {i} ^ {(M - 1)}\right), \tag {3} +$$ + +$$ +o _ {i} = y _ {i} + \operatorname {F F N} (y _ {i}), \tag {4} +$$ + +where $W_{q}, W_{k}, W_{v}$ are projections for query, key and value. $m$ is the index of $M$ attention heads and $d$ is the feature dimension. $\mathrm{PE}(\cdot)$ is the positional encoding function for input positions, and $\mathrm{FFN}(\cdot)$ represents a position-wise feedforward network. $\sigma (\cdot)$ is a normalization function and SoftMax is mostly adopted. + +In the following sections, for simplicity, we use + +$$ +O = \operatorname {T r a n s b l o c k} (F, \mathrm {P E} (X)), \tag {5} +$$ + +to represent the basic Transformer block $(\mathrm{Eq.(1)}\sim$ Eq.(4)). Readers can refer to [30] for further details. + +# 3.2. Local Transformer + +In order to build a hierarchical representation for a point cloud scene, we follow the high level methodology to build feature learning blocks on different resolutions [22]. Given an input point cloud $\mathcal{P} = \{x_1,x_2,\dots ,x_N\}$ , we first use furthest point sampling (FPS) to choose a subset of points $\{x_{c_1},x_{c_2},\ldots ,x_{c_{N'}}\}$ as a set of centroids. For each centroid, ball query is applied to generate $K$ points in the local region within a given radius. Then we group these features around the centroids, and feed them as a point sequence to a Transformer layer, as shown in Figure 3. Let $\{x_i,f_i\}_t$ denote the local region for $t_\mathrm{th}$ centroid, where $x_{i}\in \mathbb{R}^{3}$ and $f_{i}\in \mathbb{R}^{C}$ represent the coordinates and features of the $i$ -th points in the group, respectively. Subsequently, a shared $L$ -layer Transformer block is applied to all local regions which receives the input of $\{x_i,f_i\}_t$ as follows: + +$$ +f _ {i} ^ {(0)} = \operatorname {F F N} \left(f _ {i}\right), \forall i \in \mathcal {N} \left(x _ {c _ {t}}\right), \tag {6} +$$ + +$$ +F ^ {(l + 1)} = \operatorname {T r a n s b l o c k} \left(F ^ {(l)}, \operatorname {P E} (X)\right), l = 0,.., L - 1, \tag {7} +$$ + +where $F = \{f_{i}|i\in \mathcal{N}(x_{c_{t}})\}$ and $X = \{x_{i}|i\in \mathcal{N}(x_{c_{t}})\}$ denote the set of features and coordinates in the local region with centroid $x_{c_t}$ . + +Compared to the existing local feature extraction modules in [36, 37, 29], the proposed Local Transformer has several advantages. First, the dense self-attention operation in the Transformer block greatly enhances its expressiveness. Several graph learning based approaches can be approximated as special cases of the LT module with learned + +parameter space carefully designed. For instance, a generalized graph feature learning function can be formulated as: + +$$ +e _ {i j} = \operatorname {F F N} \left(\operatorname {F F N} \left(x _ {i} \oplus x _ {j}\right) + \operatorname {F F N} \left(f _ {i} \oplus f _ {j}\right)\right), \tag {8} +$$ + +$$ +f _ {i} ^ {\prime} = \mathcal {A} \left(\sigma \left(e _ {i j}\right) \times \operatorname {F F N} \left(f _ {j}\right), \forall j \in \mathcal {N} \left(x _ {i}\right)\right), \tag {9} +$$ + +where most of the models utilize summation as the aggregation function $\mathcal{A}$ and the operation $\oplus$ is chosen from {Concatenation, Plus, Inner-product}. Therefore, the edge function $e_{ij}$ is at most a quadratic function of $\{x_i,x_j,f_i,f_j\}$ . For a one-layer Transformer block, the learning module can be formulated with the inner-product self-attention mechanism as follows: + +$$ +e _ {i j} = \frac {f _ {i} W _ {q} W _ {k} ^ {T} f _ {j} ^ {T}}{\sqrt {d}} + \mathrm {P E} \left(x _ {i}, x _ {j}\right), \tag {10} +$$ + +$$ +f _ {i} ^ {\prime} = \mathcal {A} \left(\sigma \left(e _ {i j} \times \operatorname {F F N} \left(f _ {j}\right), \forall j \in \mathcal {N} \left(x _ {i}\right)\right), \right. \tag {11} +$$ + +where $d$ is the feature dimension of $f_{i}$ and $f_{j}$ . We can observe that the edge function is also a quadratic function of $\{x_{i}, x_{j}, f_{i}, f_{j}\}$ . With sufficient number of layers in FFNs, the graph-based feature learning module has the same expressive power as a one-layer Transformer encoder. When it comes to Pointformer, as we stack more Transformer layers in the block, the expressiveness of our module is further increased and can extract better representations. + +Moreover, feature correlations among the neighbor points are also considered, which are commonly omitted in other models. Under some circumstances, neighbor points can be even more informative than the centroid point. Therefore, by leveraging message passing among all points, features in the local region are equally considered, which makes the local feature extraction module more effective. + +# 3.3. Coordinate Refinement + +Furthest point sampling (FPS) is widely used in many point cloud frameworks, as it can generate a relatively uniform sampled points while keeping the original shape, which ensures that a large fraction of the points can be covered with limited centroids. However, there are two main issues in FPS: (1) It is notoriously sensitive to the outlier points, leading to highly instability especially when dealing with real-world point cloud data. (2) Sampled points from FPS must be a subset of original point clouds, which makes it challenging to infer the original geometric information in the cases that objects are partially occluded or not enough points of an object are captured. Considering that points are mostly captured on the surface of objects, the second issue may become more critical as the proposals are generated from sampled points, resulting in a natural gap between the proposal and ground truth. + +To overcome the aforementioned drawbacks, we propose a point coordinate refinement module with the help of the self-attention maps. As shown in Figure 3, we first take out + +the self-attention map of the last layer of the Transformer block for each attention head. Then, we compute the average of the attention maps and utilize the particular row for the centroid point as a weight vector: + +$$ +W = \frac {1}{M} \sum_ {m = 1} ^ {M} A _ {0,:} ^ {(m)}, \tag {12} +$$ + +where $M$ represents the number of attention heads and $A^{(m)}$ is the attention map for the $m_{\mathrm{th}}$ head. Lastly, the refined centroid coordinates are computed as weighted average of all points in the local region: + +$$ +x _ {c _ {t}} ^ {\prime} = \sum_ {k = 1} ^ {K} w _ {k} x _ {k}, \tag {13} +$$ + +where $w_{k}$ is the $k_{\mathrm{th}}$ entry of $W$ . With the proposed coordinate refinement module, centroid points are adaptively moving closer to object centers. Moreover, by utilizing the self-attention map, our module introduces little computational cost and no additional learning parameters, making the refinement process more efficient. + +# 3.4. Global Transformer + +Global information representing scene contexts and feature correlations between different objects is also valuable in the detection tasks. Prior work using PointNet++ [22] or sparse 3D convolution to extract high level features for 3D point clouds enlarges the receptive field as the depth of their networks increases. However, this has limitations on modeling long-range interactions. + +As a remedy, we leverage the power of Transformer modules on modeling non-local relations and propose a Global Transformer to achieve message passing through the whole point cloud. Specifically, all points are gathered to a single group $\mathcal{P}$ and serves as input to a Transformer module. The formulation for GT is summarized as follows: + +$$ +f _ {i} ^ {(0)} = \operatorname {F F N} \left(f _ {i}\right), \forall i \in \mathcal {P}, \tag {14} +$$ + +$$ +F ^ {(l + 1)} = \operatorname {T r a n s b l o c k} \left(F ^ {(l)}, \operatorname {P E} (X)\right), l = 0,.., L - 1. \tag {15} +$$ + +By leveraging the Transformer on the scene level, we can capture the context-aware representations and promote message passing among different objects. Moreover, global representations can be particularly helpful for detecting objects with very few points. + +# 3.5. Local-Global Transformer + +Local-Global Transformer is also a key module to combine the local and global features extracted by the LT and GT modules. As shown in Figure 2, the LGT adopts a multiscale cross-attention module and generates relations between low resolution centroids and high resolution points. Formally, we apply cross attention similar to the encoder-decoder attention used in Transformer. The output of LT + +serves as query and the output of GT from the higher resolution is used as key and value. With the $L$ -layer Transformer block, the module is formulated as: + +$$ +f ^ {(0)} = \operatorname {F F N} \left(f _ {i}\right), \forall i \in \mathcal {P} ^ {l}, \tag {16} +$$ + +$$ +f _ {j} ^ {\prime} = \operatorname {F F N} \left(f _ {j}\right), \forall j \in \mathcal {P} ^ {h}, \tag {17} +$$ + +$$ +F ^ {(l + 1)} = \operatorname {T r a n s b l o c k} \left(F ^ {(l)}, F _ {j} ^ {\prime}, \operatorname {P E} (X)\right), l = 0,.., L - 1, \tag {18} +$$ + +where $\mathcal{P}^l$ (keypoints, the output of LT in Figure 2) and $\mathcal{P}^h$ (the input of a Pointformer block in Figure 2) represent subsamples of point cloud $\mathcal{P}$ from low and high resolution respectively. Through the Local-Global Transformer module, we utilize whole centroid points to integrate global information via an attention mechanism, which makes the feature learning of both more effective. + +# 3.6. Positional Encoding + +Positional encoding is an integral part of Transformer models as it is the only mechanism that encodes position information for each token in the input sequence. When adapting Transformers for 3D point cloud data, positional encoding plays a more critical role as the coordinates of point clouds are valuable features indicating the local structures. Compared to the techniques used in natural language processing, we propose a simple and yet efficient approach. For all Transformer modules, coordinates of each input point are firstly mapped to the feature dimension. Then, we subtract the coordinates of the query and key points and use relative positions for encoding. The encoding function is formalized as: + +$$ +\mathrm {P E} \left(x _ {i}, x _ {j}\right) = \operatorname {F F N} \left(x _ {i} - x _ {j}\right). \tag {19} +$$ + +# 3.7. Computational Cost Reduction + +Since Pointformer is a pure attention model based on Transformer blocks, it suffers from extremely heavy computational overhead. Applying a conventional Transformer to a point cloud with $n$ points consumes $O(n^{2})$ time and memory, leading to much more training cost. + +Some recent advances in efficient Transformers have mitigated this issue [14, 13, 32, 4, 35], among which Linformer [32] reduces the complexity to $O(n)$ by low-rank factorization of the original attention. Under the hypothesis that the self attention mechanism is low rank, i.e. the rank of the $n \times n$ attention matrix + +$$ +A = \operatorname {s o f t m a x} \left(\frac {Q K ^ {\top}}{\sqrt {d _ {k}}}\right), \tag {20} +$$ + +is much smaller than $n$ , Linformer projects the $n$ -dimension keys and values to the ones with lower dimension $k \ll n$ and $k$ is closer to the rank of $A$ . Therefore, the $i$ -th head in the projected multi-head self-attention is + +$$ +\operatorname {h e a d} _ {i} = \operatorname {s o f t m a x} \left(\frac {Q \left(E _ {i} K\right) ^ {\top}}{\sqrt {d _ {k}}}\right) F _ {i} V, \tag {21} +$$ + +
MethodModalityCar(IoU=0.7)Pedestrian (IoU=0.5)Cyclist (IOU=0.5)
EasyModerateHardEasyModerateHardEasyModerateHard
PointRCNN [25]LiDAR85.9475.7668.3249.4341.7838.6373.9359.6053.59
+ PointformerLiDAR87.1377.0669.2550.6742.4339.6075.0159.8053.99
+ +Table 1. Performance comparison of PointRCNN with and without Pointformer on KITTI test split by submitting to official test server. The evaluation metric is Average Precision(AP) with IoU threshold 0.7 for car and 0.5 for pedestrian/cyclist. + +
MethodModalityCarPedBusBarrierTCTruckTrailerMotoCons. Veh.BicyclemAP
CBGS [42]LiDAR81.180.154.965.770.948.542.951.510.522.352.8
+ PointformerLiDAR82.381.855.666.072.248.143.455.08.622.753.6
+ +Table 2. Performance comparison of PointRCNN with and without Pointformer on the nuScenes benchmark. + +
MethodEasyCar(IoU=0.7) +ModerateHard
PointRCNN88.8878.6377.38
+ Pointformer90.0579.6578.89
+ +Table 3. Performance comparison of PointRCNN with and without Pointformer on the car class of KITTI val split set. + +
RoIsRecall(IoU=0.5)Recall(IoU=0.7)
PointRCNN +PointformerPointRCNN +Pointformer
1086.6687.5129.8735.46
5096.0196.5240.2842.45
10096.7996.9174.8175.82
20098.0397.9976.2976.51
+ +Table 4. Recall of proposal generation network with different number of RoIs and 3D IoU thresholds for the car class on the val split at moderate difficulty. + +where $E_{i},F_{i}\in \mathbb{R}^{k\times n}$ are the projection matrices, which reduces the complexity from $O(n^{2})$ to $O(kn)$ . + +Compared with the Taylor expansion approximation technique used in MLCVNet [35], Linformer is easier to implement in out method. We thus adopt it to replace the Transformer layers in the vanilla Pointformer. Practically, we map the number of points $n$ to $k = \frac{n}{r}$ , where $r$ is a factor controlling the number of projected dimensions. We apply this mapping in Local Transformer, Global Transformer and Local-Global Transformer blocks. By setting an appropriate factor $r$ for each block, there would be a significant boost in both time and space consumption with little performance decay. + +# 4. Experimental Results + +In this section, we use Pointformer as the backbone for state-of-the-art object detection models and conduct experiments on several indoor and outdoor benchmarks. In Sec. 4.1, we introduce the implementation details of the experiments. In Sec. 4.2 and Sec. 4.3, we show the comparison results on indoor and outdoor datasets respectively. In Sec. 4.4, we conduct extensive ablation studies to analyze our proposed Pointformer model. Finally, we show qualitative results in Sec. 4.5. More analysis and visualizations are + +provided in the appendix. + +# 4.1. Experimental Setup + +Datasets. We adopt SUN RGB-D [27] and ScanNet V2 [7] for indoor 3D detection benchmark. SUN RGB-D has 5K training images annotated with oriented 3D bounding boxes for 37 object categories and ScanNet V2 has 1513 labeled scenes with 40 semantic classes. We follow the same setting in VoteNet [19] and report performance on the 10 classes on SUN RGB-D and 18 classes on ScanNet V2. For outdoor datasets, we choose KITTI [10] and nuScenes [1] for evaluation. KITTI contains 7,481 training samples and 7,518 test samples for autonomous driving. NuScenes contains 1k different scenes with 40K key frames, which has 23 categories and 8 attributes. We follow the evaluation protocol proposed along with the datasets. + +Experimental setups. We use the Pointformer as the backbone for three 3D detection models, including VoteNet [19], PointRCNN [25] and CBGS [42]. VoteNet is a point-based approach for indoor datasets, while PointRCNN and CBGS are adopted for outdoor datasets. PointRCNN is a classic approach for autonomous driving detection and CBGS is the champion of nuScenes 3D detection Challenge held in CVPR 2019. For a fair comparison, we adopt the same detection head, number of points for each resolution, hyperparameters and training configurations as baseline models. + +# 4.2. Outdoor Datasets + +KITTI. We first evaluate our method comparing with PointRCNN on KITTI's 3D detection benchmark. PointR-CNN uses PointNet++ as its backbone with four set abstraction layers. Similarly, we adopt the same architecture, while switching the set abstraction layer in PointNet++ with the proposed Transformer block. The comparison results on the KITTI test server are shown in Table 1. + +For the car category, we also report the performance of 3D detection results on the val split as shown in Table 3. As we can observe, by adopting Pointformer, our model achieves consistent improvements comparing to the original PointRCNN. Especially in the hard difficulty, our method shows the most promising result with $1.5\%$ AP improvement. We believe the better performance on hard objects is + +
MethodbathtubbedbookshelfchairdeskdressernightstandsofatabletoiletmAP
VoteNet [19]74.483.028.875.322.029.862.264.047.390.157.7
VoteNet*75.585.632.077.424.827.958.667.451.190.559.1
+ Pointformer80.184.332.076.227.037.464.064.951.592.261.1
+ +Table 5. Performance comparison of VoteNet with and without Pointformer on SUN RGB-D validation dataset. The evaluation metric is Average Precision with 0.25 IoU threshold.* denotes the model implemented in MMDetection3D [5]. + +
MethodcabbedchairsofatabledoorwindbkshfpiccntrdeskcurtfridgshowrtoilsinkbathofurnmAP
VoteNet [19]36.387.988.789.658.847.338.144.67.856.171.747.245.457.194.954.792.137.258.6
VoteNet*47.788.789.589.362.154.140.854.312.063.969.452.052.573.395.952.095.142.462.9
+ Pointformer46.788.490.588.765.755.047.755.818.063.869.155.448.566.298.961.586.747.464.1
+ +attributed to the higher expressiveness of local Transformer module. For hard objects which are often small or occluded, GT captures context-dependent region features, which contributes to the bounding box regression and classification. + +Additionally, we evaluate the performance of proposal generation network by calculating the recall of 3D bounding box with various number of proposals and 3D IoU threshold. As shown in Table 4, our backbone module significantly enhances the performance of proposal generation network under almost all the settings. Analyzing the figures vertically, we observe that our backbone shows better performance when the number of RoIs are relatively small. As stated in Sec.3, the GT and LGT help to capture context-aware representations and models the relations among different objects (proposals). This provides additional references for locating and reasoning the bounding boxes. Therefore, despite the lack of RoIs, we can still improve the performance of the proposal generation module and achieve higher recall. + +NuScenes. We also validate the effectiveness of Pointformer on the nuScenes dataset, which greatly extends KITTI in dataset size, number of object categories and number of annotated objects. Furthermore, nuScenes suffers from severe class imbalance issues, making the detection task more difficult and challenging. In this part, we adopt CBGS, the champion of nuScenes 3D detection Challenge held in CVPR 2019, as the baseline model and show the comparison results when replacing the backbone with Pointformer. We summarize the results in Table 2. As we can observe, by utilizing Pointformer as the backbone, our model achieves 0.8 higher mAP than baseline. For 8 of 10 classes, our model shows better performance, which demonstrates the effectiveness of Pointformer on larger and more challenging datasets. + +# 4.3. Indoor Datasets + +We evaluate our Pointformer accompanied by VoteNet [19] on SUN RGB-D and ScanNet V2. We follow the same hyperparameters on the backbone structure as VoteNet. Fol + +Table 6. Performance comparison of VoteNet with and without Pointformer on ScanNetV2 validation dataset. The evaluation metric is Average Precision with 0.25 IoU threshold.* denotes the model implemented in MMDetection3D [5]. + +
LTGTLGTCoReCar (IoU=0.7)
EasyModerateHard
1----88.8878.6377.38
2✓---89.4678.9177.65
3✓--✓89.7679.2478.43
4✓✓--89.6879.2278.52
5✓✓✓-89.8279.3478.62
6✓✓✓✓90.0579.6578.89
+ +Table 7. Effects of each component on the val split of KITTI. CoRe represents the coordinates refinement module. + +
Positional EncodingCar (IoU=0.7)
EasyModerateHard
1-85.4275.6772.34
2✓90.0579.6578.89
+ +Table 8. Effects of positional encoding on the val split of KITTI. + +owed by the Pointformer blocks, two feature propagation(FP) modules proposed in PointNet++ [22] serve as upsamplers to increase the resolution for the subsequent detection heads. + +SUN RGB-D. We report the average precision(AP) over 10 common classes in SUN RGB-D, as shown in Table 5. Compared with the PointNet++ [22] in VoteNet [19], our Pointformer provides a significant boost with $2\%$ mAP over the implementation in MMDetection3D [5]. On some categories with large and complex objects like dresser or bath-tub, Pointformer shows its splendid capability on extracting non-local information by a sharp increase over $5\%$ AP, which we attribute to the GT module in Pointformer. + +ScanNet V2. We report the average precision(AP) over 18 classes in ScanNet V2, as shown in Table 6. Compared with VoteNet, Pointformer outperforms its original version by $1.2\%$ mAP with MMDetection3D. + +# 4.4. Ablation Study + +In this section, we conduct extensive ablation experiments to analyze the effectiveness of different components of Pointformer. All experiments are trained on the train split + +![](images/e4519ef4c389830e37bb4eb90a991a80c2f65a152cc149e0e27a560b9ecd790a.jpg) +Image of the scene + +![](images/2a5560d397b0a70742d672da4e658e3e7f5579d856c995c3ba937eaa6e4713f2.jpg) +Predictions + +![](images/37d827818e27910ba83d9467316d606e7a9f3ea7f665246383d2f9f3f1e83f9b.jpg) +Ground truth + +![](images/9218f7f35062ac0acaa01b88e32ed99e06dfb65b3efc4b8e66035cb11e5ae573.jpg) +Image of the scene +Figure 4. Qualitative results of 3D object detection on SUN RGB-D. From left to right: Original scene image, our model's prediction, and annotated ground truth boxes. + +![](images/0ec68b41f652d8cd07d4777fb0b093d7fa8083dd550fdd6e8bd0938124640f9c.jpg) +Predictions + +![](images/d5890704eeec6f10739b2b5567338021db3054019f925d96877102928e20025f.jpg) +Ground truth + +![](images/ab24b63bf6c391ddbcc1d134953270c9b51218c4e0c35439a3f6cf3bdba61e5a.jpg) +Image of the scene + +![](images/dfb5225f74f6be86e3c0dfa29ddaec8e3c559d3597bc230e7137e2d9321acc2f.jpg) +Top-50 attention + +![](images/8a0849dce0bcc3502eedd19637113d59a06b87fa998268b74a26dd89e73e4a07.jpg) +Ground truth + +![](images/cd0a831d5eb9094a11cb6c53485bcc26c421aec149665da6cfae733810ca6477.jpg) +Top-100 attention + +![](images/75063313f7815ec512e4302ae81e398d5c2e9a3fc6f7e9f9a7b4259fd1c375bf.jpg) +Overall attention + +![](images/f7e3b72f85e408e51c32ed6f76654dccaa3dd2efa18d0d00449ca1d1b7788993.jpg) +Top-200 attention +Figure 5. Visualization results of the attention maps. In top-k attention, darker color indicates larger attention weight, in overall attention red indicates large value. + +with PointRCNN detection head and evaluated on the val split with the car class. + +Effects of each component. We validate the effectiveness of each Transformer component and the coordinate refinement module, and summarized the results in Table 7. The first row corresponds to the PointRCNN baseline and the last row is the full Pointformer model. By comparing the first row and second row, we can observe that easy objects benefit more from the local Transformer with 0.6 AP improvement. By comparing the second row and fourth row, we can see that global Transformer is more suitable for hard objects with 0.9 AP improvement. This observation is consistent with our analysis in Sec. 4.2. As for Local-Global Transformer and coordinate refinement, the improvement is similar under three difficulty settings. + +Positional Encoding. Playing a critical role in Transformer, position encoding can have huge impact on the learned representation. As we have shown in Table 8, we compare the performance of Pointformer without positional encoding and with two approaches to position encoding (adding or concatenating positional encoding with the attention map). We can observe that Pointformer without positional encoding suffers from a huge performance drop, as the coordinates of points can capture the local geometric information. + +# 4.5. Qualitative Results and Discussion + +Qualitative results on SUN RGB-D. Figure 4 shows representative examples of detection results on SUN RGB-D with VoteNet + Pointformer. As we can observe, our model achieves robust results despite the challenges of clutter and scanning artifacts. Additionally, our model can even recognize the missing objects in the ground truth. For instance, + +the dresser in the left scene is only partially observed by the sensor. However, our model can still generate precise proposals for the object with proper bounding box sizes. Similar results are shown in the right scene, where the table in the front suffers from clutter because of the books on it. + +Inspecting Pointformer with attention maps. To validate how modules in Pointformer affect learned point features, we visualize the attention maps from the GT module of the second last Pointformer block. We show the attention of the particular points in Figure 5. The second row shows the 50, 100, 200 points with highest attention values towards the points marked with star. We can observe that Pointformer first focuses on the local region of the same object, then spread the attention to other regions, and finally attends points from other objects globally. The overall attention map shows the average attention weights of all the points in the scene, indicating that our model mostly focuses on points on the objects. These visualization results show that Pointformer can capture local and global dependencies, and enhance message passing on both object and scene levels. + +# 5. Conclusion + +This paper introduces Pointformer, a highly effective feature learning backbone for 3D point clouds that is permutation invariant to points in the input and learns local and global context-aware representations. We apply Pointformer as the drop-in replacement backbone for state-of-the-art 3D object detectors and show significant performance improvements on several benchmarks including both indoor and outdoor datasets. + +Comparing to classification and segmentation tasks including part-segmentation and semantic segmentation in prior work, 3D object detection typically involves more points $(4\times -16\times)$ in a scene, which makes it harder for Transformer-based models. For future work, we would like to explore extensions to these two tasks and other 3D tasks such as shape completion, normal estimation, etc. + +# Acknowledgments + +This work is supported in part by the National Science and Technology Major Project of the Ministry of Science and Technology of China under Grants 2018AAA0100701, the National Natural Science Foundation of China under Grants 61906106 and 62022048, the Institute for Guo Qiang of Tsinghua University and Beijing Academy of Artificial Intelligence. + +# References + +[1] H. Caesar, Varun Bankiti, A. Lang, Sourabh Vora, Venice Erin Liong, Q. Xu, A. Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscene: A multimodal dataset for autonomous driving. CVPR, pages 11618-11628, 2020. +[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-End object detection with transformers. In ECCV, May 2020. +[3] Mark Chen, Alec Radford, Rewon Child, Jeff Wu, Heewoo Jun, Prafulla Dhariwal, David Luan, and Ilya Sutskever. Generative pretraining from pixels. ICML, 2020. +[4] Krzysztof Choromanski, Valerii Likhosherstov, David Dohan, Xingyou Song, Andreea Gane, Tamas Sarlos, Peter Hawkins, Jared Davis, Afroz Mohiuddin, Lukasz Kaiser, David Belanger, Lucy Colwell, and Adrian Weller. Rethinking attention with performers, 2020. +[5] MMDetection3D Contributors. MMDetection3D: Open-MMLab next-generation platform for general 3d object detection. https://github.com/open-mmlab/mmdetection3d, 2020. +[6] Jean-Baptiste Cordonnier, Andreas Loukas, and Martin Jaggi. On the relationship between self-attention and convolutional layers. arXiv preprint arXiv:1911.03584, 2019. +[7] Angela Dai, Angel X Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In CVPR, pages 5828-5839, 2017. +[8] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: Pre-training of deep bidirectional transformers for language understanding. In NAACL-HLT, pages 4171–4186, Minneapolis, Minnesota, June 2019. Association for Computational Linguistics. +[9] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale, 2020. +[10] Andreas Geiger, Philip Lenz, and Raquel Urtasun. Are we ready for autonomous driving? the kitti vision benchmark suite. In CVPR, 2012. +[11] Benjamin Graham, Martin Engelcke, and Laurens van der Maaten. 3d semantic segmentation with submanifold sparse convolutional networks. In CVPR, June 2018. +[12] Ji Hou, Angela Dai, and Matthias Niessner. 3d-sis: 3d semantic instance segmentation of rgb-d scans. In CVPR, June 2019. +[13] Angelos Katharopoulos, Apoorv Vyas, Nikolaos Pappas, and Francois Fleuret. Transformers are rnns: Fast autoregressive transformers with linear attention. ArXiv, abs/2006.16236, 2020. +[14] Nikita Kitaev, Lukasz Kaiser, and Anselm Levskaya. Reformer: The efficient transformer. *ICLR*, 2020. +[15] Alex H Lang, Sourabh Vora, Holger Caesar, Lubing Zhou, Jiong Yang, and Oscar Beijbom. Pointpillars: Fast encoders for object detection from point clouds. In CVPR, 2019. + +[16] Juho Lee, Yoonho Lee, Jungtaek Kim, Adam Kosiorek, Seungjin Choi, and Yee Whye Teh. Set transformer: A framework for attention-based permutation-invariant neural networks. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, ICML, volume 97 of Proceedings of Machine Learning Research, pages 3744-3753, Long Beach, California, USA, 09-15 Jun 2019. PMLR. +[17] Ming Liang, Bin Yang, Yun Chen, Rui Hu, and Raquel Urtasun. Multi-task multi-sensor fusion for 3d object detection. In CVPR, June 2019. +[18] Youngmin Park, Vincent Lepetit, and W. Woo. Multiple 3d object tracking for augmented reality. 2008 7th IEEE/ACM International Symposium on Mixed and Augmented Reality, pages 117-120, 2008. +[19] Charles R Qi, Or Litany, Kaiming He, and Leonidas J Guibas. Deep hough voting for 3d object detection in point clouds. In CVPR, pages 9277-9286, 2019. +[20] Charles R Qi, Wei Liu, Chenxia Wu, Hao Su, and Leonidas J Guibas. Frustum pointnets for 3d object detection from rgb-d data. In CVPR, 2018. +[21] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. arXiv preprint arXiv:1612.00593, 2016. +[22] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. In NeurIPS, pages 5099-5108, 2017. +[23] Prajit Ramachandran, Niki Parmar, Ashish Vaswani, I. Bello, Anselm Levskaya, and Jonathon Shlens. Stand-alone self-attention in vision models. In NeurIPS, 2019. +[24] Shaoshuai Shi, Chaoxu Guo, L. Jiang, Zhe Wang, Jianping Shi, X. Wang, and Hongsheng Li. Pv-rcnn: Point-voxel feature set abstraction for 3d object detection. CVPR, pages 10526–10535, 2020. +[25] Shaoshuai Shi, Xiaogang Wang, and Hongsheng Li. Pointr-cnn: 3d object proposal generation and detection from point cloud. In CVPR, June 2019. +[26] Weijing Shi and Raj Rajkumar. Point-gnn: Graph neural network for 3d object detection in a point cloud. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 1711-1719, 2020. +[27] Shuran Song, Samuel P Lichtenberg, and Jianxiong Xiao. Sun rgb-d: A rgb-d scene understanding benchmark suite. In CVPR, pages 567-576, 2015. +[28] Shuran Song and Jianxiong Xiao. Deep sliding shapes for amodal 3d object detection in rgb-d images. In CVPR, June 2016. +[29] H. Thomas, Charles R. Qi, Jean-Emmanuel Deschaud, B. Marcotegui, F. Goulette, and L. Guibas. Kpconv: Flexible and deformable convolution for point clouds. ICCV, pages 6410–6419, 2019. +[30] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In NeurIPS, pages 5998-6008, 2017. +[31] Sourabh Vora, Alex H. Lang, Bassam Helou, and Oscar Bei-jbom. Pointpainting: Sequential fusion for 3d object detection. In CVPR, June 2020. + +[32] Sinong Wang, Belinda Li, Madian Khabsa, Han Fang, and Hao Ma. Linformer: Self-attention with linear complexity. arXiv preprint arXiv:2006.04768, 2020. +[33] Shenlong Wang, Simon Suo, Wei-Chiu Ma, Andrei Pokrovsky, and Raquel Urtasun. Deep parametric continuous convolutional neural networks. In CVPR, June 2018. +[34] Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E Sarma, Michael M Bronstein, and Justin M Solomon. Dynamic graph cnn for learning on point clouds. Acm Transactions On Graphics (tog), 38(5):1-12, 2019. +[35] Qian Xie, Yu-Kun Lai, Jing Wu, Zhoutao Wang, Yiming Zhang, Kai Xu, and Jun Wang. Mlcvnet: Multi-level context votenet for 3d object detection. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10447-10456, 2020. +[36] Qiangeng Xu, Xudong Sun, Cho-Ying Wu, Panqu Wang, and U. Neumann. Grid-gcn for fast and scalable point cloud learning. CVPR, pages 5660-5669, 2020. +[37] Xu Yan, C. Zheng, Zhuguo Li, S. Wang, and Shuguang Cui. Pointasnl: Robust point clouds processing using nonlocal neural networks with adaptive sampling. CVPR, pages 5588-5597, 2020. +[38] Jiancheng Yang, Qiang Zhang, Bingbing Ni, Linguo Li, Jinxian Liu, Mengdie Zhou, and Qi Tian. Modeling point clouds with self-attention and gumbel subset sampling. In CVPR, June 2019. +[39] M. Ye, Shuangjie Xu, and Tongyi Cao. Hvnet: Hybrid voxel network for lidar based 3d object detection. CVPR, pages 1628-1637, 2020. +[40] Zaiwei Zhang, Bo Sun, Haitao Yang, and Qixing Huang. H3dnet: 3d object detection using hybrid geometric primitives. In European Conference on Computer Vision, pages 311-329. Springer, 2020. +[41] Yin Zhou and Oncel Tuzel. Voxelnet: End-to-end learning for point cloud based 3d object detection. In CVPR, June 2018. +[42] Benjin Zhu, Zhengkai Jiang, Xiangxin Zhou, Zeming Li, and Gang Yu. Class-balanced Grouping and Sampling for Point Cloud 3D Object Detection. arXiv e-prints, page arXiv:1908.09492, Aug 2019. +[43] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. 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Even though this produces convincing results, it has two major shortcomings. As the GAN is limited to reproduce the dataset the AE was trained on, we cannot reuse a trained AE for novel data. Furthermore, it is difficult to add spatial supervision into the generation process, as the AE only gives us a global representation. To remedy these issues, we propose to train the GAN on grids (i.e. each cell covers a part of a shape). In this representation each cell is equipped with a latent vector provided by an AE. This localized representation enables more expressiveness (since the cell-based latent vectors can be combined in novel ways) as well as spatial control of the generation process (e.g. via bounding boxes). Our method outperforms the current state of the art on all established evaluation measures, proposed for quantitatively evaluating the generative capabilities of GANs. We show limitations of these measures and propose the adaptation of a robust criterion from statistical analysis as an alternative. + +# 1. Introduction + +Training stable 3D GANs can be challenging and often better results are obtained by splitting the generation process into two parts. First an autoencoder (AE) is trained to obtain a compressed latent representation, then a GAN is trained to model the density of this global latent space. This simplifies the task, as the AE typically generates reasonable output for a wide range of latent vectors. Training the AE can be seen as imposing a bias on the generation process to produce shapes similar to those seen during its training. + +This procedure has obtained convincing results both for the generation of point clouds [1] and implicit functions [5]. However, using the latent space of an AE as intermediate shape representation has some severe drawbacks. Small variations of shapes are usually of local nature. As the latent representation used in prior work is of inherently global nature, such changes cannot be modeled easily. This makes it difficult to add any localized modifications or con + +straints into the generation process. Tasks such as conditional generation based on semantic information (e.g. segmentation/part labels) become hard to train. Another problem is that the AE limits the space of shapes that can be generated. Indeed every AE, which does not represent the entire space of possible shapes in its latent space, limits the expressiveness of the GAN through the bias it imposes. E.g. if we train a GAN to create tables in such a manner, this is unlikely to work with the latent space of an AE trained for chairs. + +A more natural choice of representation is to view a shape as a composition of many different local parts. This allows the network to choose parts that occur in different objects and arrange them to create new shapes. Recently, Jiang et al. [13] learned local latent representations by subdividing the object space into a grid to reconstruct scenes from point clouds with high fidelity. This can be seen as only imposing a localized bias on the shape generation process. Learning to capture the geometry within a single grid cell is much simpler than learning to represent the whole shape. Thus the reconstruction quality of the AE is much improved. + +We argue that this representation has several further advantages. Training a generative model on this localized latent space enables more variety in the generated shapes, as latent vectors belonging to different shapes or even different object classes can be mixed, giving the generator more degrees of freedom. Its expressiveness is thus not limited by the AEs ability to generalize. In fact we do not even need to train an AE for each specific class. An AE trained on cells of e.g. tables can still be used to generate chairs, as on part level both classes share similarities. Furthermore, we can use convolutional architectures and thus build on existing research in image generation. Although this argument applies to voxel based models as well [34], those are limited by the grid resolution that can fit into memory. As we can represent complex surfaces per grid cell, we can model realistic shapes while still keeping the grid resolution low. Lastly, the spatial decomposition of the latent space allows us to perform conditional generation based on spatial information, such as bounding boxes or semantic labels. + +When it comes to evaluating GANs there is no univer + +sally established measure to quantitatively rate, to what degree such networks are able to approximate a data distribution. Image GANs are usually evaluated with the inception score [29] or Fréchet inception distance [11]. The computation of both measures involves the application of the inception network [32]. Since many different representations are used to encode 3D shapes (point clouds, voxel grids, implicit functions, etc.), this is not straightforward to apply for our use case. While previous quality scores for 3D data have been proposed, we show that they have some limitations. Therefore, we propose to apply a statistic measure from a two sample test for multivariate sets [4] to compute the statistical difference between a set of generated objects and a test set of unseen shapes from the data distribution. + +Our key contributions are as follows: + +- We show that localized grid-based implicit functions are better suited for 3D shape generation with GANs than global implicit functions for three reasons. First, they offer higher quality results, since each cell only has to represent fairly simple geometry. Second, localized implicit functions can be combined together in novel ways and therefore offer more flexibility. Third, localized grid-based implicit functions allow us to control the generation process spatially, which is difficult to accomplish with global implicit functions. +- We show that common evaluation techniques for 3D shape generation have several drawbacks. To alleviate this we propose a new robust score inspired from statistical analysis. + +# 2. Related Work + +Many different representations (and network architectures) for processing 3D shapes have been proposed. In the context of this paper we will focus on previous work on the representation of shapes as functions via neural networks as well as prior work on generation of shapes with GANs. + +# 2.1. Representing Shapes as Functions + +There are two families of functions that can be used to represent shapes: parametric and implicit functions. The parametric approach to describe a surface (preferably an orientable 2-manifold in 3D) is to define a function $\mathbb{R}^2\to \mathbb{R}^3$ . Evaluating this function (e.g. on a 2D unit square) then gives positions on the surface of a shape in $\mathbb{R}^3$ . Such maps can be learned and represented by neural networks [31]. Since a single map is often insufficient to represent complex shapes, this idea has been modified in AtlasNet [8] to instead learn several functions, where each describes part of a single shape. A different approach is taken by [17] who instead represent a shape with localized functions in a grid, where each function models the surface within a grid cell. + +Implicit functions come in two types: signed distance functions $\mathbb{R}^3\to \mathbb{R}$ map each point in 3D to a distance value, that is by convention negative inside of the shape and positive outside. The surface of the shape is then the zero level-set of this function. On the other hand there are binary functions $\mathbb{R}^3\rightarrow \{0,1\}$ , that classify a point as being inside or outside of a given shape. Methods such as Marching Cubes [18] can be used in both cases to extract a surface. Recently several approaches have been published, that apply neural networks to represent such functions [25, 21, 5]. As a global function can have difficulties representing a shape with all its details, several methods have been proposed to mitigate this problem by using localized functions embedded in a grid structure. Chibane et al. [6] employ a multi-scale approach, where feature vectors at different scales and grid points are interpolated based on the current point position, while Jiang et al. [13] save a single feature vector per grid cell and classify a point (in local coordinates) together with its cell vector. We use a similar approach for our generative model. + +# 2.2. GANs in 3D + +To the best of our knowledge [34] were the first to develop GANs for the 3D setting, choosing voxels as a representation. This allowed them to use convolutional networks both as the generator and discriminator. However, the results generated by their method are limited by the low resolution of $64^{3}$ grids (mainly due to memory constraints). Achlioptas et al. [1] developed GANs for point clouds in two settings. They trained a generator and discriminator directly on the point clouds but also introduced a two step approach. They first trained an autoencoder for reconstructing point clouds and then fitted a generative model to the latent space. For this they proposed both a GAN and a Gaussian Mixture Model. A similar approach is used by [16]. The idea of splitting GAN training into two steps proved to be applicable to implicit functions as well, as IM-GAN [5] demonstrated. Very recently [15] showed that it is also possible to train GANs directly on implicit functions, however they do not reach the same quality as latent approaches. + +# 3. 3D Shape Generation with Localized Implicit Functions + +We propose a two step procedure for the generation of 3D shapes (see Figure 1) similar to [5]. Firstly, we train an autoencoder that maps inputs to localized implicit functions. Secondly, we train a GAN that learns the distribution of such functions. We will discuss our autoencoder first and then describe our proposed unconditional and conditional generation methods. Details of the different architectures and the training procedure can be found in the supplementary material (Appendix B, C). + +![](images/08e0759dfd07c0195aa4573a7554c3671965ad15b929ec70b691c4c056d0c932.jpg) +Figure 1: Overview of our method: With the help of an AE (Enc & Dec) we can represent 3D shapes as a grid of latent vectors. Our proposed GAN (G & D) generates new grids of latent vectors, from which shapes can be extracted via the decoder (Dec). Furthermore, we can optionally (dashed arrows) condition, e.g. on bounding boxes, for spatial control in the generation process. + +# 3.1. Autoencoder + +The architecture we employ for our autoencoder is related to [13]. Our encoder takes as input high-resolution binary voxel grids $(n^3)$ and after several (strided) convolutions outputs (comparably) low-resolution grids $(k^3)$ , where each grid cell is equipped with an $h$ -dimensional latent vector. Thus each cell of the output encodes the geometry of an overlapping cubical subset of the high-resolution voxel grid. In all of our experiments the resolution of the latent grid is chosen as $k = 32$ and the number of channels as $h = 8$ . + +The decoder evaluates the implicit function represented by this grid of latent cells at a set of sample points. To this end, we find the cell a point is contained in and concatenate its latent vector with the point's position (in local coordinates of the cell). Then we feed this vector into a MLP with a scalar output. The resulting score (0 for outside and 1 for inside of a shape) can be trained with a binary cross entropy loss. + +As independent functions in neighboring cells can lead to discontinuities of the implicit function at the boundary between cells, we interpolate the results obtained from neighboring grid cells, leading to smoother results. + +$$ +f (x, C, \theta) = \sum_ {j \in \mathcal {N}} w _ {j} \operatorname {D e c} _ {\theta} \left(c _ {j} \in C, k \left(x - x _ {j}\right)\right), \tag {1} +$$ + +where $C$ is the grid of latent vectors, $c_{j}$ is the vector corresponding to cell $j$ and $x_{j}$ is its cell center, $\mathcal{N}$ is the neighborhood of point $x$ and $w_{j}$ the trilinear interpolation weight of $x$ with regard to the center of cell $j$ . We refer to the resolution of the latent grid as $k$ . The decoder Dec has pa + +rameters $\theta$ . This interpolation is especially important in our GAN setting, as it simplifies the task of generating matching cells. To make sure that the necessary information for this is stored in the latent vectors, we choose the receptive field of the encoder so that each latent grid cell can encode the geometric information of neighboring cells as well. + +# 3.2. Unconditional Generation + +After we have trained an autoencoder, as described in the previous section, we can now train a GAN on its latent space. Chen et al. [5] learn a single latent vector for the entire shape and therefore train simple MLPs as generator and discriminator to generate new vectors and thus new shapes. We on the other hand generate a full grid of latent vectors, each describing a local part of the shape, that together constitute the object. Thus, it is not only important that the local geometry described by the implicit function for each grid cell itself is reasonable, it must match with its neighbors as well. Although these considerations put an additional burden on the GAN, this approach has a decisive advantage over previous latent approaches. As it is possible to arrange the grid cells in various ways, we are less constrained by any bias the autoencoder may introduce. This is because we only need the autoencoder to reconstruct building blocks instead of entire shapes. + +Our task can be seen as being analogous to image generation, therefore similar considerations apply. Instead of generating a 2D grid with 3 channels, we generate a 3D grid with $h$ channels. For this reason we use 3D convolutional networks as generator and discriminator. The generator is a simple 3D CNN with stripped convolutions, batch normalization and LeakyReLU as non-linearity. We do not use any + +residual layers or skip connections. + +In order to provide feedback to the generator at various scales, we use three patch discriminators (adapted from pix2pix [12]) that have residual layers and apply spectral normalization [23]. All three discriminators have the same architecture, but do not share parameters. Each discriminator is run convolutionally over the latent grid, rating each local patch separately. The scores are then averaged for the discriminators' final output. The discriminators work at different input resolutions $(32^{3}, 16^{3}$ , and $8^{3}$ ) and thus inspect features of different scale. The lower resolutions are computed by trilinear interpolation of the latent vectors. This training scheme puts a strong focus on local details, emphasizing the higher complexity and expressiveness of single grid cells compared to images or binary voxel grids. The effectiveness of patch discriminators is shown in Appendix D. + +For better convergence we use a gradient penalty on interpolations between true and fake data as introduced in [9]. We obtained the best results with zero-centered gradient penalty [28, 20] and maximum reduction [14]. As loss we use the standard non-saturating (NS) loss [7]. + +# 3.3. Conditional Generation + +In many use cases we would like to control certain characteristics of the generated objects. To this end we can guide the generation process with conditional GANs [22]. These conditions can be of global nature, like class labels, or more localized. An example for this are architectures that create images based on information in the form of other images (e.g. photos from label maps) [12, 33, 26]. For this purpose the input image is used as a mask providing a pixelwise conditioning. + +The spatial organisation of our latent space easily allows us to adapt this approach to 3D data. For our generator we use the architecture of SPADE [26] adapted to 3D. The key idea is to compute a cell-wise scale and bias depending on a mask and apply it to the feature maps at different layers. We use the same discriminators as for unconditional generation. The only difference is that we concatenate the mask with the generated grid in the beginning. We experiment with different ways to provide these masks (e.g. bounding boxes, shape parts, silhouettes), depending on the respective application. The losses and training parameters are the same as for unconditional generation. + +# 4. Evaluation + +In this section we present the measure we use to compare the performance of different GANs as well as motivate its effectiveness compared to previous measures. Furthermore, we show quantitative and qualitative results of our unconditional and conditional generation scheme. All evaluations are performed on the ShapeNet Core dataset (v1) + +[2]. For comparability reasons we follow the training split and evaluation setup from [5] and generate distributions for the categories car, chair, plane, rifle and table. As ground truth we use the voxelized models from [10]. In each category we sorted the models by name and used the first $80\%$ for training and the rest for testing. + +# 4.1. Quality Measures + +Several approaches have been suggested to evaluate the fidelity of generative models. Generally any evaluation method needs to answer two questions: + +1. How to measure the similarity of individual data points (e.g. 3D shapes)? +2. How to compare two data distributions? + +The answer to the first question typically depends on the domain, while the answer to the second question is domain agnostic for the most part. In the realm of 3D shapes, several similarity measures have been proposed. For point cloud based methods the Chamfer distance (CD) and Earth Mover distance (EMD) were introduced [1]. On the other hand [30] proposes to use features extracted from a pretrained PointNet network [27]. As we generate surfaces instead of point clouds, using these methods would require to sample all shapes, by which we lose fine details of the underlying surface. Chen et al. [5] argue that point based distances do not align well with visual similarity and instead propose to use the light field descriptor (LFD) [3] to measure similarity. We follow this reasoning and use the LFD for our evaluation. Note that the similarity between LFDs is measured in a non-Euclidean manner. + +Having answered the first question, i.e. how to compare individual data points, we will now discuss how two distributions can be compared. We use the test set as a proxy of a different unseen sampling drawn from the data distribution that generated the training set. We refer to the generated data set as $\mathcal{A}$ and to the test set as $\mathcal{B}$ . + +Two options for comparing distributions $\mathcal{A}$ and $\mathcal{B}$ were introduced by Achlioptas et al. [1]. Coverage is meant to measure the diversity of $\mathcal{A}$ (with regard to $\mathcal{B}$ ). For each shape in $\mathcal{A}$ we mark the closest neighbor in $\mathcal{B}$ according to the distance defined above. We then count the percentage of shapes in $\mathcal{B}$ , that have been marked. If our generative scheme has low diversity, for example due to mode collapse, the generated shapes would lie close together and cover only a small subset of the space spanned by $\mathcal{B}$ . This measure however does not evaluate the fidelity of individual shapes within $\mathcal{A}$ , as the actual distance between shapes does not matter. To take this into account the Minimum Matching Distance (MMD) is introduced. Here we compute the distance from each shape in $\mathcal{B}$ to its closest neighbor in $\mathcal{A}$ and take the mean over those. + +![](images/affa9254e6bfa84624208bffecde32545a92667304d210dd82c0a1fc437130a2.jpg) +Figure 2: Comparing different distribution measures on two Gaussian distributions with different dimensions (1, 10, 100, 1000) and zero mean. $\mathcal{B}$ has a variance of 1, while the variance of $\mathcal{A}$ varies. + +![](images/7528852e20de163e50522ddd90e2bdb40719bf296d049dc37a8528f87a6b597a.jpg) + +![](images/d77c1292ee22a8644843779c6d9ed9c7a2ef06fde59516d2a1bc02e940fcebac.jpg) + +Another option to compare distributions that is popular for evaluating GANs on images, is the Fréchet inception distance (FID) [11]. This measure assumes the distributions to be Gaussian and thus computes mean and covariance of the descriptors within $\mathcal{A}$ and $\mathcal{B}$ and then computes the Fréchet distance. Note that this method assumes Euclidean distance between feature maps and does not work on general distance measures. Therefore, it cannot be applied to the LFD. + +We argue that these metrics all have shortcomings in evaluating the quality of a generated distribution. For Coverage and MMD the outliers in $\mathcal{A}$ are not penalized in any way, whereas outliers in $\mathcal{B}$ can have a significant impact. Furthermore, considering only the nearest neighbor is not sufficient to compare the actual density of distributions, as differences in local densities do not have much of an impact. On the other hand FID runs into problems, when the underlying distributions are not Gaussian. + +An easy example, where coverage and MMD already fail, is to compare (based on the Euclidean distance) samples from two isotropic Gaussian distributions with zero mean for various dimensions (Figure 2). $\mathcal{B}$ was sampled from a Gaussian with variance 1, while we mimic different generative models by sampling multiple sets of $\mathcal{A}$ from different Gaussians with varying variance. Ideally, the measures would give the best results for $\mathcal{A}$ sampled from a Gaussian with variance 1. However, the coverage never reaches 1 even when $\mathcal{A}$ and $\mathcal{B}$ are drawn from the same distribution. More critically, depending on the dimension, the coverage does not have its peak at 1, as would be expected. The MMD is either not much affected, or has its minimum, when the variance is minimal. Thus, even in combination, the two measure are not reliable in order to determine how likely it is that the two sets come from the same distribution. + +To show the deficiencies of the Fréchet distance as an evaluation measure, we compare different types of distributions, whose values we choose so that they all have zero mean and unit variance (Table 1). By definition the Fréchet distance is not able to differentiate between any of these distributions, as the fitted Gaussians are identical. + +
Gaussianuniformbinary
Gaussian5.315.275.24
1.5552.73163.58
uniform5.185.16
1.58135.21
binary5.06
1.95
+ +Table 1: Comparing different measures on different distributions. Fréchet distance in blue, ECD in black. The samples are always 100 dimensional, where each value is chosen from a distribution with parameters chosen so that we have zero mean and unit variance. The binary distribution consists of the values -1 and 1. + +We therefore are interested in a test, that remedies these issues. It should take local densities into account, consider the complete distribution of $\mathcal{A}$ and $\mathcal{B}$ without being too much affected by outliers and actually decrease when the two distributions are similar. Furthermore it should be able to distinguish all kinds of distributions and not be restricted to Gaussians. Testing whether two sample sets come from the same underlying distribution is a well known problem in statistical analysis and referred to as a two sample test. Since we want to measure the distance between $\mathcal{A}$ and $\mathcal{B}$ by considering the likelihood of them being sampled from the same distribution, this problem is closely related to ours. We propose to use a statistic introduced in [4] as a distance measure between our two sets, since it is fairly robust even for multivariate data. This approach builds a $k$ -minimum spanning tree of the neighborhood graph of $\mathcal{A} \cup \mathcal{B}$ . Edges in this tree are classified according to whether they connect shapes within $\mathcal{A}$ , within $\mathcal{B}$ or between $\mathcal{A}$ and $\mathcal{B}$ . The final score is computed as a weighted difference between the number of these edges and the edge count we would expect if $\mathcal{A}$ and $\mathcal{B}$ were from the same distribution. The exact formula for this measure can be found in Appendix A. Throughout the rest of this paper we will refer to this measure as Edge Count Difference (ECD). + +
PlaneCarChairRifleTableAvg. w/o planesAvg.
COV(%)3DGAN12.1325.0762.3218.8029.58
PC-GAN73.5561.4070.0661.4777.5067.6168.80
IM-GAN70.3369.3375.4465.2686.4374.1273.36
Our81.5880.6782.0881.4786.1983.1082.80
Train85.0485.6784.7384.0087.1385.3885.13
MMD3DGAN1,9934,3654,4765,2084,010
PC-GAN3,7371,3603,1433,8912,8222,8042,991
IM-GAN3,6891,2872,8933,7602,5272,6172,831
Our3,2261,2252,7683,3662,3962,4532,607
Train2,2259842,3173,0852,0662,1132,135
+ +Table 2: Quantitative evaluation of generative models. As 3DGAN was not trained on plane models, this entry is missing. Results for the train set are reported to give reference values. + +
PlaneCarChairRifleTable
3DGAN28,85526,2796,49532,116
IM-GAN6,54320,6062,5533,2881,018
Our3551,06214494188
Train111125
+ +Table 3: Quantitative evaluation of generative models with ECD. We do not report averages, as values for different dataset sizes are not comparable. + +As shown in Figure 2 this measure performs reliably on the toy example with Gaussian distributions introduced above. It actually achieves its minimum, when $\mathcal{A}$ and $\mathcal{B}$ are sampled from the same distribution. Furthermore it has no problems distinguishing different distributions with the same variance (Table 1). As we only need to be able to obtain distances between samples to compute the ECD, we are not restricted to the Euclidean space and thus can apply this test together with the LFD. + +# 4.2. Results + +To compare our method to the state of the art, we evaluate the results w.r.t. both previous measures Coverage and MMD (Table 2). We compare to 3DGAN [34] (a voxel based method), IM-GAN [5], which is a latent-GAN that works on global implicit functions, as well as PC-GAN [1]. Note that a comparison here is difficult, since this method produces point clouds that need to be transformed to meshes first. For all other methods, meshes are created from generated or sampled voxel grids with marching cubes [18]. The quantitative results for previous methods are taken from [5]. Furthermore, following [5] all measures are evaluated on meshes that have been extracted from a voxelisation with resolution $64^{3}$ . Therefore, the different methods have been trained and sampled at resolution $64^{3}$ as well. The size of the generated dataset is always 5 times the size of the test + +dataset. Note that while IM-GAN and PC-GAN trained specific AEs for each separate class, we trained a single AE on the train split of the entire shapenet dataset. Table 2 shows that our method outperforms the state of the art when it comes to coverage on all but one class, showing the higher diversity of our generated samples. Furthermore, we always have a lower MMD showcasing the higher quality of our sampled shapes. + +We also compare against 3DGAN and IM-GAN on the introduced ECD (Table. 3) Here we average the score of 10 random sub-samplings of the generated set with equal number to the test set. Qualitative results of the different methods can be seen in Figure 3. Although the results of IM-GAN sometimes appear smoother than the ones our method produces, this comes at the cost of less diversity. + +As we can see in Figure 4 on the example of the rifle dataset, IM-GAN does not fully capture the distribution of the test set, whereas for our method both distributions are well mixed. This is supported by our quantitative evaluation, where we strongly outperform IM-GAN on the ECD even though our qualitative results are comparable. + +A reason for the weaker quantitative results of IM-GAN might be that due to problems during GAN training we are observing mode collapse. Another possible explanation for this effect might be found with the strong shape bias the AE enforces, as this bias can make it harder for the GAN to faithfully capture the data distribution. This could be due to the AE mapping larger regions of the latent space to similar shapes. The localized latent grid structure we employ is less prone to such problems, as it is able to represent a much wider variety of shapes. + +Conditional Generation As described in Section 3.3, our method is able to incorporate spatial guidance into the generation process. As we make use of the grid structure of our latent space for this, approaches based on a global latent + +![](images/918395c2a9c3704d3ab3dbaebe0c86848463e27150f52c81abc0c05e2d72ad16.jpg) +Figure 3: Typical generative results for each model on each category. For 3DGAN we do not show a plane model, since it was not trained on the plane dataset. + +![](images/f1433c0320065d60ead979b240e87e4859bbe1283dab120f3da3df3708a33e69.jpg) +Figure 4: t-SNE [19] (perplexity = 10) low dimensional embeddings of the combined generated and test set from the rifle dataset. On the left distinct clusters are visible, hinting at different densities of the sets. This is not the case on the right. + +![](images/7facc0e32385127eff2f980d121cf1c78a7567a4cbb78e803feadf242404a5c2.jpg) + +space are unable to offer such guidance in a straightforward manner. This guidance can be provided in many different ways. This information can take the form of binary values, class labels, or even complex encodings. This flexibility allows for several applications, some of which we will present in the following. + +The simplest possibility to offer guidance is to provide a single binary variable for each grid cell. With this we can for example generate shapes that fit into a predefined bounding box. This bounding box is simply discretized to our grid resolution so that each cell gets the information whether it is inside or outside of it. Exemplary results of this gen + +![](images/e6266ad6700fa1aa5233b9abbf0d47a0d2e8dfb6099ab2b53aa08d0470816f82.jpg) +Figure 5: Conditionally generated examples shown with their input bounding boxes. On the right side, we added an additional "negative" box, that is supposed to stay empty. + +eration process, as well as the bounding boxes they were conditioned on, can be seen in Figure 5. We can not only prescribe a bounding box, that should contain all of the geometry, but allow the user to further restrict the shape space, by specifying "negative" bounding boxes, that should not contain any geometry. + +If semantic information is available (in our case given by the PartNet dataset [24]), this can be used for more fine grained generation (Figure 6). This means we can prescribe a bounding box for each semantic part of the object. In this + +![](images/3d302fad5b246fc69615e5c3719eed8072f5dc6654dc436d13c04c3f6c21a464.jpg) +Figure 6: Example for shapes conditioned on part based bounding boxes. The differently colored bounding boxes represent different semantic parts. + +![](images/bf962d5db54f1b9ea8422da404ff58883421b2a9efed00f9d84cf52e452123a1.jpg) + +![](images/6f5c3df24ed08616471140d22dad0a8c91f18b14a7c46c458bb25ba0c646cae3.jpg) +Figure 7: Example for silhouette based generation. The 3D masks are extracted from the low resolution silhouettes shown in the insets. + +case, we do not provide binary data, but part labels per grid cell. + +Bounding boxes are however not the only option to provide this simple guidance. Another possible application, would be to compute this information from a silhouette, given as a binary 2D image (Figure 7). For simplicity, we assume the viewing direction to be axis aligned. The information can be presented as a single image, or as multiple images corresponding to different axes. + +In all previous examples, we provided one-hot vectors per cell. However, complex encodings can be used for this kind of conditioning as well. As an example, we show the application of shape completion on chairs. For this we cut out one semantic part from the object (backrest, armrest, seat or legs) and train the network to insert this missing part. This is implemented by conditioning the GAN on the geometry that is still available. We provide this information by using our AE to encode the present geometry into latent vectors for each cell (Figure 8). As can be seen, our generated shape follows the provided guidance, where it is + +![](images/979c225a2a9939ac17d8daed3ce140c60f4476885d5f07dff208b3b23defd3f3.jpg) +Figure 8: Example for shape completion. On the left we see the given conditioning, on the right the generated chair. + +![](images/c185e9b077ed4f77ed987708d620090c6b9caf9cfc2aeb109b9324ef45307892.jpg) + +given, and is reasonably completed, where it is not. For all examples we obtained the supervision masks from unseen examples of the test set. + +# 5. Conclusion + +We introduced a GAN that generates piecewise implicit functions organized in grids to represent 3D shapes. By learning on localized latent representations instead of global ones (as in previous work) we are able to model the data generating distribution more closely than prior methods. We showed this by evaluating our method quantitatively with measures from prior work as well as with the proposed usage of ECD. Due to the convolutional nature of our GAN architecture we are able to incorporate spatial guidance (in a wide variety of forms) in the generation process. We only showed few examples, but expect this approach to viable for a wide range of tasks. + +The results generated from global latent representations appear smoother since they are less likely to capture the details of the ground truth. As the AE part in our generation process is able to learn fine details of the underlying shapes, it tends to reproduce voxelization artifacts from the ground truth. We therefore expect higher resolution ground truth shapes to lead to even better results for our method. + +Acknowledgements This work was supported by the Gottfried-Wilhelm-Leibniz Programme of the Deutsche Forschungsgemeinschaft DFG, project number KO2064/6-1, as well as DFG project number KO2064/9-1 + +# References + +[1] P. Achlioptas, O. Diamanti, I. Mitliagkas, and L. J. Guibas. Learning representations and generative models for 3d point clouds. International Conference on Machine Learning, 2018. + +[2] A. X. Chang, T. Funkhouser, L. Guibas, P. Hanrahan, Q. Huang, Z. Li, S. Savarese, M. Savva, S. Song, H. Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015. +[3] D.-Y. Chen, X.-P. Tian, Y.-T. Shen, and M. Ouhyoung. On visual similarity based 3d model retrieval. Computer Graphics Forum, 22(3):223-232, 2003. +[4] H. Chen and J. H. Friedman. A new graph-based two-sample test for multivariate and object data. Journal of the American statistical association, 112(517):397-409, 2017. +[5] Z. Chen and H. Zhang. Learning implicit fields for generative shape modeling. IEEE Conf. on Computer Vision and Pattern Recognition, 2019. +[6] J. Chibane, T. Alldieck, and G. Pons-Moll. Implicit functions in feature space for 3d shape reconstruction and completion. IEEE Conf. on Computer Vision and Pattern Recognition, pages 6970-6981, 2020. +[7] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio. Generative adversarial nets. Advances in Neural Information Processing Systems, pages 2672-2680, 2014. +[8] T. Groueix, M. Fisher, V. G. Kim, B. Russell, and M. Aubry. AtlasNet: A Papier-Mâché Approach to Learning 3D Surface Generation. IEEE Conf. on Computer Vision and Pattern Recognition, 2018. +[9] I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. C. Courville. Improved training of wasserstein gans. Advances in Neural Information Processing Systems, pages 5767-5777, 2017. +[10] C. Hane, S. Tulsiani, and J. Malik. Hierarchical surface prediction for 3d object reconstruction. 2017 International Conference on 3D Vision (3DV), pages 412-420, 2017. +[11] M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, and S. Hochreiter. Gans trained by a two timescale update rule converge to a local nash equilibrium. Advances in Neural Information Processing Systems, pages 6626-6637, 2017. +[12] P. Isola, J.-Y. Zhu, T. Zhou, and A. A. Efros. Image-to-image translation with conditional adversarial networks. IEEE Conf. on Computer Vision and Pattern Recognition, pages 1125-1134, 2017. +[13] C. M. Jiang, A. Sud, A. Makadia, J. Huang, M. Nießner, and T. Funkhouser. Local implicit grid + +representations for 3d scenes. IEEE Conf. on Computer Vision and Pattern Recognition, 2020. +[14] A. Jolicoeur-Martineau and I. Mitliagkas. Connections between support vector machines, wasserstein distance and gradient-penalty gans. arXiv preprint arXiv:1910.06922, 2019. +[15] M. Kleineberg, M. Fey, and F. Weichert. Adversarial generation of continuous implicit shape representations. arXiv preprint arXiv:2002.00349, 2020. +[16] C. Li, M. Zaheer, Y. Zhang, B. Póczos, and R. Salakhutdinov. Point cloud GAN. Deep Generative Models for Highly Structured Data, ICLR 2019 Workshop, New Orleans, Louisiana, United States, May 6, 2019, 2019. +[17] I. Lim, M. Ibing, and L. Kobbelt. A convolutional decoder for point clouds using adaptive instance normalization. Computer Graphics Forum, 38(5):99-108, 2019. +[18] W. E. Lorensen and H. E. Cline. Marching cubes: A high resolution 3d surface construction algorithm. ACM siggraph computer graphics, 21(4):163-169, 1987. +[19] L. v. d. Maaten and G. Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579-2605, 2008. +[20] L. Mescheder, A. Geiger, and S. Nowozin. Which training methods for gans do actually converge? arXiv preprint arXiv:1801.04406, 2018. +[21] L. Mescheder, M. Oechsle, M. Niemeyer, S. Nowozin, and A. Geiger. Occupancy networks: Learning 3d reconstruction in function space. IEEE Conf. on Computer Vision and Pattern Recognition, 2019. +[22] M. Mirza and S. Osindero. Conditional generative adversarial nets. arXiv preprint arXiv:1411.1784, 2014. +[23] T. Miyato, T. Kataoka, M. Koyama, and Y. Yoshida. Spectral normalization for generative adversarial networks. arXiv preprint arXiv:1802.05957, 2018. +[24] K. Mo, S. Zhu, A. X. Chang, L. Yi, S. Tripathi, L. J. Guibas, and H. Su. PartNet: A large-scale benchmark for fine-grained and hierarchical part-level 3D object understanding. IEEE Conf. on Computer Vision and Pattern Recognition, 2019. +[25] J. J. Park, P. Florence, J. Straub, R. Newcombe, and S. Lovegrove. Deepsdf: Learning continuous signed distance functions for shape representation. IEEE Conf. on Computer Vision and Pattern Recognition, 2019. + +[26] T. Park, M.-Y. Liu, T.-C. Wang, and J.-Y. Zhu. Semantic image synthesis with spatially-adaptive normalization. IEEE Conf. on Computer Vision and Pattern Recognition, pages 2337-2346, 2019. +[27] C. R. Qi, H. Su, K. Mo, and L. J. Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. IEEE Conf. on Computer Vision and Pattern Recognition, pages 652-660, 2017. +[28] K. Roth, A. Lucchi, S. Nowozin, and T. Hofmann. Stabilizing training of generative adversarial networks through regularization. Advances in Neural Information Processing Systems, pages 2018-2028, 2017. +[29] T. Salimans, I. Goodfellow, W. Zaremba, V. Cheung, A. Radford, and X. Chen. Improved techniques for training gans. Advances in Neural Information Processing Systems, pages 2234-2242, 2016. +[30] D. W. Shu, S. W. Park, and J. Kwon. 3d point cloud generative adversarial network based on tree structured graph convolutions. Proceedings of the IEEE International Conference on Computer Vision, pages 3859-3868, 2019. +[31] A. Sinha, A. Unmesh, Q. Huang, and K. Ramani. Surfnet: Generating 3d shape surfaces using deep residual networks. IEEE Conf. on Computer Vision and Pattern Recognition, pages 6040-6049, 2017. +[32] C. Szegedy, V. Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna. Rethinking the inception architecture for computer vision. IEEE Conf. on Computer Vision and Pattern Recognition, pages 2818-2826, 2016. +[33] T.-C. Wang, M.-Y. Liu, J.-Y. Zhu, A. Tao, J. Kautz, and B. Catanzaro. High-resolution image synthesis and semantic manipulation with conditional gans. IEEE Conf. on Computer Vision and Pattern Recognition, pages 8798-8807, 2018. +[34] J. Wu, C. Zhang, T. Xue, B. Freeman, and J. Tenenbaum. Learning a probabilistic latent space of object shapes via 3d generative-adversarial modeling. 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Schwing $^{2}$ Rohit Girdhar $^{1}$ $^{1}$ Facebook AI Research University of Illinois at Urbana-Champaign + +https://facebookresearch.github.io/WyPR + +![](images/2a1a486a90b2717e1ff665e7f211754bae09b779aa59f303e98b67061f2064ef.jpg) +Figure 1: (Left) Our framework, WyPR, jointly learns semantic segmentation and object detection for point cloud data from only scene-level class tags. We find that encouraging consistency between the two tasks is key. (Right) Sample segmentation results from ScanNet val set, without seeing any point-level labels during training. Please refer to § 4.4 and Appendix F for more analysis and visualizations. + +![](images/27d1784f812c5cb0c4696f8c5058b0f4ef8ed81183d2bdc26b14275a1a33db9e.jpg) + +# Abstract + +We introduce WyPR, a Weakly-supervised framework for Point cloud Recognition, requiring only scene-level class tags as supervision. WyPR jointly addresses three core 3D recognition tasks: point-level semantic segmentation, 3D proposal generation, and 3D object detection, coupling their predictions through self and cross-task consistency losses. We show that in conjunction with standard multiple-instance learning objectives, WyPR can detect and segment objects in point cloud data without access to any spatial labels at training time. We demonstrate its efficacy using the ScanNet and S3DIS datasets, outperforming prior state of the art on weakly-supervised segmentation by more than $6\%$ mIoU. In addition, we set up the first benchmark for weakly-supervised 3D object detection on both datasets, where WyPR outperforms standard approaches and establishes strong baselines for future work. + +# 1. Introduction + +Recognition (i.e., segmentation and detection) of 3D objects is a key step towards scene understanding. With the recent development of consumer-level depth sensors (e.g., LiDAR [13, 43]) and the advances of computer vision algorithms, 3D data collection has become more convenient and inexpensive. However, existing 3D recognition systems often fail to scale as they rely on strong supervision, such as point level semantic labels or 3D bounding + +boxes [9, 29, 32], which are time consuming to obtain. For example, while the popular large-scale indoor 3D dataset ScanNet [10] was collected by only 20 people, the annotation effort involved more than 500 annotators spending nearly 22.3 minutes per scan. Furthermore, due to the high annotation cost, existing 3D object detection datasets have limited themselves to a small number of object classes. This time consuming labeling process is a major bottleneck preventing the community from scaling 3D recognition. + +Motivated by this observation, we study 3D weakly-supervised learning with only scene-level class tags available as supervision to train semantic segmentation and object detection models. Scene-level tags are very efficient to annotate, taking only a second or less for each object in the scene [36]. Hence, methods that rely on such supervision can be scaled more easily than those that rely on box-level supervision. + +For this we develop the novel weakly-supervised framework called WyPR, shown in Fig. 1. Using just scene level tags, it jointly learns both segmentation of point cloud and detection of 3D boxes. Why should joint learning of segmentation and detection perform better than independently learning the two tasks? First, since these two tasks are related, joint training is mutually beneficial for representation learning. Second, these tasks naturally constrain each other, leading to effective self-supervised objectives that further improve performance. For example, the semantic labels of points within a bounding box should be consistent, and vice versa. Lastly, directly learning to regress to dimensions of 3D bounding boxes, as common in supervised ap + +
Methods[46][56][59][51][53][33]WyPR
Weak labels2D boxes2D inst segsparse label2D sem segregion & scene tagsscene tagsscene tags
Tasksdetdetsegsegsegdetdet + seg
Datasetindooroutdoorindoor & objectsindoorindooroutdoorindoor
+ +Table 1: Summary of closely related work in weakly-supervised 3D recognition. Compared to prior work, our proposed method (WyPR) uses the readily available scene tags, and jointly learns detection and segmentation in the more challenging indoor room setting. + +proaches [28, 29, 39], is extremely challenging using weak labels. Learning weakly-supervised segmentation first permits a two-stage detection framework, where object proposals are generated bottom-up conditioned on segmentation prediction and further classified using a weakly-supervised detection algorithm. + +To achieve this, WyPR operates on point cloud data of complex indoor scenes and combines a weakly-supervised semantic segmentation stage (§ 3.1) with a weakly-supervised object detection stage (§ 3.2). The latter takes as input the geometric representation of the input scene and a set of computed 3D proposals from GSS, our novel Geometric Selective Search algorithm (§ 3.3). GSS uses local geometric structures (e.g., planes) and the previously computed segmentation, for bottom-up proposal generation. Due to the uninformative nature of weak labels, weakly-supervised frameworks often suffer from noisy prediction and high variance. We address this by encouraging both cross-task and cross-transformation consistency through self-supervised objectives. We evaluate WyPR on standard 3D datasets, i.e., ScanNet and S3DIS (§ 4), improving over prior work on weakly-supervised 3D segmentation by more than $6\%$ mIoU, and establishing new benchmarks and strong baselines for weakly-supervised 3D detection. + +Our contributions are as follows: 1) a novel point cloud framework to jointly learn weakly-supervised semantic segmentation and object detection, which significantly outperforms single task baselines; 2) an unsupervised 3D proposal generation algorithm, geometric selective search (GSS), for point cloud data; and 3) state-of-the-art results on weakly-supervised semantic segmentation, and benchmarks on weakly-supervised proposal generation and object detection. + +# 2. Related work + +3D datasets. Semantically labeled 3D data can be broadly classified into indoor [2, 5, 10, 41] and outdoor [7, 8, 14, 44] settings. ScanNet [10], a popular 3D detection and segmentation dataset, contains 20 classes labeled in 1500 scenes. While this dataset is large, it is small in comparison to 2D datasets, which reach tens of millions of images [21] and thousands of instance labels [17]. While the popularity of advanced 3D sensors [13, 43] could lead to a similar growth in 3D data, annotating that data would still be + +extremely time consuming. This underscores the need to develop weakly-supervised techniques for 3D recognition. + +3D representations. 3D data is often represented via a point cloud, and processed using one of two main backbone architectures. The first [9, 15, 16, 37] projects points to intermediate volumetric grids, and then processes them using convolutional nets. These methods are efficient but suffer from information loss due to the discretization into voxels. The second operates directly on points [31, 32, 47, 52], processing them in parallel either using a pointwise MLP [31, 32], graph convolution [52], or point convolution [47]. Our method is compatible with either backbone architecture. We adopt PointNet++ [32] for experimentation. + +3D tasks. Semantic segmentation [2, 6, 10], object detection [29, 30, 39, 42], and classification [57] are the standard recognition tasks defined on 3D data. For segmentation, the two most common tasks are point-level object parts segmentation [6] and scene object segmentation [2, 10], the latter of which we address in this work using weak supervision. For 3D object detection, standard techniques leverage either only a point cloud [29, 39, 61], or a point cloud together with the corresponding multi-view RGB images [18, 28, 30]. Unlike 2D where offline proposal generation methods [48, 64] are widely studied and generalize well to unseen datasets, 3D proposals generated from a point cloud are often trained in a supervised manner [20, 29, 39] and overfit to the training set. We propose an unsupervised 3D proposal generation algorithm GSS, which we further improve using weak supervision. + +Weakly-supervised learning. Weak labels in the form of image-level class tags are widely studied in 2D tasks such as image localization [58, 63], semantic segmentation [27, 55], and object detection [3, 35, 45]. Prior work mostly formulates weakly-supervised learning as a multiple instance learning problem, where the target tasks are learned implicitly in a multi-label classification framework. Pipelined [40, 54] or end-to-end self-training modules [35, 45] have also been demonstrated to be beneficial. + +Weakly-supervised learning in 3D. Compared to its 2D counterpart, weakly-supervised learning for 3D tasks is relatively unexplored. We summarize all relevant prior work in Tab. 1. For semantic segmentation, Wang et al. [51] leverage 2D segmentation as weak labels, Xu et al. [59] use a sparsely labeled point cloud, and Wei et al. [53] utilize both area and scene-level class tags during training. For object detection, recent work uses small sets of labeled 3D + +![](images/c4afa63cd303c8c300b65d428b815eac608daa8fcf4271997611e8083905e97f.jpg) +Figure 2: Approach Overview. A backbone network extracts geometric features which are used by the segmentation head to compute a point-level segmentation map. The segmentation map is passed into the 3D proposal generation module GSS, and the resulting proposals along with original features are used to detect 3D object instances. Through a series of self and cross-task consistency losses along with multiple-instance learning objectives, WyPR is trained end-to-end using only scene-level tags as supervision. + +data [24, 46, 62], 2D instance segmentation [56], and click annotation [24] as supervision. However, obtaining these labels is still time consuming. A closely related concurrent work [33] focuses on autonomous driving, building upon a small number of relatively easy objects (e.g., car, pedestrian) while still using image data. In contrast, we focus on complex indoor scenes, exclusively relying on the 3D point cloud, i.e., no images are required. + +Multi-task learning. Multi-task learning [4] has been widely studied for various vision tasks [12, 19, 25, 34]. It is of particular importance for weakly-supervised [23, 36] or self-supervised 2D object detection [11, 34] as multitasking provides mutual regularization and hence better representation learning. For detection and segmentation, prior work has studied joint training with 2D data [23] or supervised 3D data [49]. In this paper, we develop a novel framework for learning both tasks under weak supervision. + +# 3. WyPR + +Our goal is to use weak supervision in the form of scene-level tags and learn a joint 3D segmentation and detection model, which we refer to as WyPR. Specifically, we assume availability of data $\mathcal{D} = \{(\mathcal{P},\mathbf{y})\}$ of point cloud $\mathcal{P}$ and corresponding scene-level tags $\mathbf{y}\in \{0,1\} ^C$ , which indicate absence or presence of the $C$ object classes. $\mathcal{P}$ is a set of six-dimensional points $\mathbf{p}\in \mathcal{P}$ , represented by their 3D location and RGB-color. Note, $\mathbf{y}$ only indicates existence of objects in the scene and does not contain any information about perpoint semantic labels or object locations. + +Approach overview. Fig. 2 provides an overview of our model which consists of three parametric modules: a backbone network, followed by a segmentation and a detection head. We first extract geometric features from the input point cloud using the backbone network. Specifically, we use the variant of PointNet++ [32] following VoteNet [29], which is an encoder-decoder network with skip connections. The features are then fed into the segmentation and detection modules. The segmentation module assigns each point from the input point cloud $\mathcal{P}$ to one of $C$ classes. We use this segmentation output to generate 3D region proposals $\mathcal{R}$ that are likely to contain objects in the scene. Finally, + +the detection module classifies each proposal into either one of $C$ classes or background (not an object) class, using the backbone features corresponding to that proposal. + +Notation. We denote the output of the segmentation module as $\mathbf{S}_{\mathrm{seg}} \in \mathbb{R}^{|\mathcal{P}| \times C}$ , where the rows represent the score logits over the $C$ classes for all points $\mathcal{P}$ . The detection module produces a score matrix $\mathbf{S}_{\mathrm{det}} \in \mathbb{R}^{|\mathcal{R}| \times (C + 1)}$ over the $C$ classes and background for all 3D proposals $\mathcal{R}$ . For readability, we also use $\mathbf{p}, \mathbf{r}$ as indices into $\mathbf{S}_{\mathrm{seg}}, \mathbf{S}_{\mathrm{det}}$ in the following sections. + +# 3.1. Weakly-supervised 3D semantic segmentation + +The segmentation module consists of two identical heads that independently process the backbone features using a series of unit PointNet [31] and nearest neighbor upsampling layers (Fig. 2 green region). The output from these heads are two score matrices $\mathbf{U}_{\mathrm{seg}}$ , $\mathbf{S}_{\mathrm{seg}} \in \mathbb{R}^{|\mathcal{P}| \times C}$ respectively, containing logits over $C$ object classes for all points $\mathbf{p} \in \mathcal{P}$ . The parameters of the backbone and the segmentation module are optimized to minimize a composed loss + +$$ +\mathcal {L} _ {\mathrm {s e g}} = \mathcal {L} _ {\mathrm {s e g}} ^ {\mathrm {M I L}} + \mathcal {L} _ {\mathrm {s e g}} ^ {\mathrm {S E L F}} + \mathcal {L} _ {\mathrm {s e g}} ^ {\mathrm {C S T}} + \mathcal {L} _ {\mathrm {d} \rightarrow \mathrm {s}} + \mathcal {L} _ {\text {s m o o t h}}, \tag {1} +$$ + +where $\mathcal{L}_{\mathrm{seg}}^{\mathrm{MIL}}$ denotes a multiple-instance learning (MIL) loss, $\mathcal{L}_{\mathrm{seg}}^{\mathrm{SELF}}$ denotes a self-training loss, $\mathcal{L}_{\mathrm{seg}}^{\mathrm{CST}}$ and $\mathcal{L}_{\mathrm{d}\rightarrow \mathrm{s}}$ represent consistency loss across geometric transformations and tasks respectively, and $\mathcal{L}_{\mathrm{smooth}}$ is a smoothness regularization loss. We describe the individual loss terms next. + +MIL loss. The multiple-instance learning loss [54, 55] encourages to learn the per-point semantic segmentation logits without access to point-level supervision. We first convert the per-point logits $\mathbf{U}_{\mathrm{seg}}$ into a scene-level prediction $\phi$ via average pooling and a sigmoid normalization + +$$ +\phi [ c ] = \operatorname {s i g m o i d} \left(\frac {1}{| \mathcal {P} |} \sum_ {\mathbf {p} \in \mathcal {P}} \mathbf {U} _ {\mathrm {s e g}} [ \mathbf {p}, c ]\right). \tag {2} +$$ + +The scene-level prediction $\phi$ is then supervised using the scene-level tags $\mathbf{y}$ using the binary cross-entropy loss + +$$ +\mathcal {L} _ {\mathrm {s e g}} ^ {\mathrm {M I L}} = - \sum_ {c = 1} ^ {C} \mathbf {y} [ c ] \log \phi [ c ] - (1 - \mathbf {y} [ c ]) \log (1 - \phi [ c ]). \tag {3} +$$ + +Algorithm 1 Segmentation pseudo label generation +Input: class label $\mathbf{y}$ , segmentation logits $\mathbf{U}_{\mathrm{seg}}$ , threshold $p_1$ +Output: pseudo label $\tilde{\mathbf{Y}}_{\mathrm{seg}}$ +1: $\hat{\mathbf{Y}}_{\mathrm{seg}} = \mathbf{0}$ initialize to zero matrix +2: for each point $\mathbf{p}\in \mathcal{P}$ do +3: $c = \operatorname {argmax}(\mathbf{y}\odot \mathbf{U}_{\mathrm{seg}}[\mathbf{p},:])$ element-wise product +4: $\hat{\mathbf{Y}}_{\mathrm{seg}}[\mathbf{p},c] = 1$ +5: for ground-truth class $c$ where $\mathbf{y}[c] = 1$ do +6: $\mathcal{P}'[c]\gets$ lowest $p_1$ -th percentile of $\hat{\mathbf{Y}}_{\mathrm{seg}}[:,c]$ +7: $\hat{\mathbf{Y}}_{\mathrm{seg}}[\mathbf{p},c] = 0\forall \mathbf{p}\in \mathcal{P}'[c]$ ignore points with low score + +Self-training loss. Inspired by the success of self-training in weakly-supervised detection [35, 45, 50], we further incorporate a self-training loss. The previously computed segmentation logits $\mathbf{U}_{\mathrm{seg}}$ are used to supervise the final segmentation logits $\mathbf{S}_{\mathrm{seg}}$ via a cross-entropy loss + +$$ +\mathcal {L} _ {\mathrm {s e g}} ^ {\mathrm {S E L F}} = - \frac {1}{| \mathcal {P} |} \sum_ {\mathbf {p} \in \mathcal {P}} \sum_ {c = 1} ^ {C} \hat {\mathbf {Y}} _ {\mathrm {s e g}} [ \mathbf {p}, c ] \log \psi [ \mathbf {p}, c ], \tag {4} +$$ + +where $\psi[\mathbf{p}, c] = \mathrm{softmax}(\mathbf{S}_{\mathrm{seg}}[\mathbf{p}, c])$ denotes the probability of point $\mathbf{p}$ belonging to class $c$ , and $\hat{\mathbf{Y}}_{\mathrm{seg}}[\mathbf{p}, c] \in \{0, 1\}$ is the point-level pseudo class label inferred from score matrix $\mathbf{U}_{\mathrm{seg}}$ . We detail the process of computing the pseudo label in Alg. 1. Intuitively, the algorithm ignores noisy predictions in $\mathbf{U}_{\mathrm{seg}}$ , leading to robust self-supervision for $\mathbf{S}_{\mathrm{seg}}$ . Cross-transformation consistency loss. In addition, we use $\mathcal{L}_{\mathrm{seg}}^{\mathrm{CST}}$ to encourage that the segmentation predictions are consistent across data augmentations $\mathcal{T}$ . We obtain an augmented point cloud $\tilde{\mathcal{P}} = \mathcal{T}(\mathcal{P})$ by changing the original scene $\mathcal{P}$ via standard augmentations (see §4 and Appendix C.1 for details). We predict the semantic segmentation $\tilde{\mathbf{S}}_{\mathrm{seg}}$ on this transformed point cloud. The consistency loss is then formulated as + +$$ +\mathcal {L} _ {\mathrm {s e g}} ^ {\mathrm {C S T}} = \frac {1}{| \mathcal {P} \cap \tilde {\mathcal {P}} |} \sum_ {\mathbf {p} \in \mathcal {P} \cap \tilde {\mathcal {P}}} D _ {\mathrm {K L}} (\psi [ \mathbf {p}, \cdot ] | | \tilde {\psi} [ \mathbf {p}, \cdot ]), \tag {5} +$$ + +where $\psi[\mathbf{p}, c] = \text{softmax}(\mathbf{S}_{\text{seg}}[\mathbf{p}, c])$ and $\tilde{\psi}[\mathbf{p}, c] = \text{softmax}(\tilde{\mathbf{S}}_{\text{seg}}[\mathbf{p}, c])$ are the probabilities of the point $\mathbf{p}$ belonging to class $c$ , and $D_{\mathrm{KL}}$ is the KL divergence over $C$ classes for points that are common across the transformation. This loss encourages the probability distributions for semantic segmentation of corresponding points within the point cloud $\mathcal{P}$ and $\tilde{\mathcal{P}}$ to match. + +Cross-task consistency loss. We further employ a cross-task regularization term $\mathcal{L}_{\mathrm{d}\to \mathrm{s}}$ . It uses the detection results to refine the segmentation prediction. Intuitively, all points within a confident bounding box prediction should have the same semantic label. Assume we have access to a set of confident bounding boxes $\mathbf{r} \in \mathcal{R}^*$ and their corresponding predicted score matrix $\mathbf{S}_{\mathrm{det}} \in \mathbb{R}^{|\mathcal{R}^*| \times (C + 1)}$ . Using this information, we encourage consistency via a cross entropy + +Algorithm 2 Detection pseudo label generation +Input: class label $\mathbf{y}$ detection logits $\mathbf{U}_{\mathrm{det}}$ proposals $\mathcal{R}$ threshold $\tau ,p_{2}$ Output: pseudo label $\hat{\mathbf{Y}}_{\mathrm{det}}$ +1: for ground-truth class $c$ where $\mathbf{y}[c] = 1$ do +2: $\hat{\mathbf{Y}}_{\mathrm{det}} = \mathbf{0}$ initialize to zero matrix +3: $\mathcal{R}^{\prime}[c]\gets$ top $p_2$ -th percentile of $\mathbf{U}_{\mathrm{det}}[:,c]\triangleright \mathcal{R}^{\prime}[c]$ is descending +4: $\mathcal{R}^{*}[c]\leftarrow \mathbf{r}_{1}^{\prime}$ save 1st RoI (top-scoring) $\mathbf{r}_1^\prime \in \mathcal{R}^\prime [c]$ +5: for $i\in \{2,\dots ,|\mathcal{R}'[c]|\}$ do start from the 2nd highest +6: $\mathcal{R}^{*}[c]\gets \mathbf{r}_{i}^{\prime}$ if IoU $(\mathbf{r}_i',\hat{\mathbf{r}})$ $< \tau \forall \hat{\mathbf{r}}\in \mathcal{R}^{*}[c]$ +7: $\hat{\mathbf{Y}}_{\mathrm{det}}[\mathbf{r},c] = 1\forall \mathbf{r}\in \mathcal{R}^{*}[c]$ + +loss on the point-level predictions, with the box-level prediction as a soft target + +$$ +\mathcal {L} _ {\mathrm {d} \rightarrow \mathrm {s}} = - \frac {1}{| \mathcal {R} ^ {*} |} \sum_ {\mathbf {r} \in \mathcal {R} ^ {*}} \frac {1}{| \mathcal {P} ^ {r} |} \sum_ {\mathbf {p} \in \mathcal {P} ^ {\mathbf {r}}} \sum_ {c = 1} ^ {C} \boldsymbol {\xi} [ \mathbf {r}, c ] \log \psi [ \mathbf {p}, c ], \tag {6} +$$ + +where $\psi[\mathbf{p}, c]$ is the point probability from Eq. (4), $\xi[\mathbf{r}, c] = \text{softmax}(\mathbf{S}_{\text{det}}[\mathbf{r}, c])$ denotes the probability of proposal $\mathbf{r}$ belonging to object class $c$ , and $\mathcal{P}^{\mathbf{r}}$ denotes the set of points within proposal $\mathbf{r}$ . In practice, the confident bounding boxes $\mathcal{R}^*$ are obtained from Alg. 2, discussed later in §3.2. + +Smoothness regularization. Finally, we compute $\mathcal{L}_{\mathrm{smooth}}$ to encourage local smoothness. We first detect a set of planes $\mathcal{G}$ from input point cloud $\mathcal{P}$ using an unsupervised off-the-shelf shape detection algorithm [22] detailed in Appendix B. We then compute + +$$ +\mathcal {L} _ {\text {s m o o t h}} = - \sum_ {i = 1} ^ {| \mathcal {G} |} \frac {1}{| \mathcal {G} [ i ] |} \sum_ {\mathbf {p} \in \mathcal {G} [ i ]} \sum_ {c = 1} ^ {C} \bar {\psi} [ c ] \log \psi [ \mathbf {p}, c ], \tag {7} +$$ + +where $\bar{\psi}[c] = \frac{\sum_{\mathbf{p} \in \mathcal{G}[i]} \psi[\mathbf{p}, c]}{|\mathcal{G}[i]|}$ is the mean probability of all the points which lie inside plane $\mathcal{G}[i]$ for class $c$ . + +# 3.2. Weakly-supervised 3D object detection + +Our object detection module assumes access to a set of 3D region proposals $\mathcal{R}$ (discussed in § 3.3) and uses the backbone features to classify the proposals into one of the $C$ object classes or background (Fig. 2 blue region). Each region of interest (RoI) $\mathbf{r} \in \mathbb{R}^6$ is represented by a six-dimensional vector denoting its center location and its width, height and length. We extract RoI features by averaging the backbone features of all the points within each proposal. Inspired by prior 2D literature [3], we use three separate linear layers to extract classification logits $\mathbf{S}_{\mathrm{cls}} \in \mathbb{R}^{|\mathcal{R}| \times (C + 1)}$ , objectness logits $\mathbf{S}_{\mathrm{obj}} \in \mathbb{R}^{|\mathcal{R}| \times (C + 1)}$ , and final detection logits $\mathbf{S}_{\mathrm{det}} \in \mathbb{R}^{|\mathcal{R}| \times (C + 1)}$ from the RoI features. As in [3], we normalize $\mathbf{S}_{\mathrm{cls}}$ using a softmax function over rows to obtain the probability over object classes for each proposal. Similarly, we normalize $\mathbf{S}_{\mathrm{obj}}$ over columns to obtain a probability over proposals for each class. Intuitively, $\mathbf{S}_{\mathrm{cls}}[\mathbf{r}, c]$ represents the probability of region $\mathbf{r}$ being classified as class $c$ , and $\mathbf{S}_{\mathrm{obj}}[\mathbf{r}, c]$ is the probability of detecting region $\mathbf{r}$ for class $c$ . We aggregate the evidence from + +![](images/864cace8b4d634695d63363dc46959eb04e5da6ffe531455a6891f40a360b4e2.jpg) +Point cloud + +![](images/6d7d33615c5e6be3ce52aee042f1ad4836e20b133414995f1ca50cacf6e310dd.jpg) +Detected shapes +Figure 3: Geometric Selective Search (GSS). Our algorithm takes as input the point cloud and detected planes (left column). It then hierarchically groups the neighboring planes into sub-regions and generates 3D proposals for the combined regions (middle column). We run the algorithm multiple times with different grouping criteria to encourage high recall of final output proposals (right column). + +![](images/51dae4151a07b0d27f1c685cd4efcf1215760c4ef3736bb6a86387c774dbe545.jpg) +HACiter20 + +![](images/c7e7bb3630b65be937d72b8893c1b5de0c4987935050db69a357695a7f1aee10.jpg) +HACiter40 + +![](images/318511fe2195132bae4b6d3176823575aa87924c0c4f4c46fae7add9cc6abd19.jpg) +HACiter60 + +![](images/4b2dab7adbe21a480253031abb9acff58be3d32ae233e248f14a5fd729019bd6.jpg) +GSS proposals + +both matrices via element-wise multiplication to obtain the score matrix $\mathbf{U}_{\mathrm{det}} = \mathbf{S}_{\mathrm{cls}}\odot \mathbf{S}_{\mathrm{obj}}$ . Similar to the self-training discussed earlier for segmentation, we infer pseudo-labels from $\mathbf{U}_{\mathrm{det}}$ to supervise the final detection logits $\mathbf{S}_{\mathrm{det}}$ . We learn the backbone and the detection module using the loss + +$$ +\mathcal {L} _ {\det } = \mathcal {L} _ {\det } ^ {\mathrm {M I L}} + \mathcal {L} _ {\det } ^ {\mathrm {S E L F}} + \mathcal {L} _ {\det } ^ {\mathrm {C S T}}, \tag {8} +$$ + +where $\mathcal{L}_{\mathrm{det}}^{\mathrm{MIL}}$ is a MIL objective for detection, $\mathcal{L}_{\mathrm{det}}^{\mathrm{SELF}}$ is a self-training loss, and $\mathcal{L}_{\mathrm{det}}^{\mathrm{CST}}$ is the cross-transformation consistency loss. All the terms are described next. + +MIL loss. Similar to the segmentation head, the multiple instance learning (MIL) loss for detection is + +$$ +\mathcal {L} _ {\det } ^ {\mathrm {M I L}} = - \sum_ {c = 1} ^ {C + 1} \mathbf {y} [ c ] \log \boldsymbol {\mu} [ c ] - (1 - \mathbf {y} [ c ]) \log (1 - \boldsymbol {\mu} [ c ]), \tag {9} +$$ + +where $\pmb{\mu}[c] = \sum_{\mathbf{r} \in \mathcal{R}} \mathbf{U}_{\mathrm{det}}[\mathbf{r}, c]$ is the row-sum of the score matrix $\mathbf{U}_{\mathrm{det}}$ for class $c$ . This sum-pooling operation aggregates RoI scores into a scene-level score vector $\pmb{\mu}$ , which is used for multi-label scene classification. + +Self-training loss. As done before for segmentation, we incorporate a self-training loss for detection as well. The final detection logits $\mathbf{S}_{\mathrm{det}}$ are supervised by $\mathbf{U}_{\mathrm{det}}$ via + +$$ +\mathcal {L} _ {\det } ^ {\text {S E L F}} = - \frac {1}{| \mathcal {R} |} \sum_ {\mathbf {r} \in \mathcal {R}} \sum_ {c = 1} ^ {C + 1} \hat {\mathbf {Y}} _ {\det } [ \mathbf {r}, c ] \log \boldsymbol {\xi} [ \mathbf {r}, c ], \tag {10} +$$ + +where $\xi[\mathbf{r}, c] = \mathrm{softmax}(\mathbf{S}_{\mathrm{det}}[\mathbf{r}, c])$ denotes the probability of proposal $\mathbf{r}$ belonging to object class $c$ , and $\hat{\mathbf{Y}}_{\mathrm{det}}[\mathbf{r}, c] \in \{0, 1\}$ is the RoI pseudo class label inferred from score matrix $\mathbf{U}_{\mathrm{det}}$ . The pseudo label $\hat{\mathbf{Y}}_{\mathrm{det}}$ is computed using Alg. 2. Conceptually, this algorithm selects a set of confident yet diverse predictions as the pseudo labels for self-training. + +Cross-transformation consistency loss. Following the consistency loss for semantic segmentation (Eq. (5)), we encourage detection predictions to be consistent under transformation $\mathcal{T}$ via + +$$ +\mathcal {L} _ {\det } ^ {\mathrm {C S T}} = \frac {1}{| \mathcal {R} |} \sum_ {\mathbf {r} \in \mathcal {R}} D _ {\mathrm {K L}} \left(\boldsymbol {\xi} [ \mathbf {r}, \cdot ] \mid \mid \tilde {\boldsymbol {\xi}} [ \mathcal {T} (\mathbf {r}), \cdot ]\right), \tag {11} +$$ + +where $\xi[\mathbf{r}, c]$ refers to the RoI probability introduced in Eq. (10), $\tilde{\xi}[\mathcal{T}(\mathbf{r}), c]$ denotes the RoI probability obtained from the transformed input $\tilde{\mathcal{P}} = \mathcal{T}(\mathcal{P})$ and proposal $\mathcal{T}(\mathbf{r})$ via the same backbone and detection module. + +# 3.3. Geometric Selective Search (GSS) + +The detection module uses a proposal set $\mathcal{R}$ as input. In weakly-supervised learning, proposals are necessary because it is not possible to mimic supervised methods that directly predict 3D bounding box parameters (e.g., size and location). The key observation which inspires our novel 3D proposal generation algorithm is that most indoor objects are rigid and mainly consist of basic geometric structures (e.g., planes, cylinders, spheres). We thus devise a bottom-up solution termed Geometric Selective Search (GSS), first detecting basic geometric shapes which are then grouped hierarchically to form 3D proposals (Fig. 2 brown region). + +Given an input point cloud with unoriented normals, we adopt a region-growing-based method [22, 26] for detecting primitive shapes (e.g., planes) as shown in Fig. 3 left. We choose region-growing over the popular RANSAC-based methods [38] because 1) it is deterministic; 2) it performs better in the presence of large scenes with fine-grained details. We then apply hierarchical agglomerative clustering (HAC) to iteratively group the detected shapes into sub-regions. In each HAC iteration, we compute the similarity score $s$ between all spatially overlapping sub-regions and group the two most similar regions. We iterate until no neighbors can be found or only one region is left. Every time we generate a new region, we also compute the axis-aligned bounding boxes of the new region and add it into the proposal pool. We illustrate the process of growing the proposal pool during HAC in Fig. 3 (middle columns). + +In order to pick which two regions $\mathbf{n}_i, \mathbf{n}_j$ to group, HAC uses a similarity score + +$$ +s \left(\mathbf {n} _ {i}, \mathbf {n} _ {j}\right) = w _ {1} s _ {\text {s i z e}} + w _ {2} s _ {\text {v o l u m e}} + w _ {3} s _ {\text {f i l l}} + w _ {4} s _ {\text {s e g}}, \tag {12} +$$ + +where $w_{i}\in \{0,1\} \forall i\in \{1,\dots ,4\}$ are binary indicators. $s_{\mathrm{size}}$ and $s_{\mathrm{volume}}\in [0,1]$ measure size and volume compatibility and encourage small regions to merge early; $s_{\mathrm{fill}}\in [0,1]$ measures how well two regions are aligned. Besides similarities of low-level cues, we also measure highlevel semantic similarities by incorporating segmentation similarity $s_{\mathrm{seg}}\in [0,1]$ . This score is the histogram intersection of the normalized $C$ -dimensional class histogram of two regions' points. The class labels of these points are computed from $\mathbf{S}_{\mathrm{seg}}$ using the inference procedure de + +scribed in § 4. Please see Appendix A for the exact formulation of the above metrics. During training, as the segmentation module improves, $s_{\mathrm{seg}}$ increasingly prefers grouping regions which correspond to the same object. A similar idea to compute proposals from segmentations has also been widely adopted in the 2D case [1, 48]. In practice, we find that multiple runs of HAC with different $w_i$ values, results in a more diverse set of proposals as each run uses a different weighted similarity measure. We provide the values of $w_i$ for different runs in Appendix A. + +GSS can be made completely unsupervised by removing the segmentation term $s_{\mathrm{seg}}$ from Eq. (13). This variant is also valuable as the proposals can be pre-computed offline and are of decent quality (verified in § 4). These proposals are independent of any specific supervision and can benefit various downstream unsupervised or weakly-supervised 3D recognition tasks, akin to Selective Search [48] or Edge Boxes [64] in 2D. This is distinct from existing 3D proposal techniques that either use 2D image cues [33] or full bounding box supervision [28, 29]. + +# 4. Experiments + +We empirically evaluate WyPR on two standard 3D benchmarks. We first provide the key implementation details (more details in Appendix C) and describe the baseline methods we compare to ( $\S$ 4.1). We then present the quantitative results ( $\S$ 4.2 and 4.3), ablate our design choices and present qualitative results ( $\S$ 4.4). + +Input. Our network takes as input a fixed-size point cloud, where 40K points are randomly sub-sampled from the original scan. In addition to using color (RGB) and coordinates (XYZ) as input features, following [29], we include surface normal and a height feature of each point. + +Augmentation. We augment the input point cloud at two places in our framework: (1) data augmentation at the input, and (2) to compute the consistency loss in Eq. (5) and Eq. (11). In practice, we find it beneficial to apply different geometric transformations for the above two purposes. To augment the input, we follow [29] and use random sub-sampling of 40K points, random flipping in both horizontal and vertical directions, and random rotation of $[-5,5]$ degrees around the upright-axis. To compute the consistency loss, we use random flipping, point jittering, random rotation with an angle uniform in $[0,30]$ degrees around the upright-axis, random scaling by a factor from $[0.8,1.2]$ , and point dropout ( $p = 0.1$ ). Finally, we also find that jittering the point cloud is crucial to obtain good proposals for noisy point clouds (analyzed in § 4.4). + +Network architecture. (1) Backbone. We use Point-Net++ [32] as the backbone model to compute the point cloud features. The model has 4 set abstraction (SA) layers and 2 feature propagation (FP) layers. The four SA layers sub-sample the point cloud to 2048, 1024, 512 and + +
MethodSplitmIoU
Weakly-supervised methods
PCAM [53]train22.1
MPRM [53]train24.4
WyPRtrain30.7
MIL-segval20.7
WyPRval29.6
WyPR+priorval31.1
WyPRtest24.0
Supervised methods
VoteNet [29]test55.7
SparseConvNet [9]test73.6
+ +Table 2: 3D semantic segmentation on ScanNet. WyPR outperforms standard baselines and existing state-of-the-art [53]. We also report fully supervised methods for reference. Note that models on train and val sets leverage axis alignment information from [29], which is not present and hence not used for experiments on the test set. See Appendix E for per-class performance. + +256 points using a receptive radius of 0.2, 0.4, 0.8 and 1.2 meters respectively. The two FP layers up-sample the last SA layer's output back from 256 to 1024 points. The final output has $(256 + 3)$ dimensions (feature $+$ 3D coordinates). (2) Segmentation module. This module is implemented as two FP layers which upsample the backbone features (1024 points) to the input size (40K points), and a two layer MLP (implemented as two $1\times 1$ convolutional layers) which convert the features into per-point classification logits. (3) Detection module. This module has 3 fully-connected layers, computing the classification $\mathbf{S}_{\mathrm{cls}}$ , objectness $\mathbf{S}_{\mathrm{obj}}$ , and final classification logits $\mathbf{S}_{\mathrm{det}}$ respectively, as described in § 3.2. + +Training. We train the entire network end-to-end from scratch with an Adam optimizer for 200 epochs. We use 8 GPUs with a batch size of 32. The initial leaning rate is 0.003 and is decayed by $10 \times$ at epoch $\{120, 160, 180\}$ . + +Inference. (1) Segmentation. We generate the segmentation mask from the predicted logits $(\mathbf{S}_{\mathrm{seg}})$ by taking the class with highest score for each point. We then post-process the output for smoothness by using the detected planes (as in Eq. (7)), and assign each point in the plane to the most frequently occurring class. (2) Detection. Following [29], we post-process the final output probability, $\mathrm{softmax}(\mathbf{S}_{\mathrm{det}})$ , by thresholding to drop predictions with score $< 0.01$ and class-wise non-maximum suppression (NMS) with IoU threshold 0.25. + +Dataset. We use the ScanNet [10] and S3DIS [2] datasets to evaluate our method. ScanNet contains 1.2K training and 300 validation examples of hundreds of different rooms, annotated with 20 semantic categories. We extract ground truth bounding boxes from instance segmentation masks following [29]. To demonstrate the generalizability of our method, we further evaluate on S3DIS, which contains 6 + +
MethodsProposalDetection
#boxesMABOARmAP
Unsupervised methods
Qin et al. [33]1k0.09223.6-
GSS≤2560.32173.4-
GSS≤1k0.37886.2-
Weakly-supervised methods
MIL-det (unsup. GSS)≤1k0.37886.29.6
WyPR≤1k0.40989.318.3
WyPR+prior≤1k0.42790.519.7
Supervised methods
F-PointNet [30]---10.8
GSPN [60]---17.7
3DSIS [18]---40.2
VoteNet [29]2560.43684.758.6
VoteNet [29]1k0.45088.155.3
+ +floors of 3 different buildings and 13 objects classes. We use the fold #1 split following prior work [2, 9], where area 5 is used for testing and the rest for training. + +Evaluation. We report mean intersection over union (mIoU) across all classes for semantic segmentation, mean average precision (mAP) across all classes at IoU 0.25 for object detection, and average recall (AR) and mean average best overlap (MABO) across all classes for proposal generation. Please see [10, 29, 48] for more on these metrics. + +# 4.1. Baselines + +Besides comparing to the few existing 3D weakly-supervised learning methods, we build the following baselines, using standard weakly-supervised learning techniques: + +MIL-seg: Single task segmentation trained with Eq. (3). + +MIL-det: Single task object detection, which uses the unsupervised GSS proposals and is trained with Eq. (9). + +WyPR: Our full model trained with Eq. (1) and Eq. (8). + +WyPR+prior: We compute per-class mean shapes using external synthetic datasets [6, 57], and use those to reject proposals and pseudo labels in the WyPR detection module that do not satisfy the prior. We also use a floor height prior for segmentation. Please see Appendix D for details. + +# 4.2. Quantitative results on ScanNet + +Semantic Segmentation. Apart from the above baselines we compare WyPR to recent approaches, PCAM [53] and MPRM [53]. PCAM can be interpreted as MIL-seg with a KPCov [47] backbone, and MPRM adds multiple additional self-attention modules to PCAM. Since prior work + +Table 3: 3D object detection on ScanNet. Unsupervised GSS outperforms concurrent work [33] by a large margin. In the weakly-supervised setting, WyPR outperforms standard baselines and even some fully supervised approaches [30, 60]. + +
MethodsSegmentation mIoUProposal MABO ARDetection mAP
Weakly-supervised methods
MIL-seg17.6---
MIL-det (unsup. GSS)-0.41284.915.1
WyPR22.30.44188.319.3
Supervised methods
PointNet++ [31]41.1---
SparseConvNet [9]62.4---
Armeni et al. [2]---49.9
+ +Table 4: Generalizing to S3DIS. WyPR seamlessly generalizes to S3DIS, and outperforms standard baselines for both weakly-supervised segmentation and detection. + +
RemovedSeg. lossesDet. lossesSeg. Det.
\( \mathcal{L}_{\text{seg}}^{\text{SELF}} \)\( \mathcal{L}_{\text{seg}}^{\text{CST}} \)\( \mathcal{L}_{\text{d-s}} \)\( \mathcal{L}_{\text{smooth}} \)\( \mathcal{L}_{\text{det}}^{\text{SELF}} \)\( \mathcal{L}_{\text{det}}^{\text{CST}} \)mIoUmAP
Self-training✓✓✓✓22.113.2
Cross-transformation cst.✓✓✓✓28.216.9
Cross-task consistency✓✓✓✓✓26.717.4
Local smoothness✓✓✓✓✓27.317.8
WyPR✓✓✓✓✓✓29.618.3
+ +Table 5: Ablation study of losses. We remove one set of losses at a time. All models are trained with $\mathcal{L}_{\mathrm{seg}}^{\mathrm{MIL}}$ and $\mathcal{L}_{\mathrm{det}}^{\mathrm{MIL}}$ . + +reports results on the training set only, we compare against their results on the training set in Tab. 2 (top 3 rows). WyPR outperforms both methods (PCAM and MPRM) by a significant margin $(+8.6\% / +6.3\%)$ . Since the main difference between prior work and our method is our joint detection-segmentation framework, these results show the effectiveness of joint-training. When comparing against our baselines on the validation set (Tab. 2 middle) our joint model outperforms the single-task baseline (MIL-seg) by $8.9\%$ . We observe a large performance gap when comparing against state-of-the-art fully supervised models (bottom two rows). One possible solution to minimize the gap is to utilize an external object prior (e.g., shape) from readily-available synthetic data, which improves results by $+1.5\%$ . + +Object Detection. To the best of our knowledge, no prior work has explored weakly-supervised 3D object detection using scene-level tags. We compare against our baseline methods in Tab. 3 (middle rows). Our model significantly outperforms the single-task baseline (MIL-det) by $8.7\%$ mAP, and achieves competitive results compared to even some fully supervised methods (F-PointNet [30] and GSPN [60], numbers borrowed from [29]). However, the performance gap is large when compared to the state-of-the-art fully supervised methods. Similar to segmentation, the performance of our model can be further improved by incorporating an external object prior $(+1.4\%)$ . + +Proposal Generation. GSS can be made unsupervised by relying only on low-level shape and color cues, i.e., removal + +![](images/6c19214c69bd733613a0d6bb40231aa4f7741268adfef29cea94d4b01c45e9f7.jpg) +Figure 4: Effect of jittering and #proposals. Jittering the point cloud before proposal generation results in a $>2\%$ gain in AP. The performance varies gracefully with #proposals, and we find 1000 proposals to have the right balance for high precision and recall. + +ing $s_{\mathrm{seg}}$ from Eq. (13) (\$ 3.3). We compare the unsupervised GSS to a concurrent unsupervised 3D proposal approach by Qin et al. [33]. We adapt their method, originally designed for outdoor environments, to indoor scenes by replacing their front-view projection to a Y-Z plane projection. For a fair comparison we use 1000 proposals and report results in Tab. 3 (top rows). Unsupervised GSS outperforms [33] by a large margin, and obtains recall values comparable to even supervised approaches. The complete GSS, including the weakly-supervised similarity $s_{\mathrm{seg}}$ , further improves over the unsupervised baseline (+3.1% AR/+0.031 MABO), and outperforms supervised methods on recall (+1.2%), indicating the importance of joint training. + +# 4.3. Generalizing to S3DIS + +We train WyPR on S3DIS following the settings of § 4.2. Since there is no prior weakly-supervised work on this dataset, we compare against our baselines from § 4.1. The results are summarized in Tab. 4, where WyPR outperforms both single-task baselines with gains of $4.7\%$ mIoU for segmentation, $3.4\%$ AR for proposal generation, and $4.2\%$ mAP for detection. These results demonstrate that our design choices are not specific to ScanNet and generalize to other 3D datasets. + +# 4.4. Analysis + +Which loss terms matter? In Tab. 5 we analyze the relative contribution of the loss terms in Eq. (1) and (8). We find self-training to be the most critical. Removing $\mathcal{L}_{\mathrm{seg}}^{\mathrm{SELF}}$ and $\mathcal{L}_{\mathrm{det}}^{\mathrm{SELF}}$ leads to a significant drop in both metrics: $-7.5\%$ mIoU and $-5.1\%$ mAP. This is consistent with observations in prior work on weak-supervision [34, 54]. Next, we find enforcing consistency between detection and segmentation tasks to add large gains, especially for segmentation: $2.9\%$ mIoU. Enforcing consistency across transformations is particularly important for detection, leading to a $1.4\%$ mAP gain. Finally, encouraging smoothness over primitive structures improves both metrics by $1.7\%$ mIoU and $0.5\%$ mAP. + +Jittering for proposal generation. We observe that scanned point clouds are often imperfect, with large holes + +![](images/bc5f71244fb6558d5c64cba500792fd61d28b54edc2595a13a9c74f433cd97a9.jpg) +Figure 5: Qualitative results on ScanNet. WyPR+prior is able to segment, generate proposals and detect objects without having ever seen any spatial annotations. + +in objects due to occlusions, clutter or sensor artifacts. This makes it challenging for GSS to correctly group parts. To overcome this, we jitter the points in 3D space using a random multiplier within range $[1 - \delta /2,1 + \delta /2]$ and decide the neighboring regions based on the jittered points. This simple technique counts spatially close but non-overlapping regions as neighbors, and greatly improves GSS results. We show the impact of $\delta$ in Fig. 4 (left). + +Number of proposals. We randomly sample at most 250, 500, 1000, 1500, 2000 regions from the same set of computed proposals and report the recall and detection mAP in Fig. 4 (right). Using fewer proposals hurts both the recall and precision since the model misses many relevant objects. In contrast, a large number of proposals increases recall but hurts precision, presumably because too many proposals increase the false positive rate of the detection module. We find 1000 proposals to be a good balance between precision and recall, and use this number for all our experiments. + +Qualitative results. Fig. 5 shows a few representative examples of our model's predictions on ScanNet. As can be seen, input point clouds are quite challenging, with large amounts of clutter and sensor imperfections. Nevertheless, our model is able to recognize objects such as chairs, tables, and sofa with good accuracy. Please see Appendix F for more results, analysis and failure modes. + +# 5. Conclusion + +We propose WyPR, a novel framework for joint 3D semantic segmentation and object detection, trained using only scene-level class tags as supervision. It leverages a novel unsupervised 3D proposal generation approach (GSS) along with natural constraints between the segmentation and detection tasks. Through extensive experimentation on standard datasets we show WyPR outperforms single task baselines and prior state-of-the-art methods on both tasks. + +Acknowledgements. This work was supported in part by NSF under Grant #1718221, 2008387 and MRI #1725729, NIFA award 2020-67021-32799. The authors thank Zaiwei Zhang and the Facebook AI team for helpful discussions and feedback. + +# References + +[1] P. Arbeláez, J. Pont-Tuset, J. Barron, F. Marques, and J. Malik. Multiscale combinatorial grouping. In CVPR, 2014. 6 +[2] Iro Armeni, Sasha Sax, Amir R Zamir, and Silvio Savarese. Joint 2d-3d-semantic data for indoor scene understanding. arXiv:1702.01105, 2017. 2, 6, 7 +[3] Hakan Bilen and Andrea Vedaldi. Weakly supervised deep detection networks. In CVPR, 2016. 2, 4 +[4] Rich Caruana. Multitask learning. Machine Learning, 1997. 3 +[5] Angel Chang, Angela Dai, Thomas Funkhouser, Maciej Halber, Matthias Niessner, Manolis Savva, Shuran Song, Andy Zeng, and Yinda Zhang. Matterport3d: Learning from rgb-d data in indoor environments. In 3DV, 2017. 2 +[6] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. Shapenet: An information-rich 3d model repository. arXiv:1512.03012, 2015. 2, 7, 14 +[7] Ming-Fang Chang, John Lambert, Patsorn Sangkloy, Jagjeet Singh, Slawomir Bak, Andrew Hartnett, De Wang, Peter Carr, Simon Lucey, Deva Ramanan, et al. Argoverse: 3d tracking and forecasting with rich maps. In CVPR, 2019. 2 +[8] Sungjoon Choi, Qian-Yi Zhou, Stephen Miller, and Vladlen Koltun. A large dataset of object scans. arXiv:1602.02481, 2016. 2 +[9] Christopher Choy, JunYoung Gwak, and Silvio Savarese. 4d spatio-temporal convnets: Minkowski convolutional neural networks. In CVPR, 2019. 1, 2, 6, 7 +[10] Angela Dai, Angel X Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In CVPR, 2017. 1, 2, 6, 7 +[11] Carl Doersch and Andrew Zisserman. Multi-task self-supervised visual learning. In ICCV, 2017. 3 +[12] David Eigen and Rob Fergus. Predicting depth, surface normals and semantic labels with a common multi-scale convolutional architecture. In ICCV, 2015. 3 +[13] Cat Franklin. Apple unveils new ipad pro with breakthrough lidar scanner and brings trackpad support to ipados. https://www.apple.com/, 2020. 1, 2 +[14] Andreas Geiger, Philip Lenz, Christoph Stiller, and Raquel Urtasun. Vision meets robotics: The kitti dataset. *IJRR*, 2013. 2 +[15] Rohit Girdhar, David Ford Fouhey, Mikel Rodriguez, and Abhinav Gupta. Learning a predictable and generative vector representation for objects. In ECCV, 2016. 2 +[16] Benjamin Graham, Martin Engelcke, and Laurens van der Maaten. 3d semantic segmentation with submanifold sparse convolutional networks. In CVPR, 2018. 2 +[17] Agrim Gupta, Piotr Dollar, and Ross Girshick. LVIS: A dataset for large vocabulary instance segmentation. In CVPR, 2019. 2 +[18] Ji Hou, Angela Dai, and Matthias Nießner. 3d-sis: 3d semantic instance segmentation of rgb-d scans. In CVPR, 2019. 2, 7 +[19] Iasonas Kokkinos. _Ubernet: Training a 'universal' convolutional neural network for low-, mid-, and high-level vision using diverse datasets and limited memory_. In _CVPR_ 2017. + +3 + +[20] Jason Ku, Melissa Mozifian, Jungwook Lee, Ali Harakeh, and Steven L Waslander. Joint 3d proposal generation and object detection from view aggregation. In IROS, 2018. 2 +[21] Alina Kuznetsova, Hassan Rom, Neil Alldrin, Jasper Uijlings, Ivan Krasin, Jordi Pont-Tuset, Shahab Kamali, Stefan Popov, Matteo Malloci, Tom Duerig, et al. The open images dataset v4: Unified image classification, object detection, and visual relationship detection at scale. arXiv:1811.00982, 2018. 2 +[22] Florent Lafarge and Clément Mallet. Creating large-scale city models from 3d-point clouds: a robust approach with hybrid representation. *IJCV*, 2012. 4, 5, 11, 13 +[23] Xiaoyan Li, Meina Kan, Shiguang Shan, and Xilin Chen. Weakly supervised object detection with segmentation collaboration. In CVPR, 2019. 3 +[24] Qinghao Meng, Wenguan Wang, Tianfei Zhou, Jianbing Shen, Luc Van Gool, and Dengxin Dai. Weakly supervised 3d object detection from lidar point cloud. In ECCV, 2020. 3 +[25] Ishan Misra, Abhinav Shrivastava, Abhinav Gupta, and Martial Hebert. Cross-stitch networks for multi-task learning. In CVPR, 2016. 3 +[26] Sven Oesau, Yannick Verdie, Clément Jamin, Pierre Alliez, Florent Lafarge, Simon Giraudot, Thien Hoang, and Dmitry Anisimov. Shape detection. In CGAL User and Reference Manual. CGAL Editorial Board, 5.1 edition, 2020. 5, 13 +[27] Deepak Pathak, Philipp Krahenbuhl, and Trevor Darrell. Constrained convolutional neural networks for weakly supervised segmentation. In ICCV, 2015. 2 +[28] Charles R. Qi, Xinlei Chen, Or Litany, and Leonidas J. Guibas. Imvotenet: Boosting 3d object detection in point clouds with image votes. In CVPR, 2020. 2, 6 +[29] Charles R Qi, Or Litany, Kaiming He, and Leonidas J Guibas. Deep hough voting for 3d object detection in point clouds. In ICCV, 2019. 1, 2, 3, 6, 7, 13, 14 +[30] Charles R Qi, Wei Liu, Chenxia Wu, Hao Su, and Leonidas J Guibas. Frustum pointnets for 3d object detection from rgb-d data. In CVPR, 2018. 2, 7 +[31] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In CVPR, 2017. 2, 3, 7 +[32] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. In NeurIPS, 2017. 1, 2, 3, 6 +[33] Zengyi Qin, Jinglu Wang, and Yan Lu. Weakly supervised 3d object detection from point clouds. In ACM MM, 2020. 2, 3, 6, 7, 8 +[34] Zhongzheng Ren and Yong Jae Lee. Cross-domain self-supervised multi-task feature learning using synthetic imagery. In CVPR, 2018. 3, 8 +[35] Zhongzheng Ren, Zhiding Yu, Xiaodong Yang, MingYu Liu, Yong Jae Lee, Alexander G. Schwing, and Jan Kautz. Instance-aware, context-focused, and memory-efficient weakly supervised object detection. In CVPR, 2020. 2,4 +[36] Zhongzheng Ren, Zhiding Yu, Xiaodong Yang, Ming-Yu Liu, Alexander G. Schwing, and Jan Kautz. $\mathbf{UFO}^2$ : A unified framework towards omni-supervised object detection. In + +ECCV, 2020. 1, 3 +[37] Gernot Riegler, Ali Osman Ulusoy, and Andreas Geiger. Octnet: Learning deep 3d representations at high resolutions. In CVPR, 2017. 2 +[38] Ruwen Schnabel, Roland Wahl, and Reinhard Klein. Efficient ransac for point-cloud shape detection. In Computer graphics forum, 2007. 5, 13 +[39] Shaoshuai Shi, Xiaogang Wang, and Hongsheng Li. Pointr-cnn: 3d object proposal generation and detection from point cloud. In CVPR, 2019. 2 +[40] Krishna Kumar Singh, Fanyi Xiao, and Yong Jae Lee. Track and transfer: Watching videos to simulate strong human supervision for weakly-supervised object detection. In CVPR, 2016. 2 +[41] Shuran Song, Samuel P Lichtenberg, and Jianxiong Xiao. SUN RGB-D: A rgb-d scene understanding benchmark suite. In CVPR, 2015. 2 +[42] Shuran Song and Jianxiong Xiao. Deep sliding shapes for amodal 3d object detection in rgb-d images. In CVPR, 2016. 2 +[43] Scott Stein. Lidar on the iphone 12 pro. https://www.cnet.com/, 2020. 1, 2 +[44] Pei Sun, Henrik Kretzschmar, Xerxes Dotiwalla, Aurelien Chouard, Vijaysai Patnaik, Paul Tsui, James Guo, Yin Zhou, Yuning Chai, Benjamin Caine, et al. Scalability in perception for autonomous driving: Waymo open dataset. In CVPR, 2020. 2 +[45] Peng Tang, Xinggang Wang, Xiang Bai, and Wenyu Liu. Multiple instance detection network with online instance classifier refinement. In CVPR, 2017. 2, 4 +[46] Yew Siang Tang and Gim Hee Lee. Transferable semi-supervised 3d object detection from rgb-d data. In CVPR, 2019. 2, 3 +[47] Hugues Thomas, Charles R. Qi, Jean-Emmanuel Deschaud, Beatrix Marcotegui, François Goulette, and Leonidas J. Guibas. Kpconv: Flexible and deformable convolution for point clouds. In ICCV, 2019. 2, 7 +[48] J.R.R. Uijlings, K.E.A. van de Sande, T. Gevers, and A.W.M. Smeulders. Selective search for object recognition. IJCV, 2013. 2, 6, 7, 11 +[49] Ozan Unal, Luc Van Gool, and Dengxin Dai. Improving point cloud semantic segmentation by learning 3d object proposal generation. arXiv:2009.10569, 2020. 3 +[50] Fang Wan, Chang Liu, Wei Ke, Xiangyang Ji, Jianbin Jiao, and Qixiang Ye. C-mil: Continuation multiple instance learning for weakly supervised object detection. In CVPR, 2019. 4 +[51] Haiyan Wang, Xuejian Rong, Liang Yang, Shuihua Wang, and Yingli Tian. Towards weakly supervised semantic segmentation in 3d graph-structured point clouds of wild scenes. In BMVC, 2019. 2 +[52] Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E. Sarma, Michael M. Bronstein, and Justin M. Solomon. Dynamic graph cnn for learning on point clouds. ACM Transactions on Graphics, 2019. 2 +[53] Jiacheng Wei, Guosheng Lin, Kim-Hui Yap, Tzu-Yi Hung, and Lihua Xie. Multi-path region mining for weakly supervised 3d semantic segmentation on point clouds. In CVPR, 2020. 2, 6, 7, 14, 15 +[54] Yunchao Wei, Jiashi Feng, Xiaodan Liang, Ming-Ming + +Cheng, Yao Zhao, and Shuicheng Yan. Object region mining with adversarial erasing: A simple classification to semantic segmentation approach. In CVPR, 2017. 2, 3, 8 +[55] Yunchao Wei, Huaxin Xiao, Honghui Shi, Zequn Jie, Jiashi Feng, and Thomas S Huang. Revisiting dilated convolution: A simple approach for weakly-and semi-supervised semantic segmentation. In CVPR, 2018. 2, 3 +[56] Benjamin Wilson, Zsolt Kira, and James Hays. 3d for free: Crossmodal transfer learning using hd maps. arXiv:2008.10592, 2020. 2, 3 +[57] Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguuang Zhang, Xiaou Tang, and Jianxiong Xiao. 3d shapenets: A deep representation for volumetric shapes. In CVPR, 2015. 2, 7, 14 +[58] Jia Xu, Alexander Schwing, and Raquel Urtasun. Tell Me What You See and I will Show You Where It Is. In CVPR, 2014. 2 +[59] Xun Xu and Gim Hee Lee. Weakly supervised semantic point cloud segmentation: Towards 10x fewer labels. In CVPR, 2020. 2 +[60] Li Yi, Wang Zhao, He Wang, Minhyuk Sung, and Leonidas J Guibas. Gspn: Generative shape proposal network for 3d instance segmentation in point cloud. In CVPR, 2019. 7 +[61] Zaiwei Zhang, Bo Sun, Haitao Yang, and Qixing Huang. H3dnet: 3d object detection using hybrid geometric primitives. In ECCV, 2020. 2 +[62] Na Zhao, Tat-Seng Chua, and Gim Hee Lee. Sess: Self-ensembling semi-supervised 3d object detection. In CVPR, 2020. 3 +[63] Bolei Zhou, Aditya Khosla, Agata Lapedriza, Aude Oliva, and Antonio Torralba. Learning deep features for discriminative localization. In CVPR, 2016. 2 +[64] C. Lawrence Zitnick and Piotr Dólar. Edge boxes: Locating object proposals from edges. 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Going beyond prior works that leverage geometry information, typically paired depth maps, we present a new approach, a 3D-to-2D distillation framework, that enables us to leverage 3D features extracted from largescale 3D data repositories (e.g., ScanNet-v2) to enhance 2D features extracted from RGB images. Our work has three novel contributions. First, we distill 3D knowledge from a pretrained 3D network to supervise a 2D network to learn simulated 3D features from 2D features during the training, so the 2D network can infer without requiring 3D data. Second, we design a two-stage dimension normalization scheme to calibrate the 2D and 3D features for better integration. Third, we design a semantic-aware adversarial training model to extend our framework for training with unpaired 3D data. Extensive experiments on various datasets, ScanNet-V2, S3DIS, and NYU-v2, demonstrate the superiority of our approach. Also, experimental results show that our 3D-to-2D distillation improves the model generalization. + +# 1. Introduction + +Indoor scene parsing from images plays an important role in many applications such as robot navigation and augmented reality. Though a considerable amount of advancements have been obtained with convolutional neural networks, this task is still very challenging, since the task inherently suffers from various issues, including distorted object shapes, severe occlusions, viewpoint variations, and scale ambiguities. + +One approach to address the issues is to leverage auxiliary geometric information to obtain structured information that complements the RGB input. For the auxiliary input, existing methods typically employ the depth map that associates with the input RGB image. However, earlier methods [15, 11, 6, 37, 41, 47, 10] require the availability of the depth map + +![](images/64096e3493beb1fd0895b8a5d7658dcfdc5d212609d706d8ecafa75cd75cf6f0.jpg) +(a) + +![](images/c715a7982f38ef10838e49a11ceb998b332ffb0318ac60e12c5f291415464631.jpg) +(b) +Figure 1. Compared with extracting features solely from the input image (a) for semantic parsing, our new approach (b) efficiently distills 3D features learned from a large-scale 3D data repository to train the 2D CNN to learn to enhance its features for better semantic parsing. Our framework needs point cloud inputs only in training but not in testing, and the point cloud can be paired or unpaired. + +inputs not only in the training but also in the testing. As a result, they have limited applicability to general situations, in which depth is not available. This is in contrast to the ubiquity of 2D images, which can be readily obtained by the many photo-taking devices around us. + +To get rid of the constraint, several methods [50, 58, 54, 59, 22] propose to predict a depth map from the RGB input, then leverage the predicted depth to boost the scene parsing performance. However, depth prediction from a single image is already a very challenging task on its own. Hence, the performance of these methods largely depends on the quality of the predicted depth. Also, the additional depth prediction raises the overall complexity of the network. + +Besides the above issues, a common limitation of the prior works is that they only explore the depth map as the auxiliary geometry cue. Yet, a depth map can only give a partial view of a 3D scene, so issues like occlusions and viewpoint variations are severe. Further, they all require paired RGB-depth data in training. So, they are limited for use on datasets with + +depth maps, which require tedious manual preparation, e.g., hardware setups, complicated calibrations, etc. + +In this work, we present the first flexible and lightweight framework (see Figure 1), namely 3D-to-2D distillation, to distill occlusion-free, viewpoint-invariant 3D representations derived from 3D point clouds for embedding into 2D CNN features by training the network to learn to simulate 3D features from the input image. Our approach leverages existing large-scale 3D data repositories such as ScanNet-v2 [8] and S3DIS [1] and recent advancements in 3D scene understanding [14, 7, 17, 21] for 3D feature extraction, and allows the use of unpaired 3D data to train the network. + +For the 2D CNN to effectively learn to simulate 3D features, our 3D-to-2D distillation framework incorporates a two-stage dimension normalization (DN) module to explicitly align the statistical distributions of the 2D and 3D features. So, we can effectively reduce the numerical distribution gap between the 2D and 3D features, as they are from different data modalities and neural network models. Also, a Semantic Aware Adversarial Loss (SAAL) is designed to serve as the objective of model optimization without paired 2D-3D data to make the framework flexible to leverage existing 3D data repository and boost its applicability. + +We conduct extensive experiments on indoor scene parsing datasets ScanNet-v2 [8], S3DIS [1], and NYU-v2 [44]. With only a negligible amount of extra computation cost, our approach consistently outperforms the baselines including the state-of-the-art depth-assisted semantic parsing approach [22] and our two baselines that leverage depth maps, manifesting the superiority of our approach. Besides, our further in-depth experiments on a depth reconstruction task implies that our framework can effectively embed 3D representations into 2D features and produce much better reconstruction results. More importantly, our model obtains a significant performance gain (19.08% vs. 27.22% mIoU), even when evaluated on data from an unseen domain, suggesting that the 3D information embedded by our 3D-to-2D distillation helps promote the generalizability of CNNs. + +# 2. Related Work + +Semantic segmentation. The computer vision community has gained remarkable achievements on semantic segmentation [29, 55, 33, 38, 2, 4, 61, 62, 51, 63, 56, 57, 49]. PSPNet [62] is a representative work that has inspired many follow-ups. In this work, we adopt PSPNet as the baseline model for semantic segmentation, as it has an open-source repository with good reproducibility and delivers competitive performance even compared with the latest works. + +3D semantic segmentation. Methods for 3D semantic segmentation are generally point-based or voxel-based. Point-based networks adopt raw point clouds as input. Along this line of works, [35, 36] are pioneering ones. Later, var + +ious convolution-based methods [25, 46, 53, 3] were proposed for 3D semantic segmentation on point clouds. Recently, Kundu et al. [23] proposed to fuse features from multiple 2D views for 3D semantic segmentation. + +On the other hand, Voxel-based networks first voxelize the raw data into regular 3D grids for feature learning [39, 14, 45, 9, 64]. The recently-proposed methods MinkowskiNet [7] and OccuSeg [17] are two of the representative works in this branch. In this work, we adopt PointWeb [60] and MinkowskiNet [7] as the architectures for extracting point-based and voxel-based 3D features, respectively. + +Knowledge distillation. Our work shares a similar spirit as knowledge distillation techniques [19, 42, 16, 30, 12, 18, 28] in that we both aim to transfer features from a source model (i.e., the teacher model in knowledge distillation or the 3D network in our work) to a target model (i.e., the student model in knowledge distillation or the 2D network in our work) to enhance the performance of the target model. However, conventional knowledge distillation techniques are designed typically for scenarios, in which (i) the source data to be distilled has the same modality [19, 42, 16, 30] or similar modalities [12] as the target, (ii) the two networks for the feature extraction have the same or similar architecture (e.g., convolution neural networks), and (iii) the distillation objective typically requires paired source-target data. + +Recently, cross-modality distillation has also been studied in [32, 13, 40]. However, their methods are not suitable in our, since they cannot distinguish features of different categories. To this end, we propose to associate 2D and 3D features by the object category and formulate the SAAL to enable unpaired training. The experimental result shows that our approach outperforms the most recent semantic segmentation knowledge distillation method [28]. + +# 3. Method + +This section presents our proposed 3D-to-2D distillation framework for effective distillation of 3D features learned from point clouds to improve the performance of 2D indoor scene parsing. Figure 2 shows the overall architecture of the framework. During the training, our framework takes a 2D image and a 3D point cloud as its inputs. To begin, we use a 3D CNN to extract 3D feature $f_{\mathrm{3D}}$ from the input 3D point cloud (blue region in Figure 2). On the other hand, we use a 2D CNN to extract 2D feature $f_{\mathrm{2D}}$ from the input image, and produce also simulated 3D feature $f_{\mathrm{3D\_sim}}$ in the 2D network (orange region in Figure 2). For the 2D CNN, we adopt PSPNet [62] for the case of semantic segmentation, whereas for the 3D CNN, we may adopt different 3D architectures, such as PointWeb [60] and MinkowskiNet [7]. Also, note that $\mathrm{DN}_1$ and $\mathrm{DN}_2$ are our dimension normalization modules. + +An important insight in our approach is that during the training, we use $f_{3\mathrm{D}}$ to supervise the generation of $f_{3\mathrm{D\_sim}}$ , so + +![](images/da1f3e5b1bad0db821c621322273afa9c911784e828ce3b65597b5fec17da865.jpg) +Figure 2. Overview of our 3D-to-2D distillation framework for 2D semantic segmentation. During the training, the framework takes a 2D image and a 3D point cloud as inputs. We transfer 3D feature $f_{\mathrm{3D}}$ from the 3D network (blue) to the 2D network (orange) with an $L_{2}$ loss (for paired 2D-3D data), such that the 2D network can learn to produce simulated 3D feature $f_{\mathrm{3D\_sim}}$ from the 2D image and we do not need $f_{\mathrm{3D}}$ and 3D point cloud input during the inference. Also, note the two dimension normalization modules $(\mathrm{DN}_{1}$ and $\mathrm{DN}_{2}$ ) for aligning 2D-3D features, and the optional module on top-right for training with unpaired 2D-3D data using the semantic-aware adversarial loss. + +that the 2D network can learn to produce $f_{3\mathrm{D\_sim}}$ that looks like $f_{3\mathrm{D}}$ . In this way, we do not need the point cloud input and 3D network when we use our framework to test on a 2D image; the 2D network alone can generate $f_{3\mathrm{D\_sim}}$ solely from the image input. Also, to resolve the statistical difference between the 2D and 3D inputs, we design a two-stage dimension normalization module (DN $_1$ and DN $_2$ ) to effectively transform features before and after $f_{3\mathrm{D\_sim}}$ (Figure 2), so that the statistical distributions of the 2D and 3D features in the 2D network are better aligned to facilitate the learning of the simulated 3D feature and also its integration with the remaining part of the 2D network. Further, we design a semantic-aware adversarial loss as an optional module in the training (Figure 2 (top right)) to extend our framework for training with 2D-3D inputs that are unpaired. + +In this section, we first present how our framework is trained with paired 2D-3D inputs (Section 3.1). Then, we present our dimension normalization modules in Section 3.2 and how we extend the framework for unpaired training with the semantic aware adversarial loss in Section 3.3. + +# 3.1. Training Objectives with Paired 2D-3D Data + +Since 3D feature $f_{3\mathrm{D}}$ extracted from the input point cloud is point-wise in the 3D space, we cannot directly associate it with 2D feature $f_{2\mathrm{D}}$ and likewise the simulated 3D feature $f_{3\mathrm{D\_sim}}$ , which are both defined in 2D image space. To determine the associations, if paired 2D-3D data is available in the training, we can use the given camera parameters to transform and project the 3D points to the 2D image space. In this way, we can determine the pixel location associated with each point in the input point cloud, and obtain $f_{3\mathrm{D\_i}}$ which denotes the projected 3D feature at pixel $i$ . If more than one point projects to the same pixel, we consider only the point that is the nearest to the camera, since it should correspond to the visible pixel in the image input. + +Then, we adopt an $L_{2}$ regression loss between $f_{3\mathrm{D}}$ and $f_{3\mathrm{D\_sim}}$ to supervise the generation of $f_{3\mathrm{D\_sim}}$ in the 2D network. Clearly, the projected 3D points are sparse in the image space, so we locate the pixels covered by the points and perform the regression only on the covered pixels: + +$$ +L _ {p} = \sum_ {i} \left| \left| f _ {\mathrm {3 D} - i} - f _ {\mathrm {3 D} - \text {s i m} - i} \right| \right| _ {2} ^ {2}, \tag {1} +$$ + +where $i$ indexes the pixels covered by the projected 3D points and $L_{p}$ denotes the loss to guide the generation of $f_{\mathrm{3D\_sim}}$ . + +To train the whole framework for the semantic segmentation task, we employ the cross-entropy loss below: + +$$ +L _ {s} = \sum_ {i} \sum_ {c} - \mathbb {1} _ {i, c} \log p _ {i, c}, \tag {2} +$$ + +where $p_{i,c}$ denotes the probability of pixel $i$ belonging to category $c$ and $\mathbb{1}_{i,c}$ is an indicator function that equals 1 if the ground-truth category of pixel $i$ is $c$ ; otherwise, it is zero. + +# 3.2. Dimension Normalization + +To resolve the statistical difference between 2D and 3D representations induced by different data modalities and neural network architectures, we design the dimension normalization modules $\mathrm{DN}_1$ and $\mathrm{DN}_2$ to explicitly calibrate the distribution of the 2D and 3D features; see Figure 2. + +Figure 3 illustrates the technical details. Give a batch of $N$ feature maps as inputs to $\mathrm{DN}_1$ or $\mathrm{DN}_2$ , each of the dimensions $H$ (height), $W$ (width), and $C$ (channels), we compute channel-wise means and variances of the feature map over the $N$ , $H$ , and $W$ dimensions: $(\mu_{2\mathrm{D}}, \sigma_{2\mathrm{D}})$ for the input 2D feature map to $\mathrm{DN}_1$ or $(\mu_{3\mathrm{D}}, \sigma_{3\mathrm{D}})$ for the input 3D feature map to $\mathrm{DN}_2$ . On the other hand, as shown in Figure 2, $\mathrm{DN}_1$ receives statistics $(\bar{\mu}_{3\mathrm{D}}, \bar{\sigma}_{3\mathrm{D}})$ of the 3D feature $f_{3\mathrm{D}}$ , whereas $\mathrm{DN}_2$ receives statistics $(\bar{\mu}_{2\mathrm{D}}, \bar{\sigma}_{2\mathrm{D}})$ of the 2D feature $f_{2\mathrm{D}}$ . Below, we detail the procedure inside each DN: + +
BNAdaBNDN
x̂ = γ x - μ2D / σ2D + βx̂ = γ x - μ3D / σ3D + βx̂3D = Δσ3D(¯σ3D x - μ2D / σ2D +¯μ3D) + Δμ3D, x̂2D = Δσ2D(¯σ2D x - μ3D / σ3D +¯μ2D) + Δμ2D
+ +Table 1. Batch Normalization (BN), Adaptive Batch Normalization (AdaBN), and Dimension Normalization (DN). $\gamma$ , $\beta$ and $\Delta$ are learnable parameters, whereas $\mu$ and $\sigma$ indicate mean and variance. + +![](images/4a71d210817a3cf51e23d90fe509c2a3820f29e36eb3413145ca158864f01c83.jpg) +Figure 3. Dimension normalization modules. Note that $\otimes$ means element-wise multiplication; $\oplus$ means element-wise addition; and $\mathrm{Conv}_1$ to $\mathrm{Conv}_3$ are additional convolutional layers. + +- The purpose of $\mathrm{DN}_1$ is to transform the input 2D feature to align its distribution with that of the 3D feature for effective feature learning. Here, we first use two convolution layers of $3\times 3$ and $1\times 1$ (Conv $_1$ in Figure 3) to transform the input features to have the same channel dimension as the penultimate layer in 3D network $f_{3\mathrm{D}}$ . Then, we normalize the transformed features by $\mu_{2\mathrm{D}}$ and $\sigma_{2\mathrm{D}}$ , and use $\bar{\mu}_{3\mathrm{D}}$ and $\bar{\sigma}_{3\mathrm{D}}$ to scale and adjust the normalized features. Ideally, $\bar{\mu}_{3\mathrm{D}}$ and $\bar{\sigma}_{3\mathrm{D}}$ should correspond to $f_{3\mathrm{D}}$ . However, $f_{3\mathrm{D}}$ is available only in the training but not in the inference, so we pre-compute $\bar{\mu}_{3\mathrm{D}}$ and $\bar{\sigma}_{3\mathrm{D}}$ globally over the entire data, and use the pre-computed values in both training and inference. As a result, we further use learnable parameters $\Delta \sigma_{3\mathrm{D}}$ and $\Delta \mu_{3\mathrm{D}}$ in $\mathrm{DN}_1$ to adjust the features, followed by two subsequent convolution layers of $3\times 3$ and $1\times 1$ (Conv $_2$ in Figure 3) to produce the simulated 3D features. +- The purpose of $\mathrm{DN}_2$ is to calibrate the learned 3D feature $f_{\mathrm{3D\_sim}}$ back to $f_{\mathrm{2D}}$ for smooth 2D-3D feature concatenation. Its structure follows that of $\mathrm{DN}_1$ (Figure 3), except that we do not need any additional convolutional layer to pre-transform the input feature. + +Different from standard batch normalization (BN) [20], which further learns a linear transform to enhance the representative capability as shown in Table 1, our 3D-to-2D distillation module modulates the normalized distribution with a global pre-calculated 3D statistics $\bar{\sigma}_{\mathrm{3D}}$ and $\bar{\mu}_{\mathrm{3D}}$ and then uses learnable offsets $\Delta \sigma_{\mathrm{3D}}$ and $\Delta \mu_{\mathrm{3D}}$ to further adjust the result. With 3D-to-2D distillation, we can explicitly align the distributions of the 2D and 3D features. Yet, our approach still retains the advantage of BN by normalizing features in a batch-wise manner during the training. Then, during the inference, $\mu_{\mathrm{2D}}$ and $\sigma_{\mathrm{2D}}$ are replaced by the accumulated $\bar{\mu}_{\mathrm{2D}}$ and $\bar{\sigma}_{\mathrm{2D}}$ similar to BN. + +Relation to BN and AdaBN. Fundamentally, BN is proposed to facilitate the training of deep neural networks by + +normalizing the data distribution in a batch as shown in Table 1. It helps to reduce the internal co-variant shift [20] or smooth the objective function [43]. However, BN is domain-dependent, which has side-effects in our cross-modality knowledge transfer task. Further, AdaBN [26] is proposed for domain adaptation. In the inference stage, AdaBN uses $(\bar{\mu}_{3\mathrm{D}},\bar{\sigma}_{3\mathrm{D}})$ of the target domain instead of the accumulated $(\bar{\mu}_{2\mathrm{D}},\bar{\sigma}_{2\mathrm{D}})$ in the source domain to normalize the features. AdaBN is designed for the case, in which the model is trained in the source domain and tested in the target domain, which is different from our setup where training and inference are both performed in the 2D domain. + +# 3.3. Adversarial Training with Unpaired Data + +With paired 2D-3D data, we can distill 3D feature with an $L_{2}$ loss, since we can correspond the 2D and 3D features in the same image domain. However, paired 2D-3D data are typically expensive to acquire in a large quantity, given the amount of works needed in data collection, calibration, and annotation. To this end, we design a new adversarial training approach to correlate 2D and 3D features and supervise the generation of the simulated 3D features. + +There are two key insights in our approach. First, we observe that existing 2D and 3D datasets usually have common object categories, e.g., ScanNet-v2 [8] has 20 object categories in its 3D point clouds, whereas NYU-v2 [44] has 40 object categories in its 2D images; the 20 categories in ScanNet-v2 can all be found in the categories in NYU-v2. Hence, we propose to correspond 2D and 3D features by their associated object categories. Second, given a 3D feature of a certain category and another 2D feature of the same category, we propose a novel adversarial training model with a per-category discriminator. The goal of our model is to generate simulated 3D features solely from the 2D features, such that the discriminator cannot differentiate the 3D features from the simulated one of the same category. In this way, the 2D network should learn to generate simulated 3D features solely without requiring paired 2D-3D data. + +Figure 2 (top-right) shows the optional module we designed for unpaired training. It has $N$ individual discriminators, where $N$ is the number of object categories common to the 2D and 3D data. We implement each discriminator using six fully-connected layers and denote the discriminator of category $c$ as $D_{c}$ . There are two kinds of inputs to $D_{c}$ : (i) a 3D feature vector $f_{\mathrm{3D\_i}}$ from 3D network or (ii) a simulated 3D feature vector $f_{\mathrm{3D\_sim\_j}}$ from 2D network, and both should belong to category $c$ . For each input to $D_{c}$ , it should + +predict a confidence score that indicates whether the input feature vector comes from the 2D or 3D network. + +Before we present how we train the whole framework for unpaired data, we first denote $\Phi_{2\mathrm{D}}$ as the 2D network. During the training, the 3D network is fixed, and we alternatively train $\Phi_{2\mathrm{D}}$ and the set of discriminators $\{D_c\}$ , similar to the way the generator (like $\Phi_{2\mathrm{D}}$ ) and discriminator (like $D_c$ 's) are trained in a conventional GAN model. + +- When we train the discriminators, we fix $\Phi_{2\mathrm{D}}$ and use the following objective to train each $D_c$ : + +$$ +\begin{array}{l} L _ {\mathrm {a d v}} \left(D _ {c}\right) = - \sum_ {i} \mathcal {N} _ {c, i} \log \left(1 - D _ {c} \left(f _ {\mathrm {3 D} _ {-} \mathrm {s i m} _ {-} \mathrm {i}}\right)\right) \\ - \sum_ {j} \mathcal {M} _ {c, j} \log \left(D _ {c} \left(f _ {\mathrm {3 D} - \mathrm {j}}\right)\right), \tag {3} \\ \end{array} +$$ + +where $\mathcal{N}_{c,i}$ (or $\mathcal{M}_{c,j}$ ) equals 1, if the 2D pixel $i$ (or 3D point $j$ ) belongs to category $c$ ; otherwise, it equals 0. Note that we treat $f_{\mathrm{3D\_sim\_i}}$ as a negative sample and $f_{\mathrm{3D\_j}}$ as a positive sample, so the goal of $D_{c}$ is to learn to differentiate them; by then, $\Phi_{\mathrm{2D}}$ should learn to generate better $f_{\mathrm{3D\_sim\_i}}$ to deceive $\{D_c\}$ . + +- When we train the 2D network $\Phi_{\mathrm{2D}}$ , we fix all $D_c$ 's and use the following objective in the training: + +$$ +L _ {\mathrm {a d v}} \left(\Phi_ {2 \mathrm {D}}\right) = - \sum_ {i} \sum_ {c} \mathcal {N} _ {c, i} \log \left(D _ {c} \left(f _ {3 \mathrm {D} - \text {s i m} - \mathrm {i}}\right)\right). \tag {4} +$$ + +Overall, to train $\Phi_{2\mathrm{D}}$ , the overall loss is constructed by combining the softmax-cross entropy loss [62] for semantic segmentation with the paired regression loss $L_{p}$ or with the adversarial loss $L_{\mathrm{adv}}(\Phi_{2\mathrm{D}})$ , if paired data is unavailable. The loss weights are validated on a small validation set. + +# 4. Experiments and Results + +Datasets We conduct experiments on three indoor scene parsing datasets—ScanNet-v2 [8], S3DIS [1], and NYU-v2 [31]. ScanNet-v2 [8] contains 1,513 scenes with 3D scans and 2D images. S3DIS [1] contains 3D scans with associated 2D images of 271 rooms, and each 3D point and 2D pixel are annotated as one of the 13 categories in the dataset. To be noted, for both datasets, we can only obtain sparse paired 2D-3D points, due to the calibration and projection issues as illustrated in the supplementary material. Only $16.38\%$ and $10.57\%$ of 2D pixels have corresponding 3D points in ScanNet-v2 and S3DIS, respectively. NYU-v2 [31] contains 1,449 images without reconstructed 3D scene. + +Implementation details. We implement our framework using PyTorch [34], and train all the models and baselines with the SGD optimizer. The batch size is 16 and the initial learning rate is 0.01, which is scheduled based on the "poly" learning rate policy with power 0.9 [62]. Since different + +![](images/9bf49fe5346ae579a2976c2fecba83622158bec1cdc46f928429d723babc855d.jpg) +(a) Multitask + +![](images/6b1a136cbe7ec613aa85d072b92a3830a90f1da574896fa2694150a808728232.jpg) +(b) Cascade +$\langle \widehat{\mathbb{C}}\rangle$ concatenation +Figure 4. Illustrating the Multitask and Cascade approaches of leveraging depth for 2D semantic segmentation. + +datasets have different numbers of training samples, we train models with different numbers of epochs on different datasets to equalize the number of training iterations: ScanNet-v2 for 50 epochs; S3DIS for 20 epochs on Area 1,2,3,4,6; and NYU-v2 with the officially split training samples for 300 epochs. By default, we empirically set the loss weights on $L_{s}$ , $L_{\mathrm{adv}}$ and $L_{p}$ as 1, 0.01 and 0.03, respectively. + +Network architectures. By default, we adopt the representative architecture PSPNet-50 [62] for semantic segmentation. For 3D feature extraction, we employ the voxel-based architecture, i.e., MinkowskiNet [7] on ScanNet [8], and the point-based architecture, i.e., PointWeb [60] on S3DIS. The 3D network weights are fixed during the training. + +# 4.1. Comparing with Related Geometry-Assisted and Knowledge Distillation Methods + +First, we present extensive experiments to compare our 3D-to-2D distillation approach with major competitors. They are alternative ways of leveraging depth or 3D information to enrich 2D features for semantic segmentation. In these experiments, we use the latest large-scale indoor scene parsing dataset ScanNet-v2 [8], which provides paired 2D-3D data for training various models for semantic segmentation. + +(i) Baseline: the original PSPNet-50 model [62]. +(ii) Multitask: we use PSPNet-50 to additionally predict a depth map (Figure 4 (a)), which is supervised by using data from ScanNet-v2; this model is similar to ours, in the sense that we replace the simulated 3D feature in our model by a depth map prediction. +(iii) Cascade: we use a state-of-the-art depth prediction method $[24]^1$ to predict a depth map and take the predicted depth map as an auxiliary input to assist PSPNet (Figure 4 (b)); so, this approach also does not require 3D data in the inference like ours, but the knowledge comes from the depth map predicted by [24]. +(iv) Geo-Aware [22]: this is the most recent method that distills features from depth maps for assisting 2D semantic segmentation; since code is not available, we + +
MethodmIoU
BaselinePSPNet-5053.40
Depth methodsMultitask54.08
Cascade53.72
Geo-Aware [22]56.90
KDStructured KD56.36
Ours3D-2D Distillation58.22
+ +simply report its ScanNet-v2 result on its paper in Table 2. Also, this method is finetuned on NYU-v2, so it leveraged more data than ours (ScanNet-v2 only). + +(v) Structured KD: we adopt the most recent knowledge distillation approach for semantic segmentation [28]; since it is designed for distilling 2D information, we replace its teacher net with a 3D network to distill 3D information for comparison with our approach. + +Table 2 reports the semantic segmentation performance of our approach and the competitors on the ScanNet-v2 validation set. Our approach outperforms all of them, and these results reveal the following: + +- Comparing with Multi-task, we can show that our full approach of predicting the simulated 3D features leads to better results than explicitly predicting a depth map using the same paired data. This result demonstrates the richness of simulated 3D features from 3D point clouds, as compared with 2.5D depth maps. +- Comparing with Cascade, we can show that even we use the state-of-the-art depth prediction network [24] to provide the predicted depth map, the predicted depth map (which is 2.5D) cannot assist the PSPNet for semantic segmentation, as good as the simulated 3D features generated by our 3D-to-2D distillation approach. +- Comparing with Geo-Aware [22], we show again that distilling features from point clouds can lead to a better performance. Note that Multitask, Cascade, and Geo-Aware are all depth-assisted methods. +- Comparing with Structured KD, we show that our 3D-to-2D distillation approach can lead to a higher performance than simply adopting a general knowledge distillation model. To be noted, Structured KD also adopts an adversarial objective to align the global segmentation map; see Section 4.4. + +# 4.2. Further Evaluations with Sparse Paired Data + +Next, we conduct further experiments on the latest largescale indoor scene parsing dataset—ScanNet-v2 and S3DIS. + +Table 2. Comparing the semantic segmentation performance (on ScanNet-v2 validation set) of various methods that use depth/3D information to assist the segmentation: two alternative methods (Multitask and Cascade) that predict depth maps, a depth-distillation method Geo-Aware [22], and Structured KD, which is a variant of [28]. All the methods are based on the ResNet-50 backbone. + +
MethodmIoU
FCN-8s [29]45.87
ParseNet [27]47.72
DeepLab-v2 [4]43.89
AdapNet [48]47.28
DeepLab-v3 [5]50.09
AdapNet++ [47]52.92
Ours (w/ PSPNet-50)57.76
+ +Table 3. Comparing our method with existing 2D image-based semantic segmentation methods on the ScanNet-v2 validation set. We follow the settings in [47], where the size of the input image is $384 \times 768$ without left-right flip and multi-scale test. + +
MethodmIoU
HRNet [49] + OCR [56]60.56
HRNet [49] + OCR [56] + Our 3D-2D distillation61.36
+ +Table 4. We adopt our method into the state-of-the-art 2D semantic segmentation approach, HRNet [49] + OCR [56], and further boost its performance. The networks use HRNet-W48 [49] as the backbone, with a comparable network complexity as ResNet-101. + +
MethodPSPNet-50Ours
mIoU43.6546.42
+ +Table 5. Semantic segmentation results on S3DIS. + +ScanNet-v2 semantic segmentation. First, we compare our method with several 2D image-based semantic segmentation approaches. Table 3 reports the results, showing that our model outperforms all of them for $4.8\%$ to $11.8\%$ mIoU. + +Further, since our method is generic, we can easily incorporate it into existing semantic segmentation architecture. Hence, we adopt it into the state-of-the-art 2D semantic segmentation network—HRNet+OCR [57, 49], which has demonstrated top performance on various datasets. As shown in Table 4, our 3D-to-2D distillation approach can further boost the performance of HRNet+OCR. + +S3DIS semantic segmentation. Further, we experiment on S3IDS [1] with PointWeb [60] as the 3D network for extracting 3D features. Results in Table 5 show that our method helps improve the baseline model, suggesting the generality and effectiveness of our method for use with different 3D network architectures on a different dataset. + +Qualitative analysis. Visual results on ScanNet-v2 and S3DIS are shown in Figures 5 and 6, respectively. The semantic segmentation quality has been consistently improved with our approach. The failure modes of the original PSP-Net model are largely caused by occlusions (Figure 5: door, bathtub and toilet, Figure 6: chair and table), uncommon viewpoints (Figure 5: table), and confusions due to similar color and texture (Figure 6: column, and chair). In comparison, our approach can successfully segment these objects. This demonstrates the potential of our distilled 3D feature for resolving issues with occlusions, viewpoints, and textures. + +![](images/f3c4056fa130ddeb3ceb7fc7b49474867a6ee7268e6eb113f4e07534fd7b6a2f.jpg) +Figure 5. Visualization of the results on the ScanNet-v2 dataset. As marked by the red boxes, our 3D-to-2D distillation has better performance for the door, floor, table, and cabinet regions benefited from the rich embedded 3D information. + +![](images/f1c851ee93a59481df3f31d2a78acf18285142c3647765572702055d188badaf.jpg) + +![](images/9732c8b4c0b0649a603ce47d3416d4e18f88c54ef3c71babe4e0955d4d12fc9c.jpg) +Figure 6. Visualization of the results on S3DIS. Ours show the result of our approach using the ResNet-50 baseline as the backbone. + +![](images/ed095a5033d3ee4deecafea8c7bb3b2dfbca7f69656224b6b60a64b7e7db1fc3.jpg) + +
MethodPSPNet-50Ours
mIoU49.5051.70
+ +This demonstrates that our model with distilled 3D feature can potentially better leverage 3D geometric information, such as the shape of objects and thus is more robust to ambiguities caused by occlusions, viewpoints and texture. + +# 4.3. 3D-to-2D Distillation without Paired Data + +When paired data is not available, we generally can only train the 2D network solely with 2D image inputs. With our adversarial training model (Section 3.3), we may distill unpaired 3D data to enrich features in the 2D network. This subsection presents an experiment to compare the performance of a 2D network (i.e., PSPNet [62]) when it is trained (i) without 3D data and (ii) with unpaired 3D data. Here, we use MinkowskiNet [7] as the 3D network, NYU-v2 as the 2D data, ScanNet-v2 as the 3D data, and the 20 categories common to both data in training and testing. + +From Table 6, we can see that without using any 3D data, the average performance of PSPNet on NYU-v2 20 classes is 49.50, and using unpaired 3D data (with almost negligible effort) can enrich the 2D features and improve the performance by almost $5\%$ relatively, i.e., from 49.50 to 51.70. Note that this is the very first work that explores the potential of using unpaired 3D data for 2D semantic segmentation. We did not explore more sophisticated techniques to further improve the results, but still, the results demonstrate the possibility of unpaired data, and we hope that this can open up a new direction for improving scene parsing from images. + +Table 6. Results on NYU-v2 20 class without paired data. + +
DatasetOurs (w/ BN)Ours (w/ DN)
ScanNet-v257.6458.22
S3DIS45.5746.42
NYU-V2†26.5427.22
DatasetOurs (w/o semantic)Ours (w/ SAAL)
NYU-v2*50.8651.84
+ +Table 7. Ablation studies. NYU- $\mathbf{v}2^{\dagger}$ is evaluated under the setting that the model is trained on ScanNet-V2 and tested on NYU-v2. NYU- $\mathbf{v}2^{*}$ is evaluated with unpaired 2D-3D data. ScanNet-v2 and S3IDS results are evaluated on the setting with paired 2D-3D data. SAAL denotes our semantic aware adversarial loss. + +# 4.4. Ablation Studies + +Next, we ablate two major components in our approach: (i) the dimension normalization modules—we replace the two DN modules with BNs while keeping the convolution part in DNs; (ii) the semantic aware adversarial loss (SAAL)—we create a baseline that adopts a shared discriminator for all the categories, similar to that in [28]. + +From the results shown in Table 7, by comparing "Ours (w/ BN)" vs. "Ours (w/ DN)", we can see that DN consistently outperforms BN including the generalization to unseen domains, i.e., NYU-v2†. Then, by comparing our SAAL with the ablated semantic aware design in the NYU-v2* row, we can see that SAAL boosts the performance, implying that our adversarial training model helps improve the discriminative ability of the features, while aligning the distributions to facilitate feature transfer. + +# 4.5. Analysis + +Further, we conduct an analysis to investigate whether our 3D-to-2D distillation can embed 3D information into the 2D CNN features and whether the 3D features can improve + +![](images/572abbeb1f10fc8506dda4e36b32a7733a9c2f5a09c675b4285ea0855e4f3ecf.jpg) +(a) Input + +![](images/1bcb7b36e2afa4142e1fa9a131ddcf305b6816c30f74cbd2b9cfd6f7ab6ccb3c.jpg) +(b) Ground truth +Figure 7. Visualization of depth reconstruction quality. Depth map of PSPNet-50 and ours are both derived from "res-block-4" features. + +![](images/41b5ccc5dce8d19bed85af8ba972f50dd878db2292b1664ebc26f3dfcd2620ad.jpg) +(c) 2D network + +![](images/ea14718fdc13f0d3c77cec2652dd994913efc89a18ef901623a35153919dda7c.jpg) +(d) Ours + +![](images/a4923a95d547bdaa535c1cba61d35ad645d4cefe2c810e4bd2078507ed0c11bc.jpg) +(a) Input + +![](images/019f88af6e7879455e034b6b0dd772da9a20ad2b15a52fbb5cbc34ad8acd0447.jpg) +(b) Ground truth + +![](images/bb1c3ca405845fa08bc3d44359f66cb41c7809811154afbececcdbdd4b48834b.jpg) +(c) 2D network + +![](images/f00b671c9df81377ebd8e56452b6842ede4bf9bc089d2f9070d8d340d8359e3b.jpg) +(d) Ours + +![](images/06bb69b4a9c49b465142c11270e745ae792396b041dd5df1d6bf604630ca85cc.jpg) +(a) SSIM vs block number + +![](images/fd9898ae2031772a10d0f29b0424432c7588316cb5d99b37e951ae0c8763a0b8.jpg) + +![](images/e3a2d514ea8e77b72d5b36cbdf762242ed96c45447bbfa94ff75cbc9ce5d4ef6.jpg) + +![](images/4181455716dd040388ab36be2c62984bf3297351afd3b4731c9b29b18c5bbd7a.jpg) +Table 8. Domain generalization results on NYU-v2 20-class using various models trained on ScanNet-v2. + +![](images/5d1b1bb5f8e831eb03baea1e407773362074e13d8ec75cfdc22b56ad760fdfdb.jpg) +(b) GT +(e) res-block2 +Figure 8. PSPNet-50 retains less 3D information in deep layers vs. shallow layers. (a) SSIM (larger is better) of depth images predicted from PSPNet-50 feature map in different layers. (b)-(g): Depth maps predicted from different layers. The PSPNet-50 is pre-trained for semantic segmentation. Please zoom in to see the details. + +![](images/9581b2a98579de25ef2830bda7517e6e47d3e81d93ba6d98732cae6e874dea1c.jpg) +(c) conv+pooling +(f) res-block3 + +![](images/81d5ab4ac4e25d868f38de4276c392dddc36e2311eb3d9776ce4bcfffb822b5f.jpg) +(d) res-block1 +(g) res-block4 + +the model's generalizability. To start, we propose a metric to evaluate how much 3D information is embedded into the 2D CNN features. Our idea is to evaluate the ability of CNN features for reconstructing depth maps. We build a depth estimation network with features from each layer as input and train it to produce the corresponding depth map. Then, we evaluate the depth reconstruction quality with the Structural Similarity Index (SSIM) [52]—larger is better. The reason for adopting SSIM instead of Mean Square Error is that depth information from a single image has scale ambiguities, while SSIM focuses more on structural similarities with the ground truth rather than the absolute values. + +3D features in baseline PSPNet. Taking inputs from different layers of PSPNet-50 trained on ScanNet-v2 for semantic segmentation, we obtain the depth prediction results shown in Figure 8. Figure 8 (a) shows that the SSIM value decreases as the feature map goes deeper. The associated visualizations in Figures 8 (b)-(g) show that the structure of the depth map becomes hard to identify when it is derived from deep features (Figure 8 (g)). Both quantitative and qualitative results suggest that deep features may retain less 3D information and have a lower capability of reconstructing depth in comparison with shallow features, even though they are more directly relevant to the final semantic parsing task. + +3D features in our models. Further, we analyze whether the 2D network in our framework can better leverage 3D information. We take the deep "res-block-4" feature map of our model trained on ScanNet-v2. The SSIM is improved by $24\%$ (baseline: 0.38 vs. our: 0.47) as compared with the baseline (the red point in Figure 8), and the quality of the reconstructed depth map is significantly improved as shown in Figure 7. The object structure and boundary can be better preserved. With 3D-to-2D distillation, higher quality depth can be reconstructed from our deep features, suggesting that + +
MethodPSPNet-50PSPNet-101MultitaskCascadeOurs
mIoU19.0820.1220.3022.5227.22
+ +our approach facilitates the 2D network to better utilize 3D information when constructing the deep features. + +# 4.6. Effectiveness in Boosting Model Generalization + +The analysis in Section 4.5 implies that the embedded 3D information in deep features may help the CNN better utilize the robust 3D cues, such as shape, for recognition, and further improve the model's generalization abilities. Next, we investigate whether 3D-to-2D distillation can improve the generalizability of the model. To this end, we directly evaluate the baseline model and our model when trained on ScanNet-v2 and tested on NYU-v2. Here, we consider only the 20 classes common to ScanNet-v2 and NYU-v2. + +Comparing Tables 8 and 2, we can see that the performance of all methods drops seriously when tested on unseen NYU-v2. However, with the 3D-enhanced 2D features, our model with the ResNet-50 backbone improves over PSPNet-50 by $43\%$ for more than $8\%$ mIoU. Also, it surpasses PSPNet-101 by more than $7\%$ mIoU. The results imply that the embedded 3D feature helps improve the generalizability of the 2D network, and such improvement cannot be achieved by using a larger network, i.e., PSPNet-101. + +# 5. Conclusion + +This paper presents a novel 3D-to-2D distillation framework that effectively leverages 3D features learned from 3D point clouds to enhance 2D networks for indoor scene parsing. At testing, the 2D network can infer simulated 3D features without any 3D data input. To bridge the statistical distribution gap between the 2D and 3D features, we propose a two-stage distillation normalization module for effective feature integration. Further, to broaden the applicability of our approach, we design an adversarial training model with the semantic aware adversarial loss to extend our framework for training with unpaired 2D-3D data. Experiments on three public indoor datasets suggest the superiority of our approach in various settings. We hope our further analysis on 3D and generalization could inspire future works on incorporating 3D information to improve model generalization. + +# References + +[1] Iro Armeni, Sasha Sax, Amir R. Zamir, and Silvio Savarese. Joint 2D-3D-semantic data for indoor scene understanding. arXiv preprint arXiv:1702.01105, 2017. +[2] Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla. SegNet: A deep convolutional encoder-decoder architecture for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), 39(12):2481-2495, 2017. +[3] Alexandre Boulch. ConvPoint: Continuous convolutions for point cloud processing. Computers & Graphics, 2020. +[4] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. DeepLab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs. IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), 40(4):834-848, 2017. +[5] Liang-Chieh Chen, George Papandreou, Florian Schroff, and Hartwig Adam. Rethinking atrous convolution for semantic image segmentation. arXiv preprint arXiv:1706.05587, 2017. +[6] Yanhua Cheng, Rui Cai, Zhiwei Li, Xin Zhao, and Kaiqi Huang. Locality-sensitive deconvolution networks with gated fusion for RGB-D indoor semantic segmentation. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR), pages 3029-3037, 2017. +[7] Christopher Choy, JunYoung Gwak, and Silvio Savarese. 4D spatio-temporal ConvNets: Minkowski convolutional neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 3075-3084, 2019. +[8] Angela Dai, Angel X. Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. ScanNet: Richly-annotated 3D reconstructions of indoor scenes. In Proc. Computer Vision and Pattern Recognition (CVPR), IEEE, 2017. +[9] Angela Dai and Matthias Nießner. 3DMV: Joint 3D-multiview prediction for 3D semantic scene segmentation. In Proceedings of the European Conference on Computer Vision (ECCV), pages 452-468, 2018. +[10] Liuyuan Deng, Ming Yang, Tianyi Li, Yuesheng He, and Chunxiang Wang. RFBNet: deep multimodal networks with residual fusion blocks for RGB-D semantic segmentation. arXiv preprint arXiv:1907.00135, 2019. +[11] David Eigen and Rob Fergus. Predicting depth, surface normals and semantic labels with a common multi-scale convolutional architecture. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 2650-2658, 2015. +[12] Nuno C. Garcia, Pietro Morerio, and Vittorio Murino. Modality distillation with multiple stream networks for action recognition. In Proceedings of the European Conference on Computer Vision (ECCV), pages 103-118, 2018. +[13] Nuno C Garcia, Pietro Morerio, and Vittorio Murino. Learning with privileged information via adversarial discriminative modality distillation. IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), 42(10):2581-2593, 2019. + +[14] Ben Graham. Sparse 3D convolutional neural networks. In The British Machine Vision Conference (BMVC), 2015. +[15] Saurabh Gupta, Ross Girshick, Pablo Arbeláez, and Jitendra Malik. Learning rich features from RGB-D images for object detection and segmentation. In European conference on computer vision (ECCV), pages 345-360. Springer, 2014. +[16] Saurabh Gupta, Judy Hoffman, and Jitendra Malik. Cross modal distillation for supervision transfer. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR), pages 2827-2836, 2016. +[17] Lei Han, Tian Zheng, Lan Xu, and Lu Fang. OccuSeg: Occupancy-aware 3D instance segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 2940-2949, 2020. +[18] Byeongho Heo, Minsik Lee, Sangdoo Yun, and Jin Young Choi. Knowledge distillation with adversarial samples supporting decision boundary. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pages 3771-3778, 2019. +[19] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531, 2015. +[20] Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167, 2015. +[21] Li Jiang, Hengshuang Zhao, Shaoshuai Shi, Shu Liu, Chi-Wing Fu, and Jiaya Jia. PointGroup: Dual-set point grouping for 3D instance segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 4867-4876, 2020. +[22] Jianbo Jiao, Yunchao Wei, Zequn Jie, Honghui Shi, Rynson WH Lau, and Thomas S. Huang. Geometry-aware distillation for indoor semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2869-2878, 2019. +[23] Abhijit Kundu, Xiaoqi Michael Yin, Alireza Fathi, David Alexander Ross, Brian Brewington, Tom Funkhouser, and Caroline Pantofaru. Virtual multi-view fusion for 3D semantic segmentation. In Proceedings of the European Conference on Computer Vision (ECCV), 2020. +[24] Jin Han Lee, Myung-Kyu Han, Dong Wook Ko, and Il Hong Suh. From big to small: Multi-scale local planar guidance for monocular depth estimation. arXiv preprint arXiv:1907.10326, 2019. +[25] Yangyan Li, Rui Bu, Mingchao Sun, Wei Wu, Xinhan Di, and Baoquan Chen. PointCNN: Convolution on X-transformed points. In Advances in neural information processing systems (NeurIPS), pages 820-830, 2018. +[26] Yanghao Li, Naiyan Wang, Jianping Shi, Jiaying Liu, and Xiaodi Hou. Revisiting batch normalization for practical domain adaptation. In International Conference on Learning Representations (ICLR), 2017. +[27] Wei Liu, A Rabinovich, and C. Berg Alexander. ParseNet: Looking wider to see better. In International Conference on Learning Representations (ICLR), 2016. +[28] Yifan Liu, Changyong Shu, Jingdong Wang, and Chunhua Shen. Structured knowledge distillation for dense predic + +tion. IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), 2020. +[29] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR), pages 3431-3440, 2015. +[30] Seyed-Iman Mirzadeh, Mehrdad Farajtabar, Ang Li, and Hassan Ghasemzadeh. Improved knowledge distillation via teacher assistant: Bridging the gap between student and teacher. arXiv preprint arXiv:1902.03393, 2019. +[31] Pushmeet Kohli Nathan Silberman, Derek Hoiem and Rob Fergus. Indoor segmentation and support inference from RGBD images. In European Conference on Computer Vision (ECCV), 2012. +[32] Shivam Pande, Avinandan Banerjee, Saurabh Kumar, Biplab Banerjee, and Subhasis Chaudhuri. An adversarial approach to discriminative modality distillation for remote sensing image classification. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, pages 0–0, 2019. +[33] Adam Paszke, Abhishek Chaurasia, Sanggil Kim, and Eugenio Culurciello. ENet: A deep neural network architecture for real-time semantic segmentation. arXiv preprint arXiv:1606.02147, 2016. +[34] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. PyTorch: An imperative style, high-performance deep learning library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems (NeurIPS) 32, pages 8024-8035. Curran Associates, Inc., 2019. +[35] Charles R. Qi, Hao Su, Kaichun Mo, and Leonidas J. Guibas. PointNet: Deep learning on point sets for 3D classification and segmentation. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR), pages 652-660, 2017. +[36] Charles R. Qi, Li Yi, Hao Su, and Leonidas J. Guibas. Point-Net++: Deep hierarchical feature learning on point sets in a metric space. In Advances in neural information processing systems (NeurIPS), pages 5099-5108, 2017. +[37] Xiaojuan Qi, Renjie Liao, Jiaya Jia, Sanja Fidler, and Raquel Urtasun. 3D graph neural networks for RGBD semantic segmentation. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 5199-5208, 2017. +[38] Xiaojuan Qi, Zhengzhe Liu, Jianping Shi, Hengshuang Zhao, and Jiaya Jia. Augmented feedback in semantic segmentation under image level supervision. In European Conference on Computer Vision (ECCV), pages 90-105. Springer, 2016. +[39] Gernot Riegler, Ali Osman Ulusoy, and Andreas Geiger. Oct-Net: Learning deep 3D representations at high resolutions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 3577-3586, 2017. +[40] Siddharth Roheda, Benjamin S Riggan, Hamid Krim, and Liyi Dai. Cross-modality distillation: A case for condi + +tional generative adversarial networks. In 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 2926-2930. IEEE, 2018. +[41] Eduardo Romero, José M. Alvarez, Luis M. Bergasa, and Roberto Arroyo. ERFNet: Efficient residual factorized ConvNet for real-time semantic segmentation. IEEE Transactions on Intelligent Transportation Systems, 19(1):263-272, 2017. +[42] Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang, Carlo Gatta, and Yoshua Bengio. FitNets: Hints for thin deep nets. arXiv preprint arXiv:1412.6550, 2014. +[43] Shibani Santurkar, Dimitris Tsipras, Andrew Ilyas, and Aleksander Madry. How does batch normalization help optimization? In Advances in Neural Information Processing Systems (NeurIPS), pages 2483-2493, 2018. +[44] Nathan Silberman, Derek Hoiem, Pushmeet Kohli, and Rob Fergus. Indoor segmentation and support inference from RGBD images. In European Conference on Computer Vision (ECCV), pages 746-760. Springer, 2012. +[45] Hang Su, Varun Jampani, Deqing Sun, Subhransu Maji, Evangelos Kalogerakis, Ming-Hsuan Yang, and Jan Kautz. Splat-Net: Sparse lattice networks for point cloud processing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2530–2539, 2018. +[46] Hugues Thomas, Charles R. Qi, Jean-Emmanuel Deschaud, Beatrix Marcotegui, François Goulette, and Leonidas J. Guibas. KPCov: Flexible and deformable convolution for point clouds. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 6411–6420, 2019. +[47] Abhinav Valada, Rohit Mohan, and Wolfram Burgard. Self-supervised model adaptation for multimodal semantic segmentation. International Journal of Computer Vision (IJCV), pages 1-47, 2019. +[48] Abhinav Valada, Johan Vertens, Ankit Dhall, and Wolfram Burgard. Adapnet: Adaptive semantic segmentation in adverse environmental conditions. In 2017 IEEE International Conference on Robotics and Automation (ICRA), pages 4644-4651. IEEE, 2017. +[49] Jingdong Wang, Ke Sun, Tianheng Cheng, Borui Jiang, Chaorui Deng, Yang Zhao, Dong Liu, Yadong Mu, Mingkui Tan, Xinggang Wang, et al. Deep high-resolution representation learning for visual recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), 2020. +[50] Peng Wang, Xiaohui Shen, Zhe Lin, Scott Cohen, Brian Price, and Alan L. Yuille. Towards unified depth and semantic prediction from a single image. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR), pages 2800-2809, 2015. +[51] Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 7794-7803, 2018. +[52] Zhou Wang, Alan C. Bovik, Hamid R Sheikh, and Eero P. Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing (TIP), 13(4):600-612, 2004. +[53] Wenxuan Wu, Zhongang Qi, and Li Fuxin. PointConv: Deep convolutional networks on 3D point clouds. In Proceedings + +of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 9621-9630, 2019. +[54] Dan Xu, Wanli Ouyang, Xiaogang Wang, and Nicu Sebe. Padnet: Multi-tasks guided prediction-and-distillation network for simultaneous depth estimation and scene parsing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 675-684, 2018. +[55] Fisher Yu and Vladlen Koltun. Multi-scale context aggregation by dilated convolutions. In International Conference on Learning Representations (ICLR), 2016. +[56] Yuan Yuhui and Wang Jingdong. OCNet: Object context network for scene parsing. arXiv preprint arXiv:1809.00916, 2018. +[57] Yuan Yuhui, Chen Xilin, and Wang Jingdong. Object-contextual representations for semantic segmentation. arXiv preprint arXiv:1909.11065, 2019. +[58] Zhenyu Zhang, Zhen Cui, Chunyan Xu, Zequn Jie, Xiang Li, and Jian Yang. Joint task-recursive learning for semantic segmentation and depth estimation. In Proceedings of the European Conference on Computer Vision (ECCV), pages 235–251, 2018. +[59] Zhenyu Zhang, Zhen Cui, Chunyan Xu, Yan Yan, Nicu Sebe, and Jian Yang. Pattern-affinitive propagation across depth, surface normal and semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 4106-4115, 2019. +[60] Hengshuang Zhao, Li Jiang, Chi-Wing Fu, and Jiaya Jia. PointWeb: Enhancing local neighborhood features for point cloud processing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5565-5573, 2019. +[61] Hengshuang Zhao, Xiaojuan Qi, Xiaoyong Shen, Jianping Shi, and Jiaya Jia. ICNet for real-time semantic segmentation on high-resolution images. In Proceedings of the European Conference on Computer Vision (ECCV), pages 405-420, 2018. +[62] Hengshuang Zhao, Jianping Shi, Xiaojuan Qi, Xiaogang Wang, and Jiaya Jia. Pyramid scene parsing network. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR), pages 2881-2890, 2017. +[63] Hengshuang Zhao, Yi Zhang, Shu Liu, Jianping Shi, Chen Change Loy, Dahua Lin, and Jiaya Jia. PSANet: Point-wise spatial attention network for scene parsing. In Proceedings of the European Conference on Computer Vision (ECCV), pages 267-283, 2018. +[64] Yu Zhao, Xiang Li, Wei Zhang, Shijie Zhao, Milad Makkie, Mo Zhang, Quanzheng Li, and Tianming Liu. Modeling 4D fMRI data via spatio-temporal convolutional neural networks (ST-CNN). In International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), pages 181-189. 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Early methods rely on feature tracking to recover either 2D or 3D frame motion, which suffer from the robustness of local feature extraction and tracking in shaky videos. Recently, learning-based methods seek to find frame transformations with high-level information via deep neural networks to overcome the robustness issue of feature tracking. Nevertheless, to our best knowledge, no learning-based methods leverage 3D cues for the transformation inference yet; hence they would lead to artifacts on complex scene-depth scenarios. In this paper, we propose Deep3D Stabilizer, a novel 3D depth-based learning method for video stabilization. We take advantage of the recent self-supervised framework on jointly learning depth and camera ego-motion estimation on raw videos. Our approach requires no data for pre-training but stabilizes the input video via 3D reconstruction directly. The rectification stage incorporates the 3D scene depth and camera motion to smooth the camera trajectory and synthesize the stabilized video. Unlike most one-size-fits-all learning-based methods, our smoothing algorithm allows users to manipulate the stability of a video efficiently. Experimental results on challenging benchmarks show that the proposed solution consistently outperforms the state-of-the-art methods on almost all motion categories. + +# 1. Introduction + +Video stabilization removes the undesired shaky motion and preserves the primary motion from a video, which is a critical module to video acquisition and pre-processing. Video stabilization methods often estimate the motion between frames at first, and then the inter-frame motion estimated can be used in a smoothing algorithm for stabilizing the input video. Traditional video stabilization methods can be categorized into two types according to the dimensionality of the motion model. The 2D-motion methods model the tracked features with 2D transformations (e.g. affinity, ho + +mography). Earlier 2D-based approaches (such as [15, 10]) adopt full-frame 2D transformations and show promising stabilization qualities. Nonetheless, the full-frame 2D motion would suffer from spatially variant motion (e.g. parallax effect) caused by complex 3D scene structures. Some 2D-based methods [21, 19] divide the frame into grids and extract the 2D local motion of each grid to handle parallax effect. Despite the local motion models show better results than full-frame models, the local motion methods are still challenging since it is difficult to coordinate the gridwise transformations to avoid the local distortions thus introduced. The 3D approaches [16, 14, 8, 20] acquire 3D information to model the frame motion in 3D space by using Structure-from-Motion (SfM) or additional sensors such as inertial measurement unit (IMU) and depth sensors. Hence, the 3D approach often requires expensive costs but shows superior results in contrast to the 2D approach. + +The performance of earlier 2D and 3D approaches often rely on successful feature tracking for motion estimation. Yet it is challenging to obtain robust and long feature tracks, particularly from shaky videos. This restricts the performance of early approaches. The convolution neural network (CNN)-based video stabilization methods [29, 31, 35] learn to extract the frame motion in CNN parameter space and infer the stabilization transformation directly. Some learning-based methods train the networks on synchronized stable/unstable video pairs [29] to find frame transformations from ground-truth stable video directly. However, the application would be limited by the generalization capability as it is demanding to collect all types of unsteady videos for training in advance. On the other hand, these prior studies are based on 2D transformation and thus they still suffer from parallax effect and introduce distortions. + +We introduce a novel 3D-based learning method for video stabilization. To the best of our knowledge, our proposed Deep3D Stabilizer is the first learning method that handles the stabilization process with learned 3D information. The pipeline of our method is provided in Figure 1. The CNNs jointly learn the scene depth and 3D camera motion for the input video during test time in an optimization + +![](images/766a0b01a39bb2af056701ee24c73f52eb069ebd5c71033f7229ff75a94d0f7f.jpg) +Figure 1. Pipeline of the proposed method: The pipeline consists of two stages. Firstly, the 3D geometry optimization stage estimates the 3D camera trajectory and the dense scene depth of the input RGB sequence with PoseNet and DepthNet, respectively, via test-time training. The optimization stage takes the input sequence and the corresponding optical flows as the guidance signal for learning the 3D scene. Secondly, the frame rectification stage takes the estimated camera trajectory and scene depth as input to perform view synthesis on a smoothed trajectory. The smoothing process enable users to manipulate the parameter of smoothing filter to attain different levels of stability of the resulted video, which is then wrapped and cropped to produce the stabilized video. + +framework without needing training data. Our solution only requires input frames and the precomputed optical flow between consecutive frames as guidance signals for 3D geometry optimization. Consequently, the rectification stage takes the optimized 3D information to perform stabilization via smoothing the camera motion and reprojecting the input frames with scene depth. Our method can model the 3D scene structure and lead to low distortion, particularly when dealing with the videos with parallax effect. Moreover, our smoothing algorithm enables users to manipulate or alter the stability of the stabilized video online, which is a critical functionality for video stabilization while is overlooked by most previous learning-based studies since their methods are difficult to provide such freedom of manipulation. In sum, main contributions of our approach include: + +- We introduce the first 3D-based deep CNN method for video stabilization without needing training data. +- Our approach can handle parallax effect more properly leveraging 3D motion model. +- Our stabilization solution allows users to manipulate the stability of a video in real-time (34.5 fps). + +# 2. Related Works + +Our approach is related to previous studies on video stabilization, monocular depth estimation, and test-time training. They are briefly reviewed as follows. + +# 2.1. Video Stabilization + +Video stabilization methods can be categorized into 2D, 3D, and deep learning approaches. + +The 2D-based methods, which smooth the 2D linear transformations (e.g. affinity, homography) estimated between consecutive frames, require only a low computational + +complexity in general. Grundmann et al. [10] apply a full-frame 2D motion model and employ cinematography rules for motion design by using L1-norm optimization. Liu et al. [21] divide frames into grids to acquire bundled local transformations for spatially variant motions. Liu et al. [22] propose pixel profiles as a novel motion model rather than traditional feature tracks so as to prevent from lost-tracking of features; they continue to present more efficient mesh profiles to enable real-time processing [19] and extend the work to video coding [18]. However, 2D approaches usually suffer from tackling parallax effects as 2D transformations are insufficient to model the entire 3D scene structure. + +The 3D-based methods estimate 3D camera motions or scene structure from videos. Liu et al. [16] utilize 3D camera trajectory and sparse 3D point cloud reconstructed by Structure-from-Motion (SfM) to guide the warping. Liu et al. [17] utilize subspace constraints [13] on feature trajectories to enable more robust feature extraction. Goldstein and Fattal [8] exploit epipolar geometry to enhance the length of feature tracks. Some 3D methods utilize additional hardware sensors to capture 3D information. Smith et al. [27] and Liu et al. [20] employ light field and depth cameras for 3D projection, respectively. Karpenko et al. [14] use gyroscope for 3D rotation estimation. However, the 3D methods would either require expensive costs for 3D reconstruction or suffer from the robustness issue in SfM. The results would be easily fragile due to the failure of feature tracking. + +Recent works explore deep learning models for video stabilization. Wang et al. [29] propose a supervised learning framework with inferring multi-grid 2D transformations. Xu et al. [31] apply adversarial networks to supervised learning with full-frame affine transformations. Zhao et al. [35] estimate pixel-wise warping maps in a supervised manner. These supervised methods are trained with Deep-Stab dataset [29] that contains 61 synchronized stable and unstable pairs of videos. However, they often suffer from + +the confined generalization capability because of the limited variation of training videos in DeepStab. + +In contrast, Yu and Ramamoorthi [33] directly perform test-time training with optical flow for stabilization but require extremely expensive computation time. They further propose a self-supervised method trained with only unstable videos based on optical flow field [34]. Choi and Kweon [4] train a frame interpolation network to smooth the frame motion in a self-supervised manner. The approach exploits the relationship between video stabilization and inter-frame interpolation, but an issue is that the interpolation easily yields severe distortion when the input video contains large motion. Moreover, these methods are all based on 2D information so that they could still suffer from parallax effect. + +# 2.2. Monocular Depth Estimation + +Besides the related works of video stabilization, our solution is also related to the automatic scene depth estimation with a monocular camera. Traditional depth estimation relies on the disparity estimated among multi-view images. With the recent development of deep neural networks, learning-based depth estimation methods have been introduced. Eigen et al. [5] employ a coarse-to-fine model with the ground truth depths captured by depth sensors as the supervision signal for single-image depth estimation. However, this method relies on the known depth for training, which restricts its applicability to unknown scene classes. + +Garg et al. [6] and Gordard et al. [7] propose to solve the problem in a self-supervised manner, which use view synthesis with stereo training image pairs for single-image depth estimation problem. However, the settings require two cameras for self-supervision, which is unsuitable for a monocular video. Zhou et al. [37] propose a jointly self-supervised learning framework, where the monocular depth estimation and relative pose estimation can be learned from monocular sequences simultaneously. Further studies improve the jointly learning self-supervised framework via additional cues, such as optical flow [32, 38, 36], motion segmentation [25, 2, 9] and geometric constraints [24, 1, 3]. + +# 2.3. Test-Time Training + +Learning directly from the testing data has been used to reduce the distribution difference between training and testing domains. Yu and Ramamoorthi [33] treat CNN as an optimizer to overfit a smoothing objective function to solve the video stabilization problem. Casser et al. [2] and Chen et al. [3] use testing sequences to fine-tune the pre-trained models to improve the monocular depth estimation results. Luo et al. [23] refine the pre-trained models with temporal consistency for sequential depth estimation. + +A limitation of test-time training is its expensive computation time in test phase. Our method leverages the continuity of video, which propagates the learned weights for scene + +reconstruction to the subsequent snippets in a video, so as to reduce the optimization time. + +# 3. Proposed Method + +Given an unsteady sequence $\{I_t\}_{t=1}^N$ of $N$ frames, the goal is to synthesize steady frames $\{I'_t\}_{t=1}^N$ . The proposed pipeline mainly comprises two stages: 3D geometry optimization and frame rectification. The 3D geometry optimization stage learns the 3D geometry information including dense scene depth $\{D_t\}_{t=1}^N$ and 3D camera trajectory $\{P_t\}_{t=1}^N$ from $\{I_t\}_{t=1}^N$ . The frame rectification stage reconstructs the stabilized output $\{I'_t\}_{t=1}^N$ by smoothing $\{P_t\}_{t=1}^N$ and performing view synthesis with $\{I_t\}_{t=1}^N$ and $\{D_t\}_{t=1}^N$ . They are respectively presented in the following. + +# 3.1. 3D Geometry Optimization + +Inspired by the self-supervised framework of Zhou et al. [37], scene depth and camera ego-motion can be jointly trained by monocular RGB sequences. However, due to the difference between training and testing data distributions, a learned model on the training set often fails to be applied to the testing video. To address this issue, we exploit test-time training to the framework (as shown in Figure 2). + +Moreover, inference of the depth and pose on separated clips cannot retain temporal consistency for an input sequence. To get temporally consistent sequential estimation, our framework contains two CNNs, DepthNet and PoseNet; both take a snippet $\{I_t\}_{t = k}^{k + T}$ of the input sequence with length $T$ at each time. The length- $N$ sequence is divided into multiple length- $T$ snippets, with length- $\Omega$ overlap between nearby snippets. The networks learn the scene depth $\{D_t\}_{t = k}^{k + T}$ and camera pose $\{P_t\}_{t = k}^{k + T}$ , respectively. + +Consider one frame $I_{s}$ in $\{I_t\}_{t = k}^{k + T}$ as a source view. When the scene depths and camera poses are estimated, we can use the source view to synthesize a novel target view in $\{I_t\}_{t = k}^{k + T}$ ( $t \neq s$ ) via the re-projection of $D_{s}$ with the relative pose transformation $P_{s \rightarrow t} = P_{t}P_{s}^{-1}$ . Let $x_{t}$ and $x_{s}$ denote the homogeneous coordinates of a pixel in $I_{t}$ and $I_{s}$ , respectively. The point transformation via 3D projection can be formulated as follows: + +$$ +x _ {t} = K P _ {s \rightarrow t} D _ {s} \left(x _ {s}\right) K ^ {- 1} x _ {s}, \tag {1} +$$ + +where $K$ denotes the camera intrinsic parameters. Following this transformation, we can synthesize the entire novel view of any $t$ from $s$ , and we denote the synthesized view as $I_{s \rightarrow t}$ . Similarly, we can also synthesize the optical-flow map from $s$ to $t$ . The estimated 2D projection of 3D scene flow (i.e. rigid flow) $F_{s \rightarrow t}$ from $I_{s}$ to $I_{t}$ can be obtained by + +$$ +F _ {s \rightarrow t} \left(x _ {s}\right) = x _ {t} - x _ {s}. \tag {2} +$$ + +Besides, via the rigid transformation $P_{s \to t}$ , the depth map estimated for the source view $s$ can be converted to the target view $t$ as well, resulting in a synthesized depth map + +![](images/08ede03473e9456abb76dadd1b09f96c53eea8a66878eddfc26f3a385aeabd56.jpg) +Figure 2. 3D geometry optimization framework: The Depth-Net and PoseNet estimate dense scene depth and camera pose trajectory based on a snippet of the input sequence. The loss terms measured via 3D reprojection are used to update the parameters of DepthNet and PoseNet via back-propagation in test-time. + +$D_{s\rightarrow t}$ with the viewpoint of $t$ 's frame. The synthesized novel images $(I_{s\rightarrow t})$ , optical-flow maps $(F_{s\rightarrow t})$ , and depth maps $(D_{s\rightarrow t})$ are employed for conducting the loss terms enabling an end-to-end trainable model for simultaneous 3D scene reconstruction and camera ego-motion estimation. Loss terms. The loss is composed of three terms: photometric loss $\mathcal{L}_P(t,s)$ , geometric loss $\mathcal{L}_G(t,s)$ , and opticalflow loss $\mathcal{L}_F(t,s)$ . The photometric loss $\mathcal{L}_P(t,s)$ measures the appearance difference between the synthesized $I_{s\rightarrow t}$ and actual frame $I_{t}$ using an $L_{1}$ component and structural similarity loss [30] with a trade-off weight $\gamma (= 0.5)$ + +$$ +\mathcal {L} _ {P} (t, s) = \frac {1}{| V |} \sum_ {x _ {t} \in V} (1 - \gamma) \| I _ {s \rightarrow t} \left(x _ {t}\right) - I _ {t} \left(x _ {t}\right) \| _ {1} + \tag {3} +$$ + +$$ +\gamma \frac {1 - S S I M _ {I _ {s \rightarrow t} , I _ {t}} (x _ {t})}{2}, +$$ + +where $V$ represents the valid points successfully projected onto the image plane of $I_{t}$ , and $|V|$ is the number of points. + +The geometric loss proposed by Bian et al. [1] enforces the scale consistency of depth and pose estimation among consecutive frames. The geometric loss is formulated as: + +$$ +\mathcal {L} _ {G} (t, s) = \frac {1}{| V |} \sum_ {x _ {t} \in V} \frac {\left\| D _ {s \rightarrow t} \left(x _ {t}\right) - D _ {t} \left(x _ {t}\right)\right\| _ {1}}{D _ {s \rightarrow t} \left(x _ {t}\right) + D _ {t} \left(x _ {t}\right)}, \tag {4} +$$ + +where the difference of $D_{s\rightarrow t}$ and $D_{t}$ is normalized by their sum to make $\mathcal{L}_G$ numerically steady in training [1]. + +In addition to DepthNet and PoseNet, inspired by Zhou et al. [36], we adopt a pre-trained CNN model for the optical flow estimation (as shown in Figure 2), which can help regularize the solutions found for depth and pose. The purpose of optical-flow loss is to strengthen the supervision on texture-less or small displacement areas, which are the weakness of photometric loss. The optical-flow loss directly computes the difference between the estimated $F_{s\rightarrow t}$ and the precomputed flow $\hat{F}_{s\rightarrow t}$ using pre-trained PWC-Net + +[28]. We use $L_{1}$ loss to build our optical flow error function, + +$$ +\mathcal {L} _ {F} (t, s) = \frac {1}{| V |} \sum_ {x _ {t} \in V} \| F _ {s \rightarrow t} (x _ {t}) - \hat {F} _ {s \rightarrow t} (x _ {t}) \| _ {1}. \tag {5} +$$ + +Multiple source views. Single-source projection consistency is fragile due to occlusion, illumination variation, etc. Therefore, we adopt a set of source views $\mathbf{S}_{\mathbf{t}}$ for the 3D reconstruction and reprojection. When the frame interval between the source and target views is large, the common region between them could be small and yield easily unreliable reconstruction. Thus, we set the farthest frame interval as $\Omega$ . Given the target view $I_{t}$ , its source view are chosen in $\mathbf{S}_{\mathbf{t}} = \{I_{t - \Omega}: I_{t + \Omega}\}$ and note that $\Omega$ also serves as the overlapping length of the neighboring snippets ( $\Omega = 9$ by default). The loss function $\mathcal{L}(I_t,\mathbf{S}_t)$ becomes + +$$ +\begin{array}{l} \mathcal {L} \left(I _ {t}, \mathbf {S} _ {\mathbf {t}}\right) = \sum_ {s _ {i} \in \mathbf {S} _ {\mathbf {t}}} \omega_ {\alpha} ^ {s _ {i}} \left(\lambda_ {P} \mathcal {L} _ {P} (t, s _ {i}) + \lambda_ {G} \mathcal {L} _ {G} (t, s _ {i})\right) + \tag {6} \\ \omega_ {\beta} ^ {s _ {i}} \lambda_ {F} \mathcal {L} _ {F} (t, s _ {i}), \\ \end{array} +$$ + +where $\lambda_{P},\lambda_{G},\lambda_{F}$ are some constant weights. $\omega_{\rho}^{s_i}$ is an exponential weight varying with the frame intervals. + +$$ +\omega_ {\rho} ^ {s _ {i}} = \frac {\rho^ {\left| s _ {i} - t \right|}}{\sum_ {s _ {j} \in \mathbf {S} _ {\mathbf {t}}} \rho^ {\left| s _ {j} - t \right|}}. \tag {7} +$$ + +As for the photometric and depth losses, we use $\rho = \alpha (= 1.2)$ to increase the weights of the farther source views, which benefits from the learning of 3D scene with larger baselines. As for the optical-flow loss, since the accuracy of precomputed flow $\hat{F}_{t\rightarrow s_i}$ is often higher for small frame intervals but tends to collapse for the farther views, we use $\beta (= 0.85)$ to emphasize the flow influence of closer frames. Finally, the optimal depths $\{D_t^*\}_{k}^{k + T}$ and camera poses $\{P_{t}^{*}\}_{k}^{k + T}$ are obtained by minimizing the overall loss: + +$$ +\left\{D _ {t} ^ {*}, P _ {t} ^ {*} \right\} _ {k} ^ {k + T} = \underset {\left\{D _ {t}, P _ {t} \right\} _ {k} ^ {k + T}} {\arg \min } \frac {1}{T} \sum_ {t = k} ^ {k + T} \mathcal {L} \left(I _ {t}, \mathbf {S} _ {\mathbf {t}}\right). \tag {8} +$$ + +**Snippets**. To enforce the temporal consistency of the sequential snippets, for each snippet $\{I_t\}_{t = k}^{k + T}$ , we freeze the depth and pose estimated already in the overlapping area of the previous snippet (i.e. $\{D_t^*, P_t^*\}_{t = k}^{k + \Omega}$ ), as shown in Figure 3. The optimization framework computes the loss of $\{D_t, P_t\}_{t = k + \Omega}^{k + T}$ with $\{D_t^*, P_t^*\}_{t = k}^{k + \Omega}$ fixed, so as to enhance the temporal consistency of depth and poses. The test-time training with snippet coherence is thus formulated as: + +$$ +\left\{D _ {t} ^ {*}, P _ {t} ^ {*} \right\} _ {k + \Omega} ^ {k + T} = \underset {\left\{D _ {t}, P _ {t} \right\} _ {k + \Omega} ^ {k + T}} {\arg \min } \frac {1}{T} \sum_ {t = k} ^ {k + T} \mathcal {L} \left(I _ {t}, \mathbf {S} _ {\mathbf {t}}\right). \tag {9} +$$ + +Parameter propagation. Unlike 2D optical-flow based testing-time training methods (e.g. [33]) for video stabilization, the 3D depth map employed in our approach often holds strong temporal continuity in a video, and thus + +![](images/9ecd0f39a76b88f832d585f3d8baecd61065d415f2460ede557a0b3093e4b96f.jpg) +Figure 3. Illustration of overlapping snippets: An input sequence $\{I_t\}_{t=1}^N$ is sequentially divided into length- $T$ snippets with $\Omega$ frames overlap. For a current snippet (except for the first one), the 3D depth and pose estimations of the overlapping area (gray with $\times$ ) are frozen as the optimal $\{D^*, P^*\}$ estimated for the previous snippet. The learning framework only updates the non-overlapping $\{D, P\}$ (green) to enforce the temporal coherence. + +![](images/5edd2fcb39b0e87752775699f4d26c8260f8654f180d2f0673877b96495aa620.jpg) +Figure 4. Convergence speeds comparison: The convergence curves averaged on all snippets (except for the first snippet) are shown for different parameter initialization strategies. Among them, parameter propagation shows the fastest convergence speed compared to training from scratch and ImageNet [26] pre-trained weights, which increases the test-time training speed better. + +the previously estimated depth is easily transferable to the next snippet and serves as good initialization for better optimization. In our test-time training, the snippets are learned one by one according to their sequential order, and the optimal estimation $\{D_t^*, P_t^*\}_{t=1}^N$ are obtained through only a single-round process of the image sequence $\{I_t\}_{t=1}^N$ . For the first snippet, both DepthNet and PoseNet are initialized with ImageNet [26]. Afterwards, the trained parameters of the current snippet are propagated to the next snippet for initializing the optimization with fewer iterations to converge. Note that the optical-flow maps between consecutive frame pairs [33] of an unsteady video would not have such continuity property to be exploited. As shown in Figure 4, training with parameter propagation shows a far faster convergence speed and a further loss descent, compared with training from scratch or ImageNet pre-trained weights. We also show the speed comparison with the test-time video stabilization method [33] in the experiments. + +![](images/d9d3da97a70dcafdd0037fb6884f19ee48c6d545d9be8e6c82d519817d59fc9a.jpg) +Figure 5. Example of camera trajectory smoothing: (a) Input video. (b) Depth $D^{*}$ of (a). (c) The 3D model of the input video reconstructed by $\{D_t^*, P_t^*\}_{t=1}^N$ . The green/blue paths represent the original/smoothed camera trajectories in 3D model, respectively. + +![](images/dd52ad1760f6d9b3ee34c4ac6c7133445e9073e831ecb09731081bd0d10b089e.jpg) + +![](images/7fb47ee08f60df0190efcdb2eae3a6fc610e967b15ad192966788f10938dc250.jpg) + +![](images/8c3922ee7b5d22c4e4d7050edea004fc75667bb8ae1d952fd1a44a0a78ff0c12.jpg) + +![](images/6ec647031df00bf6f3467ad33cf2b8fdea90a66e29ae6c3430525d8586d6df26.jpg) + +![](images/5068ccfc5d0883c81fb8608dc4f1dd2f1440008f652e200786bd7ea630d20c31.jpg) +Figure 6. Visual comparison tackling dynamic objects: The input (a) contains two dynamic pedestrians, yielding large values in the loss map $\mathcal{L}$ and unreliable estimate of $D^{*}$ (cyan boxes in (d) and (e)). The resulted (b) synthesized with $D^{*}$ contains distortions in dynamic area (red box). Post-processing $D^{*}$ to obtain $\tilde{D}$ with an adaptive smoothing filter based on $\mathcal{L}$ . (c) synthesized with $\tilde{D}$ eliminates the distortions. The blue, red and green boxes present the details of moving pedestrians in (a), (b) and (c), respectively. + +![](images/83eb95467144523ab8eb5a8d50c95fc1173eb9bc1da2950f213458ac6ce952fe.jpg) + +![](images/bcc8a65f345bf3172fed8afe4335ed70ec8e8a40e66714cad3b6ef4bd759c5bd.jpg) + +# 3.2. Frame Rectification. + +Once we obtain the solutions of depths and camera poses of the entire sequence, each stabilized frame $I_{t}^{\prime}$ is synthesized with $I_{t}$ and a compensated warp field $F_{t}^{\prime}$ which is computed by the depth $D_{t}^{*}$ and a smoothed camera pose $P_{t}^{\prime}$ . The smoothed camera pose $\{P_{t}^{\prime}\}_{t=1}^{N}$ (as illustrated in Figure 5) is typically obtained with a Gaussian filter. Our approach thus enables users to manipulate the stability by adjusting the smoothness degree ( $\sigma$ of Gaussian) of the trajectory. To our best knowledge, most previous learning-based methods [29, 31, 34, 35] do not enable the freedom of manipulation since their models are one-size-fits-all for inferring transformation directly. Hence, when the users hope to change the smoothness degree, they need to retrain the entire networks for finding the new solution. + +Post-processing tackling dynamic objects. The 3D opti + +mization framework assumes the scene of input videos is static. Thus the networks will produce unreliable results on moving-object regions, yielding artifacts in stabilized videos (e.g. Figure 6e). Some recent joint depth and pose learning methods improve the outcomes based on optical flow [32, 38] or motion segmentation [2, 25, 9]. Yet these additional techniques would be either unreliable enough or increase heavily computational costs in test-time training. + +To tackle this issue, we perform spatially variant smoothing based on the loss map obtained. As with test-time training, the map of loss $\mathcal{L}$ (Eq. 6) is available in our approach. We adaptively smooth the depth map $\{D_t^*\}_{t=1}^N$ with a spatially variant filter to obtain $\{\tilde{D}_t\}_{t=1}^N$ , where the smoothing degree is varying with the sites in the loss map (the larger is the loss value, the larger is the smoothing degree and vice versa). The adaptively smoothed map $\{\tilde{D}_t\}_{t=1}^N$ is then employed for the view synthesis. As the large-loss areas are often caused by the dynamic objects since they violate the rigid-motion constraint, adopting a stronger smoothing tends to fit planar warping to these areas, so as to alleviate the artifacts. An illustration is given in Figure 6. + +# 3.3. Implementation Details + +We realize DepthNet and PoseNet using ResNet18 [12]. The optimization framework is implemented in PyTorch with Adam, where $\beta_{1} = 0.9$ , $\beta_{2} = 0.99$ , and learning rate $= 2 \times 10^{-4}$ . The input frames are downsampled to $192 \times 128$ with the purpose of enlarging the snippet length $T$ (= 80 as default). For each input unsteady video, we optimize the first snippet for 300 forward-backward iterations and 100 iterations for each of the subsequent snippets. The Gaussian filter in rectification stage is set with $\sigma = 12$ and window size 59 as default for the following experiments. + +# 4. Experiments + +We compare our Deep3D Stabilizer with several state-of-the-art methods on NUS dataset [21], which contains 144 short unsteady videos of 6 categories based on the camera motion and scene types: regular, large parallax, crowd, running, quick rotation and zooming. We use publicly available codes of the state-of-the-art method in the experiments. The stabilizer of commercial software Adobe Premiere Pro CC 2020 is known as the traditional 3D-based method [17] using subspace constraints. Bundled [21] divides frames into grids to extract local homography transformations in offline processing. DIFRINT [4] performs learning-based frame interpolation on unsteady frames without cropping in offline. As for online stabilization methods, including MeshFlow [19] and StabNet [29], which aim to stabilize streaming videos and do on-the-fly thus cannot refer to the future frames. MeshFlow [19] computes pixel profiles as 2D local motion. StabNet [29] uses a pre-trained feedforward network to infer grid-wise 2D transformations. We + +conduct both visual and quantitative comparisons. + +Visual comparison. We highly encourage readers to see visual comparisons in supplementary video since it is difficult to compare the visual quality of stabilized videos in thumbnails. As shown in Figure 7, we visualize the stability of resulted videos with optical flow tracking. Examples 1 and 2 are videos with parallax effects. Bundled [21] uses grid-wise homography transformation and the different motions of parallax effects in a single cell cause the wrong motion estimation and shear in resulted video. MeshFlow [19] derives local distortion in Example 2 because their grid-based transformation does not coordinate the spatial continuity of warping with neighboring grids. Our method estimates the frame motion in 3D motion model with dense depth maps to tackle parallax effect properly. Example 3 contains horizontal rotation motion. Adobe [17] and Stab-Net [29] show horizontal overcropping due to the large rotation. On the other hand, as DIFRINT [4] uses frame interpolation with nearby frames, the result suffers from severe local distortion in rotation. Example 4 also contains multiple moving pedestrians. DIFRINT [4] produces severe distortions in the pedestrians on the frame boundaries. Our method smooths the warping of non-rigid objects spatially in the adaptive filtering of post-processing to prevent from distortion. Example 5 is captured in running with severely shakes. Our method shows the best stability with the smoothest motion trajectory. + +Quantitative comparison. We evaluate the results on NUS dataset [21] following the metrics proposed by Liu et al. [21]. Specifically, the metrics include three aspects: cropping ratio, global distortion and stability. + +The cropping ratio measures the view preservation from input to output caused by warping and cropping. We compute the homography $H_{t}$ between the input frame $I_{t}$ and output frame $I_{t}^{\prime}$ . The region that $I_{t}$ have been warped onto $I_{t}^{\prime}$ by $H_{t}$ indicates the preserved view $V_{t}$ . The cropping ratio of the entire stabilized video is the average ratio of the preserved area, $\frac{1}{N}\sum_{t = 1}^{N}|V_{t}|$ . The score ranges from 0 to 1 and the larger represents the better view preservation. + +The global distortion metric measures the distortion in output videos caused by non-isotropic scaling transformation from input to output, which can be extracted from the affine part of $H_{t}$ by SVD decomposition [11]. The distortion score of the entire stabilized video, ranging from 0 to 1, is determined by the worst frame. The larger value indicates the better preservation of the shape in the input video. + +The cropping-ratio and global-distortion metrics above prefer invariant images. The original image $I_{t}$ gets the highest scores on these metrics, and thus they are only circumstantial. As for stability metric, we follow the idea of Liu et al. [21] to perform frequency analysis on estimated motion of a video. The assumption is that low frequency part + +![](images/ff79a1b39657af60e94dab3fea3e03eab677dd947bd10d2abd3dc0350796b0eb.jpg) +Figure 7. Visual comparison of the state-of-the-art methods: The artifacts are noted below thumbnails. The magenta paths on the thumbnails indicate the optical flow motion of the resulted videos. Smoother paths represent the more steady results. To visualize the cropping loss of each result, we rescale each video to the input scale. The distortion and shear are pointed out by yellow and red arrows, respectively. Zoom in for a better (more detailed) visualization. + +of the estimated motion represents the dominant motion of a video. By using an off-the-shelf optical flow estimation network (PWC-Net [28]) to extract the motion of resulted video, we measure the SNR value to represent the stability score of the video, where the energy of the lowest $5\%$ frequency components and the rest of the energy are treated as the signal and noise, respectively. A larger value indicates a more stable result. Note that there is a trade-off between the stability and cropping metrics, while one is larger, the other is low. Since a stabilized video often yields poor content preservation when pursuing high stability, the stability metric is often the main metric on experimental comparison. + +The quantitative comparisons to state-of-the-art methods are shown in Table 1. As can be seen, our method performs the best (gets rank-1) on the stability metric for all categories except the regular category. Since the regular category contains simpler scene and motion types, many approaches perform averagely well on this category. Despite the stability score of our method is slightly lower than that of Bundled [21] and MeshFlow [19] in this category, our approach provides more steady videos. DIFRINT [4] shows the highest score in cropping ratio and global distortion metrics since they utilize frame interpolation to keep the view content, whereas resulting in the worst stability. + +For parallax and crowd categories that contain parallax effects and dynamically moving human in the videos + +respectively, our method achieves the best stability score while still holds very well cropping and global distortion effects. It means that our method can produce more steady videos with smaller content distortion. In contrast, 2D Grid-based methods especially MeshFlow [19] and StabNet [29] introduce much larger distortion. + +As for running category, Bundled [21] provides less cropping loss but with poor stability. Again, our method shows the highest stability and distortion scores with fairly well cropping value. Our approach provides a freedom of online manipulation, as they are trade-offs to each other. Furthermore, MeshFlow [19] shows the second highest stability but has the most distorted effects. In general, our method is more favorable to preserve the original shape of the videos with severe shaky motion. + +For quick rotation and zooming categories, our method also achieves the least distortion effects comparing to frame interpolation-based DIFRINT [4] and the best stability. In sum, our method is able to provide not only the best visual quality results for almost all categories but also the flexibility of adjustable stability. As for learning-based methods, StabNet [29] shows the worst results in overall due to the difficulty of generalization. DIFRINT [4] uses a novel frame interpolation method to preserve the view content and shape but the stability is restricted. + +
CategoryMetricInputAdobe [17]Bundled [21]DIFRINT [4]MeshFlow[19]StabNet [29]Deep3D
RegularCropping-0.70(3)0.67(4)0.98(1)0.67(4)0.54(6)0.79(2)
Distortion-0.94(5)0.95(3)0.98(1)0.95(3)0.82(6)0.97(2)
Stability11.0814.27(4)16.31(1)13.14(6)15.72(2)13.85(5)15.53(3)
Large ParallaxCropping-0.60(4)0.74(3)0.98(1)0.55(5)0.46(6)0.78(2)
Distortion-0.83(4)0.91(3)0.94(1)0.75(5)0.71(6)0.93(2)
Stability14.4916.07(4)16.16(3)15.33(5)16.68(2)15.07(6)16.81(1)
CrowdCropping-0.53(4)0.70(2)0.98(1)0.50(5)0.41(6)0.70(2)
Distortion-0.86(4)0.89(3)0.94(1)0.78(5)0.65(6)0.93(2)
Stability16.7118.45(3)18.25(4)17.63(5)18.76(2)17.58(6)18.80(1)
RunningCropping-0.41(5)0.67(2)0.96(1)0.44(4)0.41(5)0.50(3)
Distortion-0.85(3)0.85(3)0.89(1)0.80(5)0.77(6)0.89(1)
Stability10.3014.85(3)13.14(4)12.50(6)15.62(2)12.88(5)15.81(1)
Quick RotationCropping-0.38(6)0.70(2)0.98(1)0.39(4)0.39(4)0.58(3)
Distortion-0.85(3)0.86(2)0.83(4)0.41(6)0.67(5)0.87(1)
Stability19.5118.05(6)20.44(2)20.12(3)19.01(4)18.13(5)21.91(1)
ZoomingCropping-0.48(5)0.61(3)0.98(1)0.52(4)0.47(6)0.62(2)
Distortion-0.87(4)0.93(2)0.89(3)0.84(5)0.71(6)0.95(1)
Stability17.0918.28(5)20.19(3)19.06(4)20.47(2)17.25(6)20.90(1)
+ +Table 1. Quantitative comparison of the state-of-the-art methods: The scores are averaged over each category. The higher value of cropping ratio, global distortion and stability the better. The subscript of each value indicates the ranking in the methods compared. + +
Metricw/o LG and LFw/o LFfull
Cropping0.570.620.66
Distortion0.870.890.92
Stability16.9517.3518.29
+ +Table 2. Ablation study on the loss terms. + +
MethodsRuntime
online (streaming)MeshFlow [19]25 ms
StabNet [29]118 ms
offlineBundled [21]392 ms
Yu and Ramamoorthi [33]1610 ms
DIFRINT [4]67 ms
Yu and Ramamoorthi [34]570 ms
Deep3D (Ours)670 ms
- optimization stage641 ms
- rectification stage29 ms
+ +Table 3. Per-frame runtime comparison. + +Ablation study. We conduct an ablation study of the loss terms $(\mathcal{L}_P, \mathcal{L}_G, \mathcal{L}_F)$ on entire NUS [21] (shown in Table 2). The $\mathcal{L}_G$ and $\mathcal{L}_F$ are the objectives of geometric regularization to acquire consistent 3D estimations and prevent from distortion. With the aids of both $\mathcal{L}_G$ and $\mathcal{L}_F$ , the results show considerably improvements in all metrics. + +Runtime comparison. We analyze the runtime of the proposed method on NUS [21] and compare with the state-of-the-art methods. The time is measured on an RTX2080Ti GPU. Table 3 summarizes the runtime comparison. Despite our method takes a longer period on the optimization stage + +in contrast to some other offline methods, we simply use parameter-propagation that leverages the scene continuity of input video to give more than twice times speedup in contrast to the test-time training method [33]. Moreover, the rectification stage takes only $29\mathrm{ms}$ per-frame (34.5 fps) so that our algorithm enables real-time stability manipulation to users. + +# 5. Conclusions and Future Work + +We propose Deep3D Stabilizer, a novel 3D-based self-supervised method for video stabilization, The depths and camera poses of a video are estimated by a 3D optimization framework without pre-training data. The rectification stage incorporates the estimated 3D geometry to perform smoothing for generating a stable video. To our knowledge, this is the first study on learning-based stabilizer leveraging 3D cues. Our method can handle parallax effect and severe camera shakes, while attaining high stability and low distortion. Experimental results reveal that our Deep3D Stabilizer outperforms the state-of-the-art methods in general. + +Our future directions include tackling the undesired intra-frame effects (e.g. motion blur, rolling shutter) and performing frame extrapolation outside the cropped area of the stabilized videos to further enhance the visual quality. + +Acknowledgement. This work was partially supported by MediaTek Inc., and Ministry of Science and Technology in Taiwan (MOST 109-2221-E-002-207-MY3 and MOST 110-2634-F-002-047). + +# References + +[1] Jiawang Bian, Zhichao Li, Naiyan Wang, Huangying Zhan, Chunhua Shen, Ming-Ming Cheng, and Ian Reid. Unsupervised scale-consistent depth and ego-motion learning from monocular video. In NeurIPS, pages 35-45, 2019. +[2] Vincent Casser, Soeren Pirk, Reza Mahjourian, and Anelia Angelova. Depth prediction without the sensors: Leveraging structure for unsupervised learning from monocular videos. AAAI, 33:8001-8008, 2019. +[3] Yuhua Chen, Cordelia Schmid, and Cristian Sminchisescu. Self-supervised learning with geometric constraints in monocular video: Connecting flow, depth, and camera. In ICCV, pages 7063-7072, 2019. +[4] Jinsoo Choi and In So Kweon. Deep iterative frame interpolation for full-frame video stabilization. In SIGGRAPH Asia, 2019. +[5] David Eigen, Christian Puhrsch, and Rob Fergus. Depth map prediction from a single image using a multi-scale deep network. NeurIPS, 3(January):2366-2374, 2014. +[6] Ravi Garg, Vijay Kumar Bg, Gustavo Carneiro, and Ian Reid. Unsupervised cnn for single view depth estimation: Geometry to the rescue. In ECCV, pages 740-756. Springer, 2016. +[7] Clément Godard, Oisin Mac Aodha, and Gabriel J Brostow. Unsupervised monocular depth estimation with left-right consistency. In CVPR, pages 270-279, 2017. +[8] Amit Goldstein and Raanan Fattal. Video stabilization using epipolar geometry. ACM TOG, 31(5):1-10, 2012. +[9] Ariel Gordon, Hanhan Li, Rico Jonschkowski, and Anelia Angelova. Depth from videos in the wild: Unsupervised monocular depth learning from unknown cameras. In ICCV, pages 8977-8986, 2019. +[10] Matthias Grundmann, Vivek Kwatra, and Irfan Essa. Autodirected video stabilization with robust 11 optimal camera paths. In CVPR, pages 225-232. IEEE, 2011. +[11] Richard Hartley and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003. +[12] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, pages 770-778, 2016. +[13] Michal Irani. Multi-frame correspondence estimation using subspace constraints. *IJCV*, 48(3):173–194, 2002. +[14] Alexandre Karpenko, David Jacobs, Jongmin Baek, and Marc Levoy. Digital video stabilization and rolling shutter correction using gyroscopes. CSTR, 1(2011):2, 2011. +[15] Ken-Yi Lee, Yung-Yu Chuang, Bing-Yu Chen, and Ming Ouhyoung. Video stabilization using robust feature trajectories. In ICCV, pages 1397-1404. IEEE, 2009. +[16] Feng Liu, Michael Gleicher, Hailin Jin, and Aseem Agarwala. Content-preserving warps for 3d video stabilization. ACM TOG, 28(3):1-9, 2009. +[17] Feng Liu, Michael Gleicher, Jue Wang, Hailin Jin, and Aseem Agarwala. Subspace video stabilization. ACM TOG, 30(1):1-10, 2011. +[18] Shuaicheng Liu, Mingyu Li, Shuyuan Zhu, and Bing Zeng. Codingflow: Enable video coding for video stabilization. IEEE TIP, 26(7):3291-3302, 2017. + +[19] Shuaicheng Liu, Ping Tan, Lu Yuan, Jian Sun, and Bing Zeng. Meshflow: Minimum latency online video stabilization. In ECCV, pages 800-815. Springer, 2016. +[20] Shuaicheng Liu, Yinting Wang, Lu Yuan, Jiajun Bu, Ping Tan, and Jian Sun. Video stabilization with a depth camera. In CVPR, pages 89-95. IEEE, 2012. +[21] Shuaicheng Liu, Lu Yuan, Ping Tan, and Jian Sun. Bundled camera paths for video stabilization. ACM TOG, 32(4):1-10, 2013. +[22] Shuaicheng Liu, Lu Yuan, Ping Tan, and Jian Sun. Steadyflow: Spatially smooth optical flow for video stabilization. In CVPR, pages 4209-4216, 2014. +[23] Xuan Luo, Jia-Bin Huang, Richard Szeliski, Kevin Matzen, and Johannes Kopf. Consistent video depth estimation. ACM TOG, 39(4), 2020. +[24] Reza Mahjourian, Martin Wicke, and Anelia Angelova. Unsupervised learning of depth and ego-motion from monocular video using 3d geometric constraints. In CVPR, pages 5667-5675, 2018. +[25] Anurag Ranjan, Varun Jampani, Lukas Balles, Kihwan Kim, Deqing Sun, Jonas Wulff, and Michael J. Black. Competitive collaboration: Joint unsupervised learning of depth, camera motion, optical flow and motion segmentation. CVPR, 2019-June(1):12232-12241, 2019. +[26] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. IJCV, 115(3):211-252, 2015. +[27] Brandon M Smith, Li Zhang, Hailin Jin, and Aseem Agarwala. Light field video stabilization. In ICCV, pages 341-348. IEEE, 2009. +[28] Deqing Sun, Xiaodong Yang, Ming-Yu Liu, and Jan Kautz. Pwc-net: Cnns for optical flow using pyramid, warping, and cost volume. In CVPR, pages 8934-8943, 2018. +[29] Miao Wang, Guo-Ye Yang, Jin-Kun Lin, Song-Hai Zhang, Ariel Shamir, Shao-Ping Lu, and Shi-Min Hu. Deep online video stabilization with multi-grid warping transformation learning. IEEE TIP, 28(5):2283-2292, 2019. +[30] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE TIP, 13(4):600-612, 2004. +[31] Sen-Zhe Xu, Jun Hu, Miao Wang, Tai-Jiang Mu, and ShiMin Hu. Deep video stabilization using adversarial networks. In Computer Graphics Forum, volume 37, pages 267-276. Wiley Online Library, 2018. +[32] Zhichao Yin and Jianping Shi. Geonet: Unsupervised learning of dense depth, optical flow and camera pose. CVPR, pages 1983-1992, 2018. +[33] Jiyang Yu and Ravi Ramamoorthi. Robust video stabilization by optimization in cnn weight space. In CVPR, pages 3800-3808, 2019. +[34] Jiyang Yu and Ravi Ramamoorthi. Learning video stabilization using optical flow. In CVPR, pages 8159-8167, 2020. +[35] Minda Zhao and Qiang Ling. Pwstablenet: Learning pixelwise warping maps for video stabilization. IEEE TIP, 29:3582-3595, 2020. + +[36] Junsheng Zhou, Yuwang Wang, Kaihuai Qin, and Wenjun Zeng. Moving indoor: Unsupervised video depth learning in challenging environments. In ICCV, pages 8618-8627, 2019. +[37] Tinghui Zhou, Matthew Brown, Noah Snavely, and David G Lowe. Unsupervised learning of depth and ego-motion from video. In CVPR, pages 1851-1858, 2017. +[38] Yuliang Zou, Zelun Luo, and Jia-Bin Huang. Df-net: Unsupervised joint learning of depth and flow using cross-task consistency. 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However, HSPA devices have to scan an object exhaustively in the spatial and spectral domains; and the acquired data tend to suffer from complex noise. This time-consuming scanning process and noise severely affects the usability of HSPA. It is therefore critical to examine the feasibility of 4D HSPA data restoration from an incomplete and noisy observation. In this work, we present a data reliability analysis for the depth and spectral domain. On the basis of this analysis, we explore the inherent data correlations and develop a restoration algorithm to recover 4D HSPA cubes. Experiments on real data verify that the proposed method achieves satisfactory restoration results. + +# 1. Introduction + +Discovered in 1880 [4], the photoacoustic (PA) effect is a phenomenon in which materials emit acoustic signals under light irradiation. In the last few decades, photoacoustic imaging (PAI) [32] has emerged as a 3D imaging technology that combines light and ultrasound to form images. It has the advantages of both optical imaging (high optical contrast) and ultrasonic imaging (better penetration capability) [33] and thus is an alternative to X-ray exposure as a way to visualize the interiors of objects in a noninvasive manner. PAI uses light as an excitation source and an ultrasound sensor to detect sound waves generated by the optically excited targets. It can be used to analyze the properties and interior structure of a 3D volume [32, 33, 34, 37]. + +Thanks to the evolution of wavelength-tunable lasers, multispectral or hyperspectral photoacoustic (HSPA) imaging techniques have been developed. HSPA irradiates the material with different wavelengths of light and provides 4D data cubes, e.g. a 3D volume for each wavelength, as shown in Fig. 1. The amount of light absorbed by the material is determined by the spectral absorption coefficient of + +![](images/fe5051cdf02f5ebaecec2f8c289898ff7558534a918504460459996440f2eb60.jpg) +Leaf + +![](images/8d647af591d39df5df6bc0bfda27913ae869337c09b7f0d420b6d0f658255d73.jpg) + +![](images/a17c791ceedd4ba88656568173fc078e1e5bd7bca2079b6769666152a96b81f1.jpg) + +![](images/c9a99899830ae80a839bf791bf867eba353dae0e4d258d63d9cf43d3dff09a8a.jpg) +460 nm +$500\mathrm{nm}$ +Figure 1. 4D HSPA data of leaf (rendering by KURUMI viewer [1]). The variance at each wavelength is clearly visible. + +![](images/743b38c572062e3c4b06e7aed146281be0667727a23c8bce928aab4254ed2cef.jpg) +480 nm +$520\mathrm{nm}$ + +the material at each wavelength. HSPA has the capability of providing spectral absorbance information on the interiors of a target material, which support many tasks such as medical diagnosis, classification, and segmentation. Previous studies have shown that HSPA is promising in comprehensive clinical applications [35, 9, 20, 21]. + +A typical HSPA system is shown in Fig. 2, where an object is scanned by moving a wavelength-tunable laser and ultrasonic transducer along the surface of the object. There are two obstacles that severely limit practical use of HSPA: long acquisition time and complex noise. The data scanning process is time-consuming because it is performed exhaustively in the spatial and spectral domains. The ability to use fewer samples would speed up the data acquisition. HSPA also suffers from a very low signal to noise ratio (SNR) when the amount of received incident light is weak and when the spectral absorption coefficient is low. Thus, the SNR of HSPA should be adaptively enhanced. This issue motivated us to devise a method to restore full-grid, noise-free 4D HSPA data from incomplete and noisy observations. + +In this paper, we first conduct a reliability analysis for different depths and spectrum wavelengths. Based on the analysis, we formulate the 4D HSPA restoration task as an optimization problem. We explore the data correlations, in + +![](images/c09a2bd84bbf5bc54f6cca7ae4fc7f0781126adea3f28cddc51bee1661d5fa1c.jpg) +Figure 2. Scanning-based hyperspectral photoacoustic imaging system, whose scanning process is usually time-consuming. + +cluding transform sparsity and local self-similarity, and represent them into regularization terms. Finally, we develop a numerical algorithm to reconstruct clear and high-quality data. Our contributions are summarized as follows: + +1. For the first time, we consider the variance of the reliability of PA data and perform a depth and spectral reliability analysis. +2. On the basis of the results of the analysis, we propose an integral framework for 4D data restoration, in which data completion and denoising are simultaneously conducted. + +# 2. Related Works + +# 2.1. PA data completion + +Various studies have used compressive sensing (CS) theory [11, 8] to complete PA data from a limited number of measurements and thereby accelerate the data acquisition. Provost and Lesage [29] proposed to use CS theory instead of the back-projection algorithm and achieved better performance than the simple pseudo-inverse on simulation data. Guo et al. [14] utilized CS theory to reduce the number of measurements and tested their method both on simulation data and in in vivo experiments. Liu et al. [24] used the alternating direction method to further accelerate the calculation. Arridge et al. [3] combined a model-based spatial subsampling scheme and total variation (TV) regularization to dramatically increase the acquisition speed. Haltmeier et al. [15] developed a sparsifying temporal transform and proposed a reconstruction algorithm with low complexity. The framework proposed in [16] jointly explores the sparsity of the original PA signal and the second-order derivative. Antholzer et al. [2] introduced a deep-learning method to solve the CS problem on PA data. Their method outperformed the default CS on simulation data, while it performed comparably to CS on real data due to the lack of training data. + +All of the previous studies focused on 3D PA data completion; thus, they only studied sub-sampling in the spatial domain. This means there hasn't been enough research on 4D HSPA. + +# 2.2. PA denoising + +Some studies have tried to enhance the SNR or reduce the noise of 3D PA data. Telenkov and Mandelis [31] proposed to use chirped modulation waveforms to increase the SNR. Haq et al. [17] utilized K-means singular value decomposition to eliminate noise; it has been shown to perform better than Wiener or wavelet filtering. Zhang et al. [38] demonstrated that acoustic sub-aperture processing could be used to improve the SNR of PA data. Zhou et al. [41] proposed a denoising method combining empirical mode decomposition with conditional mutual information. There has also been a study on denoising of 4D multi-spectral PA data. Kazakeviciute et al. [19] treated the spectral bands as time series; they used an auto regressive model to estimate the noise and Wiener filter to perform denoising. However, they only explored the frontward spectrum correlation and ignored the backward correlation, because the auto regressive model only uses short wavelength data to predict the noise for long wavelength band. + +The variance of the reliability of PA data was not well studied nor considered in previous works. Here, we propose a depth/spectral reliability analysis for HSPA data and enhance the SNR for different parts adaptively. + +# 2.3. Low-rank representation + +Low-rank representations have been proved to be effective in data restoration and are used in many applications. The key idea is to represent the data in a low-rank form and recover the underlying low-rank matrix from degraded observations [26]. Ji et al. [18] proposed to restore video by exploiting low-rank representations and sparsity. Zhang et al. [39] used low-rank matrix recovery to remove different kinds of noise and stripes from remote-sensing im + +ages. Dong et al. [10] proposed to use nonlocal low-rank regularization to recover MRI images. Fu et al. [12] explored spectral-spatial correlations via two low-rank terms and developed a reconstruction algorithm for coding-based HS imaging systems. Liu et al. [23, 22] proposed a system combining low-rank representations with CS theory and obtained 3D PA data with low sampling rates. In this study, we utilize low-rank representations for HSPA restoration. + +In summary, most of the previous work focused on restoration of 3D data, while 4D HSPA restoration is a much more complicated issue, because: i) the signal amplitude is smaller due to the low energy conversion efficiency from light to sound [41]; ii) the observations are not equally reliable; it correlates with depth and spectral band; iii) it is challenging to observe sufficient PA effects from deep layers and bands with weak absorption. Thus, more constraints are needed for restoration. Below, we directly process 4D cubes to explore data correlations in different dimensions in HSPA. + +# 3. Data Analysis + +Let us first analyze the depth and spectral reliability of HSPA data. Unlike other high-dimensional data, such as video or hyper-spectral images, HSPA data have a special feature in which observations on different parts have dissimilar reliabilities depending on the absorbed light energy. This reliability correlates with both depth and spectral band; thus in this section, we discuss how to represent them. + +# 3.1. Depth reliability analysis + +During PA imaging, the object is irradiated by a laser pulse, and the absorbed light is converted into thermal energy, causing thermoelastic expansion. The expansion in turn causes a pressure change, which propagates as an acoustic wave. PAI utilizes ultrasonic transducer to capture this wave and translates it into an electric signal. The electrical signal is then amplified, digitized, and transformed by a computer into 3D volumetric data [32, 30]. + +The intensity of the PA signal is correlated with the amount of energy absorbed from the incident light. As light propagates in the material, its energy inevitably becomes weaker because of scattering and attenuation. Thus, objects deep inside the material absorb less light energy and consequently have a weaker signal intensity and lower SNR. Developers of PA imaging systems have reported that PA signal decays linearly with depth for a homogeneous material. This allows us to represent the depth-dependent PA-signal reliability by considering the depth of an interior point from the surface. For a small data patch $\mathcal{X}_d$ in depth $d$ , its depth-dependent reliability can be described as + +$$ +\gamma_ {d e p} (d) = \frac {I (d) - I _ {m i n}}{I _ {m a x} - I _ {m i n}}, \tag {1} +$$ + +![](images/ba9b5d4315ac0bde8c4b9f775e23a4a59f0703fcc664fdff279e402352383790.jpg) +Figure 3. 3D printed objects and PA data. The decay in signal intensity with depth can be seen. + +![](images/778d09c27471d776716a5d073ca9ed0398284740a17ffb3557f91b411d758bbb.jpg) +Figure 4. Comparison of SNRs at different depths and predicted reliability. + +where $I(d)$ is the average signal intensity in $\mathcal{X}_d$ , and $I_{max}$ and $I_{min}$ are the maximum and minimum intensity of the whole PA cube, respectively. $\gamma_{dep} \in [0,1]$ , where 0 means a totally unreliable observation and 1 means a most reliable observation. + +We verified the above depth-dependent reliability by examining the signal intensity of a 3D printed checker object. The checker pattern is installed at a tilt, covering with an translucent object, as shown in Fig. 3. It can be clearly observed that the lines in the deeper layer have a weaker signal intensity and suffer from more noise; the deepest line at the bottom is almost invisible. We uniformly selected eight depth layers and calculated their SNRs. Then we compared the SNRs with the proposed $\gamma_{dep}$ , as shown in Fig. 4. We can see that $\gamma_{dep}$ fits the tendency of the real SNR; this demonstrates the validity of the proposed depth reliability. + +# 3.2. Spectral reliability analysis + +PA imaging can provide spectral absorbance information on the interiors of target materials. Accordingly, another factor determining PA signal intensity is the spectral absorption of the material that determines the amount of light absorbed by that material. By considering the differences in PA signal intensities caused by differences in spectral absorption of the materials in the interior, we can represent the spectral reliability of the HSPA data captured at each wavelength length $\lambda$ as + +$$ +\gamma_ {s p e c} (\lambda) = \eta (\lambda) \cdot \phi (\lambda), \tag {2} +$$ + +![](images/7bed807e093101c2e5be857c5e3d8eb5b60aec0343ccda457db94e263ef7aeba.jpg) +Figure 5. Three tubes containing ink, water, and horse blood. PA images acquired at different wavelengths. + +![](images/f8982e02f367903ca0848442533ec8ac5455144d318eba8f8003a8491d9674a5.jpg) +Figure 6. Comparison of SNR and predicted reliability for horse blood. + +where $\eta(\cdot)$ is the laser emitter output energy function, and $\phi(\cdot)$ is the object's absorption spectrum. Moreover, as we did with depth reliability, we perform normalization on $\gamma_{spec}$ , to make $\gamma_{spec} \in [0,1]$ , where 0 means a totally unreliable band and 1 means a most reliable band. + +We examined the validity of the proposed spectral reliability by measuring a scene consisting of three tubes of black ink, water, horse blood (Fig. 5). For this experiment, a laser light from $500~\mathrm{nm}$ to $700~\mathrm{nm}$ was used to irradiate the target scene at $20~\mathrm{nm}$ intervals. We can see that the water tube is always invisible, because water is transparent, while the ink has constant light absorption at all wavelengths. Thus, the ink was captured in the PA images at all wavelengths. The blood tube has the strongest intensity at $540~\mathrm{nm}$ , as the blood absorption spectrum has a peak here, and it is invisible beyond $600~\mathrm{nm}$ . We calculated the SNR of the horse blood tube in each band and compared them with the proposed $\gamma_{spec}$ , as shown in Fig. 6. We can see that the variation in $\gamma_{spec}$ is similar to the tendency of the real SNR. This demonstrates the validity of the proposed spectral-reliability measure. + +Finally, combining $\gamma_{dep}$ and $\gamma_{spec}$ , we define the total reliability as: + +$$ +\gamma (d, \lambda) = c _ {1} \cdot \gamma_ {\text {d e p}} (d) \cdot \gamma_ {\text {s p e c}} (\lambda) + c _ {2}, \tag {3} +$$ + +where $c_{1}$ is the scalar and $c_{2}$ is the offset. + +![](images/6fba906f688aeda8c28c16a167ae7ae76658d71d32f6aa1cbc5f6e727fc73b31.jpg) +Figure 7. Overview of the proposed HSPA restoration method. + +# 4. HSPA Data Restoration + +First, we formulate the 4D HSPA restoration problem; then, we explore the data correlation globally and locally and incorporate the findings in regularization terms for optimization. Finally, we develop a numerical algorithm to solve the optimization problem. The overall framework is shown in Fig. 7. + +# 4.1. Problem formulation + +Consider HSPA data $\mathcal{P} \in \mathbb{R}^{n_1 \times n_2 \times n_3 \times n_4}$ , where $(n_1, n_2)$ is the spatial resolution, $n_3$ is the depth resolution, and $n_4$ is the spectral resolution. We formulate the degradation as: + +$$ +\mathcal {O} = \mathcal {D} (\mathcal {P}) + \mathcal {N}, \tag {4} +$$ + +where $\mathcal{D}(\cdot)$ is a sub-sampling function, $\mathcal{N}$ is additive noise, $\mathcal{O}$ is the observation. + +Our target is to restore clear, full-grid data $\mathcal{P}$ from a degraded observation $\mathcal{O}$ . Obviously, this problem is ill-posed as there are many fewer observations than unknowns, and many observations are unreliable. To solve the optimization problem, we will explore the correlations between data and formulate them into an objective function. + +# 4.2. Data constraints as regularization + +We will explore two data constraints, i.e., global transform sparsity and local self-similarity. First, let us discuss the transform sparsity constraint. By specifying the spatial location $(i,j)$ and spectral band $\lambda$ , we can get a 1D vector $\mathbf{p}_{i,j,\lambda}$ along the depth direction. We call this 1D vector defined by fixing all indices but one a Fiber. According to the PA imaging mechanism, Fiber is a bipolar waveform signal [32]. We can always use an appropriate sparse transform for de-correlation [13]. Thus, we will impose the following constraint: the depth Fiber should be sparse in a transform domain. Popular sparse transforms include the Karhunen-Loeve transform (KLT), Fourier transform (FT), discrete cosine transform (DCT), etc. Here, we will use DCT for simplicity. Mathematically, sparsity can be achieved by minimizing the $l_{1}$ norm of the transformed coefficients: + +$$ +\hat {\mathcal {P}} = \operatorname {a r g m i n} \| \mathcal {T} _ {d c t} (\mathcal {P}) \| _ {1}, s. t. \| \mathcal {O} - \mathcal {D} (\mathcal {P}) \| _ {F} = 0, \tag {5} +$$ + +where $\mathcal{T}_{dct}(\mathcal{P}) = \sum_{i}\sum_{j}\sum_{\lambda}\mathrm{dct}(\mathbf{p}_{i,j,\lambda})$ is the sum of DCTs of all depth Fibers. + +Now, let us examine the local self-similarity constraint: in a local region, a small patch should have a similar structure to its neighbor patches. This similarity can be captured with a low-rank regularization term. Mathematically, we split the HSPA data $\mathcal{P}$ into several non-overlapping small patches $\{\pmb{x}_1,\pmb{x}_2,\dots\}$ ; the size of each patch is $\pmb{x} \in \mathbb{R}^{m_1 \times m_2 \times m_3 \times m_4}$ . We will consider a patch $\pmb{x}_l$ at location $l$ and find the $k$ nearest patches in a neighboring region in 4D space, denoted as $\{\Omega_{Nei}(\pmb{x}_l)|\pmb{x}_{N_1},\pmb{x}_{N_2},\dots,\pmb{x}_{N_k}\}$ . Note that we do not split the HSPA data into spatial and spectral domains; instead, we explore all of the data correlations simultaneously. + +We reform the patch $\mathcal{X}_l$ into a vector $\mathbf{x}_l\in \mathbb{R}^M$ , where $M = m_{1}*m_{2}*m_{3}*m_{4}$ . We perform the same vectorization on all neighboring patches in $\Omega_{Nei}(\mathcal{X}_l)$ and write them as a matrix $\mathbf{X}_l\in \mathbb{R}^{M\times (k + 1)}$ , where each row is a vectorized patch. This matrix has a low-rank structure in rows, because of the patches' self-similarity. Thus, we consider a noise model $\mathbf{X}_l = \mathbf{Y}_l + \mathbf{N}$ , where $\mathbf{Y}_l$ is the desired noise-free low-rank matrix, and can be recovered as + +$$ +\hat {\mathbf {Y}} _ {l} = \operatorname {a r g m i n} \operatorname {r a n k} (\mathbf {Y} _ {l}), s. t. \| \mathbf {X} _ {l} - \mathbf {Y} _ {l} \| _ {F} \leq \sigma_ {N} ^ {2}, \tag {6} +$$ + +where $\sigma_N^2$ is the noise level. + +# 4.3. Numerical algorithm + +By writing equation (5), (6) in Lagrange function form and combining them with equation (4), we obtain the final objective function: + +$$ +\begin{array}{l} (\hat {\mathcal {P}}, \hat {\mathbf {Y}}) = \operatorname {a r g m i n} \| \mathcal {O} - \mathcal {D} (\mathcal {P}) \| _ {F} ^ {2} + \alpha \| \mathcal {T} _ {d c t} (\mathcal {P}) \| _ {1} \\ + \sum_ {l} \left[ \gamma (d, \lambda) \| \mathbf {X} _ {l} - \mathbf {Y} _ {l} \| _ {F} ^ {2} + \beta \cdot r a n k (\mathbf {Y} _ {l}) \right], \tag {7} \\ \end{array} +$$ + +where $\alpha$ and $\beta$ are Lagrange multipliers and $\gamma (d,\lambda)$ is the adaptive reliability of each local patch, as defined in section 3.2. This objective function contains two parts (global transform sparsity and local self-similarity), and we solve them sequentially. + +Step 1: for global transform sparsity, we denote $\mathcal{Q} = \mathcal{T}_{dct}(\mathcal{P})$ ; thus, equation (5) becomes + +$$ +\hat {\boldsymbol {Q}} = \operatorname {a r g m i n} \frac {1}{2} \| \boldsymbol {\mathcal {O}} - \mathcal {D} (\mathcal {T} _ {i d c t} (\boldsymbol {\mathcal {Q}})) \| _ {F} ^ {2} + \frac {\alpha}{2} \| \boldsymbol {\mathcal {Q}} \| _ {1}, \tag {8} +$$ + +where $\mathcal{T}_{idct}(\cdot)$ is the sum of inverse DCTs of all depth Fibers. Equation (8) is a typical Lasso problem; we solve it by using the alternating direction method of multipliers (ADMM) [5]. Consequently, we get the intermediate result $\tilde{\mathcal{P}} = \mathcal{T}_{idct}(\hat{\mathcal{Q}})$ . + +Step 2: we split $\hat{\mathcal{P}}$ into small patches and calculate the reliability for each patch based on their depth and spectral + +band, as defined in equation (3). We write out the low-rank matrix and local self-similarity constraint equation for each patch, as described in the previous sub-section. The rank term in equation (6) is non-convex and NP-hard; a common solution is to approximate it using the nuclear norm [7]. Thus, we rewrite equation (6) as + +$$ +\hat {\mathbf {Y}} = \operatorname {a r g m i n} \frac {1}{2} \| \mathbf {X} - \mathbf {Y} \| _ {F} ^ {2} + \frac {\beta}{2 \gamma} \| \mathbf {Y} \| _ {*}, \tag {9} +$$ + +where $\| \cdot \|_{*}$ is the nuclear norm. According to [6], equation (9) can be optimized as + +$$ +\hat {\mathbf {Y}} = \mathbf {U} \mathcal {S} (\boldsymbol {\Sigma}, \frac {\beta}{2 \gamma}) \mathbf {V} ^ {\top}, \mathcal {S} (\boldsymbol {\Sigma}, \frac {\beta}{2 \gamma}) = \operatorname {d i a g} \left\{\left(\sigma_ {X} - \frac {\beta}{2 \gamma}\right) _ {+} \right\}, \tag {10} +$$ + +where $\mathbf{U}\pmb{\Sigma}\mathbf{V}^{\top}$ is the singular value decomposition of $\mathbf{X}$ , and $\sigma_{X}$ are the singular values. $S(\cdot)$ is the singular value shrinkage operator, $(a)_{+} = \max (0,a)$ . + +Step 3: we reconstruct clear small patches $\hat{\mathcal{X}}$ from $\hat{\mathbf{Y}}$ and combine them to form the final restoration result $\hat{\mathcal{P}}$ . + +# 5. Experimental Results + +First, we will describe the dataset used in the experiments and the reference for the performance evaluation. Then, we will present qualitative and quantitative results on the proposed restoration method and verify the depth and spectral reliabilities. + +# 5.1.Data set + +Our dataset consists of two types of data: 4D HSPA data and high-resolution blood vessel PA data. The HSPA data include 'Leaf', 'Tube', and 'Banana'. They were captured using a photoacoustic microscope machine (ADVANTEST, Hadatomo™ Z WEL5200) connected to a wavelength tunable laser emitter (Japan Laser, Opolette HR 355). We measured a $6\mathrm{mm}^2$ area with a $30~\mu \mathrm{m}$ scanning interval over 1280 time steps. The resulting 4D volumetric data had a resolution of $200\times 200\times 1280\times$ bands. For Leaf and Banana, we uniformly measured 9 bands ranging from $420\mathrm{nm}$ to $580\mathrm{nm}$ . For Tube, we uniformly measured 11 bands ranging from $500\mathrm{nm}$ to $700\mathrm{nm}$ . The entire HSPA data are shown in the supplementary material. + +The blood vessel PA data consisted of 'Hand' and 'Leg'. They were captured by the PAI-05 system proposed in [28]. The blood vessel PA is provided at a higher resolution for large body parts by fusing several PA data. Because of scanning time limitations, 'Hand' and 'Leg' consist of only single-band PA data. The wavelength of the incident light was $797~nm$ , which is the isosbestic point of oxyhemoglobin and de-oxygenated hemoglobin [28]. The full resolution is $2480 \times 1760 \times 160$ for Hand, and $2176 \times 1440 \times 256$ for Leg. + +# 5.2. Evaluation reference + +The major challenge of evaluating the performance of PA restoration algorithms is the lack of a reliable baseline. The original data contains noise, and typical techniques such as averaging over multiple shots are difficult to perform because of mechanical misalignment between shots. Thus we first acquire a noise-removed full-grid data by considering local self-similarity and data reliability. This clear data will be later used as a reference in the following evaluations. + +Here we examined the validity of noise-removed full-grid reference using a simple scene consisting of a single opaque plane. In this care, only a point $(x,y,z)$ on the plane should exhibit a strong PA signal. From this, we fitted a plane by applying the least squares method and calculated the ground-truth surface locations $(x,y,z)_{gt}$ . Then we compared locations of maximum intensity points from the original noisy observation and our reference data with $(x,y,z)_{gt}$ . We captured an opaque plane with five different orientations. The average sum of squares of errors (SSE) for the noisy observations was 114.9421, while the average SSE for our reference was only 2.7237, which demonstrates the validity of our reference data. The full error matrices for each orientation are in the supplementary material. + +# 5.3. Performance evaluation and comparison + +We quantitatively and qualitatively evaluated i) the overall performance of our method, ii) the effectiveness of depth reliability, and iii) the effectiveness of spectral reliability. + +For the quantitative evaluation, the most widely used metrics are the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [36]. These metrics were originally designed for 2D gray-scale images, while the PA data has more dimensions and contains negative values. Thus, we applied a Hilbert transform and re-scaled the PA data to [0, 255]; then, we calculated the quality metrics on each 2D slice by fixing the depth and spectral band. We used the average value among all slices for the evaluation; larger numbers indicate better restoration quality. + +# 5.3.1 Restoration method evaluation + +We verified our methods on incomplete and noisy observations, which were randomly sub-sampled from the original data. We evaluated the restoration quality against those of other approaches, including the default compressive sensing (CS) algorithm, CS with a Wiener filter $(\mathrm{CS} + \mathrm{Wiener})$ and CS with partially known support (CS-PKS) algorithm [27]. We also compared with sophisticated restoration techniques that are not originally developed for PA data, including BM4D[25] and SMF-LRTC[40]. The visualizations for restoration results are shown in Fig. 8 (visualizations of Tube and Banana are in the supplementary material). We visualize a part of original data $(480~nm$ for Leaf, palm for + +Hand, ankle for Leg) in (a), and show 2D slices for reference data and different approaches in (b-g). The quantitative metrics are listed in Table 1, the results show that our method outperforms the others with or without reliability. + +The default CS result is very noisy and has the lowest PSNR and SSIM. This is because CS utilizes the basis pursuit algorithm as the solver, which doesn't take noise into consideration. CS + Wiener, CS + BM4D, and SMF-LRTC outperformed default CS, but still had obvious defects. CS-PKS over-smoothed the edge and lost some details, because of the total variation term in the objective function, which optimizes the global smoothness in the spatial domain. Our method produced a noise-free and detailed restoration; the visual quality was close to that of the reference data. Quantitatively, our method had the highest PSNR and SSIM for almost all data and all sampling ratios. This is because our method does not split the high-dimensional PA data into spatial and depth domains; instead it allowed all of the data correlations to be explored simultaneously. + +We further visualize the restoration result of our method on other portions of Hand data, as shown in Fig. 9. A satisfactory and stable restoration performance can be observed for them. + +# 5.3.2 Depth reliability verification + +We verified the depth reliability by observing two different depth layers of Hand and Leg, as shown in Fig. 10, where the first row shows a shallow layer and the second row shows a deep layer. The reference data, restoration results with reliability (marked in red), and results without reliability (marked in green) are in columns (a), (b), (d) and (e), respectively. Utilizing the reference data as a baseline, we calculated the absolute error map of the results with and without reliability, as shown in column (c) and (f). It can be seen that for the shallow layer, the results with and without reliability have similar restoration quality. On the other hand, for the deep layer where the signal intensity is low, reliability obviously improves the performance. These results demonstrate the effectiveness of depth reliability. + +# 5.3.3 Spectral reliability verification + +The PSNR and SSIM results across all spectral bands are plotted in Fig. 11. For Banana, our method achieve a similar degree of improvement across all bands, as the data has strong signal intensity due to the consistent high absorptions. For Leaf in wavelengths with high absorptions (420 to $480~\mathrm{nm}$ ), our method produces a marginal improvement over other approaches. On the other hand, for wavelengths with low absorptions (500 to $580~\mathrm{nm}$ ), the data have much lower signal intensity. Our method with reliability has higher PSNR, because it adaptively adjusts the optimization + +![](images/c0b05ab99d17afc27911c5fe279317c7eebe3beda40aa17c9e81ce578e3d0eed.jpg) + +![](images/d79c726b578bf0052ca82b7b67135b56dba1c49134bea86bfb9bb668a27fa1f7.jpg) + +![](images/a3c34ed1ba838924a1c6a8a0bcc8262bc0d2ae06e9684ad34c9a14295a4b876e.jpg) +(a) Original data + +![](images/0f94075b5759051312dd1ebbbc06763d01423f337095a416e7b1cf9352a65a28.jpg) + +![](images/7c26c8ee904bdf1d1f0c9f9c610b1ebddee899ce6c3d6cd3ab692e6fd39479d1.jpg) + +![](images/b29d1eb3b0de2b99eb381177b440f148f7576896f6ffd8f4b56fa9e0e1eeeceb.jpg) +(b) Reference + +![](images/8b9ab4df08a9ff228cca79d4c32c8277d5766b7a9f42290cf050c0e5d5cb1ad1.jpg) + +![](images/2db89d978a74f29f87883f0888e9886bfad202adf7870001fbcc9975d73712d6.jpg) + +![](images/f4ce6bfd3f89f3826f51e4e66454c6bc5d65e41ede237eecaa9b5fc44d2648a5.jpg) +(c) Input + +![](images/db47379a5925fc47f39c3b8262352a5fffcd7802e3ff060028e515f996c4f770.jpg) + +![](images/cb90916a9a90400d83d2cc651d1460cd4bde166717336ed0da098d02439c68ed.jpg) + +![](images/2431d149731f80e33c1de0a736f8067bf8b8f05310c8a46a32bd8a74631a0337.jpg) +(d) CS + BM4D + +![](images/1ad425e81af485712c5493ec967ce6aa0f0bc4c55d6fd5eafdbf83c824c9c439.jpg) + +![](images/7670c881728890ea81a4268b7c4a28cea4183d291bc607019d43594fcf81d2c4.jpg) + +![](images/c81d4cec2e0c3e8f9f92356c752f71e35d0fe020bda2370776746ceac4cd3c6f.jpg) +(e) CS-PKS +Figure 8. The visualization of restoration results by different methods on $50\%$ sampled data. + +![](images/cf0816abdb6eb81fe8ac36a64e082fe9dfebbffc67f61874642acaed343f6063.jpg) + +![](images/bf2b4b6c4239a98b9c6c9b70b3cfc6fd2529827e52269221923c9218b85cdf97.jpg) + +![](images/3e5f253d5d0fa6ee5f41becef9ff701a73daa2cc48ab61c6a5a3a159e69ecac7.jpg) +(f) SMF-LRTC + +![](images/a742485a46069cefbadb9a2b6e3a63ca295cd123ca157ea5cc718d04103136e5.jpg) + +![](images/c3a37fa15bd00d0feeca44c714729bf5be02b76566b8e6a76b07b7a08bc2d5fc.jpg) + +![](images/4ae483ef30690db266f5e0c286c8d6788e9cff68151f62f3a26b35cedcdc405b.jpg) +(g) Ours + +Table 1. The quantitative results for different methods + +
Sample RatioMethodLeafTubeBananaHand - palmLeg - ankle
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
0.7default CS31.780.148031.180.113034.800.183837.460.211939.480.3173
CS + Wiener36.380.236638.630.188535.350.213040.440.255942.330.3646
CS + BM4D37.680.220439.020.146536.110.253441.230.270143.200.3846
CS-PKS35.840.165037.730.087735.790.292540.100.257741.980.3721
SMF-LRTC32.510.171331.600.133337.360.240037.760.213839.860.3222
Ours w/o reliab.37.770.509438.920.460439.270.408142.940.290945.840.4398
Ours w/ reliab.44.350.552845.860.498942.750.812953.010.969555.970.9784
0.5default CS31.580.127731.710.090932.270.127737.470.209439.430.3123
CS + Wiener35.500.197138.920.150831.830.138339.930.253241.770.3584
CS + BM4D36.510.190239.450.123132.060.150040.910.276942.820.3856
CS-PKS34.920.142538.630.076034.570.262239.570.253441.330.3612
SMF-LRTC32.840.162632.430.125437.240.230738.080.214540.260.3253
Ours w/o reliab.36.630.384038.930.327337.150.385542.720.301345.250.4437
Ours w/ reliab.40.130.414843.330.357738.450.652346.750.885649.190.9033
0.3default CS31.130.088932.350.063029.540.069136.750.189138.580.2797
CS + Wiener34.030.141938.660.101529.030.071438.360.233540.080.3226
CS + BM4D34.820.141839.350.088929.230.085839.050.264240.890.3564
CS-PKS32.940.104938.640.058132.500.203737.280.200239.050.2910
SMF-LRTC32.990.147633.620.115236.550.211738.170.211040.490.3238
Ours w/o reliab.35.020.268238.820.215534.660.325440.690.305642.730.4295
Ours w/ reliab.35.990.287040.410.239834.790.437941.130.687943.510.7101
+ +weight according to the reliability of the prior knowledge. This result verifies the effectiveness of spectral reliability. + +# 6. Conclusions + +We studied the hyperspectral photoacoustic (HSPA) data restoration problem. We discussed the variance in reliabil + +ity at different depths and in different spectral bands. On the basis of the reliability analysis, we proposed a framework to reconstruct clear, high-quality HSPA data from incomplete, noisy observations. The correlations of the data in different dimensions can be explored simultaneously by using low-rank representations and sparsity regularization. We verified our method on captured HSPA data and blood vessel + +![](images/5af7e371f5227f46e2ad8975442ecfbc87ae1c790cb06b0478f75fb4072a0c79.jpg) +(a) Full hand + +![](images/a2cd1cac8b808d91a1c961b6227343e5e0e23d47dcd435eb7b09d9b179f1f5e5.jpg) +(PSNR: 47.93, SSIM: 0.8267) + +![](images/9e6f999d10e02345a0b53e68c94ac4fc6253f24b990a817dc4872abbbdacb791.jpg) +(b) Two fingers +(PSNR: 51.07, SSIM: 0.8798) +(c) Thumb + +![](images/09ae90c3ad69ee3b1cb483e641134f7bd20fba4fc2900dc2914aaeed370b2d68.jpg) +(PSNR: 46.62, SSIM: 0.8911) +(d) Wrist + +![](images/06b9ee62d322745c29f81610c974d165762c7d1cdc5def460156e8e751b981b3.jpg) +(PSNR: 48.48, SSIM: 0.9275) +(e) Forearm + +![](images/bda9eec38840336b7d7214ac62df6378c5771dc5aff62d2fcea749eb0e24a34a.jpg) +Figure 9. The visualization of restoration results for different portions of $50\%$ sampled Hand data. +$(d = 40)$ + +![](images/7d947b34487b191298339a16bac8fdbc237d937efb2aa4d380acbcce2b852517.jpg) + +![](images/9ff4bc392064345009f023214f782f7c785308c7a23bc8658188069b849f8409.jpg) + +![](images/bb3eae7a53f3de326edfd59ed0d80e15185598215d72ad153d5dba60da24d16c.jpg) +$(d = 50)$ + +![](images/b378918cab27f01ce0e562402d7f84b041dc6cdf5508b81bfcaaf115a7efbefe.jpg) + +![](images/fd9803df1728225e4e3c27cabdd2d6ec818130e226942905d99bad485db1f166.jpg) + +![](images/15db6efc45b2a157c08355efb7a7fa6db8bb84b8c921e0ec7f8ed130f61512a2.jpg) + +![](images/f10fee389dbebc00511b3498e7f03d9526361740ae7261b6c643b4baf61bd508.jpg) +$(d = 80)$ +(a) Reference - Hand + +![](images/6d3edf6c0d9da868fb49cb837adf7f119675b80ff9ab44ce4a4b77c27585ee9a.jpg) +(b) Restoration +Figure 10. Results of restoration on $50\%$ sampled data at different depths (Hand and Leg). The results with reliability are marked in red, and results without reliability are marked in green. + +![](images/aeac5966c27d324f8ac5180830957ac9b8c3b697679ec8e5f6612c49cc7d76d6.jpg) +(c) Error map + +![](images/4434fc2ce0dfcd5761aa051afa4e28e603a943d133822a1e4515cf33e7a8bc8f.jpg) +$(d = 120)$ +(d) Reference - Leg + +![](images/8b041a9bfeb4f3dfd8a9c25bb18f351aec5d92b77cc9542f52b2b71708e010bd.jpg) +(e) Restoration + +![](images/1d5986718abed2e1521cdf2c33bc95504246b8782563c22f18646deea3da0924.jpg) +(f) Error map + +![](images/ae455e21f448a148542eb3db62332bd4cce6ba1b151185adb210b6d4fcc5b784.jpg) +- default CS -CS + Wiener CS + BM4D -CS-PKS SMF-LRTC -Ours w/o reliability -Ours w/ reliability +(a) Leaf - PSNR result +Figure 11. Quality of restoration on $50\%$ sampled data across spectral bands (Leaf and Banana). + +![](images/94e18ee6fd79ad1b7dd6a05ce87fa120e0e7a95982668b67f166ce93d79debbd.jpg) +(b) Leaf - SSIM result + +![](images/52c527794be4bb5347ceacc26092b3d5b0f0f39909c0197dd5febca7e3319437.jpg) +(c) Banana - PSNR result + +![](images/6a5b937ba6a10c034bcf1786b9a7905c4b15a6235dc876bda44e293e71582a03.jpg) +(d) Banana - SSIM result + +PA data. The results show that our method has satisfactory restoration performance. + +# Acknowledgment + +This work was partially supported by ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan). We thank Mr. Taichiro + +Ida and Mr. Hideaki Iwazaki (ADVANTEST Co.) for providing the HSPA data captured by HadatomoTM Z. We thank Mr. Takayuki Yagi (Luxonus Inc.), Prof. Kazuo Kishi (Keio Univ.), and Dr. Hiroki Kajita (Keio Univ.) for providing the blood vessel PA data. The authors are grateful to Prof. Sadakazu Aiso (Keio Univ.) and Assoc Prof. Nobuaki Imanishi (Keio Univ.) for their support and advice. + +# References + +[1] Kyoto university rapid and universal mip imager. https://www.kuhp.kyoto-u.ac.jp/~diag_rad/intro/tech/kurumi.html#KURUMI_EN. Accessed: 2020-03-05. 1 +[2] Stephan Antholzer, Johannes Schwab, Johnnes Bauer-Marschallinger, Peter Burgholzer, and Markus Haltmeier. Nett regularization for compressed sensing photoacoustic tomography. In *Photons Plus Ultrasound: Imaging and Sensing* 2019, volume 10878, page 108783B. International Society for Optics and Photonics, 2019. 2 +[3] Simon Arridge, Paul Beard, Marta Betcke, Ben Cox, Nam Huynh, Felix Lucka, Olumide Ogunlade, and Edward Zhang. Accelerated high-resolution photoacoustic tomography via compressed sensing. arXiv preprint arXiv:1605.00133, 2016. 2 +[4] Alexander Graham Bell. Upon the production and reproduction of sound by light. Journal of the Society of Telegraph Engineers, 9(34):404-426, 1880. 1 +[5] Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, Jonathan Eckstein, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends® in Machine learning, 3(1):1-122, 2011. 5 +[6] Jian-Feng Cai, Emmanuel J Candès, and Zuowei Shen. A singular value thresholding algorithm for matrix completion. SIAM Journal on optimization, 20(4):1956-1982, 2010. 5 +[7] Emmanuel J Candès and Benjamin Recht. Exact matrix completion via convex optimization. Foundations of Computational mathematics, 9(6):717, 2009. 5 +[8] Emmanuel J Candès and Michael B Wakin. An introduction to compressive sampling. IEEE signal processing magazine, 25(2):21-30, 2008. 2 +[9] Yingchun Cao, Ayeeshik Kole, Lu Lan, Pu Wang, Jie Hui, Michael Sturek, and Ji-Xin Cheng. Spectral analysis assisted photoacoustic imaging for lipid composition differentiation. Photoacoustics, 7:12-19, 2017. 1 +[10] Weisheng Dong, Guangming Shi, Xin Li, Yi Ma, and Feng Huang. Compressive sensing via nonlocal low-rank regularization. IEEE Transactions on Image Processing, 23(8):3618-3632, 2014. 3 +[11] David L Donoho. Compressed sensing. IEEE Transactions on information theory, 52(4):1289-1306, 2006. 2 +[12] Ying Fu, Yinqiang Zheng, Imari Sato, and Yoichi Sato. Exploiting spectral-spatial correlation for coded hyperspectral image restoration. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3727-3736, 2016. 3 +[13] Roger G Ghanem and Pol D Spanos. Stochastic finite elements: a spectral approach. Courier Corporation, 2003. 4 +[14] Zijian Guo, Changhui Li, Liang Song, and Lihong V Wang. Compressed sensing in photoacoustic tomography in vivo. Journal of biomedical optics, 15(2):021311, 2010. 2 +[15] Markus Haltmeier, Thomas Berer, Sunghwan Moon, and Peter Burgholzer. Compressed sensing and sparsity in photoacoustic tomography. Journal of Optics, 18(11):114004, 2016. 2 + +[16] Markus Haltmeier, Michael Sandbichler, Thomas Berer, Johannes Bauer-Marschallinger, Peter Burgholzer, and Linh Nguyen. A sparsification and reconstruction strategy for compressed sensing photoacoustic tomography. The Journal of the Acoustical Society of America, 143(6):3838-3848, 2018. 2 +[17] Israr Ul Haq, Ryo Nagaoka, Syahril Siregar, and Yoshifumi Saijo. Sparse-representation-based denoising of photoacoustic images. Biomedical Physics & Engineering Express, 3(4):045014, 2017. 2 +[18] Hui Ji, Sibin Huang, Zuowei Shen, and Yuhong Xu. Robust video restoration by joint sparse and low rank matrix approximation. SIAM Journal on Imaging Sciences, 4(4):1122-1142, 2011. 2 +[19] Agne Kazakeviciute, Chris Jun Hui Ho, and Malini Olivo. Multispectral photoacoustic imaging artifact removal and denoising using time series model-based spectral noise estimation. IEEE transactions on medical imaging, 35(9):2151-2163, 2016. 2 +[20] Hoong-Ta Lim and Vadakke Matham Murukeshan. Hyperspectral photoacoustic spectroscopy of highly-absorbing samples for diagnostic ocular imaging applications. International Journal of Optomechatronics, 11(1):36-46, 2017. 1 +[21] Ning Liu, Sihua Yang, and Da Xing. Photoacoustic and hyperspectral dual-modality endoscope. Optics letters, 43(1):138-141, 2018. 1 +[22] Ting Liu, Mingjian Sun, Yang Liu, Depeng Hu, Yiming Ma, Liyong Ma, and Naizhang Feng. Admm based low-rank and sparse matrix recovery method for sparse photoacoustic microscopy. Biomedical Signal Processing and Control, 52:14-22, 2019. 3 +[23] Ting Liu, Mingjian Sun, Jing Meng, Zhenghua Wu, Yi Shen, and Naizhang Feng. Compressive sampling photoacoustic microscope system based on low rank matrix completion. Biomedical Signal Processing and Control, 26:58-63, 2016. 3 +[24] Xueyan Liu, Dong Peng, Wei Guo, Xibo Ma, Xin Yang, and Jie Tian. Compressed sensing photoacoustic imaging based on fast alternating direction algorithm. International journal of biomedical imaging, 2012, 2012. 2 +[25] Matteo Maggioni, Vladimir Katkovnik, Karen Egiazarian, and Alessandro Foi. Nonlocal transform-domain filter for volumetric data denoising and reconstruction. IEEE transactions on image processing, 22(1):119-133, 2012. 6 +[26] Ivan Markovsky and KONSTANTIN Usevich. Low rank approximation. Springer, 2012. 2 +[27] Jing Meng, Lihong V Wang, Leslie Ying, Dong Liang, and Liang Song. Compressed-sensing photoacoustic computed tomography in vivo with partially known support. Optics Express, 20(15):16510-16523, 2012. 6 +[28] Kenichi Nagae, Yasufumi Asao, Yoshiaki Sudo, Naoyuki Murayama, Yuusuke Tanaka, Katsumi Ohira, Yoshihiro Ishida, Atsushi Otsuka, Yoshiaki Matsumoto, Susumu Saito, et al. Real-time 3d photoacoustic visualization system with a wide field of view for imaging human limbs. F1000Research, 7, 2018. 5 + +[29] Jean Provost and Frédéric Lesage. The application of compressed sensing for photo-acoustic tomography. IEEE transactions on medical imaging, 28(4):585-594, 2008. 2 +[30] Allan Rosencwaig and Allen Gersho. Theory of the photoacoustic effect with solids. Journal of Applied Physics, 47(1):64-69, 1976. 3 +[31] Sergey Telenkov and Andreas Mandelis. Signal-to-noise analysis of biomedical photoacoustic measurements in time and frequency domains. Review of Scientific Instruments, 81(12):124901, 2010. 2 +[32] Lihong V Wang. Tutorial on photoacoustic microscopy and computed tomography. IEEE Journal of Selected Topics in Quantum Electronics, 14(1):171-179, 2008. 1, 3, 4 +[33] Lihong V Wang and Song Hu. Photoacoustic tomography: in vivo imaging from organelles to organs. science, 335(6075):1458-1462, 2012. 1 +[34] Lihong V Wang and Junjie Yao. A practical guide to photoacoustic tomography in the life sciences. Nature methods, 13(8):627, 2016. 1 +[35] Pu Wang, Ping Wang, Han-Wei Wang, and Ji-Xin Cheng. Hyperspectral vibrational photoacoustic imaging of lipids and collagen. In *Photons Plus Ultrasound: Imaging and Sensing* 2012, volume 8223, page 82231I. International Society for Optics and Photonics, 2012. 1 +[36] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600-612, 2004. 6 +[37] Minghua Xu and Lihong V Wang. Photoacoustic imaging in biomedicine. Review of scientific instruments, 77(4):041101, 2006. 1 +[38] Ge Zhang, Bingxue Wang, Antonio Stanziola, Anant Shah, Jeffrey Bamber, and Meng-Xing Tang. High signal-to-noise ratio contrast-enhanced photoacoustic imaging using acoustic sub-aperture processing and spatiotemporal filtering. In 2019 IEEE International Ultrasonics Symposium (IUS), pages 494-497. IEEE, 2019. 2 +[39] Hongyan Zhang, Wei He, Liangpei Zhang, Huanfeng Shen, and Qiangqiang Yuan. Hyperspectral image restoration using low-rank matrix recovery. IEEE Transactions on Geoscience and Remote Sensing, 52(8):4729-4743, 2013. 2 +[40] Yu-Bang Zheng, Ting-Zhu Huang, Teng-Yu Ji, Xi-Le Zhao, Tai-Xiang Jiang, and Tian-Hui Ma. Low-rank tensor completion via smooth matrix factorization. Applied Mathematical Modelling, 70:677-695, 2019. 6 +[41] Meng Zhou, Haibo Xia, Hongtao Zhong, Jiayao Zhang, and Fei Gao. A noise reduction method for photoacoustic imaging in vivo based on emd and conditional mutual information. 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Semantic and panoptic segmentation assign semantic classes and determine instances in 3D space. Multi-object tracking encompasses 3D object detection in space, followed by association over time. 4D panoptic LiDAR segmentation jointly tackles semantic and instance segmentation in 3D space over time. + +![](images/f0c2e41c60b9e5713079120cfb72e59e1f0471cfdacd7a4c78ba8d6b3b4692ea.jpg) + +![](images/a59c58c86f88869dc125405cedf8585cfb69ed175596ab6ee49e62d4e1c244e3.jpg) + +![](images/65cc8fd6cc4ee1d4d3b373ace0de0fa960fd671358be68298e1abdd0ea95dc38.jpg) + +# Abstract + +Temporal semantic scene understanding is critical for self-driving cars or robots operating in dynamic environments. In this paper, we propose 4D panoptic LiDAR segmentation to assign a semantic class and a temporally-consistent instance ID to a sequence of 3D points. To this end, we present an approach and a point-centric evaluation metric. Our approach determines a semantic class for every point while modeling object instances as probability distributions in the 4D spatio-temporal domain. We process multiple point clouds in parallel and resolve point-to-instance associations, effectively alleviating the need for explicit temporal data association. Inspired by recent advances in benchmarking of multi-object tracking, we propose to adopt a new evaluation metric that separates the semantic and point-to-instance association aspects of the task. With this work, we aim at paving the road for future developments of temporal LiDAR panoptic perception. + +# 1. Introduction + +Spatio-temporal interpretation of raw sensory data is important for autonomous vehicles to understand how to interact with the environment and perceive how trajectories of moving agents evolve in 3D space and time. + +In the past, different aspects of dynamic scene understanding such as semantic segmentation [22, 18, 48, 72, 85, 69], object detection [23, 62, 40, 65, 64, 66], instance segmentation [28], and multi-object tracking [43, 8, 53, 10, 76, 61, 58] have been tackled independently. The developments in these fields were largely fueled by the rapid progress in deep learning-based image [37] and point-set representation learning [59, 60, 72], together with contributions of large-scale datasets, benchmarks, and unified evaluation metrics [44, 22, 25, 19, 17, 74, 26, 5, 18, 13, 68]. In the pursuit of image-based holistic scene understanding, recent community efforts have been moving towards convergence of tasks, such as multi-object tracking (MOT) and segmentation [74, 83], and semantic and instance segmentation, i.e., panoptic segmentation [35]. Recently, panoptic segmentation was extended to the video domain [34]. Here, the dataset, task formalization, and evaluation metrics focused on interpreting short and sparsely labeled video snippets in 3D (2D image+time) in an offline setting. Autonomous vehicles, however, need to continuously interpret sensory data and localize objects in a 4D continuum. + +Tackling sequence-level LiDAR panoptic segmentation is a challenging problem, since state-of-the-art methods [72] usually need to downsample even single-scan point clouds to satisfy the memory constraints. Therefore, the common approach in (3D) multi-object tracking is detect- + +ing objects in individual scans, followed by temporal association [24, 76, 77], often guided by a hand-crafted motion model. In this paper, we take a substantially different approach, inspired by the unified space-time treatment philosophy. We form overlapping 4D volumes of scans (see Fig. 1) and, in parallel, assign to 4D points a semantic interpretation while grouping object instances jointly in 4D space-time. + +Importantly, these 4D volumes can be processed in a single network pass, and the temporal association is resolved implicitly via clustering. This way, we retain inference efficiency while resolving long-term association between overlapping volumes based on the point overlap, alleviating the need for explicit data association. + +For the evaluation, we introduce a point-centric higher-order tracking metric, inspired by recent metrics for multiobject tracking [45] and concurrent work on video panoptic segmentation [75] which differ from the available metrics [35, 9] that overemphasize the recognition part of the tasks. Our metric consists of two intuitive terms, one measuring the semantic aspect and second the spatio-temporal association of the task. Together with the recently proposed SemanticKITTI [5, 6] dataset, this gives us a test bed to analyze our method and compare it with existing LiDAR semantic/instance segmentation [40, 72, 76, 47] approaches, adapted to the sequence-level domain. + +In summary, our contributions are: (i) we propose a unified space-time perspective to the task of 4D LiDAR panoptic segmentation, and pose detection/segmentation/tracking jointly as point clustering which can effectively leverage the sequential nature of the data and process several LiDAR scans while maintaining memory efficiency; (ii) we adopt a point-centric evaluation protocol that fairly weights semantic and association aspects of this task and summarizes the final performance with a single number; (iii) we establish a test bed for this task, which we use to thoroughly analyze our model's performance and the existing LiDAR panoptic segmentation methods used in conjunction with a tracking-by-detection mechanism. Our code, experimental data1 and benchmark2 are publicly available. + +# 2. Related Work + +Our work is related to tasks covering different aspects of scene perception, such as semantic segmentation, object detection/segmentation, and tracking. In the following, we review related methods and tasks. + +Datasets and Metrics. The growing interest in autonomous vehicles has sparked interest in scene perception using LiDAR sensors. Here the progress has been fueled by advances in deep learning on point sets [59, 60, 31, 36, 38, + +79, 80, 70, 72, 47] and datasets with standardized benchmarks for 3D semantic/instance segmentation [25, 5] and 3D object detection and multi-object tracking [13, 68]. This confirms the importance of advancing both spatial and temporal aspects of mobile robot perception. Our proposed task formulation and evaluation metric is the first that unifies both aspects to the best of our knowledge. + +Recent community efforts in the field of image-based perception have been moving towards the convergence of different tasks. For instance, Kirillov et al. [35] proposed to unify semantic and instance segmentation, which they termed panoptic segmentation, together with an evaluation metric, the panoptic quality (PQ). Others proposed to tackle multi-object tracking and instance segmentation (MOTS) in videos jointly [74, 83]. Moreover, [34] recently extended panoptic segmentation to videos – however, the dataset and the evaluation metrics focus on interpreting short and sparse video snippets offline. This is reflected in the evaluation metric, which is essentially PQ evaluated based on the 3D IoU [83] and averaged over temporal windows of varying sizes to compensate that the difficulty of the task depends on the sequence length. This setting is not suitable for autonomous vehicles that need to interpret raw sensor data continuously. Hurtado et al. [32] proposes to combine ideas from MOTA [9] and PQ [35] by adding a penalty related to ID switches to the PQ. Nonetheless, both PQ and MOTA were criticized [57, 45], and the proposed evaluation inherits all of their well-known issues. + +In this paper, we propose a different approach and bring ideas recently introduced in the context of benchmarking vision-based multi-object tracking [45] to the domain of sequential LiDAR semantic and instance segmentation. Together with the metric, we also propose an approach that operates directly on spatio-temporal point clouds providing object instances in space and time. + +Point Cloud Segmentation. Semantic segmentation or point-wise classification of point clouds is a well-known research topic [2]. Traditionally, it was solved using feature extractors in combination with traditional classifiers [1] and conditional random fields to enforce label consistency of neighboring points [73, 50, 81]. Availability of large-scale datasets, such as S3DIS [3], Semantic3D [27], and recently SemanticKITTI [5], made it possible to also investigate end-to-end pipelines [39, 48, 72, 30, 85, 63, 60, 59, 47]. Similar to recent trends in RGB-D [33, 20] and LiDAR segmentation [78], our method performs bottom-up point grouping in a data-driven fashion. However, different from the aforementioned, we perform grouping in 3D space and time. We use the backbone by [72] that applies deformable point convolutions directly on the point clouds. In our case, this empirically performed better compared to backbones, specifically designed for point sequences [15, 63]. + +Multi-Object Tracking and Segmentation. The majority of vision-based MOT methods follow tracking-by-detection [52]. Here the idea is to first run a pre-trained object detector independently in each video frame and then associate detections across time. In the past, there was a strong focus on developing robust and, preferably, globally optimal methods for data association [84, 42, 56, 11, 12]. Recent data-driven trends mainly focus on learning to associate detections [41, 67] or to regress targets [8], often in combination with end-to-end learning [16, 82, 10]. + +In the realm of robot vision, it is critical to localize object trajectories in 3D space and time. Early methods localized monocular detections in 3D e.g., using stereo [43, 53, 21], or performed tracking in a category-agnostic manner by first performing bottom-up segmentation based on spatial proximity followed by point-segment association [71, 29]. Recently, LiDAR-based MOT became popular, thanks to the emergence of reliable 3D object detectors [65, 40] and LiDAR-centric datasets [13, 68]. Weng et al. [76] demonstrated that simple methods based on linear assignment and constant-velocity motion models can perform surprisingly well when 3D detections are localized reliably. Our method departs from 3D object detection in the spatial domain, followed by the detection association in the temporal domain. Instead, we follow recent advances in image [51, 14] and video instance segmentation [4]. We localize possible object instance centers within a 4D volume and associate points to estimated centers in a bottom-up manner, while a semantic branch assigns semantic classes to points. + +# 3. Method + +In this paper, we propose a method and a metric for 4D Panoptic LiDAR Segmentation task that tackles LiDAR semantic segmentation and instance segmentation jointly in the spatial and temporal domain. Given a sequence of LiDAR scans, the goal of this task is to predict for each 3D point (i) a semantic label for both stuff and thing classes, and (ii) a unique, identity-preserving object instance ID that should persist over the whole sequence. + +# 3.1. 4D Panoptic LiDAR Segmentation: 4D-PLS + +In this work, we take a different path compared to the tracking-by-detection paradigm to video-instance and video-panoptic segmentation [74, 83, 34, 32]. We pose 4D panoptic segmentation as two joint processes. The first one is responsible for point grouping in the 4D continuum using clustering, while the second assigns a semantic interpretation to each point. + +We provide an overview of our method in Fig. 2. In a nutshell, we first form 4D point clouds from several consecutive LiDAR scans. In parallel, within a single network pass, we localize the most likely object centers (inspired by point-based tracking methods by [86, 14]) in the sequence + +![](images/5ea31871f58b2fda037a84a6a227eaa2c9cc782c7f270a4d2c1d198fed0e7df1.jpg) +Figure 2: Visualization of our method. We sample points from past scans to form a 4D point cloud. Our encoder-decoder network estimates point objectness map $(O)$ , point variance map $(\Sigma)$ , and point embeddings $(\varepsilon)$ . We use these maps to assign points to their respective instances via density-based clustering in a 4D continuum. We obtain semantic interpretation from the semantic decoder $(S)$ . + +(objectness map $O$ ), assign semantic classes to points (semantic map $S$ ), and compute per-point embeddings (embedding map $\varepsilon$ ) and variances (variance map $\Sigma$ ). + +The clustering can be performed efficiently by evaluating the probability of each 4D point belonging to a certain "seed" point, which is similarly performed in the context of images and video segmentation [51, 4]. Finally, to associate 4D sub-volumes, we examine point intersections between overlapping point volumes. + +4D Volume Formation. During inference and training, we form overlapping 4D point cloud volumes in an online setting. In particular, for scan $t$ and temporal window size $\tau$ , we align together point clouds within temporal window $\{\max(0, t - \tau), \dots, t\}$ using ego-motion estimates provided by a SLAM approach [7]. Our experiments in Sec. 4.1 reveal that processing multiple point clouds significantly improves spatial and temporal point association performance. However, due to the linear growth in memory requirements, stacking point clouds along the temporal dimension is prohibitively expensive. To overcome this issue, we build on the intuition that thing classes are most critical for a stable temporal association, since these classes correspond to potentially moving objects. As we operate in an online setting, where the past scans have already been processed, we can sample points that belong to thing classes or lie near to an object centers from earlier scans. + +Density-based Clustering. We model object instances via Gaussian probability distributions. Given an estimate of the object center, i.e., clustering "seed" point, we can assign points to their respective instance by evaluating each point under the Gaussian pdf based on the point's embedding vectors. The estimated centers do not need to correspond to exact object centers but are merely used to initiate the clustering. Thus, our approach is in practice fairly robust to occlusions and cross-time view changes. We note that the Gaussian assumption is only valid for shorter temporal windows. In particular, given a point $\mathbf{p}_i$ representing the instance center and its embedding vector $e_i$ , and a query point $p_j$ with its embedding vector $e_j$ , we can evaluate the + +probability of point $p_j$ belonging to its center "seed" point $p_i$ as: + +$$ +\hat {p} _ {i j} = \frac {1}{(2 \pi) ^ {\frac {D}{2}} | \Sigma_ {i} | ^ {\frac {1}{2}}} \exp \left(- \frac {1}{2} (e _ {i} - e _ {j}) ^ {\top} \Sigma_ {i} ^ {- 1} (e _ {i} - e _ {j})\right) (1) +$$ + +where $\Sigma_{i}$ is a diagonal matrix constructed using variance prediction $\sigma_{i}$ of point $p_i$ . We concatenate coordinate values $(x,y,z,t)$ with the learned point embedding vectors to combine spatial and temporal coordinates with learned embeddings. We account for these additional dimensions during the training of the variance map. + +Network and Training. To perform such clustering, we need to identify most likely instance centers, i.e., "seed" points, in a 4D point cloud. We also need variance predictions for each point to evaluate probability scores during clustering, and a posterior over all semantic classes. + +We estimate all these quantities using an encoder-decoder architecture that operates directly on the 4D point cloud $P \in \mathbb{R}^{N \times 4}$ . The encoder network is based on the KP-Conv [72] backbone that uses deformable point convolutions. The decoder predicts point-wise feature embeddings $\varepsilon \in \mathbb{R}^{N \times D}$ using consecutive point convolutions. On top of the encoder, we add an object centerness decoder in $\mathbb{R}^{N \times 1}$ , point variance decoder in $\mathbb{R}^{N \times D}$ , and semantic decoder in $\mathbb{R}^{N \times C}$ . We train our network in an end-to-end manner and in online fashion. + +To train the semantic decoder, we use cross-entropy classification loss $L_{\mathrm{class}}$ . As the semantic classes are highly imbalanced, we sample points to ensure that the probability of sampling a point from a certain class is roughly uniform. + +To learn the point centerness and point variance, we use three different losses. First, we impose the mean squared error (MSE) loss to train the object centerness decoder. However, there will generally be no points near the actual object centers, unlike the image and video domain [51, 4]. Therefore, instead of predicting per-point centerness, we predict the proximity of the point to its instance center. We compute for each point $\mathbf{p}_i$ its objectness $o_i$ as Euclidean distance between the point and its instance center, i.e., mean point of all instance points, normalized to $[0,1]$ . This objectness $o_i$ is then compared to the regressed objectness $\hat{o}_i$ : + +$$ +L _ {\mathrm {o b j}} = \sum_ {i = 1} ^ {N} \left(\hat {o} _ {i} - o _ {i}\right) ^ {2}, \quad \hat {o} _ {i}, o _ {i} \in [ 0, 1 ] \tag {2} +$$ + +Since we want the embeddings of instances to form clusters in the spatio-temporal domain, we introduce our instance loss. Given a 4D point cloud of $N$ points and $K$ instances, it is defined as: + +$$ +L _ {\text {i n s}} = \sum_ {j = 1} ^ {K} \sum_ {i = 1} ^ {N} \left(\hat {p} _ {i j} - p _ {i j}\right) ^ {2}, p _ {i j} = \left\{ \begin{array}{l l} 1, & \text {i f} \mathbf {p} _ {i} \in I _ {j} \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +where $\hat{p}_{ij}$ is evaluated under the Gaussian pdf (Eq. 1) with points embedding $e_i$ as well as instance embedding and variance $e_j$ and $\sigma_j$ . In addition, we employ variance smoothness loss $L_{\mathrm{var}}$ , similar to [4, 51] for training the variance decoder. In summary, we use four different losses to train our network in end-to-end manner: $L = L_{\mathrm{class}} + L_{\mathrm{obj}} + L_{\mathrm{ins}} + L_{\mathrm{var}}$ . + +Inference. We resolve point-to-instance associations in two stages, first within a processed 4D volume, and then across volumes. First, based on the point cloud centerness map, we select the point $\mathbf{p}_i$ , which has the highest objectness score. Then, we evaluate probabilities $p_{ij}$ for all candidate points and assign them to the cluster in case $p_{ij} > 0.5$ . The assigned points are then removed from the candidate pool. We repeat these steps until the next highest objectness score is below a certain threshold. To transfer identities across processed 4D volumes, we perform cross-volume association greedily based on the overlap score, taking all scans into account. When the overlap is below a threshold, we assign a new id. + +# 3.2. Measuring Performance + +The central question when proposing a novel task and benchmark is how to evaluate and compare different methods. Preferably, we would like to summarize performance with a single number to rank the methods while retaining the capability of looking at different aspects of the task. + +# 3.2.1 Existing Evaluation Measures + +To motivate our approach to evaluation, we first briefly discuss established metrics for image-based panoptic segmentation (PQ [35]) and multi-object tracking and segmentation (MOTSA/MOTSP [9, 74]). Then, we discuss two recently proposed extensions of PQ to the temporal domain and argue why we do not promote their adaptation for the task of 4D LiDAR panoptic segmentation. + +Segment-centric Evaluation. PQ and MOTSA/MOTSP are instance-centric evaluation metrics. Both first determine a unique matching between sets of ground-truth objects and model predictions for each frame individually to determine true positives (TPs), false positives (FPs), and false negatives (FNs). Both metrics provide measures for the segmentation and recognition aspects of the task. The segmentation quality (SQ) term of PQ and MOTSP integrates IoUs over the set TPs and normalizes it by the size of the TP set. The recognition quality (RQ) term of PQ is expressed as the $F_{1}$ score. Similarly, MOTSA combines detection errors (FNs and FPs) with ID switch (IDSW) penalty in a single term. IDSW occurs when a track is lost, and the tracker assigns a new identity to a tracked object. This is the only term that takes the temporal aspect of the task into account. + +A criticism of PQ is that it over-emphasizes the importance of very small segments and stuff classes can be difficult to match [57]. MOTSA overemphasizes the detection compared to the association aspect and it is nonintuitive, since the score can be negative and is unbounded, as can be seen in Sec. 4. Furthermore, the influence of the ID switches on the final score depends on the frame rate, and MOTSA does not reward trackers that recover from incorrect associations. Importantly, both metrics are sensitive to the selection of the matching threshold. Thus, instances that slightly miss this threshold will cause both a FN and a FP. This is not the case for pixel or point centric metrics used for evaluating semantic segmentation. The standard mean IoU (mIoU) metric [22] computes sets of TPs, FPs and FNs pixel (or point) basis, effectively bypassing the segment matching. + +PQ Extensions. Recent work [34] proposes video panoptic quality, a variant of PQ for the sequential domain. Different from PQ, gt-to-prediction mapping is established based on the sequential IoU matching criterion [83]. As objects are not present throughout the clip and the difficulty of the task critically depends on the length of the temporal window, the final metric is averaged over varying temporal window sizes. This is suitable for the setting defined in [34], where the task is to evaluate short, sparsely labeled video snippets. However, this approach does not scale to real-world sequences of arbitrary length. Another extension to PQ, panoptic tracking quality (PTQ) [32] combines MOTA and PQ by adding an ID penalty to the PQ measure. This approach inherits issues from both PQ and MOTSA metrics. + +# 3.2.2 LiDAR Segmentation and Tracking Quality + +In the following, we assume a sequence of 3D point clouds of length $l$ , sampled at discrete time-steps: $\Omega = \{(\mathbf{p},n)\in$ $\mathbb{R}^3\times \mathbb{N}|n < l\}$ . We define the ground-truth assignment function as $gt(\mathbf{p},n)\to (c,id)$ and a prediction function as $pr(\mathbf{p},n)\rightarrow (c,id)$ , that map each 4D tuple, consisting of a point $\mathbf{p}$ and a timestamp $n$ , to a certain class $c$ and identity $id$ . In the following, we devise an evaluation metric that, for each pair $(\mathbf{p},n)$ , evaluates whether (i) it was assigned to a correct class, and (ii) for the thing classes, whether it was assigned to the correct object instance. Inspired by the recently introduced Higher Order Tracking Accuracy (HOTA) [45], proposed in the context of MOT, and concurrent work on video panoptic segmentation proposing the Segmentation and Tracking Quality (STQ) [75], our LSTQ (LiDAR Segmentation and Tracking Quality) consists of two terms, the classification score $S_{cls}$ and the association score $S_{assoc}$ . + +We adopt a fundamentally different evaluation philosophy compared to other metrics [45, 35, 34, 32]. In particular, we drop the concept of the frame-level "detection" and do not match segments between ground-truth and predic + +tion. Our association score measures point-to-instance association quality in a unified way – in space and time at point level, which is more natural for segmentation tasks. + +Classification Score. For the classification score, we first define instance-agnostic ground-truth and predictions sets: + +$$ +g t _ {\mathrm {a g n}} (c) = \left\{\left(\mathbf {p}, n\right) \mid \operatorname {g t} (\mathbf {p}, n) = (c, *) \right\}, +$$ + +$$ +p r _ {\mathrm {a g n}} (c) = \left\{(\mathbf {p}, n) \mid \operatorname {p r} (\mathbf {p}, n) = (c, *) \right\}, +$$ + +representing the ground truth and predicted points that belong to class $c$ irrespective of their assigned ids. Then, the TP, FP, FN sets are computed as in semantic segmentation evaluation with respect to gt class $c$ and predicted class $c'$ : + +$$ +\mathrm {T P} _ {c} = \left| p r _ {\mathrm {a g n}} (c) \cap g t _ {\mathrm {a g n}} (c) \right|, +$$ + +$$ +\mathrm {F P} _ {c} = \left| p r _ {\text {a g n}} (c) - p r _ {\text {a g n}} (c) \cap g t _ {\text {a g n}} (c) \right|, +$$ + +$$ +\mathrm {F N} _ {c} = \left| g t _ {\mathrm {a g n}} (c) - p r _ {\mathrm {a g n}} (c) \cap g t _ {\mathrm {a g n}} (c) \right|. +$$ + +The classification score then simply boils down to intersection-over-union (IoU) over these sets, which is the standard approach for evaluating semantic segmentation (however, this is different from segment-centric PQ, where points contribute to the $\mathrm{TP}_c$ term only if the segment that they belong is matched). We follow the standard procedure and average over the classes: + +$$ +S _ {c l s} = \frac {1}{| \mathcal {C} |} \sum_ {c = 1} ^ {\mathcal {C}} \frac {| \mathrm {T P} _ {c} |}{| \mathrm {T P} _ {c} | + | \mathrm {F N} _ {c} | + | \mathrm {F P} _ {c} |} = \frac {1}{C} \sum_ {c = 1} ^ {\mathcal {C}} I o U (c). +$$ + +Association Score. To evaluate the association score, we introduce the following class-agnostic predictions and ground-truth for the thing classes: + +$$ +g t _ {i d} (i d) = \left\{\left(\mathbf {p}, n\right) \mid g t (\mathbf {p}, n) = (c, i d), c \in t h i n g s \right\}, +$$ + +$$ +p r _ {i d} (i d) = \left\{(\mathbf {p}, n) \mid p r (\mathbf {p}, n) = (c, i d), c \in t h i n g s \right\}. +$$ + +We define the true positive association (TPA) set between a ground-truth object $t$ with identity $id$ and prediction $s$ , that was assigned identity $id'$ . This gives us a set of points with mutually consistent identities $id$ and $id'$ : + +$$ +T P A (i d, i d ^ {\prime}) = \left| p r _ {i d} (i d ^ {\prime}) \cap g t _ {i d} (i d) \right|. \tag {4} +$$ + +Similarly, we define the set of false positive associations: + +$$ +F P A (i d, i d ^ {\prime}) = \left| p r _ {i d} \left(i d ^ {\prime}\right) - p r _ {i d} \left(i d ^ {\prime}\right) \cap g t _ {i d} (i d) \right|. \tag {5} +$$ + +Intuitively, this set contains predicted point assignments with identity $id'$ , that were assigned a different ground-truth identity ( $\neq id$ ), or were not assigned to a valid object instance. Finally, the set of false negative assignments: + +$$ +F N A (i d, i d ^ {\prime}) = \left| g t _ {i d} (i d) - p r _ {i d} (i d ^ {\prime}) \cap g t _ {i d} (i d) \right| \tag {6} +$$ + +![](images/f2d30483b7e9a59090c91d343a35f9b9dfc74e9dc46f83d4683984493c8f7963.jpg) +Figure 3: Predictions from 2 and 4 scan versions, MOTSA=1.0/0.0, $S_{assoc} = 0.96 / 0.93$ , $S_{cls} = 0.86 / 0.75$ . While both models track the instance correctly, due to slight difference in semantic segmentation predictions, MOTSA scores differ drastically. + +contains ground-truth points with identity $id$ that were assigned an identity, different to $id'$ , or were missed. We note that the concept of TPA, FPA and FNA was first introduced in the context of MOT evaluation for measuring the quality of temporal detection association. Therefore, to establish these sets, a bijective mapping between gt and pred needs to be established (as in the case of [9]). However, in $LSTQ$ , these sets are established with respect to each 4D point, treating association in space and time in a unified manner. + +Once we have quantified these sets, we can evaluate how well a predicted segment $s$ agrees with ground-truth segment $t$ . Because a ground truth segment $t$ may be explained by multiple different predictions, we sum contributions of all pairs with non-zero overlap: + +$$ +S_{assoc} = \frac{1}{|\mathcal{T}|}\sum_{t\in \mathcal{T}}\frac{1}{|gt_{id}(t)|}\sum_{\substack{s\in S\\ s\cap t\neq 0}}TPA(s,t)IoU(s,t), \tag{7} +$$ + +where the $IoU$ term is evaluated using the TPA, FNA and FPA sets (Eq. 4, 6, 5). In practice, we do not need to perform any point segment association, and even a prediction with a single common point will contribute to this term. We normalize these contributions by the tube volume, and we weigh each contribution by the volume of the TPA set. This weighting term ensures that instances with larger temporal spans have a higher contribution to the final score. Finally, our metric is computed as a geometric mean of the two terms: $LSTQ = \sqrt{S_{cls} \times S_{assoc}}$ . The advantage over the arithmetic mean is that the final score will become zero if any of the two terms approach zero. This reflects our intuition that failing at either of two aspects of the task should yield a very low final score. + +$LSTQ$ tolerates different semantic predictions within a spatio-temporal segment by design (the $IoU$ term in Eq. 7 is evaluated in a class-agnostic manner). Following STQ [75], we decouple semantic and association errors, otherwise, e.g., a truck mistaken for a bus would be harshly penalized by the association term, even though it was tracked correctly. This behavior that dis-entangles association and classification errors is different from MOTSA/PTQ/VPQ where semantics and temporal association are entangled. + +# 4. Experimental Evaluation + +In this section, we first evaluate different strategies for forming 4D point cloud volumes, assess the impact of processing multiple scans on the final performance, and discuss several possibilities for the embeddings used for point grouping. We compare our method to baselines for single-scan LiDAR panoptic segmentation [6] and 4D panoptic LiDAR segmentation by extending existing methods. + +We use the SemanticKITTI [5] LiDAR dataset to conduct our experiments. It contains 22 sequences from KITTI odometry dataset [25] and provides point-wise semantic and temporally consistent instance annotations [6]. We use the training/validation/test split by SemanticKITTI [5, 6]. + +# 4.1. Ablation studies + +We perform all ablations on the validation set and interpret results through the lens of LSTQ metric (Sec. 3.2.2). + +Point Propagation. As discussed in Sec. 3, we cannot simply stack point clouds temporarily due to the memory constraints. We build on the intuition that we can subsample a set of points from the past scans that are most beneficial for the end-task performance. As we are operating in an online setting, and the past scans have been already processed, we can leverage past predictions. + +In this experiment, we discuss different temporal point sampling strategies for varying temporal window sizes of $\tau = 2,4,6$ . In the thing-propagation strategy, we exclusively sample points which are assigned only to a thing class, as they represent only a small number of all points. In the importance sampling strategy, we sample $10\%$ of points with a probability proportional to the objectness. This way, we focus on points likely to represent thing classes, while still allowing to propagate points belonging to stuff classes, which can aid the semantic segmentation of the task. Similarly, the temporal decay sampling uses the objectness score as a deciding factor, but we decay the number of sampled points based on the proximity to the current scan. Finally, the strided sampling samples points with a stride of 2 along the temporal dimension. + +As can be seen in Tab. 1, the importance sampling strategy yields higher performance compared to sampling only + +
Strategy# fr.LSTQSassocSclsIoUStIoUThMem.
Base151.9245.1659.6964.6060.401x
Thing-prop.259.2058.7159.6964.0461.161.05x
460.9463.9557.8463.9556.671.15x
658.8861.1356.7163.8653.971.25x
Importance samp.259.8658.7960.9564.9663.061.1x
462.7465.1160.4665.3661.261.3x
661.5264.2858.8865.3257.381.5x
Temporal decay259.8658.7960.9564.9663.061.1x
462.1464.0560.3065.3360.911.3x
661.0363.3458.8165.3857.111.5x
Temporal stride262.2963.5261.0865.1063.181.1x
461.6362.8960.3965.4560.391.3x
659.3359.9558.7265.3956.881.5x
+ +Table 1: Ablation study on point sampling strategies for building 4D point cloud volumes with respect to different temporal window sizes. + +
Mixing# Sc.LSTQSassocSclsIoUStIoUTh
xyz251.6543.7760.9564.9663.06
xyzt251.9544.3060.9364.8063.15
Emb.248.5843.6354.1059.5450.41
Emb. + xyz254.1556.6355.1161.1453.71
Emb. + xyzt259.8658.7960.9564.9663.06
xyz454.2948.7760.4465.2961.32
xyzt454.4649.5559.8764.8061.15
Emb.456.7760.6353.1758.0052.25
Emb. + xyz458.4363.9054.6861.1252.67
Emb. + xyzt462.7465.1160.4665.3661.26
+ +thing classes, at a slightly increased memory cost. As expected, this approach improves association quality and aids semantics as it also propagates points representing stuff. + +Interestingly, even a temporal window of size 2 drastically improves the performance compared to a single scan baseline, at negligible memory consumption $(1.1\times)$ . We observe the largest gains when the scans are temporally close: our 4-scan multi-scan baseline improves performance $51.92\rightarrow 62.74$ in terms of $LSTQ$ . The association term benefits more from processing multiple scans compared to the segmentation term. This confirms that our model learns to exploits temporal cues very well. While temporal decaying does aid semantic or temporal aspect, introducing a temporal stride of 2 yields the highest performance gains for semantic point classification. However, denser sampling in the temporal domain benefits association. Hence, we focus on the importance sampling strategy with $\tau = 4$ . In the supplementary, we highlight the performance with temporal window size $\tau = 1,2,3,4,6,8$ . As can be seen, the association accuracy is increasing up to $\tau = 4$ and then saturates, while classification accuracy saturates a $\tau = 2$ ; however, it only decreases marginally. + +**Embedding Design.** In this experiment, we study different point embeddings for clustering and show our findings in Tab. 2. We investigate the base performance of using only 3D spatial $(xyz)$ and 4D spatio-temporal point coordinates $(xyzt)$ , and using only learned embeddings (Emb.). + +Table 2: Embedding design ablation. + +
MethodPQ\( {PQ}^{ \dagger } \)SQRQmIoU
RangeNet++ [48] + PointPillars [40]37.145.975.947.052.4
KPConv [72] + PointPillars [40]44.552.580.054.458.8
Panoptic RangeNet [47]38.047.076.548.250.9
Our method (single scan)50.357.881.661.061.3
+ +Table 3: Single scan Panoptic Segmentation (test set). + +
MethodLSTQSassocSclsIoUStIoUTh
RangeNet++[48] + PP + MOT35.5224.0652.4364.5235.82
KPConv [72] + PP + MOT38.0125.8655.8666.9047.66
RangeNet++[48] + PP + SFP34.9123.2552.4364.5235.82
KPConv [72] + PP + SFP38.5326.5855.8666.9047.66
Our (single scan) + MOT40.1828.0757.5166.9551.50
Our (single scan) + SFP43.8833.4857.5166.9551.50
Ours (multi scan)56.8956.3657.4366.8651.64
+ +Table 4: 4D Panoptic (test set). MOT - tracking-by-detection by [76]; SFP - tracking-by-detection via scene flow based propagation [49]; PP - PointPillars [40]. + +Next, we investigate the performance of the coordinate mixing formulation that combines learned embeddings with 3D spatial and 4D spatio-temporal coordinates. As can be seen, the variant in which we combine both yields the best results, not only in terms of $S_{assoc}$ , but also $S_{cls}$ . This shows that a well-designed embedding branch has a positive effect on learning the backbone features. Note that for the baseline that uses only spatio-temporal coordinates, we still use our fully trained network. + +# 4.2. Benchmark Results + +Single-scan Prediction. First, we evaluate our method using single-scan LiDAR panoptic segmentation [5, 6] to demonstrate the effectiveness of our network solely in the spatial domain. We use points from single scans during training and testing. We follow the standard evaluation protocol and compare to published and peer-reviewed methods. + +As can be seen from Tab. 3, our method achieves state-of-the-art results on all metrics for semantic and panoptic segmentation [35, 5, 6]. The first two entries use two different networks for object detection and semantic segmentation, followed by fusion of the results. We use a single network to obtain both semantic and instance segmentation of the point cloud in a single network pass. We note that the recently proposed Panoptic RangeNet [47] and RangeNet++ [48] combined with PointPillars [40] detector operate on the range image and not the point cloud, and therefore, use a different backbone. However, KPConv with PointPillars uses the same backbone as our method. + +4D Panoptic Segmentation. For evaluation in the multi-scan setting for the 4D panoptic segmentation task, we extend all single-scan methods reported in Tab. 3, except for the Panoptic RangeNet [47]. We adapt them to the sequential domain using two strategies. AB3DMOT [76] uses a constant-velocity motion model to obtain track predictions associated with object detection based on a 3D bounding + +
MethodLSTQSassocSclsIoUStIoUThsPTQPTQsMOTSAMOTSA
RangeNet++[48] + PP + MOT43.7636.2852.7860.4942.1734.5833.83-7.88-4.57
KPConv [72] + PP + MOT46.2737.5856.9764.2154.1339.1338.11-6.16-2.41
RangeNet++[48] + PP + SFP43.3835.6652.7860.4942.1735.8335.46-3.13-0.01
KPConv [72] + PP + SFP45.9537.0756.9764.2154.1341.4441.052.836.1
MOPT [32]24.8011.7352.4162.3745.2741.8242.3912.8817.07
Our (single scan) + MOT51.9245.1659.6964.6060.4048.3647.846.6512.69
Our (single scan) + SFP45.4534.6159.6964.6060.4048.2447.723.017.93
Ours (2 scans)59.8658.7960.9564.9663.0651.1450.6729.0433.2
Ours (4 scans)62.7465.1160.4665.3661.2651.5051.200.344.8
+ +Table 5: 4D Panoptic (validation set). MOT - tracking-by-detection method by [76]; SFP - tracking-by-detection via scene flow based segment propagation [49]; PP - PointPillars [40] detector. + +
Category# Instances% Instances# ScansTPFPFNIDSPrecisionRecallMOTSASassocScls
Motorcycle2550.01220915146310.580.820.110.560.88
42317472490.240.91-2.060.810.74
Other-vehicle21380.06277836213601620.680.360.120.170.56
4102211311116990.470.48-0.100.380.55
+ +Table 6: Per-class evaluation on SemanticKITTI validation set (2 and 4 scan versions). + +box overlap. The second strategy, Scene Flow Propagation (SFP) is inspired by standard baselines that perform optical flow warping of points, followed by mask-IoU based association. This approach is commonly used in vision-based video object segmentation [46], video instance segmentation [83], and multi-object tracking and segmentation [54, 55, 74]. Instead of optical flow, we use state-of-the-art LiDAR scene flow [49]. We outline our results, obtained on the test set in Tab. 4. As can be seen, the baseline that uses KPCov [72] to obtain per-pixel classification, PointPillars (PP) detector [40] and a network for point cloud propagation (SFP [49]) performs slightly better in terms of association accuracy than the standard 3D MOT baseline. Our method that unifies all three aspects in a single network outperforms all tracking-by-detection baselines by a large margin, including our single-scan baseline. This confirms the importance of tackling all three aspects of these tasks in a unified manner. An important contribution of our paper is the finding that even when processing smaller overlapping sub-sequences with our network (and resolving intra-window associations with a simple overlap-based approach), we perform significantly better compared to single-scan baselines that use more elaborate association techniques (e.g., Kalman filter), as can be confirmed in Tab. 4. + +Metric Insights. In this section, we analyze the performance on the validation split (Tab. 5) through the lens of several evaluation metrics and analyze per-class performance (Tab. 6). Our method outperforms all baselines with respect to all metrics. However, while our 4-scan variant performs better than the 2-scan variant in terms of $LSTQ$ , we + +observe a significant drop in the MOTSA score. Our analysis shows that this is caused by negative MOTSA scores on some classes due to a decrease in precision while having fewer ID switches (see Tab. 6, and supplementary). We visualize such case in Fig. 3. As can be seen, the difference is due to the semantic interpretation of the points and not due to the segmentation and tracking quality at the instance level. This confirms the nonintuitive behavior of MOTSA, while our metric provides insights on both semantic interpretation and instance segmentation and tracking. For a more details, we refer to the supplementary. + +# 5. Conclusion + +In this paper, we extended LiDAR panoptic segmentation to the temporal domain resulting in the 4D Panoptic Segmentation task. We presented an evaluation metric suitable for analyzing this task's performance and proposed a new model. Importantly, we have shown that a single model tackling semantic segmentation and point-to-instance association jointly in space and time substantially outperforms methods that independently tackle these aspects. We hope that our unified view and model, accompanied by a public benchmark, will pave the road to future developments. + +Acknowledgements. This project funded by the Humboldt Foundation through the Sofja Kovalevskaja Award, the EU Horizon 2020 research and innovation programme under grant agreement No.101017008 (Harmony) and the German Federal Ministry of Education and Research (BMBF) under grant No.01IS18036B. The authors of this work take full responsibility for its content. We thank authors of [32] for providing results for their approach, Ismail Elezi and the whole DVL group for helpful discussions. + +# References + +[1] Anuraag Agrawal, Atsushi Nakazawa, and Haruo Takemura. MMM-classification of 3D Range Data. In ICRA, 2009. 2 +[2] Dragomir Anguelov, Ben Taskar, Vassil Chatalbashev, Daphne Koller, Dinkar Gupta, Geremy Heitz, and Andrew Ng. Discriminative Learning of Markov Random Fields for Segmentation of 3D Scan Data. In CVPR, 2005. 2 +[3] Iro Armeni, Ozan Sener, Amir R. Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3D Semantic Parsing of Large-Scale Indoor Spaces. In CVPR, 2016. 2 +[4] Ali Athar, Sabarinath Mahadevan, Aljosa Osep, Laura Leal-Taixe, and Bastian Leibe. Stem-seg: Spatio-temporal embeddings for instance segmentation in videos. In ECCV, 2020. 3, 4 +[5] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Juergen Gall. SemanticKITTI: A Dataset for Semantic Scene Understanding of LiDAR Sequences. In ICCV, 2019. 1, 2, 6, 7 +[6] Jens Behley, Andres Milioto, and Cyril Stachniss. A benchmark for LiDAR-based panoptic segmentation based on KITTI. In ICRA, 2021. 2, 6, 7 +[7] Jens Behley and Cyrill Stachniss. Efficient Surfel-Based SLAM using 3D Laser Range Data in Urban Environments. In RSS, 2018. 3 +[8] Philipp Bergmann, Tim Meinhardt, and Laura Leal-Taixe. Tracking without bells and whistles. In ICCV, 2019. 1, 3 +[9] Keni Bernstein and Rainer Stiefelhagen. Evaluating multiple object tracking performance: The clear mot metrics. JIVP, 2008:1:1-1:10, 2008. 2,4,6 +[10] Guillem Braso and Laura Leal-Taixe. Learning a neural solver for multiple object tracking. In CVPR, June 2020. 1, 3 +[11] William Brendel, Mohamed R. Amer, and Sinisa Todorovic. Multi object tracking as maximum weight independent set. CVPR, 2011. 3 +[12] Asad A. Butt and Robert T. Collins. Multi-target tracking by lagrangian relaxation to min-cost network flow. In CVPR, June 2013. 3 +[13] Holger Caesar, Varun Bankiti, Alex H. Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giacarlo Baldan, and Oscar Beijbom. nuScenes: A multimodal dataset for autonomous driving. In CVPR, 2020. 1, 2, 3 +[14] Bowen Cheng, Maxwell D Collins, Yukun Zhu, Ting Liu, Thomas S Huang, Hartwig Adam, and Liang-Chieh Chen. Panoptic-deeplab: A simple, strong, and fast baseline for bottom-up panoptic segmentation. In CVPR, 2020. 3 +[15] Christopher Choy, JunYoung Gwak, and Silvio Savarese. 4D spatio-temporal convnets: Minkowski convolutional neural networks. In CVPR, 2019. 2 +[16] Peng Chu and Haibin Ling. FAMNet: Joint learning of feature, affinity and multi-dimensional assignment for online multiple object tracking. In ICCV, 2019. 3 +[17] Marius Cordts, Mohamed Omran, Sebastian Ramos, Timo Rehfeld, Markus Enzweiler, Rodrigo Benenson, Uwe Franke, Stefan Roth, and Bernt Schiele. The cityscapes + +dataset for semantic urban scene understanding. In CVPR, 2016. 1 +[18] Angela Dai, Angel X. Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In CVPR, 2017. 1 +[19] Patrick Dendorfer, Aljosa Osep, Anton Milan, Konrad Schindler, Daniel Cremers, Ian Reid, and Stefan Roth Laura Leal-Taixe. Motchallenge: A benchmark for single-camera multiple target tracking. IJCV, pages 1-37, 2020. 1 +[20] Francis Engelmann, Martin Bokeloh, Alireza Fathi, Bastian Leibe, and Matthias Nießner. 3D-MPA: Multi Proposal Aggregation for 3D Semantic Instance Segmentation. In CVPR, 2020. 2 +[21] Andreas Ess, Bastian Leibe, Konrad Schindler, and Luc Van Gool. Robust multiperson tracking from a mobile platform. PAMI, 31(10):1831-1846, 2009. 3 +[22] Mark Everingham, Luc van Gool, Christopher K.I. Williams, John Winn, and Andrew Zisserman. The Pascal Visual Object Classes (VOC) Challenge. *IJCV*, 88(2):303–338, 2010. 1, 5 +[23] Pedro Felzenszwalb, David Mcallester, and Deva Ramanan. A Discriminatively Trained, Multiscale, Deformable Part Model. In CVPR, 2008. 1 +[24] Davi Frossard and Raquel Urtasun. End-to-end learning of multi-sensor 3d tracking by detection. ICRA, 2018. 2 +[25] Andreas Geiger, Philip Lenz, and Raquel Urtasun. Are we ready for autonomous driving? the KITTI vision benchmark suite. In CVPR, 2012. 1, 2, 6 +[26] Agrim Gupta, Piotr Dollar, and Ross Girshick. LVIS: A dataset for large vocabulary instance segmentation. In CVPR, 2019. 1 +[27] Timo Hackel, Nikolay Savinov, Lubor Ladicky, Jan D. Wegner, Konrad Schindler, and Marc Pollefeys. SEMANTIC3D.NET: A new large-scale point cloud classification benchmark. In ISPRS, 2017. 2 +[28] Kaiming He, Georgia Gkioxari, Piotr Dollár, and Ross Girshick. Mask R-CNN. In ICCV, 2017. 1 +[29] David Held, Jesse Levinson, Sebastian Thrun, and Silvio Savarese. Combining 3d shape, color, and motion for robust anytime tracking. In RSS, 2014. 3 +[30] Qingyong Hu, Bo Yang, Linhai Xie, Stefano Rosa, Yulan Guo, Zhihua Wang, Niki Trigoni, and Andrew Markham. Randla-net: Efficient semantic segmentation of large-scale point clouds. In CVPR, 2020. 2 +[31] Binh-Son Hua, Minh-Khoi Tran, and Sai-Kit Yeung. Pointwise convolutional neural networks. In CVPR, 2018. 2 +[32] Juana Valeria Hurtado, Rohit Mohan, and Abhinav Valada. MOPT: Multi-object panoptic tracking. In CVPR Workshops, 2020. 2, 3, 5, 8 +[33] Li Jiang, Hengshuang Zhao, Shaoshuai Shi, Shu Liu, Chi-Wing Fu, and Jiaya Jia. Pointgroup: Dual-set point grouping for 3d instance segmentation. In CVPR, 2020. 2 +[34] Dahun Kim, Sanghyun Woo, Joon-Young Lee, and In So Kweon. Video panoptic segmentation. In CVPR, 2020. 1, 2, 3, 5 + +[35] Alexander Kirillov, Kaiming He, Ross Girshick, Carsten Rother, and Piotr Dólár. Panoptic segmentation. In CVPR, 2019. 1, 2, 4, 5, 7 +[36] Artem Komarichev, Zichun Zhong, and Jing Hua. A-cnn: Annually convolutional neural networks on point clouds. In CVPR, 2019. 2 +[37] Alex Krizhevsky, Ilya Sutskever, and Geoffrey Hinton. Image-net classification with deep convolutional neural networks. In NIPS, 2012. 1 +[38] Shiyi Lan, Ruichi Yu, Gang Yu, and Larry S Davis. Modeling local geometric structure of 3d point clouds using geo-cnn. In CVPR, 2019. 2 +[39] Loic Landrieu and Martin Simonovsky. Large-scale point cloud semantic segmentation with superpoint graphs. In CVPR, 2018. 2 +[40] Alex H Lang, Sourabh Vora, Holger Caesar, Lubing Zhou, Jiong Yang, and Oscar Beijbom. Pointpillars: Fast encoders for object detection from point clouds. In CVPR, 2019. 1, 2, 3, 7, 8 +[41] Laura Leal-Taixe, Cristian Canton-Ferrer, and Konrad Schindler. Learning by tracking: Siamese cnn for robust target association. CVPR Workshops, 2016. 3 +[42] Laura Leal-Taixe, Gerard Pons-Moll, and Bodo Rosenhahn. Everybody needs somebody: Modeling social and grouping behavior on a linear programming multiple people tracker. In ICCV Workshops, 2011. 3 +[43] Bastian Leibe, Konrad Schindler, Nico Cornelis, and Luc Van Gool. Coupled object detection and tracking from static cameras and moving vehicles. PAMI, 30(10):1683-1698, 2008. 1, 3 +[44] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dolkar, and C. Lawrence Zitnick. Microsoft COCO: Common objects in context. In ECCV, 2014. 1 +[45] Jonathon Luiten, Aljosa Osep, Patrick Dendorfer, Philip Torr, Andreas Geiger, Laura Leal-Taixe, and Bastian Leibe. Hota: A higher order metric for evaluating multi-object tracking. IJCV, 2020. 2, 5 +[46] Jonathon Luiten, Paul Voigtlaender, and Bastian Leibe. Premvos: Proposal-generation, refinement and merging for video object segmentation. In ACCV, 2018. 8 +[47] Andres Milioto, Jens Behley, Chris McCool, and Cyril Stachniss. Lidar panoptic segmentation for autonomous driving. In IROS, 2020. 2, 7 +[48] Andres Milioto, Ignacio Vizzo, Jens Behley, and Cyril Stachniss. RangeNet++: Fast and Accurate LiDAR Semantic Segmentation. In IROS, 2019. 1, 2, 7, 8 +[49] Himangi Mittal, Brian Okorn, and David Held. Just go with the flow: Self-supervised scene flow estimation. In CVPR, 2020. 7, 8 +[50] Daniel Munoz, J. Andrew Bagnell, Nicolas Vandapel, and Martial Hebert. Contextual Classification with Functional Max-Margin Markov Networks. In CVPR, 2009. 2 +[51] Davy Neven, Bert De Brabandere, Marc Proesmans, and Luc Van Gool. Instance segmentation by jointly optimizing spatial embeddings and clustering bandwidth. In CVPR, 2019. 3, 4 + +[52] Kenji Okuma, Ali Taleghani, Nando De Freitas, James J Little, and David G Lowe. A boosted particle filter: Multitarget detection and tracking. In ECCV, 2004. 3 +[53] Aljoša Osep, Wolfgang Mehner, Markus Mathias, and Bastian Leibe. Combined image- and world-space tracking in traffic scenes. In ICRA, 2017. 1, 3 +[54] Aljoša Osep, Wolfgang Mehner, Paul Voigtlaender, and Bastian Leibe. Track, then decide: Category-agnostic vision-based multi-object tracking. ICRA, 2018. 8 +[55] Aljosa Osep, Paul Voigtlaender, Mark Weber, Jonathon Luiten, and Bastian Leibe. 4d generic video object proposals. ICRA, 2020. 8 +[56] Hamed Pirsiavash, Deva Ramanan, and Charles C.Fowlkes. Globally-optimal greedy algorithms for tracking a variable number of objects. In CVPR, 2011. 3 +[57] Lorenzo Porzi, Samuel Rota Bulo, Aleksander Colovic, and Peter Kontschieder. Seamless scene segmentation. In CVPR, 2019. 2, 5 +[58] Johannes Pöschmann, Tim Pfeifer, and Peter Protzel. Factor graph based 3d multi-object tracking in point clouds. arXiv preprint arXiv:2008.05309, 2020. 1 +[59] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In CVPR, 2017. 1, 2 +[60] Charles R Qi, Li Yi, Hao Su, and Leonidas J Guibas. Point-net++: Deep hierarchical feature learning on point sets in a metric space. In NIPS, 2017. 1, 2 +[61] Haozhe Qi, Chen Feng, Zhiguo Cao, Feng Zhao, and Yang Xiao. P2b: Point-to-box network for 3d object tracking in point clouds. In CVPR, 2020. 1 +[62] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster R-CNN: Towards real-time object detection with region proposal networks. In NIPS, 2015. 1 +[63] Hanyu Shi, Guosheng Lin, Hao Wang, Tzu-Yi Hung, and Zhenhua Wang. Spsequencenet: Semantic segmentation network on 4d point clouds. In CVPR, 2020. 2 +[64] Shaoshuai Shi, Chaoxu Guo, Li Jiang, Zhe Wang, Jianping Shi, Xiaogang Wang, and Hongsheng Li. Pv-rcnn: Point-voxel feature set abstraction for 3d object detection. In CVPR, 2020. 1 +[65] Shaoshuai Shi, Xiaogang Wang, and Hongsheng Li. PointR-CNN: 3D Object Proposal Generation and Detection From Point Cloud. In CVPR, 2019. 1, 3 +[66] Shaoshuai Shi, Zhe Wang, Jianping Shi, Xiaogang Wang, and Hongsheng Li. From Points to Parts: 3D Object Detection from Point Cloud with Part-aware and Part-aggregation Network. PAMI, 2020. 1 +[67] Jeany Son, Mooyeol Baek, Minsu Cho, and Bohyung Han. Multi-object tracking with quadruplet convolutional neural networks. In CVPR, 2017. 3 +[68] Pei Sun, Henrik Kretzschmar, Xerxes Dotiwalla, Aurelien Chouard, Vijaysai Patnaik, Paul Tsui, James Guo, Yin Zhou, Yuning Chai, Benjamin Caine, et al. Scalability in perception for autonomous driving: Waymo open dataset. In CVPR, 2020. 1, 2, 3 +[69] Haotian Tang, Zhijian Liu, Shengyu Zhao, Yujun Lin, Ji Lin, Hanrui Wang, and Song Han. Searching Efficient 3D Ar + +chitectures with Sparse Point-Voxel Convolution. In ECCV, 2020.1 +[70] Maxim Tatarchenko, Jaesik Park, Vladlen Koltun, and Qian-Yi Zhou. Tangent convolutions for dense prediction in 3d. In CVPR, 2018. 2 +[71] Alex Teichman and Sebastian Thrun. Tracking-based semi-supervised learning. *IJRR*, 31(7):804–818, 2012. 3 +[72] Hugues Thomas, Charles R. Qi, Jean-Emmanuel Deschaud, Beatz Marcotegui, François Goulette, and Leonidas J. Guibas. Kpconv: Flexible and deformable convolution for point clouds. In ICCV, 2019. 1, 2, 4, 7, 8 +[73] Rudolph Triebel, Krisitian Kersting, and Wolfram Burgard. Robust 3D Scan Point Classification using Associative Markov Networks. In ICRA, 2006. 2 +[74] Paul Voigtlaender, Michael Krause, Aljoša Osep, Jonathon Luiten, B.B.G Sekar, Andreas Geiger, and Bastian Leibe. MOTS: Multi-object tracking and segmentation. In CVPR, 2019. 1, 2, 3, 4, 8 +[75] Mark Weber, Jun Xie, Maxwell Collins, Yukun Zhu, Paul Voigtaender, Hartwig Adam, Bradley Green, Andreas Geiger, Bastian Leibe, Daniel Cremers, Aljosa Osep, Laura Leal-Taixe, and Liang-Chieh Chen. STEP: Segmenting and Tracking Every Pixel. arXiv preprint arXiv:2102.11859, 2021. 2, 5, 6 +[76] Xinshuo Weng, Jianren Wang, David Held, and Kris Kitani. 3D Multi-Object Tracking: A Baseline and New Evaluation Metrics. IROS, 2020. 1, 2, 3, 7, 8 +[77] Xinshuo Weng, Yongxin Wang, Yunze Man, and Kris Kitani. GNN3DMOT: Graph neural network for 3d multi-object tracking with multi-feature learning. In CVPR, 2020. 2 +[78] Kelvin Wong, Shenlong Wang, Mengye Ren, Ming Liang, and Raquel Urtasun. Identifying unknown instances for autonomous driving. In CoRL, 2020. 2 +[79] Bichen Wu, Alvin Wan, Xiangyu Yue, and Kurt Keutzer. Squeezeseg: Convolutional neural nets with recurrent crf for real-time road-object segmentation from 3d lidar point cloud. In ICRA, 2018. 2 +[80] Bichen Wu, Xuanyu Zhou, Sicheng Zhao, Xiangyu Yue, and Kurt Keutzer. Squeezesegv2: Improved model structure and unsupervised domain adaptation for road-object segmentation from a lidar point cloud. In ICRA, 2019. 2 +[81] Xuehan Xiong, Daniel Munoz, J. Andrew Bagnell, and Martial Hebert. 3-D Scene Analysis via Sequenced Predictions over Points and Regions. In ICRA, 2011. 2 +[82] Yihong Xu, Aljosa Osep, Yutong Ban, Radu Horaud, Laura Leal-Taixe, and Xavier Alameda-Pineda. How to train your deep multi-object tracker. In CVPR, 2020. 3 +[83] Linjie Yang, Yuchen Fan, and Ning Xu. Video instance segmentation. In ICCV, 2019. 1, 2, 3, 5, 8 +[84] Li Zhang, Li Yuan, and Ramakant Nevatia. Global data association for multi-object tracking using network flows. In CVPR, 2008. 3 +[85] Yang Zhang, Zixiang Zhou, Philip David, Xiangyu Yue, Zerong Xi, Boqing Gong, and Hassan Foroosh. Polarnet: An improved grid representation for online lidar point clouds semantic segmentation. In CVPR, 2020. 1, 2 + +[86] Xingyi Zhou, Vladlen Koltun, and Philipp Krahenbuhl. Tracking objects as points. 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Feature Pyramid Network (FPN) is the classic architecture to build a feature pyramid with high-level semantics throughout. However, intrinsic defects in feature extraction and fusion inhibit FPN from further aggregating more discriminative features. In this work, we propose Attention Aggregation based Feature Pyramid Network ( $A^2$ -FPN), to improve multi-scale feature learning through attention-guided feature aggregation. In feature extraction, it extracts discriminative features by collecting-distributing multi-level global context features, and mitigates the semantic information loss due to drastically reduced channels. In feature fusion, it aggregates complementary information from adjacent features to generate location-wise reassembly kernels for content-aware sampling, and employs channel-wise reweighting to enhance the semantic consistency before element-wise addition. $A^2$ -FPN shows consistent gains on different instance segmentation frameworks. By replacing FPN with $A^2$ -FPN in Mask R-CNN, our model boosts the performance by $2.1\%$ and $1.6\%$ mask AP when using ResNet-50 and ResNet-101 as backbone, respectively. Moreover, $A^2$ -FPN achieves an improvement of $2.0\%$ and $1.4\%$ mask AP when integrated into the strong baselines such as Cascade Mask R-CNN and Hybrid Task Cascade. + +# 1. Introduction + +Instance segmentation is one of the most challenging tasks in computer vision. It aims to categorize and localize individual objects with pixel-wise instance masks. Accurate instance segmentation has wide applications in real scenarios including automatic driving and video surveillance. Driven by the rapid advances in deep convolutional networks (ConvNets), the development of instance segmentation frameworks, e.g., Mask R-CNN [14], PANet [26], and + +![](images/baad2ec5988f468fe02d720a7d30e6e613c4f483446429bf54846be73ca86ad3.jpg) +Figure 1. Defects in the construction of feature pyramid: (1) information loss, (2) content-agnostic sampling, and (3) semantic inconsistency between adjacent features. + +HTC [5], has substantially pushed forward the state-of-the-art. Learning multi-scale feature representations is of great significance because high-performance instance segmentation needs to recognize varying numbers of instances across a broad range of scales and locations. + +To address the issue of multi-scale processing, Feature Pyramid Network (FPN) [22] is widely adopted in existing frameworks. FPN leverages the inherent feature hierarchy and constructs a feature pyramid that has strong semantics at all scales by fusing adjacent features through lateral connections and a top-down pathway. PAFPN in PANet [26] shortens the information path from the low level to top ones by adding an extra bottom-up pathway, further improving the localization capability of the feature pyramid. + +Although FPN and PAFPN are effective in learning multi-scale feature representations, the simple designs inhibit feature pyramids from further aggregating more discriminative features. We decompose the construction of feature pyramid into feature extraction and fusion, and find each step has some intrinsic defects, as shown in Figure 1. + +In feature extraction, lateral connections using $1 \times 1$ convolutional layers are employed to generate features of the same channel dimension. However, the extracted feature maps, especially the high levels, suffer from serious information loss because of drastic dimension reduction. In the first step of feature fusion, feature maps are upsampled using interpolation in the top-down pathway or downsam + +pled through strided convolution in the bottom-up pathway. However, interpolation executes the upsampling process in a sub-pixel neighborhood according to the relative positions of pixels, failing to capture rich semantic information. Strided convolution applies the content-agnostic downsampling kernel across the entire image, neglecting the underlying content of features. In the second step of feature fusion, two adjacent features are merged by element-wise addition, which ignores the semantic gap between feature maps caused by different depths. + +In this work, we propose Attention Aggregation based Feature Pyramid Network ( $A^2$ -FPN), to improve multiscale feature learning through attention-guided feature aggregation. Compared to existing frameworks, $A^2$ -FPN is distinctive in three significant aspects: (1) It extracts discriminative features by collecting global context features from the whole feature hierarchy and distributing them to each level. (2) It aggregates complementary information from adjacent features to produce location-wise reassembly kernels for content-aware upsampling and downsampling. (3) It applies channel-wise reweighting to enhance the semantic consistency before element-wise addition. + +Without bells and whistles, $A^2$ -FPN in Mask R-CNN framework leads to an improvement of $2.1\%$ and $1.6\%$ mask AP compared with the FPN based counterpart when using ResNet-50 and ResNet-101 as backbone, respectively. Moreover, when integrated into the state-of-the-art instance segmentation methods such as Cascade Mask RCNN and HTC [5], it achieves $2.0\%$ and $1.4\%$ higher mask AP than baseline models on the MS COCO dataset [24]. + +Our main contributions are summarized as follows: (1) We propose Attention Aggregation based Feature Pyramid Network ( $A^2$ -FPN), which effectively aggregates pyramidal feature representations through attention-guided feature extraction and fusion. (2) We demonstrate that not only cross-scale connections are important, but the node operations to aggregate features are also crucial to the construction of feature pyramid. (3) We evaluate $A^2$ -FPN on the challenging COCO dataset [24] through comprehensive experiments, and it can bring consistent and substantial improvements upon various frameworks and backbone networks. + +# 2. Related Work + +Instance Segmentation. Current instance segmentation methods can be roughly divided into two categories, detection-based and segmentation-based. Detection-based methods employ object detectors [32, 23, 33, 3] to generate region proposals or bounding boxes, and then produce a pixel-wise mask for each instance. DeepMask [30], SharpMask [31] and MultiPathNet [41] predict object segments using discriminative ConvNets and improve progressively. MNC [8] decomposes instance segmentation into three sub-tasks: instance differentiation, mask estimation, + +and object categorization. FCIS [20] is proposed to predict instance masks fully convolutionally based on InstanceFCN [8]. Mask R-CNN [14] extends Faster R-CNN [33] by adding a mask prediction branch in parallel with the existing branch for classification and bounding box regression. PANet [26] shortens the information path in FPN [22] by adding an extra bottom-up pathway and aggregates features from all levels through adaptive feature pooling. Mask Scoring R-CNN [17] calibrates the misalignment between mask quality and mask score by learning a maskIoU for each mask instead of using its classification score. HTC [5] integrates cascade into instance segmentation by interweaving bounding box regression and mask prediction in a multi-stage cascade manner, and incorporates contextual information by adding a semantic segmentation branch. + +Segmentation-based methods first exploit a pixel-wise segmentation map over the entire image and then group the pixels of different instances. InstanceCut [18] combines semantic segmentation and boundary detection for instance partition. SGN [25] employs a sequence of neural networks to handle progressive sub-grouping problems. Deep learning and watershed transform are integrated in [2] to produce pixel-level energy values for instance derivation. Recent methods [9, 29, 10] use metric learning to learn per-pixel embedding and group pixels to form the instance masks. + +Feature Pyramid. Pyramidal feature representations form the basis of solutions to multi-scale problems. SSD [27] firstly attempts to perform object detection on the pyramidal features. FPN [22] builds a feature pyramid of strong semantics through lateral connections and a top-down pathway. Based on FPN, PAFPN in PANet [26] introduces bottom-up augmentation to facilitate the information flow. EfficientDet [35] repeats bidirectional path multiple times for more high-level feature fusion. NAS-FPN [12] takes advantage of neural architecture search to seek a more powerful feature pyramid structure. Unlike the previous works that focus on the topological structure constructed by different cross-scale connections, node operations to aggregate features are explored in this work. + +Attention Mechanism. Self-attention is first proposed in [36] for machine translation, where scaled dot-product attention is adopted. The effectiveness of Non-local operation to computer vision tasks is explored later in [38]. Graph reasoning is employed to model semantic nodes in [19, 21, 7, 42]. However, multi-level global context modeling is rarely explored in detectors. Channel attention is used to explicitly model interdependencies between channels in [16]. DANet [11] and GCNet [4] combine self-attention and channel attention to capture rich contextual dependencies. + +# 3. Methodology + +The overall framework of $A^2$ -FPN is illustrated in Figure 2. We take ResNet [15] as backbone like FPN [22] and + +![](images/2a6186f25ee67663d703060e65f6ba6014fc6b3ec53b4d581d43c7a2b8da88cc.jpg) +Figure 2. Overall pipeline of $A^2$ -FPN. $A^2$ -FPN extracts and fuses the pyramidal features progressively through three proposed modules, the MGC module, the GACARAFE module, and the GACAP module. For brevity, only three feature levels are plotted here. + +utilize $\{\mathcal{F}_2^{bb},\mathcal{F}_3^{bb},\mathcal{F}_4^{bb},\mathcal{F}_5^{bb}\}$ to denote the feature hierarchy. In addition, an extra feature $\mathcal{F}_6^{bb}$ is produced through a $3\times 3$ convolutional layer with stride 2 from the feature $\mathcal{F}_5^{bb}$ . Note that the pyramidal features have strides of $\{4,8,16,32,64\}$ pixels w.r.t. the input image. $\{\mathcal{P}_2^{lc},\mathcal{P}_3^{lc},\mathcal{P}_4^{lc},\mathcal{P}_5^{lc},\mathcal{P}_6^{lc}\}$ are the context-rich features extracted from the feature hierarchy in the Multi-level Global Context (MGC) module (Section 3.1). $\{\mathcal{P}_2^{td},\mathcal{P}_3^{td},\mathcal{P}_4^{td},\mathcal{P}_5^{td},\mathcal{P}_6^{td}\}$ are the features after top-down path augmentation with the Global Attention CARAFE (GACARAFE) module (Section 3.2), and $\{\mathcal{P}_2^{bu},\mathcal{P}_3^{bu},\mathcal{P}_4^{bu},\mathcal{P}_5^{bu},\mathcal{P}_6^{bu}\}$ are the features after bottom-up path augmentation with the Global Attention Content-Aware Pooling (GACAP) module (Section 3.3). + +# 3.1. Multi-level Global Context + +In feature extraction, pyramidal features suffer from information loss due to channel reduction. ParseNet [28] distributes the global context feature to all locations for information supplement. However, a single context feature collected by global average pooling ignores different needs across scales and locations. Inspired by this, we propose the Multi-level Global Context (MGC) module to extract more discriminative features by aggregating multi-level global context features and mitigate semantic information loss. + +MGC consists of three steps to adaptively aggregate global context features from the feature hierarchy, as shown in Figure 3. First, the Context Collector collects global context features from all feature levels through attention pooling. Second, the Graph Convolutional Networks (GCNs) are employed to reason contextual relations. Third, the Context Distributor distributes the context features to each level. Each step will be discussed in detail as follows. + +Context Collector. Given the i-th feature $\mathcal{F}_i^{bb} \in \mathbb{R}^{c_i \times h \times w}$ from the backbone, where $c_i$ denotes channel dimension and $h, w$ are spatial size, Context Collector generates a new feature $\mathcal{G}_i \in \mathbb{R}^{c \times n_i}$ comprising $n_i$ different context features of dimension $c$ . Inspired by AN [39], we assume that the features of different stages differ in semantic richness and intensity, and are composed of diverse semantic entities. Here the feature $\mathcal{F}_i^{bb}$ is supposed to consist + +of $n_i$ semantic entities, and the feature points are gathered into different context features according to their cosine similarity to the semantic entities. + +In Context Collector, one $1 \times 1$ convolutional layer $\psi$ with $n_i$ filters is adopted as semantic entities, and another $1 \times 1$ convolutional layer $\phi$ is used to embed the input feature. In particular, we formulate this procedure as Eqn. 1. + +$$ +\mathcal {G} _ {i} = W _ {\phi} \mathcal {F} _ {i} ^ {b b} \operatorname {S o f t m a x} \left(\sqrt {c _ {i}} \cdot W _ {\psi} \operatorname {N o r m} \left(\mathcal {F} _ {i} ^ {b b}\right)\right) ^ {T}, \tag {1} +$$ + +$$ +L _ {o} = \lambda_ {o} \| W _ {\psi} W _ {\psi} ^ {T} - I \| _ {F} ^ {2}, \tag {2} +$$ + +where $W_{\psi} \in \mathbb{R}^{n_i \times c_i}$ , $W_{\phi} \in \mathbb{R}^{c \times c_i}$ , and Norm represents $L_2$ normalization. To normalize the semantic entities for computing cosine similarity and learn more diverse patterns, orthogonal regularization is applied to the weights $W_{\psi}$ as shown in Eqn. 2. Different from the scaled dot-product attention in [36] which divides each dot product by $\sqrt{c_i}$ , we multiply the cosine similarity by $\sqrt{c_i}$ to maintain the variance at different values of $c_i$ . Then we apply a softmax function spatially to generate the attention masks, and collect context features using attention pooling accordingly. + +We call our particular attention mechanism "Scaled Cosine-similarity Attention", which computes the compatibility function based on scaled cosine similarity. It focuses on semantic content instead of intensity and can avoid strongly activated keys surpassing other keys. For brevity, we reformulate the compatibility function out of Eqn. 1: + +$$ +\boldsymbol {C F} \left(W _ {\psi} ^ {T}, \mathcal {F} _ {i} ^ {b b}, c _ {i}\right) = \operatorname {S o f t m a x} \left(\sqrt {c _ {i}} \cdot W _ {\psi} \operatorname {N o r m} \left(\mathcal {F} _ {i} ^ {b b}\right)\right) ^ {T}. \tag {3} +$$ + +GCN. Once we obtain context features $\mathcal{G}_i\in \mathbb{R}^{c\times n_i}$ , we utilize GCNs to model and reason the contextual relations between them first in single level. The formula of the GCN with a residual connection [15] is interpreted as Eqn. 4, where $W_{1}^{gcn}\in \mathbb{R}^{\frac{c}{4}\times c},W_{2}^{gcn}\in \mathbb{R}^{\frac{c}{4}\times c},W_{3}^{gcn}\in \mathbb{R}^{c\times c}$ are weight matrices of 1D convolutional layers. The convolutional weight of the GCN is $W_{3}^{gcn}$ and the adjacent matrix is dynamically generated through self-attention described in Eqn. 3. After contextual relations are reasoned in each level independently, all context features are concatenated and reasoned together in multi-level by the GCN as Eqn. + +![](images/66ff3e02e8a617eeddabbe96c0e2ddd092ce8ce3c2b9c15bec007e7b43b1f038.jpg) +Figure 3. Detailed illustration of the Multi-level Global Context (MGC) module. MGC collects, reasons, and distributes multi-level global context features through three children modules, the Context Collector, the GCNs, and the Context Distributor, respectively. + +5. In this work, we collect $\{n_2, n_3, n_4, n_5\}$ context features from the feature maps $\{\mathcal{F}_2^{bb}, \mathcal{F}_3^{bb}, \mathcal{F}_4^{bb}, \mathcal{F}_5^{bb}\}$ , respectively. + +$$ +\tilde {\mathcal {G}} _ {i} = W _ {3} ^ {g c n} \mathcal {G} _ {i} C F (W _ {1} ^ {g c n} \mathcal {G} _ {i}, W _ {2} ^ {g c n} \mathcal {G} _ {i}, \frac {c}{4}) + \mathcal {G} _ {i}, \quad (4) +$$ + +$$ +\tilde {\mathcal {G}} = \boldsymbol {G} \boldsymbol {C} \boldsymbol {N} ([ \dots , \tilde {\mathcal {G}} _ {i - 1}, \tilde {\mathcal {G}} _ {i}, \tilde {\mathcal {G}} _ {i + 1}, \dots ]). \tag {5} +$$ + +Context Distributor. Context Distributor distributes the multi-level global context features $\tilde{\mathcal{G}}\in \mathbb{R}^{c\times n}$ to each level using the proposed scaled cosine-similarity attention. As shown in Eqn. 6, $W_{o}\in \mathbb{R}^{c\times c}$ , $W_{\theta}\in \mathbb{R}^{c\times c_i}$ and $W_{\xi}\in \mathbb{R}^{c\times c_i}$ are weights of $1\times 1$ convolutional layers. The feature maps $\mathcal{F}_i^{bb}$ are queries and the global context features $\tilde{\mathcal{G}}$ are shared as keys and values. + +$$ +\mathcal {P} _ {i} ^ {l c} = W _ {o} \tilde {\mathcal {G}} C F (W _ {\theta} \mathcal {F} _ {i} ^ {b b}, \tilde {\mathcal {G}}, c) + W _ {\xi} \mathcal {F} _ {i} ^ {b b}. \qquad (6) +$$ + +# 3.2. Global Attention CARAFE + +In the top-down pathway of feature fusion, interpolation depends only on the relative positions and direct elementwise addition ignores the semantic gap between adjacent features. Recently, CARAFE [37] is proposed to upsample features through content-aware reassembly. However, CARAFE only leverages the information of low-resolution feature and fails to capture complementary semantics from the high-resolution level. As shown in Figure 4 (left), we propose the Global Attention CARAFE (GACARAFE) module for feature fusion, where the complementary information is aggregated to guide content-aware upsampling and channel attention [16] is employed to enhance the semantic consistency before merging adjacent features. + +The feature $\mathcal{P}_i^{lc} \in \mathbb{R}^{c \times h \times w}$ is extracted through the MGC module and the feature $\mathcal{P}_{i+1}^{td} \in \mathbb{R}^{c \times \frac{h}{s} \times \frac{w}{s}}$ is the upper level in the top-down pathway, where $s = 2$ is the scale factor. We downsample the feature $\mathcal{P}_i^{lc}$ using max-pooling and concatenate $\mathcal{P}_{i+1}^{td}$ and $\tilde{\mathcal{P}}_i^{lc}$ together. As shown in Figure 4 (left), the feature $\mathcal{P}_{i+1}^{td}$ is upsampled as $\tilde{\mathcal{P}}_{i+1}^{td}$ through two steps. GACARAFE predicts a location-wise kernel $\mathcal{K}_{i+1}^{up}(x,y)$ based on the $k_{en}^{up} \times k_{en}^{up}$ neighbor of feature + +points $\mathcal{P}_{i + 1}^{td}\left(\frac{x}{s},\frac{y}{s}\right)$ and $\tilde{\mathcal{P}}_i^{lc}\left(\frac{x}{s},\frac{y}{s}\right)$ , as shown in Eqn. 7. And then it reassembles the $k_{up}\times k_{up}$ neighbor of $\mathcal{P}_{i + 1}^{td}\left(\frac{x}{s},\frac{y}{s}\right)$ with the kernel $\mathcal{K}_{i + 1}^{up}(x,y)$ , as presented in Eqn. 8. + +$$ +\mathcal {K} _ {i + 1} ^ {u p} (x, y) = \pmb {K} (\mathcal {N} ([ \mathcal {P} _ {i + 1} ^ {t d}, \tilde {\mathcal {P}} _ {i} ^ {l c} ] (\frac {x}{s}, \frac {y}{s}), k _ {e n} ^ {u p})), \quad (7) +$$ + +$$ +\tilde {\mathcal {P}} _ {i + 1} ^ {t d} (x, y) = \boldsymbol {R} (\mathcal {N} (\mathcal {P} _ {i + 1} ^ {t d} (\frac {x}{s}, \frac {y}{s}), k _ {u p}), \mathcal {K} _ {i + 1} ^ {u p} (x, y)), \quad (8) +$$ + +where $\pmb{K}$ and $\pmb{R}$ are the kernel prediction module and content-aware reassembly module altered from CARAFE [37], respectively. The kernel prediction module contains three convolutions: the first one of $1\times 1$ kernel for reducing channel dimension from $2c$ to $c_{m}^{up}$ , the second one of $3\times 3$ kernel with ReLU activation for blending features, and the third one of $k_{en}^{up}\times k_{en}^{up}$ kernel for predicting upsampling kernels. The kernels $\mathcal{K}_{i + 1}^{up}$ are deformed using pixel shuffle [34] and normalized with a softmax function. + +Besides, we apply channel attention to learn two vectors $\hat{S}_i^{up}$ and $\check{S}_i^{up}$ to recalibrate the adjacent features. As shown in Eqn. 9, we squeeze the global spatial information into a channel descriptor using attention pooling. Specifically, a $1\times 1$ convolutional layer is employed to predict the attention mask $\mathcal{M}_i^{up}$ and channel-wise statistics $\mathcal{Z}_i^{up}$ is generated by shrinking the concatenated feature accordingly. And then a simple gating mechanism with $2\cdot$ sigmoid activation is adopted to model channel-wise interdependencies. + +$$ +\mathcal {M} _ {i} ^ {u p} = \operatorname {S o f t m a x} \left(W _ {1} ^ {u p} \left[ \mathcal {P} _ {i + 1} ^ {t d}, \tilde {\mathcal {P}} _ {i} ^ {l c} \right]\right) ^ {T}, +$$ + +$$ +\mathcal {Z} _ {i} ^ {u p} = \left[ \mathcal {P} _ {i + 1} ^ {t d}, \tilde {\mathcal {P}} _ {i} ^ {l c} \right] \mathcal {M} _ {i} ^ {u p}, \tag {9} +$$ + +$$ +[ \tilde {S} _ {i} ^ {u p}, \tilde {S} _ {i} ^ {u p} ] = 2 \sigma \left(W _ {3} ^ {u p} \operatorname {R e L U} \left(\operatorname {L N} \left(W _ {2} ^ {u p} \mathcal {Z} _ {i} ^ {u p}\right)\right)\right). +$$ + +Here LN stands for LayerNorm [1], $W_1^{up} \in \mathbb{R}^{1 \times 2c}$ , $W_2^{up} \in \mathbb{R}^{\frac{c}{2} \times 2c}$ and $W_3^{up} \in \mathbb{R}^{2c \times \frac{c}{2}}$ . $2\sigma$ indicates the activation function $2 \cdot$ sigmoid, which can keep the mean of channel-wise weights being 1 after successive multiplications and excite or restrain features selectively. Finally, the adjacent features $\tilde{\mathcal{P}}_{i+1}^{td}$ and $\mathcal{P}_i^{lc}$ are reweighted and merged by element-wise addition as shown in Eqn. 10. + +$$ +\mathcal {P} _ {i} ^ {t d} = \hat {\mathcal {S}} _ {i} ^ {u p} \odot \tilde {\mathcal {P}} _ {i + 1} ^ {t d} + \check {\mathcal {S}} _ {i} ^ {u p} \odot \mathcal {P} _ {i} ^ {l c}. \tag {10} +$$ + +![](images/ba93b1cb45011144eb780e0f53f48642d7bf4a2cba221ffaf45fae50d01fefca.jpg) +Figure 4. The details of the Global Attention CARAFE (GACARAFE) module (left) and the Global Attention Content-Aware Pooling (GACAP) module (right). Noting that the fused features $\mathcal{P}_i^{td}$ and $\mathcal{P}_i^{bu}$ after element-wise addition are omitted for simplification. + +![](images/d615d4b0bcb91ebfe29b201252f1b411f84c347d5e941c8d38926a60406ceed2.jpg) + +# 3.3. Global Attention Content-Aware Pooling + +In the bottom-up pathway, stripped convolution applies the same kernel across the entire image and ignores the underlying content. To aggregate more discriminative features, we propose the Global Attention Content-Aware Pooling (GACAP) module to execute the bottom-up fusion. As shown in Figure 4 (right), the Content-Aware Pooling (CAP) operator extends the idea of CARAFE [37] to feature pooling and the GACAP module differs from the GACARAFE module in several aspects. + +First, GACAP unsamples the feature $\mathcal{P}_i^{td} \in \mathbb{R}^{c \times h \times w}$ to get $\tilde{\mathcal{P}}_i^{td}$ through bilinear interpolation and concatenates $\mathcal{P}_{i-1}^{bu} \in \mathbb{R}^{c \times sh \times sw}$ with it. Second, GACAP downsamples the feature $\mathcal{P}_{i-1}^{bu}$ as $\tilde{\mathcal{P}}_{i-1}^{bu}$ , as shown in Eqn. 11 and 12. + +$$ +\begin{array}{l} \mathcal {K} _ {i - 1} ^ {d n} (x, y) = \boldsymbol {K} (\mathcal {N} ([ \mathcal {P} _ {i - 1} ^ {b u}, \tilde {\mathcal {P}} _ {i} ^ {t d} ] (s x, s y), k _ {e n} ^ {d n})), (11) \\ \tilde {\mathcal {P}} _ {i - 1} ^ {b u} (x, y) = \boldsymbol {R} \left(\mathcal {N} \left(\mathcal {P} _ {i - 1} ^ {b u} \left(s x, s y\right), k _ {d n}\right), \mathcal {K} _ {i - 1} ^ {d n} (x, y)\right), (12) \\ \end{array} +$$ + +where the kernel prediction module $\pmb{K}$ applies a $k_{en}^{dn} \times k_{en}^{dn}$ convolutional layer with stride $s$ to generate downsampling kernels $\mathcal{K}_{i-1}^{dn}$ directly. The other parts of GACAP are exactly the same with GACARAFE described in Section 3.2. After the channel attention vectors $\hat{S}_i^{dn}$ and $\check{S}_i^{dn}$ are obtained, the adjacent features are fused to generate feature $\mathcal{P}_i^{bu}$ as Eqn. 13. Notably, we finally append a $3 \times 3$ convolution on each merged feature map to reduce the aliasing effect, whether in the top-down pathway or the bottom-up pathway. + +$$ +\mathcal {P} _ {i} ^ {b u} = \hat {\mathcal {S}} _ {i} ^ {d n} \odot \mathcal {P} _ {i} ^ {t d} + \tilde {\mathcal {S}} _ {i} ^ {d n} \odot \tilde {\mathcal {P}} _ {i - 1} ^ {b u}. \tag {13} +$$ + +# 4. Experiments + +# 4.1. Datasets and Evaluation Metrics + +Datasets. We conduct experiments on the challenging MS COCO dataset [24]. It contains 115k images for train- + +ing (train2017), 5k images for validation (val2017), and 20k images for testing (test-dev). The labels of test-dev are not publicly available. We train our models on train2017 subset and report results on val2017 subset for ablation study. we also report results on test-dev for comparison. + +Evaluation Metrics. We report the standard COCO-style Average Precision (AP) metric including AP (averaged over IoU thresholds), $\mathrm{AP}_{50}$ , $\mathrm{AP}_{75}$ (AP at different IoU thresholds), and $\mathrm{AP}_S$ , $\mathrm{AP}_M$ , $\mathrm{AP}_L$ (AP at different scales). Since our framework is general to both instance segmentation and object detection, both mask AP and box AP (superscripted as “bb”) are evaluated. + +# 4.2. Implementation Details + +All experiments are implemented based on MMDetection [6]. We train detectors with a batchsize of 8 over 4 GPUs (2 images per GPU) for 12 epochs with an initial learning rate of 0.01, and decrease it by 0.1 after 8 and 11 epochs, respectively. Images are resized to a maximum scale of $1333 \times 800$ pixels without changing the aspect ratio. If not otherwise specified, $A^2$ -FPN adopts a fixed set of hyper-parameters in experiments, where $c = 256$ , $n_i = 64(6 - i)$ , and $\lambda_o = 0.0001$ in Eqn. 2 in the MGC module, $C_m^{up} = 64$ , $k_{en}^{up} = 3$ and $k_{up} = 5$ in the GACARAFE module, $C_m^{dn} = 64$ , $k_{en}^{dn} = 3$ and $k_{dn} = 5$ in the GACAP module. All other hyper-parameters in this work follow the default setting of MMDetection [6]. + +# 4.3. Benchmarking Results + +We integrate $A^2$ -FPN into the state-of-the-art detectors and evaluate the performance on the COCO test-dev. For a fair comparison, we re-implement the corresponding FPN based methods as baselines. + +Instance Segmentation Results. $A^2$ -FPN, combined + +![](images/8f4efa45ecd036a38d7f3a9f99d09739a2e8a9029b2253253cfec8d83a4fbcda.jpg) +Figure 5. Comparison of instance segmentation results between FPN (top row) and $A^2$ -FPN (bottom row) on COCO val2017. + +![](images/80b4bbe280fca0670746b4dc8c0b51eaddbc8cde346548027777b8997225999c.jpg) + +![](images/9b2a84adf0e538ad31a9456a8acd5f04b0e477bf3b7c7cd89d875d9fb6005f3e.jpg) + +![](images/0a4e0463f84fc4b9f9b115619b9a5385f82876c626bf0b32a0da8700137294ce.jpg) + +![](images/b602455c2499f720669e392e71448f0ee088687823bad4c265096ed920bdb4a2.jpg) + +Table 1. Instance segmentation mask AP and object detection box AP, vs. the state-of-the-art on COCO test-dev. "ms" in [] indicates multi-scale training and the symbol * denotes our re-implementation results. The letters 'R' and 'X' stand for the backbone networks ResNet [15] and ResNeXt [40], respectively. 'Sch.' is short for the training schedule, which follows the setting of MMdetection [6]. + +
MethodBackboneSch.AP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)\( AP^{bb} \)\( AP_{50}^{bb} \)\( AP_{75}^{bb} \)\( AP_S^{bb} \)\( AP_M^{bb} \)\( AP_L^{bb} \)
Faster R-CNN [22]R-101-FPN-------36.259.1-18.239.048.2
Mask R-CNN [14]R-101-FPN-35.758.037.815.538.152.438.260.341.720.141.150.2
Mask R-CNN [14]X-101-FPN-37.160.039.416.939.953.539.862.343.422.143.251.2
Mask R-CNN [13]R-101-AugFPN1x37.860.440.420.441.049.841.363.544.924.244.852.0
PANet [26]R-50-PAFPN-36.658.039.316.338.153.141.260.444.422.744.054.6
PANet[ms] [26]R-50-PAFPN-38.260.241.419.141.152.642.562.346.426.347.052.3
PANet [26]X-101-PAFPN-40.062.843.118.842.357.245.065.048.625.448.659.1
PANet[ms] [26]X-101-PAFPN-42.065.145.722.444.758.147.467.251.830.151.760.0
Cascade R-CNN [3]R-50-FPN-------40.659.944.022.642.752.1
Cascade R-CNN [3]R-101-FPN-------42.862.146.323.745.555.2
HTC [5]R-50-FPN20e38.460.041.520.440.751.243.6-----
HTC [5]R-101-FPN20e39.761.843.121.042.253.545.3-----
HTC [5]X-101-FPN20e41.263.944.722.843.954.647.1-----
Mask R-CNN*R-50-FPN1x34.556.336.718.637.344.737.659.540.621.840.846.4
Mask R-CNN(ours)R-50-\( A^2 \)-FPN-Lite1x36.458.938.719.639.147.839.862.343.423.642.849.9
Mask R-CNN(ours)R-50-\( A^2 \)-FPN1x36.659.339.119.839.348.040.262.743.723.743.250.2
Mask R-CNN[ms](ours)R-50-\( A^2 \)-FPN2x38.862.041.622.141.750.442.865.247.026.545.953.3
Mask R-CNN*R-101-FPN1x36.358.538.919.439.347.839.961.643.623.143.250.0
Mask R-CNN(ours)R-101-\( A^2 \)-FPN1x37.960.840.520.641.850.141.764.145.524.645.052.5
Cascade Mask R-CNN*R-50-FPN1x36.157.138.919.138.647.441.559.845.123.444.352.7
Cascade Mask R-CNN(ours)R-50-\( A^2 \)-FPN1x38.160.141.020.640.550.443.962.847.725.446.856.0
Cascade Mask R-CNN*R-101-FPN1x37.458.940.519.540.149.643.361.647.224.146.255.3
Cascade Mask R-CNN(ours)R-101-\( A^2 \)-FPN1x39.161.342.221.041.951.845.164.148.925.748.257.7
HTC*R-50-FPN20e38.460.041.420.340.651.243.562.647.324.545.955.9
HTC(ours)R-50-\( A^2 \)-FPN20e39.862.343.021.642.452.845.464.949.126.348.257.7
HTC*R-101-FPN20e39.661.642.921.142.253.145.164.349.025.747.958.2
HTC(ours)R-101-\( A^2 \)-FPN20e40.863.644.122.343.554.446.666.250.427.149.659.9
HTC*X-101-FPN20e41.364.044.822.743.954.847.266.651.427.750.060.2
HTC(ours)X-101-\( A^2 \)-FPN20e42.165.345.723.644.856.048.368.052.428.951.361.7
HTC[ms](ours)X-101-\( A^2 \)-FPN2x44.067.547.925.747.157.650.470.154.931.653.763.7
+ +with different instance segmentation frameworks and backbone networks, achieves better performance compared with baseline models. As shown in Table 1, by replacing FPN with $A^2$ -FPN, Mask R-CNN using ResNet-50 (denoted as R-50- $A^2$ -FPN) achieves $36.6\%$ mask AP, which is $2.1\%$ higher than the counterpart. Moreover, when using ResNet-101 as the feature extractor, $A^2$ -FPN still brings a gain of $1.6\%$ , proving that $A^2$ -FPN can consistently improve the performance even with a more powerful backbone. + +$A^2$ -FPN-Lite is the lightweight setting of $A^2$ -FPN in- + +cluding three differences, halving the channel $(c = 128)$ and number $(n_i = 32(6 - i))$ of context features, removing $\mathcal{F}_6^{bb}$ and generating $\mathcal{F}_6^{bu}$ from $\mathcal{F}_5^{bu}$ using max-pooling like FPN [22], and removing the $3\times 3$ convolution after $\mathcal{F}_2^{bu}$ like PAFPN [26]. As shown in Table 1, $A^2$ -FPN-Lite improves the performance of Mask R-CNN by $1.9\%$ mask AP. + +Besides, our proposed method works well with different frameworks. $A^2$ -FPN combined with Cascade Mask R-CNN leads to a gain of $2.0\%$ and $1.7\%$ for ResNet-50 and ResNet-101, respectively. It is noteworthy that $A^2$ -FPN + +Table 2. Effect of each module in our design. MC: the MGC module, GE: the GACARAFE module, GP: the GACAP module. Results are reported on COCO val2017. + +
MCGEGPAPbbAPAP50AP75APSAPMAPL
FPN [22]37.134.155.436.218.437.346.0
PAFPN [26]37.634.455.936.418.737.547.2
✓38.635.457.437.519.538.648.3
✓39.435.757.937.819.139.048.6
✓38.335.056.637.218.038.448.3
✓✓39.836.158.638.420.239.449.4
✓✓38.935.557.737.619.039.248.8
✓✓39.635.958.237.919.839.048.9
✓✓✓40.036.258.438.120.139.249.6
+ +further boosts the performance of HTC by $1.4\%$ when using ResNet-50 as backbone, while PAFPN only shows a limited $0.1\%$ gain in the extensive study in HTC [5]. Meanwhile, HTC achieves $40.8\%$ and $42.1\%$ mask AP when using R-101- $A^2$ -FPN and X-101- $A^2$ -FPN as backbone, pushing the powerful HTC by $1.2\%$ and $0.8\%$ , respectively. Particularly, $A^2$ -FPN equipped with HTC achieves $44.0\%$ mask AP under the setting of a '2x' schedule and multi-scale training. The improvements demonstrate that $A^2$ -FPN further improves the multi-scale feature learning of feature pyramid through attention-guided aggregation. In Figure 5, we show some examples of instance segmentation results, where $A^2$ -FPN generates more accurate instance masks compared to the FPN based baseline. + +Object Detection Results. We also evaluate $A^2$ -FPN on object detection task as shown in Table 1. By replacing FPN with $A^2$ -FPN in Mask R-CNN, the performance is boosted by $2.6\%$ and $1.8\%$ for ResNet-50 and ResNet-101. $A^2$ -FPN-Lite also boosts the performance of Mask R-CNN by $2.2\%$ . Moreover, Cascade Mask R-CNN can be improved by $2.4\%$ and $1.8\%$ correspondingly when using ResNet-50 and ResNet-101 as backbone. Meanwhile, $A^2$ -FPN equipped with HTC contributes a gain of $1.9\%$ , $1.5\%$ , and $1.1\%$ for ResNet-50, ResNet-101, and ResNeXt-101, respectively. When adopting the setting of a '2x' schedule and multi-scale training, $A^2$ -FPN achieves $50.4\%$ box AP. In brief, $A^2$ -FPN effectively improves the performance of state-of-the-art detectors not only on instance segmentation but also on object detection. As shown in Table 1, $A^2$ -FPN brings consistent gains on various backbone networks, frameworks, and even different tasks, which verifies the effectiveness and generalization ability of $A^2$ -FPN. + +# 4.4. Ablation Study + +In this section, we conduct extensive ablation experiments to analyze the effects of main components in $A^2$ -FPN. Note that the baseline method for all ablation studies is Mask R-CNN with R-50-PAFPN. + +Component-wise Analysis. Firstly, we investigate the importance of each component in $A^2$ -FPN. The base- + +Table 3. Ablation study of each module on COCO val2017. "w/ ·" indicates $A^2$ -FPN only equipped with the module . + +
Methodsetting\( AP^{bb} \)AP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
\( A^2 \)-FPN-40.036.258.438.120.139.249.6
\( A^2 \)-FPNw/o GCN39.635.958.438.019.239.449.0
w/ MGC-38.635.457.437.519.538.648.3
w/ MGCw/o GCN38.535.256.937.519.138.747.8
w/ GACARAFE-39.435.757.937.819.139.048.6
w/ CARAFE [37]-38.935.457.137.619.038.448.7
w/ GACAP-38.335.056.637.218.038.448.3
w/ CAP-38.034.856.237.017.738.048.5
+ +line PAFPN is extended from FPN, where the difference from the original implementation in PANet [26] is that we do not use Synchronized BatchNorm. And then MGC, GACARAFE, and GACAP are gradually applied to PAFPN by substituting the corresponding operations with them. + +As shown in Table 2, each module effectively improves the performance of baseline. Specifically, the MGC module boosts both mask AP and box AP by $1.0\%$ . This benefits from that MGC sufficiently extracts discriminative features through cross-scale self-attention based on scaled cosine-similarity attention, and alleviates semantic information loss. The GACARAFE module contributes an improvement of $1.8\%$ and $1.3\%$ in terms of box AP and mask AP. Similarly, $0.7\%$ and $0.6\%$ for the GACAP module. These results indicate that content-aware sampling aggregates more semantic information and attention-guided fusion mitigates the inconsistency between adjacent levels. Besides, the GACARAFE module plays a key role in the construction of feature pyramid since there is only one top-down pathway but two bottom-up pathways. + +When combining any two modules, the performance of baseline is further improved. For example, MGC and GACARAFE lead to a gain of $2.2\%$ box AP and $1.7\%$ mask AP. When integrating all three modules together, it achieves $40.0\%$ box AP and $36.2\%$ mask AP, with a gain of $2.4\%$ and $1.8\%$ . The improvements of $\mathrm{AP}_S$ , $\mathrm{AP}_M$ and $\mathrm{AP}_L$ are $1.4\%$ , $1.7\%$ and $2.4\%$ respectively, suggesting that $A^2$ -FPN is beneficial to various scales, especially the large scale. + +Ablation study of each module. As shown in Table 3, the performance of MGC and $A^2$ -FPN degrades by $0.2\%$ and $0.3\%$ respectively when removing the GCNs. These results indicate that GCN can model the contextual relations between context features and benefit the subsequent feature fusion. Compared with CARAFE [37], GACARAFE further leads to a gain of $0.5\%$ box AP and $0.3\%$ mask AP. Similarly, $0.3\%$ box AP and $0.2\%$ mask AP for GACAP. These improvements benefit from that GACARAFE and GACAP aggregate complementary information from adjacent features for content-aware sampling and employ channel attention to enhance the semantic consistency. + +Impact of the number of context features. To investigate the impact of $n_i$ , the number of context features collected from each level, we conduct contrast experiments + +![](images/860b7e708fdec10c7fadc7fc2ffcd57959c8ea789cf01db40f448ce6ee9b7110.jpg) + +![](images/09a1628ac2cac957369e70984b8be83f9d950a34006953a1a91143b7a953b126.jpg) + +![](images/86c194dde15020c82a1a2f2d7c4e7cccc3ba913ca33bb676135cafe2b061b5fd.jpg) + +![](images/22c1dd90ac158f409159b13bcf6578f6af989b8f783a52803e031e94f27c22ca.jpg) + +![](images/6066bf66463ae937b444854c66dd75bc1777164b0ba32203170829c6ac5355f8.jpg) + +![](images/5a7e6235dddd399767d97231a7cc5bdf41555ed9dd44e8229576789056c8b491.jpg) +Figure 6. Instance segmentation results of $A^2$ -FPN equipped with HTC on COCO val2017. + +![](images/81ff6a49fb696865f3503c957f1f5a2fb909a4c36577ba0f421fb2f6e4966b3d.jpg) + +![](images/e96eb73ccb97151e65253a5149c1a08204fc4222fc3a4730f3483ddebdcb8d63.jpg) + +![](images/1ce042130500bd367494ba96973414128b42238933d0e999bcf494e59278821a.jpg) + +![](images/21fb6126980bb57f9d62982c2ef208bae3ef79019f0f18a3ce388be3c5c27350.jpg) + +Table 4. Impact of the number of context features on COCO val2017. $n_i$ means the number of context features collected from the i-th feature level $\mathcal{F}_i^{bb}$ . + +
MethodniAPbbAPAP50AP75APSAPMAPL
FPN [22]-37.134.155.436.218.437.346.0
PAFPN [26]-37.634.455.936.418.737.547.2
w/ MGC64(i-1)38.735.457.837.419.238.848.1
w/ MGC16038.835.357.437.619.238.748.2
w/ MGC64(6-i)38.635.457.437.519.538.648.3
+ +Table 5. Effectiveness of activation function $2 \cdot$ sigmoid on COCO val2017. "Act." is short for activation function, and $\sigma$ means the sigmoid function. + +
MethodAct.\( AP^{bb} \)AP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
FPN [22]-37.134.155.436.218.437.346.0
PAFPN [26]-37.634.455.936.418.737.547.2
w/ GACARAFEσ38.935.557.537.719.238.848.3
w/ GACARAFE2σ39.435.757.937.819.139.048.6
w/ GACAPσ38.234.856.337.018.338.347.7
w/ GACAP2σ38.335.056.637.218.038.448.3
+ +with different settings. As shown in Table 4, the MGC module is robust to the setting of number $n_i$ and achieves similar performance where the difference is only $0.1\%$ at most. Considering that the more context features from the high levels, the more parameters are introduced because of high dimension, we set the hyper-parameters as $n_i = 64(6 - i)$ , i.e., $n_i = \{256, 192, 128, 64\}$ and $n = 640$ . + +Effectiveness of activation function 2 $\cdot$ sigmoid. To verify the effectiveness of activation function 2 $\cdot$ sigmoid, we compare it with the conventional function sigmoid in both GACARAFE and GACAP. As shown in Table 5, the GACARAFE module with function 2 $\cdot$ sigmoid achieves $39.4\%$ box AP and $35.7\%$ mask AP respectively, which is $0.5\%$ and $0.2\%$ higher than the counterpart with function sigmoid. Meanwhile, function 2 $\cdot$ sigmoid contributes a gain of $0.1\%$ box AP and $0.2\%$ mask AP in the GACAP module. The pyramidal features are iteratively reweighted in the feature fusion, and the final calibration weights are the product of several activated weights. When using sigmoid as the activation function, the mean of channel-wise weights would be always less than 1 and decay exponentially after successively reweighting, so that pyramidal features would be sup- + +Table 6. Complexity analysis of ${A}^{2}$ -FPN on COCO val2017. + +
MethodImage Size#FLOPs#ParamsFPSAPbbAP
FPN [22]1280 × 832283.28G44.18M13.137.134.1
PAFPN [26]1280 × 832309.05G47.72M12.837.634.4
A2-FPN1280 × 832375.39G57.49M9.540.036.2
A2-FPN-Lite1280 × 832319.91G48.83M11.139.636.0
+ +pressed in the iterative fusion. On the contrary, the activation function 2-sigmoid can keep the mean of channel-wise weights being 1 and excite or restrain features selectively. + +# 4.5. Complexity Analysis + +As shown in Table 6, we analyze the complexity of $A^2$ -FPN. $A^2$ -FPN adds some computation cost, but $A^2$ -FPN-Lite can reduce it greatly at a small performance sacrifice. Compared to PAFPN, $A^2$ -FPN-Lite improves the performance significantly while increases the computation complexity acceptably, proving that the improvement mostly comes from our attention-guided feature aggregation. + +# 5. Conclusion + +We propose Attention Aggregation based Feature Pyramid Network ( $A^2$ -FPN), which improves multi-scale feature learning through attention-guided feature aggregation. $A^2$ -FPN extracts discriminative features by collecting-distributing multi-level global context features, and fuses adjacent levels using content-aware sampling and channel-wise reweighting before element-wise addition. Upon various backbone networks and instance segmentation frameworks, $A^2$ -FPN consistently and substantially improves the performance of baseline methods. + +Acknowledgments. This work was supported by the National Natural Science Foundation of China under Grant No. 61771288, Cross-Media Intelligent Technology Project of Beijing National Research Center for Information Science and Technology (BNRist) under Grant No. BNR2019TD01022 and the research fund under Grant No. 2019GQG0001 from the Institute for Guo Qiang, Tsinghua University. We also thank for the funding support of Huawei Technologies Co. Ltd. + +# References + +[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016. 4 +[2] Min Bai and Raquel Urtasun. Deep watershed transform for instance segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5221-5229, 2017. 2 +[3] Zhaowei Cai and Nuno Vasconcelos. Cascade r-cnn: Delving into high quality object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6154-6162, 2018. 2, 6 +[4] Yue Cao, Jiarui Xu, Stephen Lin, Fangyun Wei, and Han Hu. Gcnet: Non-local networks meet squeeze-excitation networks and beyond. In Proceedings of the IEEE International Conference on Computer Vision Workshops, pages 0-0, 2019. 2 +[5] Kai Chen, Jiangmiao Pang, Jiaqi Wang, Yu Xiong, Xiaoxiao Li, Shuyang Sun, Wansen Feng, Ziwei Liu, Jianping Shi, Wanli Ouyang, et al. Hybrid task cascade for instance segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4974-4983, 2019. 1, 2, 6, 7 +[6] Kai Chen, Jiaqi Wang, Jiangmiao Pang, Yuhang Cao, Yu Xiong, Xiaoxiao Li, Shuyang Sun, Wansen Feng, Ziwei Liu, Jiarui Xu, Zheng Zhang, Dazhi Cheng, Chenchen Zhu, Tianheng Cheng, Qijie Zhao, Buyu Li, Xin Lu, Rui Zhu, Yue Wu, Jifeng Dai, Jingdong Wang, Jianping Shi, Wanli Ouyang, Chen Change Loy, and Dahua Lin. MMDetection: Open mmlab detection toolbox and benchmark. arXiv preprint arXiv:1906.07155, 2019. 5, 6 +[7] Yunpeng Chen, Marcus Rohrbach, Zhicheng Yan, Yan Shuicheng, Jiashi Feng, and Yannis Kalantidis. Graph-based global reasoning networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 433-442, 2019. 2 +[8] Jifeng Dai, Kaiming He, and Jian Sun. Instance-aware semantic segmentation via multi-task network cascades. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3150-3158, 2016. 2 +[9] Bert De Brabandere, Davy Neven, and Luc Van Gool. Semantic instance segmentation with a discriminative loss function. arXiv preprint arXiv:1708.02551, 2017. 2 +[10] Alireza Fathi, Zbigniew Wojna, Vivek Rathod, Peng Wang, Hyun Oh Song, Sergio Guadarrama, and Kevin P Murphy. Semantic instance segmentation via deep metric learning. arXiv preprint arXiv:1703.10277, 2017. 2 +[11] Jun Fu, Jing Liu, Haijie Tian, Yong Li, Yongjun Bao, Zhiwei Fang, and Hanqing Lu. Dual attention network for scene segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3146-3154, 2019. 2 +[12] Golnaz Ghiasi, Tsung-Yi Lin, and Quoc V Le. Nas-fpn: Learning scalable feature pyramid architecture for object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7036-7045, 2019. 2 + +[13] Chaoxu Guo, Bin Fan, Qian Zhang, Shiming Xiang, and Chunhong Pan. Augfpn: Improving multi-scale feature learning for object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12595-12604, 2020. 6 +[14] Kaiming He, Georgia Gkioxari, Piotr Dólar, and Ross Girshick. Mask r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 2961-2969, 2017. 1, 2, 6 +[15] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 2, 3, 6 +[16] Jie Hu, Li Shen, and Gang Sun. Squeeze-and-excitation networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7132-7141, 2018. 2, 4 +[17] Zhaojin Huang, Lichao Huang, Yongchao Gong, Chang Huang, and Xinggang Wang. Mask scoring r-cnn. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6409-6418, 2019. 2 +[18] Alexander Kirillov, Evgeny Levinkov, Bjoern Andres, Bogdan Savchynskyy, and Carsten Rother. Instancecut: from edges to instances with multicut. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5008-5017, 2017. 2 +[19] Yin Li and Abhinav Gupta. Beyond grids: Learning graph representations for visual recognition. In Advances in Neural Information Processing Systems, pages 9225–9235, 2018. 2 +[20] Yi Li, Haozhi Qi, Jifeng Dai, Xiangyang Ji, and Yichen Wei. Fully convolutional instance-aware semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2359-2367, 2017. 2 +[21] Xiaodan Liang, Zhiting Hu, Hao Zhang, Liang Lin, and Eric P Xing. Symbolic graph reasoning meets convolutions. In Advances in Neural Information Processing Systems, pages 1853-1863, 2018. 2 +[22] Tsung-Yi Lin, Piotr Dólar, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie. Feature pyramid networks for object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2117-2125, 2017. 1, 2, 6, 7, 8 +[23] Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and Piotr Dólár. Focal loss for dense object detection. In Proceedings of the IEEE international conference on computer vision, pages 2980-2988, 2017. 2 +[24] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dólar, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In European conference on computer vision, pages 740-755. Springer, 2014. 2, 5 +[25] Shu Liu, Jiaya Jia, Sanja Fidler, and Raquel Urtasun. Sgn: Sequential grouping networks for instance segmentation. In Proceedings of the IEEE International Conference on Computer Vision, pages 3496-3504, 2017. 2 +[26] Shu Liu, Lu Qi, Haifang Qin, Jianping Shi, and Jiaya Jia. Path aggregation network for instance segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 8759-8768, 2018. 1, 2, 6, 7, 8 + +[27] Wei Liu, Dragomir Anguelov, Dumitru Erhan, Christian Szegedy, Scott Reed, Cheng-Yang Fu, and Alexander C Berg. Ssd: Single shot multibox detector. In European conference on computer vision, pages 21-37. Springer, 2016. 2 +[28] Wei Liu, Andrew Rabinovich, and Alexander C Berg. Parsenet: Looking wider to see better. arXiv preprint arXiv:1506.04579, 2015. 3 +[29] Alejandro Newell, Zhiao Huang, and Jia Deng. Associative embedding: End-to-end learning for joint detection and grouping. In Advances in neural information processing systems, pages 2277-2287, 2017. 2 +[30] Pedro OO Pinheiro, Ronan Collobert, and Piotr Dólar. Learning to segment object candidates. In Advances in Neural Information Processing Systems, pages 1990-1998, 2015. 2 +[31] Pedro O Pinheiro, Tsung-Yi Lin, Ronan Collobert, and Piotr Dólar. Learning to refine object segments. In European conference on computer vision, pages 75-91. Springer, 2016. 2 +[32] Joseph Redmon and Ali Farhadi. Yolov3: An incremental improvement. arXiv preprint arXiv:1804.02767, 2018. 2 +[33] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. In Advances in neural information processing systems, pages 91-99, 2015. 2 +[34] Wenzhe Shi, Jose Caballero, Ferenc Huszár, Johannes Totz, Andrew P Aitken, Rob Bishop, Daniel Rueckert, and Zehan Wang. Real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1874-1883, 2016. 4 +[35] Mingxing Tan, Ruoming Pang, and Quoc V Le. Efficientdet: Scalable and efficient object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10781-10790, 2020. 2 +[36] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information processing systems, pages 5998-6008, 2017. 2, 3 +[37] Jiaqi Wang, Kai Chen, Rui Xu, Ziwei Liu, Chen Change Loy, and Dahua Lin. Carafe: Content-aware reassembly of features. In Proceedings of the IEEE International Conference on Computer Vision, pages 3007-3016, 2019. 4, 5, 7 +[38] Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7794-7803, 2018. 2 +[39] Yi Wang, Ying-Cong Chen, Xiangyu Zhang, Jian Sun, and Jiaya Jia. Attentive normalization for conditional image generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5094-5103, 2020. 3 +[40] Saining Xie, Ross Girshick, Piotr Dólár, Zhuowen Tu, and Kaiming He. Aggregated residual transformations for deep neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1492-1500, 2017. 6 + +[41] Sergey Zagoruyko, Adam Lerer, Tsung-Yi Lin, Pedro O Pinheiro, Sam Gross, Soumith Chintala, and Piotr Dólar. A multipath network for object detection. arXiv preprint arXiv:1604.02135, 2016. 2 +[42] Songyang Zhang, Xuming He, and Shipeng Yan. Latent-gnn: Learning efficient non-local relations for visual recognition. 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Marriott1,2 Sami Romdhani2 Liming Chen1 +1 Ecole Centrale de Lyon, France +2 IDEMIA, France +richard.marriott@idemia.com + +# Abstract + +Facial recognition using deep convolutional neural networks relies on the availability of large datasets of face images. Many examples of identities are needed, and for each identity, a large variety of images are needed in order for the network to learn robustness to intra-class variation. In practice, such datasets are difficult to obtain, particularly those containing adequate variation of pose. Generative Adversarial Networks (GANs) provide a potential solution to this problem due to their ability to generate realistic, synthetic images. However, recent studies have shown that current methods of disentangling pose from identity are inadequate. In this work we incorporate a 3D morphable model into the generator of a GAN in order to learn a nonlinear texture model from in-the-wild images. This allows generation of new, synthetic identities, and manipulation of pose, illumination and expression without compromising the identity. Our synthesised data is used to augment training of facial recognition networks with performance evaluated on the challenging CFP and CPLFW datasets. + +# 1. Introduction + +State-of-the-art facial recognition (FR) algorithms are trained using millions of images. With the internet as a resource, face-images are relatively easy to come by. However, the distribution of semantics throughout these images is usually highly unbalanced. For example, the majority of available photographs are frontal portraits of smiling subjects, with images containing large poses being relatively scarce. Robustness to pose is currently considered to be one of the largest challenges for FR. Some researchers have attempted to avoid the problem by first frontalising probe images [17, 34, 45], whilst others have attempted to learn additional robustness to pose by synthetically augmenting training datasets [7, 8, 30, 43]. We advocate this second approach since it does not require additional resources during inference. + +Synthetic augmentation of poses in training data has typically been achieved by fitting some 3D face model to in- + +![](images/2934d9222eb52c65e425ff1ab9278d61c0dd4e734cb3618c217d1beefc89595f.jpg) +Figure 1. Instances of the FLAME 3D morphable model rendered at various poses with nonlinear textures (and background) learned by our 3D GAN from the MultiPIE dataset. (The model instances correspond to the Neutral expression column of Figure 4.) + +put images, extracting textures, and then re-projecting those textures at modified poses [7, 43]. With recent advances in the development of Generative Adversarial Networks (GANs), however, a viable alternative has emerged. GANs have been shown to be capable of generating realistic images of new identities and so restricting data-augmentation to existing identities is not necessary. In order to generate fully synthetic training data, however, disentanglement of identity from other characteristics, such as pose, is necessary. Recent studies have shown that 2D GAN methods struggle to achieve this disentanglement [29]. In this work we incorporate a 3D morphable model (3DMM) [26] into a GAN so that images of new, synthetic identities can be generated, and the pose modified without identity being compromised. Our contributions are: + +1. Introduction of a method of learning a nonlinear texture model from in-the-wild images that can be used to generate images of synthetic identities with fully disentangled pose. No specially captured scans of facial texture are required. +2. Demonstration of improvements to large-posed facial recognition by augmenting datasets with synthetic, 3D GAN images, and a state-of-art accuracy for CPLFW. + +# 2. Related Work + +# 2.1. Generative 3D networks + +Prior to the recent explosion in the development of GAN-related methods, the best way of generating synthetic face images was to use a 3D morphable model (3DMM) [2, 4, 39]. These models are generally built from a limited number of 3D shape and texture scans. To achieve greater representativeness, methods such as [3] were proposed in which PCA-based texture models are learnt from large datasets of in-the-wild images. While the linear spaces of these models are known to capture most of the variation in the training datasets, generated faces still appear to be smooth with textures lacking in high frequency detail. In [12] and [13] the linear texture model of the LsFM [4] is replaced by the nonlinear, CNN generator of a GAN trained to approximate the distribution of their dataset of high-quality texture scans. The quality of generated textures is outstanding. However, the dataset of scans is not available for general use. + +The difficulty of obtaining high-quality texture datasets motivates the development of methods such as our own, which aims to learn a nonlinear texture model from natural (non-scanned) images. Various other methods have a similar aim and attempt to train disentangled auto-encoders to learn texture and shape models via reconstruction of inthe-wild training images [6, 35, 38, 39, 40]. New identities, however, can only be generated by empirically exploring the latent space of their generators. The method we propose is a GAN rather than an auto-encoder, and so can more reliably and straight-forwardly generate new, synthetic identities. + +A number of recent methods have attempted to build upon the success of GANs in the generation of high-quality images by integrating 3D models to gain control over semantics. In [36] and [37], mappings from 3DMM parameters to the latent space of a pre-trained StyleGAN2 [23] are learned such that the similarity of generated images with 3DMM renderings is maximised. In [14], [25] and [11], GANs are trained to generate realistic images but are conditioning in various ways on renderings of 3D models. For each of these methods, generation takes place in image-space rather than texture-space meaning that appearance and identity are not implicitly robust to pose transformations. Pre-trained biometrics networks are therefore often applied as losses to constrain identity. The quality of these biometric networks imposes an upper limit on the usefulness of synthesised data for the application of data-augmentation for FR. + +# 2.2. Large-posed facial recognition + +Large-posed FR could be framed as a problem of limited data or as a problem of how to better learn from available data. Various generic methods have been shown to perform + +well on large-pose FR benchmarks [20, 19]. Other methods specifically disentangle pose from identity representations by regressing/classifying pose labels [5, 31, 41]. Complementary to these works are methods for synthetically augmenting pose in training images. Earlier methods involved extraction of textures from images onto the surface of a 3D model for manipulation of pose, and sometimes illumination or expression [7, 28, 30, 31]. Due to self-occlusion in images and therefore holes in the textures, various in-filling techniques were employed. In [43] this problem is tackled by refining the projected texture in image-space using an adversarial loss. This final refinement phase requires an identity-preserving loss that, as previously mentioned, limits the usefulness of the synthetic data for improving FR. + +A preferable method is to produce a complete texture in the texture reference space of the 3D model, thus ensuring that the identity remains consistent when projected to different poses. In [8], a texture-completion network is trained using a set of carefully prepared ground-truth textures. In [12] and [24] the problem of texture completion is avoided entirely by generating textures for synthetic identities. [24] uses a linear texture model whereas [12] trains a nonlinear model. Each of these methods makes use of datasets of scanned textures. The method proposed here also generates synthetic identities in order to avoid the problems of texture completion and reconstruction of existing identities. The method, however, does not require carefully prepared/captured ground-truth textures and, instead, learns a nonlinear texture model directly from in-the-wild images. + +# 3. The 3D GAN + +Generative Adversarial Networks (GANs) typically consist of a convolutional generator and discriminator that are trained alternately in a mini-max game: the discriminator is trained to distinguish generated images from those of a training set of real images, and the generator is trained to minimise the success of the discriminator. Although generated images appear to represent real-world, 3D subjects, they are of course nothing more than combinations of 2D features learned by the 2D convolutional filters of the generator. For this reason, upon linearly traversing the latent space of a GAN's generator, one tends to see "lazy", 2D transformations between forms rather than transformations that would be physically realistic in a 3D space. For example, even if a direction in the latent space is identified that influences the pose of a face in a generated image, the appearance of the face is unlikely to remain consistent. Indeed, the generator may not even be capable of generating the same face at a different pose. In order to ensure that appearance (and identity) is maintained in synthesised images upon manipulation of pose, we enhance the generator by integrating a 3DMM. + +![](images/0b04b797ae4c6818980d466a1a759fcf6870aa5e4f4b4d4d2e99b2e90125c7e9.jpg) +Figure 2. The 3D GAN's generator includes two CNNs that generate facial texture and background. Facial texture is rendered into the background using some random sample of shape from the 3D model's distribution. The random pose and expression vectors are used only for rendering, not for generation of texture, and so remain disentangled from the identity. All parameters are passed to the background generator to allow harmonisation of the background conditions with the rendered subject. Note that all vectors are randomly sampled and that no direct comparison with training images is performed. + +Typically, input to a GAN is a random vector. The inputs to our 3D GAN are random texture and background vectors, but also random 3DMM shape, expression and pose parameters. A differentiable renderer is then used to render random head-shapes into a generated "background image" with the facial texture being provided by a texture generator that learns its model from scratch from the training images. No matter what the shape, expression or pose of the random model instance, the rendered image must appear realistic to the discriminator. To achieve this, the texture generator learns to generate realistic textures with features that correctly correspond with the model shape. + +Figure 2 depicts the architecture of our 3D GAN. The lower half of the diagram depicts a standard conditional GAN in which some image is generated from random parameters, and is then fed to the discriminator along with the pose parameters to correspond with training images also labelled with poses. In our implementation, pose information is repeated spatially and concatenated as additional channels of the image. The top half of the diagram depicts the integration of a 3DMM where a learned texture is rendered into this image via a differentiable renderer. With the main subject of the image being provided by the rendered texture, the background generator learns to generate only the background and features not modelled by the 3DMM, for example, the edges of glasses, clothes and hair. Since the texture generator is not conditioned on pose, nor on expression parameters, these aspects of the image can be manipulated without affecting the texture of the 3D model, as shown in Figures 1, 4 and 7. There is therefore no need for an additional identity constraint. + +![](images/93bd7a50bea1e0a70fe109db94648ac425917b8b1389092de064c22ce565d1c9.jpg) +(a) + +![](images/8e9208186558bd062ed8d3bef2148c6af363fa4b9aace7db202bc0b3743df953.jpg) +(b) +Figure 3. a) The FLAME 3DMM's texture map where RGB represents the corresponding 3D point on the mean model shape; b) a rendering of the texture shown in (c). + +![](images/960b8a6c7354273b0a2fd34885f694d569fb001ccf0ad379f34ffd0d9772a77c.jpg) +(c) + +# 3.1. Implementation + +Our full generator is a function of five sets of random input parameters and two sets of trained parameters: + +$$ +\begin{array}{l} \mathbf {x} = G \left(\left[ \mathbf {z} _ {T}, \mathbf {z} _ {B}, \beta , \psi , \phi \right]; \left[ \theta_ {T}, \theta_ {B} \right]\right) (1) \\ = (\mathbf {1} - \mathbf {K}) \circ G _ {B} \left(\mathbf {z} _ {B}, \mathbf {z} _ {T}, \beta , \psi , \phi ; \theta_ {B}\right) \\ + \mathbf {K} \circ \mathcal {M} \left(G _ {T} \left(\mathbf {z} _ {T}, \beta ; \theta_ {T}\right), \mathbf {y}\right) (2) \\ \end{array} +$$ + +where $\mathbf{x}$ is a generated image; $G_{B}$ and $G_{T}$ are the background and texture generators; $\mathbf{z}_T\in \mathcal{N}^{N_T}$ and $\mathbf{z}_B\in \mathcal{N}^{N_B}$ are vectors of random texture and background parameters of length $N_{T}$ and $N_{B}$ respectively, selected from standard normal distributions; $\beta \in \mathcal{N}^{N_s}$ and $\psi \in \mathcal{N}^{N_e}$ are vectors of shape and expression parameters that control the form of the 3DMM, again selected from standard normal distributions; $\phi$ is pose information, typically values of yaw and pitch selected at random from the labels of the training set of images; and $\theta_T$ and $\theta_B$ parametrise the texture and background generator networks. The background image and rendered texture are combined using a binary mask, $\mathbf{K}$ , gen + +erated by the renderer. Note that the masking by $\mathbf{K}$ is not shown in Figure 2. 1 is a vector of ones of the same shape as the image and a $0\mathrm{b}$ represents the element-wise product of vectors a and b. $\mathcal{M}$ is an inverse texture-mapping function that maps interpolations from the generated texture map to appropriate locations in image space based on a rendering of texture coordinates in image-space, y. Inverse texture mapping effectively allows the generated texture to be pasted onto the model surface rather than having only single colours at each vertex and interpolation across facets. Our texture generator operates at twice the resolution of the background generator to help avoid pixelation of surfaces that are less well represented in the texture map. Rendering of y (and simultaneously, $\mathbf{K}$ ) is performed by the differentiable rendering function, $R$ : + +$$ +\mathbf {y}, \mathbf {K} = R (\mathbf {S}, \phi ; \tau , \gamma) \tag {3} +$$ + +where $\mathbf{S} \in \mathbb{R}^{N_v \times 3}$ is a vector of shape vertices for some random instance of the 3DMM; $\phi$ is pose information; $\tau \in \mathbb{Z}^{N_{\tau} \times 3}$ is the 3DMM's triangle list of $N_{\tau}$ vertex indices; and $\gamma \in \mathbb{R}^{3N_{\tau} \times 2}$ is the vector of texture coordinates where each of the $N_{\tau}$ triangles has its own set of three 2D texture vertices. The rendering function, $R$ , is implemented by DIRT (Differentiable Renderer for Tensorflow) [18] and we use the FLAME (Faces Learned with an Articulated Model and Expressions) [26] 3DMM. FLAME is an articulated model with joints controlling the head position relative to the neck, the gaze direction, and the jaw. To avoid having to estimate the distributions of these angles, during training of our 3D GAN we fix the joint parameters such that the shape is given by the following, simplified equation + +$$ +\mathbf {S} = \bar {\mathbf {S}} + \sum_ {n = 1} ^ {N _ {s}} b _ {n} \mathbf {s} _ {n} + \sum_ {n = 1} ^ {N _ {e}} c _ {n} \mathbf {e} _ {n} \tag {4} +$$ + +where $\bar{\mathbf{S}}$ is the mean model shape; $S = [\mathbf{s}_1,\dots ,\mathbf{s}_{N_s}]$ are the principal components of shape; $\epsilon = [\mathbf{e}_1,\dots ,\mathbf{e}_{N_e}]$ are the principal components of expression; and $[b_1,\dots,b_{N_s}]$ and $[c_1,\dots,c_{N_e}]$ are the individual elements of the previously defined shape and expression vectors, $\beta$ and $\psi$ , that are also fed to the generator networks in Equation (2). For the FLAME model, $N_{s} = 200$ , $N_{e} = 200$ , $N_{v} = 5023$ and $N_{\tau} = 9976$ . We also set $N_{T} = N_{B} = 200$ . + +The architectures of $G_{T}$ and $G_{B}$ are based on that of the Progressive GAN [21]. However, to simplify implementation and speed up training, no progressive growing was used. We believe that use of a 3D model may act to stabilise training since it provides prior form that need not be learned from scratch. The architecture was augmented with bilinear interpolation on upscaling (rather than nearest-neighbour upscaling), which helps to avoid checker-board artefacts, and with static Gaussian noise added to each feature map, as used in [22], which helps to prevent wave-like artefacts from forming. (See Figure 5 for examples.) + +# 3.2. Training + +Despite the more elaborate architecture of the generator, the 3D GAN can be trained like any other GAN. We choose to optimise a Wasserstein loss [1] by alternately minimising the discriminator and generator losses in Equations (5) and (6) respectively. The values of all input vectors (with the exception of the conditional pose parameters) are selected from a standard Gaussian distribution. For simplicity of notation, we agglomerate them into a single vector $\nu = [\mathbf{z}_T,\mathbf{z}_B,\beta ,\psi ]$ + +$$ +\begin{array}{l} \mathcal {L} _ {\theta_ {D}} = \mathbb {E} _ {(\mathbf {x} _ {r}, \phi) \sim p _ {d a t a}} [ D (\mathbf {x} _ {r}, \phi ; \theta_ {D}) ] \\ - \mathbb {E} _ {\nu \sim \mathcal {N}, (-, \phi) \sim p _ {d a t a}} [ D (G (\nu , \phi ; \theta_ {G}), \phi ; \theta_ {D}) ] + R e g. \tag {5} \\ \end{array} +$$ + +$$ +\mathcal {L} _ {\theta_ {G}} = \mathbb {E} _ {\nu \sim \mathcal {N}, (- \phi) \sim p _ {d a t a}} [ D (G (\nu , \phi ; \theta_ {G}), \phi ; \theta_ {D}) ] \tag {6} +$$ + +where $D$ is the discriminator network parametrised by $\theta_{D}$ ; $(\mathbf{x}_r,\phi)$ is a real image and associated pose labels selected at random from the distribution of training data, $p_{data}$ ; $\theta_{G} = [\theta_{T},\theta_{B}]$ ; and Reg. indicates the addition of a gradient penalty [16] that acts to regularise the discriminator such that it approximately obeys the required k-Lipschitz condition [1]. Note that, during training, the shape and expression parameters passed to the generator are random. There is never any direct reconstruction of training images via fitting of the 3D model. The only constraint on textures is that they must appear realistic (as judged by the discriminator) when projected at any angle and with any expression. The motivation for training our generator as a GAN and avoiding reconstruction losses is to be able to generate new identities and to avoid generation of smoothed textures caused by reconstruction errors. + +# 3.3. Limitations + +The 3D GAN method has certain limitations, the most fundamental possibly being the fact that hair, glasses and teeth are not included in the 3D shape model. This can lead to projections of these features onto the surface of the model that do not necessarily look realistic when viewed from certain angles. The inclusion of such features in the shape model would be difficult at best. Instead, it may be better to detect and remove images containing unmodelled features from the training dataset and to seek another method for augmentation with glasses and occlusion by overhanging hair, for example [28]. + +As currently formulated, the 3D GAN learns lighting effects and shadows as part of the texture. Although this helps generated images appear to be realistic, it is not ideal for our goal of improving FR since specific lighting conditions become part of the synthetic identities. Since we have the 3D shape for each generated image, a lighting model could be used to produce shading maps of randomised lighting conditions during training similar to that performed in + +![](images/9c6a7250ee8fe77f223c020fd73d9991ca09e9f24c857fbac1cc3c13684428d5.jpg) +Texture Neutral Exp 1 Exp 2 Exp 3 Exp 4 Exp 5 +Figure 4. Renderings of the FLAME morphable model for various expressions with textures learned by the 3D GAN from the Multi-PIE dataset. Output of the texture generator prior to rendering is shown in the first column. +Figure 5. Results characterising the effects of various features of the final implementation of our 3D GAN. + +[40]. Ideally, the random lighting conditions should follow the distribution of lighting in the training set. In this way the texture generator might avoid inclusion of the modelled lighting effects in the texture. + +We also make the assumption that the distributions of shape and expression in the training dataset match the natural distributions of the 3DMM. This is not necessarily the case and improvements could be possible by first fitting the model to the dataset. N.B. we suggest this only for estimating the distributions, not for reconstructing images since fitting errors would be large in individual cases. We also assume that the distributions of feature points (used for alignment) and poses are known. + +Finally, the texture map provided with the FLAME 3DMM (see Figure 3a) is spatially discontinuous. Since CNNs function by exploiting spatial coherence, these discontinuities in the texture-space lead to discontinuity artefacts in the rendered images. This can be seen, for example, in Figure 4 where the facial texture meets the texture of the back of the head. These artefacts could largely be avoided by using an alternative, spatially continuous texture mapping. + +# 4. Results + +# 4.1. Qualitative evaluation for a controlled dataset + +During development of the 3D GAN, tests were conducted by training on the controlled, Multi-PIE dataset [15]. Doing so avoided potential problems that might have arisen due to incorrect estimation of poses, which are required to condition the GAN. During these tests, the pitch of the model was not varied and so we excluded Multi-PIE's CCTV-like camera angles (8 and 19). The first column of Figure 4 shows examples of random textures learned by the 3D GAN. To demonstrate the level of correspondence with + +![](images/ecacdd99aa41d7a3fcf102d96fbefaf99cc53e0a1ae96a4662b78f8c38207e90.jpg) + +![](images/41007b85a891a297eca1affd5d21fd1644c8965f822c251423f64fa2de296947.jpg) + +![](images/42eef5a7ed807f6fb1585526803213a133e8f6d6b07fce2d7438886f493d7f4c.jpg) + +![](images/c6c00902e17b265f50cab5f6fcb3fa810ad4284742c6dc95603544879fe60d76.jpg) +a) No conditioning +d) No noise + +![](images/214161474242e8595fc71a0174b070facaec402fbe92fdd4cdf939b9aef5d41d.jpg) +b) No cond / bckd +e) Final + +![](images/2379b7619e78174a8845a38aee0417163a98f43f677df83d78d474e29450e81f.jpg) +c) No bilinear +f) Final + SH lighting + +the shape model, we render each texture for six different expressions. We see that features are well aligned and that expressions can be manipulated realistically. This is thanks to the requirement that the texture look realistic for renderings of all poses and expressions. The texture is not dependent on the expression parameters and so the identity is implicitly maintained, at least to the limit of disentangle-ment present in the 3DMM. Figure 1 shows renderings of the same textures with a neutral expression at a selection of yaw angles in the range $[-90^{\circ}, 90^{\circ}]$ . We see that the model heads are pleasingly integrated with the background with additional, unmodelled details such as hair and the edges of glasses being generated. In some cases, however, this is problematic. For example, in the final column, something resembling a protruding chin has been generated in the background for both of the male subjects. Note, however, that the background is only needed for training and that facial textures can be rendered onto arbitrary backgrounds. + +Figure 5 shows a set of images that characterise the effects of disabling/enabling various aspects of our 3D GAN. Figure 5a shows that disabling the pose-conditioning can lead to degenerate solutions where the generators conspire to generate faces as part of the background and to camouflage the model. In the given example, pose-conditioning would have caused the discriminator to expect a subject facing towards the left and to therefore penalise such an image. Attempting to avoid this problem by switching off the background generator causes a different problem that can be seen in Figure 5b. The texture generator now produces a mixture of face-like and background-like features in order to satisfy the discriminator. Figure 5c has the background and pose-conditioning enabled. It demonstrates, however, obvious checker-board artefacts in the texture. We found that this problem was caused by the nearest-neighbour upsampling of feature-maps upon resolution doubling within the generator. Following the work of [22], we switched to bilinear up-sampling. Whilst this prevented the checkerboard artefacts, it led to the wave-like artefacts that can be seen in Figure 5d. Finally, in Figures 5e and 5f, we added + +![](images/cbb3c440aa683754a59169bbe8d2c26baa05f14d2d60dd4c8b0c0f607704d243.jpg) +Figure 6. The relative pose distributions estimated for the non-synthetic datasets described in Section 4.2.1 and Table 1. + +![](images/b11e427f8720a1769ff3143ce424522ef1c3ed7f4fae99a52b34b767fb5dc753.jpg) + +
DatasetIDsImagesFRGAN
MS1M-V3 [10]93.4k5.2M✓
NetScrape (in-house)26.8k3.5M✓
CASIA Webface [42]10.6k0.5M✓
CelebA [27]10.2k0.2M✓✓
Flickr-Faces-HQ [22]N/A0.07M✓
+ +Table 1. Comparison of datasets used in our data-augmentation experiments to train FR networks and/or the 3D GAN. + +static, Gaussian noise into the generator [22]. The noise acts to provide high-frequency, stochastic features by default so that the generator need not attempt to derive these details from the random input vectors. In Figure 5f we have also enabled spherical harmonic (SH) lighting [32], which is used in our data-augmentation experiments. + +# 4.2. Data-augmentation in the wild + +In the previous section we saw that it is possible to learn textures of good quality from a controlled dataset of images containing a wide range of pose. It is unlikely, however, that the synthetic 3D GAN data would be more informative than the original, high-quality dataset. Although the 3D GAN is able to generate new identities and allows full control over the pose, the data also inevitably suffers from problems such as mode-collapse and from limited realism. In this section we demonstrate improvement to FR by making better use of noisy, in-the-wild datasets. We present experiments for various FR algorithms trained on a variety of datasets. Evaluation was performed for two challenging, large-pose datasets: Celebrities in Frontal-Profile in the Wild (CFP) [33] and Cross-Pose LFW (CPLFW) [44], as well as their frontal-frontal counterparts. Benefit from use of 3D GAN data arises from a combination of the balanced distribution of poses and expressions, the use of a 3D lighting model, the presence of additional synthetic identities, and the GAN's ability to "clean" noisy datasets. + +# 4.2.1 Training datasets + +Our baseline FR experiments are trained on either CASIA Webface [42], MS1M-V3 [10] or our in-house dataset of 3.5 million images scraped from the internet, labelled as "NetScrape" in Figure 6 and Tables 1 and 2. These datasets were then augmented using the 3D GAN trained on either CelebA [27] or Flickr-Faces-HQ (FFHQ) [22]. Since CelebA is a dataset of potential benefit to FR, it was included in additional baseline experiments to provide a cleaner comparison where the dataset was used to train the 3D GAN. Details of these datasets are presented in Table 1. In Figure 6 we show the relative distributions of yaw and pitch angles estimated using an in-house pose-estimation network. CelebA was found to have the narrowest ranges of both yaw and pitch. Despite this, in conjunction with the 3D GAN, we were able to use the dataset to improve large-pose facial recognition. CASIA Webface displays a noticeably wider distribution of yaw angles than the other datasets. Again, despite this prior advantage, we were able to improve FR results above the CASIA baselines. + +Synthetic datasets of either 10k, 20k or 30k IDs were generated, each with 120 images per ID. Yaw and pitch angles were selected randomly from uniform distributions with ranges $[-90^{\circ}, 90^{\circ}]$ and $[-45^{\circ}, 45^{\circ}]$ respectively, whereas all other parameters (shape, expression, texture and background) were selected from a standard normal distribution, as during training. Synthetic images were augmented further using an SH lighting model [32]. We augmented using only white light and chose ambient and non-ambient lighting coefficients from random uniform distributions in the ranges [0.6, 1.4] and $[-0.4, 0.4]$ respectively. In performing this lighting augmentation, we make the assumption that images in the synthetic training dataset are only ambiently lit. This is not the case, however, and learned textures can contain problematic, embedded lighting effects. Nevertheless, performing this relatively crude lighting augmentation is shown to improve FR accuracy. + +![](images/184b79714adc78baf73cd783fcb6a99311fa4de96ae4ceec13e48086441d2c2d.jpg) +Figure 7. Random instances of a selection of IDs generated by the 3D GAN trained on FFHQ. Each row of seven images represents the same identity with random pose, expression and lighting. The images have been cropped to $112 \times 112$ pixels for use in the experiments recorded in Table 3. + +![](images/a1679bcde84a03fd17eda514a8018173cd66495c841252cc260f2ff4a0d28c39.jpg) + +![](images/b2337ba49eb98e6a1e554bb6fcf2b6ffbca8caad97ac9561eb1a262f8d5b5db8.jpg) +Input + +![](images/c34b52918d583a89a784cdfb83811f2165722ec37c96fab2eeb691ec86ddd5f1.jpg) + +![](images/319770c93a266b0e5af7244e02c3dcbf9ec24316b758a865b46bad8d03949856.jpg) +Tewari'18 [38] + +![](images/169b5a1d7309e9c17019b0fdbabc17f4c881b2f09a03d0bca353677f8bb0bdeb.jpg) + +![](images/aaf53c462d244606c85d954bdb96d38d9e7e8f3d42043a1c22239dc4998c8d84.jpg) +Tran'18 [40] +Figure 8. Example 3D facial reconstructions for three disentangled auto-encoder methods with texture models learnt from in-the-wild images. Images taken from [39]. + +![](images/605970637c46919b056256326a5c1d110e02576d55b9d040bca200bc5a2e18f0.jpg) + +![](images/a685dea748b86d2e1fcaec6130b2315a325a7287122797ed5c7f6bef5475e31c.jpg) +Tran'19 [39] + +Examples of in-the-wild synthetic images can be seen in Figure 7. These examples were generated from FFHQ at a resolution of $128 \times 128$ pixels and then cropped to $112 \times 112$ for use in the data-augmentation experiments recorded in Table 3. The images are generally of lower quality than those generated from Multi-PIE and display visible artefacts. We suspect that this is due to a combination of the larger variation in textures and lighting conditions in FFHQ, the lower number of images at large poses, and the absence of reliable pose labels. Despite these issues, our experiments show that the synthetic data is of adequate quality to successfully augment FR datasets. + +In Figure 8 we provide example 3D facial reconstructions taken from [39] for qualitative comparison with the + +images of Figure 7. Despite the comparison being indirect, we believe 3D GAN images to be of a similar quality to the comparable state of the art. The 3D GAN also has the benefit of being able to 1) easily generate new identities, 2) generate full facial images, including the back of the head and the background, and 3) does not require the 3DMM to be fit to training images. + +# 4.2.2 Data-augmentation experiments + +In all of our experiments we use the ResNet architecture of [9] trained for 15 epochs. The only changes made were to the number of layers, as noted in Tables 2 and 3. Table 2 presents results for a series of experiments in which we augmented the NetScrape dataset with 3D GAN data generated from CelebA. Experiment 1 gives our baseline, trained only on the "NetScrape" dataset. Experiment 2 shows that the effect of adding in CelebA is to increase accuracy on CFP-FP and CPLFW by $0.47\%$ and $0.25\%$ respectively. The effect of adding the synthetic data, however, is to increase accuracy by up to $1.7\%$ for CFP-FP, with an accuracy of $95.29\%$ being achieved in Experiment 6, and by up to $1.69\%$ for CPLFW, with an accuracy of $86.25\%$ being achieved in Experiment 5; i.e. the 3D GAN was able to exploit the images of CelebA somewhere between three to six times more effectively. Experiments 3 and 4 show that disabling the SH lighting, and limiting the variance of the pose to that found in CelebA itself, each decrease accuracy on both CFP-FP and CPLFW, with limitation of the pose having the largest + +
ExpFR networkLossTraining setAugmentationIDsImagesCFP-FPCPLFW
1ResNet-34ArcFaceNetScrape-26.8k3.5M93.59%84.56%
2ResNet-34ArcFaceNetScrapeCelebA26.8k + 10.2k3.5M + 0.2M94.06%84.81%
3ResNet-34ArcFaceNetScrape3D Synth (no SH)26.8k + 10k3.5M + 1.2M94.46%85.55%
4ResNet-34ArcFaceNetScrape3D Synth (narrow pose)26.8k + 10k3.5M + 1.2M93.76%84.93%
5ResNet-34ArcFaceNetScrape3D Synth26.8k + 10k3.5M + 1.2M94.89%86.25%
6ResNet-34ArcFaceNetScrape3D Synth26.8k + 20k3.5M + 2.4M95.29%85.96%
7ResNet-34ArcFaceNetScrape3D Synth26.8k + 30k3.5M + 3.6M94.63%85.91%
+ +Table 2. A comparison of the effect of augmentation with 3D GAN data (trained using CelebA) on CFP [33] and CPLFW [44] verification accuracies. "no SH" indicates deactivation of SH lighting augmentation, and "narrow pose" indicates use of a Gaussian pose distribution of StdDev = 12°, similar to the distribution in CelebA. + +
MethodFR networkLossTraining setAugmentationCFP-FFCFP-FPLFWCPLFW
HumanBrain---96.24%94.57%97.27%81.21%
BaselineResNet-50ArcFaceCASIA--95.56%--
Gecer et al. (2019) [12]ResNet-50ArcFaceCASIA10k synth IDs-97.12%--
BaselineResNet-50ArcFaceCASIA-99.37%95.50%99.30%85.69%
3D GAN (FFHQ)ResNet-50ArcFaceCASIA10k synth IDs99.49%96.40%99.35%86.53%
3D GAN (FFHQ)ResNet-50ArcFaceCASIA20k synth IDs99.40%96.74%99.42%86.85%
Deng et al. (2019) [9]ResNet-100ArcFaceMS1M-V2---99.82%92.08%
Huang et al. (2020a) [19]ResNet-100ArcFace + DDLVGG--98.53%99.68%93.43%
BaselineResNet-100ArcFaceMS1M-V3-99.90%98.47%99.87%93.36%
3D GAN (FFHQ)ResNet-100ArcFaceMS1M-V320k synth IDs99.90%98.51%99.85%93.53%
+ +Table 3. A comparison of data-augmentation using synthetic identities generated by the 3D GAN (trained using FFHQ) with results from the literature (highlighted in grey). Evaluation is performed for the frontal-frontal (FF) and frontal-profile (FP) protocols of the CFP dataset as well as for LFW (view 2) and CPLFW. "DLL" refers to the Distribution Distillation Loss of [19]. + +effect. Both experiments, however, still perform better than the baseline. Finally, in Experiments 5, 6 and 7, we augment the dataset with $10\mathrm{k}$ , $20\mathrm{k}$ and $30\mathrm{k}$ synthetic identities. For each experiment the measured accuracies are above those of the baseline experiments, although performance drops for either $20\mathrm{k}$ or $30\mathrm{k}$ identities depending on the evaluation dataset. The reason for this decrease in performance could be due to synthetic identities being too densely sampled, with too many lookalikes being generated. Alternatively, it could be due to overfitting of the biometric network to 3D GAN data since, in Experiments 6 and 7, significant proportions of the training dataset were synthetic (40.7% and 50.7% as opposed to only 25.5% in Experiment 3). + +Table 3 presents the results of experiments for comparison with the 3D model-based data-augmentation method of [12], and with other results from the literature, highlighted in grey. The cleanest comparison is with the method of [12] in which synthetic data generated by their TB-GAN was used to augment CASIA Webface giving an improvement of $1.56\%$ from $95.56\%$ to $97.12\%$ verification accuracy on CFP-FP. Augmentation using 20k synthetic identities generated from FFHQ using our 3D GAN gave an improvement of $1.24\%$ from the slightly lower baseline of accuracy of $95.50\%$ up to $96.74\%$ . Note that, in this experiment, the 3D GAN extracts useful information from the noisy FFHQ + +dataset, whereas the TB-GAN of [12] is trained using a dataset of high-quality texture scans. Improvements in accuracy were also seen for CPLFW with addition of $10\mathrm{k}$ and $20\mathrm{k}$ synthetic identities leading to improvements of $0.84\%$ and $1.16\%$ respectively. Evaluation on the frontal protocol of CFP and on LFW gave only small improvements. + +Finally, experiments were performed for a ResNet-100 architecture trained on the MS1M-V3 dataset. Augmentation using 20k synthetic identities generated from FFHQ using our 3D GAN gives a state-of-the-art accuracy of $93.53\%$ on CPLFW. This improvement was achieved despite the already very high performance of the baseline network. + +# 5. Conclusions + +We proposed a novel 3D GAN formulation for learning a nonlinear texture model from in-the-wild images and thereby generating synthetic images of new identities with fully disentangled pose. We demonstrate that images synthesised by our 3D GAN can be used successfully to improve the accuracy of large-posed facial recognition. The 3D GAN enjoys the advantage of not requiring specially captured texture scans. Finally, since the 3D GAN can generate images of new identities, it provides an avenue for extraction of useful information from noisy datasets such as FFHQ. + +# References + +[1] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. In Doina Precup and Yee Whye Teh, editors, Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6-11 August 2017, volume 70 of Proceedings of Machine Learning Research, pages 214-223. PMLR, 2017. +[2] Volker Blanz and Thomas Vetter. A morphable model for the synthesis of 3d faces. In Warren N. Waggenspack, editor, Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1999, Los Angeles, CA, USA, August 8-13, 1999, pages 187-194. ACM, 1999. +[3] James Booth, Epameinondas Antonakos, Stylianos Ploumpis, George Trigeorgis, Yannis Panagakis, and Stefanos Zafeiriou. 3d face morphable models "in-the-wild". In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017, pages 5464-5473. IEEE Computer Society, 2017. +[4] James Booth, Anastasios Roussos, Stefanos Zafeiriou, Allan Ponniah, and David Dunaway. A 3d morphable model learnt from 10,000 faces. In 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, Las Vegas, NV, USA, June 27-30, 2016, pages 5543-5552. IEEE Computer Society, 2016. +[5] Kaidi Cao, Yu Rong, Cheng Li, Xiaou Tang, and Chen Change Loy. Pose-robust face recognition via deep residual equivariant mapping. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, June 18-22, 2018, pages 5187-5196. IEEE Computer Society, 2018. +[6] Bindita Chaudhuri, Noranart Vesdapunt, Linda G. Shapiro, and Baoyuan Wang. Personalized face modeling for improved face reconstruction and motion retargeting. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part V, volume 12350 of Lecture Notes in Computer Science, pages 142-160. Springer, 2020. +[7] Daniel E. Crispell, Octavian Biris, Nate Crosswhite, Jeffrey Byrne, and Joseph L. Mundy. Dataset augmentation for pose and lighting invariant face recognition. CoRR, abs/1704.04326, 2017. +[8] Jiankang Deng, Shiyang Cheng, Niannan Xue, Yuxiang Zhou, and Stefanos Zafeiriou. UV-GAN: adversarial facial UV map completion for pose-invariant face recognition. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, June 18-22, 2018, pages 7093-7102. IEEE Computer Society, 2018. +[9] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou. Arcface: Additive angular margin loss for deep face recognition. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, pages 4690-4699. Computer Vision Foundation / IEEE, 2019. + +[10] Jiankang Deng, Jia Guo, Yuxiang Zhou, Jinke Yu, Irene Kotsia, and Stefanos Zafeiriou. Retinaface: Single-stage dense face localisation in the wild. CoRR, abs/1905.00641, 2019. +[11] Baris Gecer, Binod Bhattacharai, Josef Kittler, and Tae-Kyun Kim. Semi-supervised adversarial learning to generate photorealistic face images of new identities from 3d morphable model. In Vittorio Ferrari, Martial Hebert, Cristian Sminchisescu, and Yair Weiss, editors, Computer Vision - ECCV 2018 - 15th European Conference, Munich, Germany, September 8-14, 2018, Proceedings, Part XI, volume 11215 of Lecture Notes in Computer Science, pages 230-248. Springer, 2018. +[12] Baris Gecer, Alexandros Lattas, Stylianos Ploumpis, Jiankang Deng, Athanasios Papaioannou, Stylianos Moschoglou, and Stefanos Zafeiriou. Synthesizing coupled 3d face modalities by trunk-branch generative adversarial networks. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXIX, volume 12374 of Lecture Notes in Computer Science, pages 415-433. Springer, 2020. +[13] Baris Gecer, Stylianos Ploumpis, Irene Kotsia, and Stefanos Zafeiriou. GANFIT: generative adversarial network fitting for high fidelity 3d face reconstruction. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, pages 1155-1164. Computer Vision Foundation / IEEE, 2019. +[14] Partha Ghosh, Pravir Singh Gupta, Roy Uziel, Anurag Ranjan, Michael J. Black, and Timo Bolkart. GIF: generative interpretable faces. In Vitomir Struc and Francisco Gómez Fernández, editors, 8th International Conference on 3D Vision, 3DV 2020, Virtual Event, Japan, November 25-28, 2020, pages 868-878. IEEE, 2020. +[15] Ralph Gross, Iain A. Matthews, Jeffrey F. Cohn, Takeo Kanade, and Simon Baker. Multi- PIE. Image Vis. Comput., 28(5):807-813, 2010. +[16] Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C. Courville. Improved training of wasserstein gans. In Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman Garnett, editors, Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 4-9 December 2017, Long Beach, CA, USA, pages 5767-5777, 2017. +[17] Tal Hassner, Shai Harel, Eran Paz, and Roee Enbar. Effective face frontalization in unconstrained images. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015, Boston, MA, USA, June 7-12, 2015, pages 4295-4304. IEEE Computer Society, 2015. +[18] Paul Henderson and Vittorio Ferrari. Learning single-image 3d reconstruction by generative modelling of shape, pose and shading. Int. J. Comput. Vis., 128(4):835-854, 2020. +[19] Yuge Huang, Pengcheng Shen, Ying Tai, Shaoxin Li, Xiaoming Liu, Jilin Li, Feiyue Huang, and Rongrong Ji. Improving face recognition from hard samples via distribution distillation loss. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision - ECCV + +2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXX, volume 12375 of Lecture Notes in Computer Science, pages 138-154. Springer, 2020. +[20] Yuge Huang, Yuhan Wang, Ying Tai, Xiaoming Liu, Pengcheng Shen, Shaoxin Li, Jilin Li, and Feiyue Huang. Curricularface: Adaptive curriculum learning loss for deep face recognition. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, June 13-19, 2020, pages 5900-5909. IEEE, 2020. +[21] Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of gans for improved quality, stability, and variation. In 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Conference Track Proceedings. OpenReview.net, 2018. +[22] Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, pages 4401-4410. Computer Vision Foundation / IEEE, 2019. +[23] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of stylegan. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, June 13-19, 2020, pages 8107-8116. IEEE, 2020. +[24] Adam Kortylewski, Andreas Schneider, Thomas Gerig, Bernhard Egger, Andreas Morel-Forster, and Thomas Vetter. Training deep face recognition systems with synthetic data. CoRR, abs/1802.05891, 2018. +[25] Marek Kowalski, Stephan J. Garbin, Virginia Estellers, Tadas Baltrusaitis, Matthew Johnson, and Jamie Shotton. CONFIG: controllable neural face image generation. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XI, volume 12356 of Lecture Notes in Computer Science, pages 299-315. Springer, 2020. +[26] Tianye Li, Timo Bolkart, Michael J. Black, Hao Li, and Javier Romero. Learning a model of facial shape and expression from 4d scans. ACM Trans. Graph., 36(6):194:1-194:17, 2017. +[27] Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaou Tang. Deep learning face attributes in the wild. In 2015 IEEE International Conference on Computer Vision, ICCV 2015, Santiago, Chile, December 7-13, 2015, pages 3730-3738. IEEE Computer Society, 2015. +[28] Jiang-Jing Lv, Xiaohu Shao, Jia-Shui Huang, Xiang-Dong Zhou, and Xi Zhou. Data augmentation for face recognition. Neurocomputing, 230:184-196, 2017. +[29] Richard Marriott, Safa Madiouni, Sami Romdhani, Stephane Gentric, and Liming Chen. An assessment of GANs for identity-related applications. In 2020 IEEE International Joint Conference on Biometrics (IJCB). IEEE, 2020. +[30] Iacopo Masi, Anh Tuan Tran, Tal Hassner, Jatuporn Toy Leksut, and Gerard G. Medioni. Do we really need to collect + +millions of faces for effective face recognition? In Bastian Leibe, Jiri Matas, Nicu Sebe, and Max Welling, editors, Computer Vision - ECCV 2016 - 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part V, volume 9909 of Lecture Notes in Computer Science, pages 579-596. Springer, 2016. +[31] Xi Peng, Xiang Yu, Kihyuk Sohn, Dimitris N. Metaxas, and Manmohan Chandraker. Reconstruction-based disentangle-ment for pose-invariant face recognition. In IEEE International Conference on Computer Vision, ICCV 2017, Venice, Italy, October 22-29, 2017, pages 1632-1641. IEEE Computer Society, 2017. +[32] Ravi Ramamoorthi and Pat Hanrahan. An efficient representation for irradiance environment maps. In Lynn Pocock, editor, Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2001, Los Angeles, California, USA, August 12-17, 2001, pages 497-500. ACM, 2001. +[33] Soumyadip Sengupta, Jun-Cheng Chen, Carlos Domingo Castillo, Vishal M. Patel, Rama Chellappa, and David W. Jacobs. Frontal to profile face verification in the wild. In 2016 IEEE Winter Conference on Applications of Computer Vision, WACV 2016, Lake Placid, NY, USA, March 7-10, 2016, pages 1-9. IEEE Computer Society, 2016. +[34] Yujun Shen, Ping Luo, Junjie Yan, Xiaogang Wang, and Xiaou Tang. Faceid-gan: Learning a symmetry three-player GAN for identity-preserving face synthesis. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, June 18-22, 2018, pages 821-830. IEEE Computer Society, 2018. +[35] Ayush Tewari, Florian Bernard, Pablo Garrido, Gaurav Bharaj, Mohamed Elgharib, Hans-Peter Seidel, Patrick Pérez, Michael Zollhöfer, and Christian Theobalt. FML: face model learning from videos. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, pages 10812-10822. Computer Vision Foundation / IEEE, 2019. +[36] Ayush Tewari, Mohamed Elgharib, Gaurav Bharaj, Florian Bernard, Hans-Peter Seidel, Patrick Pérez, Michael Zollhöfer, and Christian Theobalt. Stylerig: Rigging stylegan for 3d control over portrait images. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, June 13-19, 2020, pages 6141-6150. IEEE, 2020. +[37] Ayush Tewari, Mohamed Elgharib, Mallikarjun B. R., Florian Bernard, Hans-Peter Seidel, Patrick Pérez, Michael Zollhöfer, and Christian Theobalt. PIE: portrait image embedding for semantic control. ACM Trans. Graph., 39(6):223:1-223:14, 2020. +[38] Ayush Tewari, Michael Zollhöfer, Pablo Garrido, Florian Bernard, Hyeongwoo Kim, Patrick Pérez, and Christian Theobalt. Self-supervised multi-level face model learning for monocular reconstruction at over 250 hz. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, June 18-22, 2018, pages 2549-2559. IEEE Computer Society, 2018. +[39] Luan Tran, Feng Liu, and Xiaoming Liu. Towards high-fidelity nonlinear 3d face morphable model. In IEEE Con- + +ference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, pages 1126-1135. Computer Vision Foundation / IEEE, 2019. +[40] Luan Tran and Xiaoming Liu. Nonlinear 3d face morphable model. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, June 18-22, 2018, pages 7346-7355. IEEE Computer Society, 2018. +[41] Luan Tran, Xi Yin, and Xiaoming Liu. Disentangled representation learning GAN for pose-invariant face recognition. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017, pages 1283-1292. IEEE Computer Society, 2017. +[42] Dong Yi, Zhen Lei, Shengcai Liao, and Stan Z. Li. Learning face representation from scratch. CoRR, abs/1411.7923, 2014. +[43] Jian Zhao, Lin Xiong, Jayashree Karlekar, Jianshu Li, Fang Zhao, Zhecan Wang, Sugiri Pranata, Shengmei Shen, Shuicheng Yan, and Jiashi Feng. Dual-agent gans for photorealistic and identity preserving profile face synthesis. In Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman Garnett, editors, Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 4-9 December 2017, Long Beach, CA, USA, pages 66-76, 2017. +[44] Tianyue Zheng and Weihong Deng. Cross-pose LFW: A database for studying cross-posed face recognition in unconstrained environments. Beijing University of Posts and Telecommunications, Tech. Rep, 5, 2018. +[45] Xiangyu Zhu, Zhen Lei, Junjie Yan, Dong Yi, and Stan Z. Li. High-fidelity pose and expression normalization for face recognition in the wild. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015, Boston, MA, USA, June 7-12, 2015, pages 787-796. 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Despite its importance, most existing RGB-T semantic segmentation models perform primitive fusion strategies, such as concatenation, element-wise summation and weighted summation, to fuse features from different modalities. These strategies, unfortunately, overlook the modality differences due to different imaging mechanisms, so that they suffer from the reduced discriminability of the fused features. To address such an issue, we propose, for the first time, the strategy of bridging-then-fusing, where the innovation lies in a novel Adaptive-weighted Bi-directional Modality Difference Reduction Network (ABMDRNet). Concretely, a Modality Difference Reduction and Fusion (MDRF) subnetwork is designed, which first employs a bi-directional image-to-image translation based method to reduce the modality differences between RGB features and thermal features, and then adaptively selects those discriminative multi-modality features for RGB-T semantic segmentation in a channel-wise weighted fusion way. Furthermore, considering the importance of contextual information in semantic segmentation, a Multi-Scale Spatial Context (MSC) module and a MultiScale Channel Context (MCC) module are proposed to exploit the interactions among multi-scale contextual information of cross-modality features together with their long-range dependencies along spatial and channel dimensions, respectively. Comprehensive experiments on MFNet dataset demonstrate that our method achieves new state-of-the-art results. + +![](images/5b6cddefb2e97759805b1f8a841e30e1091b9c6b0f8332e5ab061b96baf344e7.jpg) +Figure 1. Illustration of modality difference reduction. (a) Bidirectional modality difference reduction. (b)-(d) Original RGB features, thermal features and their fused features, respectively. (e)-(g) RGB features, thermal features and their fused features after reducing modality differences, respectively. + +![](images/375e3b0802ab33cf6a86a2df1d87aaeec706b5b16d6c6cdc6a960c53af0756a9.jpg) + +# 1. Introduction + +Semantic segmentation aims to assign category labels to each pixel in a natural image, which plays an important role in many computer vision task, such as autonomous driving [6, 31], pedestrian detection [1], pathological analysis [20, 26] and so on. + +So far, CNN-based RGB semantic segmentation methods [14, 15, 20, 27] have achieved prominent results in many large-scale datasets [5, 16]. However, their performance may significantly degrade under poor lighting conditions. To boost semantic segmentation performance, recent researches pay more attention to RGB-T semantic segmentation [9, 22, 25], where thermal images may complement rich contour information and semantic information to RGB images under poor lighting conditions. + +Existing models for multi-modality pixel-level prediction tasks, including RGB-T semantic segmentation and RGB-T salient object detection, usually adopt simple strategies, such as element-wise summation [25], concatenation [9] and weighted summation [8,32], to capture the complementary information from paired RGB and thermal images. However, they usually ignore the modality differences between RGB images and thermal images, which are caused + +by different imaging mechanisms. Such negligence may lead to inadequate cross-modality complementary information exploitation. As shown in Fig. 1, the people region, marked by red dotted box in Fig. 1(b), has low intensity values, while the same region in Fig. 1(c) has higher intensity values. If simple fusion operations are employed, the discriminative target information in the thermal image will be noticeably suppressed in the fused features, as shown in Fig. 1(d). + +To solve this problem, we propose a novel multimodality feature fusion subnetwork, i.e., Modality Difference Reduction and Fusion (MDRF), to better exploit the multi-modality complementary information from RGB images and thermal images via a novel strategy of bridging-then-fusing. In the bridging stage, as shown in Fig. 1(a), a bi-directional image-to-image translation [13, 33] based method is employed to reduce the differences between RGB and thermal features. The basic idea is that when transferring images from one modality to another, some nondiscriminative single-modality information, caused by different imaging mechanisms (e.g., Fig. 1(b) and Fig. 1(c)), will be translated into discriminative ones (e.g., Fig. 1(e) and Fig. 1(f)) by virtue of the complementary supervision information from the images of another modality. As a result, the modality differences between the extracted single-modality RGB and thermal features will be reduced for better fusion (e.g., Fig. 1(d) and Fig. 1(g)). Then, in the fusing stage, a novel fusion module, i.e., Channel Weighted Fusion (CWF) module, is presented to capture the cross-modality information between the corresponding channels of single-modality RGB and thermal features, whose modality differences have been reduced in the first step. As shown in Fig. 1(d) and Fig. 1(g), higher discriminative fused features may be obtained by using the single-modality features that have reduced modality differences than those original ones. + +Furthermore, the diversity of objects, e.g., categories, sizes and shapes, in a given image is also problematic for semantic segmentation. Multi-scale contextual information and their long-range dependencies have been proved to be effective to address such an issue in RGB semantic segmentation. However, in multi-modality semantic segmentation, especially for RGB-T semantic segmentation [9, 22, 25], multi-scale contextual information of cross-modality features and their long-range dependencies are not in place yet. In RGB-T semantic segmentation, only MFNet [9] added several mini-inception blocks in the encoder to obtain some contextual information. But this is far limited for semantic segmentation. + +Inspired by [3, 6, 30], we propose two novel modules, i.e., a Multi-Scale Spatial Context (MSC) module and a Multi-Scale Channel Context (MCC) module, to exploit the multi-scale contextual information of cross-modality features and their long-range dependencies along spatial and + +channel dimensions, respectively. First, multi-scale features are obtained by performing the Atrous Spatial Pyramid Pooling (ASPP) module [3] on the original fused cross-modality features. Then the long-range dependencies for these multi-scale features along the spatial and channel dimensions are established by jointly using the original fused cross-modality features and their corresponding multi-scale features in MSC and MCC, respectively. With MSC and MCC cooperative, the multi-scale contextual information of cross-modality features and their long-range dependencies will be fully exploited for RGB-T semantic segmentation. + +The main contributions of this paper are summarized as follows: + +(1) An end-to-end ABMDRNet is presented to facilitate RGB-T semantic segmentation by simultaneously considering multi-modality difference reduction and multi-scale contextual information of cross-modality data. Comprehensive experimental results show that our model achieves new state-of-the-art performance on MFNet dataset. +(2) An MDRF subnetwork is presented to effectively capture the cross-modality information from the RGB and thermal images via a strategy of bridging-then-fusing, which first employs a bi-directional image-to-image translation based method to bridge the modality gaps between multi-modality data and then adaptively selects those discriminative multi-modality features for RGB-T semantic segmentation. +(3) An MSC module and an MCC module are presented to fully exploit the multi-scale contextual information of cross-modality features and their long-range dependencies along the spatial and channel dimensions, respectively. + +# 2. Related work + +# 2.1. RGB-based semantic segmentation + +Early RGB-based semantic segmentation methods mainly rely on low-level hand-crafted features combined with flat classifiers, such as Random Forests [23] and multiclass fuzzy Support Vector Machine [19]. Recently, deep learning based semantic segmentation models [2,6,15,18,20,27] have become the mainstream and achieved significant improvements. These models are usually based on Fully Convolutional Network (FCN) [15] for its simple but reasonable architecture for pixel-wise prediction. As well, to address the diversity of objects, these FCN-based models mainly exploit some pyramid structures, such as Pyramid Pooling Module (PPM) [34] and Atrous Spatial Pyramid Pooling (ASPP) [3], to capture the discriminative multiscale contextual information from input images. Although these multi-scale contextual information extraction modules have achieved great successes in semantic segmentation, their receptive fields are still limited, thus failing to exploit the global contextual information. Recently, many mod + +![](images/b3bfa7857e3b7a560c5b86b13dccccc66cafcbfe1280625bf9dae057c7e69a0a.jpg) +Figure 2. Overall framework of our proposed model. The blue and red dotted boxes represent the bi-directional modality difference reduction stage in MDRF subnetwork. + +els [17, 30] try to exploit the long-range dependencies to address such issue and have achieved promising results. For example, non-local operation [30] was proposed to compute the response at a position as a weighted sum of the features for capturing long-range dependencies. + +# 2.2. Multi-modality semantic segmentation + +Recently, with the rapid development of imaging techniques, many studies [4,7,9,12,21,22,25,29] employ multimodality data (e.g., RGB-T images and RGB-D images) to address some issues arising from the traditional RGB semantic segmentation. These multi-modality semantic segmentation models are usually divided into two categories, i.e., feature-level fusion based and image-level fusion based ones. Specifically, feature-level fusion based models first extract single-modality features from each input modality data and then fuse them to capture complementary information for semantic segmentation. For example, [11] proposed an Attention Complementary Module (ACM) to capture more high-quality single-modality RGB features and depth features from different channels for boosting the RGB-D semantic segmentation. [9] adopted an Encoder-Decoder architecture, which first extracted RGB features and thermal features respectively and then fused them by the tailored short-cut blocks. [25] first fused the multi-level RGB features and thermal features by element-wise summation and then employed an upception block to improve the decoding results. Different from them, image-level fusion based models directly take the combination of multi-modality images as inputs. For example, [22] proposed a sequential dualstream CNN architecture, which concatenated an RGB image, the matched thermal image and the coarse mask predicted by RGB features as a five-channel input to predict the result. + +In contrast to RGB-D semantic segmentation, RGB-T semantic segmentation attracts less attention. Most exist + +ing RGB-T semantic segmentation models [9, 22, 25] employ simple fusion strategies, such as element-wise summation [25] and concatenation [9, 22], to capture the cross-modality features, while ignoring the modality differences caused by different imaging mechanisms. Alternatively, in this paper, a novel strategy of bridging-then-fusing is presented to capture the cross-modality features, where the modality differences between multi-modality data are first reduced and then the discriminative multi-modality features are adaptively selected for RGB-T semantic segmentation. + +# 3. Method + +As shown in Fig. 2, the proposed RGB-T semantic segmentation framework, i.e., ABMDRNet, consists of three components, including MDRF subnetwork, MSC module and MCC module. The details of them will be discussed in the following contents. + +# 3.1.MDRF + +Although paired RGB images and thermal images can provide much complementary information to each other, the modality differences, caused by different imaging mechanisms, may hinder the integration and exploitation of multimodality complementary information from RGB images and thermal images. Unfortunately, this has been ignored by most existing models. To address this issue, we design a novel multi-modality feature fusion subnetwork, i.e., MDRF subnetwork, via a strategy of bridging-then-fusing, which first reduces the modality differences bi-directionally and then exploits the multi-modality complementary information. Specifically, the MDRF subnetwork consists of two stages. The first stage is bi-directional modality difference reduction, which aims to obtain discriminative single-modality features with fewer modality differences from RGB images and thermal images, respectively. The second stage is discriminative single-modality features fusion, + +which aims to effectively exploit the complementary information from multi-modality features. + +# 3.1.1 Bi-directional modality difference reduction + +Inspired by those image-to-image translation methods [13, 33], we employ a bi-directional bridging strategy to reduce the modality differences caused by different imaging mechanisms. The strategy starts with a bi-directional difference reduction, including the reduction from RGB to thermal and that from thermal to RGB. Specifically, the multilevel single-modality features extracted from one modality are employed to generate a matched pseudo image of another modality. Meanwhile, its corresponding real image of another modality is also available in RGB-T semantic segmentation. Considering that, we reduce the differences from one modality to another modality by enforcing the features from the pseudo image and those from the real image of the same modality to be similar as possible. + +As shown in Fig. 2, we exactly employ the same modality difference reduction structure for RGB images and thermal images (i.e., region marked by blue dotted box and red dotted box). Therefore, in the following contents, we will take the procedure of transferring RGB images into thermal images as an example to show the details of our structure for modality difference reduction. + +First, a ResNet-50 [10] is employed to extract the single-modality features from an RGB image. The average pooling and the fully connected layers of the ResNet-50 are removed to maintain more spatial information. Therefore, five levels of single-modality RGB features $\{\mathbf{F}_n^{RGB}|n = 1,2,3,4,5\}$ are obtained, which have the resolutions of $1 / 2$ , $1 / 4$ , $1 / 8$ , $1 / 16$ and $1 / 32$ of the original image sizes, respectively. Then, the last four levels of single-modality RGB features are fed into an RGB-to-T translation network to generate the corresponding pseudo thermal image. The translation network first performs four $1\times 1$ convolutional layers on the four levels of single-modality RGB features $\{\mathbf{F}_n^{RGB}|n = 2,3,4,5\}$ to generate one-channel feature maps. Then, all of the generated feature maps are upsampled and fused to generate a pseudo thermal image $(\mathbf{I}^{pse - T})$ . After that, to make the generated pseudo thermal image similar to its corresponding real thermal image and further reduce the modality differences, two auxiliary ResNet-18s [10] are employed to extract five levels of auxiliary features (i.e., $\{\mathbf{F}_n^{pse - T}|n = 1,2,3,4,5\}$ and $\{\mathbf{F}_n^{real - T}|n = 1,2,3,4,5\}$ ) from the pseudo thermal image and its real thermal image, respectively. The average pooling and the fully connected layers of the two ResNet-18s are also removed to maintain the spatial information. By enforcing the two sets of features to be similar as possible, the extracted single-modality features $\{\mathbf{F}_n^{RGB}|n = 1,2,3,4\}$ from RGB modality may share some similar properties with those features $\{\mathbf{F}_n^T|n = 1,2,3,4\}$ from thermal modal + +![](images/19417a24ad3cab8948bebcdde88b2bdeaacf85bdaaa0e49bf08e89f7df29a11a.jpg) +Figure 3. Structure of the proposed CWF module. The weight vector $\mathbf{W}_n$ is able to weigh the importance of feature maps from RGB modality. + +ity, thus reducing the modality differences between the two modality data. + +For a thermal image, we can also obtain its pseudo RGB image $\mathbf{I}^{pse - RGB}$ together with its corresponding pseudo and real RGB image features $\{\mathbf{F}_n^{pse - RGB}|n = 1,2,3,4,5\}$ and $\{\mathbf{F}_n^{real - RGB}|n = 1,2,3,4,5\}$ . Furthermore, the extracted single-modality features $\{\mathbf{F}_n^T |n = 1,2,3,4\}$ from the thermal image may also be enforced to share some similar properties with those from the RGB image by using the same way, which will further reduce the modality differences between the two modality data. + +In this stage, the following loss is employed for supervision, i.e., + +$$ +\begin{array}{l} \mathcal {L} _ {M D} = \sum_ {n = 1} ^ {5} \mathcal {L} _ {1} \left(\mathbf {F} _ {n} ^ {p s e - T}, \mathbf {F} _ {n} ^ {r e a l - T}\right) + \tag {1} \\ \sum_ {n = 1} ^ {5} \mathcal {L} _ {1} \left(\mathbf {F} _ {n} ^ {p s e - R G B}, \mathbf {F} _ {n} ^ {r e a l - R G B}\right), \\ \end{array} +$$ + +where $\mathcal{L}_1(*)$ denotes L1 loss. Because of the bi-directional modality difference reduction, there will be smaller differences between the RGB features $\{\mathbf{F}_n^{RGB}|n = 1,2,3,4\}$ and the thermal features $\{\mathbf{F}_n^T |n = 1,2,3,4\}$ extracted from the ResNet-50s. This will improve the discriminability of the fused cross-modality features, as discussed in the earlier section. + +# 3.1.2 Channel-Wise Weighted Features Fusion + +Having the single-modality features, the next step is to capture their complementary information by using some fusion strategies for RGB-T semantic segmentation. The most intuitive ways are element-wise summation or concatenation, which cannot exploit the multi-modality complementary information effectively. For that, some complex strategies [8, 32] obtain the fused features in a weighted summation way. However, most existing fusion strategies adopt the same weights for all of the channels. These weights may work well for some channels of features, while some undesirable fusion results may be obtained for some channels of features. In fact, different channels of features may + +correspond to different classes for semantic segmentation. Compared with features from different spatial positions, the features from different channels may have higher class-discriminability for semantic segmentation. + +Considering that, we propose a novel CWF module in the fusing stage of MDRF to effectively exploit the cross-modality complementary information by re-weighting the importance of single-modality features in a channel-dependent way, rather than in a spatial position-dependent way. Specifically, given the $n$ -th level of single-modality features (i.e., $\{\mathbf{F}_n^{RGB}|n = 1,2,3,4\}$ and $\{\mathbf{F}_n^T |n = 1,2,3,4\}$ ) from the first stage, as shown in Fig. 3, the proposed CWF module exploits their multi-modality complementary information by using the following steps. + +First, the $\mathbf{F}_n^{RGB}$ and $\mathbf{F}_n^T$ are concatenated and then fed into two convolutional layers to obtain the relative importance of the paired features from different modalities but in the same channels. The corresponding importance weight vector $\mathbf{W}_n$ is obtained by + +$$ +\mathbf {W} _ {n} = \operatorname {G A P} \left(\sigma \left(\operatorname {C o n v} \left(\operatorname {C a t} \left(\mathbf {F} _ {n} ^ {R G B}, \mathbf {F} _ {n} ^ {T}\right); \beta\right)\right)\right). \tag {2} +$$ + +Here, $\mathrm{Conv}(*;\beta)$ denotes a convolutional block with a $1\times 1$ convolutional layer and a $3\times 3$ convolutional layer and $\beta$ denotes its parameters. $\mathrm{GAP(*)}$ denotes the global average pooling operation. $\sigma (*)$ denotes the Sigmoid activation function, respectively. Higher values in $\mathbf{W}_n$ indicate that corresponding channels of features in RGB modality are more likely to be important than those corresponding channels of features from thermal images, and vice versa. As a result, the relative importance for each channel of features from different modalities are obtained. By using these channel importance weight vectors $\{\mathbf{W}_n|n = 1,2,3,4\}$ , the fused features $\{\mathbf{F}_n^{fused}|n = 1,2,3,4\}$ are obtained by + +$$ +\mathbf {F} _ {n} ^ {f u s e d} = \left\{ \begin{array}{c} \mathbf {W} _ {n} \odot \mathbf {F} _ {n} ^ {R G B} + \left(\mathbf {1} - \mathbf {W} _ {n}\right) \odot \mathbf {F} _ {n} ^ {T}, \quad n = 1 \\ \mathrm {D} \left(\mathbf {F} _ {n - 1} ^ {f u s e d}\right) + \mathbf {W} _ {n} \odot \mathbf {F} _ {n} ^ {R G B} + \left(1 - \mathbf {W} _ {n}\right) \odot \mathbf {F} _ {n} ^ {T}, \\ n = 2, 3, 4 \end{array} \right. \tag {3} +$$ + +where $\odot$ denotes the channel-wise multiplication and 1 denotes a vector of 1's with the same size of $\mathbf{W}_n$ . $\mathbf{F}_{n - 1}^{fused}$ denotes the fused features from the previous level and $\mathrm{D}(*)$ is a convolutional block with stride of 2 for downsampling. + +With several CWF modules, corresponding channels of single-modality features from different modalities are reweighted and fused. Compared with those fusion strategies sharing the same weights for different channels, our proposed CWF module may better select those channels of features with high discriminability from multi-modality data for semantic segmentation. + +# 3.2. MSC Module and MCC Module + +As discussed in Section 1, multi-scale contextual information and long-range dependencies have been proved + +![](images/69b1fa97d782e41bb1ccad2366ec4a8d9a808f84fa3f7cf3228c31aa0ab4002d.jpg) +Figure 4. Structure of the proposed MSC module. The blue annotations denote the sizes of the input and output features of MSC. + +to be effective for alleviating the issue of objects diversity in RGB semantic segmentation, but they are still not well exploited in RGB-T semantic segmentation. For that, we propose an MSC module and an MCC module to simultaneously exploit the multi-scale contextual information of cross-modality features and their long-range dependencies along the spatial and channel dimensions, respectively. More specifically, the MSC module is performed on the 3rd level of the fused features $\mathbf{F}_3^{fused}$ and the MCC module is performed on the 4-th level of the fused features $\mathbf{F}_4^{fused}$ , considering the number of parameters in the entire model. + +# 3.2.1 MSC Module + +The structure of MSC is shown in Fig. 4. Given the 3rd level of the fused features $\mathbf{F}_3^{fused} \in R^{H \times W \times 512}$ , MSC exploits their multi-scale contextual information of cross-modality features and their long-range dependencies along the spatial dimension by using the following steps. + +First, an ASPP module [3] is employed to extract multiscale contextual information from the input fused features. For that, the ASPP module employs four parallel convolutional branches to obtain four scales of features. In each branch, a $1 \times 1$ standard convolutional layer and a $3 \times 3$ atrous convolutional layer with different dilation rates (i.e., 1, 6, 12 and 18, respectively) are employed. Then, the four scales of features are concatenated and fed into a $1 \times 1$ convolutional layer to reduce their channels, thus obtaining the final multi-scale features $\mathbf{F}_3^{ms} \in R^{H \times W \times 512}$ . Subsequently, inspired by [6] and [17], a self-spatial correlation matrix $\mathbf{M}_{ss} \in R^{HW \times HW}$ is computed from the fused multi-scale features by + +$$ +\mathbf {M} _ {s s} = \operatorname {R e s h a p e} \left(\mathbf {F} _ {3} ^ {m s}\right) \times \left(\operatorname {R e s h a p e} \left(\mathbf {F} _ {3} ^ {m s}\right)\right) ^ {\mathrm {T}}, \tag {4} +$$ + +where $(*)^{\mathrm{T}}$ denotes matrix transpose and Reshape $(\ast)$ transfers the size of the input matrix from $R^{H\times W\times C}$ to $R^{HW\times C}$ . This self-spatial correlation matrix $\mathbf{M}_{ss}$ captures the paired-wise similarities of two arbitrary positions in the multi-scale features and can be employed to extract + +the long-range spatial dependencies among the multi-scale contextual features. + +Meanwhile, considering that the long-range dependencies among the multi-scale contextual features should consist with those of original input features, a cross-spatial correlation matrix $\mathbf{M}_{cs} \in R^{HW \times HW}$ is also computed from the original input features to complement the self-spatial correlation matrix $\mathbf{M}_{ss}$ for better capturing the long-range dependencies along the spatial dimension. + +$$ +\mathbf {M} _ {c s} = \operatorname {R e s h a p e} \left(\mathbf {F} _ {3} ^ {f u s e d}\right) \times \left(\operatorname {R e s h a p e} \left(\mathbf {F} _ {3} ^ {f u s e d}\right)\right) ^ {\mathrm {T}}. \tag {5} +$$ + +With the self-spatial and cross-spatial correlation matrices $\mathbf{M}_{ss}$ and $\mathbf{M}_{cs}$ , the final spatial correlation matrix $\mathbf{M}_s\in$ $R^{HW\times HW}$ is obtained by + +$$ +\mathbf {M} _ {s} = \text {N o r m a l i z a t i o n} \left(\mathbf {M} _ {s s} + \mathbf {M} _ {c s}\right), \tag {6} +$$ + +where Normalization $(\ast)$ denotes Min-Max Normalization. + +After that, the multi-scale contextual information of the fused features and their corresponding long-range dependencies along the spatial dimension are obtained by + +$$ +\mathbf {F} _ {3} ^ {f u s e d ^ {\prime}} = \text {R e s h a p e} ^ {\prime} \left(\left(\mathbf {M} _ {s} \times \text {R e s h a p e} \left(\mathbf {F} _ {3} ^ {m s}\right)\right)\right) + \mathbf {F} _ {3} ^ {f u s e d}, \tag {7} +$$ + +where $\mathrm{Reshape}^{\prime}(*)$ denotes the inverse process of $\mathrm{Reshape}(*)$ . + +# 3.2.2 MCC Module + +Given the 4-th level of the fused features $\mathbf{F}_4^{fused} \in R^{M \times N \times 1024}$ , MCC follows similar steps with MSC to exploit the multi-scale contextual information of cross-modality features and their long-range dependencies along the channel dimension. The differences between MSC and MCC are in the ways of computing correlation matrix. In MCC, a self-channel correlation matrix $\mathbf{M}_{sc} \in R^{1024 \times 1024}$ and a cross-channel correlation matrix $\mathbf{M}_{cc} \in R^{1024 \times 1024}$ are computed. Specifically, after obtaining the multi-scale features $\mathbf{F}_4^{ms} \in R^{M \times N \times 1024}$ from their input features $\mathbf{F}_4^{fused}$ , $\mathbf{M}_{sc}$ and $\mathbf{M}_{cc}$ are computed by + +$$ +\mathbf {M} _ {s c} = \left(\operatorname {R e s h a p e} \left(\mathbf {F} _ {4} ^ {m s}\right)\right) ^ {T} \times \operatorname {R e s h a p e} \left(\mathbf {F} _ {4} ^ {m s}\right), \tag {8} +$$ + +$$ +\mathbf {M} _ {c c} = \left(\operatorname {R e s h a p e} \left(\mathbf {F} _ {4} ^ {f u s e d}\right)\right) ^ {\mathrm {T}} \times \operatorname {R e s h a p e} \left(\mathbf {F} _ {4} ^ {f u s e d}\right). \tag {9} +$$ + +Similar to that in MSC, the cross-channel correlation matrix $\mathbf{M}_{cc}$ in MCC is also used to complement the self-channel correlation matrix $\mathbf{M}_{sc}$ for better capturing the long-range dependencies along the channel dimension. Different from that in MSC, the channel correlation matrixes capture the paired-wise similarities of two arbitrary channels in the multi-scale features and can be employed to extract the long-range channel dependencies among the multiscale contextual features. The final channel correlation matrix $\mathbf{M}_c\in R^{1024\times 1024}$ is computed by + +$$ +\mathbf {M} _ {c} = \text {N o r m a l i z a t i o n} \left(\mathbf {M} _ {s c} + \mathbf {M} _ {c c}\right). \tag {10} +$$ + +![](images/d54bc679bc083fdbf456cb6d772c8d758bb5675f1d841fcd19aa7957d56c6abf.jpg) +Figure 5. Visual results of multi-scale cross-modality feature maps before and after employing MSC and MCC modules. + +After that, the multi-scale contextual information of the fused features and their corresponding long-range dependencies along the channel dimension are obtained by + +$$ +\mathbf {F} _ {4} ^ {f u s e d ^ {\prime}} = \operatorname {R e s h a p e} ^ {\prime} \left(\left(\operatorname {R e s h a p e} \left(\mathbf {F} _ {4} ^ {m s}\right) \times \mathbf {M} _ {c}\right)\right) + \mathbf {F} _ {4} ^ {f u s e d}. \tag {11} +$$ + +By using MSC and MCC, the multi-scale contextual information of the cross-modality features and their long-range dependencies along the spatial and channel dimensions are captured simultaneously. As shown in Fig. 5, the discriminability of the fused cross-modality features will be greatly boosted by introducing those contextual information. + +# 3.3. Loss Function + +The total loss function $\mathcal{L}_{\text{total}}$ for training our model consists of the semantic segmentation loss $\mathcal{L}_s$ and multimodality differences loss $\mathcal{L}_{MD}$ , i.e., + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {s} (\mathbf {S}, \mathbf {G}) + \lambda_ {2} \mathcal {L} _ {M D}, \tag {12} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ denote two hyper-parameters for balancing the two losses. They are empirically set to 1 and 5 in our experiments, respectively. $\mathbf{G}$ denotes the ground truth and $\mathbf{S}$ denotes the final prediction. Considering the imbalance of pixels of each class presented in the MFNet dataset, inspired by [18], we employ the weighted cross-entropy loss as the semantic segmentation loss $\mathcal{L}_s$ , which is defined by + +$$ +\mathcal {L} _ {s} = - \sum_ {i = 1} ^ {m} \sum_ {j = 1} ^ {n} w \left(x _ {i j}\right) \times p \left(x _ {i j}\right) \times \log \left(q \left(x _ {i j}\right)\right), \tag {13} +$$ + +where $m$ and $n$ represent the width and height of an image. $(i,j)$ represents the coordinate of a pixel. $w(x_{ij})$ represents the weight coefficient of the pixel class. $p(x_{ij})$ represents the ground truth label of the pixel and $q(x_{ij})$ represents the predicted result on the pixel. + +# 4. Experiments + +# 4.1. The Dataset and Evaluation Metrics + +Our model is verified in MFNet dataset [9], which is the only public dataset of natural images for RGB-T semantic segmentation. This dataset contains 1569 annotated RGB and thermal natural image pairs, in which 820 image pairs + +
MethodsmAccmIoU
BS57.3047.99
+BMDR62.3751.98
+BMDR+IFCNN [49]62.6852.62
+BMDR+CW [50]63.6152.52
+BMDR+CWF (MDRF)64.0152.91
+MDRF+MSC-S65.5753.31
+MDRF+MSC-C64.4153.27
+MDRF+MSC66.9353.39
+MDRF+MSC+MCC-S68.2253.67
+MDRF+MSC+MCC-C66.5153.60
+MDRF+MSC+MCC69.5254.80
+ +Table 1. Quantitative results (\%) of ablation study. 'BS' denotes the baseline and 'BMDR' denotes the bi-directional modality difference reduction stage in MDRF. Meanwhile, MSC-S (MSC-C) and MCC-S (MCC-C) indicate only capturing the self (cross) long-range dependencies among cross-modality features along the spatial (channel) dimension, respectively. + +are taken at daytime and 749 image pairs are taken at nighttime. There are 9 semantic classes, including the unlabeled background class. All of the images in this dataset have the same resolution of $480 \times 640$ . For fair comparisons, we follow the same training, testing and verification setting as in [9]. We adopt the widely-used evaluation metrics (i.e., mean Accuracy (mAcc) and mean Intersection over Union (mIoU)) to evaluate the performance of different models. + +# 4.2. Implementation Details + +The proposed network is implemented by PyTorch on an NVIDIA GTX 1080 Ti GPU. The stochastic gradient descent (SGD) method with a momentum of 0.9 and a weight decay of 0.0005 is adopted to train our proposed network. The initial learning rate is set to 0.01, which is decreased by adopting the exponential decay scheme with base 0.95 during training. Moreover, the training data are augmented by using random flipping, cropping and noise injecting techniques. We train the network about 300 epochs to its convergence. + +# 4.2.1 Ablation Study + +In this section, we validate the effectiveness of each component in our proposed model. The proposed MDRF subnetwork, MSC module and MCC module are first removed from our model as the baseline (denoted by 'BS'). Here, 'BMDR' denotes the bi-directional modality difference reduction stage in MDRF. Meanwhile, MSC-S (MSC-C) and MCC-S (MCC-C) indicate only capturing the self (cross) long-range dependencies among cross-modality features along the spatial (channel) dimension, respectively. + +The quantitative experimental results are shown in Table 1. 'BS+BMDR' indicates that reducing the modal- + +ity differences between multi-modality features benefits the exploitation of cross-modality complementary information, thus boosting the RGB-T semantic segmentation. Furthermore, it can also be observed that, compared with other fusion modules (e.g., 'BS+BMDR+IFCNN', 'BS+BMDR+CW'), our proposed CWF module can more effectively select those discriminative features for semantic segmentation. The results of ('BS+MDRF+MSC-S' and 'BS+MDRF+MSC-C') and ('BS+MDRF+MSC+MCC-S' and 'BS+MDRF+MSC+MCC-C') indicate that the introduction of long-range dependencies along the spatial or channel dimension may provide more effective multi-scale contextual information for semantic segmentation. Meanwhile, the results of 'BS+MDRF+MSC+MCC' indicate that digging complementarity between the self and cross-spatial correlation matrices or the self and cross-channel correlation matrices can further facilitate the exploitation of long-range dependencies for RGB-T semantic segmentation. + +# 4.3. Comparison with State-of-the-art Methods + +We compare our model with 9 state-of-the-art (SOTA) methods, including 3 deep learning based RGB semantic segmentation methods (DUC [28], DANet [6] and HRNet [24]), 3 RGB-T semantic segmentation approaches (MFNet [9], RTFNet [25] and PSTNet [22]) and 3 RGB-D semantic segmentation models (LDFNet [12], ACNet [11] and SA-Gate(ResNet-50) [4]). The procedure of converting the RGB semantic segmentation model into an extended RGB-T model is described as follows. First, we repeat the one-channel thermal image three times as a three-channel image. Then, their proposed networks are taken as the backbones of the RGB and thermal branches, respectively. Finally, the last output features before the prediction layers from the two branches are added and then fed into the prediction layers to obtain the final semantic segmentation maps. For the RGB-D models, we directly replace the input one-channel or HHA-encoded three-channel depth images with the one-channel thermal images or three-channel thermal images obtained by the same way in extending RGB models. + +The quantitative results are shown in Table 2, which demonstrates that our method outperforms other SOTA methods by a large margin on the MFNet dataset. This indicates that our method can better exploit the complementary information from RGB-T images for semantic segmentation. Fig. 6 provides the visual comparisons of different models. As shown in the first two rows, under some simple scenes, most models can accurately segment targets. However, as shown in the 3rd-5th rows, our proposed method achieves significant superiorities over other SOTA models under poor lighting conditions. This owes to the strategy of bridging-then-fusing in MDRF. In addition, as shown in the 6th-8th rows, our method still outperforms other SOTA + +
MethodsUnlabeledCarPersonBikeCurveCar StopGuardrailColor ConeBumpmAccmIoU
AccIoUAccIoUAccIoUAccIoUAccIoUAccIoUAccIoUAccIoUAccIoU
DUC[28]98.897.792.482.584.169.471.358.958.440.125.520.917.33.460.042.152.240.961.250.7
DANet[6]97.496.391.371.382.748.179.251.848.030.225.518.25.20.747.630.319.918.855.241.3
HRNet[24]99.498.090.886.975.167.370.259.239.135.328.023.112.11.750.446.655.847.357.951.7
LDFNet[12]96.295.387.067.983.958.282.737.267.430.432.920.18.20.867.427.155.646.064.642.5
ACNet [11]97.696.793.779.486.864.777.852.757.232.951.528.47.00.857.516.949.844.464.346.3
SA-Gate[4]98.296.886.073.880.859.269.451.356.738.424.719.30.00.056.924.552.148.858.345.8
MFNet[9]98.796.977.265.967.058.953.942.936.229.912.59.90.10.030.325.230.027.745.139.7
RTFNet[25]99.698.291.386.378.267.871.558.259.843.732.124.313.43.640.426.073.557.262.251.7
PSTNet[22]—97.0—76.8—52.6—55.3—29.6—25.1—15.1—39.4—45.0—48.4
Ours98.697.894.384.890.069.675.760.364.045.144.133.131.05.161.747.466.250.069.554.8
+ +Table 2. Quantitative results of different models (%) on the test set of [9]. The value 0.0 represents that there are no true positives. ’-’ denotes that the corresponding results are missed in [22]. + +![](images/f6f8f0f85e3212f0d8b531a11375e1c331c761eb457a489e45466d8e60b9710b.jpg) +Figure 6. Visual comparisons of different methods. (a) RGB images; (b) Thermal images; (c) DUC [28]; (d) DANet [6]; (e) HRNet [24]; (f) LDFNet [12]; (g) ACNet [11]; (h) SA-Gate [4]; (i) MFNet [9]; (j) RTFNet [25]; (k) Ours; (l) GT. + +models under complex scenes with multiple objects. This may benefit from the exploitation of multi-scale contextual information of cross-modality features and their long-range dependencies along the spatial and channel dimensions by using our proposed MSC and MCC modules. + +# 5. Conclusion + +In this paper, a novel ABMDRNet has been presented for RGB-T semantic segmentation, where the modality difference reduction and multi-scale contextual information are simultaneously considered. By virtue of the strategy of bridging-then-fusing, the proposed MDRF subnetwork can obtain higher discriminative cross-modality features than + +those traditional fusion modules do. This greatly improves the semantic segmentation performance of our proposed model. Owing to the proposed MSC and MCC modules, the multi-scale contextual information of the cross-modality features and their long-range dependencies along the spatial and channel dimensions are well exploited. Thanks to that, the issue of objects diversity in semantic segmentation can be addressed to a large extent. With the collaboration of these subnetworks and modules, our proposed RGB-T semantic segmentation model achieves new SOTA results on MFNet dataset. + +Acknowledgements This work is supported by the National Natural Science Foundation of China under Grant No.61773301. + +# References + +[1] Yanpeng Cao, Dayan Guan, Yulun Wu, Jiangxin Yang, Yanlong Cao, and Michael Ying Yang. Box-level segmentation supervised deep neural networks for accurate and real-time multispectral pedestrian detection. ISPRS, 150:70-79, 2019. 1 +[2] Abhishek Chaurasia and Eugenio Culurciello. Linknet: Exploiting encoder representations for efficient semantic segmentation. In VCIP, pages 1-4. IEEE, 2017. 2 +[3] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. PAMI, 40(4):834-848, 2017. 2, 5 +[4] Xiaokang Chen, Kwan-Yee Lin, Jingbo Wang, Wayne Wu, Chen Qian, Hongsheng Li, and Gang Zeng. Bidirectional cross-modality feature propagation with separation-and-aggregation gate for rgb-d semantic segmentation. arXiv preprint arXiv:2007.09183, 2020. 3, 7, 8 +[5] Marius Cordts, Mohamed Omran, Sebastian Ramos, Timo Rehfeld, Markus Enzweiler, Rodrigo Benenson, Uwe Franke, Stefan Roth, and Bernt Schiele. The cityscapes dataset for semantic urban scene understanding. In CVPR, pages 3213-3223, 2016. 1 +[6] Jun Fu, Jing Liu, Hajie Tian, Yong Li, Yongjun Bao, Zhiwei Fang, and Hanqing Lu. Dual attention network for scene segmentation. In CVPR, pages 3146-3154, 2019. 1, 2, 5, 7, 8 +[7] Chuang Gan, Yandong Li, Haoxiang Li, Chen Sun, and Boqing Gong. Vqs: Linking segmentations to questions and answers for supervised attention in vqa and question-focused semantic segmentation. In ICCV, pages 1811–1820, 2017. 3 +[8] Dayan Guan, Yanpeng Cao, Jiangxin Yang, Yanlong Cao, and Michael Ying Yang. Fusion of multispectral data through illumination-aware deep neural networks for pedestrian detection. Information Fusion, 50:148-157, 2019. 1, 4 +[9] Qishen Ha, Kohei Watanabe, Takumi Karasawa, Yoshitaka Ushiku, and Tatsuya Harada. Mfnet: Towards real-time semantic segmentation for autonomous vehicles with multi-spectral scenes. In IROS, pages 5108-5115, 2017. 1, 2, 3, 6, 7, 8 +[10] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, pages 770-778, 2016. 4 +[11] Xinxin Hu, Kailun Yang, Lei Fei, and Kaiwei Wang. Acnet: Attention based network to exploit comple + +mentary features for rgbd semantic segmentation. In ICIP, pages 1440-1444, 2019. 3, 7, 8 +[12] Shang-Wei Hung, Shao-Yuan Lo, and Hsueh-Ming Hang. Incorporating luminance, depth and color information by a fusion-based network for semantic segmentation. In ICIP, pages 2374–2378, 2019. 3, 7, 8 +[13] Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A Efros. Image-to-image translation with conditional adversarial networks. In CVPR, pages 1125-1134, 2017. 2, 4 +[14] Simon Jégou, Michal Drozdzal, David Vazquez, Adriana Romero, and Yoshua Bengio. The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation. In CVPRW, pages 11-19, 2017. 1 +[15] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In CVPR, pages 3431-3440, 2015. 1, 2 +[16] Everingham Mark, Ali Eslami S, M, Van Gool Luc, Williams Christopher K, I, Winn John, and Zisserman Andrew. The pascal visual object classes challenge: A retrospective. volume 111, pages 98-136, 2015. 1 +[17] Lichao Mou, Yuansheng Hua, and Xiao Xiang Zhu. A relation-augmented fully convolutional network for semantic segmentation in aerial scenes. In CVPR, pages 12416-12425, 2019. 3, 5 +[18] Adam Paszke, Abhishek Chaurasia, Sanggil Kim, and Eugenio Culurciello. Enet: A deep neural network architecture for real-time semantic segmentation. arXiv preprint arXiv:1606.02147, 2016. 2, 6 +[19] Chang-Yong Ri and Min Yao. Semantic image segmentation based on spatial context relations. In ISISE, pages 104-108, 2012. 2 +[20] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In MICCAI, pages 234-241, 2015. 1, 2 +[21] Andrew Rouditchenko, Hang Zhao, Chuang Gan, Josh McDermott, and Antonio Torralba. Self-supervised audio-visual co-segmentation. In ICASSP, pages 2357–2361, 2019. 3 +[22] Shreyas S Shivakumar, Neil Rodrigues, Alex Zhou, Ian D Miller, Vijay Kumar, and Camillo J Taylor. Pst900: Rgb-thermal calibration, dataset and segmentation network. In ICRA, pages 9441-9447, 2020. 1, 2, 3, 7, 8 +[23] Jamie Shotton, Matthew Johnson, and Roberto Cipolla. Semantic texton forests for image categorization and segmentation. In CVPR, pages 1-8, 2008. 2 +[24] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang. Deep high-resolution representation learning for hu + +man pose estimation. In CVPR, pages 5693-5703, 2019. 7, 8 +[25] Yuxiang Sun, Weixun Zuo, and Ming Liu. Rtfnet: RGB-thermal fusion network for semantic segmentation of urban scenes. RAL, 4(3):2576-2583, 2019. 1, 2, 3, 7, 8 +[26] Hiroki Tokunaga, Yuki Teramoto, Akihiko Yoshizawa, and Ryoma Bise. Adaptive weighting multi-field-of-view cnn for semantic segmentation in pathology. In CVPR, pages 12597-12606, 2019. 1 +[27] Badrinarayanan Vijay, Kendall Alex, and Cipolla Roberto. Segnet: A deep convolutional encoder-decoder architecture for image segmentation. PAMI, 39(12):2481-2495, 2017. 1, 2 +[28] Panqu Wang, Pengfei Chen, Ye Yuan, Ding Liu, Zehua Huang, Xiaodi Hou, and Garrison Cottrell. Understanding convolution for semantic segmentation. In WACV, pages 1451-1460. IEEE, 2018. 7, 8 +[29] Weiyue Wang and Ulrich Neumann. Depth-aware cnn for rgb-d segmentation. In ECCV, pages 135-150, 2018. 3 +[30] Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. In CVPR, pages 7794-7803, 2018. 2, 3 +[31] Pingping Zhang, Wei Liu, Hongyu Wang, Yinjie Lei, and Huchuan Lu. Deep gated attention networks for large-scale street-level scene segmentation. PR, 88:702-714, 2019. 1 +[32] Qiang Zhang, Tonglin Xiao, Nianchang Huang, Dingwen Zhang, and Jungong Han. Revisiting feature fusion for rgb-t salient object detection. TCSVT, 2020. 1, 4 +[33] Richard Zhang, Phillip Isola, and Alexei A Efros. Colorful image colorization. In ECCV, pages 649-666, 2016. 2, 4 +[34] Hengshuang Zhao, Jianping Shi, Xiaojuan Qi, Xiaogang Wang, and Jiaya Jia. Pyramid scene parsing network. 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Since human emotions are ambiguous and subjective, it is more reasonable to address VEA in a label distribution learning (LDL) paradigm rather than a single-label classification task. Different from other LDL tasks, there exist intrinsic relationships between emotions and unique characteristics within them, as demonstrated in psychological theories. Inspired by this, we propose a well-grounded circular-structured representation to utilize the prior knowledge for visual emotion distribution learning. To be specific, we first construct an Emotion Circle to unify any emotional state within it. On the proposed Emotion Circle, each emotion distribution is represented with an emotion vector, which is defined with three attributes (i.e., emotion polarity, emotion type, emotion intensity) as well as two properties (i.e., similarity, additivity). Besides, we design a novel Progressive Circular (PC) loss to penalize the dissimilarities between predicted emotion vector and labeled one in a coarse-to-fine manner, which further boosts the learning process in an emotion-specific way. Extensive experiments and comparisons are conducted on public visual emotion distribution datasets, and the results demonstrate that the proposed method outperforms the state-of-the-art methods. + +# 1. Introduction + +Emotion serves as one of the most essential factors that distinguish human beings from other species, which affects almost every aspect of our daily lives. With the prevalence of social networks, more and more people tend to express their feelings by sharing images on the internet. There- + +![](images/df449a9220e6d60521c1349c33308a87ee9a8f1866e80232653ac146b603a77f.jpg) +Figure 1. Four images with different emotion distributions from the involved datasets. Rather than a dominant emotion, images often evoke multiple emotions with different description degrees. + +fore, Visual Emotion Analysis (VEA) has drawn great attention recently, which aims at understanding how people feel emotionally towards different visual stimuli. The development in VEA may also bring benefit to other related tasks (e.g. aesthetic assessment [2, 14], memorability estimation [5, 31], and stylized image captioning [3, 9]), as well as potential applications (e.g. opinion mining [20, 32], intelligent advertising [13, 24], and mental disease treatment [15, 34]). + +Most of the existing work often regard VEA as a single-label classification task [29, 36, 38, 42, 47], assuming that each image only evokes a dominant emotion. However, these attempts over-simplified the complexity of human emotions and neglected the ambiguity and subjectivity lies in them. In reality, different people may experience different emotions towards one image (i.e., subjectivity), and even an individual may have diverse emotions towards one image (i.e., ambiguity). Label Distribution Learning (LDL) is proposed to deal with the problem when an instance is covered by a certain number of labels with different description degrees [7]. Thus, it is more reasonable to address VEA in an LDL paradigm rather than a single-label classification + +![](images/9a6be94b0f8547787fefde719b6715d8c7f5a3a34cfe52e87759c88fe7b32dba.jpg) +(a) Mikel's Wheel + +![](images/ce53e57d487c4903e350e470209e8e29a3ebd7b0d7e911f9d76d409835c24e96.jpg) +(b) Emotion Circle +Figure 2. Mikel's Wheel from psychological model (a), and the proposed Emotion Circle (b) with eight basic emotion vectors evenly distributed in accordance with Mikel's Wheel. + +task, as shown in Fig. 1. Various methods have been proposed to deal with visual emotion distribution learning so far, including the earlier traditional algorithms [7, 39, 43] and the recent deep learning ones [11, 26, 35, 37, 39]. Most of the aforementioned methods simply implement general LDL algorithms for VEA. However, unlike other LDL tasks, there exist intrinsic relationships between distinct emotion labels, which can be viewed as useful prior knowledge of this task. + +The study of human emotions is not only limited to computer vision field, but also being heated discussed in psychology [17, 33], biology [22, 28], as well as sociology [12, 30]. Psychologists developed various emotion models to illustrate the intrinsic relationships among emotions, including the well-known Plutchik's Wheel [27] and Mikel's Wheel [23, 45]. Besides, it has been demonstrated in psychology that people experience eight basic emotions, which can be expressed at different intensities and can be combined to form any emotional state [27]. + +Inspired by the above studies, we propose a well-grounded circular-structured representation for visual emotion distribution learning, aiming to effectively utilize the intrinsic relationships between emotions and unique characteristics within them. To be specific, we construct an Emotion Circle to unify any emotional state within it, including both basic emotions and the compound ones. On the proposed Emotion Circle, each emotional state can be well-presented as an emotion vector with three attributes (i.e., emotion polarity, emotion type and emotion intensity) and two properties, namely similarity and additivity. As shown in Fig. 2, basic emotions are defined with a set of unit vectors evenly-distributed on the Emotion Circle (b), corresponding to the circular structure of the eight basic emotions (i.e., amusement, awe, contentment, excitement, anger, disgust, fear, sad) in Mikel's Wheel (a) [23, 45]. In addition to the above basic emotions, there also exist complex emotional states in reality (e.g., emotion distributions). Therefore, considering that basic emotions have intensities and can be combined to form any emotional state [27], we + +propose a systematic approach to map any emotion distribution to a compound emotion vector on the Emotion Circle. In detail, each emotion distribution is first projected on basic emotion vectors with different emotion intensities according to their description degrees. Weighted basic emotion vectors are then combined to form a compound emotion vector, which can be regarded as the specific circular-structured representation of a given emotion distribution. + +Most visual emotion distribution learning methods [11, 37, 39] simply leverage the Kullback-Leibler (KL) loss [18] to directly measure the differences between labeled emotion distributions and the predicted ones. However, rather than a set of uncorrelated labels, emotions are closely related to each other and circularly distributed according to psychological models. To exploit such prior knowledge, we propose a novel Progressive Circular (PC) loss to learn the dissimilarities between the labeled emotion vector and the predicted one on the Emotion Circle in a coarse-to-fine manner. In detail, We first construct polar loss to penalize the difference between the predicted polarity and the labeled one, which can be viewed as a coarse constraint towards a specific emotional state. After divide emotions into two polarities, we build up a more fine-grained constraint on emotion type by calculating the distance between them. Since emotion intensity is regarded as a crucial factor when describing a specific emotional state [27], we further leverage it as the confidence degree to constrain the above two losses. By implementing both the KL loss and the proposed PC loss, the learning process of emotion distribution is not only optimized through its conventional mechanism, but also further boosted in a novel emotion-specific circular-structured manner. + +Our contributions can be summarized as follows: + +- We propose a well-grounded circular-structured representation to learn visual emotion distribution by utilizing the intrinsic relationships between emotions, which consistently outperforms the state-of-the-art methods on several emotion distribution datasets. To the best of our knowledge, it is the first time to systematically exploit emotion relationships as prior knowledge for visual emotion distribution learning. +- We construct an Emotion Circle to unify any emotional state within it, where each emotion distribution is represented as a compound emotion vector with three attributes as well as two properties according to psychological models. +- We design a novel Progressive Circular loss to penalize the dissimilarities between labeled emotion vectors and the predicted ones on the Emotion Circle from coarse to fine, which further boosts the visual emotion distribution learning process in an emotion-specific circular-structured manner. + +![](images/2872cedb9a435328875ba05d6845f16c4972ed7b0daff9e4ae49d148299448a1.jpg) +Figure 3. Framework of the proposed circular-structured representation. On the proposed Emotion Circle, both the predicted emotion distribution and the labeled one are represented with compound emotion vectors through a systematic approach. We then propose the Progressive Circular loss in a coarse-to-fine manner, which is further exploited to train the network together with Kullback-Leibler loss. + +# 2. Related Work + +# 2.1. Visual Emotion Analysis + +Researchers have been devoted to visual emotion analysis (VEA) for more than two decades [19], during which approaches vary from the early traditional ones to the recent deep learning ones. Earlier works in VEA mainly focused on designing hand-crafted features to mine emotions from affective images [1, 21, 44, 46]. Inspired by psychology and art theory, Machajdik et al. [21] extracted rich handcrafted features including color, texture, composition, and content. Zhao et al. [46] extracted features from low-level elements-of-art, mid-level principles-of-art, to high-level semantics in a multi-graph learning framework. Although hand-crafted features have been proven to be effective on several small-scale datasets, they are still limited to cover all the important factors in visual emotion. Recently, researchers in VEA have adopted Convolutional Neural Network (CNN) to predict emotions and have achieved gratifying results [29, 36, 38, 40, 41, 42]. A multi-level deep representation network (MldrNet) was constructed by Rao et al. [29] to extract emotional features from image semantics, aesthetics, and low-level features simultaneously. Aiming to focus on local regions instead of the holistic one, Yang et al. [38] constructed a local branch to discover affective regions (AR) by implementing the off-the-shelf detection tools. A weakly supervised coupled network (WSCNet) [36] was further proposed by Yang et al. to discover emotion regions as well as to predict visual emotions in an end-to-end manner. However, these methods simply regard VEA as a single-label classification task, which neglects the ambiguity and subjectivity lies in human emotions. To be specific, different people may evoke different emotions towards one image (i.e., subjectivity) and even an individual + +may experience multiple emotions towards one image (i.e., ambiguity). Thus, rather than a single-label classification task, it is more reasonable to consider VEA in a Label Distribution Learning [27] paradigm. + +# 2.2. Label Distribution Learning + +Label distribution learning (LDL) is proposed by Geng et al. [7] to address the problem when an instance is covered by a certain number of labels with different description degrees, which is a more general learning framework covering both single-label and multi-label learning tasks. Traditional algorithms in LDL can be roughly divided into three strategies, i.e., problem transfer (PT), algorithm adaption (AA), and specialized algorithms (SA) [7]. With the help of deep networks, deep label distribution learning (DLDL) is proposed by Gao et al. [6] to effectively prevent the network from over-fitting by utilizing the label ambiguity in both feature learning and classifier learning. Consequently, LDL was then introduced to VEA to deal with subjectivity and ambiguity lies in it [11, 26, 35, 37, 39, 43]. Peng et al. [26] proposed convolutional neural network regressions (CNNR) to address VEA in LDL for the first time. Subsequently, Yang et al. [37] proposed a joint network (JCDL) to learn visual emotion from distribution and classification simultaneously, by optimizing both softmax loss and Kullback-Leibler (KL) loss. Most of the aforementioned methods simply employ general LDL mechanisms and consequently ignore the intrinsic relationships between emotions, which can be regarded as prior knowledge for visual emotion distribution learning. Motivated by psychological theories [23, 27, 45], we propose a circular-structured representation to utilize the intrinsic relationships between emotions and unique characteristics within it. + +![](images/8a128aab514f6df8b00cfd6f0e4c8eec497784cd805856cd711fb2ae03b4d98c.jpg) +(a) Emotion distribution + +![](images/76d47a1d7527f39c6417317d62b806d4a68377d3fcc99131cf8eb8907fd8e469.jpg) +(b) Weight +Figure 4. Mapping from the emotion distribution (a) to the compound emotion vector (d) on the Emotion Circle. We first weigh eight basic emotions with different description degrees (b) and then combine them to form a compound emotion vector through vector addition operations (c). The final emotion vector can be viewed as a specific circular-structured representation of a given emotion distribution. + +![](images/07c724d0357ea1489d287cbb0c373eeff1bc9632101c1e19ef673b32601b2cc1.jpg) +(c) Combination + +![](images/c767c2bc960d5fb3c32b6e5b8db5a98c6a7e0f73e91d0f92b1c071dd3e6b079e.jpg) +(d) Emotion vector + +# 3. Methodology + +# 3.1. Emotion Circle + +Unlike other label distribution learning tasks, emotion labels are closely related to each other with circular structure and unique characteristics based on psychological models [23, 27, 45]. Inspired by this, aiming at learning emotions in a more specific and reasonable way, we construct an Emotion Circle to unify any emotional states in it. On the proposed Emotion Circle, each emotional state is represented with an emotion vector $\mathbf{e}_i$ , which is described as + +$$ +\mathbf {e} _ {\mathrm {i}} = \left(p _ {i}, \theta_ {i}, r _ {i}\right), \tag {1} +$$ + +where $p_i, \theta_i, r_i$ denotes the emotion polarity, emotion type and emotion intensity respectively. We give detailed definitions of the above three emotion attributes as follows and further introduce two properties for emotion vectors according to psychological theories. + +- Emotion Polarity $(p_i)$ : In addition to its given emotion label (i.e., amusement, awe, contentment, excitement, anger, disgust, fear, sad), each emotion is also naturally grouped into a specific emotion polarity (i.e., positive, negative). Specifically, amusement, awe, contentment, excitement belong to positive emotions while anger, disgust, fear, sad are negative ones. Hence, we divide the Emotion Circle to half positive and half negative, as given in Eq. 2, in accordance with the polar structure on the Mikel's Wheel [23, 45]: + +$$ +p _ {i} = \left\{ \begin{array}{l l} 0, & \theta_ {i} \in \left[ 0, \frac {1}{2} \pi\right) \cup \left[ \frac {3}{2} \pi , 2 \pi\right), \\ 1, & \theta_ {i} \in \left[ \frac {1}{2} \pi , \frac {3}{2} \pi\right). \end{array} \right. \tag {2} +$$ + +- Emotion Type $(\theta_{i})$ : We define emotion type with the polar angle $\theta_{i} \in [0,2\pi]$ , in order to preserve the circular-distributed emotions on the Mikel's Wheel. There are basic emotions and compound emotions in reality [27], which both can be well-represented on the Emotion Circle. In Fig. 2(b), we first set a series of evenly-distributed unit vectors on the Emotion Circle + +to represent eight basic emotions, denoted as + +$$ +\theta^ {j} = \frac {2 j - 1}{8} \pi , j \in [ 1, C ], \tag {3} +$$ + +where $C$ denotes the number of emotion categories in psychological models. Besides, there also exist compound emotion types, which are distributed in the blank space between these basic vectors. + +- Emotion Intensity $(r_i)$ : As mentioned in a psychological literature [27], "Each emotion can exist in varying degrees of intensity." Thus, polar diameter $r_i \in [0,1]$ is introduced to describe the intensity of a specific emotion type $\theta_i$ , where $r_i = 1$ indicates the strongest degree and $r_i = 0$ the weakest. To be specific, the emotion intensity of each basic emotion is set as + +$$ +r ^ {j} = 1, j \in [ 1, C ], \tag {4} +$$ + +indicating that only a single emotion described the specific emotional state with all its weight. + +- Similarity: The similarity between different emotions are measured with the distance between their polar angles, i.e., image $i_1$ and image $i_2$ share the same emotion type if and only if $\theta_{i_1} = \theta_{i_2}$ . As mentioned in a psychological literature [27], "since a circle combines the concepts of degree of similarity (nearness) and degree of opposition". The larger the distance between two polar angles, the greater the dissimilarities between two emotion types. + +- Additivity: According to psychological theories [27], basic emotion vectors can be intensified and combined to produce any complex emotional states. Thus, each compound emotion can be defined as a weighted combination of basic emotions, which can be calculated through vector addition operations. + +Based on the aforementioned attributes and properties, we develop a systematic approach to map an emotion distribution to a compound emotion vector on the Emotion Circle, as shown in Algorithm 3.1. Besides the strict arithmetic procedures, we also vividly illustrate the mapping process in Fig. 4 for better comprehension. In general, each + +Algorithm 1 Circular-structured emotion representation +Input: Emotion distribution: $\mathbf{d_i} = [d_i^1, \dots, d_i^C]$ +Output: Compound emotion vector: $\mathbf{e_i} = (p_i, \theta_i, r_i)$ +1: for $i = 1$ ; $i < N$ ; $i + +$ do +2: for $j = 1$ ; $j < C$ ; $j + +$ do +3: Initialize basic emotion vectors, +4: $\mathbf{e_j} = (p_j^j, \theta_j^j, r_j^j)$ ; +5: Weight basic emotion vectors, +6: $\mathbf{e_i^j} = d_i^j \times \mathbf{e_j^j} \triangleq (p_i^j, \theta_i^j, r_i^j)$ ; +7: Polar coordinate to Cartesian coordinate, +8: $\left\{ \begin{array}{l} x_i^j = r_i^j \cos \theta_i^j, \\ y_i^j = r_i^j \sin \theta_i^j; \end{array} \right.$ +9: Combination of weighted basic emotion vectors, +10: $x_i = \sum_{j=1}^{C} x_i^j$ , $y_i = \sum_{j=1}^{C} y_i^j$ ; +11: Cartesian coordinate to Polar coordinate, +12: $\left\{ \begin{array}{l} r_i = \sqrt{x_i^2 + y_i^2}, \\ \theta_i = \arctan(y_i / x_i); \end{array} \right.$ +13: if $\theta_i \in [0, \frac{1}{2}\pi) \cup [\frac{3}{2}\pi, 2\pi)$ then +14: $p_i = 0$ , +15: else +16: $p_i = 1$ ; +17: Compound emotion vector: $\mathbf{e_i} = (p_i, \theta_i, r_i)$ ; +18: return $\mathbf{e_i}$ + +emotion distribution is first projected on basic emotion vectors with different emotion intensities according to their description degrees. Weighted basic emotion vectors are then combined, based on the intrinsic circular structure between emotions, to form a compound emotion vector, which can be regarded as the specific circular-structured representation of a given emotion distribution. + +# 3.2. Progressive Circular Loss + +Most of the previous methods simply implement the Kullback-Leibler (KL) [18] loss for visual emotion distribution learning, which measure the information loss caused by the inconsistency between the predicted distribution and the labeled one: + +$$ +\mathcal {L} _ {K L} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {C} \mathbf {d} _ {\mathbf {i}} (j) \ln \hat {\mathbf {d}} _ {\mathbf {i}} (j), \tag {5} +$$ + +$$ +\hat {\mathbf {d}} _ {\mathbf {i}} (j \mid \mathbf {f} _ {i}, \mathbf {W}) = \frac {\exp \left(\mathbf {w} _ {i , j} \mathbf {f} _ {i}\right)}{\sum_ {j = 1} ^ {C} \exp \left(\mathbf {w} _ {i , j} \mathbf {f} _ {i}\right)}, \tag {6} +$$ + +where $\mathbf{d_i}$ denotes the labeled emotion distribution from datasets and $\hat{\mathbf{d}}_{\mathrm{i}}$ represents the predicted one. $N$ denotes the number of images in a specific dataset and $C$ represents the involved emotion categories. + +However, rather than a set of uncorrelated labels, emotions are intrinsically distributed in a circular structure in + +psychological models [23, 45]. In order to effectively exploit such prior knowledge, we propose a Progressive Circular (PC) loss to learn the emotion distribution from coarse to fine. The proposed PC loss, conducted on the Emotion Circle described in Sec. 3.1, is designed to penalize the difference between two emotion vectors, i.e., the labeled one $\mathbf{e_i} = (p_i,\theta_i,r_i)$ and the predicted one $\hat{\mathbf{e}}_{\mathrm{i}} = (\hat{p}_i,\hat{\theta}_i,\hat{r}_i)$ . To be specific, we progressively establish constraints on three attributes of emotion vectors, i.e., emotion polarity $(p_i)$ , emotion type $(\theta_{i})$ and emotion intensity $(r_i)$ . Since polarity is the coarse attribute of an emotion, we first devise polar loss to measure the differences between emotion polarities, by implementing the Mean Square Error (MSE) loss: + +$$ +\mathcal {L} _ {p} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left(p _ {i} - \hat {p} _ {i}\right) ^ {2}, \tag {7} +$$ + +where $p_i$ denotes the labeled emotion polarity and $\hat{p}_i$ represents the predicted one. Eq. 7 ensures the correctness in emotion polarity prediction, which is the first goal towards accurate emotion prediction. As mentioned in Sec. 3.1, distance between polar angles can measure the similarities between different emotion types. Thus, after divide emotions into two polarities, we build up a more fine-grained constraint on emotion type, denoted as type loss: + +$$ +\mathcal {L} _ {t} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left(\theta_ {i} - \hat {\theta} _ {i}\right) ^ {2}. \tag {8} +$$ + +In Eq. 8, the closer the two polar angles are, the more similarity lies in their emotional states. However, it is insufficient to merely take emotion type into account, as emotion intensity is also considered as a crucial factor towards a specific emotional state [27]. Suppose there are two images with the same emotion type, i.e., $\theta_{i_1} = \theta_{i_2}$ , and quite different emotion intensities, i.e., $r_{i_1} = 1$ , $r_{i_2} = 0.01$ , it is really hard to group them into the same emotional state. Therefore, serving as the confidence degree for both emotion type $\theta_i$ and emotion polarity $p_i$ , we further add emotion intensity $r_i$ to the proposed loss function for a precise and detailed constraint for visual emotion distribution learning: + +$$ +\mathcal {L} _ {P C} = \frac {1}{N} \sum_ {i = 1} ^ {N} r _ {i} \left(\left(p _ {i} - \hat {p} _ {i}\right) ^ {2} + \left(\theta_ {i} - \hat {\theta} _ {i}\right) ^ {2}\right). \tag {9} +$$ + +Based on the Emotion Circle, our PC loss is eventually constructed with three constraints in a coarse-to-fine manner in Eq. 9. Our loss function is integrated with both KL loss and PC loss in a weighted combination: + +$$ +\mathcal {L} = (1 - \mu) \mathcal {L} _ {K L} + \mu \mathcal {L} _ {P C}, \tag {10} +$$ + +where $\mu$ is a hyper-parameter balancing the importance between the two losses and is further ablated in Sec. 4.4.2. So + +Table 1. Comparison with the state-of-the-art methods on Flickr_LDL dataset. + +
MeasuresPTAASACNN-based
PT-BayesPT-SVMAA-kNNAA-BPSA-IISSA-BFGSSA-CPNNCNNRDLDLACPNNJCDLSSDLE-GCNOurs
Chebyshev ↓0.44(13)0.55(14)0.28(8)0.36(11)0.31(10)0.37(12)0.30(9)0.25(5)0.25(5)0.25(5)0.24(4)0.23(2)0.23(2)0.21(1)
Clark ↓0.89(14)0.87(13)0.57(1)0.82(8)0.82(8)0.86(12)0.82(8)0.84(11)0.78(5)0.77(2)0.77(2)0.78(5)0.78(5)0.77(2)
Canberra ↓0.85(14)0.83(13)0.41(1)0.75(10)0.75(10)0.82(12)0.74(9)0.73(8)0.70(7)0.70(5)0.70(5)0.69(3)0.69(3)0.68(2)
KL ↓1.88(13)1.69(12)3.28(14)0.82(10)0.66(7)1.06(11)0.71(9)0.70(8)0.54(5)0.62(6)0.53(4)0.46(3)0.44(2)0.41(1)
Cosine ↑0.63(13)0.32(14)0.79(7)0.72(9)0.78(8)0.70(11)0.70(11)0.72(9)0.81(5)0.80(6)0.82(4)0.85(3)0.86(2)0.87(1)
Intersection ↑0.49(13)0.29(14)0.64(5)0.53(12)0.60(9)0.56(11)0.60(9)0.62(7)0.64(5)0.62(7)0.65(4)0.68(3)0.69(2)0.71(1)
Average Rank ↓13.3(13)13.3(13)6(7)10(11)8.7(9)11.5(12)9.2(10)8(8)5.3(6)5.2(5)3.8(4)3.2(3)2.7(2)1.3(1)
Accuracy ↑0.47(13)0.37(14)0.61(5)0.52(11)0.58(9)0.50(12)0.58(9)0.61(5)0.61(5)60.0(8)0.64(4)0.70(2)0.69(3)0.72(1)
+ +Table 2. Comparison with the state-of-the-art methods on Twitter_LDL dataset. + +
MeasuresPTAASACNN-based
PT-BayesPT-SVMAA-kNNAA-BPSA-IISSA-BFGSSA-CPNNCNNRDLDLACPNNJCDLSSDLE-GCNOurs
Chebyshev ↓0.53(13)0.63(14)0.28(7)0.37(11)0.28(7)0.37(11)0.36(10)0.28(7)0.26(5)0.27(6)0.25(3)0.25(3)0.24(2)0.22(1)
Clark ↓0.85(7)0.91(14)0.58(1)0.89(12)0.86(11)0.89(12)0.85(7)0.84(3)0.84(3)0.85(7)0.83(2)0.84(3)0.85(7)0.84(3)
Canberra ↓0.77(6)0.88(14)0.41(1)0.84(12)0.79(11)0.84(12)0.78(8)0.76(2)0.77(6)0.78(8)0.76(2)0.76(2)0.78(8)0.76(2)
KL ↓1.31(12)1.65(13)3.89(14)1.19(10)0.64(7)1.19(10)0.85(9)0.67(7)0.54(5)0.58(6)0.53(4)0.51(3)0.46(2)0.44(1)
Cosine ↑0.53(13)0.25(14)0.82(7)0.71(11)0.82(7)0.71(11)0.75(10)0.82(7)0.83(6)0.84(5)0.85(4)0.86(3)0.87(2)0.89(1)
Intersection ↑0.40(13)0.21(14)0.66(5)0.59(9)0.63(8)0.57(11)0.56(12)0.58(10)0.65(6)0.64(7)0.68(4)0.69(3)0.70(2)0.72(1)
Average Rank ↓10.7(12)13.8(14)5.8(6)10.8(11)8.5(9)11.2(13)9.3(10)6(7)5.2(5)6.5(8)3.2(3)2.8(2)3.8(4)1.5(1)
Accuracy ↑0.45(13)0.40(14)0.73(7)0.72(9)0.70(10)0.57(12)0.70(10)0.74(5)0.73(7)0.74(5)0.76(3)0.77(2)0.76(3)0.78(1)
+ +far, the emotion distribution is not only learned in a conventional mechanism, but further gains a performance boost in an emotion-specific and circular-structured manner. + +# 4. Experimental Results + +# 4.1. Datasets + +We evaluate our method on three public visual emotion distribution datasets, including Flickr_LDL, Twitter_LDL [39] and Abstract Paintings [21]. Built on Mikel's eight emotion space, there are 11,150 images in Flickr_LDL and 10,045 images in Twitter_LDL. Eleven viewers are hired to label Flickr_LDL and eight viewers are hired to label Twitter_LDL, where the detailed votes from all the workers are integrated to generate the ground truth label distribution for each image. The Abstract Paintings dataset is also labeled with Mikel's eight emotions, which consists only of combinations of color and texture without any recognizable objects and contains 280 images in total. + +# 4.2. Implementation Details + +In the experiment, our backbone network is built on ResNet-50 [10] following the same setting as previous methods [11], which is pre-trained on a large-scale visual recognition dataset, ImageNet [4]. Specifically, the output dimension of the last fully connected layer is changed to emotion numbers according to the datasets. Following the same setting in [39], Flickr_LDL, Twitter_LDL and Abstract Paintings datasets are randomly split into training set (80%) and testing set (20%). For training/testing sets, after resizing each image to 480 on its shorter side, we then crop it to $448 \times 448$ randomly followed by a horizontal flip [10]. + +The whole network is trained by the adaptive optimizer Adam [16] in an end-to-end manner with KL loss and the proposed PC loss. With a weight decay of 5e-5, the learning rate of Adam starts from 1e-5 and divided by 10 every 10 epochs, and the total epoch number is set to 50. Our framework is implemented using PyTorch [25] and our experiments are performed on an NVIDIA GTX 1080Ti GPU. + +# 4.3. Comparison with the State-of-the-art Methods + +To evaluate the effectiveness of the proposed circular-structured representation, we conduct extensive experiments compared with the state-of-the-art methods on three public visual emotion distribution datasets, including Flickr_LDL, Twitter_LDL and Abstract Paintings, as shown in TABLE 1, TABLE 2 and TABLE 3 respectively. In general, the state-of-the-art methods can be divided into four types: PT, AA, SA and CNN-based. + +- Problem Transformation (PT): Based on the representative algorithms Bayes classifier and SVM, PT-Bayes and PT-SVM are designed to transfer the LDL problem into a single-label learning (SLL) one [7]. Since these methods roughly turn a complex LDL task into a simple SLL one, performance drops may exist when measuring the differences between distributions. +- Algorithm Adaptation (AA): The existing machine learning algorithms k-NN and BP neural network are extended to deal with label distributions, which are denoted by AA-kNN and AA-BP respectively [7]. In TABLE 1 and TABLE 2, AA-kNN achieves insurmountable results in Clark distance and Canberra metric, owing to its superiority in dealing with overlapping samples in visual emotion distributions. + +Table 3. Comparison with the state-of-the-art methods on Abstract Paintings dataset. + +
MeasuresPTAASACNN-based
PT-BayesPT-SVMAA-kNNAA-BPSA-IISSA-BFGSACPNNOurs
Chebyshev ↓0.360(7)0.298(6)0.245(3)0.297(5)0.296(4)0.472(8)0.234(2)0.226(1)
Clark ↓0.674(7)0.632(4)0.621(2)0.641(5)0.660(6)0.834(8)0.625(3)0.562(1)
Canberra ↓0.594(7)0.537(4)0.513(2)0.544(6)0.564(5)0.781(8)0.522(3)0.456(1)
KL ↓3.268(8)0.708(5)0.515(3)0.782(6)0.644(4)2.282(7)0.513(2)0.441(1)
Cosine ↑0.653(5)0.643(6)0.753(3)0.636(7)0.692(4)0.573(8)0.763(2)0.773(1)
Intersection ↑0.518(7)0.539(6)0.608(3)0.540(5)0.577(4)0.417(8)0.618(2)0.654(1)
Average Rank ↓6.83(7)5.17(6)2.68(3)4.83(5)3.83(4)7.83(8)2.33(2)1(1)
+ +Table 4. Ablation study of loss function on Flickr_LDL dataset. + +
Measures\( {\mathcal{L}}_{KL} \)\( {\mathcal{L}}_{KL} + {\mathcal{L}}_{p} \)\( {\mathcal{L}}_{KL} + {\mathcal{L}}_{t} \)\( {\mathcal{L}}_{KL} + {\mathcal{L}}_{p} + {\mathcal{L}}_{t} \)\( {\mathcal{L}}_{KL} + {\mathcal{L}}_{PC} \)
Chebyshev \( \downarrow \)0.2390.2250.2220.2180.213
Clark \( \downarrow \)0.7830.7790.7790.7750.774
Canberra \( \downarrow \)0.6970.6890.6870.6820.685
KL \( \downarrow \)0.4350.4410.4200.4140.408
Cosine ↑0.8430.8620.8690.8700.874
Intersection ↑0.6780.6930.7050.7030.709
Accuracy ↑0.6690.6950.7000.7180.721
+ +Table 5. Ablation study of loss function on Twitter_LDL dataset. + +
Measures\( {\mathcal{L}}_{KL} \)\( {\mathcal{L}}_{KL} + {\mathcal{L}}_{p} \)\( {\mathcal{L}}_{KL} + {\mathcal{L}}_{t} \)\( {\mathcal{L}}_{KL} + {\mathcal{L}}_{p} + {\mathcal{L}}_{t} \)\( {\mathcal{L}}_{KL} + {\mathcal{L}}_{PC} \)
Chebyshev \( \downarrow \)0.2590.2400.2330.2300.224
Clark \( \downarrow \)0.8610.8510.8480.8460.842
Canberra \( \downarrow \)0.7970.7780.7750.7720.764
KL \( \downarrow \)0.4640.4760.4550.4500.439
Cosine \( \uparrow \)0.8480.8700.8780.8820.886
Intersection \( \uparrow \)0.6860.7060.7030.7130.717
Accuracy \( \uparrow \)0.7440.7640.7700.7790.781
+ +- Specialized Algorithm (SA): Specialized algorithms are designed by directly matching the characteristics of LDL, including SA-IIS, SA-BFGS, SA-CPNN [7, 8]. By implementing a similar strategy to Improved Iterative Scaling (IIS), SA-IIS assumes the parametric model to be the maximum entropy mode [7, 8]. However, IIS often performs worse compared with other optimization algorithms such as conjugate gradient and quasi-Newton methods. Thus, SA-BFGS is further developed with an effective quasi-Newton method named Broyden-Fletcher-Goldfarb-Shanno for LDL [7]. SA-CPNN is proposed based on a three-layer conditional probability neural network [8]. Compared with the above PT and AA methods, SA has achieved improved results for their specially designed features. +- CNN-based methods (CNN-based): Benefiting from its powerful representation ability, CNN-based methods gain a significant performance boost compared with those traditional ones. Specifically, CNNR [26] is proposed to treat VEA in a label distribution paradigm for the first time, which achieved a great performance with an end-to-end network. DLDL [6] replaces the Euclidean loss with KL loss to well describe the differences between two distributions. In order to learn visual emotion distribution and classification in a joint manner, JCDL [37] further boosts the performance by optimizing both KL loss and softmax loss. + +![](images/070ce5660da912f9fa762dd944a33173311d600aae0dd752f9c5a8de5fdda293.jpg) +Figure 5. Effect of $\mu$ for combined loss on Twitter.LDL dataset. Note that $\mu = 1$ suggests only using PC loss while $\mu = 0$ means implementing KL loss alone. + +Following the same setting as the previous work [7, 11, 35, 37, 39], we evaluate the performance of visual emotion distribution learning task with six commonly-used measurements, i.e., Chebyshev distance $(\downarrow)$ , Clark distance $(\downarrow)$ , Canberra metric $(\downarrow)$ , Kullback-Leibler divergence $(\downarrow)$ , cosine coefficient $(\uparrow)$ , and intersection similarity $(\uparrow)$ . Among these measurements, the first four are distance measures and the last two are similarity measures, where $\downarrow$ suggests the lower the better and $\uparrow$ the higher the better. As KL divergence is not well defined with zero value, we use a small value $\varepsilon = 10^{-10}$ to approximate it. Besides, since the maximum values of Clark distance and Canberra metric are determined by the number of emotions, we divided Clark distance by the square root of number of emotions and divided Canberra metric by the number of emotions for standardized comparisons. In addition to the above six measurements, we further introduce top-1 accuracy as another evaluation metric, which ensures the prediction results of the dominant emotions in the distributions. From the above analysis, it is obvious that the proposed method consistently outperforms the state-of-the-art methods on three widely-used datasets, owing to the effectiveness in circular-structured representation for visual emotion distribution learning. + +# 4.4. Ablation Study + +# 4.4.1 Effectiveness of the PC Loss + +In TABLE 4 and TABLE 5, we conduct ablation study on the proposed PC loss with two large-scale datasets, aiming to verify the effectiveness of each proposed constraint (i.e., polar loss, type loss and emotion intensity). By adopting + +![](images/d2e306e034258b150410f789640546142f3bb1950c28cc7cee614565f71f4e7f.jpg) + +![](images/7adc6ac155f84b2793c448680a4f567eb6ab3286b466d5a0d350a9f80588290d.jpg) + +![](images/b8949b2d8465b5c35b68de059e07fea8f4cdb8dd0e5c4d8c0d9f7be5406129d9.jpg) + +![](images/7e85a36ceca12b2ad8310892e6e9d360d60e3fed014fb671a737a2960e20a057.jpg) + +![](images/9fd013baf9b0e05e3200f72fe8be8d32e89d2ed3702ae4304fdb9817181e84d5.jpg) + +![](images/52f9b825ba6cdce7cb39e38530fe9ca1dfa7748847e35bef1de6a2fe1b899b5f.jpg) + +![](images/a74bc7d83570d540784331361666839e520e7cec9c8ef600d4bed451aeae87bf.jpg) + +![](images/50e815fb923360b17aaa0fceadbbd495fe42e8bb4fc48291759c2999b88a3f38.jpg) + +![](images/d428223dd6a67a7a236ee1ca67af42d070d704247090d1b862bc1501bf75e192.jpg) + +![](images/a68efc0cf96b8d9d24ad1d2a5f6e216d9d8d5d1c24e316a01410cb636f1a4827.jpg) + +![](images/35e1dbff354bfec8cabd8a75729bda5af8c79b3adf48ca72d045ae33d197edbf.jpg) + +![](images/6ecafbec35cac63a5fc42c654726fc31b6a3f48651e8384a0d798ce5f3bad7b9.jpg) + +![](images/25819ade1891713975e73afb0d2625e8414115f170c9d500a656e3f2be09e192.jpg) + +![](images/6b18ef9407d3ec33661e9a11135e4e2b5bf605eb94a23f7016234125214e7f77.jpg) + +![](images/32eeae009215d6c00bd145ddc9b9710275f426ee38006d59d0893ed67fd39f67.jpg) + +![](images/67f1877f6c25433e0040c461a5e4ec6b1f42c6a472856221b234c02d25c9ea92.jpg) + +![](images/79046fefc595bad0d4edd37d67bd1280df46200a06d544682b55f96072892866.jpg) + +![](images/7e796d2205b92c3e4aef0390ab0be763745eef41d77cdad136a0c8e500993f9f.jpg) + +![](images/680fccb63c708b247c1b05bd500269f29a5a19f63e5a2a00e09102aa84ae94b0.jpg) +Figure 6. Visualization of the predicted emotion distributions (predicted) and the ground-truth (GT) ones, where images in the first line come from Flickr_LDL dataset and second line the Twitter_LDL. Each number on the horizontal axis corresponds to an emotion category. + +![](images/0a79c926cbbf03fb0fbd570fc0f8d1eda4b62c655da74f5cdc0d5fddf669c335.jpg) + +![](images/0b1c414455e2b1e201da9fe323473a6d9dbd53762f82e7d5d48d86468b39a9c8.jpg) + +![](images/fef6e1dfc974e82eccfed7381921ffc3fc3ed342ab455e2065a52b38bcded20a.jpg) + +![](images/29ebecb7743c9a6b895228e1b60e611bb789cc41f441242a48c50c259b66368e.jpg) + +![](images/05fe89a9aaf7be20a49ef6fcf65deb70a0e42b9063c40c477ae66bec36078df0.jpg) + +KL loss alone, we first evaluate the baseline of our method with six measurements and top-1 accuracy. Polarity loss and type loss are then separately and jointly added to KL loss, where both bring significant performance boosts as emotion polarity and emotion type serve as the basic and decisive attributes in visual emotion distribution learning. For a more fine-grained description, emotion intensity further improves all the measurements and gains the optimal result eventually. From the above analysis, we can conclude that each constraint in PC loss is indispensable, jointly and progressively contributing to the final result. + +# 4.4.2 Hyper-Parameter Analysis + +As $\mu$ controls the relative importance between the proposed PC loss and KL loss, we conduct experiments to validate the choice of $\mu = 0.7$ in Eq. 10, as shown in Fig. 5. The greater the value of $\mu$ , the more importance lies in the proposed PC loss. Based on the Twitter_LDL dataset, we implement three measurements, namely KL divergence, Cosine coefficient and Accuracy, to demonstrate how $\mu$ influences the performance of the proposed method. We find that all the three measurements constantly grows as $\mu$ varies from 0 to 0.7 and drops after $\mu = 0.7$ , which suggests that a combination of PC loss and KL loss achieves the best performance. As KL loss solves the problem of general label distribution learning while PC loss considers emotion-specific circular structure as prior knowledge, each loss encounters performance drop when acting alone, which further suggests that both losses are essential and complementary in visual emotion distribution learning. + +# 4.5. Visualization + +We further visualize the predicted emotion distributions (predicted) and the ground-truths (GT) on both Flickr_LDL and Twitter_LDL datasets in Fig. 6. It is obvious that the proposed method restores the original emotion distribution to a large extent on both emotion polarity, emotion type and emotion intensity. Specifically, we can infer from the visualized results that once an emotion distribution only involves a single polarity, the prediction is more accurate with the help of the polar loss. When encounters complex emotional state, i.e., an emotional state is made up of different polarized emotions, our proposed method can still achieve relatively good results, owing to the effectiveness of the proposed type loss and emotion intensity. + +# 5. Conclusion + +In this paper, we have proposed a circular-structured representation for visual emotion distribution learning by exploiting the intrinsic relationships between emotions based on psychological models. We first constructed the Emotion Circle to present any emotional state with emotion vectors and then designed a Progressive Circular (PC) loss to constraint emotion vectors in a coarse-to-fine manner. Extensive experiments and comparisons have shown that the proposed method consistently outperforms the state-of-the-art methods on three visual emotion distribution datasets. + +Acknowledgments: This work was supported in part by the National Natural Science Foundation of China under Grants (62036007, 61772402, 62050175, 61972305, 61871308 and 61771473), Natural Science Foundation of Jiangsu Province under Grant (BK20181354). + +# References + +[1] Damian Borth, Rongrong Ji, Tao Chen, Thomas Breuel, and Shih-Fu Chang. Large-scale visual sentiment ontology and detectors using adjective noun pairs. In ACMMM, pages 223-232, 2013. 3 +[2] Qiuyu Chen, Wei Zhang, Ning Zhou, Peng Lei, Yi Xu, Yu Zheng, and Jianping Fan. Adaptive fractional dilated convolution network for image aesthetics assessment. In CVPR, pages 14114-14123, 2020. 1 +[3] Tianlang Chen, Zhongping Zhang, Quanzeng You, Chen Fang, Zhaowen Wang, Hailin Jin, and Jiebo Luo. "factual" or "emotional": Stylized image captioning with adaptive learning and attention. In ECCV, pages 519-535, 2018. 1 +[4] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In CVPR, pages 248–255, 2009. 6 +[5] Jiri Fajtl, Vasileios Argyriou, Dorothy Monekosso, and Paolo Remagnino. Amnet: Memorability estimation with attention. In CVPR, pages 6363-6372, 2018. 1 +[6] Bin-Bin Gao, Chao Xing, Chen-Wei Xie, Jianxin Wu, and Xin Geng. Deep label distribution learning with label ambiguity. IEEE Transactions on Image Processing, 26(6):2825-2838, 2017. 3, 7 +[7] Xin Geng. Label distribution learning. IEEE Transactions on Knowledge and Data Engineering, 28(7):1734-1748, 2016. 1, 2, 3, 6, 7 +[8] Xin Geng, Chao Yin, and Zhi-Hua Zhou. Facial age estimation by learning from label distributions. IEEE transactions on pattern analysis and machine intelligence, 35(10):2401-2412, 2013. 7 +[9] Longteng Guo, Jing Liu, Peng Yao, Jiangwei Li, and Hanqing Lu. Mscap: Multi-style image captioning with unpaired stylized text. In CVPR, pages 4204-4213, 2019. 1 +[10] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, pages 770-778, 2016. 6 +[11] Tao He and Xiaoming Jin. Image emotion distribution learning with graph convolutional networks. In ICMR, pages 382-390, 2019. 2, 3, 6, 7 +[12] Arlie Russell Hochschild. The sociology of emotion as a way of seeing. Emotions in social life: Critical themes and contemporary issues, pages 3-15, 1998. 2 +[13] Morris B Holbrook and John O'Shaughnessy. The role of emotion in advertising. Psychology & Marketing, 1(2):45-64, 1984. 1 +[14] Vlad Hosu, Bastian Goldlucke, and Dietmar Saupe. Effective aesthetics prediction with multi-level spatially pooled features. In CVPR, pages 9375-9383, 2019. 1 +[15] Ming Jiang and Qi Zhao. Learning visual attention to identify people with autism spectrum disorder. In ICCV, pages 3267-3276, 2017. 1 +[16] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. 6 +[17] Sander L Koole. The psychology of emotion regulation: An integrative review. Cognition and emotion, 23(1):4-41, 2009. 2 + +[18] Solomon Kullback and Richard A Leibler. On information and sufficiency. The annals of mathematical statistics, 22(1):79-86, 1951. 2, 5 +[19] Peter J Lang, Margaret M Bradley, Bruce N Cuthbert, et al. International affective picture system (iaps): Technical manual and affective ratings. NIMH Center for the Study of Emotion and Attention, 1:39-58, 1997. 3 +[20] Zuhe Li, Yangyu Fan, Bin Jiang, Tao Lei, and Weihua Liu. A survey on sentiment analysis and opinion mining for social multimedia. Multimedia Tools and Applications, 78(6):6939-6967, 2019. 1 +[21] Jana Machajdik and Allan Hanbury. Affective image classification using features inspired by psychology and art theory. In ACMM, pages 83-92, 2010. 3, 6 +[22] Neil McNaughton, N McNaughton, and Colin Mcnaughton. *Biology and emotion*. Cambridge University Press, 1989. 2 +[23] Joseph A Mikels, Barbara L Fredrickson, Gregory R Larkin, Casey M Lindberg, Sam J Maglio, and Patricia A Reuter-Lorenz. Emotional category data on images from the international affective picture system. Behavior research methods, 37(4):626-630, 2005. 2, 3, 4, 5 +[24] Andrew A Mitchell. The effect of verbal and visual components of advertisements on brand attitudes and attitude toward the advertisement. Journal of Consumer Research, 13(1):12-24, 1986. 1 +[25] Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. 2017. 6 +[26] Kuan-Chuan Peng, Tsuhan Chen, Amir Sadovnik, and Andrew C Gallagher. A mixed bag of emotions: Model, predict, and transfer emotion distributions. In CVPR, pages 860-868, 2015. 2, 3, 7 +[27] Robert Plutchik. A general psychoevolutionary theory of emotion. In Theories of emotion, pages 3-33. Elsevier, 1980. 2, 3, 4, 5 +[28] Robert Plutchik. The psychology and biology of emotion. HarperCollins College Publishers, 1994. 2 +[29] Tianrong Rao, Xiaoxu Li, and Min Xu. Learning multi-level deep representations for image emotion classification. Neural Processing Letters, pages 1-19, 2016. 1, 3 +[30] Ole Riis and Linda Woodhead. A sociology of religious emotion. Oxford University Press, 2010. 2 +[31] Oleksii Sidorov. Changing the image memorability: From basic photo editing to gans. In CVPR, pages 0–0, 2019. 1 +[32] Pawel Sobkowicz, Michael Kaschesky, and Guillaume Bouchard. Opinion mining in social media: Modeling, simulating, and forecasting political opinions in the web. Government information quarterly, 29(4):470-479, 2012. 1 +[33] Kenneth T Strongman. The psychology of emotion: Theories of emotion in perspective. John Wiley & Sons, 1996. 2 +[34] Matthias J Wieser, Elisabeth Klupp, Peter Weyers, Paul Pauli, David Weise, Daniel Zeller, Joseph Classen, and Andreas Muhlberger. Reduced early visual emotion discrimination as an index of diminished emotion processing in parkinsons disease?—evidence from event-related brain potentials. Cortex, 48(9):1207–1217, 2012. 1 + +[35] Haitao Xiong, Hongfu Liu, Bineng Zhong, and Yun Fu. Structured and sparse annotations for image emotion distribution learning. In AAAI, volume 33, pages 363-370, 2019. 2, 3, 7 +[36] Jufeng Yang, Dongyu She, Yu-Kun Lai, Paul L Rosin, and Ming-Hsuan Yang. Weakly supervised coupled networks for visual sentiment analysis. In CVPR, pages 7584-7592, 2018. 1, 3 +[37] Jufeng Yang, Dongyu She, and Ming Sun. Joint image emotion classification and distribution learning via deep convolutional neural network. In *IJCAI*, pages 3266–3272, 2017. 2, 3, 7 +[38] Jufeng Yang, Dongyu She, Ming Sun, Ming-Ming Cheng, Paul L Rosin, and Liang Wang. Visual sentiment prediction based on automatic discovery of affective regions. IEEE Transactions on Multimedia, 20(9):2513-2525, 2018. 1, 3 +[39] Jufeng Yang, Ming Sun, and Xiaoxiao Sun. Learning visual sentiment distributions via augmented conditional probability neural network. In AAAI, pages 224-230, 2017. 2, 3, 6, 7 +[40] Quanzeng You, Hailin Jin, and Jiebo Luo. Visual sentiment analysis by attending on local image regions. In AAAI, 2017. 3 +[41] Quanzeng You, Jiebo Luo, Hailin Jin, and Jianchao Yang. Robust image sentiment analysis using progressively trained and domain transferred deep networks. In AAAI, 2015. 3 +[42] Wei Zhang, Xuanyu He, and Weizhi Lu. Exploring discriminative representations for image emotion recognition with cnns. IEEE Transactions on Multimedia, 22(2):515-523, 2019. 1, 3 +[43] Sicheng Zhao, Guiguang Ding, Yue Gao, Xin Zhao, Youbao Tang, Jungong Han, Hongxun Yao, and Qingming Huang. Discrete probability distribution prediction of image emotions with shared sparse learning. IEEE Transactions on Affective Computing, 2018. 2, 3 +[44] Sicheng Zhao, Yue Gao, Xiaolei Jiang, Hongxun Yao, Tat-Seng Chua, and Xiaoshuai Sun. Exploring principles-of-art features for image emotion recognition. In ACMMM, pages 47-56, 2014. 3 +[45] Sicheng Zhao, Hongxun Yao, Yue Gao, Rongrong Ji, Wenlong Xie, Xiaolei Jiang, and Tat-Seng Chua. Predicting personalized emotion perceptions of social images. In ACMMM, pages 1385-1394, 2016. 2, 3, 4, 5 +[46] Sicheng Zhao, Hongxun Yao, You Yang, and Yanhao Zhang. Affective image retrieval via multi-graph learning. In ACMM, pages 1025-1028, 2014. 3 +[47] Xinge Zhu, Liang Li, Weigang Zhang, Tianrong Rao, Min Xu, Qingming Huang, and Dong Xu. Dependency exploitation: A unified cnn-rnn approach for visual emotion recognition. 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Recent works have observed that CNN-generated images share a systematic shortcoming in replicating high frequency Fourier spectrum decay attributes. Furthermore, these works have successfully exploited this systematic shortcoming to detect CNN-generated images reporting up to $99\%$ accuracy across multiple state-of-the-art GAN models. + +In this work, we investigate the validity of assertions claiming that CNN-generated images are unable to achieve high frequency spectral decay consistency. We meticulously construct a counterexample space of high frequency spectral decay consistent CNN-generated images emerging from our handcrafted experiments using DCGAN, LSGAN, WGAN-GP and StarGAN, where we empirically show that this frequency discrepancy can be avoided by a minor architecture change in the last upsampling operation. We subsequently use images from this counterexample space to successfully bypass the recently proposed forensics detector which leverages on high frequency Fourier spectrum decay attributes for CNN-generated image detection. + +Through this study, we show that high frequency Fourier spectrum decay discrepancies are not inherent characteristics for existing CNN-based generative models—contrary to the belief of some existing work—and such features are not robust to perform synthetic image detection. Our results prompt re-thinking of using high frequency Fourier spectrum decay attributes for CNN-generated image detection. Code and models are available at https://keshik6.github.io/FourierDiscrepancies-CNN-Detection/ + +# 1. Introduction + +With serious concerns over Deepfakes being widely used for malicious purposes [18, 19, 30, 37, 2, 36, 9, 32], detec + +tion of deepfake multimedia content has become an important research field. With substantial improvement of CNN-based generative modelling in the recent years [22, 45, 23, 24, 21, 35, 8, 3, 46, 33, 27, 1, 4, 16, 38, 39], it is becoming more and more difficult to assess the "fakeness" of such synthetic content in the RGB pixel space. + +# 1.1. Fourier spectrum discrepancies in CNN-generated images + +Recent research suggests that CNN-based generation methods are unable to reproduce high frequency distribution of real images. Existing work tends to conclude that this incompetence is an intrinsic property of CNN-based generative models [12, 10, 25]. While Zhang et al. [44] and Wang et al. [42] report that CNN generated images have frequency artifacts, Dzanic et al. [12] and Durall et al. [10] suggest spectrum discrepancies in high frequency: CNN-generated images at the highest frequencies do not decay as usually observed in real images (Figure 1). In particular, + +- Dzanic et al. [12] analyze high frequency of real and deep network generated images, and conclude that "deep network generated images share an observable, systematic shortcoming in replicating the attributes of these high-frequency modes". +- Durall et al. [10] observe that "CNN based generative deep neural networks are failing to reproduce spectral distributions", and "this effect is independent of the underlying architecture". +- Dzanic et al. [12] take a step further and propose to exploit this frequency discrepancies for detection of deep network generated images, claiming an accuracy of up to $99.2\%$ across multiple state-of-the-art GAN and VAE models. + +Some works also propose different techniques to disguise these high frequency discrepancies via post-processing the deep network generated images [12, 25], or modifying the GAN training objective to avoid these discrepancies [10]. + +![](images/81a513c3257212de1b22dbd120d1ee127032cf65c035d97d9a3bd14737cea90e.jpg) + +![](images/1bb9ea6990f9d92495cd92874a3a69977f0ebbee3e3859aabcd4c400f17c0fac.jpg) +Figure 1. The curves show the average azimuthal integration over the power spectrum. (See section 3). Top row shows the evaluation on DCGAN [34], LSGAN [31], WGAN-GP [17]. Note the discrepancies at the highest frequencies, the same as reported in recent works. Note also that these models use transpose convolutions. The bottom row shows the evaluation after replacing the last feature map scaling operation with nearest and bilinear interpolation methods. Refer to table 1 for experiment codes. All evaluation are done using CelebA [29] (128x128). We observe that spectral consistent GANs are obtained when using nearest and bilinear interpolation methods for the last feature map scaling operation. + +It should be noted that the cause of this discrepancy1 has not been agreed upon. Zhang et al. [44] and Durall et al. [10] suggest that this discrepancy could be caused by transposed convolution. As transposed convolution is used throughout the generator architectures, it is difficult to replace them. Therefore, Durall et al. [10] propose spectral regularization to counteract this throughout the GAN training. Meanwhile, Dzanic et al. [12] attribute this discrepancy to the linear dependencies in the spectrum of convolutional filters [25], which hinder learning of high frequencies. + +# 1.2. CNN-generated Image Detectors + +Many works have addressed the possibilities of creating detectors to identify synthetic images apart from real images. Though synthetic image detectors (CNN-based) + +worked reasonably with RGB inputs [42, 5], with spectral discrepancies being observed, several works have proposed to use the corresponding Fourier representation to train these detectors [44, 13]. In particular, Frank et al. [13] showed that detectors using frequency domain yielded better results compared to using the RGB counterpart. + +Though observations corresponding to distinguishable frequency footprints being left by CNN-generated images remained mostly qualitative, Dzanic et al. [12] and Durall et al. [10, 11] studied the spectral decay attributes and quantified this behaviour via averaging the power spectrum over frequencies radially to represent them as 1D information. Through this, they observed high frequency spectral decay inconsistencies in CNN-generated images. Furthermore, Dzanic et al. [12] proposed to use a simple KNN classifier using high frequency spectral attributes (3 features extracted per image) that surprisingly obtained very high accuracy in identifying synthetic images only with very small amount of training data. Similarly, Durall et al. [11] used the entire 1d-power spectrum (contains all frequency information) as features to perform detection using Logistic regression, SVM and K-means clustering algorithms. These detectors [12, 11] rely on the belief that high frequency decay discrepancies are intrinsic in CNN-generated images. + +# 1.3. Our contributions + +In this work, we take a closer look at the high frequency decay discrepancies in CNN-generated images. Analysis of CNN-generated images is a daunting task: a large number of different architectures, algorithms and objective functions have been proposed to train generators. Instead, our study focuses on the last layer of the generators. Our justification is as follows. Based on Sampling Theorem [20], the frequency contents of the outputs of individual layers are limited by the sampling resolution of the corresponding outputs. As previous work has reported the discrepancies between real and CNN-generated images at the highest frequencies, we hypothesize that inner generator layers (which produce lower resolution outputs) are not directly responsible for the high frequency discrepancies. Therefore, we focus on the last upsampling layer of generative CNN models. + +Due to our focus being localized at the last layer, we are able to pinpoint the component that is related to this discrepancy across multiple GAN loss functions, architectures, datasets and resolutions. Our candidate GANs are similar to Durall et al. [10]: DCGAN [34], LSGAN [31], WGAN-GP [17] and we also extend to StarGAN [7]. Our experiments suggest that the frequency discrepancies can be largely avoided by simply modifying the feature map scaling of the last layer. Importantly, using the same training algorithms, objective functions and network architectures (except using a different scaling in the last layer) as in standard GAN models, we are able to avoid the spectral dis + +crepancies. Therefore, our work provides counterexamples to argue that high frequency discrepancies are not intrinsic for CNN-generated images. Furthermore, we are able to successfully bypass the synthetic image detector proposed by Dzanic et al. [12] with only such change in the last scaling step, showing that such approach may not be reliable for detection of deep network generated images. The key takeaway from our work is: + +- High frequency spectral decay discrepancies are not intrinsic for CNN-generated images. Therefore, we urge re-thinking in using such features for CNN-generated image detection. + +# 2. Related Work + +Dzanic et al. [12] show that CNN-generated images (GANs and VAEs) demonstrate different Fourier spectrum decay characteristics. Since the spectra of natural images tend to behave following the power law [41], Dzanic et al. [12] show that the Fourier modes of deep network generated images at the highest frequencies did not decay as seen in real images, but instead stayed approximately constant. Furthermore, they propose to exploit these discrepancies to detect CNN-generated synthetic images by fitting a decay function to the reduced spectra, and using the parameters of the fitted decay function to build a simple kNN classifier. + +Durall et al. [10] show that popular GAN image generators fail to approximate the spectral distributions of real data, and they attribute this to the use of transpose convolutions for upsampling. They show that this effect is independent of the underlying architecture using 1-dimensional spectral characteristics of images generated from DCGAN [34], LSGAN [31], WGAN-GP[17] and DRAGAN [26]. Since transpose convolutions are used in the entire generator models, the propose to counteract their effects by adding a spectral regularization term to the Generator, thereby penalizing the generator for spectral distorted samples. + +Khayatkhoei and Elgammal [25] suggest the presence of a systematic bias in GANs against learning high frequencies. They specifically show that for a given kernel size, as resolution increases, the correlation/ dependency of the kernel's spectrum increases thereby systematically preventing GANs to learn high frequencies without affecting the adjacent frequencies. To alleviate this shortcoming, they propose frequency shifted generators whose frequencies are shifted towards specific high frequencies. + +# 3. Background + +The 2D discrete Fourier transform $F(k_{x},k_{y})$ of a $M\times N$ 2D image $f(x,y)$ can be written as, + +$$ +F \left(k _ {x}, k _ {y}\right) = \frac {1}{M N} \sum_ {u = 0} ^ {M - 1} \sum_ {v = 0} ^ {N - 1} f (u, v) e ^ {- i 2 \pi \left(\frac {k _ {x} u}{M} + \frac {k _ {y} v}{N}\right)} \tag {1} +$$ + +for $k_{x} \in \{0,1,2,\dots,M - 1\}$ , $k_{y} \in \{0,1,2,\dots,N - 1\}$ . We follow the convention in [12, 10] and compute the azimuthally average of the magnitude of Fourier coefficients over radial frequencies to obtain the reduced spectrum and normalize it. The reduced spectra indicate the strength of the signal with respect to different spatial frequencies. Since our study focuses on high frequency Fourier attributes, we pay attention to the last $25\%$ of the spatial frequencies (0.75 - 1.0 normalized spatial frequencies) similar to [12]. + +The Sampling Theorem ([20], chapter 4.2) states that: A bandlimited image $f(x,y)$ with bandwidths $\xi_{x0}, \xi_{y0}$ can be recovered without error from the sample values provided the sampling rate is greater than the Nyquist rate: $2\xi_{x0}, 2\xi_{y0}$ . The image $f(x,y)$ with bandwidths $\xi_{x0}, \xi_{y0}$ means that there is no frequency content outside a bounded region in the frequency plane defined by $\xi_{x0}, \xi_{y0}$ . Details and mathematical proofs can be found in [20] chapter 4.2. + +# 4. Last Upsampling Operation and Fourier Discrepancies + +Based on last section, the maximum frequency represented by a discrete 2D signal is constrained by the spatial resolution (sampling) of the signal. Previous work has consistently reported discrepancies in the highest frequencies [10, 12]. Therefore, we hypothesize that inner generator layers that produce lower resolution outputs may not be directly responsible for the high frequency discrepancies. Therefore, we focus on the last upsampling step. In particular, we split the last step into 2 operations, 1) Feature map scaling and 2) Convolution. + +# 4.1. Feature Map Scaling + +Feature map scaling is a non-parametric operation that scales the input in both dimensions by some factor (Usually 2 in most GAN architectures). In this work, we focus on 3 common feature map scaling techniques. 1) Zero-insert scaling inserts zero between every row and column, scaling the input in both dimensions which is also used by transpose convolutions. 2) Nearest interpolation scales the input by inserting nearest neighbour values. 3) Bilinear interpolation scales the input by inserts new values by taking the weighted average of adjacent values. + +From frequency perspective, zero-insertion introduces the largest amount of high frequency content as it replicates the low frequency spectrum for the high frequencies [44], followed by billinear and nearest interpolation. We focus more on the "spectral trend" than the frequency values, and show a schematic example of these upsampling effects on the normalized reduced spectra in Figure 2 by upsampling a reference image of $128 \times 128$ from CelebA. [29] + +![](images/4fe849abe1c0c01eb9a337dcc330f6d9ec83ceb50bb4532a5ffd8596a178fcac.jpg) +Figure 2. Example showing normalized spectral effects of upsampling an image. Vertical line at 88 shows the maximum radial frequency of reference image. + +# 4.2. Convolution + +The subsequent convolution operation learns kernels in order to satisfy the optimization objective. Convolutional kernels are capable of suppressing/ amplifying high frequencies. e.g. A Gaussian kernel suppresses high frequencies and a bilateral kernel amplifies high frequencies. So when designing upsampling blocks in GANs, the general intuition is that irrespective of the feature map scaling method, the kernels will learn to manipulate the scaled feature maps to satisfy the objective function. + +# 5. Experiments + +Here we discuss the main experiments. Additional experiments and analysis can be found in Supplementary. + +In order to investigate the effects of these 2 operations, we design a rigorous test bed that can address feature map scaling, kernel size and number of kernels independently. Our aim is to isolate the effects of these 2 operations and understand their roles (if any) in causing the high frequencies discrepancies. We use celebA [29] dataset at $128 \times 128$ resolution and use 3 GANs with identical architectures but different loss functions namely 1) DCGAN [34], 2) LSGAN [31] and 3) WGAN-GP [17]. All baseline models consist of transpose convolutions with kernel size 4 identical to most out of the box GAN architectures including CycleGAN [46], StarGAN [7] and VQ-VAE [40]. + +Proposed Test Bed. Table 1 summarizes our test bed. All baseline experiments using transpose convolutions of kernel size 4 are indicated by the experiment code Baseline and our handcrafted experiments are indicated using the 3 character code: An experiment code of X.Y.Z indicates X type of feature map scaling (Possible values are Z : Zero-insertion, N: Nearest interpolation, B: Bilinear interpolation), Y number of convolutional blocks and Z sized convolutional kernels for the last upsampling step. e.g. A code of N.1.5 indicates nearest interpolation feature map scaling with a single convolutional block of $5 \times 5$ kernel for the last upsampling step. Note that we focus on up scaling + +
CodeDetails
BaselineTranspose convolution (4x4 kernel)
N.1.5Nearest Upsampling + 1 conv block of 5x5 kernel
Z.1.5Zero insert Upsampling + 1 conv block of 5x5 kernel
B.1.5Bilinear Upsampling + 1 conv block of 5x5 kernel
N.1.3Nearest Upsampling + 1 conv block of 3x3 kernel
N.1.7Nearest Upsampling + 1 conv block of 7x7 kernel
Z.1.3Zero insert Upsampling + 1 conv block of 3x3 kernel
Z.1.7Zero insert Upsampling + 1 conv block of 7x7 kernel
B.1.3Bilinear Upsampling + 1 conv block of 3x3 kernel
B.1.7Bilinear Upsampling + 1 conv block of 7x7 kernel
N.3.5Nearest Upsampling + 3 conv blocks of 5x5 kernel
Z.3.5Zero insert upsampling + 3 conv blocks of 5x5 kernel
B.3.5Bilinear upsampling + 3 conv blocks of 5x5 kernel
+ +Table 1. Test Bed to study the effect of feature map scaling and convolution in the last upsampling step of the generator, for different GANs: DCGAN, LSGAN, WGAN-GP, StarGAN. "Baseline" refers to public released code of the GAN model, which uses transpose convolution of $4 \times 4$ kernel. For other models, we replace the last transpose convolution in Baseline with the corresponding configurations shown. We emphasize that we only modify the last step specified as above; the algorithms, learning objectives and architectures (except the last step) are kept identical as the public released code for different GAN models. + +by a factor of 2 as used in most GAN models. Our test bed summary is shown in table 1 and it contains experiments addressing the following factors: + +Feature Map scaling. In order to investigate the effect of feature map scaling on high frequency Fourier attributes, we use experiments Z.1.5, N.1.5 and B.1.5. We explicitly conduct experiments using zero-insert feature map scaling as sanity check experiments to verify the effects of transpose convolutions. Do note that we had to use odd size kernel to maintain the spatial size after scaling, and hence we use kernels of size 5 for the last convolutional block. + +Kernel Size. We use experiments x.1.3, x.1.5 and x.1.7 to investigate the kernel size effects on high frequency Fourier behaviour. Here x refers to Z, N or B for different types of scaling as discussed. + +Number of kernels. Further, we use experiments x.1.5 and x.3.5 to study the effect of number of kernels on the high frequency Fourier behaviour. + +# 6. Metrics + +Spectral behaviour of synthetic images have been analysed only qualitatively, not quantitatively in previous works [12, 10, 11]. Defining a spectral consistency metric is nontrivial and to be consistent, we will qualitatively analyse the high frequency spectral distribution in our experiments. Synthetic images are spectral consistent if they demonstrate power spectrum decay behaviour similar to their training data, and if not, vice versa. We use 4000 real and GAN images to generate spectral distribution curves. To ensure + +that our setups were trained properly, we use FID scores to assess the quality of samples and make sure that they are consistent with the FID scores from baseline experiments. + +# 7. Results + +# 7.1. Effect of Feature Map Scaling Methods + +Figure 3 illustrates the resulting spectral distributions when using different feature map scaling methods. We observe that images from Z.1.5 and Baseline experiments are spectral inconsistent for all 3 GANs. Nearest and bilinear interpolation methods are able to replicate the spectral distribution of real data reasonably across all 3 GAN models. Since the only change in our models is the feature map scaling method in the last layer while the algorithms, objective functions and majority of the network architectures are identical to public released code, these results qualify to support our thesis that high frequency Fourier discrepancies are not inherent to GANs. + +# 7.2. Effect of Kernel Size + +From Figure 4, we observe that smaller kernel sizes result in more turbulent spectral behaviour for N.1.3 and B.1.3 LSGAN experiments. Apart from this observation, experiments using nearest and bilinear interpolation methods are able to reproduce spectral distributions of real data reasonably well, and zero-insertion based methods always result in high frequency spectral distortions. Further, from Figure 5, we observe that when using larger kernels, all experiments using nearest and bilinear interpolation methods are able to replicate spectral behaviour of real data, and even with larger kernels zero-insertion based methods produce high frequency spectral distortions (Z.1.7). + +# 7.3. Effect of Number of Kernels + +Figure 6 illustrates that increasing the number of kernels do not yield spectral consistency by itself. Apart from N.3.5 DCGAN experiment, we observe that all other experiments using nearest and bilinear interpolation methods are able to approximate the spectral behaviour of real data. Also, GAN objective functions do not impose any spectral requirements. Thus the kernels do not have any direct incentive for imposing spectral consistency. + +Key observations. Throughout all 39 rigorous experiments, we observe that zero insertion based feature map scaling methods (including Baseline) are consistently showing high frequency spectral discrepancies, and most experiments (22/24) using bilinear and nearest interpolation methods are able to avoid these high frequency spectral discrepancies. All these results support our statement that high frequency spectral discrepancies are not inherent characteristics to GANs. The FID scores for all experiments were comparable with the baseline FID, and are included in the + +supplementary. We show image samples from WGAN-GP for Baseline, N.1.5 and B.1.5 setups in Figure 7. Do note that for all experiments, we use the exact same discriminator architecture as the Baseline experiment. + +# 8. Fourier Synthetic Image Detector + +Dzanic et al. [12] state that the spectral properties of real and deep network generated images are fundamentally different, and proposed a synthetic image detection method using a "simple" k-nearest neighbours (KNN) classifier to emphasize the extent of these spectral differences. We follow the exact procedure as the original authors to train these classifiers and details can be found in Supplementary. + +# 8.1. Experiment Setup + +With nearest and bilinear interpolation methods obtaining spectral consistent GANs for the previous experiments, we question whether the classifier proposed above would be robust enough to detect these samples as fake. To investigate this we follow the following steps: + +1. We train 3 KNN classifiers, one for DCGAN, LSGAN and WGAN-GP respectively. For GAN images, we use images generated from the Baseline experiment (using transpose convolutions) as training data. +2. We test these classifiers using GAN images generated from the setups in our test bed to evaluate the robustness of the classifier. +3. We also repeat the experiments using $50\%$ data for training the classifier (The original work used only $10\%$ ) to observe any improvements in accuracy. + +# 8.2. Detection Results + +The complete detection results are shown in table 2. We observe that all setups corresponding to N.x.x and B.x.x experiments are able to easily bypass the classifier. Even when $50\%$ training data is used, we are able to bypass the classifier with ease (Included in Supplementary). The results clearly demonstrate that the proposed classifier relying on high frequency Fourier attributes to detect synthetic images, fails to detect images generated from identical GAN models with last feature map scaling replaced by nearest or bilinear interpolation methods. These results are consistent with the observed spectral distributions. By combining these detection results with the empirical finding that high frequency spectral discrepancies are not inherent characteristics of CNN-generated images, we suggest re-thinking of using such discrepancies to detect synthetic images. + +# 9. Extended experiments + +With observations that high frequency Fourier spectrum discrepancies are not intrinsic characteristics of GANs, we + +![](images/5a5bb3e5e9b0cbf93afe1b1bc4bfdefbbfcc65275ea0d4afbef3a3bcea64d2fd.jpg) +Figure 3. Feature Map Scaling Results. We observe that experiments using nearest and bilinear interpolation methods in the last step are able to produce spectral consistent GANs. Refer to table 1 for experiment details. + +![](images/e0f97f6d72156bb2a35b2748f79ccddf014dc48d8a415eee1117c7921e6a360e.jpg) +Figure 4. Smaller Kernel (3x3) Results. We observe that smaller kernels do not substantially deteriorate spectral consistent GANs except for some turbulent behaviour observed in LSGAN for N.1.3 and B.1.3 experiments. Refer to table 1 for experiment details. + +
SetupDCGANLSGANWGAN-GP
N.1.50.09 ± 0.03%0.34 ± 0.08%0.14 ± 0.05%
Z.1.584.82 ± 3.72%88.16 ± 3.98%99.75 ± 0.14%
B.1.50 ± 0%0.1 ± 0%0.2 ± 0.12%
N.1.30 ± 0%0.06 ± 0.05%0.24 ± 0.13%
N.1.70 ± 0%0 ± 0%0.06 ± 0.05%
Z.1.398.73 ± 0.56%73.09 ± 3.5%97.94 ± 0.87%
Z.1.797.23 ± 1.1%95.66 ± 1.93%99.94 ± 0.07%
B.1.30 ± 0%0.19 ± 0.1%0.07 ± 0.05%
B.1.70 ± 0%0.1 ± 0%0.17 ± 0.13%
N.3.50.16 ± 0.05%0 ± 0%0 ± 0%
Z.3.577.67 ± 6%67.66 ± 11.9%99.9 ± 0.19%
B.3.50.03 ± 0.05%0.48 ± 0.04%0.13 ± 0.05%
+ +Table 2. Detection results for the detectors proposed by Dzanic et al. [12], using CelebA dataset. We follow exactly the procedure in [12] to train the detector for each GAN model (10% data for training). Then, the images generated by GAN models using different Setups are tested on the corresponding detectors. The table shows the successful detection rates, and we highlight the cases when the detection rates are inferior (less than 10%). The results consistently show that when a GAN model is trained with the last feature scaling method based on nearest or bilinear, a detector trained using high frequency features such as [12] fails to detect GAN images (Consistent with spectral plot observations). All reported detection rates are averaged over 10 independent runs + +extend our experiments to address different dataset, image resolution and GAN objective function to further find evi + +dences to support our thesis statement. We select 3 setups from our test bed Z.1.5, N.1.5 and B.1.5 to conduct extended experiments since we have observed that kernel size/number of kernels do not substantially manipulate high frequencies compared to feature map scaling methods. Similar to previous experiments, we analyze the resulting spectral distributions and evaluate the robustness of the synthetic detector proposed by Dzanic et al. [12]. + +# 9.1. LSUN Bedrooms Dataset + +In this experiment we use a subset of LSUN Bedrooms Dataset [43] (128x128) to train DCGAN [34], LSGAN [31] and WGAN-GP [17] identical to previous setups. The spectral plots are shown in Figure 8. We observe identical results to CelebA experiment (Figure 3). That is we observe N.1.5 and B.1.5 are producing spectral consistent GANs and this further supports our statement that high frequency spectral discrepancies are not inherent in GANs. We also evaluate the synthetic image detector and observe that N.1.5 and B.1.5 samples can easily bypass the detector. (See table 3) + +# 9.2. Image-to-Image Translation + +We extend our experiments to Image-to-Image translation domain using StarGAN [7]. Here we use resized CelebA [29] (256x256) used by the official StarGAN [7] implementation to study whether spectral consistency can be achieved by modifying the last feature map scaling oper + +![](images/60c9709645d6c979703d7098fdf7a1ab976e81dcb6fe3d0a5d5116bb809b920f.jpg) +Figure 5. Larger Kernel (7x7) Results. We observe that larger kernels do not substantially manipulate the discrepancies in Z.1.7 experiments. Refer to table 1 for experiment details. + +![](images/e522d3a4e783ddd85d76488476c6f6f047ea60e333e2a23872fe290d3e0b5880.jpg) +Figure 6. Increased number of kernels (3 conv blocks) Results. We see that even with more number of kernels in the last upsampling step, Z.3.5 experiment is not able to produce spectral consistent GANs. Refer to table 1 for experiment details. + +
SetupDCGANLSGANWGAN-GP
N.1.51.5 ± 2.09%0.62 ± 0.43%0.03 ± 0.05%
Z.1.597.88 ± 1.04%95.79 ± 2.07%99.87 ± 0.13%
B.1.53.54 ± 6.15%0.07 ± 0.09%0.14 ± 0.13%
+ +Table 3. Detection results for the forensics classifiers proposed by Dzanic [12], using LSUN dataset (128x128). The table shows the successful detection rates (10% data for training). + +
SetupN.1.5Z.1.5B.1.5
Accuracy52.06 ± 3.77%64.3 ± 2.7%0 ± 0%
+ +Table 4. Detection results for the forensics classifiers proposed by Dzanic [12], using CelebA dataset (256x256). The table shows the successful detection rates (10% data for training). + +ation. We train StarGANs for Z.1.5, N.1.5 and B.1.5 setups. The spectral plots are shown in Figure 9. We observe that only B.1.5 is able to produce spectral consistent GANs and N.1.5 produces high frequency Fourier discrepancies. We would not ask ourselves why nearest interpolation method behaves differently than bilinear, but rather confirm that we are able to find bilinear interpolation results as more evidence to support our statement that high frequency spectral discrepancies are not inherent characteristics to GANs. We further evaluate the synthetic image detector and observe that B.1.5 samples can bypass the classifier. (See table 4) + +# 10. Spectral Regularization + +The recent Spectral regularization (SR) by Durall et al. [10] proposed to add a regularizer term to the generator loss to explicitly penalize the generator for spectral distortions. Using SR, they were able to obtain spectral consistency for DCGAN [34], LSGAN [31], WGAN-GP [17] and DRA-GAN [26] using the celebA [29] (128x128). This method encounters computational overhead due to calculation of reduced spectrum for images during training. We show that by modifying the last feature map scaling operation, we are able to achieve spectral consistent GANs without SR. Importantly, we show that no change in objective functions is needed. These results and more discussion on SR can be found in Supplementary. + +# 11. Discussion + +In this study, we investigated the validity of contemporary beliefs that CNN-based generative models are unable to reproduce high frequency decay attributes of real images. We employ a systematic study to design counterexamples to challenge the existing beliefs. With maximum frequency bounded by the spatial resolution, and Fourier discrepancies reported at the highest frequencies, we hypothesized that the last upsampling operation is mostly related to this shortcoming. With carefully designed experiments span + +![](images/adee4c030ebd9dac8f4e4d534de05e1100fa71b46f2dcebdf89a9c434c1d949e.jpg) +Figure 7. WGAN-GP samples for Baseline (Left), N.1.5 (Middle) and B.1.5 (Right) for CelebA [29]. We observe that the visual quality is comparable when replacing the last transpose convolutions with nearest and bilinear methods. More visual results in supplementary. + +![](images/f3588b407e335db3bad622e09cb146e57c8e95166e75390629256e6656fce081.jpg) + +![](images/ad90677cb1bb2da2a3f4116b23e52fa84f701d20b7da8d3c407538b8b9adf19f.jpg) + +![](images/e33f54eacaf73783eb1ff8457d0bba3e7e3344736d1ec0bd39675f8ff3a3a2cb.jpg) +Figure 8. LSUN results. We observe spectral plots identical to CelebA [29] experiments. Refer to table 1 for experiment details + +![](images/66ee76231f3b22a8da39c013da73ba74b7f13f9b6e282c48b5508de08abe7c4f.jpg) + +![](images/85a9fd1511b5c31727f2e604f4ea6fd9c7e36c76d8836b1301121b3995d62038.jpg) + +ning multiple GAN architectures, loss functions, datasets and resolutions, we observe that high frequency spectral decay discrepancies can be avoided by replacing zero insertion based scaling used by transpose convolutions with nearest or bilinear at the last step. Note that we do not claim that modifying the last feature map scaling method will always fix spectral decay discrepancies in every situation, but rather the goal of our study is to provide counterexamples to argue that high frequency spectral decay discrepancies are not inherent characteristics of CNN-generated images. Further, we easily bypass the recently proposed synthetic image detector that exploits this discrepancy information to detect CNN-generated images indicating that such features are not robust for the purposes of synthetic image detection. + +In Supplementary material, we provide more GAN models [6, 28] with no high frequency decay discrepancies. We also investigate whether such high frequency decay discrepancies are found in other types of computational image synthesis methods (synthesis using Unity game engine $^{2}$ ) [15, 14]. To conclude, through this work we hope to help image forensics research manoeuvre in more plausible directions to combat the fight against CNN-synthesized visual disinformation. + +![](images/0af936841972eef0ec92afbe1bb06979be4bd93f4d422151ff0fb49080f5a3e4.jpg) +Figure 9. Spectral plots for StarGAN images. We observe that Bilinear feature map scaling produces spectral consistent GANs. + +Acknowledgments: This project was supported by SUTD project PIE-SGP-AI-2018-01. This research was also supported by the National Research Foundation Singapore under its AI Singapore Programme [Award Number: AISG-100E2018-005]. This work was also supported by ST Electronics and the National Research Foundation (NRF), Prime Minister's Office, Singapore under Corporate Laboratory @ University Scheme (Programme Title: STEE, Infosec - SUTD Corporate Laboratory). + +We also gratefully acknowledge the support of NVIDIA AI Technology Center (NVAITC) for our research. + +# References + +[1] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein gan, 2017. 1 +[2] Paul Baines. Uk election 2019: after fake keir starmer clip, how much of a problem areDoctored videos?, Aug 2020. 1 +[3] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale GAN training for high fidelity natural image synthesis. In International Conference on Learning Representations, 2019. 1 +[4] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis, 2019. 1 +[5] Lucy Chai, David Bau, Ser-Nam Lim, and Phillip Isola. What makes fake images detectable? understanding properties that generalize. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision – ECCV 2020, pages 103–120, Cham, 2020. Springer International Publishing. 2 +[6] Qifeng Chen and V. Koltun. Photographic image synthesis with cascaded refinement networks. 2017 IEEE International Conference on Computer Vision (ICCV), pages 1520-1529, 2017. 8 +[7] Yunjey Choi, Minje Choi, Munyoung Kim, Jung-Woo Ha, Sunghun Kim, and Jaegul Choo. Stargan: Unified generative adversarial networks for multi-domain image-to-image translation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018. 2, 4, 6 +[8] Yunjey Choi, Youngjung Uh, Jaejun Yoo, and Jung-Woo Ha. Stargan v2: Diverse image synthesis for multiple domains. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020. 1 +[9] Danielle Citron and Robert Chesney. Deepfakes and the new disinformation war, Jun 2020. 1 +[10] Ricard Durall, Margret Keuper, and Janis Keuper. Watch your up-convolution: Cnn based generative deep neural networks are failing to reproduce spectral distributions. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020. 1, 2, 3, 4, 7 +[11] Ricard Durall, Margret Keuper, Franz-Josef Pfreundt, and Janis Keuper. Unmasking deepfakes with simple features, 2020. 2, 4 +[12] Tarik Dzanic, Karan Shah, and Freddie Witherden. Fourier spectrum discrepancies in deep network generated images. In Thirty-fourth Annual Conference on Neural Information Processing Systems (NeurIPS), December 2020. 1, 2, 3, 4, 5, 6, 7 +[13] Joel Frank, Thorsten Eisenhofer, Lea Schonherr, Asja Fischer, Dorothea Kolossa, and Thorsten Holz. Leveraging frequency analysis for deep fake image recognition. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 3247-3258. PMLR, 13-18 Jul 2020. 2 +[14] A. Gaidon, Q. Wang, Y. Cabon, and E. Vig. Virtualworlds as proxy for multi-object tracking analysis. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 4340-4349, 2016. 8 + +[15] Andreas Geiger, Philip Lenz, and Raquel Urtasun. Are we ready for autonomous driving? the kitti vision benchmark suite. In Conference on Computer Vision and Pattern Recognition (CVPR), 2012. 8 +[16] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, and K. Q. Weinberger, editors, Advances in Neural Information Processing Systems, volume 27, pages 2672-2680. Curran Associates, Inc., 2014. 1 +[17] Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville. Improved training of wasserstein gans. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30, pages 5767-5777. Curran Associates, Inc., 2017. 2, 3, 4, 6, 7 +[18] Karen Hao and Will Douglas Heaven. The year deepfakes went mainstream, Dec 2020. 1 +[19] Ellie Harrison. Shockingly realistic tom cruise deepfakes go viral on tiktok, Feb 2021. 1 +[20] Anil K. Jain. Fundamentals of Digital Image Processing. Prentice-Hall, Inc., USA, 1989. 2, 3 +[21] Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of GANs for improved quality, stability, and variation. In International Conference on Learning Representations, 2018. 1 +[22] Tero Karras, Miika Aittala, Janne Hellsten, Samuli Laine, Jaakko Lehtinen, and Timo Aila. Training generative adversarial networks with limited data. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 12104-12114. Curran Associates, Inc., 2020. 1 +[23] Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2019. 1 +[24] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of stylegan. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020. 1 +[25] Mahyar Khayatkhoei and Ahmed Elgammal. Spatial frequency bias in convolutional generative adversarial networks, Oct 2020. 1, 2, 3 +[26] Naveen Kodali, Jacob Abernethy, James Hays, and Zsolt Kira. On convergence and stability of gans, 2017. 3, 7 +[27] C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi. Photo-realistic single image super-resolution using a generative adversarial network. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 105-114, 2017. 1 +[28] K. Li, T. Zhang, and J. Malik. Diverse image synthesis from semantic layouts via conditional imle. In 2019 IEEE/CVF International Conference on Computer Vision (ICCV), pages 4219-4228, 2019. 8 + +[29] Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaou Tang. Deep learning face attributes in the wild. In Proceedings of International Conference on Computer Vision (ICCV), December 2015. 2, 3, 4, 6, 7, 8 +[30] Sophie Maddocks. 'a deepfake porn plot intended to silence me': exploring continuities between pornographic and 'political' deep fakes. Porn Studies, 0(0):1-9, 2020. 1 +[31] X. Mao, Q. Li, H. Xie, R. Y. K. Lau, Z. Wang, and S. P. Smolley. Least squares generative adversarial networks. In 2017 IEEE International Conference on Computer Vision (ICCV), pages 2813-2821, 2017. 2, 3, 4, 6, 7 +[32] Rachel Metz. The number of deepfake videos online is spiking. most are porn, Oct 2019. 1 +[33] Taesung Park, Ming-Yu Liu, Ting-Chun Wang, and Jun-Yan Zhu. Semantic image synthesis with spatially-adaptive normalization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2019. 1 +[34] Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks, 2016. 2, 3, 4, 6, 7 +[35] Ali Razavi, Aaron van den Oord, and Oriol Vinyals. Generating diverse high-fidelity images with vq-vae-2. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32, pages 14866-14876. Curran Associates, Inc., 2019. 1 +[36] Tom Simonite. What happened to the deepfake threat to the election?, Nov 2020. 1 +[37] Daniel Thomas. Deepfakes: A threat to democracy or just a bit of fun?, Jan 2020. 1 +[38] Ngoc-Trung Tran, Tuan-Anh Bui, and N. Cheung. Dist-gan: An improved gan using distance constraints. In ECCV, 2018. 1 +[39] Ngoc-Trung Tran, Viet-Hung Tran, Bao-Ngoc Nguyen, Linxiao Yang, and Ngai-Man (Man) Cheung. Self-supervised gan: Analysis and improvement with multiclass minimax game. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019. 1 +[40] Aaron van den Oord, Oriol Vinyals, and koray kavukcuoglu. Neural discrete representation learning. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30, pages 6306-6315. Curran Associates, Inc., 2017. 4 +[41] A. van der Schaaf and J.H. van Hateren. Modelling the power spectra of natural images: Statistics and information. Vision Research, 36(17):2759 - 2770, 1996. 3 +[42] Sheng-Yu Wang, Oliver Wang, Richard Zhang, Andrew Owens, and Alexei A. Efros. Cnn-generated images are surprisingly easy to spot... for now. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020. 1, 2 +[43] Fisher Yu, Yinda Zhang, Shuran Song, Ari Seff, and Jianxiong Xiao. Lsun: Construction of a large-scale image dataset + +using deep learning with humans in the loop. arXiv preprint arXiv:1506.03365, 2015. 6 +[44] X. Zhang, S. Karaman, and S. Chang. Detecting and simulating artifacts in gan fake images. In 2019 IEEE International Workshop on Information Forensics and Security (WIFS), pages 1-6, 2019. 1, 2, 3 +[45] Shengyu Zhao, Zhijian Liu, Ji Lin, Jun-Yan Zhu, and Song Han. Differentiable augmentation for data-efficient gan training. In Conference on Neural Information Processing Systems (NeurIPS), 2020. 1 +[46] Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networkss. 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Humans, even young toddlers, can induce causal relationships surprisingly well in various settings despite its notorious difficulty. However, in contrast to the commonplace trait of human cognition is the lack of a diagnostic benchmark to measure causal induction for modern Artificial Intelligence (AI) systems. Therefore, in this work, we introduce the Abstract Causal REasoning (ACRE) dataset for systematic evaluation of current vision systems in causal induction. Motivated by the stream of research on causal discovery in Bicket experiments, we query a visual reasoning system with the following four types of questions in either an independent scenario or an interventional scenario: direct, indirect, screening-off, and backward-blocking, intentionally going beyond the simple strategy of inducing causal relationships by covariation. By analyzing visual reasoning architectures on this testbed, we notice that pure neural models tend towards an associative strategy under their chance-level performance, whereas neuro-symbolic combinations struggle in backward-blocking reasoning. These deficiencies call for future research in models with a more comprehensive capability of causal induction. + +# 1. Introduction + +"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact." + +— Mark Twain [64] + +The history of scientific discovery is full of intriguing anecdotes. Mr. Twain is accurate in summarizing how influential science theories are distilled from sparse and limited investments. From only three observations, Edmond Halley precisely predicted the orbit of the Halley comet and its next visit, which he did not live to see. From a few cathode + +![](images/e3ae8310d98cc88bd4c0d140fd0fe4d8e50ad3ea20c609d0208d0028c30ab85d.jpg) +Figure 1. Abstract causal reasoning tasks administered to human participants [22, 61]. The Bicket machine possesses various activation patterns in these four cases. One needs to discover the hidden causal relations to answer two types of questions: whether object A / B is a Bicket, and how to make the machine stop / go. + +rays, Joseph Thomson proved and derived the existence of electrons. From merely crossbreeding of pea plants, Gregor Mendel established the laws of Mendelian inheritance much beyond pea plants. Out of many other possible conjectures, pioneering scientists picked the most plausible ones. + +The above examples of causal induction are only a few acclaimed cases of omnipresent causal reasoning scenarios in science history and our daily life. In fact, despite the notorious complexity in causal discovery, humans, even young toddlers, can felicitously identify and, sometimes, intervene in the unobservable mechanisms from only a trifling number of samples of observable events [19, 58]. + +This captivating commonplace trait of human cognition and its paramount connection to human learning mechanism motivate us to ask a counterpart question for modern Artificial Intelligence (AI) systems: + +At what level do current visual reasoning systems induce causal relationships? + +To answer this question, we propose the Abstract Causal REaasoning (ACRE) dataset. ACRE is inspired by the established stream of research on Blicket detection originally administered to young toddlers [7, 19, 20, 21, 22, 23, 35, 42, 44, 58, 60, 61, 66, 67]. The original experiments designed by Gopnik and Sobel [21] introduced a novel setup for investigating children's ability of causal induction, in which children were given a special machine referred to as "Blicket detector." Its underlying mechanism is intuitive: A Blicket detector would activate, lighting up and making + +noise, when a "Bicket" was put on it. The experimenter demonstrated a series of trials to participants by placing various (combinations of) objects on the Bicket detector and showing whether the detector was activated or not. At length, the participants were asked which object is a Bicket and how to make an (in)activated Bicket machine stop (go). + +This line of work's intricate nature lies in how the context and query were designed to test abstract causal reasoning beyond the simple strategy of covariation; see an illustration in Fig. 1. As a base test on causal discovery by covariation, Sobel et al. [61] show that children can correctly associate cause and effect using direct evidence. They also show that with only indirect evidence asserting the Bicketness of object B, children still made accurate predictions [22]. However, one must go beyond the simple covariation strategy to discover the hidden causal relations in the screening-off case and the backward-blocking case. Specifically, in the screening-off setting (Fig. 1 Top), object B (non-Bicket) is screened-off by A (Bicket) from probabilistically activating the machine [22]. The backward-blocking setting (Fig. 1 Bottom) is even more intriguing as object B, not independently tested, has undetermined Bicketness despite the fact that every appearance of it is associated with an activated machine [61]. See Section 3 for details and the supplementary for a symbolic summary. + +The proposed ACRE dataset is built following a similar querying manner in the Bicket experiments to study how well existing visual reasoning systems can learn to derive ample causal information from scarce observation. In particular, inspired by the recent endeavors of visual reasoning in controlled environments [17, 32, 70], we adopt the CLEVR universe [32] in ACRE's design and add a Bicket machine to signal its state of activation, intentionally simplifying visual information processing and emphasizing causal reasoning. Following attempts made in abstract spatial-temporal reasoning benchmarks [31, 55, 72], we provide the visual reasoning system with sets of panel images as context and use image-based queries to ease language understanding, echoing the setup and the learning theories in developmental literature [19, 20, 21, 22, 23]. + +Specifically, each problem in ACRE consists of 10 panels: 6 for context and 4 for query. The 6 context panels are divided into two sets, the first of which serves as an introduction to the Bicket mechanism that some objects activate the machine, and others do not. This simpler set of panels resembles the introductory trials administered to children in human experiments [22, 61]. Instead of bringing in the concept of Bicket1, in queries, we only ask a visual reasoning system to predict the state of the Bicket machine given the objects in the queries. Half of the queries concern the inde + +pendent scenarios, wherein a single object is presented, and the system is challenged to reason about whether this object is one of the causes that could activate the Bicket machine. The remaining half of the queries are for interventional scenarios, wherein we intervene in an existing context panel and ask what the state of the Bicket machine would be under the intervention. Each query is independent such that statistical bias [22, 61] and potential cheating for abstract reasoning [31, 72] are minimized. In summary, ACRE includes 30,000 abstract causal reasoning problems, supports all 4 types of reasoning queries (direct, indirect, screening-off, and backward-blocking), and is fully annotated with object attributes, bounding boxes, and masks. We further design two Out-Of-Distribution (O.O.D.) generalization splits in ACRE to evaluate models' generalizability. + +In experiments, we use the ACRE dataset to analyze current visual reasoning systems' ability in causal induction. Despite remarkable results in other visual reasoning tasks, we notice that pure neural networks [8, 28, 55, 68, 77] favor a covariation-based reasoning strategy and thus can only achieve performance marginally above the chance level. As the first attempt in the exploration to empower visual reasoning systems for causal induction, we resort to neurosymbolic models [26, 39, 43, 50, 51, 70, 71, 74, 76] that combine neural visual processing [27] and symbolic causal reasoning [18, 49, 53, 62, 78, 79], which turn out to struggle in backward-blocking cases in abstract causal reasoning. + +To sum up, this paper makes three primary contributions: + +- We propose the Abstract Causal REaasoning (ACRE) dataset to probe current visual reasoning systems' capacity in causal induction. The dataset is inspired by the Blicket experiments and contains 30,000 problems. ACRE covers all 4 types of causal reasoning queries (direct, indirect, screening-off, and backward-blocking) with additional O.O.D. generalization splits. +- We benchmark and analyze state-of-the-art visual reasoning models in ACRE. Experimental results show that neural models tend to capture statistical correlations in observation but fail to induce the underlying causal relationships demonstrated in the trials. +- We propose neuro-symbolic combinations that improve on pure neural networks. However, our analysis shows that even with the inductive bias in causality, they still fail to distinguish a true cause from superficial covariation in backward-blocking cases. Taken together, these deficiencies call for future research in models with a more comprehensive capability of causal induction. + +# 2. Related Work + +Abstract Visual Reasoning To date, the computer vision and AI community's efforts in abstract visual reasoning primarily focus on the specific task of Raven's Progressive Matrices (RPM) [5, 52], commonly known as Intelligence + +![](images/409ea6bdd7217490ba1875ad8e6c5a0b7e3011d910c1c772917bb4146a49437f.jpg) +ContextTrials + +![](images/5621f90790b7eba53f3f2a7fce27f17b8a5aac7608347f710e840fa99d373b36.jpg) +Independent Queries: + +![](images/5ef53e4301498624b58deb672ffaee1bb6d59fec6cec05d75e12cd2a66aced29.jpg) + +![](images/3f4b5917d4d5334f1686a24a2f5aa738e9648d38c8d5771cd069fced440fb2f4.jpg) +Interventional Queries on the Fourth Trial: + +![](images/470c093eef310e19162c42cb9a13d8188230c43892ffd7f38d0ea2aa2089f0ce.jpg) + +![](images/3cd021febecb4e5b5bec4d4164a8782b41cbe4ba726ee047c412c623eb96e065.jpg) + +![](images/8ad592203dc17b7dee5e923a5946e49b50f21bc5620984796167b5547977c939.jpg) +What would be the machine's state given the object? +Figure 2. A sample problem in ACRE. Of the 6 context trials, we devote the first set of 3 panels for an introduction to the Bicket machinery and allow more complex configurations in the second set of panels. Queries are either on independent objects or interventional combinations for an existing trial. In this example, the first query tests causal reasoning from direct evidence, as the gray cube is independently tested and always associated with an activated machine. The second query requires comparing the fourth and fifth trial to realize that the Bicket machine is activated by the cube, not the cylinder, based on indirect evidence. As such, we infer that the red and green cylinders in the sixth trial may not activate the machine because the purple cube can already do so; despite their association with an activated machine only, their Bicketness is backward-blocked in the interventional trial. The cyan cube is screened-off by the gray cube's Bicketness from probabilistically activating the machine. Of note, the screening-off and the backward-blocking case cannot be solved by covariation. + +![](images/098d53c7aabf0d566e86fef42f0c6b5bdc6b074e349acbcefc5e1beb99a8ad60.jpg) + +![](images/6539a3460001dfc81ad9f97a443532f367f5be3f5b2f2121f840d25d71fa1c6c.jpg) +What would be the machine's state given the intervention? + +![](images/11eb570fff684b7a19ecb5fa8d28eb76a7ae439d16f03043d64a6e386647bb55.jpg) + +Quotient (IQ) tests, that studies how visual reasoning systems can induce the hidden spatial-temporal transformation from limited context and apply it to derive a missing panel. Santoro et al. [55] extended the relational module [56] to take panel-based representation and introduced the Wild Relational Network (WReN). Zhang et al. [72] proposed to incorporate structural annotations in a neural modular manner. Methods considering contrast at data-level [29] or module-level [73] were later shown to improve performance significantly. Zheng et al. [77] formulated the problem as teacher-student learning, Wang et al. [68] used a multiplex graph model to capture the hidden relations, and Spratley et al. [63] revisited ResNet models combined with unsupervised learning. More recently, Zhang et al. [74] disentangled perception and reasoning from a monolithic model, wherein the visual perception frontend predicts objects' attributes, later aggregated by a scene inference engine to produce a probabilistic scene representation, and the symbolic logical reasoning backend abduces the hidden rules. + +The proposed ACRE dataset complements the spectrum of abstract visual reasoning tasks by challenging visual reasoning systems with causal induction from a limited number of trials and adding missing dimensions of causal understanding into the prior spatial-temporal task set. + +Causal Reasoning Equipping visual reasoning systems with causal reasoning capability has been an emerging topic in computer vision research [12, 41, 46]. Recent causal reasoning datasets [1, 70] established video + +based benchmarks² for either trajectory prediction in counterfactual scenarios or visual question answering with explanatory, predictive, and counterfactual questions. Nevertheless, causal induction in prior computer vision research relies heavily on covariation. For instance, psychological research [2, 3, 15, 16, 34] points out that the key to solving these two problems is intuitive physics, with covariation-based causal reasoning in associating collision with object dynamics. Moreover, Edmonds et al. [9, 10, 11] further demonstrate that covariation would result in catastrophic failures when the visual features are similar but the underlying causal mechanisms dramatically differ. These results necessitate causal induction beyond covariation: Asymmetries in learning under various causal structures [65] refute parsimonious associative learning [59]. + +With a particular emphasis on causal induction beyond the simple causal reasoning strategy of covariation [36], we design ACRE with diversified causal queries, requiring a visual reasoning system to induce the hidden causal mechanism from only limited observation. From a cognitive standpoint, it is argued that Bayesian networks [48, 49] and the theory-theory [11, 19, 20, 23, 25, 60] play vital roles in abstract causal reasoning. However, how young toddlers induce accurate Bayesian representation and form a correct theory during such a short exposure remains unclear [14]. + +![](images/d29e2fb29bf0156ed063a99dab58da19d50256fd73495079302d6e854cd31702.jpg) +(a) +Figure 3. Distributions of (a) labels and (b) query types in ACRE. + +![](images/7ef23db3aa848d0bf8beb2b706acc9f5550e372469d6a1c6bcd8ceb52aab6ded.jpg) +(b) + +# 3. Building ACRE + +The ACRE dataset is designed to be light in visual recognition and heavy in causal induction. Specifically, we ground every panel in a fully-controlled synthetic environment by adopting the CLEVR universe [32] where all objects, including the Bicket machine, are placed on a tabletop with three-point lighting. All potential Bicket objects are of the same size and come with 3 possible shapes (cube, sphere, or cylinder), 2 possible materials (metal or rubber), and 8 possible colors (gray, red, blue, green, brown, cyan, purple, or yellow). For the context panels, we set all objects on a pink Bicket machine at the center of the scene and signal its state of activation by lighting it up. For the query panels, we directly put all objects on the tabletop. In both cases, objects are randomly distributed across the scenes. To avoid confusion during reference, every object is uniquely identifiable by its shape, material, and color. Other than the constraints, every object's attributes are randomly sampled from the aforementioned space. Collectively, every ACRE problem contains 5 to 8 unique objects. We keep other scene configurations the same as the original setup in CLEVR [32] and generate images by Blender [6]. Every image is also fully-annotated with object attributes, bounding boxes, and masks; see Fig. 2 for a sample problem in ACRE and refer to the supplementary for more examples. + +ACRE Context Every ACRE problem contains 10 panels, of which 6 serve as context panels. Following the original design [22, 61], we further divide the 6 panels into 2 sets and use the first simpler set as the familiarization set. Specifically, for the first set of 3 panels, we randomly sample 2 objects and assign one to be a Bicket and another to be a non-Bicket. Both objects are independently tested on the Bicket machine and then placed together on it. These 3 simple trials reveal the nature of a Bicket detector: The machine will be activated when a Bicket is placed on it. For the second set of panels, we allow more random sampling; in particular, we sample another group of objects that is disjoint with the first one and partition it into 3 potentially overlapping subgroups, corresponding to the configurations for each of the rest panels. Either one or two of them are associated with an activated Bicket machine. + +ACRE Query The Bicket machine's activation pattern in context panels supports all 4 types of queries (direct, indirect, screening-off, and backward-blocking) and provide sufficient clues for determining Bicketness for each object; see illustrations in Figs. 1 and 2. Based on explanations of the Bicket mechanism [20, 22, 23, 61], we detail query categorization in the following. Intuitively, an object is a Bicket if it is independently and always associated with an activated machine, which can be determined based on direct evidence; the same reasoning strategy is applicable to resolve non-Bickets. An object is also considered a Bicket if the machine activates when we place it together with other objects but not alone, and the other objects fail to activate the machine. In these cases, the Bicketness is resolved by indirect evidence; no direct observation is available. An object is considered a non-Bicket when putting it with other potential Bickets together will activate the machine, but it fails to do so by itself; this derivation is referred to as screening-off reasoning. In addition to being a Bicket or non-Bicket, an object's Bicketness could also be undetermined, which occurs when the object is not directly tested, but can activate the machine together with other potential Bickets; this is referred to as backward-blocking reasoning. Note that the Bicketness of an individual object may be undetermined, but together with other undetermined ones, they can form a set that activates the machine; as such queries happen in the indirect setting, we also refer to them as indirect reasoning. + +The rich causal relations embedded in the context panels afford us to probe a reasoning system's causal induction capability. In particular, we design 4 queries in each ACRE problem, 2 for independent scenarios and another 2 for interventional scenarios, similar to the questions administered in human experiments [22, 61]. In the independent scenario, we randomly sample one object from those tested in the trials. In the interventional scenario, we pick a trial with an inactivated machine and add a set of objects randomly picked from those in the context panels. The reasoning system is then asked to tell the status of the Bicket machine after placing the objects on it, either inactivated, undetermined, or activated. To avoid statistical bias [22, 61] or potential cheating [31, 72], all queries in a problem are independent. + +Generalization Splits ACRE comes with additional O.O.D. splits to measure model generalization in causal induction; we focus on compositionality and systematicity in systematic generalization [13, 24, 38, 69]. In the compositionality split, we assign different shape-material-color combinations to the training and test set and ensure the training set contains every shape, material, and color, similar to the Compositional Generalization Test (CoGenT) in CLEVR [32]. In the systematicity split, we vary the distribution of an activated Bicket detector in the context panels, with the machine lighting up 3 times in the training set and 4 + +times during testing. Note the strategy for causal induction remains the same irrespective of the distribution change. + +In total, ACRE contains 30,000 problems, evenly partitioned into an Independent and Identically Distributed (I.I.D.) split, a compositionality split, and a systematicity split. The dataset covers all 4 types of queries, and the label distribution is adjusted to be roughly uniform; see Fig. 3 for the label distribution and query type distribution in the dataset. Please refer to the supplementary for detailed distributions of labels and query types for each split. + +# 4. Reasoning Systems on ACRF + +This section details the deep neural models adopted to benchmark the proposed ACRE dataset and the neurosymbolic combinations explicitly designed to incorporate inductive bias for causal induction. + +# 4.1. Deep Neural Models + +As ACRE shares the inductive nature with RPM, we test several established models designed for it [55, 68, 77]. We also test methods commonly used for linguistic or visual modeling [8, 28]. Each context-query pair is independently fed into the network and treated as a classification problem. + +CNN-MLP We concatenate context panels with the query panel in the channel dimension and use a 4-layer standard CNN architecture to extract features. The CNN architecture interleaves batch normalization and ReLU activation between convolution layers. The final convolved features are passed to a 2-layer Multilayer Perceptron (MLP) with a dropout layer with a rate of 0.5 in between the two layers. + +ResNet-MLP In this model, we replace the CNN backbone in CNN-MLP with ResNet-18 [28]. + +CNN-LSTM We use a standard LSTM model [30] to further process visual features. Specifically, we independently extract image features of each panel using a CNN, append a one-hot position tag to each feature map, and pass them sequentially into the LSTM module. The final hidden state is further processed by a linear layer to produce logits. + +CNN-BERT A visual BERT [8] model is also tested. We compute image features using a CNN and follow practices in BERT: For the sequence of image features, we preprocess $\langle \mathrm{CLS}\rangle$ , separate the context panels and the query panel with $\langle \mathrm{SEP}\rangle$ , and add position and segment embeddings. Output from $\langle \mathrm{CLS}\rangle$ is then used for classification. + +WReN We adopt the WReN model proposed by Santoro et al. [55], which applies the relational module [56] on panel-based image representations. + +LEN LEN [77] stems from WReN but takes into account the row-wise and column-wise compositions in RPM, deeper features, and the multi-choice setting. We adapt the original LEN design to the proposed ACRE by removing branches for the column-wise composition and making the prediction on each query independent. + +MXGNet A similar strategy in LEN is used to make MXGNet [68] compatible with ACRE. The two sets of context trials are treated as rows in the model. + +# 4.2. Neuro-Symbolic Models + +In preliminary experiments, we notice that pure neural models tend to capture statistical correlation rather than modeling the hidden causal relations out of the context trials. To overcome this issue, we propose neuro-symbolic combinations and explicitly incorporate various forms of causal inductive bias for the abstract causal reasoning task. + +Specifically, we draw inspirations from recent advances in neuro-symbolic literature [26, 39, 43, 50, 51, 70, 71, 74, 76] and decompose our model into a neural perception frontend and a causal reasoning backend. By design, the frontend is responsible for parsing each context trial to form an object-based representation, whereas the backend takes the symbolic output from the frontend and performs causal induction; see an overview of the method in Fig. 4. + +Neural Perception Frontend As the first attempt to solve ACRE problems, we disentangle our neural perception frontend and independently pretrain the model to parse each scene. Specifically, we use Mask-RCNN [27] with ResNet-50 FPN [28, 40] backbone. The perception model is tasked with predicting the Blicket machine's state, object masks, and object attributes (shape, material, and color) for each object in the scene. Both context and query panels in the training set of each split are used to train the frontend. + +Causal Reasoning Backend Due to its efficiency and accuracy, we use a score-based continuous optimization method, denoted as NS-Opt, to simultaneously learn a generalized Structural Equation Model (SEM) and derive the hidden causal relations [78, 79]. In particular, denoting the existence of object $j$ in panel $i$ as $X_{i,j} \in \{0,1\}$ , we can arrange the symbolic parsing results from the neural perception frontend into a data matrix $X \in \{0,1\}^{6 \times n}$ , where $n$ equals the number of unique objects in all context panels plus the Bicket machine. A generalized SEM assumes that the state of object $j$ is related to states of its parents via a function and can be represented as + +$$ +X _ {j} = f _ {j} \left(X _ {\mathrm {p a} (j)}\right) = g _ {j} (X), \tag {1} +$$ + +where $X = [X_{1}|X_{2}|\ldots |X_{j}|\ldots]$ , and $\operatorname{pa}(j)$ denotes the parents of object $j$ . The parent finding process is further generalized in $g_{j}(\cdot)$ and put into optimization constraints. + +Following [79], we formulate causal discovery as an optimization problem + +$$ +\begin{array}{l} \underset {g: g _ {j}, \forall j \in [ n ]} {\text {m i n i m i z e}} \quad \frac {1}{n} \sum_ {j} \ell \left(X _ {j}, g _ {j} (X)\right) \tag {2} \\ \text {s u b j e c t} \quad h (W (g)) = 0, \\ \end{array} +$$ + +where $W(g)_{k,j} = \|\partial_k g_j\| \forall k, j \in [n]$ , and $h(W) = \operatorname{Tr}(e^{W \circ W} - I)$ . We use $[n]$ to denote an integer set from + +![](images/e61bb317e4351e078e97a535d94e2e49178aff8ebe040b61398f31126c38ae4d.jpg) +Figure 4. An illustration of the proposed neuro-symbolic combination (NS-Opt) for ACRE. The neural frontend is responsible for scene parsing. In particular, we use a Mask RCNN to detect objects and classify their attributes as well as the Bicket machine's state. The parsed results are arranged into data matrices and sent into the causal reasoning backend for optimization. A generalized SEM is learned from context trials during reasoning, which is further used to infer the state of the Bicket machine for each query. + +1 to $n$ , $\| \cdot \|$ the $L^2$ function norm, and $\circ$ the Hadamart product. Using the binary cross entropy loss as $\ell(\cdot, \cdot)$ for each object $j$ , the optimization problem regularizes the generalized SEM to reconstruct the observation, while constraining the relations among the variables to be a causal Directed Acyclic Graph (DAG): $W(g)$ can be regarded as the adjacency matrix among variables, and $h(\cdot)$ a metric for acyclicity. We use an MLP for each $g_j(\cdot)$ and optimize the problem by Augmented Lagrangian; see [78, 79] for details. + +With a learned generalized SEM representing the hidden causal relations in the context trials, we treat each query as another optimization problem. Specifically, we construct a partial data vector for each panel from the symbolic representation parsed by the neural perception frontend. Denoting the Bicket machine as object $n$ , the query vector can be represented as $X_{1:n-1}$ . Treating $X_{n}$ as the probability of the Bicket machine being activated, the query optimization is formulated as + +$$ +\underset {X _ {n}} {\text {m i n i m i z e}} \quad \frac {1}{n} \sum_ {j} \ell \left(X _ {j}, g _ {j} \left([ X _ {1: n - 1} \mid X _ {n} ]\right)\right) \tag {3} +$$ + +$$ +\text {s u b j e c t} \quad \mathbf {0} \preceq X _ {n} \preceq \mathbf {1}. +$$ + +We solve it using L-BFGS-B [4] and set thresholds on $X_{n}$ to predict the final state of the Bicket machine. + +We also test a constraint-based method [18, 62] and the well-known Rescorla-Wagner (RW) model [53] for the causal reasoning backend. The constraint-based method (denoted as NS-PC) first uses the state-of-the-art PC algorithm [62] to test conditional independence and search for an underlying causal DAG among objects and the Bicket machine. It then finds the parent nodes for the Bicket machine and estimates its conditional probability table, which can be directly read out for each query configuration. For the RW model (denoted as NS-RW), we simply treat co-occurrence of an object with an activated Bicket machine as its Bicketness. A query configuration's state is predicted based on the maximum Bicketness of all objects in it. + +# 5. Experiments + +# 5.1. Experimental Setup + +ACRE is equally partitioned into 3 splits, i.e., the I.I.D. split, the compositionality (comp) split, and the systematicity (sys) split. Each of the splits contains 10,000 problems. We further divide each split into 10 folds, with 6 folds for training, 2 folds for validation, and 2 folds for testing. All models are trained on the training sets, with hyperparameters tuned on the validation sets. Results are reported for the best models on the test sets. In particular, we report two metrics: query accuracy and problem accuracy. The former measures how a model performs on each query, and the later whether a model correctly answers all 4 queries in a problem instance. Note that based on the label distribution shown in Fig. 3, a simple strategy of always predicting activation will yield around $37.3\%$ query accuracy and $1.87\%$ problem accuracy, and a completely random guess would yield $33.3\%$ query accuracy and $1.19\%$ problem accuracy. All neural models, including the neural perception frontend in the neuro-symbolic models, are implemented in PyTorch [47] and optimized using Adam [33]. All experiments were run on an Nvidia Titan XP GPU. + +# 5.2. Performance on the I.I.D. Setting + +The first portion of Table 1 reports how various models perform under the I.I.D. setting of ACRE. Surprisingly, existing state-of-the-art methods for the abstract spatial-temporal reasoning task [68, 77] do not fare much better (even worse in certain cases) than a simple CNN-MLP model. In particular, MXGNet performs slightly worse than a random guess, only correctly answering $1\%$ of problems. With a relational module, WReN is on par with the CNN-MLP model. CNN-LSTM and ResNet-MLP achieve similar performance, with the LSTM-based reasoning model performing better in problem accuracy. Of all pure neural mod + +
MethodMXGNetLENCNN-MLPWReNCNN-LSTMResNet-MLPCNN-BERTNS-RWNS-PCNS-Opt
I.I.D.Qry.33.01%38.08%40.86%40.39%41.91%42.00%43.56%46.61%59.26%66.29%
Pro.1.00%2.05%3.25%2.30%3.60%3.35%3.50%6.45%21.15%27.00%
Comp.Qry.35.56%38.45%41.97%41.90%42.80%42.80%43.79%50.69%61.83%69.04%
Pro.1.55%2.10%2.90%2.65%2.80%2.60%2.40%8.10%22.00%31.20%
Sys.Qry.33.43%36.11%37.45%39.60%37.19%37.71%39.93%42.18%62.63%67.44%
Pro.0.60%1.90%2.55%1.90%1.85%1.75%1.90%4.00%29.20%29.55%
+ +Table 1. Performances of models on the I.I.D. split, the compositionality split (Comp.), and the systematicity split (Sys.) in ACRE. We report 2 evaluation metrics: query accuracy (Qry.) and problem accuracy (Pro.). Please refer to the experimental setup for details. + +els, the BERT model achieves the best in query accuracy, slightly overtaken by CNN-LSTM in problem accuracy. + +Among the 3 neuro-symbolic models tested, NS-RW strictly follows the covariation strategy in solving the causal discovery problems. We notice that such a simple causal reasoning method can only handle less than half of ACRE queries and less than $10\%$ of ACRE problems, verifying and necessitating our efforts to create a benchmark for causal induction beyond covariation. NS-PC serves as an oracle model for causal discovery as it adopts independence tests and search methods. However, our experiments show that NS-PC is inferior to the optimization-based NS-Opt method. We believe such a result is due to the sparse and limited observation in ACRE problems, making it difficult to perform reliable independence tests. This challenge further perplexes the underlying mechanisms on how humans, even toddlers, derive the hidden relations so quickly and accurately from scarce observation. The proposed NS-Opt method successfully handles two-thirds of the queries but still has much room to improve on problem accuracy. + +# 5.3. Performance on the O.O.D. Settings + +The second and third portions of Table 1 depict the models' performance on the O.O.D. settings, i.e., compositionality and systematicity. Comparing both query accuracy and problem accuracy in the compositionality split with those in the I.I.D. setting, we notice that models' performances have no significant changes. Considering the fact that the training set and the test set in the compositionality split contain completely different object attribute combinations, it is likely that neural models indeed have emerged a certain level of causal reasoning, though not perfect, to solve the problems, rather than entirely relying on statistical visual features from the training set. However, their underlying representation of causal knowledge is still elusive; future work is in need to discover their precise mechanisms. + +Even if neural models emerged a causal reasoning strategy, such a strategy is not systematic, as demonstrated in the comparison between the systematicity split and the I.I.D. split. Note that only the distributions of an activated machine are different in the training set and the test set of the systematicity split, while the solutions can be derived in the same way. We note that except for the NS-PC model and the NS-Opt model, all other models experience per + +formance drop; some of them are even worse than always predicting "activated". This observation echoes the recent empirical results that pure neural models still struggle to systematically generalize [13, 37, 54]. + +Across the 3 splits, we also notice the conspicuously large gap between the query accuracy and problem accuracy. We hypothesize that the result indicates the existence of the bucket effect, which we verify in the next section. + +# 5.4. A Closer Look at Queries + +The drastic difference between query accuracy and problem accuracy motivates us to perform a closer inspection on how models perform on each type of queries; see Table 2 for a summary of our experimental results. + +In general, we notice that neural models tend to capture causal relations by covariation. Most of them excel in query types directly solvable by this strategy, achieving the best performance in direct queries or indirect queries or both across the different splits. This effect is particularly significant in CNN-based reasoning models (CNN-MLP and ResNet-MLP) that even reach $87\%$ accuracy for indirect queries by learning from only target labels. However, in contrast to the satisfactory performance on covariation-based reasoning, they are unable to handle the screening-off queries and the backward-blocking queries, which go beyond co-occurrence. Specifically, the best-performing neural model (CNN-BERT) embarrassingly fails on screening-off queries in the systematicity split, while CNN-based reasoning models also struggle in these settings. Among the relation-module-based models (MXGNet, LEN, and WReN), LEN and WReN are relatively stable across the different types of queries. However, with a multiplex graph, MXGNet shows different dynamics, learning best in the backward-blocking queries but counter-intuitively underperforming in the direct and indirect queries. It is also worth noting that causal reasoning that supports backward-blocking for MXGNet does not consistently enable screening-off reasoning. A converse observation is found in CNN-LSTM: The model shines in screening-off reasoning but fades in backward-blocking in 2 of the splits. Taking these results together, we hypothesize that pure neural visual reasoning systems have not yet mastered causal induction to a comparable level humans displayed in the developmental studies [22, 61]. + +Performance differences in queries among the neuro + +
MethodMXGNetLENCNN-MLPWReNCNN-LSTMResNet-MLPCNN-BERTNS-RWNS-PCNS-Opt
I.I.D.D.R.27.73%49.07%55.56%51.04%48.20%54.87%52.24%88.88%84.46%91.64%
I.D.29.63%45.11%56.31%41.04%36.76%48.37%44.50%99.29%29.33%69.25%
S.O.14.88%33.68%44.88%29.75%53.23%42.29%42.59%7.21%78.31%85.37%
B.B.59.09%23.91%9.71%35.61%24.91%21.12%32.15%1.66%20.50%11.98%
Comp.D.R.36.93%47.58%57.59%55.29%56.58%62.79%54.07%91.74%89.50%92.50%
I.D.55.99%52.51%64.38%66.94%65.10%70.01%46.88%99.80%28.66%76.05%
S.O.0.00%18.01%31.66%8.44%19.69%30.52%40.57%4.07%85.28%88.33%
B.B.52.35%33.63%15.26%35.99%29.27%8.54%28.79%0.67%15.21%13.48%
Sys.D.R.15.24%46.22%70.79%53.56%42.57%65.19%55.97%92.44%89.76%94.73%
I.D.5.42%47.90%87.61%71.35%37.61%85.07%68.25%99.89%57.08%88.38%
S.O.42.58%30.91%11.57%16.80%63.28%9.57%0.00%0.20%73.93%82.76%
B.B.56.38%24.89%3.60%31.62%8.70%13.38%45.59%0.46%24.88%16.06%
+ +Table 2. A closer look at how models perform on each type of queries on different splits of ACRE: direct (D.R.), indirect (I.D.), screening-off (S.O.), and backward-blocking (B.B.). + +symbolic models potentially point out an Achilles' heel for solving abstract causal reasoning problems. NS-RW's inferior performance is expected as the model only considers covariation and will surely fail the screening-off and backward-blocking queries, despite its success in direct and indirect queries. NS-RW's results also serve as a sanity check for queries in ACRE that nearly all of the direct and indirect queries can be solved by covariation (except for a minimum number of interventional cases) and nearly none of the screening-off and backward-blocking queries can (except for a minimum number of coincidences). Comparing NS-PC and NS-Opt, we notice that both models achieve fair performance on direct queries and the screening-off queries. However, the latter fares significantly better in indirect queries. We argue that the strict independence tests and search methods used in PC make the model less robust against noise, especially under the sparse-and-limited-data scenario. What is evident in both models, and more significant in NS-Opt, is their inability in differentiating the superficial correlation with an activated machine and the undetermined Bicketness within. This close inspection also indicates that adequately addressing the issue can further improve the general causal reasoning performance. By comparing the low accuracy of NS-Opt and pure neural networks in backward-blocking, we hypothesize that a potential solution to causal reasoning would be to combine the best of both worlds in learning and symbolic reasoning, keeping both the learnability of neural methods and the interpretability of symbolic methods. + +# 6. Conclusion + +In this work, we present a new dataset for Abstract Causal REasoning (ACRE), aiming to measure and improve causal induction in visual reasoning systems. Apart from the inductive reasoning nature, the defining feature of the ACRE dataset is the requirement to perform causal reasoning beyond covariation. Inspired by the established stream of research on Bicket experiments, the ACRE dataset is grounded on a similar setting using the synthetic CLEVR universe [32]. To measure causal induction beyond covari- + +ation, we challenge a visual reasoning system with 4 types of queries in either independent scenarios or interventional scenarios: direct, indirect, screening-off, and backward-blocking. The first 2 types of queries can be answered by counting co-occurrence, while the last 2 types require in-depth causal representation. To better measure generalization in causal discovery, we further propose the compositionality and the systematicity O.O.D. split. + +We devise an optimization-based neuro-symbolic method to equip a visual reasoning system with the causal discovery ability. In particular, we decompose the model into a neural perception frontend and a causal reasoning backend. The neural perception frontend parses a given trial using a Mask RCNN [27], whereas the causal reasoning backend performs continuous optimization for causal discovery [78, 79]. The context trials are leveraged to learn a generalized SEM, and the answer to a query trial is solved by finding the best value to fit the SEM. As the first attempt, we separately train the two components, leaving the problem of closing the loop between visual perception and causal discovery for future work [39, 74, 75]. + +Existing visual reasoning systems' causal induction capability has been benchmarked on ACRE. Specifically, we notice that pure neural models tend to perform causal reasoning by capturing the statistical correlation, achieving satisfactory results on direct and indirect queries but failing on screening-off and backward-blocking ones. For neurosymbolic models, we notice that all of them struggle on backward-blocking and that the sparse and limited observation further adds to the complexity of the problem. Comparing performances of these 2 types of models on various queries, we hypothesize that further combining learning and symbolic reasoning would be a promising direction for causal induction and broader causal reasoning problems. + +At length, we hope challenges in this causal reasoning task would call for attention into visual systems with human-level spatial, temporal, and causal reasoning ability. + +Acknowledgement: The work reported herein was supported by ONR MURI N00014-16-1-2007, DARPA XAI N66001-17-2-4029, and ONR N00014-19-1-2153. + +# References + +[1] Fabien Baradel, Natalia Neverova, Julien Mille, Greg Mori, and Christian Wolf. Cophy: Counterfactual learning of physical dynamics. In International Conference on Learning Representations (ICLR), 2020. 3 +[2] Peter W Battaglia, Jessica B Hamrick, and Joshua B Tenenbaum. Simulation as an engine of physical scene understanding. Proceedings of the National Academy of Sciences (PNAS), 110(45):18327-18332, 2013. 3 +[3] Neil R Bramley, Tobias Gerstenberg, Joshua B Tenenbaum, and Todd M Gureckis. Intuitive experimentation in the physical world. Cognitive Psychology, 105:9-38, 2018. 3 +[4] Richard H Byrd, Peihuang Lu, Jorge Nocedal, and Ciyou Zhu. A limited memory algorithm for bound constrained optimization. SIAM Journal on scientific computing, 16(5):1190-1208, 1995. 6 +[5] Patricia A Carpenter, Marcel A Just, and Peter Shell. What one intelligence test measures: a theoretical account of the processing in the raven progressive matrices test. Psychological review, 97(3):404, 1990. 2 +[6] Blender Online Community. Blender-a 3d modelling and rendering package, 2016. 4 +[7] Claire Cook, Noah D Goodman, and Laura E Schulz. Where science starts: Spontaneous experiments in preschoolers' exploratory play. Cognition, 120(3):341-349, 2011. 1 +[8] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the Conference of the North American Chapter of the Association for Computational Linguistics (NAACL), 2019. 2, 5 +[9] Mark Edmonds. Decomposing human causal leaning: bottom-up associative learning and top-down schema reasoning. In Proceedings of the Annual Meeting of the Cognitive Science Society (CogSci), 2019. 3 +[10] Mark Edmonds, James Kubricht, Colin Summers, Yixin Zhu, Brandon Rothrock, Song-Chun Zhu, and Hongjing Lu. Human causal transfer: Challenges for deep reinforcement learning. In Proceedings of the Annual Meeting of the Cognitive Science Society (CogSci), 2018. 3 +[11] Mark Edmonds, Xiaojian Ma, Siyuan Qi, Yixin Zhu, Hongjing Lu, and Song-Chun Zhu. Theory-based causal transfer: Integrating instance-level induction and abstract-level structure learning. In Proceedings of AAAI Conference on Artificial Intelligence (AAAI), 2020. 3 +[12] Amy Fire and Song-Chun Zhu. Learning perceptual causality from video. ACM Transactions on Intelligent Systems and Technology (TIST), 7(2):1-22, 2015. 3 +[13] Jerry A Fodor, Zenon W Pylyshyn, et al. Connectionism and cognitive architecture: A critical analysis. Cognition, 28(1-2):3-71, 1988. 4, 7 +[14] Caren A Frosch, Teresa McCormack, David A Lagnado, and Patrick Burns. Are causal structure and intervention judgments inextricably linked? a developmental study. Cognitive Science, 36(2):261-285, 2012. 3 +[15] Tobias Gerstenberg, Matthew F Peterson, Noah D Goodman, David A Lagnado, and Joshua B Tenenbaum. Eye-tracking causality. Psychological science, 28(12):1731-1744, 2017. 3 + +[16] Tobias Gerstenberg and Joshua B Tenenbaum. Intuitive theories. In Oxford handbook of causal reasoning, pages 515-548. Oxford University Press New York, NY, 2017. 3 +[17] Rohit Girdhar and Deva Ramanan. Cater: A diagnostic dataset for compositional actions & temporal reasoning. In International Conference on Learning Representations (ICLR), 2020. 2 +[18] Clark Glymour, Kun Zhang, and Peter Spirtes. Review of causal discovery methods based on graphical models. Frontiers in genetics, 10:524, 2019. 2, 6 +[19] Alison Gopnik. Scientific thinking in young children: Theoretical advances, empirical research, and policy implications. Science, 337(6102):1623-1627, 2012. 1, 2, 3 +[20] Alison Gopnik, Clark Glymour, David M Sobel, Laura E Schulz, Tamar Kushnir, and David Danks. A theory of causal learning in children: causal maps and bayes nets. Psychological review, 111(1):3, 2004. 1, 2, 3, 4 +[21] Alison Gopnik and David M Sobel. Detecting blickets: How young children use information about novel causal powers in categorization and induction. Child development, 71(5):1205-1222, 2000. 1, 2 +[22] Alison Gopnik, David M Sobel, Laura E Schulz, and Clark Glymour. Causal learning mechanisms in very young children: Two-, three-, and four-year-olds infer causal relations from patterns of variation and covariation. Developmental psychology, 37(5):620, 2001. 1, 2, 4, 7 +[23] Alison Gopnik and Henry M Wellman. Reconstructing constructivism: Causal models, bayesian learning mechanisms, and the theory theory. Psychological bulletin, 138(6):1085, 2012. 1, 2, 3, 4 +[24] Jonathan Gordon, David Lopez-Paz, Marco Baroni, and Diane Bouchacourt. Permutation equivariant models for compositional generalization in language. In International Conference on Learning Representations (ICLR), 2019. 4 +[25] Thomas L Griffiths and Joshua B Tenenbaum. Theory-based causal induction. Psychological Review, 116(4):661, 2009. 3 +[26] Chi Han, Jiayuan Mao, Chuang Gan, Josh Tenenbaum, and Jiajun Wu. Visual concept-metaconcept learning. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2019. 2, 5 +[27] Kaiming He, Georgia Gkioxari, Piotr Dólar, and Ross Girshick. Mask r-cnn. In Proceedings of International Conference on Computer Vision (ICCV), 2017. 2, 5, 8 +[28] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016. 2, 5 +[29] Felix Hill, Adam Santoro, David Barrett, Ari Morcos, and Timothy Lillicrap. Learning to make analogies by contrasting abstract relational structure. In International Conference on Learning Representations (ICLR), 2019. 3 +[30] Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory. Neural computation, 9(8):1735-1780, 1997. 5 +[31] Sheng Hu, Yuqing Ma, Xianglong Liu, Yanlu Wei, and Shihao Bai. Hierarchical rule induction network for abstract visual reasoning. arXiv preprint arXiv:2002.06838, 2020. 2, 4 + +[32] Justin Johnson, Bharath Hariharan, Laurens van der Maaten, Li Fei-Fei, C Lawrence Zitnick, and Ross Girshick. Clevr: A diagnostic dataset for compositional language and elementary visual reasoning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. 2, 4, 8 +[33] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. 6 +[34] James R Kubricht, Keith J Holyoak, and Hongjing Lu. Intuitive physics: Current research and controversies. Trends in Cognitive Sciences, 21(10):749-759, 2017. 3 +[35] Tamar Kuhnir and Alison Gopnik. Conditional probability versus spatial contiguity in causal learning: Preschoolers use new contingency evidence to overcome prior spatial assumptions. Developmental psychology, 43(1):186, 2007. 1 +[36] David A Lagnado, Michael R Waldmann, York Hagemayer, and Steven A Sloman. Beyond covariation. In Causal learning: Psychology, philosophy, and computation, pages 154-172. Oxford University Press, 2007. 3 +[37] Brenden Lake and Marco Baroni. Generalization without systematicity: On the compositional skills of sequence-to-sequence recurrent networks. In Proceedings of International Conference on Machine Learning (ICML), 2018. 7 +[38] Brenden M Lake, Tomer D Ullman, Joshua B Tenenbaum, and Samuel J Gershman. Building machines that learn and think like people. Behavioral and Brain Sciences, 40, 2017. 4 +[39] Qing Li, Siyuan Huang, Yining Hong, Yixin Chen, Ying Nian Wu, and Song-Chun Zhu. Closed loop neural-symbolic learning via integrating neural perception, grammar parsing, and symbolic reasoning. arXiv preprint arXiv:2006.06649, 2020. 2, 5, 8 +[40] Tsung-Yi Lin, Piotr Dollar, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie. Feature pyramid networks for object detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. 5 +[41] David Lopez-Paz, Robert Nishihara, Soumith Chintala, Bernhard Scholkopf, and Léon Bottou. Discovering causal signals in images. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. 3 +[42] Christopher G Lucas, Sophie Bridgers, Thomas L Griffiths, and Alison Gopnik. When children are better (or at least more open-minded) learners than adults: Developmental differences in learning the forms of causal relationships. Cognition, 131(2):284-299, 2014. 1 +[43] Jiayuan Mao, Chuang Gan, Pushmeet Kohli, Joshua B Tenenbaum, and Jiajun Wu. The neuro-symbolic concept learner: Interpreting scenes, words, and sentences from natural supervision. In International Conference on Learning Representations (ICLR), 2019. 2, 5 +[44] Andrew N Meltzoff, Anna Waismeyer, and Alison Gopnik. Learning about causes from people: Observational causal learning in 24-month-old infants. Developmental psychology, 48(5):1215, 2012. 1 +[45] Albert Michotte. The perception of causality, volume 21. Routledge, 2017. 3 + +[46] Roozbeh Mottaghi, Mohammad Rastegari, Abhinav Gupta, and Ali Farhadi. "what happens if..." learning to predict the effect of forces in images. In Proceedings of European Conference on Computer Vision (ECCV), 2016. 3 +[47] Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. NIPS-W, 2017. 6 +[48] Judea Pearl. Causality. Cambridge university press, 2009. 3 +[49] Judea Pearl and Thomas S Verma. A theory of inferred causation. In Studies in Logic and the Foundations of Mathematics, volume 134, pages 789-811. Elsevier, 1995. 2, 3 +[50] Siyuan Qi, Baoxiong Jia, Siyuan Huang, Ping Wei, and Song-Chun Zhu. A generalized earley parser for human activity parsing and prediction. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2020. 2, 5 +[51] Siyuan Qi, Baoxiong Jia, and Song-Chun Zhu. Generalized earley parser: Bridging symbolic grammars and sequence data for future prediction. In Proceedings of International Conference on Machine Learning (ICML), 2018. 2, 5 +[52] J. C. et al. Raven. Raven's progressive matrices. Western Psychological Services, 1938. 2 +[53] Robert A Rescorla. A theory of pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. Current research and theory, pages 64-99, 1972. 2, 6 +[54] Laura Ruis, Jacob Andreas, Marco Baroni, Diane Bouchacourt, and Brenden M Lake. A benchmark for systematic generalization in grounded language understanding. arXiv preprint arXiv:2003.05161, 2020. 7 +[55] Adam Santoro, Felix Hill, David Barrett, Ari Morcos, and Timothy Lillicrap. Measuring abstract reasoning in neural networks. In Proceedings of International Conference on Machine Learning (ICML), 2018. 2, 3, 5 +[56] Adam Santoro, David Raposo, David G Barrett, Mateusz Malinowski, Razvan Pascanu, Peter Battaglia, and Timothy Lillicrap. A simple neural network module for relational reasoning. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2017. 3, 5 +[57] Brian J Scholl and Patrice D Tremoulet. Perceptual causality and animacy. Trends in Cognitive Sciences, 4(8):299-309, 2000. 3 +[58] Laura Schulz, Tamar Kushnir, and Alison Gopnik. Learning from doing: Intervention and causal inference. Causal learning: Psychology, philosophy, and computation, pages 67-85, 2007. 1 +[59] David R Shanks and Anthony Dickinson. Associative accounts of causality judgment. In *Psychology of learning and motivation*, volume 21, pages 229–261. Elsevier, 1988. 3 +[60] David M Sobel and Natasha Z Kirkham. Bickets and babies: the development of causal reasoning in toddlers and infants. Developmental psychology, 42(6):1103, 2006. 1, 3 +[61] David M Sobel, Joshua B Tenenbaum, and Alison Gopnik. Children's causal inferences from indirect evidence: Backwards blocking and bayesian reasoning in preschoolers. Cognitive science, 28(3):303-333, 2004. 1, 2, 4, 7 +[62] Peter Spirtes, Clark N Glymour, Richard Scheines, and David Heckerman. Causation, prediction, and search. MIT press, 2000. 2, 6 + +[63] Steven Spratley, Krista Ehinger, and Tim Miller. A closer look at generalisation in raven. In Proceedings of European Conference on Computer Vision (ECCV), 2020. 3 +[64] Mark Twain. Life on the Mississippi. Penguin, 1984. 1 +[65] Michael R Waldmann and Keith J Holyoak. Predictive and diagnostic learning within causal models: Asymmetries in cue competition. Journal of Experimental Psychology: General, 121(2):222, 1992. 3 +[66] Caren M Walker and Alison Gopnik. Toddlers infer higher-order relational principles in causal learning. Psychological science, 25(1):161-169, 2014. 1 +[67] Caren M Walker and Alison Gopnik. Discriminating relational and perceptual judgments: Evidence from human toddlers. Cognition, 166:23-27, 2017. 1 +[68] Duo Wang, Mateja Jamnik, and Pietro Lio. Abstract diagrammatic reasoning with multiplex graph networks. In International Conference on Learning Representations (ICLR), 2020. 2, 3, 5, 6 +[69] Sirui Xie, Xiaojian Ma, Peiyu Yu, Yixin Zhu, Ying Nian Wu, and Song-Chun Zhu. Halma: Humanlike abstraction learning meets affordance in rapid problem solving. arXiv preprint arXiv:2102.11344, 2021. 4 +[70] Kexin Yi, Chuang Gan, Yunzhu Li, Pushmeet Kohli, Jiajun Wu, Antonio Torralba, and Joshua B Tenenbaum. Clevrer: Collision events for video representation and reasoning. In International Conference on Learning Representations (ICLR), 2020. 2, 3, 5 +[71] Kexin Yi, Jiajun Wu, Chuang Gan, Antonio Torralba, Pushmeet Kohli, and Josh Tenenbaum. Neural-symbolic vqa: Disentangling reasoning from vision and language understanding. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2018. 2, 5 +[72] Chi Zhang, Feng Gao, Baoxiong Jia, Yixin Zhu, and Song-Chun Zhu. Raven: A dataset for relational and analogical visual reasoning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019. 2, 3, 4 +[73] Chi Zhang, Baoxiong Jia, Feng Gao, Yixin Zhu, Hongjing Lu, and Song-Chun Zhu. Learning perceptual inference by contrasting. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2019. 3 +[74] Chi Zhang, Baoxiong Jia, Song-Chun Zhu, and Yixin Zhu. Abstract spatial-temporal reasoning via probabilistic abduction and execution. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021. 2, 3, 5, 8 +[75] Chi Zhang, Yixin Zhu, and Song-Chun Zhu. Metastyle: Three-way trade-off among speed, flexibility, and quality in neural style transfer. In Proceedings of AAAI Conference on Artificial Intelligence (AAAI), 2019. 8 +[76] Wenhe Zhang, Chi Zhang, Yixin Zhu, and Song-Chun Zhu. Machine number sense: A dataset of visual arithmetic problems for abstract and relational reasoning. In Proceedings of AAAI Conference on Artificial Intelligence (AAAI), 2020. 2, 5 +[77] Kecheng Zheng, Zheng-Jun Zha, and Wei Wei. Abstract reasoning with distracting features. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2019. 2, 3, 5, 6 + +[78] Xun Zheng, Bryon Aragam, Pradeep K Ravikumar, and Eric P Xing. Dags with no tears: Continuous optimization for structure learning. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2018. 2, 5, 6, 8 +[79] Xun Zheng, Chen Dan, Bryon Aragam, Pradeep Ravikumar, and Eric Xing. Learning sparse nonparametric dags. In Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS), 2020. 2, 5, 6, 8 +[80] Yixin Zhu, Tao Gao, Lifeng Fan, Siyuan Huang, Mark Edmonds, Hangxin Liu, Feng Gao, Chi Zhang, Siyuan Qi, Ying Nian Wu, Josh B Tenenbaum, and Song-Chun Zhu. Dark, beyond deep: A paradigm shift to cognitive ai with humanlike common sense. 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Conventional 2D CNNs are computationally cheap but cannot catch temporal relationships; 3D CNNs can achieve good performance but are computationally intensive. In this work, we tackle this dilemma by designing a generic and effective module that can be embedded into 2D CNNs. To this end, we propose a spAtiotemporal, Channel and moTion excitaION (ACTION) module consisting of three paths: Spatio-Temporal Excitation (STE) path, Channel Excitation (CE) path, and Motion Excitation (ME) path. The STE path employs one channel 3D convolution to characterize spatio-temporal representation. The CE path adaptively recalibrates channelwise feature responses by explicitly modeling interdependencies between channels in terms of the temporal aspect. The ME path calculates feature-level temporal differences, which is then utilized to excite motion-sensitive channels. We equip 2D CNNs with the proposed ACTION module to form a simple yet effective ACTION-Net with very limited extra computational cost. ACTION-Net is demonstrated by consistently outperforming 2D CNN counterparts on three backbones (i.e., ResNet-50, MobileNet V2 and BNInception) employing three datasets (i.e., Something-Something V2, Jester, and EgoGesture). Code is provided at https://github.com/V-Sense/ACTION-Net. + +# 1. Introduction + +Video understanding has attracted an increasing amount of interest, since it is a crucial step towards real-world applications, such as Virtual Reality/Augmented Reality (VR/AR) and video-sharing social networking services. For instance, millions of videos are uploaded to TikTok, Douyin, and Xigua Video to be processed everyday, wherein video understanding acts a pivotal part. However, + +the explosive growth in this video streaming gives rise to challenges on performing video understanding at high accuracy and low computation cost. + +Action recognition, a fundamental problem in video understanding, has been a growing demand in video-related applications, such as content moderation (i.e., recognize content in videos that break terms of service) and content recommendations (i.e., videos are ranked by most liked and recommended to similar customers). The complex actions in videos are normally temporal-dependent, which do not only contain spatial information within each frame but also include temporal information over a duration. For example, symmetric action pairs ('opening a box', 'closing a box'), ('rotate fists clockwise', 'rotate fists counterclockwise') contain similar features in spatial domains, but the temporal information is completely reversed. Traditional human action recognition is more scene-related [36, 18, 15], wherein actions are not as temporal-dependent e.g., 'apply eye makeup', 'walking', 'running'. With how rapid technology is developing, like VR, which requires employing gestures to interact with environments, temporal-related action recognition has recently become a focus for research. + +The mainstreams of existing methods are 3D CNN-based frameworks and 2D CNN-based frameworks. 3D CNNs have been shown to be effective in terms of spatiotemporal modeling [39, 4, 37], but spatio-temporal modeling is unable to capture adequate information contained in videos. The two-stream architecture was proposed to take spatio-temporal information and optical flow into account [35, 3, 33], which boosted performance significantly compared to the one-stream architecture. However, computation on optical flow is very expensive, which poses challenges on real-world applications. 3D CNNs suffer from problems including overfitting and slow convergence [8]. With more large-scale datasets being released, such as Kinetics [3], Moments in Time [29] and ActivityNet [2], optimizing 3D CNNs becomes much easier and more popular. However, heavy computations inherent in 3D CNN-based frameworks contribute to slow inferences, which would limit their deployment on real-world applications, such as VR that relies on online video recognition. Current 2D + +![](images/c6b5c178aa239603325e5b2346215cbef0c0f2ace0a4dd5cb84f0f2602cb178d.jpg) +Raw + +![](images/77d9664c313f3038f4366d3a76ee459547c1b9a43e6cfb2a49b8d828287d6ccb.jpg) + +![](images/45bb08779dfae08ca2d4990724dfd0b6bbf5e2cae18776ddbf2d5205b8a1034e.jpg) + +![](images/4577e2bee5f8b50bd444ed4c6cf4082d1ece8522cd74f1845fbf8e5cfe02fdf3.jpg) + +![](images/5545a5600a1c0af620bcb97158291075f7c0a6aa0b2999ffe86cea78af5958ed.jpg) + +![](images/fc35b6886b71e350e240b3732c1132350dc8b02f38122ab32f9917cc6bc513cd.jpg) + +![](images/bbf4eaa5c055783ac5ba6a08c0f3d8f5033cc8b681d5d9efe52d844006864499.jpg) + +![](images/481c3207924d2e15b2ffcb6482920f17e8d8d1ae5d7755e8b1021c3beb78ee43.jpg) + +![](images/e3bfb6c2012bfb98c021a55d9edcdd67262ba9c5604f62092c18875d4d659405.jpg) +TSN + +![](images/4d8c48d25e105444c96b90a51015abd51c961eb72dbaf2449f7e58ae9ce3458c.jpg) + +![](images/673354a9847b3f525b7419f326d1acd0d4b6baaf61ebf7ae1a8372229a681c85.jpg) + +![](images/f80a75075282d00f70b414abc5bbdf6175b556c66c5168233c0b1f2fca57608c.jpg) + +![](images/0e28db39f1434266dd76237b44add03b129e0b09800c8eb5d4ffe986d9a60e70.jpg) + +![](images/2d132a5378c7e1881ead287e96ff41a445cecc940b37297da8d21618ea323d21.jpg) + +![](images/5a793ad178d01607c8ef01011e8d98fb3347c5fbc62a9b718b8b20d9710128f6.jpg) + +![](images/bd8b5a51f47bf18f8faa90dccd36625f86b151be00355e3fbeb261d0ac2205d0.jpg) + +![](images/5aa5e07bc77441c986fa89a812173e4ecd609d4852151230dacc8195d01f7b8c.jpg) +TSM + +![](images/08fa79369456d52c73d604672a826683718b28cf58bf90d3e0c64cd382d7a368.jpg) + +![](images/6c96dc9071aaf3fb8679277c28fb2f6eb447d6b681f14f0edb3ea97ce74c5c04.jpg) + +![](images/fc6bb9790a4ec539b9d68e704937f5383d5e81dcf2420ef498531c5427f88f08.jpg) + +![](images/5293e0a30e8d1355131bd5734f581a3284c4aee24a5b00295dc45874ae72bf57.jpg) + +![](images/8ec9849f96b38ea28f69f5c63c9ad84d6072312f9da425299260145e8c198d2a.jpg) + +![](images/d41868b55f8ef148ffd2a05d9aff67dfc6e7d968cea34423b8364014ba090028.jpg) + +![](images/5dc98f22543ac254d1c23364c787b4894895724ea71a914fe56f07517b292afc.jpg) + +![](images/a4cfadda7af7f588597daac4b864c1b4780e669e9bda09b5a18b1d12bcbd1dc1.jpg) +Ours + +![](images/b1d46b30ee9121055cd2587bb424a84912f30a791e495b5978995d8994346bc0.jpg) +Figure 1: Visualization for significant features extracted by TSN, TSM and our ACTION-Net for the action 'Rotate fists counterclockwise'. Features extracted by each method are visualized by using CAM [48]. Compared to TSN and TSM, it can be noticed that ACTION-Net is able to extract features that are related to movements in an action especially for highlighted frames i.e., 4th and 5th columns. More examples can be referred to Supplementary Materials. + +![](images/f6b7e5acb31d45e15b882d3dd7f4d90d686acf8c0a1a43b3b74321de59268a69.jpg) + +![](images/dd5b19db1b96e8380d825193db4be104d28f1270d527bafa0aca4fb77d9372da.jpg) + +![](images/72325891aeff49bc8823b1d952d60d16047e91b505e9737e0b73eef580824a67.jpg) + +![](images/49121eecedfcb1c667e19e18520e12b89528938c6a23452b7efd1f51d4e5755d.jpg) + +![](images/8841cb8e549682969c8538f61786ad73076e98a95c0aca29f3abcdc1e625863c.jpg) + +![](images/fcb6c383c56940ea99367e4060a3531b60026bfc22d88a34bf76356c2e434234.jpg) +13 + +CNN-based frameworks [14, 35, 41, 47, 22, 20] enjoy lightweight and fast inferences. These approaches operated on a sequence of short snippets (known as segments) sparsely sampled from the entire video and were initially introduced in TSN [41]. Original 2D CNNs lack the ability of temporal modeling, which causes losing essential sequential information in some actions e.g., 'opening a box' vs 'closing a box'. TSM [22] introduced temporal information to 2D CNN-based frameworks by shifting a part of channels on the temporal axis, which significantly improved the baseline for 2D CNN-based frameworks. However, TSM still lacks explicit temporal modeling for an action, such as motion information. Recent works [19, 13, 21, 24, 25] introduced embedded modules into 2D CNNs in terms of ResNet architecture [9], which possessed the capability for motion modeling. In order to capture multi-type information contained by videos, previous works normally operated on input-level frames. For instance, SlowFast networks sampled raw videos at multiple rates to characterize slow and fast actions; two-stream networks utilized precomputed optical flow for reasoning motion information. This kind of approaches commonly require multi-branch networks, which need expensive computations. + +Inspired by the aforementioned observation, we propose a new plug-and-play and lightweight spAtio-temporal, Channel and moTion excitatION (ACTION) module to effectively process the multi-type information on the feature + +level inside a single network by adopting multipath excitation. The combination of spatio-temporal features and motion features can be understood similarly as the two-stream architecture [35], but we model the motion inside the network based on the feature level rather than generating another type of input (e.g., optical flow [11]) for training the network, which significantly reduces computations. Inspired by SENet, the channel-wise features are extracted based on the temporal domain to characterize the channel interdependencies for the network. Correspondingly, a neural architecture equipped with such a module is dubbed ACTION-Net. ACTION comprises three components for extracting aforementioned features (1) Spatio-Temporal Excitation (STE), (2) Channel Excitation (CE) and (3) Motion Excitation (ME). Figure 1 visualizes features characterized by TSN, TSM, and ACTION-Net for the action 'rotate fists counterclockwise'. It can be observed that both TSN and TSM focus on recognizing objects (two fists) independently instead of reasoning an action. Compared to TSN and TSM, our proposed ACTION-Net better characterizes an action by representing feature maps that cover the two fists, especially for the highlighted 4th and 5th columns. In a nutshell, our contributions are three-fold: + +- We propose an ACTION module that works in a plitg-and-play manner, which is able to extract appropriate spatio-temporal patterns, channel-wise features and motion information to recognize actions. + +- A simple yet effective neural architecture referred to ACTION-Net. We test it on three backbones (ResNet50 [9], BNception [12] and MobileNet V2 [31]). +- We conducted extensive experiments and shown our superior performances on three datasets Something-Something V2 [7], Jester [27] and EgoGesture [46]. + +# 2. Related Works + +In this section, we discuss related works by taking 2D and 3D CNN-based frameworks into account, wherein SENet [10] and TEA [21] inspired us to propose the ACTION-Net. + +# 2.1. 3D CNN-based Framework + +The 3D CNN-based framework has a spatio-temporal modeling capability, which enhances model performance for video action recognition [39, 8, 39]. I3D [3] inflated the ImageNet pre-trained 2D kernels to 3D kernels for capturing spatio-temporal information. To better represent motion patterns, I3D utilized pre-computed optical flow together with RGB (also known as the two-stream architecture). SlowFast networks [5] were proposed to handle inconsistent speeds of actions in videos e.g., running and walking, which involved a slow branch and a fast branch to model slow actions and fast actions, respectively. Although 3D CNN-based approaches have achieved exciting results on several benchmark datasets, they contain massive parameters. In this case, various problems are caused, such as easily overfitting [8] and difficulty in converging [40], which pose challenges including ineffective inferences for online streaming videos in real-world applications. Although recent works [30, 40] have demonstrated that 3D convolution can be factorized to lessen computations to some extent, the computation is still much more of a burden when compared to 2D CNN-based frameworks. + +# 2.2. 2D CNN-based Framework + +TSN [41] was the first proposed framework that applied 2D CNNs for video action recognition, which introduced the concept of 'segment' to process videos i.e., extract short snippets over a long video sequence with a uniform sparse sampling scheme. However, the direct use of 2D CNNs lacks temporal modeling for video sequences. TSM [22] firstly introduced temporal modeling to 2D CNN-based frameworks, in which a shift operation for a part of channels was embedded into 2D CNNs. However, TSM lacks explicit temporal modeling for actions such as differences among neighbouring frames. Recently, several works have proposed modules to be embedded into 2D CNNs. These modules are able to model the motion and temporal information. For instance, MFNet [19], TEINet [24] and TEA [21], which introduced this type of modules, + +were demonstrated to be effective on the ResNet architecture. STM [13] proposed a block for modeling the spatiotemporal and motion information instead of the ordinary residual block. GSM [38] leverages group spatial gating to control interactions in spatial-temporal decomposition. + +# 2.3. SENet and Beyond + +Hu et al. [10] introduced a SENet architecture. A squeeze-and-excitation (SE) block was proposed to be embedded into 2D CNNs. In this case, the learning of channelwise features regarding image recognition tasks was enhanced by explicitly modeling channel interdependencies. To tackle this, the SE block utilized two fully connected (FC) layers in a squeeze-and-unsqueeze manner then applied a Sigmoid activation for exciting essential channelwise features. However, it processes each image independently without considering critical information such as temporal properties for videos. To tackle this issue, TEA [21] introduces motion excitation (ME) and multiple temporal aggregation (MTA) in tandem to capture short- and long-range temporal evolution. It should be noted that MTA is specifically designed for Res2Net [6], which means TEA can only be embedded into Res2Net. Inspired by these two previous works, we first propose STE and CE modules beyond the SE module by addressing the spatio-temporal perspective and channel interdependencies in temporal dimension. The ACTION module is then constructed by assembling STE, CE and ME in a parallel manner, in which case, multi-type information in videos can be activated. + +# 3. Design of ACTION + +In this section, we are going to introduce technical details for our proposed ACTION-Net together with ACTION module. As the ACTION module consists of three sub-modules i.e., Spatio-Temporal Excitation (STE), Channel Excitation (CE) and Motion Excitation (ME), we firstly introduce these three sub-modules respectively and then give an overview on how to integrate them to an ACTION module. Notations used in this section are: $N$ (batch size), $T$ (number of segments), $C$ (channels), $H$ (height), $W$ (width) and $r$ (channel reduce ratio). It should be noticed that all tensors outside the ACTION module are 4D i.e., $(\mathrm{N} \times \mathrm{T}, \mathrm{C}, \mathrm{H}, \mathrm{W})$ . We first reshape the input 4D tensor to 5D tensor (N, T, C, H, W) before feeding to the ACTION in order to enable the operation on specific dimension inside the ACTION. The 5D output tensor is then reshaped to 4D before being fed to the next 2D convolutional block. + +# 3.1. Spatio-Temporal Excitation (STE) + +STE is efficiently designed for exciting spatio-temporal information by utilizing 3D convolution. To achieve this, STE generates a spatio-temporal mask $\mathbf{M} \in \mathbb{R}^{N \times T \times 1 \times H \times W}$ that is used for element-wise multiplying + +the input $\mathbf{X} \in \mathbb{R}^{N \times T \times C \times H \times W}$ across all channels. As illustrated in Fig. 2(a), given an input $\mathbf{X} \in \mathbb{R}^{N \times T \times C \times H \times W}$ , we first average the input tensor across channels in order to get a global spatio-temporal tensor $\mathbf{F} \in \mathbb{R}^{N \times T \times 1 \times H \times W}$ with respect to the channel axis. Then we reshape $\mathbf{F}$ to $\mathbf{F}^* \in \mathbb{R}^{N \times 1 \times T \times H \times W}$ to be fed to a 3D convolutional layer $\mathbf{K}$ with kernel size $3 \times 3 \times 3$ , which can be formulated as + +$$ +\mathbf {F} _ {o} ^ {*} = \mathbf {K} * \mathbf {F} ^ {*} \tag {1} +$$ + +We finally reshape $\mathbf{F}_o^*$ back to $\mathbf{F}_o\in \mathbb{R}^{N\times T\times 1\times H\times W}$ and feed it to a Sigmoid activation in order to get the mask $\mathbf{M}\in \mathbb{R}^{N\times T\times 1\times H\times W}$ , which can be represented as + +$$ +\mathbf {M} = \delta (\mathbf {F} _ {o}) \tag {2} +$$ + +The final output can be interpreted as + +$$ +\mathbf {Y} = \mathbf {X} + \mathbf {X} \odot \mathbf {M} \tag {3} +$$ + +Compared to the conventional 3D convolutional operation, STE is much more computationally efficient as the input feature $\mathbf{F}^*$ is averaged across channels. Each channel of the input tensor $\mathbf{X}$ can perceive the importance of spatio-temporal information from a refined feature excitation $\delta (\mathbf{F}_o)$ . + +# 3.2. Channel Excitation (CE) + +CE is designed similarly to SE block [10] as shown in Fig. 2(b). The main difference between CE and SE is that we insert a 1D convolutional layer between two FC layers to characterize temporal information for channel-wise features. Concretely, given an input $\mathbf{X} \in \mathbb{R}^{N \times T \times C \times H \times W}$ , we firstly access the global spatial information of the input feature by spatial average pooling the input, which can be represented as + +$$ +\mathbf {F} = \frac {1}{H \times W} \sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} \mathbf {X} [:,::, i, j ] \tag {4} +$$ + +where $\mathbf{F} \in \mathbb{R}^{N \times T \times C \times 1 \times 1}$ . We squeeze the number of channels for $\mathbf{F}$ by a scale ratio $r$ ( $r = 16$ in this work), which can be interpreted as + +$$ +\mathbf {F} _ {r} = \mathbf {K} _ {1} * \mathbf {F} \tag {5} +$$ + +where $\mathbf{K}_1$ is a $1 \times 1$ 2D convolutional layer and $\mathbf{F}_r \in \mathbb{R}^{N \times T \times \frac{C}{r} \times 1 \times 1}$ . We then reshape $\mathbf{F}_r$ to $\mathbf{F}_r^* \in \mathbb{R}^{N \times \frac{C}{r} \times T \times 1 \times 1}$ to enable the temporal reasoning. A 1D convolutional layer $\mathbf{K}_2$ with kernel size 3 is utilized to process $\mathbf{F}_r^*$ as + +$$ +\mathbf {F} _ {\text {t e m p}} ^ {*} = \mathbf {K} _ {2} * \mathbf {F} _ {r} ^ {*} \tag {6} +$$ + +where $\mathbf{F}_{temp}^{*}\in \mathbb{R}^{N\times \frac{C}{r}\times T\times 1\times 1}$ . $\mathbf{F}_{temp}^{*}$ is then reshaped to $\mathbf{F}_{temp}\in \mathbb{R}^{N\times T\times \frac{C}{r}\times 1\times 1}$ , which is then unsqueezed by using a $1\times 1$ 2D convolutional layer $\mathbf{K}_3$ and fed to a Sigmoid + +![](images/95e6e7accb51a4d8d9fb1175299b4708cdcf3a49230910ec942ea3dea377c7bf.jpg) +(a) + +![](images/aaafdf09945a4d3fa2959c70acdcf7650336246f67d17610f8dda0b2e78a4e9d.jpg) +(b) + +![](images/2c73ebcdc22de1b4ff98630dff3452c3d3d2d81c8de71aba3e912d805f224edb.jpg) +(c) +Figure 2: ACTION module consists of three sub-modules (a) Spatio-Temporal Excitation (STE) module, (b) Channel Excitation (CE) module and (c) Motion Excitation (ME) module. + +activation. These are the last two steps to obtain the channel mask $\mathbf{M}$ , which can be formulated respectively + +$$ +\mathbf {F} _ {o} = \mathbf {K} _ {3} * \mathbf {F} _ {\text {t e m p}} \tag {7} +$$ + +$$ +\mathbf {M} = \delta (\mathbf {F} _ {o}) \tag {8} +$$ + +where $\mathbf{F}_o\in \mathbb{R}^{N\times T\times C\times 1\times 1}$ and $\mathbf{M}\in \mathbb{R}^{N\times T\times C\times 1\times 1}$ . Finally, the output of CE is formulated as the same as in equation (3) using the new generated mask. + +![](images/0e4b33c109bebf0a48d9d6687c67b1f077492d93ae8b676f6b01d35502eef13d.jpg) +Figure 3: ACTION-Net architecture for ResNet-50 [9]. The size of output feature map is given for each layer (CLS refers to number of classes and $T$ refers to number of segments). The input video is firstly split into T segments equally and then one frame from each segment is randomly sampled [41]. The ACTION module is inserted at the start in each residual block. Performance of different embedded locations can be referred to Supplementary Materials. + +# 3.3. Motion Excitation (ME) + +ME has been explored by [13, 21] previously, which aims to model motion information based on the feature level instead of the pixel level. Different from previous work [13, 21] that proposed a whole block for extracting motion, we use the ME in parallel with two modules mentioned in previous two sections. As illustrated in Fig. 2(c), the motion information is modeled by adjacent frames. We adopt the same squeeze and unsqueeze strategy as used in the CE sub-module by using two $1 \times 1$ 2D convolutional layers, which can be referred to equation (5) and equation (7) respectively. Given the feature $\mathbf{F}_r \in \mathbb{R}^{N \times T \times \frac{C}{r} \times H \times W}$ processed by the squeeze operation, motion feature is modeled following the similar operation presented in [13, 21], which can be represented as + +$$ +\mathbf {F} _ {m} = \mathbf {K} * \mathbf {F} _ {r} [:, t + 1, :, :, : ] - \mathbf {F} _ {r} [:, t, :, :, : ] \tag {9} +$$ + +where $\mathbf{K}$ is a $3\times 3$ 2D convolutional layer and $\mathbf{F}_m\in$ $\mathbb{R}^{N\times 1\times \frac{C}{r}\times H\times W}$ . The motion feature is then concatenated to each other according to the temporal dimension and 0 is padded to the last element i.e., $\mathbf{F}_M = [\mathbf{F}_m(1),\dots ,\mathbf{F}_m(t - 1),0],\mathbf{F}_M\in \mathbb{R}^{N\times T\times \frac{C}{r}\times H\times W}$ . The $\mathbf{F}_M$ is then processed by spatial average pooling same as in equation (4). The feature output $\mathbf{F}_o\in \mathbb{R}^{N\times T\times C\times 1\times 1}$ and the mask $\mathbf{M}\in \mathbb{R}^{N\times T\times C\times 1\times 1}$ can then be achieved similarly as in CE through equation (7) and equation (8) respectively. + +# 3.4. ACTION-Net + +The overall ACTION module takes the element-wise addition of three excited features generated by STE, CE and ME respectively (see ACTION module block in Fig. 3). By doing this, the output of the ACTION module can perceive information from a spatio-temporal perspective, channel interdependencies and motion. Figure 3 shows the ACTION-Net architecture for ResNet-50, wherein the ACTION module is inserted at the beginning in each residual block. It + +does not require any modification for original components in the block. Details of ACTION-Net architectures for MobileNet V2 and BNInception can be referred to Supplementary Materials. + +# 4. Experiments + +We first show that ACTION-Net is able to consistently improve the performance for 2D CNNs compared to previous two fundamental works TSN [41] and TSM [22] on three datasets i.e., EgoGesture [46], Something-Something V2 [7] and Jester [27]. We then perform extensive experiments for comparing ACTION-Net with state-of-the-arts on these three datasets. Abundant ablation studies are conducted to analyze the efficacy for each excitation path in ACTION-Net. Finally, we further compare ACTION-Net with TSM on three backbones i.e., ResNet-50, MobileNet V2 and BNInception by considering performance and efficiency $(\eta)$ . + +# 4.1. Datasets + +We evaluated the performance for the proposed ACTION-Net on three large-scale and widely used action recognition datasets i.e., Something-Something V2 [7], Jester [27] and EgoGesture [46]. The Something-Something V2 dataset [19, 24, 44, 49] is a large collection of humans performing actions with everyday objects. It includes 174 categories with 168,913 training videos, 24,777 validation videos and 27,157 testing videos. Jester [13, 16, 45, 28, 17] is a third-person view gesture dataset, which has a potential usage for human computer interaction. It has 27 categories with 118,562 training videos, 14,787 validation videos and 14,743 testing videos. EgoGesture [16, 43, 33, 32, 1, 34] is a large-scale dataset for egocentric hand gesture recognition recorded by a head-mounted camera, which is designed for VR/AR use cases. It involves 83 classes of gestures with 14,416 training sam + +plies, 4,768 validation samples and 4,977 testing samples. + +# 4.2. Implementation Details + +Training. We conducted our experiments on video action recognition tasks by following the same strategy mentioned in TSN [41]. Given an input video, we firstly divided it into $T$ segments of equal duration. Then we randomly selected one frame from each segment to obtain a clip with $T$ frames. The size of the shorter side of these frames is fixed to 256 and corner cropping and scale-jittering were utilized for data augmentation. Each cropped frame was finally resized to $224 \times 224$ , which was used for training the model. The input fed to the model is of the size $N \times T \times 3 \times 224 \times 224$ , in which $N$ is the batch size, $T$ is the number of segments. + +The models were trained on a NVIDIA DGX station with four Tesla V100 GPUs. We adopted SGD as optimizer with a momentum of 0.9 and a weight decay of $5 \times 10^{-4}$ . Batch size was set as $N = 64$ when $T = 8$ and $N = 48$ when $T = 16$ . Network weights were initialized using ImageNet pretrained weights. For Something-Something V2, we started with a learning rate of 0.01 and reduced it by a factor of 10 at 30, 40, 45 epochs and stopped at 50 epochs. For Jester dataset, we started with a learning rate of 0.01 and reduced it by a factor of 10 at 10, 20, 25 epochs and stopped at 30 epochs. For EgoGesture dataset, we started with a learning rate of 0.01 and reduced it by a factor of 10 at 5, 10, 15 epochs and stopped at 25 epochs. + +Inference. We utilized the three-crop strategy following [13, 42, 5] for inference. We firstly scaled the shorter side to 256 for each frame and took three crops of $256 \times 256$ from scaled frames. We randomly sampled from the full-length video for 10 times. The final prediction was the averaged Softmax score for all clips. + +# 4.3. Improving Performance of 2D CNNs + +We compare ACTION-Net to two fundamental 2D CNN counterparts TSN and TSM. As illustrated in Table 1, ACTION-Net consistently outperforms these two 2D CNN counterparts on all three datasets. It is worth noting that TSN does not contain any component that is able to model the temporal information. By employing a temporal shift operation to a part of channels, TSM introduces some temporal information to the network, which significantly improves the 2D CNN baseline compared to TSN. However, TSM still lacks explicit temporal modeling. By adding the ACTION module to TSN, ACTION-Net takes spatiotemporal modeling, channel interdependencies modeling and motion modeling into account. It can be noticed that the Top-1 accuracy of ACTION-Net is improved by $2\%$ , $3.8\%$ and $2.7\%$ compared to TSM with respect to EgoGesture, Something-Something V2 and Jester datasets. + +Table 1: ACTION-Net consistently outperforms 2D counterparts on three representative datasets. All methods use ResNet-50 as backbone and 8 frames input for the fair comparison. + +
DatasetModelTop-1\( \bigtriangleup \)Top-1Top-5\( \bigtriangleup \)Top-5
EgoGesture*TSN83.1-97.3-
TSM92.1+ 9.098.3+ 1.0
ACTION-Net94.2+ 11.198.7+ 1.4
SomethingV2TSN27.8-57.6-
TSM58.7+ 30.984.8+ 27.2
ACTION-Net62.5+ 34.787.3+ 29.7
JesterTSN81.0-99.0-
TSM94.4+ 13.499.7+ 0.7
ACTION-Net97.1+ 16.199.8+ 0.8
+ +* We re-implement TSN and TSM using the official public code in [22]. + +# 4.4. Comparisons with the State-of-the-Art + +We compare our approach with the state-of-the-art on Something-Something V2, Jester and EgoGesture, which is summarized in Table 2. We mainly compare our approach with 2D CNN counterparts as 3D CNN-based frameworks are more favored in scene-related datasets e.g., Kinetics [30, 5]. The superiority of ACTION-Net on Jester and EgoGesture is quite impressive. It is clear that even ACTION-Net with 8 RGB frames as input achieves the state-of-the-art performance compared to other methods, which confirms the remarkable ability of ACTION-Net for integrating useful information from three excitation paths. In terms of Something-Something V2, ACTION-Net also achieves competitive results compared to STM and TEA. It should be noted that both STM and TEA are specifically designed for ResNet and Res2Net respectively, while our ACTION enjoys being flexibly equipped by other architectures i.e., MobileNet V2 and BNInception. + +# 4.5. Ablation Study + +In this section, we investigate the design of our ACTION-Net with respect to (1) efficacy of each excitation and (2) impact of the number of ACTION modules in ACTION-Net regarding the ResNet-50 architecture. We carry out ablation experiments using 8 frames as the input on the EgoGesture dataset for inspecting these two aspects. + +Efficacy of Three Excitations. To validate the contribution of each excitation sub-module, we compare the performance for each individual module and the combination of all sub-modules (ACTION-Net) in Table 3. We also provide visualization results in Supplementary Materials. Results show that each excitation module is able to improve the performance for 2D CNN baselines provided by TSN and TSM with limited added computational cost. Con + +Table 2: Comparisons with the state-of-the-arts on Something-Something V2, Jester and EgoGesture datasets. + +
MethodBackbonePlug-and-playPretrainFrameSomething V2JesterEgoGesture
Top-1Top-5Top-1Top-5Top-1Top-5
C3D + RSTTM [46]-Scratch16----89.3-
C3D [16]ResNext-101Kinetics16--95.9-90.9-
TRN Multiscale [22]BNInceptionImageNet848.877.695.3---
MFNet-C50 [19]ResNet-50ImageNet7--96.199.7--
TSN [22]✓Kinetics827.857.681.099.083.198.3
1630.060.582.399.2--
TSM [13]✓Kinetics858.784.894.499.792.198.3
1661.286.995.399.8--
GST [26]ImageNet861.687.2----
1662.687.9----
bLVNet-TAM [24]ImageNet3261.788.1----
CPNet [23]ImageNet2457.784.0----
TEINet [24]✓ImageNet862.7-----
1663.0-----
STM [13]ImageNet862.388.896.699.9--
1664.289.896.799.9--
TEA [21]ImageNet8--96.599.892.398.3
1664.589.896.799.892.598.5
ACTION-Net1✓ImageNet862.587.397.199.894.298.7
1664.089.397.199.994.498.8
+ +1 ACTION is inserted into each residual block in this experiment. + +Table 3: Accuracy and model complexity on EgoGesture dataset. Three excitation types are compared to TSM and TSN. All methods use ResNet-50 as backbone and 8 frames input for fair comparison. The least FLOPs/△FLOPs/Param. and the best performance for ACTION-Net and sub-modules are highlighted as bold. + +
MethodFLOPs△FLOPsParam.Top-1
TSN33G-23.68M83.1
TSM33G-23.68M92.1
OursSTE33.1G+0.1G (+0.3%)23.9M93.8
CE33.16G+0.16G (+0.5%)26.08M93.8
ME34.69G+1.69G (+5.1%)25.9M93.9
ACTION-Net34.75G+1.75G (+5.3%)28.08M94.2
+ +Table 4: Ablation study of having AC-TION included or not in each residual block stage regarding ResNet-50 backbone on EgoGesture dataset by using 8 frames input. More ACTION engaged yields better performance. + +
StageTop-1Top-5
res292.398.2
res2,392.998.5
res2,3,493.198.5
res2,3,4,594.298.7
+ +Table 5: ACTION-Net generalizes well across backbones and datasets (TSM is used as a baseline). Accuracy and model complexity on three backbones using Something-Something V2, Jester and EgoGesture with 8 frames as input. The most significant improvements on accuracy and the least extra FLOPs are highlighted as bold. + +
BackboneMethodFLOPsParam.Something V2JesterEgoGesture
ResNet-50TSM33G23.68M58.794.492.1
ACTION-Net34.75G (+5.3%)28.08M62.5 (+3.8)97.1 (+2.7)94.2 (+2.1)
BNIceptionTSM16.39G10.36M53.594.692.3
ACTION-Net16.94G (+3.4%)11.59M56.7 (+3.2)96.6 (+2.0)93.2 (+0.9)
MobileNet V2TSM2.55G2.33M54.995.092.4
ACTION-Net2.57G (+0.8%)2.36M58.5 (+3.6)96.7 (+1.7)93.5 (+1.1)
+ +cretely, STE and CE both add negligible extra computation + +compared to TSM by averaging channels globally and av- + +![](images/3244582f38f0140c093061225374118422672759c6d6ba55e8609501707330a0.jpg) +(a) EgoGesture + +![](images/77f47e8e6235d68bddf7858b011c43f91ed9f45d7326c2a62b6e13f9ac537103.jpg) +(b) Jester +Figure 4: Top-1 accuracy and FLOPs for ACTION-Net and TSM on three backbones i.e., ResNet-50, BNInception and MobileNet V2 using three datasets (from left to right: EgoGesture, Jester and Something-something V2). $\eta$ is calculated using equation (10) for each backbone on three datasets. EgoGesture: ResNet-50 $\eta = 2.65\%$ , BNInception $\eta = 3.73\%$ , MobileNet V2 $\eta = 0.71\%$ . Jester: ResNet-50 $\eta = 1.96\%$ , BNInception $\eta = 1.68\%$ , MobileNet V2 $\eta = 0.46\%$ . Something V2: ResNet-50 $\eta = 1.40\%$ , BNInception $\eta = 1.05\%$ , MobileNet V2 $\eta = 0.22\%$ . + +![](images/26d841f9056feea702b38ec1391f3939fce0fdc6bc6331ef00687d0373a4a282.jpg) +(c) Something-something V2 + +eraging spatial information globally yet they both provide useful information to the network. ME adds more computation and parameters to the network than the previous two yet it is acceptable. It captures temporal differences on the spatial domain among adjacent frames over the time and achieves better performance compared to STE and CE. When integrating all these three sub-modules to constitute the ACTION, it can be seen that the ACTION-Net achieves the highest accuracy and increases $2.1\%$ Top-1 accuracy together with increasing $5.3\%$ FLOPs. To better capture the relation between boosted performance and add-on computation, we define the efficiency formulated as + +$$ +\eta = \frac {\triangle \mathrm {F L O P s}}{\triangle \mathrm {T o p} - 1} \tag {10} +$$ + +where both $\triangle$ FLOPs and $\triangle$ Top-1 are in percent, $\eta$ is the efficiency that represents how many extra FLOPs in percent are introduced with respect to increasing $1\%$ Top-1 accuracy (smaller indicates more efficient apparently). Efficiency $\eta$ for STE, CE, ME and ACTION-Net is $0.18\%$ , $0.29\%$ , $2.83\%$ and $2.52\%$ respectively. It can be noticed that STE is the most efficient when taking $\eta$ into account. + +Impact of the Number of ACTION Blocks. The architecture of ResNet-50 can be divided into 6 stages i.e., $\mathrm{conv}_1$ , $\mathrm{res}_2$ , $\mathrm{res}_3$ , $\mathrm{res}_4$ , $\mathrm{res}_5$ and FC. The ACTION module can be inserted into any residual stage from $\mathrm{res}_2$ to $\mathrm{res}_5$ . We investigate the impact of the number of residual stages that contain the ACTION module as shown in Table 4. Results show that more stages including the ACTION module results in better performance, which indicates the efficacy for our proposed approach. + +# 4.6. Analysis of Efficiency and Flexibility + +Compared to recent 2D CNN approaches e.g., STM [13] and TEA [21], our ACTION module enjoys a plug-and-play manner like TSM, which can be embedded to any 2D + +CNN. To validate the efficacy for our proposed approach, we compare ACTION-Net with TSM on three backbones i.e., ResNet-50, BNInception and MobileNet V2. We report FLOPs and Top-1 accuracy for ACTION-Net and TSM respectively. We also report $\eta$ calculated using equation 10 when replacing TSM with ACTION, which indicates the penalization of computation when improving the accuracy. Table 5 demonstrates recognition performance and computation for ACTION-Net employing three backbones. TSM is used as a baseline since TSM benefits good performance and zero extra introduced computational cost compared to TSN. It can be noticed that ACTION-Net outperforms TSM consistently regarding the accuracy for all three backbones yet with limited add-on computational cost. ResNet-50 is boosted most significantly regarding the performance and MobileNet V2 holds the least added FLOPs. Figure 4 demonstrates the efficiency $\eta$ for ACTION-Net based on TSM on different backbones using three datasets. It can be noticed that MobileNet V2 achieves the lowest $\eta$ (the most efficient) while ResNet-50 achieves the highest $\eta$ (the least efficient) for all three datasets, which indicates that MobileNet V2 benefits mostly from the ACTION module regarding the efficiency. + +# 5. Conclusion + +We target at designing a module to be inserted to 2D CNN models for video action recognition and introduce a novel ACTION module that utilizes multipath excitation for spatio-temporal features, channel-wise features and motion features. The proposed module could be leveraged by any 2D CNN to build a new architecture ACTION-Net for video action recognition. We demonstrate efficacy and efficiency for ACTION-Net on three large-scale datasets. We show that ACTION-Net achieves consistently improvements compared to 2D CNN counterparts with limited extra computations introduced. + +# References + +[1] Mahdi Abavisani, Hamid Reza Vaezi Joze, and Vishal M Patel. Improving the performance of unimodal dynamic hand-gesture recognition with multimodal training. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1165-1174, 2019. +[2] Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, and Juan Carlos Niebles. Activitynet: A large-scale video benchmark for human activity understanding. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 961-970, 2015. +[3] Joao Carreira and Andrew Zisserman. Quo vadis, action recognition? a new model and the kinetics dataset. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 6299-6308, 2017. +[4] Yunpeng Chen, Yannis Kalantidis, Jianshu Li, Shuicheng Yan, and Jiashi Feng. A^2-nets: Double attention networks. In Advances in neural information processing systems, pages 352-361, 2018. +[5] Christoph Feichtenhofer, Haoqi Fan, Jitendra Malik, and Kaiming He. Slowfast networks for video recognition. In Proceedings of the IEEE international conference on computer vision, pages 6202-6211, 2019. +[6] Shanghua Gao, Ming-Ming Cheng, Kai Zhao, Xin-Yu Zhang, Ming-Hsuan Yang, and Philip HS Torr. Res2net: A new multi-scale backbone architecture. IEEE transactions on pattern analysis and machine intelligence, 2019. +[7] Raghav Goyal, Samira Ebrahimi Kahou, Vincent Michalski, Joanna Materzynska, Susanne Westphal, Heuna Kim, Valentin Haenel, Ingo Fruend, Peter Yianilos, Moritz Mueller-Freitag, et al. The" something something" video database for learning and evaluating visual common sense. In ICCV, volume 1, page 5, 2017. +[8] Kensho Hara, Hirokatsu Kataoka, and Yutaka Satoh. Can spatiotemporal 3d cnns retrace the history of 2d cnns and imageNet? In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pages 6546-6555, 2018. +[9] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. +[10] Jie Hu, Li Shen, and Gang Sun. Squeeze-and-excitation networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7132-7141, 2018. +[11] Eddy Ilg, Nikolaus Mayer, Tonmoy Saikia, Margret Keuper, Alexey Dosovitskiy, and Thomas Brox. Flownet 2.0: Evolution of optical flow estimation with deep networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2462-2470, 2017. +[12] Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167, 2015. +[13] Boyuan Jiang, MengMeng Wang, Weihao Gan, Wei Wu, and Junjie Yan. STM: Spatiotemporal and motion encoding for action recognition. In Proceedings of the IEEE International Conference on Computer Vision, pages 2000-2009, 2019. + +[14] Andrej Karpathy, George Toderici, Sanketh Shetty, Thomas Leung, Rahul Sukthankar, and Li Fei-Fei. Large-scale video classification with convolutional neural networks. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pages 1725–1732, 2014. +[15] Will Kay, Joao Carreira, Karen Simonyan, Brian Zhang, Chloe Hillier, Sudheendra Vijayanarasimhan, Fabio Viola, Tim Green, Trevor Back, Paul Natsev, et al. The kinetics human action video dataset. arXiv preprint arXiv:1705.06950, 2017. +[16] Okan Kopukli, Ahmet Gunduz, Neslihan Kose, and Gerhard Rigoll. Real-time hand gesture detection and classification using convolutional neural networks. In 2019 14th IEEE International Conference on Automatic Face & Gesture Recognition (FG 2019), pages 1-8. IEEE, 2019. +[17] Okan Kopukli, Thomas Ledwon, Yao Rong, Neslihan Kose, and Gerhard Rigoll. Drivermhg: A multi-modal dataset for dynamic recognition of driver micro hand gestures and a real-time recognition framework. arXiv preprint arXiv:2003.00951, 2020. +[18] Hildegard Kuehne, Hueihan Jhuang, Estíbaliz Garrote, Tomaso Poggio, and Thomas Serre. Hmdb: a large video database for human motion recognition. In 2011 International Conference on Computer Vision, pages 2556-2563. IEEE, 2011. +[19] Myunggi Lee, Seungeui Lee, Sungjoon Son, Gyutae Park, and Nojun Kwak. Motion feature network: Fixed motion filter for action recognition. In Proceedings of the European Conference on Computer Vision (ECCV), pages 387-403, 2018. +[20] Duo Li, Jie Hu, Changhu Wang, Xiangtai Li, Qi She, Lei Zhu, Tong Zhang, and Qifeng Chen. Involution: Inverting the inheritance of convolution for visual recognition. arXiv preprint arXiv:2103.06255, 2021. +[21] Yan Li, Bin Ji, Xintian Shi, Jianguo Zhang, Bin Kang, and Limin Wang. TEA: Temporal excitation and aggregation for action recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 909–918, 2020. +[22] Ji Lin, Chuang Gan, and Song Han. TSM: Temporal shift module for efficient video understanding. In Proceedings of the IEEE International Conference on Computer Vision, pages 7083-7093, 2019. +[23] Xingyu Liu, Joon-Young Lee, and Hailin Jin. Learning video representations from correspondence proposals. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4273–4281, 2019. +[24] Zhaoyang Liu, Donghao Luo, Yabiao Wang, Limin Wang, Ying Tai, Chengjie Wang, Jilin Li, Feiyue Huang, and Tong Lu. Teinet: Towards an efficient architecture for video recognition. In AAAI, pages 11669-11676, 2020. +[25] Zhaoyang Liu, Limin Wang, Wayne Wu, Chen Qian, and Tong Lu. Tam: Temporal adaptive module for video recognition. arXiv preprint arXiv:2005.06803, 2020. +[26] Chenxu Luo and Alan L Yuille. Grouped spatial-temporal aggregation for efficient action recognition. In Proceedings of the IEEE International Conference on Computer Vision, pages 5512-5521, 2019. + +[27] Joanna Materzynska, Guillaume Berger, Ingo Bax, and Roland Memisevic. The jester dataset: A large-scale video dataset of human gestures. In Proceedings of the IEEE International Conference on Computer Vision Workshops, pages 0–0, 2019. +[28] Joanna Materzynska, Tete Xiao, Roei Herzig, Huijuan Xu, Xiaolong Wang, and Trevor Darrell. Something-else: Compositional action recognition with spatial-temporal interaction networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1049–1059, 2020. +[29] Mathew Monfort, Alex Andonian, Bolei Zhou, Kandan Ramakrishnan, Sarah Adel Bargal, Tom Yan, Lisa Brown, Quanfu Fan, Dan Gutfreund, Carl Vondrick, et al. Moments in time dataset: one million videos for event understanding. IEEE transactions on pattern analysis and machine intelligence, 42(2):502-508, 2019. +[30] Zhaofan Qiu, Ting Yao, and Tao Mei. Learning spatiotemporal representation with pseudo-3d residual networks. In proceedings of the IEEE International Conference on Computer Vision, pages 5533–5541, 2017. +[31] Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zhoginov, and Liang-Chieh Chen. *Mobilenetv2: Inverted residuals and linear bottlenecks*. In *Proceedings of the IEEE conference on computer vision and pattern recognition*, pages 4510-4520, 2018. +[32] Lei Shi, Yifan Zhang, Jian Cheng, and Hanqing Lu. Skeleton-based action recognition with directed graph neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7912-7921, 2019. +[33] Lei Shi, Yifan Zhang, Jian Cheng, and Hanqing Lu. Two-stream adaptive graph convolutional networks for skeleton-based action recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 12026-12035, 2019. +[34] Lei Shi, Yifan Zhang, Jian Cheng, and Hanqing Lu. Skeleton-based action recognition with multi-stream adaptive graph convolutional networks. IEEE Transactions on Image Processing, 29:9532-9545, 2020. +[35] Karen Simonyan and Andrew Zisserman. Two-stream convolutional networks for action recognition in videos. In Advances in neural information processing systems, pages 568-576, 2014. +[36] Khurram Soomro, Amir Roshan Zamir, and Mubarak Shah. Ucf101: A dataset of 101 human actions classes from videos in the wild. arXiv preprint arXiv:1212.0402, 2012. +[37] Jonathan Stroud, David Ross, Chen Sun, Jia Deng, and Rahul Sukthankar. D3d: Distilled 3d networks for video action recognition. In The IEEE Winter Conference on Applications of Computer Vision, pages 625-634, 2020. +[38] Swathikiran Sudhakaran, Sergio Escalera, and Oswald Lanz. Gate-shift networks for video action recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1102-1111, 2020. +[39] Du Tran, Lubomir Bourdev, Rob Fergus, Lorenzo Torresani, and Manohar Paluri. Learning spatiotemporal features with + +3D convolutional networks. In Proceedings of the IEEE international conference on computer vision, pages 4489-4497, 2015. +[40] Du Tran, Heng Wang, Lorenzo Torresani, Jamie Ray, Yann LeCun, and Manohar Paluri. A closer look at spatiotemporal convolutions for action recognition. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pages 6450-6459, 2018. +[41] Limin Wang, Yuanjun Xiong, Zhe Wang, Yu Qiao, Dahua Lin, Xiaou Tang, and Luc Van Gool. Temporal segment networks: Towards good practices for deep action recognition. In European conference on computer vision, pages 20-36. Springer, 2016. +[42] Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7794-7803, 2018. +[43] Zhengwei Wang, Qi She, Tejo Chalasani, and Aljosa Smolic. Catnet: Class incremental 3d convnets for lifelong egocentric gesture recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 230-231, 2020. +[44] Ceyuan Yang, Yinghao Xu, Jianping Shi, Bo Dai, and Bolei Zhou. Temporal pyramid network for action recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 591-600, 2020. +[45] Jingran Zhang, Fumin Shen, Xing Xu, and Heng Tao Shen. Temporal reasoning graph for activity recognition. IEEE Transactions on Image Processing, 29:5491-5506, 2020. +[46] Yifan Zhang, Congqi Cao, Jian Cheng, and Hanqing Lu. Egogesture: a new dataset and benchmark for egocentric hand gesture recognition. IEEE Transactions on Multimedia, 20(5):1038-1050, 2018. +[47] Bolei Zhou, Alex Andonian, Aude Oliva, and Antonio Torralba. Temporal relational reasoning in videos. In Proceedings of the European Conference on Computer Vision (ECCV), pages 803-818, 2018. +[48] Bolei Zhou, Aditya Khosla, Agata Lapedriza, Aude Oliva, and Antonio Torralba. Learning deep features for discriminative localization. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2921-2929, 2016. +[49] Mohammadreza Zolfaghari, Kamaljeet Singh, and Thomas Brox. Eco: Efficient convolutional network for online video understanding. 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In order to reduce the huge cost of stereo matching at the original resolution, our model only runs dense matching at a very low resolution and uses sparse matching at different higher resolutions to recover the disparity of lost details scale-by-scale. After the decomposition of stereo matching, our model iteratively fuses the sparse and dense disparity maps from adjacent scales with an occlusion-aware mask. A refinement network is also applied to improving the fusion result. Compared with high-performance methods like PSMNet and GANet, our method achieves $10 - 100 \times$ speed increase while obtaining comparable disparity estimation results. + +# 1. Introduction + +Stereo matching aims to estimate the disparity from a pair of images. It has various downstream applications, such as 3D reconstruction, AR, autonomous driving, robot navigation, etc. Despite years of research on stereo matching, many state-of-the-art methods still face the problem of excessive growth in computational cost and memory consumption as the resolution increases. This problem limits the ability of existing methods to process high-resolution images, and restricts the use of stereo matching methods in practical situations with memory/speed constraints. + +In this paper, we propose a decomposition model for stereo matching. Compared with the excessive growth of many state-of-the-art methods, our model reduces the growth rate by several orders of magnitude as shown in Figure 1. The design of our model is inspired by the following two observations: + +(1) It is not necessary to estimate the disparity of all pixels at the highest resolution, such as the disparities on the + +![](images/c7c9668d23598f99e6cea2e7fb3ae57ae6b983559663a4fa8df0938c084a5ac0.jpg) +Figure 1: As the resolution increases, the growth in time cost of state-of-the-art methods on one 1080 Ti GPU with 11GB of memory. The stopped growth of some curves is because the corresponding method cannot run at the expected resolution on the GPU. Compared to GANet [48], our model is 100 times faster. Compared to PSMNet [5], our model achieves almost $15 \times$ speed increase. Compared to DeepPruner [8], our model achieves almost twice the running speed and lower memory consumption. + +wall and the floor. As long as the content is not significantly lost during downsampling, the disparity of most areas can be efficiently estimated at low resolution, and then refined at high resolution. + +(2) It only needs to consider the disparity estimation of some image details that are lost during downsampling. Fortunately, those lost details are sparse, and their stereo matching is also sparse (i.e., the lost details in the left image mostly only match the lost details in the right image). The sparse matching means less time and memory cost compared to the dense matching. + +Based on the first observation, our model only runs dense matching at a very low resolution (such as $20 \times 36$ , called reference resolution), ensuring disparity estimation for most regions that are not lost during downsampling. Based on the second observation, our model uses a series of sparse + +matching, each at a suitable higher resolution, to recover the disparity of lost details scale-by-scale. By decomposing the original stereo matching into a dense matching at the lowest resolution and a series of sparse matching at higher resolutions, the huge cost of original stereo matching can be significantly reduced. + +The specific pipeline of our model is shown in Figure 2. Our model uses a full cost volume and a cost regularization for dense matching at the reference resolution. From the reference resolution, a series of operations are performed scale-by-scale, until the original input resolution is reached. These operations include four modules: detail loss detection, sparse matching, disparity upsampling, and disparity fusion. The corresponding implementation of the four modules are as follows: (1) In the detail loss detection module, the lost image details are learned unsupervised based on the square difference between deep features from adjacent scales. (2) In the sparse matching module, the sparse disparity map is estimated via cross-correlation and soft-max under the guidance of detected lost details. (3) In the disparity upsampling module, the estimated disparity map from the previous scale is upsampled to the resolution at the current scale via content-aware weights. (4) In the disparity fusion module, the results of the disparity upsampling module and sparse matching module are fused via an occlusion-aware soft mask. A refinement network is also used in this module to improve the fused disparity map. + +We analyze the complexity of stereo matching in this paper. For convenience, we define the complexity of matching as the size of the search space [21]. We prove that the complexity of original dense stereo matching grows cubically as the input resolution increases, while the complexity of sparse matching in our model only grows logarithmically. In our model, the complexity of dense matching at the reference resolution is fixed, and independent of the input resolution. At the same time, the three other operations, i.e., detail loss detection, disparity upsampling, and disparity fusion, could be efficiently implemented. + +In the experiment, we compare our model with state-of-the-art methods over the growth in computation cost and memory consumption. The results show that our model reduces the growth rate by several orders of magnitude. We also compare our model with state-of-the-art methods on Scene Flow dataset [23], KITTI 2015 dataset [24, 25, 26], and Middlebury dataset [34]. The results show that our model is comparable to or even better than state-of-the-art methods with much faster running time and much lower memory cost. + +# 2. Related Work + +Stereo Matching has been studied for decades [39, 22, 33]. In the early stage, researchers focus on the analysis of binocular vision and the building of its computation frame + +work [39, 30, 16, 22, 29]. Later, a series of traditional stereo matching approaches are proposed to improve the framework, including local model [2, 13, 45], global model [4, 19, 36] and semi-global model [15, 35]. Recently, deep-learning-based approaches have emerged and play the most important role in stereo matching [47, 23, 17, 5]. Although both traditional methods and deep learning methods have achieved great performance, they still suffer from the problem of excessive growth in computation cost as the resolution increases. + +Traditional Methods. In order to solve the problem, researchers propose many approaches to reduce the size of search space, by either improving the operations in dense matching, or turning for the sparse-to-dense methods. In the first perspective, researchers propose to reduce the complexity of cost aggregation in terms of the size of image [27, 9], matching window [31], or disparity space [28, 9]. The semi-global matching (SGM) [14] is also proposed to approximate the global energy function with pathwise optimizations from all directions. Different from them improving the operations on dense matching, we replace the dense matching at high resolution with sparse matching to reduce the complexity. In the second perspective, researchers mainly focus on the sparse nature in stereo matching [10, 3, 12, 21, 35]. They propose to compute the sparse disparity map over the extracted key points, and then infer the dense disparity map based on the sparse result, like efficient large-scale stereo [10] and local plane sweeps [35]. PatchMatch-based methods [3, 12, 21] are similar to them but mostly generate the sparse result via random initialization. They are based on the assumption that at least one pixel of the areas is initialized with a label close to the ground truth. Different from them only using sparse matching with local information, we use dense matching at the lowest resolution to provide global information and use sparse matching to recover the local details at high resolution. + +Deep Methods In deep learning methods, researchers try to solve the excessive growth in computation cost and memory consumption from two aspects, light-weight network, and improved the computaion with cost volume. In the first aspect, most researchers replace the expensive operations on cost volume with a specially designed module [48, 43, 40, 20]. Some others also improve the whole architecture of network to achieve less computation cost [18, 41, 37]. However, the above methods ignore the influence of cost volume. The cost volume will result in cubical growth of computation cost and memory consumption when resolution increasing. In order to further resolve the problem, researchers propose to improve the computaion with cost volume based on the assumption where most content of the cost volume is redundant. They mainly improve the computaion with cost volume via narrowing the dispar + +ity space based on the initial estimation and then upsample the result from coarse to fine [44, 8, 6, 46, 7, 11]. Among them, DeepPruner [8] achieves great performance. They use the minimum and maximum disparity regressed by CNN to sample fixed size candidate disparities for the matching at a higher resolution. They also design a light-weight architecture for more efficient cost aggregation and regression. However, they ignore the computation of details at high resolution which are lost in low-resolution matching and are difficult to be recovered with a small size of sampling. Different from the above coarse-to-fine methods, our model is coarse+fine. Instead of only depending on the initial estimation at coarse scale to generate the details at fine scale, we preserve the details in the decomposition of stereo matching. Thus, our model could perform the dense matching at a very low resolution to reduce the search space size but without significant information loss. Furthermore, we resolve the problem from a new view and propose a new pipeline for stereo matching where all the above methods could be integrated into each step in our model to build a more powerful stereo matching, which is a good supplement to the current research mainstream. + +# 3. Method + +# 3.1. Multi-Scale Stereo Matching + +Stereo matching is a dense correspondence problem. It is typically modeled as an exhaustive search process between different areas from left and right views with multi-scale analysis which is used to reduce the ambiguity caused by ill-posed areas. In order to better model this process, we recognize the image as a set of areas $\{A_l\}_{l=0}^{l=L}$ where $A_l$ represents all areas at each scale/level $l$ . The exhausting search process is then modeled as + +$$ +D _ {L} = \mathcal {F} (\acute {A} _ {L}, \dot {A} _ {L}, D _ {L - 1}), +$$ + +. + +$$ +D _ {1} = \mathcal {F} \left(\dot {A} _ {1}, \dot {A} _ {1}, D _ {0}\right), \tag {1} +$$ + +$$ +D _ {0} = \mathcal {F} (\dot {A} _ {0}, \dot {A} _ {0}), +$$ + +$$ +\tilde {D} = \phi (D _ {L}, \dots , D _ {0}). +$$ + +$\dot{A}_l$ and $\dot{A}_l$ represent the areas of image from left and right views respectively. $D_l$ is the dense disparity maps estimated at level $l$ or is the cost volume taken as the input to the next level $l + 1$ . $\mathcal{F}(\cdot)$ represents the full matching operation, $\mathcal{F}(\cdot, D_l)$ represents the full matching operation based on $D_l$ . Some methods also contain $\phi(\cdot)$ which represents the fusion of dense disparity maps at different levels. + +The $\mathcal{F}(\cdot)$ , however, has a high complexity. Given $A_{l}$ with resolution of $\mathrm{H}_l\times \mathrm{W}_l$ and disparity space size of $\mathrm{D}_l$ , we define the complexity O of $\mathcal{F}(\cdot)$ at level $l$ as the size of search space: + +$$ +\mathrm {O} _ {l} = \mathrm {W} _ {l} \mathrm {H} _ {l} \mathrm {D} _ {l}. \tag {2} +$$ + +Then, the whole complexity of exhaustive search process is + +$$ +\mathrm {O} = \sum_ {l = 0} ^ {l = L} \mathrm {O} _ {l}, \tag {3} +$$ + +After rewriting Eq. 3, we obtain the following theorem: + +Theorem 1 Supposing $s \in \{2,3,\dots\}$ is the size of upsampling ratio between adjacent levels, $1 < C \leq 8/7$ is a constant value and $\mathcal{O}(\cdot)$ represents the tight upper bound, then the complexity $O$ of exhaustive search process is + +$$ +\mathrm {O} = \mathrm {W} _ {0} \mathrm {H} _ {0} \mathrm {D} _ {0} \mathcal {O} \left(s ^ {3 L} C\right). \tag {4} +$$ + +The theorem 1 reveals the cubic growth of complexity when using exhaustive search on high resolution images. For the specific proof, please refer to the supplementary materials. + +# 3.2. Decomposition Model + +As aforementioned, as long as the content is not lost significantly during downsampling, the disparity of most areas, called coarse-grained areas by us, can be estimated efficiently at low resolution and then refined at high resolution. For the image details that are lost during downsampling, we call them fine-grained areas and their disparities should be estimated at high resolution. Therefore, the image areas $A_{l}$ at level $l$ is decomposed as + +$$ +A _ {l} = \mathrm {C A} _ {l} \cup \mathrm {F A} _ {l}, \tag {5} +$$ + +$$ +\varnothing = \mathrm {C A} _ {l} \cap \mathrm {F A} _ {l}, +$$ + +where $\mathrm{CA}_l$ and $\mathrm{FA}_l$ represents the coarse-grained areas and fine-grained areas at level $l$ respectively. + +As the stereo matching on coarse-grained areas and fine-grained areas are suitable to be carried out at low and high resolution respectively, we decompose the original stereo matching into a full matching at the lowest level and a series of sparse matching at the rest levels, as shown in Figure 2. Our model can be formulated as + +$$ +\hat {D} _ {L} = \hat {\mathcal {F}} (\mathrm {F A} _ {L}, \mathrm {F A} _ {L}), +$$ + +$$ +\vdots \tag {6} +$$ + +$$ +\hat {D} _ {1} = \widehat {\mathcal {F}} (\mathrm {F A} _ {1}, \mathrm {F A} _ {1}), +$$ + +$$ +D _ {0} = \mathcal {F} (\dot {A} _ {0}, \dot {A} _ {0}), +$$ + +$$ +\tilde {D} = \hat {D} _ {L} \cup \dots \cup \hat {D} _ {1} \cup D _ {0}, \tag {7} +$$ + +where $\widehat{\mathcal{F}} (\cdot)$ represents the sparse matching operation, $\hat{D}_l$ is the sparse disparity map estimated at level $l$ , and $\cup$ means the disparity fusion after the disparity upsampling. The fine-grained areas $\mathrm{FA}_l$ will be detected by the detail loss detection module in our model. + +![](images/efb75635cd483ff6a2f01f330a2eb54b40c39b7f4ab8aad2a4749617dafa7a3c.jpg) +Figure 2: Overview of our model. Given a pair of images, we first extract the feature map for the matching at level $l$ . We then run the dense matching at the lowest resolution $l = 0$ and use sparse matching at different higher resolutions $l \geq 1$ . For the computed dense and sparse disparity maps, we fuse them hierarchically to recover the dense disparity map at the original resolution $l = L$ . The fusion is composed of disparity upsampling, disparity fusion, and refinement. $\widehat{\mathbf{w}}$ is the warping operation between left and right view. $\odot$ represents the computation of the square difference between feature maps from adjacent levels. For details please refer to our method part. + +The complexity $\hat{\mathsf{O}}$ of $\widehat{\mathcal{F}} (\cdot)$ is calculated as + +$$ +\hat {\mathrm {O}} _ {l} = \mathrm {W} _ {l} \mathrm {H} _ {l} \mathrm {D} _ {l} r _ {s p a, l} r _ {d i s, l}, \tag {8} +$$ + +where $r_{spa,l}$ is the percentage of the sparse details in the left view that are lost during downsampling, and $r_{dis,l}$ is the percentage of the sparse disparity search space relative to the size $\mathrm{D}_l$ of the full disparity search space in right view. Without loss of generality, we use $r_{spa,l}$ to approximate $r_{dis,l}$ . It is because the stereo matching of the details in the left view is only searched on the details in the right view. And $r_{spa,l}$ represents the percentage of detail pixels in a row, which can approximate the average percentage $r_{dis,l}$ of the pixels to be searched in the full disparity search range. Therefore, the complexity $\hat{\mathcal{O}}$ of $\widehat{\mathcal{F}}(\cdot)$ can be rewritten as + +$$ +\hat {\mathrm {O}} _ {l} = \mathrm {W} _ {l} \mathrm {H} _ {l} \mathrm {D} _ {l} r _ {l} ^ {2}, \tag {9} +$$ + +$$ +r _ {l} = r _ {s p a, l}. +$$ + +After rewriting Eq. 3 with Eq. 9 and Eq. 2, we obtain the following theorem: + +Theorem 2 Supposing $s \in \{2,3,\dots\}$ is the size of upsampling ratio between adjacent levels, $C$ is a constant value and $\mathcal{O}(\cdot)$ represents the tight upper bound, then the com + +plexity $\hat{\mathrm{O}}$ in our model is + +$$ +\hat {\mathrm {O}} = \mathrm {W} _ {0} \mathrm {H} _ {0} \mathrm {D} _ {0} \mathcal {O} (L C), +$$ + +$$ +w h e n r _ {l} \leq \sqrt {C / s ^ {3 l}}. \tag {10} +$$ + +We present a statistical analysis of data to show that the condition in theorem 2 is satisfiable in most time. Specifically, we make statistical analyses according to the content-aware results of our detail loss detection module (see Sec 3.3.1). As shown in Table 1, almost all the data in Scene Flow dataset satisfy the condition $r_{l} \leq \sqrt{C / s^{3l}}$ in each level with a small value of $C$ , which shows the condition of theorem 2 holds in most time. Compared to the exponential growth of the complexity of exhaustive search process shown by the theorem 1, the complexity of stereo matching in our model grows only linearly with the number of levels $L$ . + +# 3.3. Implementation + +As shown in Figure 2, we first use U-Net [32] to obtain deep features $F_{l}$ on each level $l$ for the stereo matching. We then compute the dense disparity map $D_0$ based on dense matching at the lowest resolution $l = 0$ . We also estimate the sparse disparity map $\hat{D}_l$ with sparse matching under the guidance of the detected lost details. We fuse $D_{l - 1}$ and $\hat{D}_l$ + +
Per(%) Level C123
199.8670.0149.79
2100.0099.2792.02
3100.00100.0098.87
4100.00100.0099.74
5100.00100.0099.88
6100.00100.00100.00
+ +Table 1: The statistical result about the percentage of data in SceneFlow dataset that satisfy the condition $r_l \leq \sqrt{C / s^{3l}}$ in each level. + +to compute the dense disparity map $D_{l}$ as the input to the next level or the output of our model. + +# 3.3.1 Decomposed Matching + +Dense Matching. At the lowest level, we follow the previous methods and build a full cost volume for disparity regression [17, 5]. It takes up little computation resources due to the negligible size of search space. We also use cost regularization to rectify the cost volume before the disparity regression with softmax. The cost regularization is composed of eight 3D convolutions all following a batch normalization layer. For the specific architecture please refer to the supplementary materials. + +Detail Loss Detection. We formulate $FA_{l}$ as details that would disappear in the low level. We use a binary mask $M_{FA}$ to represent the positions of lost details, which is computed by a network $\mathcal{F}_{\mathrm{DLD}}$ based on the square difference between $F_{l}$ and upsampled $F_{l - 1}^{\prime}$ : + +$$ +M _ {F A _ {l}} = \mathcal {F} _ {\mathrm {D L D}} \left(\left(F _ {l} - F _ {l - 1} ^ {\prime}\right) ^ {2}; \theta\right), \tag {11} +$$ + +where $\theta$ is the parameter of network. The network is composed of three convolution operations and a sigmoid function, and its learning is guided by an unsupervised loss. The unsupervised loss $\mathcal{L}_l^{\mathrm{DLD}}$ is designed by maximizing the differences between $F_{l}$ and $F_{l - 1}$ on $FA_{l}$ and forcing the sparsity of $FA_{l}$ : + +$$ +\mathcal {L} _ {l} ^ {\mathrm {D L D}} = \left| F A _ {l} \right| - \alpha \frac {\sum_ {(h , w) \in F A _ {l}} \| F _ {l} (h , w) - F _ {l - 1} ^ {\prime} (h , w) \| _ {2}}{\left| F A _ {l} \right|}. \tag {12} +$$ + +Benefiting from unsupervised learning, we do not need additional data annotation for training. + +Sparse Matching. After obtaining the fine-grained areas, our focus turns to how to conduct the sparse matching on the extracted $\{FA_l\}_{l=0}^{l=L}$ . It is not suitable to use cost volume representation, as $FA_l$ is content-aware whose shape and size are dynamic but not fixed. Instead, we opt for a direct computation of the disparity map. Specifically, we compute the cost via cross-correlation: + +$$ +C _ {l} (h, w, d) = < \acute {F} _ {l} (h, w), \dot {F} _ {l} (h, w - d) >, \tag {13} +$$ + +where $\hat{F}_l$ and $\hat{F}_l$ are the deep features from left and right views respectively, $(h,w)\in F^{\prime}A_{l}$ and $(h,w - d)\in FA_{l}$ . We then use softmax to get the probability distribution: + +$$ +P _ {l} (h, w, d) = \frac {\mathrm {e} ^ {C _ {l} (h , w , d) - C _ {l} ^ {m a x} (h , w)}}{\sum_ {d = 0} \mathrm {e} ^ {C _ {l} (h , w , d) - C _ {l} ^ {m a x} (h , w)}}, \tag {14} +$$ + +$$ +C _ {l} ^ {m a x} (h, w) = \max _ {d} C _ {l} (h, w, d). +$$ + +And we regress the sparse disparity map over the computed probability distribution as + +$$ +\hat {D} _ {l} (h, w) = \sum_ {d = 0} P _ {l} (h, w, d) * d. \tag {15} +$$ + +Compared to the full matching, the sparse matching not only reduces the number of points on $\dot{A}_l$ , but also eliminates a lot of redundant matching on $\dot{A}_l$ . As for the specific equation of back propagation, please refer to the supplementary materials. + +# 3.3.2 Fusion + +Disparity Upsampling. After obtaining $D_0$ and $\{\hat{D}_l\}_{l=1}^{l=L}$ , we fuse them hierarchically to compute the final output disparity map at the highest level. At each level, we first up-sample the dense disparity map from previous level $D_{l-1}$ to current level $D_l'$ in a content-aware fashion [38]. The content-aware weights are learned through three convolution operations with the input of the left feature map $\hat{A}_l$ at the current level and the dense disparity map $D_{l-1}$ from the previous level. + +Disparity Fusion. According to Eq. 7, we could model the fusion process as the union of a collection of sets, like the superposition of multiple images, which we call as hard fusion. However, such a hard fusion performs poorly in practice due to the influence of occlusion. The occlusion results in severe matching ambiguity in sparse matching, while fine-grained areas contain many edges that are easy to occur in occlusion. Therefore, we propose to fuse the sparse disparity map $\hat{D}_l$ and the upsampled dense disparity map $D_l'$ via a learned mask, which we call as soft fusion. Specifically, we use a regression network to generate the soft mask $M_l$ . The regression network contains three 2D convolution operations and a sigmoid activation function. The input of regression network is the concatenation of left features $\hat{F}_l$ , upsampled dense disparity map $D_l'$ , sparse disparity map $\hat{D}_l$ , mask of current fine-grained areas $M_{F'A_l}$ and robustness mask of sparse matching $\hat{V}_l$ . The pixel-wise robustness is formulated as the variance in sparse matching: + +$$ +\hat {V} _ {l} (h, w) = \sum_ {d = 0} P _ {l} (h, w, d) * (\hat {D} _ {l} (h, w) - d) ^ {2}, \tag {16} +$$ + +where $(h,w)\in F^{\prime}A_{l}$ and $(h,w - d)\in F^{\prime}A_{l}$ . The generation of soft mask via regression network $\mathcal{F}_{\mathrm{REG}}$ is then + +
Fusion1=1Fusion1=2Fusion1=3EPE
dynamic upsamplingdisparity fusionrefinementdynamic upsamplingdisparity fusionrefinementdynamic upsamplingdisparity fusionrefinement
---------2.104
✓--------2.086
✓✓-------2.039
✓✓✓------1.286
✓✓✓✓-----1.208
✓✓✓✓✓----1.205
✓✓✓✓✓✓---0.954
✓✓✓✓✓✓✓--0.896
✓✓✓✓✓✓✓✓-0.893
✓✓✓✓✓✓✓✓✓0.842
+ +Table 2: The influence of each component in the Fusion step obatined on the Scene Flow dataset. Fusion $l$ represents the Fusion step at level $l$ . + +
EPE Type LevelDense ResultFusion ResultHard FusionSoft Fusion
13.9193.1733.0872.039
24.9654.1341.6241.205
34.2453.9181.0100.893
+ +Table 3: The illustration of upsampled dense result $D_{l}^{\prime}$ and fusion result $\bar{D}_{l}$ on the non-occluded fine-grained areas, and the result from hard fusion and soft fusion. Experiments are conducted on the Scene Flow dataset. + +formulated as + +$$ +M _ {l} = \mathcal {F} _ {\mathrm {R E G}} \left(\operatorname {c a t} \left(\acute {F} _ {l}, D _ {l} ^ {\prime}, \hat {D} _ {l}, M _ {F ^ {\prime} A _ {l}}, \hat {V} _ {l}\right); \theta\right). \tag {17} +$$ + +$\theta$ is the parameter of regression network and $cat(\cdot)$ is the concatenation operation. After obtaining the soft mask $M_{l}$ , we compute the soft fusion of dense and sparse disparity map as + +$$ +\bar {D} _ {l} = D _ {l} ^ {\prime} \left(1 - M _ {l}\right) + \hat {D} _ {l} M _ {l}. \tag {18} +$$ + +Refinement. We further propose a refinement network to improve the sub-pixel accuracy of current dense disparity map $\bar{D}_L$ . Specifically, we use $\bar{D}_L$ to warp the right feature maps. Then, we concatenate the warped right feature maps $\hat{F}_l'$ , left feature maps $\hat{F}_l$ and current disparity map $\bar{D}_l$ to feed into a refinement network $\mathcal{F}_{\mathrm{REF}}$ : + +$$ +D _ {l} = \bar {D} _ {l} + \mathcal {F} _ {\mathrm {R E F}} \left(\operatorname {c a t} \left(\dot {F} _ {l} ^ {\prime}, \dot {F} _ {l}, \bar {D} _ {l}\right); \theta\right). \tag {19} +$$ + +$\theta$ is the parameter of the refinement network, The refinement network contains seven convolution operations. All convolutions are followed by a relu activation function and a batch normalization level, except the last convolution that is only followed by a batch normalization level. + +# 4. Experiment + +In this section, we conduct the most analysis of our model based on the Scene Flow dataset [23], except the + +complexity analysis which is carried out on the high-resolution Middlebury-v3 [34]. We also compare our model with state-of-the-art methods [23, 17, 5, 18, 37, 48, 41, 8, 1, 40, 42] based on Scene Flow [23], KITTI 2015 [24, 25, 26], and Middlebury-v3 [34]. + +We train our model end-to-end using Adam optimization with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ and batch size of 18 on 3 Nvidia 1080Ti GPUs. We set the maximum of disparity as 216 and apply color normalization to each input image during training. For the Scene Flow dataset, we train our model for 20 epochs with a learning rate of 0.001 which is then decayed by half every 7 epochs. For KITTI 2015 dataset, we fine-tune the model on mixed KITTI 2012 and KITTI 2015 training sets for 500 epochs. The initial learning rate is set as 0.001 and is decreased by half every 100 epochs after the 200th epoch. As for Middlebury-v3, we fine-tune the model pre-trained on Scene Flow. The learning rate is set to 0.001 for 300 epochs and then changed to 0.0001 for the rest of 600 epochs. + +# 4.1. Analysis + +# 4.1.1 Complexity Analysis + +We analyze the complexity of our model by comparing the growth rate in computation cost with state-of-the-art methods. In order to obtain the curve of growth rate, we resize the image in Middlebury-v3, like the image named Australia, to obtain a sequence of inputs with different resolutions. We then test the running time of each method with the official code. The testing is conducted on a 1080Ti GPU with Cuda synchronization. As shown in Figure 1, most methods stop working on the high-resolution image due to the unaffordable memory consumption, while our method can still run on the image with $5000 \times 3500$ resolution. The time cost of most state-of-the-art methods also grows exponentially when resolution increasing. Different from them, our model has a very low growth rate of time cost benefiting from our decomposition of stereo matching. Comparing + +![](images/9ddf5b81f8b65488580581e7fec58dee3e2086f9e5ebfc7a244be20a660d9e34.jpg) +Figure 3: The visualization of results from detail loss detection and soft mask. The white areas in the second to last columns represent occlusion. The red points in the third and fourth columns represent the lost details, while the red points in the last two columns represent the learned soft mask. + +
ModelsEPE>3pxTime (ms)Mem. (GB)
GA-Net-15 [48]0.84-4055*6.2*
Bi3D [1]0.73-1302*10.7*
GCNet [17]2.519.34950-
PSMNet [5]1.094.14640*6.8*
Waveletstereo [42]0.844.13270-
AANet [40]0.87-147*1.2*
Deepruner-fast [8]0.97-87*1.9*
DispNetC [23]1.689.3160-
StereoNet [18]1.10-15-
ours0.843.58501.6
+ +to the high-performing methods, GANet [48], our model is 100 times faster. Compared to the PSMNet [5], our model achieves almost $15 \times$ speed increase. As for the DeepPruner [8], we still achieve almost twice faster running speed and better performance on memory consumption, even current implementation using a fixed-size level of decomposition. According to the theorem 2, our model could achieve better speed and memory consumption with a dynamic or larger size of decomposition. + +# 4.1.2 Ablation Study + +We evaluate our model with different configurations to understand the effectiveness/influence of each component in our model. We use bicubic upsampling to upsample the prediction and compute the end-to-end point (EPE) with ground truth. As illustrated in Table 2, the error rate is reduced a little after using content-aware upsampling. The error rate is also improved after fusing the sparse results at each level. However, improvement is little. It is because the + +Table 4: The comparison of algorithms on the Scene Flow dataset. * represents the result obtained on our machine with official code after Cuda synchronization in a unified setting. $EPE$ is the mean absolute disparity error in pixels. $>3px$ is the number of pixels whose predicted disparity is deviated from their ground truth by at least 3 pixels. + +
ModelsNocAllTime (ms)
D1-bgD1-fgD1-allD1-bgD1-fgD1-all
GCNet [17]2.023.122.452.216.162.87900
Bi3D [1]1.793.112.011.953.482.21480
PSMNet [5]1.714.312.141.864.622.32410
GA-Net-15 [48]1.403.371.731.553.821.93360
Waveletstereo [42]2.044.322.422.244.622.63270
HSM [41]1.633.401.921.803.852.14140
HD3S [44]1.563.431.871.703.632.02140
DispNetC [23]4.113.724.054.324.414.3460
Deepruner-fast [8]2.133.432.352.323.912.5960
AANet [40]1.804.932.321.995.392.5560
MADNet [37]3.458.414.273.759.24.6620
StereoNet [18]---4.37.454.8315
ours1.893.532.162.073.872.3750
+ +Table 5: The comparison of algorithms on the KITTI 2015 dataset. D1 metric measures the percentage of disparity outliers that exceed 3 pixels and $5\%$ of its true value. (Note: the time presented here are not tested in a unified setting. For fair comparison, please refer to the Table 4 and Figure 1). + +EPE metric in this table is calculated on the whole spatial space while the sparse result only improves a little area at each level $l$ . Thus, we present the differences between upsampled dense result $D_{l}^{\prime}$ and fusion result $\bar{D}_l$ only on the non-occluded fine-grained areas at each level $l$ . As shown in Table 3, the fusion result $\bar{D}_l$ is better than the dense result $D_{l}^{\prime}$ , which mirrors the necessity of considering the lost details caused by downsampling. Furthermore, we compare the results from hard fusion and soft fusion to illustrate the necessity of considering the occlusion problem. As shown in Table 3, the soft fusion is much better than hard fusion at all levels. Furthermore, we analyze the effectiveness of our refinement network. As shown in Table 2, the performance is significantly improved with the refinement network. + +# 4.1.3 Visualizing Results of Detail Loss Detection + +The goal of detail loss detection is to find the fine-grained areas at each scale. We visualize the learned binary mask to + +![](images/7c49b31488b5393dc5a4beb3a26ec71dded6ce6c00bb79d0316461c97e129ec7.jpg) +Deepruner [8] + +![](images/e6f0476c9f0aa8e9c53b95586a7663d5043b8b8dc3b3dc08e2dc7c0328cfdf80.jpg) +PSMNet [5] + +![](images/2ed5cfd8c506e7da07804f6d603f2f2f426055475c945fd87b2bab9f0ff97c57.jpg) +GA-Net [48] + +![](images/d65436c0ecea3062d73e1dff2ef437f9f4c3a90b574cf64c8b367956493a1e1b.jpg) +AANet [40] + +![](images/f202fc27986217e89ef9dcbe246c356c954cfaadccb7c8f35c63c4f490064216.jpg) +Ours + +![](images/676e915587b9a6998be29e7579c9f5a5643ad8d73ee33692e178f8905c921f78.jpg) + +![](images/26a8c5f299ce6b9aadebe35f941b34bb5107b5fafd665a669def91d5ca6ae97f.jpg) + +![](images/dd934bb42073c83d109422538462fecb1c240530942c5f519aec7a233d8276f0.jpg) + +![](images/73dda46bb7d59595fc616768208092d9ac139d38e1b2246a0fe9d149cb0319e0.jpg) + +![](images/4cba7483463c1caca87d4deeb062e1f647cac6b0c763af4dcc41e33cfe9b80a9.jpg) + +![](images/b67ca4528ad9543e3eab349ae573d46042ec66852b313559c67f1b13b4bf020c.jpg) + +![](images/deac4a5eaf285d71ce86781a1530d7d5b58e1f0173cb416eb035d28e95629db9.jpg) +Figure 4: The visualization of results on Middlebury-v3. + +![](images/bc6b95a3bc10b2be95d428ad4ea230349caf1cf1d1011baef74f428916b2ab90.jpg) + +![](images/5fb84679fc010fd789e879df7475c98a0ee3fe68b88b27dacf61a4d043ec7c71.jpg) + +![](images/d298f28cd64a38a18f297ed5b20271fd714a043ffc85294e74d957dac3d6bf16.jpg) + +understand the efficacy of the detector. As shown in Figure 3, the thin or small objects are detected at a corresponding level $l$ , especially in the blue boxes of the first and third columns. + +# 4.1.4 Visualization of Soft Mask + +We compare the visualization of hard fusion, soft mask, and soft fusion to understand the efficacy of soft fusion. As illustrated in Figure 3, most non-robust points, like the occluded points, are eliminated after soft fusion, especially in the orange boxes. We also find that the average value in soft attention is getting smaller when increasing the resolution. We think it is due to the reduced context of sparse matching, which deserves feature exploration, like dense graph net or transformer for better context learning in sparse matching. + +# 4.2. Benchmark performance + +SceneFlow. Following previous methods [8, 40], we split the state-of-the-art methods into two parts according to the running time whether exceeds $100\mathrm{ms}$ . It also should be noted that the time and memory cost of some methods are obtained on our 1080Ti GPU with corresponding official code after Cuda synchronization for a fair comparison. As shown in Table 4, our method achieves comparable results among all the methods. Comparing to the high-performing method, our model reduces the cost of time and memory by order of magnitude while still achieving comparable results. We also provide qualitative results in supplementary materials to show the estimation of our model in different areas, like thin or small objects and large texture-less areas. + +KITTI 2015. In KITTI 2015 dataset, as shown in Table 5, the time cost of reference methods is obtained from the official declaration, which means the different types of GPU + +and the possibility of Cuda synchronization not being used. As presented in Table 5, our model achieves comparable results and a significant improvement in complexity comparing to the high-performing methods. As for the methods with a running time less than $100\mathrm{ms}$ , we achieve state-of-the-art results. We also provide some visualization in supplementary materials to show the competitive estimation of our model in various scenarios. + +Middlebury-v3. In Middlebury-v3, we estimate the disparities based on the full-resolution inputs when most methods can only afford half resolution. Three examples are visualized in Figure 4 to show the ability of our model on the high-resolution image. For more results please refer to the supplementary materials. + +# 5. Conclusion + +In this paper, we have proposed a decomposition model for stereo matching. Compared with many state-of-the-art methods that face the problem of excessive growth in computational cost as the resolution increases, our model can reduce the growth rate by several orders of magnitude. Through a reference implementation of the modules in our model, we achieved state-of-the-art performance among real-time methods, and comparable results among high-performance methods with much lower cost on time and memory. Our model presents a new pipeline for the research of stereo matching, and state-of-the-art methods could be integrated into each step in our model to build a more powerful stereo matching method in the future. + +# 6. Acknowledgment + +This work was supported by the Natural Science Foundation of China (NSFC) under Grant No. 61773062. + +# References + +[1] Badki. Bi3d: Stereo depth estimation via binary classifications. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1600-1608, 2020. 6, 7 +[2] Birchfield. Depth discontinuities by pixel-to-pixel stereo. International Journal of Computer Vision (IJCV), 35(3):269-293, 1999. 2 +[3] Bleyer. Patchmatch stereo-stereo matching with slanted support windows. In Proceedings of the British Machine Vision Conference (BMVC), volume 11, pages 1-11, 2011. 2 +[4] Boykov. Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 23(11):1222-1239, 2001. 2 +[5] Chang. Pyramid stereo matching network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5410-5418, 2018. 1, 2, 5, 6, 7 +[6] Chen. Point-based multi-view stereo network. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 1538-1547, 2019. 3 +[7] Cheng. Deep stereo using adaptive thin volume representation with uncertainty awareness. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2524-2534, 2020. 3 +[8] Duggal. Deeprunar: Learning efficient stereo matching via differentiable patchmatch. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 4384-4393, 2019. 1, 3, 6, 7, 8 +[9] Falkenhagen. Hierarchical block-based disparity estimation considering neighbourhood constraints. In International Workshop on Snhc and 3D Imaging, pages 115-122, 1997. 2 +[10] Geiger. Efficient large-scale stereo matching. In Proceedings of the Asian Conference on Computer Vision (ACCV), pages 25-38. Springer, 2010. 2 +[11] Gu. Cascade cost volume for high-resolution multi-view stereo and stereo matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2495-2504, 2020. 3 +[12] He. Computing nearest-neighbor fields via propagation-assisted kd-trees. In IEEE Conference on Computer Vision and Pattern Recognition, pages 111–118. IEEE, 2012. 2 +[13] Hirschmüller. Real-time correlation-based stereo vision with reduced border errors. International Journal of Computer Vision (IJCV), 47(1-3):229-246, 2002. 2 +[14] Hirschmuller. Accurate and efficient stereo processing by semi-global matching and mutual information. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), volume 2, pages 807-814. IEEE, 2005. 2 +[15] Hirschmuller. Stereo processing by semiglobal matching and mutual information. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 30(2):328-341, 2008. 2 +[16] Julesz. Foundations of cyclopean perception. 1971. 2 +[17] Kendall. End-to-end learning of geometry and context for deep stereo regression. In Proceedings of the IEEE Interna + +tional Conference on Computer Vision (ICCV), pages 66-75, 2017. 2, 5, 6, 7 +[18] Khamis. Stereonet: Guided hierarchical refinement for real-time edge-aware depth prediction. In Proceedings of the European Conference on Computer Vision (ECCV), pages 573-590, 2018. 2, 6, 7 +[19] Kolmogorov. Computing visual correspondence with occlusions using graph cuts. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), volume 2, pages 508-515. IEEE, 2001. 2 +[20] Liu. A novel recurrent encoder-decoder structure for large-scale multi-view stereo reconstruction from an open aerial dataset. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 6050-6059, 2020. 2 +[21] Lu. Patch match filter: Efficient edge-aware filtering meets randomized search for fast correspondence field estimation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1854-1861, 2013. 2 +[22] Marr. A computational theory of human stereo vision. Proceedings of the Royal Society of London. Series B. Biological Sciences, 204(1156):301-328, 1979. 2 +[23] Mayer. A large dataset to train convolutional networks for disparity. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 4040-4048, 2016. 2, 6, 7 +[24] Menze. Object scene flow for autonomous vehicles. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 3061-3070, 2015. 2, 6 +[25] Moritz Menze, Christian Heipke, and Andreas Geiger. Joint 3d estimation of vehicles and scene flow. In Isprs Workshop on Image Sequence Analysis (ISA), 2015. 2, 6 +[26] Moritz Menze, Christian Heipke, and Andreas Geiger. Object scene flow. *Isprs Journal of Photogrammetry and Remote Sensing (JPRS)*, 2018. 2, 6 +[27] Min. Cost aggregation and occlusion handling with wls in stereo matching. IEEE Transactions on Image Processing (TIP), 17(8):1431-1442, 2008. 2 +[28] Min. A revisit to cost aggregation in stereo matching: How far can we reduce its computational redundancy? In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 1567-1574. IEEE, 2011. 2 +[29] Von Noorden. Binocular vision and ocular motility. Theory and Management of Strabismus, 1990. 2 +[30] Ogle. Researches in binocular vision. 1950. 2 +[31] Richardt. Real-time spatiotemporal stereo matching using the dual-cross-bilateral grid. In Proceedings of the European Conference on Computer Vision (ECCV), pages 510-523. Springer, 2010. 2 +[32] Ronneberger. U-net: Convolutional networks for biomedical image segmentation. In Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 234-241. Springer, 2015. 4 +[33] Scharstein. A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. International Journal of Computer Vision (IJCV), 47(1-3):7-42, 2002. 2 + +[34] Scharstein. High-resolution stereo datasets with subpixel-accurate ground truth. In Proceedings of the German Conference on Pattern Recognition (GCPR), pages 31–42, 2014. 2, 6 +[35] Sinha. Efficient high-resolution stereo matching using local plane sweeps. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1582-1589, 2014. 2 +[36] Sun. Stereo matching using belief propagation. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 25(7):787-800, 2003. 2 +[37] Tonioni. Real-time self-adaptive deep stereo. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 195-204, 2019. 2, 6, 7 +[38] Wang. Carafe: Content-aware reassembly of features. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2019. 5 +[39] Wheatstone. XViii. contributions to the physiology of vision-part the first. on some remarkable. Philosophical Transactions of the Royal Society of London, (128):371-394, 1838. 2 +[40] Xu. Aanet: Adaptive aggregation network for efficient stereo matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1959-1968, 2020. 2, 6, 7, 8 +[41] Yang. Hierarchical deep stereo matching on high-resolution images. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5515-5524, 2019. 2, 6, 7 +[42] Yang. Waveletstereo: Learning wavelet coefficients of disparity map in stereo matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 12885-12894, 2020. 6, 7 +[43] Yao. Recurrent mvsnet for high-resolution multi-view stereo depth inference. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5525-5534, 2019. 2 +[44] Yin. Hierarchical discrete distribution decomposition for match density estimation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 6044-6053, 2019. 3, 7 +[45] Yoon. Adaptive support-weight approach for correspondence search. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 28(4):650-656, 2006. 2 +[46] Yu. Fast-mvsnet: Sparse-to-dense multi-view stereo with learned propagation and gauss-newton refinement. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1949-1958, 2020. 3 +[47] Zbontar. Computing the stereo matching cost with a convolutional neural network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1592-1599, 2015. 2 +[48] Zhang. Ga-net: Guided aggregation net for end-to-end stereo matching. 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The uniform volumetric mesh surrounding the surface mesh is used for prediction, where the red vertices are set to be constraints. b) At inference time, the input is an artist-specified skinned mesh without dynamics. c) Our neural network predicts the dynamic mesh with secondary motion. d) The surface mesh is rendered with textures. + +# Abstract + +Fast and light-weight methods for animating 3D characters are desirable in various applications such as computer games. We present a learning-based approach to enhance skinning-based animations of 3D characters with vivid secondary motion effects. We design a neural network that encodes each local patch of a character simulation mesh where the edges implicitly encode the internal forces between the neighboring vertices. The network emulates the ordinary differential equations of the character dynamics, predicting new vertex positions from the current accelerations, velocities and positions. Being a local method, our network is independent of the mesh topology and generalizes to arbitrarily shaped 3D character meshes at test time. We further represent per-vertex constraints and material properties such as stiffness, enabling us to easily adjust the dynamics in different parts of the mesh. We evaluate our method on various character meshes and complex motion sequences. Our method can be over 30 times more efficient than ground-truth physically based simulation, and outperforms alternative solutions that provide fast approximations. + +# 1. Introduction + +Fast and light-weight methods for animating 3D characters are desirable in various applications including computer games and film visual effects. Traditional skinning-based mesh deformation provides a fast geometric approach but often lacks realistic dynamics. On the other hand, physically-based simulation can add plausible secondary motion to skinned animations, augmenting them with visually realistic and vivid effects, but at the cost of heavy computation. + +Recent research has explored deep learning methods to approximate physically-based simulation in a much more time-efficient manner. While some approaches have focused on accelerating specific parts of the simulation [18, 7, 20], others have proposed end-to-end solutions that predict dynamics directly from mesh based features [1, 11, 11, 25]. While demonstrating impressive results, these methods still have some limitations. Most of them assume a fixed mesh topology and thus need to train different networks for different character meshes. Moreover, in order to avoid the + +computational complexity of training networks on high resolution meshes, some methods operate on reduced subspaces with limited degrees of freedom, leading to low accuracy. + +In this paper, we propose a deep learning approach to predict secondary motion, i.e., the deformable dynamics of given skinned animations of 3D characters. Our method addresses the shortcomings of the recent learning-based approaches by designing a network architecture that can reflect the actual underlying physical process. Specifically, our network models the simulation using a volumetric mesh consisting of uniform tetrahedra surrounding the character mesh, where the mesh edges encode the internal forces that depend on the current state (i.e., displacements, velocities, accelerations), material properties (e.g., stiffness), and constraints on the vertices. Mesh vertices encode the inertia. Motivated by the observation that within a short time instance the secondary dynamics of a vertex is mostly affected by its current state, as well as the internal forces due to its neighbors, our network operates on local patches of the volumetric mesh. In addition to avoiding the computational complexity of encoding high resolution character meshes as large graphs, this also enables our method to be applied to any character mesh, independent of its topology. Finally, our network encodes per-vertex material properties and constraints, giving the user the ability to easily prescribe varying properties to different parts of the mesh to control the dynamic behaviour. + +As a unique benefit of the generalization capability of our model, we demonstrate that it is not necessary to construct a massive training dataset of complex meshes and motions. Instead, we construct our training data from primitive geometries, such as a volumetric mesh of a sphere. Our network trained on this dataset can generate detailed and visually plausible secondary motions on much more complex 3D characters during testing. By assigning randomized motions to the primitives during training, we are able to let the local patches cover a broad motion space, which improves the network's online predictions in unseen scenarios. + +We evaluate our method on various character meshes and complex motion sequences. We demonstrate visually plausible and stable secondary motion while being over 30 times faster than the implicit Euler method commonly used in physically-based simulation. We also provide comparisons to faster methods such as the explicit central differences method and other learning-based approaches that utilize graph convolutional networks. Our method outperforms those approaches both in terms of accuracy and robustness. + +# 2. Related Work + +# 2.1. Physically based simulation methods + +Complementing skinning-based animations with secondary motion is a well-studied problem. Traditional approaches resort to using physically-based simulation [31, 30]. + +However, it is well-known that physically based methods often suffer from computational complexity. Therefore, in the last decade, a series of methods were proposed to accelerate the computation process, including example-based dynamic skinning [26], efficient elasticity calculation [19], formulation of motion equations in the rig subspace [9, 10], and the coupling of the skeleton dynamics and the soft body dynamics [17]. These approaches still have some limitations such as robustness issues due to explicit integration, or unnatural deformation effects due to remeshing, while our method is much more robust in handling various characters and complex motions. + +# 2.2. Learning based methods + +Grzeszczuk et al. [8] presented one of the earliest works that demonstrated the possibility of replacing numerical computations with a neural network. Since then research in this area has advanced, especially in the last few years. While some approaches have presented hybrid solutions where a neural network replaces a particular component of the physically based simulation process, others have presented end-to-end solutions. + +In the context of hybrid approaches, plug-in deep neural networks were applied in combination with the Finite Elements Method (FEM), to help accelerate the simulation. For example, the node-wise NNWarp [18] was proposed to efficiently map the linear nodal displacements to nonlinear ones. Fulton et al.[7] utilized an autoencoder to project the target mesh to a lower dimensional space to increase the computation speed. Similarly, Tan et al. [28] designed a CNN-based network for dimension reduction to accelerate thin-shell deformable simulations. Romero et al. [22] built a data-driven statistical model to kinematically drive the FEM mechanical simulation. Meister et al. [20] explored the use of neural networks to accelerate the time integration step of the Total Lagrangian Explicit Dynamics (TLED) for complex soft tissue deformation simulation. Finally, Deng et al. [6] modeled the force propagation mechanism in their neural networks. Those approaches improved efficiency but at the cost of accuracy and are not friendly to end users who are not familiar with physical techniques. Ours, instead, allows the user to adjust the animation by simply painting the constraints and stiffness properties. + +End-to-end approaches assume the target mesh is provided as input and directly predict the dynamics behaviour. For instance, Bailey et al. [1] enriched the real-time skinning animation by adding the nonlinear deformations learned from film-quality character rigs. The work of Holden et al [11] first trained an autoencoder to reduce the simulation space and then learned to efficiently approximate the dynamics projected to the subspace. Similarly, SoftSMPL [25] modeled the realistic soft-tissue dynamics based on a novel motion descriptor and a neural-network-based recurrent re + +gressor that ran in the nonlinear deformation subspace extracted from an autoencoder. While all these approaches presented impressive results, their main drawback was the assumption of a fixed mesh topology requiring different networks to be trained for different meshes. Our approach, on the other hand, operates at a local patch level and can therefore generalize to different meshes at test time. + +Lately, researchers started to utilize the Graph Convolutional Network (GCN) for simulation tasks due to its advantage in handling topology-free graphs. The GCN encodes the vertex positional information and aggregates the latent features to a certain node by using the propagation rule. For particle-based systems, graphs are constructed based on the local adjacency of the particles at each frame and fed into GCNs [16, 29, 23, 5]. Concurrently, Pfaff et al. [21] proposed a GCN for surface mesh-based simulation. While these GCN models interpret the mesh dynamics prediction as a general spatio-temporal problem, we incorporate physics into the design of our network architecture, e.g. inferring latent embedding for inertia and internal forces, which enables us to achieve more stable and accurate results (Section 4.3). + +# 3. Method + +Given a 3D character and its primary motion sequence obtained using standard linear blend skinning techniques [13], we first construct a volumetric (tetrahedral) mesh and a set of barycentric weights to linearly embed the vertices of the character's surface mesh into the volumetric mesh [14], as shown in Figure 2. Our network operates on the volumetric mesh and predicts the updated vertex positions with deformable dynamics (also called the secondary motion) at each frame given the primary motion, the constraints and the material properties. The updated volumetric mesh vertex positions then drive the original surface mesh via the barycentric embedding, and the surface mesh is used for rendering; such a setup is very common and standard in computer animation. + +We denote the reference tetrahedral mesh and its number of vertices by $X$ and $n$ , respectively. The skinned animation (primary motion) is represented as a set of time-varying positions $\mathbf{x} \in \mathbb{R}^{3n}$ . Similarly, we denote the predicted dynamic mesh by $U$ and its positions by $\mathbf{u} \in \mathbb{R}^{3n}$ . + +Our method additionally encodes mass $\mathbf{m} \in \mathbb{R}^n$ and stiffness $\mathbf{k} \in \mathbb{R}^n$ properties. The stiffness is represented as Young's modulus. By painting different material properties per vertex over the mesh, users can control the dynamic effects, namely the deformation magnitude. + +In contrast to previous works [25, 21] which trained neural networks directly on the surface mesh, we choose to operate on the volumetric mesh for several reasons. First, volumetric meshes provide a more efficient coarse representation and can handle character meshes that consist of multiple disconnected components. For example, in our experiments the "Michelle" character (see Figure 2) consists + +![](images/2e6905aa6cbe43e74adc1ad127ba5310ebefa0e2b4032af4f842c0076754596d.jpg) +Figure 2: The tetrahedral simulation mesh and the embedded surface mesh. The local patch consists of a center vertex and its neighbors, defined as the vertices of the tetrahedra touching the center vertex. + +of $14k$ vertices whereas the corresponding volumetric mesh only has $1k$ vertices. In addition, the "Big Vegas" character mesh (see Figure 1) has eight disconnected components, requiring the artist to build a watertight mesh first if using a method that learns directly on the surface mesh. Furthermore, volumetric meshes not only capture the surface of the character but also the interior, leading to more accurate learning of the internal forces. Finally, we use a uniformly voxelized mesh subdivided into tetrahedra as our volumetric mesh, which enables our method to generalize across character meshes with varying shapes and resolutions. + +Next, we will first explain the motion equations in physically-based simulation and then discuss our method in detail, drawing inspiration from the physical process. + +# 3.1. Physically-based Motion Equations + +In constraint-based physically-based simulation [2], the equations of motion are + +$$ +\mathbf {M} \ddot {\mathbf {u}} + \mathbf {D} \dot {\mathbf {u}} + \mathbf {f} _ {i n t} (\mathbf {u}) = \mathbf {0} \tag {1} +$$ + +subject to $\mathbf{Cu} = \mathbf{S}\mathbf{x}(t)$ + +where $\mathbf{M} \in \mathbb{R}^{3n \times 3n}$ is the diagonal (lumped) mass matrix (as commonly employed in interactive applications), $\mathbf{D}$ is the Rayleigh damping matrix, and $\mathbf{u} \in \mathbb{R}^{3n}$ , $\dot{\mathbf{u}} \in \mathbb{R}^{3n}$ and $\ddot{\mathbf{u}} \in \mathbb{R}^{3n}$ represent the positions, velocities and accelerations, respectively. The quantity $\mathbf{f}_{int}(\mathbf{u})$ represents the internal elastic forces. Secondary dynamics occurs because the constraint part of the mesh "drives" the free part of the mesh. Constraints are specified via the constraint matrix $\mathbf{C}$ and the selection matrix $\mathbf{S}$ . In order to leave room for secondary dynamics for 3D characters, we typically do not constrain all the vertices of the mesh, but only a subset. For example, in the Big Vegas example (see Figure 1), we constrain the legs, the arms and the core inside the torso and head, but + +do not constrain the belly and hair, so that we can generate secondary dynamics in those unconstrained regions. + +One approach to timestep Equation 1 is to use an explicit integrator, such as central differences: + +$$ +\dot {\mathbf {u}} (t + 1) = \dot {\mathbf {u}} (t) + \frac {\ddot {\mathbf {u}} (t) + \ddot {\mathbf {u}} (t + 1)}{2} \Delta t, \tag {2} +$$ + +$$ +\mathbf {u} (t + 1) = \mathbf {u} (t) + \dot {\mathbf {u}} (t) \Delta t + \ddot {\mathbf {u}} (t) \frac {\Delta t ^ {2}}{2}, +$$ + +where $t$ and $t + 1$ denote the state of the mesh in the current and next frames, respectively, and $\Delta t$ is the timestep. While the explicit integration is fast, it suffers from stability issues. Hence, the slower but stable implicit backward Euler integrator is often preferred in physically-based simulation [3]: + +$$ +\dot {\mathbf {u}} (t + 1) = \dot {\mathbf {u}} (t) + \ddot {\mathbf {u}} (t + 1) \Delta t, \tag {3} +$$ + +$$ +\mathbf {u} (t + 1) = \mathbf {u} (t) + \dot {\mathbf {u}} (t + 1) \Delta t. +$$ + +We propose to approximate implicit integration as + +$$ +\begin{array}{l} \dot {\mathbf {u}} (t + 1) = \dot {\mathbf {u}} (t) + \\ f _ {\theta} \left(\mathbf {u} (t), \dot {\mathbf {u}} (t), \ddot {\mathbf {u}} (t), \mathbf {x} (t), \dot {\mathbf {x}} (t), \ddot {\mathbf {x}} (t), \mathbf {m}, \mathbf {k}\right) \Delta t, \\ \end{array} +$$ + +$$ +\mathbf {u} (t + 1) = \mathbf {u} (t) + \dot {\mathbf {u}} (t + 1) \Delta t, \tag {4} +$$ + +where $f$ is a differentiable function constructed as a neural network with learned parameters $\theta$ . + +# 3.2. Network design + +As shown in Equation 1, predicting the secondary dynamics entails solving for $3n$ degrees of freedom for a mesh with $n$ vertices. Hence, directly approximating $f_{\theta}$ in Equation 4 to predict all the degrees of freedom at once would lead to a huge and impractical network, which would furthermore not be applicable to input meshes with varying number of vertices and topologies. Inspired by the intuition that within a very short time moment, the motion of a vertex is mostly affected by its own inertia and the internal forces from its neighboring vertices, we design our network to operate on a local patch instead. As illustrated in Figure 3, the 1-ring local patch consists of one center vertex along with its immediate neighbors in the volumetric mesh. Even though two characters might have very different mesh topologies, as shown in Figure 2, their local patches will often be more similar, boosting the generalization ability of our network. The internal forces are caused by the local stress, and the aggregation of the internal forces acts to pull the vertices to their positions in the reference motion, to reduce the elastic energy. Thus, the knowledge of the per-edge deformation and the per-vertex reference motion are needed for secondary motion prediction. + +![](images/984e5d7a9860d199fb1af2aa8d0696718afc4a1342467a99c3d8850784b4a107.jpg) +Figure 3: The input reference mesh $X$ and the target dynamic mesh $U$ . We draw the meshes in 2D for convenience. + +Hence, we propose to emulate this process as follows: + +$$ +\begin{array}{l} \mathbf {z} _ {i} ^ {\text {i n e r t i a}} = f _ {\alpha} ^ {\text {i n e r t i a}} \left(\mathbf {u} _ {i}, \mathbf {x} _ {i}, k _ {i}, m _ {i}\right), \\ \mathbf {z} _ {i, j} ^ {\text {i n t e r n a l - f o r c e}} = f _ {\beta} ^ {\text {i n t e r n a l - f o r c e}} \left(\mathbf {u} _ {i, j}, \mathbf {x} _ {i, j}, k _ {i}, m _ {i}\right), \tag {5} \\ \ddot {\mathbf {u}} _ {i} = g _ {\gamma} \big (\mathbf {z} _ {i} ^ {\text {i n e r t i a}}, \sum_ {j \in \mathbb {N} _ {i}} \mathbf {z} _ {i, j} ^ {\text {i n t e r n a l - f o r c e}} \big), \\ \end{array} +$$ + +where $f_{\alpha}^{\text{inertia}}$ , $f_{\beta}^{\text{internal\_force}}$ and $g_{\gamma}$ are three different multilayer perceptrons (MLPs) as shown in Figure 4, $\mathbb{N}_i$ are neighboring vertices of $i$ (excluding $i$ ), and the double indices $i, j$ denote the central vertex $i$ and a neighbor $j$ . Quantities $\mathbf{z}_i^{\text{inertia}}$ and $\mathbf{z}_i^{\text{internal\_force}}$ are high dimensional latent vectors that represent an embedding for inertia dynamics and the internal forces from each neighboring vertex, respectively. Perceptron $g_{\gamma}$ receives the concatenation of $\mathbf{z}_i^{\text{inertia}}$ and the sum of $\mathbf{z}_i^{\text{internal\_force}}$ to predict the final acceleration of a vertex $i$ . In practice, for simplicity, we train $g_{\gamma}$ to directly predict $\dot{\mathbf{u}}(t+1)\Delta t = \mathbf{u}(t+1) - \mathbf{u}(t)$ since we assume a fixed timestep of $\Delta t$ in our experiments. + +We implement all the three MLPs with four hidden fully connected layers activated by the Tanh function, and one output layer. During training, we provide the ground truth positions in the dynamic mesh as input. During testing, we provide the predictions of the network as input in a recurrent manner. Next, we discuss the details of these components. + +![](images/c43e5dbae0711588a0331f6d4ca5139291e372b5465471be30475bbccae485a9.jpg) +Figure 4: Our network architecture. + +MLP $f_{\alpha}^{\text {inertia }}$ : This perceptron focuses on the center vertex itself, encoding the "self-inertia" information. That is, the center vertex tends to continue its current motion, driven by both the velocity and acceleration. The input to $f_{\alpha}^{\text {inertia }}$ is the + +position of the center vertex in the last three frames both on the dynamic and skinned mesh, $\mathbf{u}(t),\mathbf{u}(t - 1),\mathbf{u}(t - 2)$ and $\mathbf{x}(t + 1),\mathbf{x}(t),\mathbf{x}(t - 1)$ , as well as its material properties, $k_{i},m_{i},k_{i} / m_{i}$ . The positions are represented in local coordinates with respect to $\mathbf{x}(t)$ , the current position of the center vertex in the reference motion. The positions in the last three frames implicitly encode the velocity and the acceleration. Since we know that the net force applied on the central vertex is divided by its mass in Equation 4 and it is relatively hard for the network to learn multiplication or division, we also include $k_{i} / m_{i}$ explicitly in the input. The hidden layer and output size is 64. + +MLP $f_{\beta}^{\text{internal_force}}$ : For an unconstrained center vertex $i$ , perceptron $f_{\beta}^{\text{internal_force}}$ encodes the "internal forces" contributed by its neighbors. The input to the MLP is similar to $f_{\alpha}^{\text{inertia}}$ , except that we provide information both for the center vertex as well as its neighbors. For each neighboring vertex $j$ , we also provide the constraint information $c_{j}$ ( $c_{j} = 0$ if a free vertex; $c_{j} = 1$ if constrained). Each $f_{\beta}^{\text{internal_force}}$ provides a latent vector for the central vertex. The hidden layer and output size is 128. + +MLP $g_{\gamma}$ : This module receives the concatenated outputs from $f_{\alpha}^{\text{inertia}}$ and the aggregation of $f_{\beta}^{\text{internal_force}}$ , and predicts the final displacement of the central vertex $i$ in the dynamic mesh. The input and hidden layer size is 192. We train the final network with the mean square error loss: + +$$ +l = \frac {1}{n} \sum_ {i} ^ {n} \left\| \dot {\mathbf {u}} _ {i} (t + 1) - \dot {\mathbf {u}} _ {i} ^ {\prime} (t + 1) \right\| _ {2} ^ {2}, \tag {6} +$$ + +where $\dot{\mathbf{u}}_i'(t + 1)$ is the ground truth. We adopted the Adam optimizer for training, with a learning rate starting from 0.0001 along with a decay factor of 0.96 at each epoch. + +# 3.3. Training Primitives + +Because our method operates on local patches, it is not necessary to train it on complex character meshes. In fact, we found that a training dataset constructed by simulating basic primitives, such as a sphere (under various motions and material properties), is sufficient to generalize to various character meshes at test time. Specifically, we generate random motion sequences by prescribing random rigid body motion of a constrained beam-shaped core inside the spherical mesh. The motion of this rigid core excites dynamic deformations in the rest of the sphere volumetric mesh. Each motion sequence starts by applying, to the rigid core, a random acceleration and angular velocity with respect to a random rotation axis. Next, we reverse the acceleration so that the primitive returns back to its starting position, and let the primitive's secondary dynamics oscillate out for a few frames. While the still motions ensure that we cover the cases where local patches are stationary (but there is + +still residual secondary dynamics from primary motion), the random accelerations help to sample a diverse set of motions of local patches as much as possible. Doing so enhances the networks's prediction stability. + +# 4. Experiments + +In this section, we show qualitative and quantitative results of our method, as well as comparisons to other methods. We also run an ablation study to verify why explicitly providing the position information on the reference mesh as input is necessary. + +# 4.1. Dataset and evaluation metrics + +For training, we use a uniform tetrahedral mesh of a sphere. We generate 80 random motion sequences at 24 fps, using the Vega FEM simulator [4, 27]. For each motion sequence, we use seven different material settings. Each motion sequence consists of 456 frames resulting in a total of 255k frames in our training set. + +We evaluate our method on 3D character animations obtained from Adobe's Mixamo dataset [12]. Neither the character meshes nor the primary motion sequences are seen in our training data. We create test cases for five different character meshes as listed in Table 1 and 15 motions in total. The volumetric meshes for the test characters use the same uniform tetrahedron size as our training data. For all the experiments, we report three types of metrics: + +- Single-frame RMSE: We measure the average root-mean-square error (RMSE) between the prediction and the ground truth over all frames, while providing the ground truth positions of the previous frames as input. +- Rollout RMSE: We provide the previous predictions of the network as input to the current frame in a recurrent manner and measure the average RMSE between the prediction and the ground truth over all frames. +- $E_{elastic}$ [min, stdev, max]: We use the concept of elastic energy in physically-based simulation to detect abnormalities in the deformation sequence, or any possible mesh explosions. For each frame, we calculate the elastic energy based on the current mesh displacements with respect to its reference state. We list the min, max as well as the standard deviation (stdev) to show the energy distribution across the animation. + +# 4.2. Analysis of Our Method + +Performance: In Table 1, we show the speed $t_{\text{ours}}$ of our method, as well as that of the ground truth method $t_{\text{GT}}$ and a baseline method $t_{\text{BL}}$ . For each method, we record the time to calculate the dynamic mesh but exclude other components such as initialization, rendering and mesh interpolation. + +We adopted the implicit backward Euler approach (Equation 3) as ground truth and the faster explicit central differ + +ences integration (Equation 2) as the baseline. Both our baseline and ground truth were optimized using the deformable object simulation library, Vega FEM [4, 27], and accelerated using multi-cores via Intel Thread Building Blocks (TBB), with 8 cores for assembling the internal forces and 16 cores for solving the linear system. The experiment platform is with $2.90\mathrm{GHz}$ Intel Xeon(R) CPU E5-2690 (32 GB RAM) which provides for a highly competitive baseline/ground truth implementation. We ran our trained model on a GeForce RTX 2080 graphics card (8 GB RAM). We also tested it on CPU, without any multi-thread acceleration. + +Moreover, we also provide performance results for the same character mesh (Big Vegas) with different voxel resolutions. To handle different resolutions of testing meshes, we resize the volumetric mesh to have the local patch similar to the training data (i.e., the shortest edge length is 0.2). + +
character# vtxtGTtBLtGPUourstCPUours
Big vegas14680.580.0560.0120.017
Kaya14170.520.0520.0120.015
Michelle11050.330.0320.0110.015
Mousey23030.830.0840.0140.020
Ortiz12580.510.0490.0120.015
Big vegas69872.450.320.0320.14
Big vegas107354.030.530.0460.24
Big vegas188518.261.060.0680.42
Big vegas3968424.242.960.140.89
+ +Table 1: The running time (s/frame) of a single step (1/24 second) for the ground truth, the baseline, and our method. + +Results indicate that when ran on GPU (CPU), our method is around 30 ( $\sim 20$ ) times faster than the implicit integrator and 3 ( $\sim 2$ ) times faster than the explicit integrator, per frame. Under an increasing number of vertices, our method has an even more competitive performance. Although the explicit method has comparable speed to our method, the simulation explodes after a few frames. In practice, explicit methods require much smaller time steps, which required additional 100 sub-steps in our experiments, to achieve stable quality. We provide a more detailed report on the speed-stability relationship of explicit integration in the supplementary material. + +Generalization: We train the network on the sphere dataset and achieve a single frame RMSE of 0.0026 on the testing split of this dataset (the sphere has a radius of 2). As listed in Table 2, when tested on characters, our method achieves a single frame RMSE of 0.0067, showing remarkable generalization capability (we note that the shortest edge length on the volumetric character meshes is 0.2). The mean rollout error increases to 0.064 after running the whole sequences due to error accumulation, but elastic energy statistics are still close to the ground truth. From the visualization of the ground truth and our results in Figure 7, we can see that + +although the predicted secondary dynamics slightly deviate from the ground truth, they are still visually plausible. We further plot the rollout prediction RMSE and elastic energy of the Big Vegas character in Figure 5. It can be seen that the prediction error remains under 0.07, and the mean elastic energy of our method is always close to the ground truth for the whole sequence, whereas the baseline method explodes quickly. We provide such rollout prediction plots for all characters and the video results1 in supplemental material. + +![](images/bf31e5dd72c9ff421a95c90680841c3eb00a9b3ad2f7951a03a5613ac8d1e71b.jpg) + +![](images/f6b74e9f28a7abe409e03b511b8e3a4f0a2491ffa209c07f1c4b5f61f0cd0dcb.jpg) +Figure 5: The rollout prediction results of our method and others, tested on the Big Vegas character with 283-frame hip hop dancing motion. + +Non-homogeneous Dynamics: Figure 6 shows how to control the dynamics by painting non-homogeneous material properties over the mesh. Varying stiffness values are painted on the hair and the breast region on the volumetric mesh. For better visualization, we render the material settings across the surface mesh in the figure. We display three different material settings, by assigning different stiffness $k$ values. Larger $k$ means stiffer material, hence the corresponding region exhibits less dynamics. In contrast, the regions with smaller $k$ show significant dynamic effects. This result demonstrates that our method correctly models the effect of material properties while providing an interface for the artist to efficiently adjust the desired dynamic effects. + +Ablation study: To demonstrate that it is necessary to incorporate the reference mesh motion into the input features of + +
Methodssingle framerollout-24rollout-48rollout-all\(E_{elastic}\) [min, stdev, max]
Ground truth\\\\[3.81E3, 4.06E5, 2.60E6]
Our method0.00670.0590.0620.064[4.84E3, 6.51E5, 6.32E6]
Ours w/o ref. motion0.0500.200.3810.09[1.62E4, 6.7E16, 4.7E17]
Baseline\7.26E1209.63E12017.5E120[9.26E0, Nan, 7.22E165]
CFD-GCN [5]0.04041.1770.55110.07[3.96E4, 1.1E22, 1.6E23]
GNS [23]0.0490.220.340.54[1.09E4, 2.0E11, 2.3E10]
MeshGraphNets [21]0.0500.110.434.46[1.69E4, 1.1E15, 1.1E14]
+ +Table 2: The single-frame RMSE, rollout-24, rollout-48 and rollout-all of our method and others tested on all five characters with 15 different motions. The shortest edge length in the test meshes is 0.2. + +![](images/debe0b6d32b85329640d9489861273dafa0c99c8118d6deab87e5561c06686ec.jpg) +Figure 6: Non-homogeneous dynamics, tested on the Michelle character with 122-frame cross-jumps motion. We only show the upper region (see Figure 2 for the full mesh). + +our network, we performed an ablation study. To ensure that the constrained vertices are still driving the dynamic mesh in the absence of the reference information, we update the positions of the constrained vertices based on the reference motion, at the beginning of each iteration. As input to our network architecture, we use the same set of features except the positions on the reference mesh. The results of “Ours w/o ref. motion” in Table 2 and Figure 7 and 5 demonstrate that this version is inferior to our original method, especially when running the network over a long time sequence. This establishes that the reference mesh is indispensable to the quality of the network's approximation. + +# 4.3. Comparison to Previous Work + +As discussed in Section 2, several recent particle-based physics and mesh-based deformation systems utilized graph convolutional networks (GCNs). In this section, we train these network models on the same training set as our method + +and test on our character meshes. + +CFD-GCN [5]: We implemented our version of the CFD-GCN architecture, adopting the convolution kernel of [15]. However, we ignored the remeshing part because we assume that the mesh topology remains fixed when predicting secondary motion. As input, we provide the same information as our method, namely the constraint states of the vertices, the displacements and the material properties. We found that the network structure recommended in the paper resulted in a high training error. We then replaced the originally proposed ReLu activation function with the Tanh activation (as used in our method), which significantly improved the training performance. Even so, as shown in Table 2 and Figure 5, the rollout prediction explodes very quickly. We speculate that although the model aggregates the features from the neighbors to a central vertex via an adjacency matrix, it treats the center and the neighboring vertices equally, whereas in reality, their roles in physically-based simulation are distinct. GNS [23]: The recently proposed GNS [23] architecture is also a graph network designed for particle systems. The model first separately encodes node features and edge features in the graph and then generalizes the GraphNet blocks in [24] to pass messages across the graph. Finally, a decoder is used to extract the prediction target from the GraphNet block output. The original paper embeds the particles in a graph by adding edges between vertices under a given radius threshold. In our implementation, we instead utilized the mesh topology to construct the graph. We used two blocks in the "processor" [23] to achieve a network capacity similar to ours. In contrast to CFD-GCN [5], the GraphNet block can represent the interaction between the nodes and edges more efficiently, resulting in a significant performance improvement in rollout prediction settings. However, we still observe mesh explosions after a few frames, as shown in Figure 7 and in the supplementary video. + +MeshGraphNets [21]: In concurrent work to us, MeshGraphNets [21] were presented for physically-based simulation on a mesh, with an architecture similar to GNS [23]. The Lagrangian cloth system presented in their paper is the most closely related approach to our work. Therefore, we + +![](images/fca5093edbbb0f131bcb897eceb059c72486c8d43e17596eb7f420e422e39123.jpg) +Figure 7: The rollout prediction results of our method and others tested on the Big Vegas character with 283-frame hip hop dancing motion. The baseline cannot be rendered because it explodes. + +followed the input formulation of their example, except that we used the reference mesh to represent the undeformed mesh space as the edge feature. In our implementation, we keep the originally proposed encoders $\epsilon^M$ and $\epsilon^V$ that embed the edge and node features, but exclude the global (world) feature encoder $\epsilon^W$ , because it is not applicable to our problem setting. Similarly, we kept the MLPs $f^M$ and $f^V$ , but removed the $f^W$ inside the graph block. We used 15 graph blocks, as suggested by their paper. The network has 10 times more parameters than ours; 2,333,187 parameters compared to our 237,571 parameters. Training lasted for 11 days, whereas our network was trained in less than a day. + +We report how MeshGraphNets perform on our test character motions in Table 2. The overall average rollout RMSE of MeshGraphNets is worse than GNS [23]. Nevertheless, we note that out of 15 motions, this approach achieved 5 stable rollout predictions without explosions, while GNS [23] failed on all of them. Our method outperforms each of the compared methods with respect to the investigated metrics. + +# 5. Conclusion + +We proposed a Deep Emulator for enhancing skinning-based animations of 3D characters with vivid secondary motion. Our method is inspired by the underlying physi + +cal simulation. Specifically, we train a neural network that operates on a local patch of a volumetric simulation mesh of the character, and predicts the updated vertex positions from the current acceleration, velocity, and positions. Being a local method, our network generalizes across 3D character meshes of arbitrary topology. + +While our method demonstrates plausible secondary dynamics for various 3D characters under complex motions, there are still certain limitations we would like to address in future work. Specifically, we demonstrated that our network trained on a dataset of a volumetric mesh of a sphere can generalize to 3D characters with varying topologies. How + +![](images/4c0824b061f70970b4823d3605389cbb112efc8fe2438a3f328f08c75fcbe1f3.jpg) + +ever, if the local geometric detail of a character is significantly different to those seen during training, e.g., the ears of the mousey character containing many local neighborhood not present in the sphere training data, the quality of our output decreases. One potential avenue for addressing this is to add additional primitive types to training, beyond tetrahedralized spheres. A thorough study on the type of training primitives and motion sequences required to cover the underlying problem domain is an interesting future direction. + +# References + +[1] Stephen W Bailey, Dave Otte, Paul Dilorenzo, and James F O'Brien. Fast and deep deformation approximations. ACM Transactions on Graphics (TOG), 37(4):1-12, 2018. 1, 2 +[2] David Baraff and Andrew Witkin. Physically based modeling: Constrained dynamics. SIGGRAPH 2001 Course Notes: Physically Based Modeling, 2001. 3 +[3] David Baraff and Andrew P. Witkin. Large Steps in Cloth Simulation. In Proc. of ACM SIGGRAPH 98, pages 43-54, July 1998. 4 +[4] Jernej Barbic, Fun Shing Sin, and Daniel Schroeder. Vega FEM Library, 2012. http://www.jernejbarbic.com/vega. 5, 6 +[5] Filipe de Avila Belbute-Peres, Thomas D Economon, and J Zico Kolter. Combining differentiable pde solvers and graph neural networks for fluid flow prediction. In Proceedings of the 37th International Conference on Machine Learning ICML, volume 2020, 2020. 3, 7 +[6] Congyue Deng, Tai-Jiang Mu, and Shi-Min Hu. Alternating convlstm: Learning force propagation with alternate state updates. arXiv preprint arXiv:2006.07818, 2020. 2 +[7] Lawson Fulton, Vismay Modi, David Duvenaud, David IW Levin, and Alec Jacobson. Latent-space dynamics for reduced deformable simulation. In Computer graphics forum, volume 38, pages 379-391, 2019. 1, 2 +[8] Radek Grzeszczuk, Demetri Terzopoulos, and Geoffrey Hinton. Neuroanimator: Fast neural network emulation and control of physics-based models. In Proc. of SIGGRAPH 1998, pages 9-20, 1998. 2 +[9] Fabian Hahn, Sebastian Martin, Bernhard Thomaszewski, Robert Sumner, Stelian Coros, and Markus Gross. Rig-space physics. ACM Trans. on Graphics (TOG), 31(4):1-8, 2012. 2 +[10] Fabian Hahn, Bernhard Thomaszewski, Stelian Coros, Robert W Sumner, and Markus Gross. Efficient simulation of secondary motion in rig-space. In Proc. of Symp. on Computer Animation (SCA), pages 165-171, 2013. 2 +[11] Daniel Holden, Bang Chi Duong, Sayantan Datta, and Derek Nowrouzezahrai. Subspace neural physics: fast data-driven interactive simulation. In Proceedings of the 18th annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pages 1-12, 2019. 1, 2 +[12] Adobe Inc. Mixamo. https://www MIXamo.com. 5 +[13] Alec Jacobson, Zhigang Deng, Ladislav Kavan, and JP Lewis. Skinning: Real-time shape deformation. In ACM SIGGRAPH 2014 Courses, 2014. 3 +[14] Doug L. James, Jernej Barbič, and Christopher D. Twigg. Squashing Cubes: Automating Deformable Model Construction for Graphics. In Proc. of ACM SIGGRAPH Sketches and Applications, Aug. 2004. 3 +[15] Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907, 2016. 7 +[16] Yunzhu Li, Jiajun Wu, Russ Tedrake, Joshua B Tenenbaum, and Antonio Torralba. Learning particle dynamics for manipulating rigid bodies, deformable objects, and fluids. In ICLR, 2019. 3 + +[17] Libin Liu, KangKang Yin, Bin Wang, and Baining Guo. Simulation and control of skeleton-driven soft body characters. ACM Transactions on Graphics (TOG), 32(6):1-8, 2013. 2 +[18] Ran Luo, Tianjia Shao, Huamin Wang, Weiwei Xu, Xiang Chen, Kun Zhou, and Yin Yang. Nnwerp: Neural network-based nonlinear deformation. IEEE Trans. on Visualization and Computer Graphics, 2018. 1, 2 +[19] Aleka McAdams, Yongning Zhu, Andrew Selle, Mark Empey, Rasmus Tamstorf, Joseph Teran, and Eftychios Sifakis. Efficient elasticity for character skinning with contact and collisions. In ACM SIGGRAPH 2011, pages 1-12. 2011. 2 +[20] Felix Meister, Tiziano Passerini, Viorel Mihalef, Ahmet Tuysuzoglu, Andreas Maier, and Tommaso Mansi. Deep learning acceleration of total lagrangian explicit dynamics for soft tissue mechanics. Computer Methods in Applied Mechanics and Engineering, 358:112628, 2020. 1, 2 +[21] Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter W Battaglia. Learning mesh-based simulation with graph networks. arXiv preprint arXiv:2010.03409, 2020. 3, 7 +[22] Cristian Romero, Miguel A. Otaduy, Dan Casas, and Jesus Perez. Modeling and estimation of nonlinear skin mechanics for animated avatars. Computer Graphics Forum (Proc. of Eurographics), 39(2), 2020. 2 +[23] Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter W Battaglia. Learning to simulate complex physics with graph networks. arXiv preprint arXiv:2002.09405, 2020. 3, 7, 8 +[24] Alvaro Sanchez-Gonzalez, Nicolas Heess, Jost Tobias Springenberg, Josh Merel, Martin Riedmiller, Raia Hadsell, and Peter Battaglia. Graph networks as learnable physics engines for inference and control. volume 80 of Proceedings of Machine Learning Research, pages 4470-4479, 2018. 7 +[25] Igor Santesteban, Elena Garces, Miguel A. Otaduy, and Dan Casas. SoftSMPL: Data-driven Modeling of Nonlinear Soft-tissue Dynamics for Parametric Humans. Computer Graphics Forum (Proc. Eurographics), 2020. 1, 2, 3 +[26] Xiaohan Shi, Kun Zhou, Yiying Tong, Mathieu Desbrun, Hujun Bao, and Baining Guo. Example-based dynamic skinning in real time. ACM Trans. on Graphics (TOG), 27(3):1-8, 2008. 2 +[27] Fun Shing Sin, Daniel Schroeder, and Jernej Barbic. Vega: non-linear fem deformable object simulator. In Computer Graphics Forum, volume 32, pages 36-48, 2013. 5, 6 +[28] Qingyang Tan, Zherong Pan, Lin Gao, and Dinesh Manocha. Realtime simulation of thin-shell deformable materials using cnn-based mesh embedding. IEEE Robotics and Automation Letters, 5(2):2325-2332, 2020. 2 +[29] Benjamin Ummenhofer, Lukas Prantl, Nils Thuerey, and Vladlen Koltun. Lagrangian fluid simulation with continuous convolutions. In International Conference on Learning Representations, 2019. 3 +[30] Bohan Wang, Mianlun Zheng, and Jernej Barbič. Adjustable constrained soft-tissue dynamics. Pacific Graphics 2020 and Computer Graphics Forum, 39(7), 2020. 2 +[31] Jiayi Eris Zhang, Seungbae Bang, David I.W. Levin, and Alec Jacobson. Complementary dynamics. 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The key idea is to use dual information, such as spatial and spectral, or local and global features, in a complementary and effective way, and extract more accurate information from current iteration to use for the next iteration. In each DIR iteration, starting from current correspondence, a zoom-in process at each point is used to select well matched anchor pairs by a local mapping distortion criterion. These selected anchor pairs are then used to align spectral features (or other appropriate global features) whose dimension adaptively matches the capacity of the selected anchor pairs. Thanks to the effective combination of complementary information in a data-adaptive way, DIR is not only efficient but also robust to render accurate results within a few iterations. By choosing appropriate dual features, DIR has the flexibility to handle patch and partial matching as well. Our comprehensive experiments on various data sets demonstrate the superiority of DIR over other state-of-the-art methods in terms of both accuracy and efficiency. + +# 1. Introduction + +Nonrigid shape matching is one of the most basic and important tasks in computer vision and shape analysis, e.g., shape registration, comparison, recognition, and retrieval. Different from 2D images, shapes are usually represented as 2-dimensional manifolds embedded in $\mathbb{R}^3$ . Many challenges for nonrigid shape matching come from embedding ambiguities, i.e. shapes sharing the same metric (isometry) or very similar metrics (nearly isometry) can have drastically different xyz-coordinates representations in $\mathbb{R}^3$ . + +To overcome these representation ambiguities, one of the commonly used strategies is to extract features which are isometrically invariant and robust to small perturbations. Along with the idea, many successful and popular approaches are based on spectral geometry [40, 31, + +52, 11, 28, 44]. Theoretically, the Laplace-Beltrami (LB) operator is isometrically invariant. As a generalization of Fourier basis functions from Euclidean domains to manifolds, the eigensystem of LB operator provides complete intrinsic spectral information of the underlying manifold. Moreover, from lower eigen-modes to higher eigen-modes, LB eigenfunctions also provide a multi-scale characterization of the underlying manifold from coarse to fine resolution. Although using spectral geometry removed possible non-rigid embedding ambiguities, new ambiguities emerge in the spectral domain due to non-uniqueness of the LB eigen-system, e.g., sign ambiguity for eigenfunctions, the ambiguity of choosing a basis for the LB eigen-space corresponding to a non-simple LB eigenvalue (due to symmetry), the ambiguity of ordering for close eigenvalues (due to small perturbations). To handle these ambiguities and use spectral features accurately and robustly, a proper linear transformation (a rigid transformation for exact isometry) needs to be found to align the spectral modes between two shapes first. This linear transformation is typically computed through some matching/correlation based on given (prior) correspondence, e.g., landmarks [35, 2, 29]. Moreover, to resolve fine details and acquire accurate correspondence between two shapes, high eigen-modes need to be used. However, the use of higher eigen-modes will not only require more computation costs but, more importantly, can also cause instability with respect to small perturbations. + +To tackle the instability issue of using high eigen-modes directly, one natural multi-scale approach is to start from a correspondence at a coarse scale using a few low modes and iteratively refine the correspondence at a finer scale by adding more higher modes gradually. The main motivation is that the linear transformation (a small matrix) on a coarse scale between two truncated spectral functional spaces spanned by a few low eigen-modes can be determined efficiently and stably from an initial approximate or limited correspondence. Once low eigen-modes are aligned well, an improved correspondence, especially between smooth parts of the two shapes, is likely obtained. The improved correspondence is then used to determine the + +![](images/b07e117e6b6b174bd899a81fe0e6ec25ec6793c6434efbe4dd8705a9af80ac97.jpg) +Figure 1. Top: First row shows examples from SHREC'16 holes, and second row shows examples from SHREC'16 cuts. We map the partial shapes in gray to full shapes in blue. Bottom: Geodesic error on SHREC'16 cuts and holes data set with comparison to other state-of-the-art methods. + +linear transformation for the next iteration which involves more LB eigen-modes. Such a multi-scale idea for shape correspondence has been proposed in [29] for multi-scale registration using rotation-invariant sliced-Wasserstein distance and in [34] as a Zoom-out process. However, for the above straightforward multi-scale approach in the spectral domain, there are two key issues. First, in each iteration, the indiscriminate determination of the linear transformation between the truncated spectral embedding of two shapes using current correspondence of all points, many of which are incorrect, might be problematic. In Theorem 1, we show that the linear transformation between two spectral functional spaces determined using all points from an inaccurate correspondence will most likely lead to errors. These errors could be very significant and can cause either a failure for later refinement or slow convergence shown in the supplementary material. The other issue is the lack of a systematic and data-adaptive way to determine how many eigen-modes can be aligned accurately and stably by the current correspondence. Thus, it is hard to decide the appropriate jump in the number of eigen-modes for the next refinement after each iteration to achieve fast convergence. Previously, an increment of one mode was typically used in Zoom-Out [34], while a prefixed sequence of eigenmodes was proposed in [29] based on the rule of thumb. + +In this work, we propose a simple and efficient dual iterative refinement strategy. This method combines complementary information, such as spatial and spectral, or local and global, to simultaneously refine the correspondence between approximately isometric shapes in an effective way. + +More specifically, spatial matching via local mapping distortion (see Definition 1) is applied point-wisely to choose well-matched correspondence - anchor pairs, at the current stage. Once anchor pairs are selected, they are used to find 1) the maximal dimension of spectral functional space that can be robustly and accurately determined by these anchor pairs based on their distribution, and 2) the linear transformation that aligns the spectral basis at the next scale which will lead to a more refined correspondence at next stage. This remarkable simple strategy addresses the aforementioned two critical issues in previous multi-scale approaches using only spectral matching and allows one to utilize all well-matched pairs from the current step to jump to the next step in an accurate, efficient, stable, and data-adaptive way. We use extensive numerical experiments to show that our simple strategy, DIR, outperforms start-of-the-art model-based methods in terms of both accuracy and efficiency markedly. By choosing appropriate and application-specific dual features, DIR enjoys the flexibility to handle different scenarios, such as raw point clouds, patch and partial matching (as illustrated in Figure 1). We defer a detailed explanation of this Figure in Section 5. + +Contributions. We summarize our main contributions: + +- By combining spatial matching via local mapping distortion and spectral matching via the LB eigen-basis, the proposed DIR goes from coarse to fine resolution stably and effectively in a data-adaptive way which overcomes the main challenges in spectral matching. +- By generalizing this dual refinement strategy to other local and global features such as local mapping distortion and global geodesic distance, DIR handles patch and partial matching. + +The rest of this paper is organized as follows. In Section 2, we provide a brief review of some related work. Then we present our proposed method, DIR, in detail followed by a discussion about a few possible extensions of our method in Section 3. After that, we conduct extensive experiments on various benchmark data sets and compare DIR to other state-of-the-art methods in terms of both accuracy and efficiency in Section 5. We conclude the paper in Section 6. + +# 2. Related work + +Designing effective shape descriptors is crucial for shape registration or correspondence. In general, descriptors can be categorized as pointwise or pairwise. Extrinsic pointwise descriptors [49, 21, 15, 41] are easy to compute but usually not very accurate, especially when a non-rigid transformation is involved. To handle non-rigid transformation, different intrinsic descriptors either in spatial domain, such as geodesics distance signatures [53], heat kernel signatures [47] and wave kernel signatures [4], or in + +spectral domain using the eigensystem of the LB operator [31, 52, 11, 28, 35, 29], are proposed. Then various nearest neighbor searching or linear assignment methods are used in the descriptor space to find the dense point correspondence. For point-wise descriptors in the spectral domain, such as functional map [35], a proper linear transformation is needed to align the spectral basis to remove ambiguities in the eigensystem of LB operator. The determination of the linear transformation itself is typically based on some prior knowledge, e.g., given landmarks, region correspondences, or orientation preserving properties [39], and can be challenging to achieve good accuracy especially when the dimension of the spectral embedding is high, which is needed to resolve fine shape features. On the other hand, spatial domain pointwise descriptors are usually defined smoothly on shapes and that makes it difficult to provide accurate correspondences. Our method aims at tackling these issues raised in aligning shapes using pointwise descriptors. + +Intrinsic pairwise descriptors, such as pairwise geodesic distance [7, 10, 55] and kernel functions [32, 46, 54] have also been proposed for non-rigid shape correspondence problems. Although the matching of pairwise descriptors is stricter and may be more robust and accurate, it requires to solve a quadratic assignment problem (QAP) which is NP-hard. Various methods have been proposed to solve the QAP approximately in a more computational tractable way e.g. sub-sampling [48], coarse-to-fine [56], geodesic distance sparsity enforcement methods [19] and various relaxation approaches [1, 8, 25, 30, 13, 16]. One popular approach is to relax the nonconvex permutation matrix (representing pointwise correspondence) constraint in the QAP to a doubly stochastic matrix (convex) constraint [1, 13]. However, both the pairwise descriptors and the doubly stochastic matrix are dense matrices, which make the relaxed QAP still challenging to solve even for a modest size problem. Recently, a novel local pairwise descriptor and a simple, effective iterative method to solve the resulting quadratic assignment through sparsity control was proposed in [57] for shape correspondence between two approximately isometric surfaces. + +# 3. Dual Iterative Refinement Method + +# 3.1. Functional map + +Spectral geometry is widely used in shape analysis [40, 31, 52, 11, 28, 35, 29, 45, 22]. Leveraging the spectral representation, functional map formalism is introduced in [35] to solve non-rigid shape correspondence problem. It improves earlier point-based spectral methods [23, 24, 33, 36] which directly match the spectral embeddings of shapes. We provide a brief introduction to the concept of functional maps which is used in our multi-scale DIR process. + +Given $(\mathcal{M}_1, g_1)$ as a closed 2-dimensional Riemannian manifold, the LB operator uniquely determines the underlying manifold up to isometry [6]. Eigen-functions of LB operator form an orthonormal basis on the underlying manifold and can be used as intrinsic and multi-scale descriptors for shapes. In discrete setting, the manifold $\mathcal{M}_1$ is usually represented as a triangulated mesh with vertices $\{\mathbf{x}_i\}_{i=1}^n$ . The LB matrix is given by $\mathcal{L}_{\mathcal{M}_1} = \mathcal{A}_1^{-1}\mathcal{W}_1$ [37], where $\mathcal{A}_1$ is the diagonal element area matrix of $\mathcal{M}_1$ and $\mathcal{W}_1$ is the standard cotangent weight matrix. The discrete truncated $k$ -dimensional spectral embedding of $\mathcal{M}_1$ can be expressed as a matrix $\Phi_{\mathcal{M}_1}^k \in \mathbb{R}^{n \times k}$ whose rows are the first $k$ LB eigen-functions evaluated at each point. Similarly, we can define the first $k$ LB eigen-embedding for $\mathcal{M}_2$ as $\Phi_{\mathcal{M}_2}^k$ . + +The key idea of functional map is to lift a shape correspondence $T: \mathcal{M}_1 \to \mathcal{M}_2$ to a linear functional map, between the function spaces $\mathcal{C}(\mathcal{M}_1)$ and $\mathcal{C}(\mathcal{M}_2)$ . The functional map for a given correspondence $T$ can be represented as a linear transformation between two given bases of $\mathcal{C}(\mathcal{M}_1)$ and $\mathcal{C}(\mathcal{M}_2)$ , which becomes a matrix when the shapes are discretized and the bases are truncated. In practice, LB eigen-functions are commonly used as the basis for the function space. For example, given a permutation matrix $\Pi$ representing a point-to-point map $T$ from $\mathcal{M}_1$ to $\mathcal{M}_2$ , the functional map $C$ is defined as: + +$$ +C = \underset {C} {\arg \min } \| \Phi_ {\mathcal {M} _ {1}} C - \Pi \Phi_ {\mathcal {M} _ {2}} \| _ {F} ^ {2} \tag {1} +$$ + +Theoretically, if $\mathcal{M}_1$ and $\mathcal{M}_2$ are isometric, then the corresponding LB eigen-functions are the same up to possible ambiguities caused by sign switch and non-simple eigenvalues, which belong to an orthonormal group. This motivates the following constrained functional map [29] + +$$ +\min _ {C \in \Re} \| \Phi_ {\mathcal {M} _ {1}} C - \Pi \Phi_ {\mathcal {M} _ {2}} \| _ {F} ^ {2} = \operatorname {P r o j} _ {\Re} \left(\Phi_ {\mathcal {M} _ {1}} ^ {\top} \Pi \Phi_ {\mathcal {M} _ {2}}\right) \tag {2} +$$ + +where $\Re = \{C\mid C^{\top}C = Id\}$ denotes the set of orthonormal matrices and the projection to $\Re$ is provided as $\mathrm{Proj}_{\Re}(A) = UV^{\top}$ with the singular value decomposition (SVD) of $A = U\Sigma V^{\top}$ . Since this paper aims at tackling nearly isometric shape matching problem, we adopt (2) which is equivalent to (1) for the isometric case. + +Typically, the functional map is obtained via a least square optimization with various constraints and regularizations, such as preservation of given landmarks, commutativity with LB operator, and sparsity [46, 39]. Once the optimized functional map $C$ is computed, for any $p \in \mathcal{M}$ , the correspondence $T(p)$ can be obtained by solving the following spectral matching problem: + +$$ +T (p) = \underset {q \in \mathcal {M} _ {2}} {\arg \min } \| \Phi_ {\mathcal {M} _ {1}} (p) C - \Phi_ {\mathcal {M} _ {2}} (q) \| _ {F} ^ {2} \tag {3} +$$ + +However, the determination of an accurate functional map $C$ can be difficult when limited prior knowledge or a + +poor correspondence is used. On the one hand, it becomes harder when more eigen-modes are involved since the degrees of freedom of the functional map grow quadratically in terms of the eigen-modes involved and, moreover, high eigen-modes are less computationally stable with respect to perturbations or noises. On the other hand, confining to low eigen-modes limits resolution of the spectral representation and hence the accuracy of shape correspondence. A natural multi-scale idea is to start the functional map from a coarse resolution involving a few low eigen-modes and construct a coarse correspondence $T$ . Then the coarse correspondence is used to help determining the functional map at a finer scale and hence a more refined correspondence. This process can be iterated until a fine enough resolution is achieved. The main motivation is that the functional map at a coarse scale – a small matrix, can be determined efficiently and stably from an initial approximate or limited correspondence, which is then used to improve the correspondence at the next iteration. This strategy leads to iteratively computing (2) and (3), or (1) and (3), which is the key idea proposed in [29] using rotation-invariant sliced Wasserstein distance and in the Zoom-out process [34]. As a crucial component of these iterative refinement methods, the new functional map $C$ is obtained from the current correspondence of all points. Since intermediate correspondence, especially at the beginning, can be quite inaccurate, this naive strategy may lead to significant errors. + +Next, we provide both theoretical evidences on the effect of correspondence error of $C$ in (2). This can be problematic for any iterative refinement procedure based on spectral geometry. Assume we have two perfectly isometric manifolds $\mathcal{M}_1, \mathcal{M}_2$ and their corresponding discrete truncated spectral embeddings $\Phi_{\mathcal{M}_1}$ , $\Phi_{\mathcal{M}_2}$ . Without loss of generality, we assume $\mathrm{Id}$ is the ground truth correspondence between $\mathcal{M}_1$ and $\mathcal{M}_2$ (otherwise, we can shuffle row vectors of $\Phi_{\mathcal{M}_2}$ according to the ground truth correspondence). The ground truth functional map is an orthonormal matrix $C_T \in \Re$ , i.e. $\Phi_{\mathcal{M}_2} = \Phi_{\mathcal{M}_1}C_T$ and $C_T = \operatorname{Proj}_{\Re}(\Phi_{\mathcal{M}_1}^\top \Phi_{\mathcal{M}_2})$ . + +Theorem 1 Given $\Phi_{\mathcal{M}_2} = \Phi_{\mathcal{M}_1}C_T$ with $C_T\in \Re$ , let us assume a one-to-one correspondence $\Pi$ is an inaccurate correspondence which maps a portion of $\Phi_{\mathcal{M}_1}$ accurately to the corresponding part of $\Phi_{\mathcal{M}_2}$ , while the remaining part of $\Pi$ is inaccurate. Without loss of generality, we write $\Phi_{\mathcal{M}_1} = \left( \begin{array}{c}X_1\\ X_2 \end{array} \right)$ and $\Phi_{\mathcal{M}_2} = \left( \begin{array}{c}Y_1\\ Y_2 \end{array} \right)$ where $X_{1},Y_{1}\in$ $\mathbb{R}^{n_1\times k}$ $X_{2}$ $Y_{2}\in \mathbb{R}^{n_{2}\times k}$ and $n_1 + n_2 = n$ . We let $\Pi \Phi_{\mathcal{M}_2} = \binom {Y_1}{\sigma Y_2}$ for a permutation matrix $\sigma \in \mathbb{R}^{n_2\times n_2}$ Let $C_a = \arg \min_{C\in \Re}\| \Phi_{\mathcal{M}_1}C - \Pi \Phi_{\mathcal{M}_2}\| _F^2$ . Then the spectral norm $\| C_a - C_T\| _2 > 0$ with probability at least $1 - \eta$ with $\eta = \sum_{j = 0}^{\lfloor n_2 / 2\rfloor}\frac{1}{2^j j!(n_2 - 2j)!}$ + +Notice that $\eta$ decreases rapidly as $n_2$ grows. For example, when $n_2 = 25$ , $\eta \approx 10^{-12}$ . We provide a detailed proof of this theorem in the supplementary material where we also numerically verify that using points from an inaccurate correspondence may lead to significant errors in the functional map. This can cause failure for iterative refinement. + +Another critical issue for multi-scale approach in the spectral domain is how to iteratively increase the resolution, i.e., the dimension of spectral embedding, in an accurate, stable and data-adaptive way. Most approaches [54, 29, 34] just adopt an empirical or prefixed increasing sequence. + +Motivated from the above difficulties and limitations of iterative refinement approaches in the spectral domain, we propose a dual iterative refinement method that iteratively updates on the spatial and spectral domains. The first key idea is to choose well-matched pairs using local spatial matching from current correspondence, called anchor pairs, and only use them to determine the functional map which helps to construct a much more improved correspondence for the next iteration. In order to choose high-quality anchor pairs from a given correspondence, we zoom in at each corresponding pair and measure local mapping distortion. This step integrates local spatial information in the spectral refinement process. The second key idea is to find the maximal dimension of spectral embedding that can be robustly and accurately determined by these anchor pairs according to their distribution in the spectral domain using singular value analysis on their correlation matrix. + +# 3.2. Local mapping distortion + +In order to choose well-matched anchor pairs, or to filter out bad correspondences, to compute the functional map $C$ more accurately, we use the following local mapping distortion (LMD) introduced in [57] to measure the matching quality of a given correspondence pair and choose those pairs with small LMD. Without relying on any information of the ground truth correspondence, this distortion provides a quantitative measurement to check the accuracy of the map through its continuity and local distance preservation. + +Definition 1 (Local mapping distortion) Let $T: \mathcal{M}_1 \to \mathcal{M}_2$ be a map between two manifolds. For any point $\mathbf{x} \in \mathcal{M}_1$ , consider its $\gamma$ -geodesic ball in $\mathcal{M}_1$ as $\mathcal{B}_{\gamma}(\mathbf{x}) = \{\mathbf{y} \in \mathcal{M}_1 \mid d_{\mathcal{M}_1}(\mathbf{x}, \mathbf{y}) \leq \gamma\}$ . LMD of $T$ at $\mathbf{x}$ is defined as: + +$$ +\mathcal {D} _ {\gamma} (T) (\mathbf {x}) = \frac {1}{| \mathcal {B} _ {\gamma} (\mathbf {x}) |} \int_ {\mathbf {y} \in \mathcal {B} _ {\gamma} (\mathbf {x})} D E _ {T} (\mathbf {x}, \mathbf {y}) d \mathbf {y} \tag {4} +$$ + +where $DE_{T}(\mathbf{x},\mathbf{y}) = |d_{\mathcal{M}_{1}}(\mathbf{x},\mathbf{y}) - d_{\mathcal{M}_{2}}(T(\mathbf{x}),T(\mathbf{y}))| / \gamma$ and $|\mathcal{B}_{\gamma}|$ is the volume of $\mathcal{B}_{\gamma}$ . + +Based on the definition of LMD, it is straightforward to check if $T$ is an isometric map, then $\mathcal{D}_{\gamma}(T)(\mathbf{x}) = 0, \forall \mathbf{x} \in \mathcal{M}_1, \gamma > 0$ . Conversely, if $\mathcal{D}_{\gamma}(T)(\mathbf{x}) = 0, \forall \mathbf{x} \in \mathcal{M}_1$ for + +some $\gamma > 0$ , then $T$ is isometric. Numerically, equation (4) can be approximated by: + +$$ +\mathcal {D} _ {\gamma} (T) \left(\mathbf {x} _ {i}\right) \approx \frac {\sum_ {\mathbf {x} _ {j} \in \mathcal {B} _ {\gamma} \left(\mathbf {x} _ {i}\right)} \mathcal {A} _ {1} (j) D E _ {T} \left(\mathbf {x} _ {i} , \mathbf {x} _ {j}\right)}{\left(\sum_ {\mathbf {x} _ {j} \in \mathcal {B} _ {\gamma} \left(\mathbf {x} _ {i}\right)} \mathcal {A} _ {1} (j)\right)} \tag {5} +$$ + +where $\mathcal{A}_1$ is the area element of the mesh representing $\mathcal{M}_1$ . By normalizing the distance with respect to $\gamma$ , LMD is ro + +![](images/1b301c8490d3292a43517cbd4397522639bba96ae5064f6cba5d0756bd4cc3c9.jpg) +Figure 2. LMD on ground truth correspondence. + +bust to global scaling as well as local sampling variation. Figure 2 shows that, for the ground truth correspondence, LMD is very small almost everywhere except in regions where non-isometric distortion is large. Hence the proposed LMD also serves as a good unsupervised error metric when ground truth is not available. + +# 3.3. Our Method + +We first precompute $K$ leading LB eigenfunctions for each shape. Here $K$ can be determined by computation cost limitation, the noise level in the data, or desired accuracy of the correspondence. In any case, it should not exceed what the mesh resolution can support for the discretized shape, i.e., a few mesh points are needed in each nodal domain. + +Our method can start with an initial correspondence provided by SHOT [49] based on extrinsic point-wise features, or a few given landmarks used as initial anchor pairs which can be fixed or updated in later refinement, or by any other (fast but not necessarily very accurate) methods. Then we start DIR which includes the following three simple steps: ① Choose anchor pairs from current correspondence using LMD criterion; ② Determine the spectral dimension and the corresponding functional map based on the selected anchor pairs; ③ Update the correspondence using the current functional map. In addition, we enforce two stopping criteria, the total number of iterations and the spectral dimension supported by anchor pairs reaches $K$ , whichever is satisfied first. Here are more detailed descriptions of each step. + +Step 1: Selecting anchor pairs. By setting a proper LMD threshold $\epsilon$ , the set of pairs $\{(x_{\ell}, T(x_{\ell})) | \mathcal{D}_{\gamma}(T)(\mathbf{x}_{\ell}) < \epsilon\}$ are selected as anchor pairs from the current correspondence which will be used to guide the next refinements. It is important to note that both the threshold $\epsilon$ and anchor pairs are updated in later refinement. By decreasing $\epsilon$ with iterations, the quality of anchor pairs is also improved. + +Step 2: There are two components described as follows. + +(1) Determining the proper spectral dimension based on anchor pairs. Given a set of anchor pairs, an important + +question is to find a proper spectral dimension that can be determined accurately and stably according to the distribution of the anchor pairs in the spectral embedding. Due to possible degeneracy of the distribution, the dimension can be quite smaller than the number of anchor pairs. We use singular value decomposition (SVD) [50], a.k.a principal component analysis, to find the dimension well expanded by a set of anchor pairs in spectral domain. + +$$ +U \Sigma V ^ {\top} = \Phi_ {\mathcal {M} _ {1}} ^ {K} \left(\left\{x _ {\ell} \right\} _ {\ell = 1} ^ {m}\right) ^ {\top} \Phi_ {\mathcal {M} _ {2}} ^ {K} \left(\left\{T \left(x _ {\ell}\right) \right\} _ {\ell = 1} ^ {m}\right). \tag {6} +$$ + +We threshold the singular values to determine the proper dimension. One can use a simple thresholding strategy. In our implementation, we adopt a normalization strategy to make the threshold adaptive to the data and noise level. After normalizing all singular values by the mean of 10 largest singular values, the dimension cut is set at where the sum of ten consecutive normalized singular values is smaller than a threshold (0.1 for all our tests). + +(2) Computing functional map based on anchor pairs. Once the proper spectral dimension, $k$ , is determined by the selected anchor pairs $\{(x_{\ell},T(x_{\ell})\mid \ell = 1,\dots ,m\}$ , we compute the functional map for $k$ dimensional spectral embedding only based on the anchor pairs as follows: + +$$ +\begin{array}{l} C = \underset {C \in \Re} {\arg \min } \sum_ {\ell = 1} ^ {m} \| \Phi_ {\mathcal {M} _ {1}} ^ {k} (x _ {\ell}) C - \Phi_ {\mathcal {M} _ {2}} ^ {k} (T (x _ {\ell})) \| _ {F} ^ {2} \tag {7} \\ = \operatorname {P r o j} _ {\Re} \left(\left(\Phi_ {\mathcal {M} _ {1}} ^ {k} (\{x _ {\ell} \} _ {\ell})\right) ^ {\top} \Phi_ {\mathcal {M} _ {2}} ^ {k} (\{T (x _ {\ell}) \} _ {\ell})\right) \\ \end{array} +$$ + +This restricted version to compute a functional map minimizes possible corruption from inaccurate correspondence and leads to a more accurate estimation of the functional map as discussed in the Section 3.1 and supplementary material. Meanwhile, it also reduces the computation cost. + +Step 3: Construct the new correspondence. Using the functional map computed from selected anchor pairs in the properly enlarged spectral embedding space, a refined correspondence is constructed by solving the assignment problem (3), where a KNN search method is applied. + +We summarize the full procedure in Algorithm 1. Computation complexity The complexity for computing $K$ leading eigen-vectors of a $n \times n$ sparse matrix corresponding to the discretized LB operator is $O(Kn\log n)$ . The complexity for checking LMD is $O(n)$ since geodesic distance is only computed in a fixed neighborhood, e.g., first ring or second ring, at each point. To compute the functional map, the complexity of matrix multiplication is at most $O(nK^2)$ and SVD decomposition is at most $O(K^3)$ since the number of anchor pairs is at most $n$ and the spectral dimension $k$ is at most $K$ which is prefixed and far less than $n$ . KNN search used to solve Equation (3) has a complexity of $O(n\log (n))$ [51]. Hence, our method is of complexity $O(n\log (n))$ altogether. It is still $O(n\log (n))$ using + +Algorithm 1: Dual Iterative Refinement (DIR) +while $i\leq N$ or $k_{i}\leq K$ do +input An initial correspondence, $\Phi_{\mathcal{M}_1}^K$ and $\Phi_{\mathcal{M}_2}^K$ (e.g. $K$ leading LB eigenfunctions), LMD error $\{\epsilon_i\}_{i = 1}^N$ thresholds and the maximum iteration $N$ . + +1. Find anchor pairs $\{(x_{\ell},T(x_{\ell}))\mid \mathcal{D}_{\gamma}(T)(x_{\ell}) < \epsilon_i\}_{\ell = 1}^{m_i}$ via LMD criterion from current correspondence $T$ + +2. Find spectral dimension $k_{i}$ from SVD of $\Phi_{\mathcal{M}_1}^K (\{x_\ell \}_\ell)^\top \Phi_{\mathcal{M}_2}^K (T(\{x_\ell \}_\ell))$ + +3. Update the functional map $C = \mathrm{Proj}_{\Re}\left(\left(\Phi_{\mathcal{M}_1}^{k_i}(\{x_\ell \}_\ell)\right)^\top \Phi_{\mathcal{M}_2}^{k_i}(\{T(x_\ell)\}_\ell)\right)$ + +4. Update the correspondence (for all $p \in \mathcal{M}_1$ ) + +$T(p) = \arg \min_{q}\| \Phi_{\mathcal{M}_1}^{k_i}(p,:)C - \Phi_{\mathcal{M}_2}^{k_i}(q,:)\|^2.$ + +end + +other global features such as geodesic distance to anchor points since we limit the maximal number of anchor points (as the number of LB eigen-functions). The complexity of computing geodesic distance and solving the resulting assignment problem is still $O(n \log(n))$ . + +# 4. Discussion + +In this section, we discuss other possible extensions of our approach and a few specific applications. + +Combination of local and global features. For shape correspondence problems, an efficient and robust approach should use both local and global features. So far we have mainly talked about using spatial and spectral features, which are perfectly complementary in the sense of local and global information. Anchor pair selection by the LMD criterion is based on local spatial features while the spectral features are global. We would like to point out that the proposed strategy of DIR process can be extended to other combinations of appropriate local and global features in different applications. For examples, one may alternatively use Heat Kernel Signature [12], Wave Kernel Signature [4] or Geodesic Distance Signature (GDS) [53] as global features. For shapes with holes and boundaries, we choose GDS which is less sensitive to local mesh distortions and boundaries for most interior points. However, if accurate spectral information is available, taking advantage of the multi-scale representation in spectral embedding leads to better accuracy and efficiency according to our tests. + +DIR with limited initial landmarks. In our previous discussion, the first collection of anchor pairs is selected from a given initial correspondence such as the one obtained from comparing SHOT features. Our method does enjoy the flexibility to incorporate given landmarks. This is applauded in applications like shape matching in morphological stud + +ies in medical imaging where landmarks could be annotated based on specific tasks [20]. Once a few human-annotated and required landmarks are given, which are taken as the initial anchor pairs and fixed in later iterations, DIR will converge to a stable solution. The fewer landmarks are provided, the more iterations are usually needed. The final convergence performance of our numerical tests, as shown in Figure 6, indicates that DIR can provide accurate correspondence based on only four landmarks and it is stable with respect to different initialization. + +Matching of point clouds without mesh. In real applications, point clouds with well-constructed global triangulation are usually hard to obtain. For point clouds without global mesh, we use the local mesh method to compute the LB eigenvalues and LMD [27, 57]. DIR works well on matching raw point clouds as shown in section 5. + +Patch/partial matching. Patch/partial matching often comes with difficulties due to artificial boundaries, different sizes and topological perturbations. Spectral information is either unavailable or unreliable to use. However, LMD is not affected by the above difficulties at interior points. By replacing spectral features with geodesic distance to anchor points, which is global and less sensitive to the above difficulties for most interior points, DIR can handle patch or partial matching well as shown in our numerical experiments. + +# 5. Experiments + +In this section, we conduct comprehensive experiments to evaluate the performance of our method on various benchmark data sets. In all experiments, no pre-processing, such as obtaining a low resolution model or pre-computing the geodesic distance matrix, is required in our algorithm. Raw point clouds (with or without meshes) are directly used. In our comparisons, all geodesic errors from existing methods are obtained from the associated error curve data appeared in the papers. Computation using ZoomOut is produced from the code on GitHub shared by the authors [34]. All experiments using our methods are conducted in Matlab with 16GB RAM and Intel i7-6800k CPU. + +Error Metric. Suppose the constructed correspondence maps $\mathbf{x} \in \mathcal{M}_1$ to $\mathbf{y} \in \mathcal{M}_2$ while the true correspondence maps $\mathbf{x}$ to $\mathbf{y}^*$ . We measure the quality of our results by computing the geodesic error defined as $e(x) = \frac{d_{\mathcal{M}_2}(y, y^*)}{diam(\mathcal{M}_2)}$ , where $diam(\mathcal{M}_2)$ is the geodesic diameter of $\mathcal{M}_2$ . + +Hyperparameters. We use the second ring neighborhood for LMD criterion; maximum iteration number is 10 with the LMD threshold as [0.26, 0.22, 0.18, 0.14, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]. The initial correspondence is given by the KNN search result based on SHOT features [49]. These hyperparameters, + +especially the LMD threshold, are not sensitive to different data sets. We use the same hyperparameters on TOSCA and SCAPE data sets. For SHREC'16 and patch matching, a maximum of 800 anchor pairs serve as reference points for computing geodesic features. + +TOSCA [9], SCAPE [3]. TOSCA data set consists of 76 shapes in 8 different categories (human and animal shapes) with vertex numbers ranging from 4k to 50k. We present the results of our method using mesh structures with the maximal spectral dimension as 1000 and 500 respectively. We also apply our method using only point clouds (no mesh) with the maximal spectral dimension as 1000 (using local mesh method [27]). We perform the same experiments on SCAPE data set which has 72 shapes (12,500 vertices for each) of the same person with different poses. + +In Figure 3, we compare our method with the following methods: Blended [26], Best Conformal [26], Smooth Shells [18], Kernel Marching [54], SEQA [57], RSWD [29], ZoomOut [34], Divergence-Free Shape Interpolation [17], SRFM [38] and BCICP [39]. Our method with 1000 spectral basis outperforms all methods, our method with 500 spectral basis outperforms almost all methods, and our method on purely point cloud inputs still achieves good performance. Moreover, the run time of our method DIR is also significantly less than other methods (see Table 1). + +Table 1 indicates the computation efficiency of our methods by showing the average run time on several examples from TOSCA including shapes with vertices ranging from $4\mathrm{k}$ to $50\mathrm{k}$ . The reported time of our method counts in all steps including the computation of LB eigenfunctions. As discussed in Section 3.3, the complexity of our method is $O(n\log (n))$ . But in practice, when computing shapes with more than 20,000 vertices, our computer suffers a computation speed slow-down from the vast RAM usage because of our limited RAM capacity. Hence, for Cat and David shape from TOSCA, the run time is higher than expected. Most state-of-the-art approaches have a computation complexity of $O(n^{2})$ and do not report run time for shapes over 10,000 vertices. Our method is very efficient compared with state-of-the-art methods which report computation time. + +
ModelWolfCentaurHorseCatDavid
Number of Vertices434415768192482789452565
SEQA (s)595318019291681
Kernel Matching (s)60NANANANA
ZoomOut(3-150 spectral basis) (s)2527744912674312
Consistent Shape Matching (s)483NA21183299NA
Our Method with 1000 spectral basis (s)361441914741774
Our Method with 500 spectral basis (s)191061313301301
+ +Table 1. Average run time for shapes from TOSCA comparing with SEQA [57], ZoomOut [34], Consistent Shape Matching [5] (without including precomputation time for the geodesic distance matrix) and Kernel Matching [54]. + +SHREC'16 [14] SHREC'16 Partial Correspondence + +![](images/9a80d0a9cd10537ff9a9e47805328635de7b031b715424382675d2bd2ed238fd.jpg) + +![](images/10eefe7d9916044f51f3554339d92867416c51ea4eb440fa6c8e26209b8f5b02.jpg) +Figure 3. Geodesic error on the TOSCA and SCAPE data sets with comparison to other methods. + +benchmark data set consists of 8 types of isometric human or animal shapes in different poses with regular 'cuts' and irregular 'holes'. We test our method by matching each partial shape to the corresponding full shape. Since spectral basis is sensitive to mesh 'cuts' and 'holes', we use geodesic distance to anchor points as global features. We still use SHOT for the initialization. In Figure 1, we compare our method with ZoomOut [34], Partial Functional Maps [42] and Random Forests [43]. The results show that our method is quite flexible and robust to handle shape matching in different scenarios. It significantly outperforms other state-of-the-art methods and achieves the highest accuracy on this data set. + +Patch Matching. Since there is no standard data set for patch matching, we report several experiments using patches cut from TOSCA data set. The first case contains two examples with boundaries, different sizes (partial patching) and topological changes simultaneously. In the first example, we take a portion of an arm (finger tips also removed) from one of two nearly isometric centaur shapes, and then map the partial arm onto the other entire centaur. In the second example, we map a body patch onto the whole shape. The original centaur is a closed surface with no holes, while the arm and the body patch are not closed and have holes and boundaries. Our method performs very well + +even for this challenging example as shown in Figure 4. + +The second case is matching two patches containing both overlap and non-overlap parts. We match an arm without the hand to a portion of an arm with the hand, where the forearm is the common part. Since there is no correspondence between the non-overlap parts, a post LMD test is added to prune out those points. The result is shown in Figure 5. Again our method performs quite well. These experiments indicate that our method is robust to size differences, artificial boundaries and topological changes. + +![](images/5ba71464949142c0582cd02e173a32311d138cd215caf2ee6f7a14d82eea3dcb.jpg) +Figure 4. Partial matching between body parts in the second column and the entire body. The first column: the entire centaurs with the ground truth color map (non-blue area). Extra points are colored in blue. Removed finger tips are highlighted by red circles. The third and fourth columns: the color map of a result using SHOT and our method, respectively. + +![](images/f251576d54002fb6c3b1cd997ddd2b80bb0b4439173bb7a4f3770d480097ea1a.jpg) +Figure 5. Patch matching. From left to right: the source patch (with the ground truth color map in the non-blue area and extra points colored in blue), the target patch, mapping result using SHOT and mapping result using our method. Blue colored regions in columns three and four indicate points not passing the post LMD test. + +Experiments Using Limited Landmarks. We select 4 pairs of centaur shapes from TOSCA, initialize our method with different numbers of randomly chosen landmark pairs (without using SHOT for initialization) and then plot the average geodesic error curve. These landmark pairs are fixed and always belong to our selected anchors pairs in later iterations. After different number of iterations, the final performance is illustrated in Figure 6. Even with four initial random landmarks, the performance is excellent although more iterations are needed. It shows stability and robustness of our method with respect to initial correspondences. + +Growth of Anchor Pairs and Spectral Dimensions. One key feature of our method is the selection of well matched pairs used to determine spectral dimension and the corresponding functional map at next iteration in an automatic + +![](images/9e8eba443e2df479f41d5150bc48565695fb113e71b6862386a7689fecd510b6.jpg) +Figure 6. Average performance of our method on several pairs of centaur shapes from TOSCA (blue centaur map to gray centaurs), given different numbers of initial random annotated landmarks. + +and data-adaptive way. A steady growth and improvement (by decreasing the mapping distortion threshold with iterations) of anchor pairs (updated in each iteration) means a steady growth of the spectral dimension and increase of resolution which leads to an effective and fast refinement of the correspondence. The left image in Figure 7 shows the average spectral dimensions for several classes of shapes from TOSCA or SPACE data set. The right image in Figure 7 shows the growth pattern of anchor pairs. These indicate that our method can extract anchor pairs and increase spectral resolution in a steady and efficient way. + +![](images/afe3e59f09e9fe219e7ced9535f98ab169e80785059549e6fab8a04f2fd5eae1.jpg) +Figure 7. Left plot: The average spectral dimension (with a maximal number of LB eigenfunctions set to 1000) for cat, horse, centaur class from TOSCA and human from SCAPE at each iteration. Right figure: Selected anchor pairs (color-coded in red) during iterations of finding the correspondence between the gray centaur and the blue one. The anchor pairs detected at iteration 1 are directly from matching SHOT descriptors. + +# 6. Conclusion + +We propose a simple and efficient iterative refinement strategy utilizing dual features, spatial and spectral or local and global. By only relying on selected well-matched pairs to guide the next refinement, our proposed method combines complementary information in an optimal and data-adaptive way. Our method shows superior performance on extensive tests compared to other state-of-the-arts methods in terms of accuracy, efficiency and stability. + +# Acknowledgement + +R. Lai's research is supported in part by an NSF Career Award DMS-1752934. H. Zhao's research is supported in part by DMS-2048877 and DMS-2012860. + +# References + +[1] Yonathan Aflalo, Alexander Bronstein, and Ron Kimmel. On convex relaxation of graph isomorphism. Proceedings of the National Academy of Sciences, 112(10):2942-2947, 2015. +[2] Yonathan Aflalo, Anastasia Dubrovina, and Ron Kimmel. Spectral generalized multi-dimensional scaling. International Journal of Computer Vision, 118(3):380-392, 2016. +[3] Dragomir Anguelov, Praveen Srinivasan, Hoi-Cheung Pang, Daphne Koller, Sebastian Thrun, and James Davis. The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces. In Advances in neural information processing systems, pages 33-40, 2005. +[4] Mathieu Aubry, Ulrich Schlickewei, and Daniel Cremers. The wave kernel signature: A quantum mechanical approach to shape analysis. In Computer Vision Workshops (ICCV Workshops), 2011 IEEE International Conference on, pages 1626-1633. IEEE, 2011. +[5] Omri Azencot, Anastasia Dubrovina, and Leonidas Guibas. Consistent shape matching via coupled optimization. In Computer Graphics Forum, volume 38, pages 13-25. Wiley Online Library, 2019. +[6] Pierre Bérard, Gérard Besson, and Sylvain Gallot. Embedding riemannian manifolds by their heat kernel. Geometric & Functional Analysis GAFA, 4(4):373-398, 1994. +[7] Alex Bronstein, Michael Bronstein, and Ron Kimmel. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proceedings of the National Academy of Sciences, 103(5):1168-1172, 2006. +[8] Alexander M Bronstein, Michael M Bronstein, and Ron Kimmel. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proceedings of the National Academy of Sciences, 103(5):1168-1172, 2006. +[9] Alexander M Bronstein, Michael M Bronstein, and Ron Kimmel. Numerical geometry of non-rigid shapes. Springer Science & Business Media, 2008. +[10] Alexander M Bronstein, Michael M Bronstein, Ron Kimmel, Mona Mahmoudi, and Guillermo Sapiro. A gromov-hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. International Journal of Computer Vision, 89(2-3):266-286, 2010. +[11] M. M. Bronstein and I. Kokkinos. Scale-invariant heat kernel signatures for non-rigid shape recognition. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1704-1711, 2010. +[12] Michael M Bronstein and Iasonas Kokkinos. Scale-invariant heat kernel signatures for non-rigid shape recognition. In 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 1704-1711. IEEE, 2010. +[13] Qifeng Chen and Vladlen Koltun. Robust nonrigid registration by convex optimization. In Proceedings of the IEEE International Conference on Computer Vision, pages 2039-2047, 2015. +[14] Luca Cosmo, Emanuele Rodolà, Jonathan Masci, Andrea Torsello, and Michael Bronstein. Matching deformable ob- + +jects in clutter. In 3D Vision (3DV), 2016 Fourth International Conference on, pages 1-10. IEEE, 2016. +[15] Anastasia Dubrovina and Ron Kimmel. Approximately isometric shape correspondence by matching pointwise spectral features and global geodesic structures. Advances in Adaptive Data Analysis, 3(01n02):203-228, 2011. +[16] Nadav Dym, Haggai Maron, and Yaron Lipman. $\mathrm{Ds} + +$ : A flexible, scalable and provably tight relaxation for matching problems. arXiv preprint arXiv:1705.06148, 2017. +[17] Marvin Eisenberger, Zorah Lähner, and Daniel Cremers. Divergence-free shape interpolation and correspondence. arXiv preprint arXiv:1806.10417, 2018. +[18] Marvin Eisenberger, Zorah Lahner, and Daniel Cremers. Smooth shells: Multi-scale shape registration with functional maps. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12265-12274, 2020. +[19] Andrea Gasparetto, Luca Cosmo, Emanuele Rodola, Michael Bronstein, and Andrea Torsello. Spatial maps: From low rank spectral to sparse spatial functional representations. In 2017 International Conference on 3D Vision (3DV), pages 477-485. IEEE, 2017. +[20] Xianfeng Gu, Yalin Wang, Tony F Chan, Paul M Thompson, and Shing-Tung Yau. Genus zero surface conformal mapping and its application to brain surface mapping. IEEE transactions on medical imaging, 23(8):949-958, 2004. +[21] Stefan Gumhold, Xinlong Wang, and Rob S MacLeod. Feature extraction from point clouds. In IMR. Citeseer, 2001. +[22] Li Han, Shuning Liu, Bing Yu, Shengsi Xu, and Rui Xiang. Orientation-preserving spectral correspondence for 3d shape analysis. Journal of Imaging Science and Technology, 2019. +[23] Varun Jain and Hao Zhang. Robust 3d shape correspondence in the spectral domain. In Shape Modeling and Applications, 2006. SMI 2006. IEEE International Conference on, pages 19-19. IEEE, 2006. +[24] Varun Jain, Hao Zhang, and Oliver van Kaick. Non-rigid spectral correspondence of triangle meshes. International Journal of Shape Modeling, 13(01):101-124, 2007. +[25] Itay Kezurer, Shahar Z Kovalsky, Ronen Basri, and Yaron Lipman. Tight relaxation of quadratic matching. In Computer Graphics Forum, volume 34, pages 115-128. Wiley Online Library, 2015. +[26] Vladimir G Kim, Yaron Lipman, and Thomas Funkhouser. Blended intrinsic maps. In ACM Transactions on Graphics (TOG), volume 30, page 79. ACM, 2011. +[27] Rongjie Lai, Jiang Liang, and Hongkai Zhao. A local mesh method for solving pdes on point clouds. Inverse Problems & Imaging, 7(3), 2013. +[28] Rongjie Lai, Yonggang Shi, Kevin Scheibel, Scott Fears, Roger Woods, Arthur W Toga, and Tony F Chan. Metric-induced optimal embedding for intrinsic 3d shape analysis. In 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 2871-2878. IEEE, 2010. +[29] Rongjie Lai and Hongkai Zhao. Multiscale nonrigid point cloud registration using rotation-invariant sliced-wasserstein distance via laplace-beltrami eigenmap. SIAM Journal on Imaging Sciences, 10(2):449-483, 2017. + +[30] Marius Leordeanu and Martial Hebert. A spectral technique for correspondence problems using pairwise constraints. In Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, volume 2, pages 1482-1489. IEEE, 2005. +[31] B. Levy. Laplace-beltrami eigenfunctions: Towards an algorithm that understands geometry. IEEE International Conference on Shape Modeling and Applications, invited talk, 2006. +[32] Xiuwen Liu, Arturo Donate, Matthew Jemison, and Washington Mio. Kernel functions for robust 3d surface registration with spectral embeddings. In 2008 19th International Conference on Pattern Recognition, pages 1-4. IEEE, 2008. +[33] Diana Mateus, Radu Horaud, David Knossow, Fabio Cuzzolin, and Edmond Boyer. Articulated shape matching using laplacian eigenfunctions and unsupervised point registration. In Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on, pages 1-8. IEEE, 2008. +[34] Simone Melzi, Jing Ren, Emanuele Rodola, Abhishek Sharma, Peter Wonka, and Maks Ovsjanikov. Zoomout: Spectral upsampling for efficient shape correspondence. ACM Transactions on Graphics (TOG), 38(6):155, 2019. +[35] Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher, and Leonidas Guibas. Functional maps: a flexible representation of maps between shapes. ACM Transactions on Graphics (TOG), 31(4):30:1-30:11, 2012. +[36] Maks Ovsjanikov, Quentin Merigot, Facundo Memoli, and Leonidas Guibas. One point isometric matching with the heat kernel. CGF, 29(5):1555-1564, 2010. +[37] Ulrich Pinkall and Konrad Polthier. Computing Discrete Minimal Surfaces and their Conjugates. Experimental mathematics, 2(1):15-36, 1993. +[38] Jing Ren, Mikhail Panine, Peter Wonka, and Maks Ovsjanikov. Structured regularization of functional map computations. In Computer Graphics Forum, volume 38, pages 39-53. Wiley Online Library, 2019. +[39] Jing Ren, Adrien Poulenard, Peter Wonka, and Maks Ovsjanikov. Continuous and orientation-preserving correspondences via functional maps. ACM Transactions on Graphics (TOG), 37(6), 2018. +[40] M. Reuter, F.E. Wolter, and N. Peinecke. Laplace-Beltrami spectra as Shape-DNA of surfaces and solids. Computer-Aided Design, 38:342-366, 2006. +[41] Emanuele Rodola, Alex M Bronstein, Andrea Albarelli, Filippo Bergamasco, and Andrea Torsello. A game-theoretic approach to deformable shape matching. In 2012 IEEE Conference on Computer Vision and Pattern Recognition, pages 182-189. IEEE, 2012. +[42] Emanuele Rodolà, Luca Cosmo, Michael Bronstein, Andrea Torsello, and Daniel Cremers. Partial functional correspondence. Computer Graphics Forum, 36(1):222-236, 2017. +[43] Emanuele Rodolà, Samuel Rota Bulò, Thomas Windheuser, Matthias Vestner, and Daniel Cremers. Dense non-rigid shape correspondence using random forests. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 4177-4184. IEEE, 2014. +[44] Raif M Rustamov. Laplace-beltrami eigenfunctions for deformation invariant shape representation. In Proceedings of + +the fifth Eurographics symposium on Geometry processing, pages 225-233. Eurographics Association, 2007. +[45] Stefan C Schonsheck, Michael M Bronstein, and Rongjie Lai. Nonisometric surface registration via conformal laplace-beltrami basis pursuit. arXiv preprint arXiv:1809.07399, 2018. +[46] Alon Shtern and Ron Kimmel. Iterative closest spectral kernel maps. In 2014 2nd International Conference on 3D Vision, volume 1, pages 499-505. IEEE, 2014. +[47] Jian Sun, Maks Ovsjanikov, and Leonidas Guibas. A concise and provably informative multi-scale signature based on heat diffusion. Computer graphics forum, 28(5):1383-1392, 2009. +[48] Art Tevs, Alexander Berner, Michael Wand, Ivo Ihrke, and H-P Seidel. Intrinsic shape matching by planned landmark sampling. In Computer Graphics Forum, volume 30, pages 543-552. Wiley Online Library, 2011. +[49] Federico Tombari, Samuele Salti, and Luigi Di Stefano. Unique signatures of histograms for local surface description. In European conference on computer vision, pages 356-369. Springer, 2010. +[50] Lloyd N Trefethen and David Bau III. Numerical linear algebra, volume 50. Siam, 1997. +[51] Pravin M Vaidya. An o (n logn) algorithm for the all-nearest-neighbors problem. Discrete & Computational Geometry, 4(2):101-115, 1989. +[52] B. Vallet and B. Levy. Spectral geometry processing with manifold harmonics. Computer Graphics Forum (Proceedings Eurographics), 2008. +[53] Oliver Van Kaick, Hao Zhang, Ghassan Hamarneh, and Daniel Cohen-Or. A survey on shape correspondence. Computer Graphics Forum, 30(6):1681-1707, 2011. +[54] Matthias Vestner, Zorah Lähner, Amit Boyarski, Or Litany, Ron Slossberg, Tal Remez, Emanuele Rodola, Alex Bronstein, Michael Bronstein, and Ron Kimmel. Efficient deformable shape correspondence via kernel matching. In 3D Vision (3DV), 2017 International Conference on, pages 517-526. IEEE, 2017. +[55] Matthias Vestner, Roee Litman, Emanuele Rodola, Alex Bronstein, and Daniel Cremers. Product manifold filter: Non-rigid shape correspondence via kernel density estimation in the product space. In Proc. CVPR, pages 6681-6690, 2017. +[56] Chaohui Wang, Michael M Bronstein, Alexander M Bronstein, and Nikos Paragios. Discrete minimum distortion correspondence problems for non-rigid shape matching. In International Conference on Scale Space and Variational Methods in Computer Vision, pages 580-591. Springer, 2011. +[57] Rui Xiang, Rongjie Lai, and Hongkai Zhao. Efficient and robust shape correspondence via sparsity-enforced quadratic assignment. 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Semantic segmentation is one of the essential components of road scene perception that provides semantic information of the surrounding environment. Recently, several methods have been introduced for 3D LiDAR semantic segmentation. While they can lead to improved performance, they are either afflicted by high computational complexity, therefore are inefficient, or they lack fine details of smaller object instances. To alleviate these problems, we propose $(\mathbf{AF})^2$ S3Net, an end-to-end encoder-decoder CNN network for 3D LiDAR semantic segmentation. We present a novel multibranch attentive feature fusion module in the encoder and a unique adaptive feature selection module with feature map re-weighting in the decoder. Our $(\mathbf{AF})^2$ -S3Net fuses the voxel-based learning and point-based learning methods into a unified framework to effectively process the potentially large 3D scene. Our experimental results show that the proposed method outperforms the state-of-the-art approaches on the large-scale nuScenes-lidarseg and SemanticKITTI benchmark, ranking $1^{\mathrm{st}}$ on both competitive public leaderboard competitions upon publication. + +# 1. Introduction + +Understanding of the surrounding environment has been one of the most fundamental tasks in autonomous robotic systems. With the challenges introduced with recent technologies such as self-driving cars, a detailed and accurate understanding of the road scene has become a main part of any outdoor autonomous robotic system in the past few years. To achieve an acceptable level of road scene understanding, many frameworks benefit from image semantic segmentation, where specific pixel-wise classes are pre + +dicted from input images, giving a clear perspective of the scene. + +![](images/8690fc2ccb1b4d2e0c7eab6fd17dd95cd19fe9ac2d62b02079b62597deb5376a.jpg) + +![](images/3bb01942e004ff6abefef3354aead25cdf9401faf6e6158c7da297ebc03e8ce2.jpg) + +![](images/1d7d7127f60a356ea68e9662cbbb13dc83579217b7b7a49e49e2d990ab1fafeb.jpg) +Figure 1: Comparison of our proposed method with SalsaNext [11] and MinkNet42 [10] on SemanticKITTI benchmark [3]. + +![](images/b35f047bbff9f47f3e6981a8abf1b89970f7127be0c6fe1f0f4628bfc1829453.jpg) + +Although image semantic segmentation is an important step in realizing self driving cars, the limitations of a vision sensor such as the inability to record data in poor lighting conditions, variable sensor sensitivity, lack of depth information and limited field-of-view (FOV) makes it difficult for vision sensors to be the sole primary source for scene understanding and semantic segmentation. In contrast, Light Detection and Ranging (LiDAR) sensors can record accurate depth information regardless of the lighting conditions with high density and frame rate, making it a reliable source of information for critical tasks such as self driving. + +LiDAR sensor generates point cloud by scanning the environment and calculating time-of-flight for the emitted laser beams. In doing so, LiDARs can collect valuable information, such as range (e.g., in Cartesian coordinates) and intensity (a measure of reflection from the surface of the objects). Recent advancement in LiDAR technology makes it possible to generate high quality, low noise and dense scans + +from desired environments, making the task of scene understanding a possibility using LiDARs. Although rich in information, LiDAR data often comes in an unstructured format and partially sparse at far ranges. These characteristics make the task of scene understating challenging using LiDAR as primary sensor. Nevertheless, research in scene understanding and in specific, semantic segmentation using LiDARs, has seen an increase in the past few years with the availability of datasets such as semanticKITTI [3]. + +The unstructured nature and partial sparsity of LiDAR data brings challenges to semantic segmentation. However, a great effort has been put by researchers to address these obstacles and many successful methods have been proposed in the literature (see Section 2). From real-time methods which use projection techniques to benefit from the available 2D computer vision techniques, to fully 3D approaches which target higher accuracy, there exist a range of methods to build on. To better process LiDAR point cloud in 3D and to overcome limitations such as non-uniform point densities and loss of granular information in voxelization step, we propose $(\mathbf{A}\mathbf{F})^{2}$ -S3Net, a next generation method based on S3Net [9] and S3CNet [8] which is built upon Minkowski Engine [10], to suit varying levels of sparsity in LiDAR point clouds, achieving state-of-the-art accuracy in semantic segmentation methods on SemanticKITTI [3]. Fig. 1 demonstrates qualitative results of our approach compared to SalsaNext [11] and MinkNet42 [10]. We summarize our contributions as, + +- An end-to-end encoder-decoder 3D sparse CNN that achieves state-of-the-art accuracy in semanticKITTI benchmark [3] and nuScenes-lidarseg competition [5]; +- A multi-branch attentive feature fusion module in the encoder to learn both global contexts and local details; +- An adaptive feature selection module with feature map re-weighting in the decoder to actively emphasize the contextual information from a feature fusion module to improve the generalizability; +- A comprehensive analysis on semantic segmentation and classification performance of our model as opposed to existing methods on three benchmarks, semanticKITTI [3], nuScenes-lidarseg [5], and ModelNet40 [38] through ablation studies, qualitative and quantitative results. + +# 2. Related Work + +# 2.1. 2D Semantic Segmentation + +SqueezeSeg [36] is one of the first works on LiDAR semantic segmentation using range-image, where LiDAR point cloud projected on a 2D plane using spherical transformation. SqueezeSeg [36] network is based on an encoder-decoder using Fully Connected Neural Network + +(FCNN) and a Conditional Random Fields (CRF) as a Recurrent Neural Network (RNN) layer. In order to reduce number of the parameters in the network, SqueezeSeg incorporates "fireModules" from [17]. In a subsequent work, SqueezeSegV2 [37] introduced Context Aggregation Module (CAM), a refined loss function and batch normalization to further improve the model. SqueezeSegV3 [39] stands on the shoulder of [36, 17], adopting a Spatially-Adaptive Convolution (SAC) to use different filters in different locations in relation to the input image. Inspired by YOLOv3 [30], RangeNet++ [25] uses a DarkNet backbone to process a range-image. In addition to a novel CNN, RangeNet++ [25] proposes an efficient way of predicting labels for the full point cloud using a fast implementation of K-nearest neighbour (KNN). + +Benefiting from a new 2D projection, PolarNet [42] takes on a different approach using a polar Birds-Eye-View (BEV) instead of the standard 2D grid-based BEV projections. Moreover, PolarNet encapsulates the information regarding each polar gird using PointNet, rather than using hand crafted features, resulting in a data-driven feature extraction, a nearest-neighbor-free method and a balanced grid distribution. Finally, in a more successful attempt, methods such as SalsaNext [11] and Lite-HDSeg [29], make a series of improvements to the backbone introduced in SalsaNet [1] such as, a new global contextual block, an improved encoder-decoder and Lovász-Softmax loss [4] to achieve state-of-the-art results in 2D LiDAR semantic segmentation using range-image input. + +# 2.2. 3D Semantic Segmentation + +The category of large scale 3D perception methods kicked off by early works such as [6, 24, 27, 34, 44] in which a voxel representation was adopted to capitalize vanilla 3D convolutions. In attempt to process unstructured point cloud directly, PointNet [26] proposed a Multi-Layer Perception (MLP) to extract features from input points without any voxelization. PointNet++ [28] which is an extension to the nominal work PointNet [26], introduced sampling at different scales to extract relevant features, both local and global. Although effective for smaller point clouds, Methods rely on PointNet [26] and its variations are slow in processing large-scale data. + +Down-sampling is at the core of the method proposed in RandLA-Net [16]. As down-sampling removes features randomly, a local feature aggregation module is also introduced to progressively increase the receptive field for each 3D point. The two techniques used jointly to achieve both efficiency and accuracy in large-scale point cloud semantic segmentation. In a different approach, Cylinder3D [43] uses cylindrical grids to partition the raw point cloud. To extract features, authors in [43] introduced two new CNN blocks: an asymmetric residual block to ensure features re + +lated to cuboid objects are being preserved and Dimension-decomposition based Context Modeling in which multiple low-rank contexts are merged to model a high-ranked tensor suitable for 3D point cloud data. + +Authors in KPConv [33] introduced a new point convolution without any intermediate steps taken in processing point clouds. In essence, KPConv is a convolution operation which takes points in the neighborhood as input and processes them with spatially located weights. Furthermore, a deformable version of this convolution operator was also introduced that learns local shifts to make them adapt to point cloud geometry. Finally, MinkowskiNet [10] introduces a novel 4D sparse convolution for spatio-temporal 3D point cloud data along with an open-source library to support auto-differentiation for sparse tensors. Overall, where we consider the accuracy and efficiency, voxel-based methods such as MinkowskiNet [10] stands above others, achieving state-of-the-art results within all sub-categories of 3D semantic segmentation. + +# 2.3. Hybrid Methods + +Hybrid methods, where a mixture of voxel-based, projection-based and/or point-wise operations are used to process the point cloud, has been less investigated in the past, but with availability of more memory efficient designs, are becoming more successful in producing competitive results. For example, FusionNet [40] uses a voxel-based MLP, called voxel-based mini-PointNet which directly aggregates features from all the points in the neighborhood voxels to the target voxel. This allows FusionNet [40] to search neighborhoods with low complexity, processing large scale point cloud with acceptable performance. In another approach, 3D-MiniNet [2] proposes a learning-based projection module to extract local and global information from the 3D data and then feeds it to a 2D FCNN in order to generate semantic segmentation predictions. In a slightly different approach, MVLidarNet [7] benefits form range-image LiDAR semantic segmentation to refine object instances in bird's-eye-view perspective, showcasing the applicability of LiDAR semantic segmentation in real-world applications. + +Finally, SPVNAS [32] builds upon the Minkowski Engine [10] and designs a hybrid approach of using 4D sparse convolution and point-wise operations to achieve state-of-the-art results in LiDAR semantic segmentation. To do this, authors in SPVNAS [32] use a Neural Architecture Search (NAS) [22] to efficiently design a Deep Neural Network (DNN), based on their novel Sparse Point-Voxel Convolution (SPVConv) operation. + +# 3. Proposed Approach + +The sparsity of outdoor-scene point clouds makes it difficult to extract spatial information compared to indoor-scene point clouds with fixed number of points or based on the + +dense image-based dataset. Therefore, it is difficult to leverage the indoor-scene or image-based segmentation methods to achieve good performance on a large-scale driving scene covering more than $100\mathrm{m}$ with non-uniform point densities. Majority of the LiDAR segmentation methods attempt to either transform 3D LiDAR point cloud into 2D image using spherical projection (i.e., perspective, bird-eye-view) or directly process the raw point clouds. The former approach abandons valuable 3D geometric structures and suffers from information loss due to projection process. The latter approach requires heavy computations and not feasible to be deployed in constrained systems with limited resources. Recently, sparse 3D convolution became popular due to its success on outdoor LiDAR semantic segmentation task. However, few methods only have proposed advanced feature extractors to replicate the success of 2D convolutions in Computer Vision models [10, 32]. + +To overcome this, we propose $(\mathrm{AF})^{2}$ -S3Net for LiDAR semantic segmentation in which a baseline model of MinkNet42 [10] is transformed into an end-to-end encoder-decoder with attention blocks and achieves state-of-the-art results. In this Section we first present the proposed network architecture along with its novel components, namely AF2M and AFSM. Then, the network optimization is introduced followed by the training details. + +# 3.1. Problem Statement + +Lets consider a semantic segmentation task in which a LiDAR point cloud frame is given with a set of unordered points $(P,L) = (\{p_i,l_i\})$ with $p_i\in \mathbb{R}^{d_{in}}$ and $i = 1,\dots,N$ where $N$ denotes the number of points in an input point cloud scan. Each point $p_i$ contains $d_{in}$ input features, i.e., Cartesian coordinates $(x,y,z)$ , intensity of returning laser beam $(i)$ , colors $(R,G,B)$ , etc. Here, $l_{i}\in \mathbb{R}$ represents the ground truth labels corresponding to each point $p_i$ . However, in object classification task, a single class label $\mathcal{L}$ is assigned to an individual scene containing $P$ points. + +Our goal is to learn a function $\mathfrak{F}_{cls}(.,\Phi)$ parameterized by $\Phi$ that assigns a single class label $\mathcal{L}$ for all the points in the point cloud or in other words, $\mathfrak{F}_{seg}(.,\Phi)$ , that assigns a per point label $\hat{c}_i$ to each point $p_i$ . To this end, we propose (AF) $^2$ -S3Net to minimize the difference between the predicted label(s), $\hat{\mathcal{L}}$ and $\hat{c}_i$ , and the ground truth class label(s), $\mathcal{L}$ and $l_i$ , for the tasks of classification and segmentation, respectively. + +# 3.2. Network Architecture + +The block diagram of the proposed method, $(\mathbf{AF})^{2}$ S3Net, is illustrated in Fig. 2. $(\mathbf{AF})^{2}$ -S3Net consists of a residual network based backbone and two novel modules, namely Attentive Feature Fusion module (AF2M) and Adaptive Feature Selection Module (AFSM). The model takes in a 3D LiDAR point cloud and transforms it into + +![](images/f08c33c97371169e97138ad49b14595ed5a7dd432d7f49062b429699c18931f9.jpg) + +![](images/cf661315b6001645c48e6624889b9e3189020f3fe44a9eb6c9df665cef290bf9.jpg) +Figure 2: Overview of $(\mathrm{AF})^{2}$ -S3Net. The top left block is Attentive Feature Fusion Module (AF2M) that aggregates Local and global context using a weighted combination of mutually exclusive learnable masks, $\alpha$ , $\beta$ , and $\gamma$ . The top right block illustrates how Adaptive Feature Selection Module (AFSM) uses shared parameters to learn inter relationship between channels across multi-scale feature maps from AF2M. (best viewed on display) + +sparse tensors containing coordinates and features corresponding to each point. Then, the input sparse tensor is processed by $(\mathbf{A}\mathbf{F})^{2}$ -S3Net which is built upon 3D sparse convolution operations which suits sparse point clouds and effectively predicts a class label for each point given a Li-DAR scan. + +A sparse tensor can be expressed as $P_{s} = [C,F]$ , where $C\in \mathbb{R}^{N\times M}$ represents the input coordinate matrix with $M$ coordinates and $F\in \mathbb{R}^{N\times K}$ denotes its corresponding feature matrix with $K$ feature dimensions [10]. In this work, we consider 3D coordinates of points $(x,y,z)$ , as our sparse tensor coordinate $C$ , and per point normal features $(n_x,n_y,n_z)$ along with intensity of returning laser beam $(i)$ as our sparse tensor feature $F$ . Exploiting normal features helps the model to learn additional directional information, hence, the model performance can be improved by differentiating the fine details of the objects. The detailed description of the network architecture is provided below. + +Attentive Feature Fusion Module (AF2M): To better extract the global contexts, AF2M embodies a hybrid approach, covering small, medium and large kernel sizes, which focuses on point-based (PointNet-style feature extractor), medium-scale voxel-based and large-scale voxel-based features, respectively. The block diagram of AF2M is depicted in Fig. 2 (top-left). Principally, the proposed AF2M fuses the features $\bar{x} = [x_1,x_2,x_3]$ at the corresponding branches using $g(\cdot)$ which is defined as, + +$$ +g \left(x _ {1}, x _ {2}, x _ {3}\right) \triangleq \alpha x _ {1} + \beta x _ {2} + \gamma x _ {3} + \Delta \tag {1} +$$ + +where $\alpha, \beta$ and $\gamma$ are the corresponding coefficients that + +scale the feature columns for each point in the sparse tensor, and are processed by function $f_{enc}(\cdot)$ as shown in Fig. 2. Moreover, the attention residuals, $\Delta$ , is introduced to stabilize the attention layers $h_i(\cdot), \forall i \in \{1, 2, 3\}$ , by adding the residual damping factor. This damping factor is the output of residual convolution layer $\pi$ . Further, function $\pi$ can be formulated as + +$$ +\pi \triangleq s i g m o i d (b n (c o n v (f _ {e n c} (\cdot)))) \tag {2} +$$ + +Finally, the output of AF2M is generated by $\mathcal{F}(g(\cdot))$ , where $\mathcal{F}$ is used to align the sparse tensor scale space with the next convolution block. As illustrated in Fig. 2 (top-left), for each $h_i$ , $\forall i \in \{1, 2, 3\}$ , the corresponding gradient of weight $w_{h_i}$ can be computed as: + +$$ +w _ {h _ {i}} = w _ {h _ {i}} - \frac {\partial J}{\partial g} \frac {\partial g}{\partial f _ {e n c}} \frac {\partial f _ {e n c}}{\partial h _ {i}} - \frac {\partial J}{\partial g} \frac {\partial g}{\partial \pi} \frac {\partial \pi}{\partial h _ {i}} \tag {3} +$$ + +where $J$ is the output of $\mathcal{F}$ . Considering $g(\cdot)$ is a linear function of concatenated features $\bar{x}$ and $\Delta$ , we can rewrite Eq. 3 as follows: + +$$ +w _ {h _ {i}} = w _ {h _ {i}} - \frac {\partial J}{\partial g} \bar {x} \frac {\partial f _ {e n c}}{\partial h _ {i}} - \frac {\partial J}{\partial g} \frac {\partial \pi}{\partial h _ {i}} \tag {4} +$$ + +where $\frac{\partial f_{enc}}{\partial h_i} = S_j(\delta_{ij} - S_j)$ is the Jacobian of softmax function $S(\bar{x}): \mathbb{R}^N \to \mathbb{R}^N$ and maps $i$ th input feature column to $j$ th output feature column, and $\delta$ is Kronecker delta function where $\delta_{i=j} = 1$ and $\delta_{i \neq j} = 0$ . As shown in Eq. 5, + +$$ +\mathcal {S} _ {j} \left(\delta_ {i j} - \mathcal {S} _ {j}\right) = \left[ \begin{array}{c c c} - S _ {1} ^ {2} & S _ {1} \left(1 - S _ {2}\right) & \dots \\ \vdots & \ddots & \\ S _ {N} \left(1 - S _ {1}\right) & \dots & - S _ {N} ^ {2} \end{array} \right] \tag {5} +$$ + +when the softmax output $S$ is close to 0, the term $\frac{\partial f_{\text{enc}}}{\partial h_i}$ approaches zero which prompts no gradient, and when $S$ is close to 1, the gradient is close to identity matrix. As a result, when $S \rightarrow 1$ , all values in $\alpha$ or $\beta$ or $\gamma$ get very high confidence and the update of $w_{h_i}$ becomes: + +$$ +w _ {h _ {i}} = w _ {h _ {i}} - \frac {\partial J}{\partial g} \frac {\partial \pi}{\partial h _ {i}} + \frac {\partial J}{\partial g} \bar {x} I \tag {6} +$$ + +and in the case of $S \to 0$ , the update gradient will only depends on $\pi$ . Fig. 3 further illustrates the capability of the proposed AF2M and highlights the effect of each branch visually. + +![](images/d69e6f71e667fdc1c472a83c39cc5af07b1abcb5b8a8d35bd71dc36d83780311.jpg) +Figure 3: Illustration of Attentive Feature Fusion and spatial geometry of point cloud. The three labels $\alpha x_{1},\beta x_{2}$ , and $\gamma x_{3}$ represent the branches in AF2M encoder block. The first branch, $\alpha x_{1}$ , learns to capture and emphasize the fine details for smaller instances such as person, pole and traffic-sign across the driving scenes with varying point densities. The shallower branches, $\beta x_{2}$ and $\gamma x_{3}$ , learn different attention-maps that focus on global contexts embodied in larger instances such as vegetation, sidewalk and road surface. (best viewed on display) + +Adaptive Feature Selection Module (AFSM): The block diagram of AFSM is shown in Fig. 2 (top-right). In AFSM decoder block, the feature maps from multiple branches in AF2M, $x_{1}$ , $x_{2}$ , and $x_{3}$ , are further processed by residual convolution units. The resulted output, $x_{1}'$ , $x_{2}'$ , and $x_{3}'$ , are concatenated, shown as $f_{dec}$ , and are passed into a shared squeeze re-weighting network [15] in which different feature maps are voted. This module acts like an + +adaptive dropout that intentionally filters out several feature maps that are not contributing to the final results. Instead of directly passing through the weighted feature maps as output, we employed a damping factor $\theta = 0.35$ , to regularize the weighting effect. It is worth noting that the skip connection connecting the attentive feature fusion module branches to the last decoder block, ensures that the error gradient propagates back to the encoder branches for better learning stability. + +# 3.3. Network Optimization + +We leveraged a linear combination of geo-aware anisotrophic [20], Exponential-log loss [35] and Lovász loss [4] to optimize our network. In particular, geo-aware anisotrophic loss is beneficial to recover the fine details in a LiDAR scene. Moreover, Exponential-log loss [35] loss is used to further improve the segmentation performance by focusing on both small and large structures given a highly unbalanced dataset. + +The geo-aware anisotropic loss can be computed by, + +$$ +L _ {g e o} (y, \hat {y}) = - \frac {1}{N} \sum_ {i, j, k} \sum_ {c = 1} ^ {C} \frac {M _ {L G A}}{\psi} y _ {i j k, c} \log \hat {y} _ {i j k, c} \tag {7} +$$ + +where $y$ and $\hat{y}$ are the ground truth label and predicted label. Parameter $N$ is the local tensor neighborhood and in our experiment, we empirically set it as 5 (a 10 voxels size cube). Parameter $C$ is the semantic classes, $M_{LGA} = \sum_{\psi=1}^{\Psi}(c_p \oplus c_{q_\psi})$ , defined in [20]. We normalized local geometric anisotropy within the sliding window $\Psi$ of the current voxel cell $p$ and its neighbor voxel grid $q_\psi \in \Psi$ . + +Therefore, the total loss used to train the proposed network is given by, + +$$ +L _ {t o t} (y, \hat {y}) = w _ {1} L _ {e x p} (y, \hat {y}) + w _ {2} L _ {g e o} (y, \hat {y}) + w _ {3} L _ {l o v} (y, \hat {y}) \tag {8} +$$ + +where $w_{1}, w_{2}$ , and $w_{3}$ denote the weights of Exponential-log loss [35], geo-aware anisotrophic, and Lovász loss, respectively. They are set as 1, 1.5 and 1.5 in our experiments. + +# 4. Experimental Results + +We base our experimental results on three different dataset, namely, SemanticKITTI, nuScenes and ModelNet40 to show the applicability of the proposed methods in different scenes and domains. As for the SemanticKITTI and ModelNet40, $(\mathbf{A}\mathbf{F})^{2}$ -S3Net is compared to the previous state-of-the-art, but due to a recently announce challenge for nuScenes-lidarseg dataset [5], we provide our own evaluation results against the baseline model. + +To evaluate the performance of the proposed method and compare with others, we leverage mean Intersection + +![](images/ed533f48a966873fa51050b91c1843b282380fa4b7e00362d3e68858e1ca4e99.jpg) +Figure 4: Compared to SalsaNext and MinkNet42, our method has a lower error (shown in red) recognizing region surface and smaller objects on nuScenes validation set, thanks to the proposed attention modules. + +over Union (mIoU) as our evaluation metric. mIoU is the most popular metric for evaluating semantic point cloud segmentation and can be formalized as $mIoU = \frac{1}{n}\sum_{c=1}^{n}\frac{TP_c}{TP_c + FP_c + FN_c}$ , where $TP_c$ is the number of true positive points for class $c$ , $FP_c$ is the number of false positives, and $FN_c$ is the number of false negatives. + +As for the training parameters, we trained our model with SGD optimizer with momentum of 0.9 and learning rate of 0.001, weight decay of 0.0005 for 50 epochs. The experiments are conducted using 8 Nvidia V100 GPUs. + +# 4.1.Quantitative Evaluation + +In this Section, we provide quantitative evaluation of $(\mathbf{AF})^2$ -S3Net on two outdoor large-scale public dataset: SemanticKITTI [3] and nuScenes-lidarseg dataset [5] for semantic segmentation task and on ModelNet40 [38] for classification task. + +SemanticKITTI Dataset: we conduct our experiments on SemanticKITTI [3] dataset, the largest dataset for autonomous vehicle LiDAR segmentation. This dataset is based on the KITTI dataset introduced in [13], containing 41000 total frames which captured in 21 sequences. We list our experiments with all other published works in Table 1. As shown in Table 1, our method achieves state-of-the-art performance in SemanticKITTI test set (single scan) in terms of mean IoU. With our proposed method, $(\mathbf{A}\mathbf{F})^{2}$ -S3Net, we see a $2.7\%$ improvement from the second best method [32] and $15.4\%$ improvement from baseline model (MinkNet42 [10]). Our method dominates greatly in classifying small objects such as bicycle, person and motorcycle, making it a reliable solution to understating complex scenes. It is worth noting that $(\mathbf{A}\mathbf{F})^{2}$ -S3Net only uses the voxelized data as input, whereas the competing methods like SPVNAS [32] use both voxelized data and point-wise + +features. + +
DatasetRandLA +Net [16]PolarNet +[42]SalsaNext +[11]TORNADO +Net [14]AMVNet +[21]SPVNAS +[32]Cylinder3D +[43](AF)2S3Net
SemanticKITTI53.954.359.563.165.367.068.969.7
nuScenes-69.4--77.377.477.978.3
+ +Table 2: Segmentation mIoU (%): nuScenes-lidarseg vs. SemanticKITTI test results + +nuScenes Dataset: to prove the generalizability of our proposed method, we trained our network with nuScenes-olidarseg dataset [5], one of the recently available large-scale datasets that provides point level labels of LiDAR point clouds. It consists of 1000 driving scenes from various locations in Boston and Singapore, providing a rich set of labeled data to advance self driving car technology. Among these 1000 scenes, 850 of them is reserved for training and validation, and the remaining 150 scenes for testing. The labels are, to some extent, similar to the SemanticKITTI dataset [3], making it a new challenge to propose methods that can handle both datasets well, given the different sensor setups and environment they record the dataset. In Table 2, we compared our proposed method with all available and published nuScenes-olidarseg test results (nuScenes-olidseg) in addition to SemanticKITTI for better comparison. The proposed method outperforms all other methods, showing reliable performance in segmentation results of various object types. Considering the large difference between nuScenes and SemanticKITTI in terms of sensors, environment and label categories, we can confirm that $(\mathbf{A}\mathbf{F})^{2}$ -S3Net can generalize well among different datasets. + +ModelNet40: to expand and evaluate the encoder module capabilities of the proposed method in different ap + +
MethodMean IoU
CarBicycleMotorcycleTruckOther-vehiclePersonBicyclistMotorcyclistRoadParkingSidewalkOther-groundBuildingFenceVegetationTrunkTerrainPoleTraffic-sign
S-BKI [12]51.383.830.643.026.019.68.53.40.092.665.377.430.189.763.783.464.367.458.667.1
RangeNet++ [25]52.291.425.734.425.723.038.338.84.891.865.075.227.887.458.680.555.164.647.955.9
LatticeNet [31]52.992.916.622.226.621.435.643.046.090.059.474.122.088.258.881.763.663.151.948.4
RandLA-Net [16]53.994.226.025.840.138.949.248.27.290.760.373.720.486.956.381.461.366.849.247.7
PolarNet [42]54.393.840.330.122.928.543.240.25.690.861.774.421.790.061.384.065.567.851.857.5
MinkNet42 [10]54.394.323.126.226.136.743.136.47.991.163.869.729.392.757.183.768.464.757.360.1
3D-MiniNet [2]55.890.542.342.128.529.447.844.114.591.664.274.525.489.460.882.860.866.748.056.6
SqueezeSegV3 [39]55.992.538.736.529.633.045.646.220.191.763.474.826.489.059.482.058.765.449.658.9
Kpconv [33]58.896.030.242.533.444.361.561.611.888.861.372.731.690.564.284.869.269.156.447.4
SalsaNext [11]59.591.948.338.638.931.960.259.019.491.763.775.829.190.264.281.863.666.554.362.1
FusionNet [40]61.395.347.537.741.834.559.556.811.991.868.877.130.892.569.484.569.868.560.466.5
KPRNet [18]63.195.554.147.923.642.665.965.016.593.273.980.630.291.768.485.769.871.258.764.1
SPVNAS [32]67.097.250.650.456.658.067.467.150.390.267.675.421.891.666.986.173.471.064.367.3
\((\mathbf{AF})^{2}\)-S3Net [Ours]69.794.565.486.839.241.180.780.474.391.368.872.553.587.963.270.268.553.761.571.0
+ +Table 1: Segmentation IoU (%) results on the SemanticKITTI [3] test dataset. + +plications, ModelNet40, a 3D object classification dataset [38] is adopted for evaluation. ModelNet40 contains 12,311 meshed CAD models from 40 different object categories. From all the samples, 9,843 models are used for training and 2,468 models for testing. To evaluate our method against existing state-of-the-art, we compare $(\mathbf{AF})^2$ -S3Net with techniques in which a single input (e.g., single view, sampled point cloud, voxel) has been used to train and evaluate the models. To make $(\mathbf{AF})^2$ -S3Net compatible for the task of classification, the decoder part of the network is removed and the output of the encoder is directly reshaped to the number of the classes in ModelNet40 dataset. Moreover, the model is trained only using cross-entropy loss. Table 3 presents the overall classification accuracy results for our proposed method and previous state-of-the-art. With the introduction of AF2M in our network, we achieved similar performance to the point-based methods which leverage fine-grain local features. + +# 4.2. Qualitative Evaluation + +In this section, we visualize the attention maps in AF2M by projecting the scaled feature maps back to original point cloud. Moreover, to better present the the improvements that has been made against the baseline model MinkNet42 [10] and SalsaNext [11], we provide the error maps which highlights the superior performance of our method. + +As shown in Fig. 5, our method is capable of capturing fine details in a scene. To demonstrate this, we train $(\mathbf{A}\mathbf{F})^{2}$ -S3Net on SemanticKITTI as explained above and visualize a test frame. In Fig. 5 we highlight the points with top $5\%$ feature norm from each scaled feature maps of $\alpha x_{1}, \beta x_{2}$ and $\gamma x_{3}$ with cyan, orange and green colors, respectively. It can be observed that our model learns to put its attention on small instances (i.e., person, pole, bicycle, etc.) as well + +![](images/5f00f612e6249f286aaaf4e860aaac6de99f58ac70b37c01f8cb7b066189d032.jpg) +Figure 5: Reference image (top), Prediction (bottom-right), attention map (bottom-left) on SemanticKITTI test set. Color codes are: ▪ road ▪ side-walk ▪ parking ▪ car ▪ bicyclist ▪ pole ▪ vegetation ▪ terrain ▪ trunk ▪ building ▪ other-structure ▪ other-object. + +as larger instances (i.e., car, region boundaries, etc.). Fig. 4 shows some qualitative results on SemanticKITTI (top) and nuScenes (bottom) benchmark. It can be observed that the proposed method surpasses the baseline (MinkNet42 [10]) and range-based SalsaNext [11] by a large margin, which failed to capture fine details such as cars and vegetation. + +# 4.3. Ablation Studies + +To show the effectiveness of the proposed attention mechanisms, namely, AF2M and AFSM introduced in Section 3, along with other design choices such as loss functions, this section is dedicated to a thorough ablation study starting from our baseline model introduced in [10]. The baseline is MinkNet42 which is a semantic segmentation residual NN model for 3D sparse data. To start off with a well trained baseline, we use Exponential Logarithmic Loss [35] to train the model which results in $59.8\%$ mIoU accu + +
MethodInputMain operatorOverall Accuracy (%)
Vox-Net [24]voxels3D Operation83.00
Mink-ResNet50 [10]voxelsSparse 3D Operation85.30
Pointnet [26]point cloudPoint-wise MLP89.20
Pointnet++ [28]point cloudLocal feature90.70
DGCNN[41] (1 vote)point cloudLocal feature91.84
GGM-Net [19]point cloudLocal feature92.60
RS-CNN [23]point cloudLocal feature93.60
Ours (AF2M)voxelsSparse 3D Operation93.16
+ +racy for the validation set on SemanticKITTI. + +Next, we add our proposed AF2M to the baseline model to help the model extract richer features from the raw data. This addition of AF2M improves the mIoU to $65.1\%$ , an increase of $5.3\%$ . In our second study and to show the effectiveness of the AFSM only, we first reduce the AF2M block to only output $\{x_{1}, x_{2}, x_{3}\}$ (see Fig. 2 for reference), and then add the AFSM to the model. Adding AFSM shows an increase of $3.5\%$ in mIoU from the baseline. In the last step of improving the NN model, we combine AF2M and AFSM together as shown in Fig. 2, which result in mIoU of $68.6\%$ and an increase of $8.8\%$ from the baseline model. + +Finally, in our last two experiments, we study the effect of our loss function by adding Lovász loss and the combination of Lovász and geo-aware anisotropic loss, resulting in mIoU of $70.2\%$ and $74.2\%$ , respectively. The ablation studies presented, shows a series of adequate steps in the design of $(\mathbf{A}\mathbf{F})^{2}$ -S3Net, proving the steps taken in the design of the proposed model are effective and can be used separately in other NN models to improve the accuracy. + +Table 3: Classification accuracy results on ModelNet40 dataset [38], for input size ${1024} \times 3$ . + +
ArchitectureAF2MAFSMLoySizLoySizA GEOmIoU
Baseline59.8
Proposed✓65.1
✓63.3
✓✓68.6
✓✓✓70.2
✓✓✓✓74.2
+ +Table 4: Ablation study of the proposed method vs baseline evaluated on SemanticKITTI [3] validation dataset (seq 08). + +# 4.4. Distance-based Evaluation + +In this section, we investigate how segmentation is affected by distance of the points to the ego-vehicle. In order to show the improvements, we follow our ablation study and compare $(\mathbf{A}\mathbf{F})^{2}$ -S3Net and the baseline (MinkNet42) on the SemanticKITTI validation set (seq 8). Fig. 6 illustrates + +the mIoU of $(\mathbf{A}\mathbf{F})^{2}$ -S3Net as opposed to the baseline and SalsaNext w.r.t. the distance to the ego-vehicle's LiDAR sensors. The results of all the methods get worse by increasing the distance due to the fact that point clouds generated by LiDAR are relatively sparse, especially at large distances. However, the proposed method can produce better results at all distances, making it an effective method to be deployed on autonomous systems. It is worth noting that, while the baseline methods attempt to alleviate the sparsity problem of point clouds by using sparse convolutions in a residual style network, it lacks the necessary encapsulation of features proposed in Section 3 to robustly predict the semantics. + +![](images/2aba129f57fcd99b171a18554ef3399022b8836a96ed70775bfc46f3f3ba9253.jpg) +Figure 6: mIoU vs Distance for $(\mathbf{A}\mathbf{F})^{2}$ -S3Net vs. baseline. + +# 5. Conclusion + +In this paper, we presented an end-to-end CNN model to address the problem of semantic segmentation and classification of 3D LiDAR point cloud. We proposed $(\mathbf{AF})^{2}$ -S3Net, a 3D sparse convolution based network with two novel attention blocks called Attentive Feature Fusion Module (AF2M) and Adaptive Feature Selection Module (AFSM), to effectively learn local and global contexts and emphasize the fine detailed information in a given LiDAR point cloud. Extensive experiments on several benchmarks, SemanticKITTI, nuScenes-lidarseg, and ModelNet40 demonstrated the ability to capture the local details and the state-of-the-art performance of our proposed model. Future work will include the extension of our method to end-to-end 3D instance segmentation and object detection on large-scale LiDAR point cloud. + +# References + +[1] Eren Erdal Aksoy, Saimir Baci, and Selcuk Cavdar. Salsanet: Fast road and vehicle segmentation in lidar point clouds for autonomous driving. In IEEE Intelligent Vehicles Symposium (IV2020), 2020. 2 +[2] Inigo Alonso, Luis Riazuelo, Luis Montesano, and Ana C Murillo. 3d-mininet: Learning a 2d representation from point clouds for fast and efficient 3d lidar semantic segmentation. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2020. 3, 7 +[3] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyrill Stachniss, and Jirgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. In 2019 IEEE/CVF International Conference on Computer Vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019, pages 9296-9306. IEEE, 2019. 1, 2, 6, 7, 8 +[4] Maxim Berman, Amal Rannen Triki, and Matthew B Blaschko. The lovasz-softmax loss: a tractable surrogate for the optimization of the intersection-over-union measure in neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4413-4421, 2018. 2, 5 +[5] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11621-11631, 2020. 2, 5, 6 +[6] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford University — Princeton University — Toyota Technological Institute at Chicago, 2015. 2 +[7] Ke Chen, Ryan Oldja, Nikolai Smolyanskiy, Stan Birchfield, Alexander Popov, David Wehr, Ibrahim Eden, and Joachim Pehserl. Mvlidarnet: Real-time multi-class scene understanding for autonomous driving using multiple views. In 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 2288-2294, 2020. 3 +[8] Ran Cheng, Christopher Agia, Yuan Ren, Xinhai Li, and Liu Bingbing. S3cnet: A sparse semantic scene completion network for lidar point clouds. arXiv preprint arXiv:2012.09242, 2020. 2 +[9] Ran Cheng, Ryan Razani, Yuan Ren, and Liu Bingbing. S3net: 3d lidar sparse semantic segmentation network. arXiv preprint arXiv:2103.08745, 2021. 2 +[10] Christopher Choy, JunYoung Gwak, and Silvio Savarese. 4d spatio-temporal convnets: Minkowski convolutional neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3075-3084, 2019. 1, 2, 3, 4, 6, 7, 8 +[11] Tiago Cortinhal, George Tzelepis, and Eren Erdal Aksoy. Salsanext: Fast semantic segmentation of lidar point clouds + +for autonomous driving. In 2020 IEEE Intelligent Vehicles Symposium (IV), pages 655-661, 2020. 1, 2, 6, 7 +[12] Lu Gan, Ray Zhang, Jessy W Grizzle, Ryan M Eustice, and Maani Ghaffari. Bayesian spatial kernel smoothing for scalable dense semantic mapping. IEEE Robotics and Automation Letters, 5(2):790-797, 2020. 7 +[13] A. Geiger, P. Lenz, and R. Urtasun. Are we ready for Autonomous Driving? The KITTI Vision Benchmark Suite. In Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pages 3354-3361, 2012. 6 +[14] Martin Gerdzhev, Ryan Razani, Ehsan Taghavi, and Bingbing Liu. Tornado-net: multiview total variation semantic segmentation with diamond inception module. arXiv preprint arXiv:2008.10544, 2020. 6 +[15] Jie Hu, Li Shen, and Gang Sun. Squeeze-and-excitation networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7132-7141, 2018. 5 +[16] Qingyong Hu, Bo Yang, Linhai Xie, Stefano Rosa, Yulan Guo, Zhihua Wang, Niki Trigoni, and Andrew Markham. Randla-net: Efficient semantic segmentation of large-scale point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11108-11117, 2020. 2, 6, 7 +[17] Forrest N Iandola, Song Han, Matthew W Moskewicz, Khalid Ashraf, William J Dally, and Kurt Keutzer. SqueezeNet: Alexnet-level accuracy with 50x fewer parameters and $<0.5\mathrm{mb}$ model size. arXiv preprint arXiv:1602.07360, 2016. 2 +[18] Deyvid Kochanov, Fatemeh Karimi Nejadasl, and Olaf Booij. Kprnet: Improving projection-based lidar semantic segmentation. ECCV Workshop, 2020. 7 +[19] Dilong Li, Xin Shen, Yongtao Yu, Haiyan Guan, Hanyun Wang, and Deren Li. Ggm-net: Graph geometric moments convolution neural network for point cloud shape classification. IEEE Access, 8:124989-124998, 2020. 8 +[20] Jie Li, Yu Liu, Xia Yuan, Chunxia Zhao, Roland Siegwart, Ian Reid, and Cesar Cadena. Depth based semantic scene completion with position importance aware loss. IEEE Robotics and Automation Letters, 5(1):219-226, 2019. 5 +[21] Venice Erin Liong, Thi Ngoc Tho Nguyen, Sergi Widjaja, Dhananjai Sharma, and Zhuang Jie Chong. Amvnet: Assertion-based multi-view fusion network for lidar semantic segmentation. arXiv preprint arXiv:2012.04934, 2020. 6 +[22] Chenxi Liu, Barret Zoph, Maxim Neumann, Jonathon Shlens, Wei Hua, Li-Jia Li, Li Fei-Fei, Alan Yuille, Jonathan Huang, and Kevin Murphy. Progressive neural architecture search. In Proceedings of the European Conference on Computer Vision (ECCV), pages 19–34, 2018. 3 +[23] Yongcheng Liu, Bin Fan, Shiming Xiang, and Chunhong Pan. Relation-shape convolutional neural network for point cloud analysis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8895-8904, 2019. 8 +[24] Daniel Maturana and Sebastian Scherer. Voxnet: A 3d convolutional neural network for real-time object recognition. In 2015 IEEE/RSJ International Conference on Intelligent + +Robots and Systems (IROS), pages 922-928. IEEE, 2015. 2, 8 +[25] Andres Milioto, Ignacio Vizzo, Jens Behley, and Cyril Stachniss. Rangenet++: Fast and accurate lidar semantic segmentation. In Proc. of the IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems (IROS), 2019. 2, 7 +[26] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 652-660, 2017. 2, 8 +[27] Charles R Qi, Hao Su, Matthias Nießner, Angela Dai, Mengyuan Yan, and Leonidas J Guibas. Volumetric and multi-view cnns for object classification on 3d data. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5648-5656, 2016. 2 +[28] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. In Advances in neural information processing systems, pages 5099-5108, 2017. 2, 8 +[29] Ryan Razani, Ran Cheng, Ehsan Taghavi, and Liu Bingbing. Lite-hdseg: Lidar semantic segmentation using lite harmonic dense convolutions. arXiv preprint arXiv:2103.08852, 2021. 2 +[30] Joseph Redmon and Ali Farhadi. Yolov3: An incremental improvement. arXiv preprint arXiv:1804.02767, 2018. 2 +[31] Radu Alexandru Rosu, Peer Schütt, Jan Quenzel, and Sven Behnke. Latticenet: Fast point cloud segmentation using permutohedral lattices. Robotics: Science and Systems (RSS), 2020. 7 +[32] Haotian* Tang, Zhijian* Liu, Shengyu Zhao, Yujun Lin, Ji Lin, Hanrui Wang, and Song Han. Searching efficient 3d architectures with sparse point-voxel convolution. In European Conference on Computer Vision, 2020. 3, 6, 7 +[33] Hugues Thomas, Charles R Qi, Jean-Emmanuel Deschaud, Beatrix Marcotegui, François Goulette, and Leonidas J Guibas. Kpconv: Flexible and deformable convolution for point clouds. In Proceedings of the IEEE International Conference on Computer Vision, pages 6411–6420, 2019. 3, 7 +[34] Zongji Wang and Feng Lu. Voxsegnet: Volumetric cnns for semantic part segmentation of 3d shapes. IEEE transactions on visualization and computer graphics, 2019. 2 +[35] Ken CL Wong, Mehdi Moradi, Hui Tang, and Tanveer Syeda-Mahmood. 3d segmentation with exponential logarithmic loss for highly unbalanced object sizes. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 612-619. Springer, 2018. 5, 7 +[36] Bichen Wu, Alvin Wan, Xiangyu Yue, and Kurt Keutzer. Squeezeseg: Convolutional neural nets with recurrent crf for real-time road-object segmentation from 3d lidar point cloud. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages 1887-1893. IEEE, 2018. 2 +[37] Bichen Wu, Xuanyu Zhou, Sicheng Zhao, Xiangyu Yue, and Kurt Keutzer. Squeezesegv2: Improved model structure and unsupervised domain adaptation for road-object segmentation from a lidar point cloud. In 2019 International Confer- + +ence on Robotics and Automation (ICRA), pages 4376-4382. IEEE, 2019. 2 +[38] Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguuang Zhang, Xiaou Tang, and Jianxiong Xiao. 3d shapenets: A deep representation for volumetric shapes. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1912-1920, 2015. 2, 6, 7, 8 +[39] Chenfeng Xu, Bichen Wu, Zining Wang, Wei Zhan, Peter Vajda, Kurt Keutzer, and Masayoshi Tomizuka. Squeeze-segv3: Spatially-adaptive convolution for efficient pointcloud segmentation, 2020. 2, 7 +[40] Feihu Zhang, Jin Fang, Benjamin Wah, and Philip Torr. Deep fusionnet for point cloud semantic segmentation. In Proceedings of the European Conference on Computer Vision (ECCV), 2020. 3, 7 +[41] Muhan Zhang, Zhicheng Cui, Marion Neumann, and Yixin Chen. An end-to-end deep learning architecture for graph classification. In Proceedings of AAAI Conference on Artificial Intelligence, 2018. 8 +[42] Yang Zhang, Zixiang Zhou, Philip David, Xiangyu Yue, Zerong Xi, Boqing Gong, and Hassan Foroosh. Polarnet: An improved grid representation for online lidar point clouds semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9601-9610, 2020. 2, 6, 7 +[43] Hui Zhou, Xinge Zhu, Xiao Song, Yuexin Ma, Zhe Wang, Hongsheng Li, and Dahua Lin. Cylinder3d: An effective 3d framework for driving-scene lidar semantic segmentation. arXiv preprint arXiv:2008.01550, 2020. 2, 6 +[44] Yin Zhou and Oncel Tuzel. Voxelnet: End-to-end learning for point cloud based 3d object detection. 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Domain generalization aims at tackling this problem by learning transferable knowledge from multiple source domains in order to generalize to unseen target domains. This paper introduces a novel Fourier-based perspective for domain generalization. The main assumption is that the Fourier phase information contains high-level semantics and is not easily affected by domain shifts. To force the model to capture phase information, we develop a novel Fourier-based data augmentation strategy called amplitude mix which linearly interpolates between the amplitude spectrums of two images. A dual-formed consistency loss called co-teacher regularization is further introduced between the predictions induced from original and augmented images. Extensive experiments on three benchmarks have demonstrated that the proposed method is able to achieve state-of-the-arts performance for domain generalization. + +# 1. Introduction + +Over the past few years, deep learning have made tremendous progress on various tasks. Under the assumption that training and testing data share the same distribution, deep neural networks (DNNs) have shown great promise for a wide spectrum of applications [18, 10, 12]. However, DNNs have demonstrated quite poor generalizability for out-of-distribution data. Such performance degeneration caused by distributional shift (a.k.a. domain shift) impairs the applications of DNNs, as in reality training and testing data often come from different distributions. + +In order to address the problem of domain shift, domain adaptation (DA) bridges the gap between source domain(s) and a specific target domain with the help of some labelled or unlabeled target data. However, DA methods fail to generalize to unknown target domains that have not been seen + +![](images/bc0864fc9b3f0c1a8533558f635f7d4695a45aca793c43e9d0eb92e58ebc6ae3.jpg) +(a) + +![](images/db0b769ea129cc4169a9ee70a7b9aa16528978edd2b85bbe8aa33291b2737baf.jpg) +(b) + +![](images/45f498ff65b41e31c2980859c853e7dedcf6fa52f831c8c904352c702652f439.jpg) +(c) +Figure 1. Examples of the amplitude-only and phase-only reconstruction: (a) original image; (b) reconstructed image with amplitude information only by setting the phase component to a constant; (c) reconstructed image with phase information only by setting the amplitude component to a constant. + +during training. Collecting data from every possible target domain and training DA models with every source-target pair are expensive and impractical. As a result, a more challenging yet practical problem setting, i.e., domain generalization (DG) [29, 20] is proposed. Unlike DA, DG aims to train model with multiple source domains that can generalize to arbitrary unseen target domains. To tackle the DG problem, many existing methods utilize adversarial training [24, 23, 38], meta learning [21, 1, 25, 4], self-supervised learning [2] or domain augmentation [44, 37, 50, 51] techniques and have shown promising results. + +In this paper, we introduce a novel Fourier-based perspective for DG. Our motivation comes from a well-known property of the Fourier transformation: the phase component of Fourier spectrum preserves high-level semantics of the original signal, while the amplitude component contains low-level statistics [32, 33, 35, 11]. For better understanding, we present an example of the images reconstructed from only amplitude information and only phase information, as well as the corresponding original image in Fig. 1. As shown in Fig. 1(c), the phase-only reconstruction reveals the important visual structures, from which one can easily recognize the "house" conveyed in the original image. On the other hand, it is hard to tell the exact object from the amplitude-only reconstruction in Fig. 1(b). Based on + +these observations, Yang et al. [48] have recently developed a Fourier-based method for DA. They propose a simple image translation strategy by replacing the amplitude spectrum of a source image with that of a random target image. By simply training on the amplitude-transferred source images, their method achieves a remarkable performance. + +Inspired by the above work, we further explore Fourier-based methods for domain generalization and introduce a Fourier Augmented Co-Teacher (FACT) framework, which consists of an implicit constraint induced by Fourier-based data augmentation and an explicit constraint in terms of co-teacher regularization, as shown in Fig. 2.1) Fourier-based data augmentation. Since the phase information is known for carrying the essential features to define an object, it is reasonable to assume that by learning more from the phase information, the model can better extract the semantic concepts of different objects that are robust to domain shifts. However, when dealing with DG, we have no access to the target domain, thus the amplitude transfer strategy as [48] is not applicable. To overcome this, we propose to augment the training data by distorting the amplitude information while keeping the phase information unchanged. Specifically, a linear interpolation strategy similar to MixUp [49] is adopted to generate augmented images. But instead of the whole images, only the amplitude of the images are mixed. Through this Fourier-based data augmentation, our model can avoid overfitting to low-level statistics carried in the amplitude information, thus pay more attention on the phase information when making decisions. 2) Co-teacher regularization. In addition to the above implicit constraint induced by Fourier-based data augmentation, we further introduce an explicit constraint to force the model to maintain the predicted class relationships between the original image and its amplitude-perturbed counterpart. This explicit constraint is designed in a form of dual consistency regularization equipped with a momentum-updated teacher [41]. Through the co-teacher regularization, the model is further constrained to focus on the invariant phase information in order to minimize the prediction discrepancy between original and augmented images. + +We validate the effectiveness of FACT on three domain generalization benchmarks, namely Digits-DG [50], PACS [20], and OfficeHome [42]. Extensive experimental results have shown that FACT outperforms several state-of-the-arts DG methods with regards to its capability to generalize to unseen domains, indicating that learning more from the phase information does help model generalize better across domains. We further carry out detailed ablation studies to show the superiority of our framework design. We also conduct an in-depth analysis about the rationales behind our hypothesis and method, which demonstrates that the visual structures in phase information contain rich semantics and our model can learn efficiently from them. + +# 2. Related Work + +Domain generalization: Domain generalization (DG) aims to extract knowledge from multiple source domains so as to generalize well to arbitrary unseen target domains. Early DG studies mainly follow the distribution alignment idea in domain adaptation by learning domain-invariant features via either kernel methods [29, 9] or domain-adversarial learning [24, 23, 38]. Later on, Li et al. [21] propose a meta learning approach that simulates the training strategy of MAML [5] by back propagating the second-order gradients calculated on a random metatest domain split from the source domains at each iteration. Subsequent meta learning-based DG methods utilize a similar strategy to meta-learn a regularizer [1], a feature-critic network [25], or how to maintain semantic relationships [4]. Another popular way to address DG problem is domain augmentation, which creates samples from fictitious domains via gradient-based adversarial perturbations [44, 37] or adversarily trained image generators [50, 51]. Recently, inspired by the robustness of a shape-biased model to out-of-distributions [8], Shi et al. [39] bias their model to shape features by filtering out texture features according to local self-information. Similarly, Carlucci et al. [2] introduce a self-supervised jigsaw task to help the model learn global shape features and Wang et al. [45] further extend this work by incorporating a momentum metric learning scheme. Other DG methods also employ low-rank decomposition [20, 36] and gradient-guided dropout [16]. Different from all the methods above, our work takes a new Fourier-based perspective for DG. By emphasizing the Fourier phase information, our method achieves a remarkable performance compared with current DG methods. + +The importance of phase information: Many early studies [32, 33, 35, 11] have shown that in the Fourier spectrum of signals, the phase component retains most of the high-level semantics in the original signals, while the amplitude component mainly contains low-level statistics. Most recently, Yang et al. [48] introduce the Fourier perspective into domain adaptation. By simply replacing a small area in the centralized amplitude spectrum of a source image with that of a target image, they can generate target-like images for training. Another concurrent work of Yang et al. [47] proposes to keep a phase consistency in source-target image translations, which is shown to be a better choice than the commonly used cycle consistency [15] for segmentation tasks under DA scenario. Inspired from the above work, we develop a novel Fourier-based framework for DG to encourage our model to focus on the phase information. + +Consistency regularization: Consistency regularization (CR) is widely-used in supervised and semi-supervised learning. Laine and Aila [17] first introduce a consistency loss between outputs from two differently perturbed models. Tarvainen and Valpola [41] further extend this work + +![](images/5f46b1db1c8a0ff6e8522a8e15256733384c344fd5f27952bc59a2730bd1186c.jpg) +Figure 2. The framework of the proposed FACT. Our framework contains two key components, namely Fourier-based data augmentation and co-teacher regularization, which are highlighted in bold. Both the original and augmented data are sent to the student model and a momentum-updated teacher model. The co-teacher regularization then imposes a dual consistency between the predictions from original data and augmented data. Note that the parameters of teacher model are not updated during back propagation. + +by using a momentum-updated teacher to provide better targets for consistency alignment. Miyato et al. [27] and Park et al. [34] develop different techniques by replacing the stochastic perturbations with adversarial ones. Verma et al. [43] also demonstrate that a interpolation consistency with MixUp [49] samples could be helpful. Some recent work [6, 40, 46] also use consistency regularization in UDA to improve the performance on target domain. In our work, we design a dual-formed consistency loss to further bias our model on the phase information. + +# 3. Method + +Given a training set of multiple source domains $\mathcal{D}_s = \{\mathcal{D}_1, \dots, \mathcal{D}_S\}$ with $N_k$ labelled samples $\{(x_i^k, y_i^k)\}_{i=1}^{N_k}$ in the $k$ -th domain $\mathcal{D}_k$ , where $x_i^k$ and $y_i^k \in \{1, \dots, C\}$ denote the inputs and labels respectively, the goal of domain generalization is to learn a domain-agnostic model $f(\cdot; \theta)$ on source domains that is expected to perform well on unseen target domains $\mathcal{D}_t$ . + +Inspired by the semantic-preserving property of Fourier phase component [32, 33, 35, 11], we assume that models highlight the phase information have better generalization ability across domains. To this end, we design a novel Fourier-based data augmentation strategy by mixing the amplitude information of images. We further add a dual-formed consistency loss, named as co-teacher regularization, to reach consensuses between predictions derived from augmented and original inputs. The consistency loss + +is implemented with a momentum-updated teacher model to provide better targets for consistency alignment as in [41]. The overall Fourier-based Augmented Co-Teacher (FACT) framework is illustrated in Fig. 2. Below we introduce the main components of FACT, i.e., Fourier-based data augmentation and co-teacher regularization. + +# 3.1. Fourier-based data augmentation + +For a single channel image $x$ , its Fourier transformation $\mathcal{F}(x)$ is formulated as: + +$$ +\mathcal {F} (x) (u, v) = \sum_ {h = 0} ^ {H - 1} \sum_ {w = 0} ^ {W - 1} x (h, w) e ^ {- j 2 \pi \left(\frac {h}{H} u + \frac {w}{W} v\right)} \tag {1} +$$ + +and $\mathcal{F}^{-1}(x)$ defines the inverse Fourier transformation accordingly. Both the Fourier transformation and its inverse can be calculated with the FFT algorithm [31] efficiently. The amplitude and phase components are then respectively expressed as: + +$$ +\begin{array}{l} \mathcal {A} (x) (u, v) = \left[ R ^ {2} (x) (u, v) + I ^ {2} (x) (u, v) \right] ^ {1 / 2} \\ \mathcal {P} (x) (u, v) = \arctan \left[ \frac {I (x) (u , v)}{R (x) (u , v)} \right], \end{array} \tag {2} +$$ + +where $R(x)$ and $I(x)$ represent the real and imaginary part of $\mathcal{F}(x)$ , respectively. For RGB images, the Fourier transformation for each channel is computed independently to get the corresponding amplitude and phase information. + +![](images/4e471529461a56ba9eff5e0651334248173708dfc1653ad6253a98edb75ae2a8.jpg) +(a) + +![](images/046e21fdbc67feed71c059b2af1ccb8e8989ab8ed7e2caa7da64c910845cf4bc.jpg) +(b) +Figure 3. Illustration of (a) AS and (b) AM strategy. + +With the semantic-preserving property of Fourier phase component, we here attempt to build models that specifically highlight the phase information, which are expected to have better generalization ability across domains. To achieve this goal, a natural choice is perturbing the amplitude information in the original images via a certain form of data augmentation. Inspired from MixUp [49], we design a novel data augmentation strategy by linearly interpolating between the amplitude spectrums of two images from arbitrary source domains: + +$$ +\hat {\mathcal {A}} \left(x _ {i} ^ {k}\right) = (1 - \lambda) \mathcal {A} \left(x _ {i} ^ {k}\right) + \lambda \mathcal {A} \left(x _ {i ^ {\prime}} ^ {k ^ {\prime}}\right), \tag {3} +$$ + +where $\lambda \sim U(0,\eta)$ , and the hyperparameter $\eta$ controls the strength of the augmentation. The mixed amplitude spectrum is then combined with the original phase spectrum to form a new Fourier representation: + +$$ +\mathcal {F} \left(\hat {x} _ {i} ^ {k}\right) (u, v) = \hat {\mathcal {A}} \left(x _ {i} ^ {k}\right) (u, v) * e ^ {- j * \mathcal {P} \left(x _ {i} ^ {k}\right) (u, v)}, \tag {4} +$$ + +which is then fed to inverse Fourier transformation to generate the augmented image. $\hat{x}_i^k = \mathcal{F}^{-1}[\mathcal{F}(\hat{x}_i^k)(u,v)]$ . This Fourier-based augmentation strategy, named amplitude mix (AM) thereafter, is illustrated in Fig. 3 (b). + +We then feed the augmented images and the original labels to the model for classification. The loss function is formulated as standard cross entropy1: + +$$ +\mathcal {L} _ {c l s} ^ {a u g} = - y _ {i} ^ {k} \log (\sigma (f (\hat {x} _ {i} ^ {k}; \theta))) \tag {5} +$$ + +where $\sigma$ is the softmax activation. We also use the original images for training, the classification loss $\mathcal{L}_{cls}^{ori}$ can then be defined similarly as Eq. 5. + +Note that the AM strategy is essentially different from the spectral transfer operation proposed in [48]. Specifically, the spectral transfer operation aims to adapt low-level statistics from the source domain to the target domain by replacing the low-frequency amplitude information of source images with that of target images. However, in domain generalization, since we have no access to target data, such an adaptive operation is impossible. Nevertheless, we can still swap the amplitude spectrums between two source images directly to create augmented images. This amplitude swap (AS) strategy is illustrate in Fig. 3 (a). Like [48], the proportion of the swapped area is controlled by a hyperparameter $r$ . However, only swapping a small area of the centralized amplitude spectrum (i.e. low-frequency amplitude information) could still cause the model to overfit on the remaining middle-frequency and high-frequency amplitude information, while swapping the whole amplitude spectrum (i.e. setting $r = 1$ ) may be too aggressive for the model to learn. On the other hand, the AM strategy perturbs each frequency component in the amplitude spectrum equally and bridge the model to the most aggressively augmented images via linear interpolation. Therefore, the model can efficiently learn from the phase information by comparing between the original and augmented images through AM augmentation. + +# 3.2. Co-teacher Regularization + +The above Fourier-based data augmentation imposes an implicit constraint which requires the model to predict the same object before and after augmentation. However, the categorical relations predicted from original and augmented images with the same phase information may be different. For example, a model may learn from the original images that horses are more similar to giraffes than houses. However, this learned knowledge may conflict to that learned from augmented images due to a different augmentation. To alleviate this kind of disagreement, we add an explicit constraint in the form of a dual consistency loss. As suggested in [41], we use a momentum-updated teacher model to provide better targets for consistency alignment. During training, the teacher model receives parameters from the student model via exponential moving average: + +$$ +\theta_ {t e a} = m \theta_ {t e a} + (1 - m) \theta_ {s t u} \tag {6} +$$ + +where $m$ is the momentum parameter. Note that no gradient flows through the teacher model during back propagation. To make full use of the knowledge learned from data, we compute the outputs with a softened softmax at a temperature $T$ [14] for both the teacher and student models. We then force the model to be consistent between the outputs derived from original images and augmented images: + +$$ +\mathcal {L} _ {c o t} ^ {a 2 o} = \mathrm {K L} \left(\sigma \left(f _ {s t u} \left(\hat {x} _ {i} ^ {k}\right) / T\right) \mid \mid \sigma \left(f _ {t e a} \left(x _ {i} ^ {k}\right) / T\right)\right), \tag {7} +$$ + +$$ +\mathcal {L} _ {\text {c o t}} ^ {o 2 a} = \mathrm {K L} \left(\sigma \left(f _ {\text {s t u}} \left(x _ {i} ^ {k}\right) / T\right) \mid \mid \sigma \left(f _ {\text {t e a}} \left(\hat {x} _ {i} ^ {k}\right) / T\right)\right). \tag {8} +$$ + +Here we align the student outputs of augmented images to the teacher outputs of original images, as well as the student outputs of original images to the teacher outputs of augmented images. Since the consistency loss takes a dual form and incorporates a momentum teacher, we rename the loss as co-teacher regularization for brevity. Through the co-teacher regularization, we want our model to learn equally from the original and augmented images. More specifically, the original image and its augmented counterpart can be seen as two views of a same object. When learning from the "original view", the student model is not only guided by the ground-truth, but also taught by the teacher model that learns from the "augmented view". So is the case when the student model learns from the "augmented view". Such a simultaneous co-teaching process enables a comprehensive knowledge sharing between the original and augmented view, and further direct the model to focus on the invariant phase information in order to reach a consistency between the two views. + +Combining all the loss functions together, we can get our full objective as: + +$$ +\mathcal {L} _ {F A C T} = \mathcal {L} _ {c l s} ^ {o r i} + \mathcal {L} _ {c l s} ^ {a u g} + \beta \left(\mathcal {L} _ {c o t} ^ {a 2 o} + \mathcal {L} _ {c o t} ^ {o 2 a}\right) \tag {9} +$$ + +where $\beta$ controls the trade-off between the classification loss and the co-teacher regularization loss. + +# 4. Experiment + +In this section, we demonstrate the superiority of our method on several DG benchmarks. We also carry out detailed ablation studies about the impact of different components and augmentation types. + +# 4.1. Datasets and settings + +We evaluate our method on three conventional DG benchmarks, which cover various recognition scenes. Details of these benchmarks are as follows: (1) Digits-DG [50]: a digit recognition benchmark consisted of four classical datasets MNIST [19], MNIST-M [7], SVHN [30], SYN [7]. The four datasets mainly differ in font style, background and image quality. We use the original train-validation split in [50] with 600 images per class per dataset. (2) PACS [20]: an object recognition benchmark including four domains (photo, art-painting, cartoon, sketch) with large discrepancy in image styles. It contains seven classes and 9,991 images totally. We use the original train-validation split provided by Li et al. [20]. (3) Office-Home [42]: an object recognition benchmark including 15,500 images of 65 classes from four domains (Art, Clip, Product, Real-World). The domain shift mainly comes from image styles and viewpoints, but is much smaller than PACS. Follow [2], we randomly split each domain into $90\%$ for training and $10\%$ for validation. + +Table 1. Leave-one-domain-out results on Digits-DG. The best and second-best results are bolded and underlined respectively. + +
MethodsMNISTMNIST-MSVHNSYNAvg.
DeepAll [50]95.858.861.778.673.7
CCSA [28]95.258.265.579.174.5
MMD-AAE [23]96.558.465.078.474.6
CrossGrad [37]96.761.165.380.275.8
DDAIG [50]96.664.168.681.077.6
Jigen [2]96.561.463.774.073.9
L2A-OT [51]96.763.968.683.278.1
FACT (ours)97.965.672.490.381.5
+ +For all benchmarks, we conduct the leave-one-domain-out evaluation. We train our model on the training splits and select the best model on the validation splits of all source domains. For testing, we evaluate the selected model on all images of the held-out target domain. All the results are reported in terms of classification accuracy and averaged over three runs. We employ a vanilla ConvNet trained from a simple aggregation of all source data as our baseline, which is named as DeepAll in the remaining sections. + +# 4.2. Implementation details + +We closely follow the implementations of [2, 50]. Here we briefly introduce the implementation details for training our model, and more details can be found in the supplementary. The source code is released at https://github.com/MediaBrain-SJTU/FACT. + +Basic details: For Digits-DG, we use the same backbone network as [50, 51]. We train the network from scratch using SGD, batch size of 128 and weight decay of 5e-4 for 50 epochs. The initial learning rate is set to 0.05 and decayed by 0.1 every 20 epochs. For PACS and OfficeHome, we use the ImageNet pretrained ResNet [12] as our backbone. We train the network with SGD, batch size of 16 and weight decay of 5e-4 for 50 epochs. The initial learning rate is 0.001 and decayed by 0.1 at $80\%$ of the total epochs. We also use the standard augmentation protocol as in [2], which consists of random resized cropping, horizontal flipping and color jittering. + +Method-specific details: For all experiments, we set the momentum $m$ for the teacher model to 0.9995 and the temperature $T$ to 10. The weight $\beta$ of the consistency loss is set to 2 for Digits-DG and PACS, and 200 for OfficeHome. We also use a sigmoid ramp-up [41] for $\beta$ with a length of 5 epochs. The augmentation strength $\eta$ of AM is chosen as 1.0 for Digits-DG and PACS, and 0.2 for OfficeHome. + +# 4.3. Evaluation on Digits-DG + +We present the results in Table 1. Among all the competitors, our method achieves the best performance, exceeding the second best method L2A-OT [51] by more than + +Table 2. Leave-one-domain-out results on PACS. The best and second-best results are bolded and underlined respectively. †: results are reported based on the best models on test splits. + +
MethodsArtCartoonPhotoSketchAvg.
ResNet18
DeepAll77.6376.7795.8569.5079.94
MetaReg [1]83.7077.2095.5070.3081.70
JiGen [2]79.4275.2596.0371.3580.51
Epi-FCR [22]82.1077.0093.9073.0081.50
MMLD [26]81.2877.1696.0972.2981.83
DDAIG [50]84.2078.1095.3074.7083.10
CSD [36]78.9075.8094.1076.7081.40
InfoDrop [39]80.2776.5496.1176.3882.33
MASF [4]†80.2977.1794.9971.6981.04
L2A-OT [51]83.3078.2096.2073.6082.80
EISNet [45]81.8976.4495.9374.3382.15
RSC [16]83.4380.3195.9980.8585.15
RSC (our imple.)80.5578.6094.4376.0282.40
FACT (ours)85.3778.3895.1579.1584.51
ResNet50
DeepAll84.9476.9897.6476.7584.08
MetaReg [1]87.2079.2097.6070.3083.60
MASF [4]†82.8980.4995.0172.2982.67
EISNet [45]86.6481.5397.1178.0785.84
RSC [16]87.8982.1697.9283.3587.83
RSC (our imple.)83.9279.5295.1582.2085.20
FACT (ours)89.6381.7796.7584.4688.15
+ +$3\%$ on average. Specifically, on the hardest target domains SVHN and SYN, where involve cluttered digits and low image qualities, our method outperforms L2A-OT with a large margin of $4\%$ and $7\%$ respectively. The success of our method indicates that training the model to focus more on the spectral phase information can significantly promote its performance on out-of-domain images. + +# 4.4. Evaluations on PACS + +The results are shown in Table 2. It is clearly that our method is among the top performing ones. We notice that the naive DeepAll baseline can get a remarkable accuracy on the photo domain, due to its similarity to the pretrained dataset ImageNet. However, DeepAll performs poorly on the art-painting, cartoon and sketch domains, which bear a larger domain discrepancy. Nevertheless, our FACT can lift the performance of DeepAll by a huge margin of $7.52\%$ on art-painting, $3.52\%$ on cartoon and $11.41\%$ on sketch. Meanwhile, the performance of our model on photo domain drops a little. This is reasonable since domains like photo contain complicated and redundant details, and the model may ignore some possibly useful low-level cues by only highlighting the phase information. Nevertheless, our + +Table 3. Leave-one-domain-out results on OfficeHome. The best and second-best results are bolded and underlined respectively. + +
MethodsArtClipartProductRealAvg.
DeepAll57.8852.7273.5074.8064.72
CCSA [28]59.9049.9074.1075.7064.90
MMD-AAE [23]56.5047.3072.1074.8062.70
CrossGrad [37]58.4049.4073.9075.8064.40
DDAIG [50]59.2052.3074.6076.0065.50
L2A-OT [51]60.6050.1074.8077.0065.60
Jigen [2]53.0447.5171.4772.7961.20
RSC [16]58.4247.9071.6374.5463.12
Jigen (our imple.)57.9549.2172.6174.9063.67
RSC (our imple.)57.6748.4872.6274.1663.23
FACT (ours)60.3454.8574.4876.5566.56
+ +model still achieves a better overall performance. + +Compared with the SOTA, our FACT clearly beats the methods based on adversarial data augmentation or meta learning, including the latest MASF [4], DDAIG [50] and L2A-OT [51], yet FACT enjoys an efficient training process without any additional adversarial or episodic training steps. The performance of our method also exceeds that of RSC [16], a recent proposed method utilizing a simple yet powerful gradient-guided dropout, by $2.11\%$ on average2. All the above comparisons reveal the effectiveness of our method and further demonstrate that the emphasis on phase information improves generalizability across domains. + +# 4.5. Evaluations on OfficeHome + +We report the results in Table 3. Due to a relatively smaller domain discrepancy and the similarity to the pretrained dataset ImageNet, DeepAll acts as a strong baseline on OfficeHome. Many previous DG methods, such as CCSA [28], MMD-AAE [23], CrossGrad [37] and Jigen [2], can not improve much over the simple DeepAll baseline. Nevertheless, our FACT achieves a consistent improvement over DeepAll on all the held-out domains. Moreover, FACT also the surpasses the latest DDAIG [50] and L2A-OT [50] in terms of average performance. This again justifies the superiority of our method. + +# 4.6. Ablation studies + +Impact of different components: We conduct an extensive ablation study to investigate the role of each component in our FACT model in Table 4. Starting from baseline, model A is trained with the AM augmentation only and already works better than the strongest competitor DDAIG [50] in Table 2. Based on model A, we add + +Table 4. Ablation studies on different components of our method on the PACS dataset with ResNet18. + +
MethodAM\( \mathcal{L}^{a2o}_{cot} \)\( \mathcal{L}^{o2a}_{cot} \)TeacherArtCartoonPhotoSketchAvg.
Baseline----77.63±0.8476.77±0.3395.85±0.2069.50±1.2679.94
Model A✓---83.90±0.5076.95±0.4595.55±0.1277.36±0.7183.44
Model B✓✓✓-83.71±0.3077.84±0.4994.73±0.1278.55±0.4683.71
Model C-✓✓✓82.68±0.4478.06±0.3995.35±0.4474.76±0.6782.71
Model D✓✓-✓83.97±0.7777.04±0.8694.59±0.0379.08±0.5683.67
Model E✓-✓✓84.07±0.4377.70±0.6595.28±0.3478.29±0.6183.84
FACT✓✓✓✓85.37±0.2978.38±0.2995.15±0.2679.15±0.6984.51
+ +a vanilla dual-formed consistency loss to obtain model B, which improves over model A slightly. Further incorporating the momentum teacher results in our FACT, which performs best in all variants. This indicates the importance of the momentum teacher that provides better targets for consistency loss. We also create a model C by excluding the AM augmentation from FACT and the performance drops a lot, showing that the Fourier-based data augmentation plays a crucial role. We further validate the necessity of the dual form in co-teacher regularization by using only $\mathcal{L}_{\mathrm{cot}}^{a2o}$ or $\mathcal{L}_{\mathrm{cot}}^{o2a}$ , and resulting in model D and E respectively. As in Table 4, neither model D or E outperforms the full FACT, suggesting the effectiveness of incorporating both original-to-augmented and augmented-to-original consistency alignment through co-teacher regularization. + +Other choices of Fourier-based data augmentation: Next we show the advantages of our AM augmentation over its alternatives in Table 5. Specifically, we compare the AM strategy with the AS strategy which is mentioned in Sec. 3.1. Follow [48], we first choose to swap only a small area in the centralized amplitude spectrum by setting ratio $r = 0.09$ , and the resulting strategy is called AS-partial. As in Table 5, the performance of AS-partial is inferior to that of AM. This is reasonable, as choosing a small value of $r$ in AS only perturbs the low-frequency components in the amplitude spectrum, while the model still has risks to overfit on the remaining amplitude information. Nevertheless, we can still perturb all frequency components with AS by setting $r = 1.0$ , and the resulting strategy is called AS-full. This choice brings some improvement but is still worse than AM. We attribute this to the negative effect caused by directly swapping the entire amplitude spectrums of two images, which may be too aggressive for the model to learn. + +# 5. Discussion + +Phase information contains meaningful semantics and helps generalization. In previous sections, we have seen that by learning more from the phase information, the model can generalize well on unseen domains. Here we further verify the importance of phase information through sin + +Table 5. Ablation studies of different choices of the Fourier data augmentation on the PACS dataset with ResNet18. + +
MethodsArtCartoonPhotoSketchAvg.
DeepAll with
AS-partial82.0076.1993.8977.2782.34
AS-full83.5076.0794.4977.1382.80
AM83.9076.9595.5577.3683.44
FACT with
AS-partial81.6176.9593.8378.3082.67
AS-full83.4677.3794.1078.6383.39
AM85.3778.3895.1579.1584.51
+ +Table 6. The performance changes of training with phase-only reconstructed images and amplitude-only reconstructed images when compared with original images. The values greater than zero (meaning an improvement) are in bold. + +
DataTest TrainPhotoArtCartoonSketch
Phase onlyPhoto-4.683.164.072.38
Art-5.351.285.9715.87
Cartoon-11.530.29-4.0818.55
Sketch10.6614.5621.26-1.09
Amplitude onlyPhoto-14.03-4.15-4.41-0.08
Art-18.40-21.96-5.59-10.72
Cartoon-13.95-7.48-15.891.36
Sketch-4.79-0.73-1.99-13.99
+ +gle domain evaluations on PACS. Specifically, we first generate phase-only reconstructed images by setting the amplitude component as a constant, and so is the amplitude-only reconstructed images. Then we train three models on original images, phase-only images and amplitude-only images respectively, and compare their performance in Table 6. For fair comparison, all the models here are trained from scratch without ImageNet pretraining. As shown in Table 6, the model trained with phase-only images performs better, or at least comparable with the baseline trained with original images in 11 out of 16 cases. This indicates that the phase information does contain useful semantics to help the + +model generalize to unseen domains. On the other hand, the model trained with amplitude-only images suffers from large performance degradation in almost all the cases, suggesting that the amplitude information hardly contains any meaningful semantics. Another interesting finding is that the model trained with phase-only images has some performance drops when generalizing to photo domain from cartoon and art domain. We conjecture that a desirable performance on the photo domain may also require the presence of amplitude information. Therefore, in our FACT framework, we do not completely eliminate the amplitude information, but instead shift model's attention to the phase information in an amplitude-perturbation fashion. It worths nothing that the performance of the model trained with phase-only images also declines in some in-domain generalization cases. This is reasonable considering the loss of amplitude information. + +Amplitude perturbation constrains the model to focus more on phase information. Our Fourier-based data augmentation are implemented via perturbing the amplitude information. Here we present a brief theoretical analysis to demonstrate that amplitude perturbation does make the model to focus more on phase information. For simplicity, we consider the case of a linear softmax classifier together with a feature extractor $\mathbf{h}$ . Suppose the distribution of Fourier-based data augmentation is $g \sim \mathcal{G}$ , and the risk of training on the augmented data is: + +$$ +\hat {R} _ {\mathrm {a u g}} = \frac {1}{N} \sum_ {n = 1} ^ {N} \mathbb {E} _ {g \sim \mathcal {G}} \left[ \ell \left(\mathbf {W} ^ {\top} \mathbf {h} (g (x)), y\right) \right] \tag {10} +$$ + +Similar as in [3, 13], we expand $\hat{R}_{\mathrm{aug}}$ with Taylor expansion: + +$$ +\begin{array}{r l} \mathbb {E} _ {g \sim \mathcal {G}} \left[ \ell \left(\mathbf {W} ^ {\top} \mathbf {h} (g (x)), y\right) \right] = & \\ \ell \left(\mathbf {W} ^ {\top} \overline {{\mathbf {h}}}, y\right) + \frac {1}{2} \mathbb {E} _ {g \sim \mathcal {G}} \left[ \Delta^ {\top} \mathbf {H} (\tau , y) \Delta \right] \end{array} \tag {11} +$$ + +where $\overline{\mathbf{h}} = \mathbb{E}_{g\sim \mathcal{G}}[\mathbf{h}(g(x))]$ , $\Delta = \mathbf{W}^{\top}(\overline{\mathbf{h}} -\mathbf{h}(g(x)))$ and $\mathbf{H}$ is the Hessian matrix. For cross-entropy loss with softmax, $\mathbf{H}$ is semi-definite and independent of $y$ . Then, minimizing the second-order term in Eq. 11 requires that for some feature $h_d$ , if its variance $h_d(g(x))$ is large, the weight $w_{i,d}$ will approach 0. Suppose that the features induced from phase information and amplitude information is $h_p$ and $h_a$ respectively, since we only perturb the amplitude information and keep the phase information unchanged, it is reasonable that: + +$$ +\left\{ \begin{array}{l} \left| h _ {p} (g (x)) - h _ {p} (x) \right| < \zeta \\ \left| h _ {a} (g (x)) - h _ {a} (x) \right| > \epsilon \end{array} \right. \tag {12} +$$ + +where $\zeta > 0$ is a small value, and $\epsilon \geq \zeta$ . Therefore, minimizing $\hat{R}_{\mathrm{aug}}$ restricts $w_{i,a} \to 0$ for those features $h_a$ derived from the amplitude information. As a result, the classifier would pay more attention to the features $h_p$ that derived from the phase information when making decisions. + +Table 7. The cosine similarities between the phase-only reconstructed images (P) and the edge images detected by Sobel operator (S) and Laplacian operator (L). + +
S&PL&PS&L
Similarity0.7900.9140.873
+ +Why does the phase information provide model with meaningful semantics? The answer may be that the phase information records the "location" of events [33] (or small local structures) and reveals the spatial relationships between them within a given image [11]. The model can then aggregate these cues to gain a correct knowledge about the objects conveyed in the image. A similar mechanism can also be found in human vision systems [11]. We also notice that the phase-only reconstructed image in Fig. 1(c) mainly preserves the contours and edges of the original image. For further investigation, we compute the cosine similarities between phase-only images and edge-detected images produced by Sobel or Laplacian operators in Table 7. As we can seen, the similarity scores between phase-only images and edge-detected images are very high, implying that the visual structures such as edges and contours are carried in the phase information. Since the visual structures are the keys to describe different objects, regardless of the underlying domain distributions, learning from such information can facilitate model to extract high-level semantics. + +# 6. Conclusions + +In this paper, we introduce a novel perspective based on Fourier transformation into domain generalization. The main idea is that learning more from the spectral phase information can help the model capture domain-invariant semantic concepts. We then propose a framework composed of an implicit constraint induced by Fourier-based data augmentation and an explicit constraint induced by co-teacher regularization. Extensive experiments on three benchmarks demonstrate that our method is able to achieve state-of-the-art performance for domain generalization. Furthermore, we conduct an in-depth analysis about the mechanisms and rationales behind our method, which gives us a better knowledge about why focusing on the phase information can help domain generalization. Considering the mainstream of related work is still domain-adversarial learning or meta learning, we hope our work can shed some lights into the community. + +Acknowledgement: This work is supported by the National Key Research and Development Program of China (No. 2019YFB1804304), SHEITC (No. 2018-RGZN-02046), 111 plan (No. BP0719010), and STCSM (No. 18DZ2270700), and State Key Laboratory of UHD Video and Audio Production and Presentation. + +# References + +[1] Yogesh Balaji, Swami Sankaranarayanan, and Rama Chellappa. Metareg: Towards domain generalization using meta regularization. In Advances in Neural Information Processing Systems, pages 998-1008, 2018. 1, 2, 6 +[2] Fabio M Carlucci, Antonio D'Innocente, Silvia Bucci, Barbara Caputo, and Tatiana Tommasi. Domain generalization by solving jigsaw puzzles. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2229-2238, 2019. 1, 2, 5, 6 +[3] Tri Dao, A. Gu, Alexander J. Ratner, V. Smith, C. D. Sa, and C. Ré. A kernel theory of modern data augmentation. Proceedings of machine learning research, 97:1528-1537, 2019. 8 +[4] Qi Dou, Daniel Coelho de Castro, Konstantinos Kamnitsas, and Ben Glocker. Domain generalization via model-agnostic learning of semantic features. In Advances in Neural Information Processing Systems, pages 6450–6461, 2019. 1, 2, 6 +[5] Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation of deep networks. volume 70 of Proceedings of Machine Learning Research, pages 1126–1135, International Convention Centre, Sydney, Australia, 06–11 Aug 2017. PMLR. 2 +[6] Geoff French, Michal Mackiewicz, and Mark Fisher. Self-ensembleing for visual domain adaptation. In International Conference on Learning Representations, 2018. 3 +[7] Yaroslav Ganin and Victor Lempitsky. Unsupervised domain adaptation by backpropagation. In International conference on machine learning, pages 1180-1189. PMLR, 2015. 5 +[8] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A. Wichmann, and Wieland Brendel. Imagenet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness. In International Conference on Learning Representations, 2019. 2 +[9] Muhammad Ghifary, David Balduzzi, W Bastiaan Kleijn, and Mengjie Zhang. Scatter component analysis: A unified framework for domain adaptation and domain generalization. IEEE transactions on pattern analysis and machine intelligence, 39(7):1414-1430, 2016. 2 +[10] Ian Goodfellow, *Yoshua Bengio*, Aaron Courville, and *Yoshua Bengio. Deep learning*, volume 1. MIT press Cambridge, 2016. 1 +[11] Bruce C Hansen and Robert F Hess. Structural sparseness and spatial phase alignment in natural scenes. JOSA A, 24(7):1873-1885, 2007. 1, 2, 3, 8 +[12] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 1, 5 +[13] Zhuoxun He, Lingxi Xie, X. Chen, Y. Zhang, Yanfeng Wang, and Q. Tian. Data augmentation revisited: Rethinking the distribution gap between clean and augmented data. ArXiv, abs/1909.09148, 2019. 8 +[14] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531, 2015. 4 + +[15] Judy Hoffman, Eric Tzeng, Taesung Park, Jun-Yan Zhu, Phillip Isola, Kate Saenko, Alexei A. Efros, and Trevor Darrell. Cycada: Cycle consistent adversarial domain adaptation. In International Conference on Machine Learning (ICML), 2018. 2 +[16] Zeyi Huang, Haohan Wang, E. Xing, and D. Huang. Self-challenging improves cross-domain generalization. In ECCV, 2020. 2, 6 +[17] S. Laine and Timo Aila. Temporal ensembling for semi-supervised learning. In International Conference on Learning Representations, 2017. 2 +[18] Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature, 521(7553):436-444, 2015. 1 +[19] Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278-2324, 1998. 5 +[20] Da Li, Yongxin Yang, Yi-Zhe Song, and Timothy M Hospedales. Deeper, broader and artier domain generalization. In Proceedings of the IEEE international conference on computer vision, pages 5542-5550, 2017. 1, 2, 5 +[21] Da Li, Yongxin Yang, Yi-Zhe Song, and Timothy M. Hospedales. Learning to generalize: Meta-learning for domain generalization. In AAAI, 2018. 1, 2 +[22] Da Li, Jianshu Zhang, Yongxin Yang, Cong Liu, Yi-Zhe Song, and Timothy M Hospedales. Episodic training for domain generalization. In Proceedings of the IEEE International Conference on Computer Vision, pages 1446-1455, 2019. 6 +[23] Haoliang Li, Sinno Jialin Pan, Shiqi Wang, and Alex C Kot. Domain generalization with adversarial feature learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5400-5409, 2018. 1, 2, 5, 6 +[24] Ya Li, Xinmei Tian, Mingming Gong, Yajing Liu, Tongliang Liu, Kun Zhang, and Dacheng Tao. Deep domain generalization via conditional invariant adversarial networks. In Proceedings of the European Conference on Computer Vision (ECCV), pages 624-639, 2018. 1, 2 +[25] Yiying Li, Yongxin Yang, Wei Zhou, and Timothy Hospedales. Feature-critic networks for heterogeneous domain generalization. volume 97 of Proceedings of Machine Learning Research, pages 3915-3924, Long Beach, California, USA, 09-15 Jun 2019. PMLR. 1, 2 +[26] Toshihiko Matsuura and Tatsuya Harada. Domain generalization using a mixture of multiple latent domains. In AAAI, pages 11749-11756, 2020. 6 +[27] Takeru Miyato, S. Maeda, Masanori Koyama, and S. Ishii. Virtual adversarial training: A regularization method for supervised and semi-supervised learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41:1979-1993, 2019. 3 +[28] Saeid Motiian, Marco Piccirilli, Donald A Adjeroh, and Gianfranco Doretto. Unified deep supervised domain adaptation and generalization. In Proceedings of the IEEE International Conference on Computer Vision, pages 5715-5725, 2017. 5, 6 + +[29] Krikamol Muandet, David Balduzzi, and Bernhard Schölkopf. Domain generalization via invariant feature representation. In International Conference on Machine Learning, pages 10-18, 2013. 1, 2 +[30] Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading digits in natural images with unsupervised feature learning. 2011. 5 +[31] Henri J Nussbaumer. The fast fourier transform. In Fast Fourier Transform and Convolution Algorithms, pages 80-111. Springer, 1981. 3 +[32] A Oppenheim, Jae Lim, Gary Kopec, and SC Pohlig. Phase in speech and pictures. In ICASSP'79. IEEE International Conference on Acoustics, Speech, and Signal Processing, volume 4, pages 632-637. IEEE, 1979. 1, 2, 3 +[33] Alan V Oppenheim and Jae S Lim. The importance of phase in signals. Proceedings of the IEEE, 69(5):529-541, 1981. 1, 2, 3, 8 +[34] Sungrae Park, JunKeon Park, Su-Jin Shin, and Il-Chul Moon. Adversarial dropout for supervised and semi-supervised learning. In 32nd AAAI Conference on Artificial Intelligence, AAAI 2018, pages 3917-3924. AAAI press, 2018. 3 +[35] Leon N Piotrowski and Fergus W Campbell. A demonstration of the visual importance and flexibility of spatial-frequency amplitude and phase. Perception, 11(3):337-346, 1982. 1, 2, 3 +[36] Vihari Piratla, Praneeth Netrapalli, and Sunita Sarawagi. Efficient domain generalization via common-specific low-rank decomposition. In International Conference on Machine Learning, 2020. 2, 6 +[37] Shiv Shankar, Vihari Piratla, Soumen Chakrabarti, Siddhartha Chaudhuri, Preethi Jyothi, and Sunita Sarawagi. Generalizing across domains via cross-gradient training. In International Conference on Learning Representations, 2018. 1, 2, 5, 6 +[38] Rui Shao, Xiangyuan Lan, Jiawei Li, and Pong C Yuen. Multi-adversarial discriminative deep domain generalization for face presentation attack detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 10023-10031, 2019. 1, 2 +[39] Baifeng Shi, Dinghuai Zhang, Qi Dai, Zhanxing Zhu, Y. Mu, and J. Wang. Informative dropout for robust representation learning: A shape-bias perspective. In International Conference on Machine Learning, 2020. 2, 6 +[40] Rui Shu, Hung Bui, Hirokazu Narui, and Stefano Ermon. A DIRT-t approach to unsupervised domain adaptation. In International Conference on Learning Representations, 2018. 3 +[41] Antti Tarvainen and Harri Valpola. Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results. In Advances in neural information processing systems, pages 1195–1204, 2017. 2, 3, 4, 5 +[42] Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5018-5027, 2017. 2, 5 + +[43] Vikas Verma, Alex Lamb, Juho Kannala, Yoshua Bengio, and David Lopez-Paz. Interpolation consistency training for semi-supervised learning. In Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI-19, pages 3635–3641. International Joint Conferences on Artificial Intelligence Organization, 7 2019. 3 +[44] Riccardo Volpi, Hongseok Namkoong, Ozan Sener, John C Duchi, Vittorio Murino, and Silvio Savarese. Generalizing to unseen domains via adversarial data augmentation. In Advances in neural information processing systems, pages 5334-5344, 2018. 1, 2 +[45] Shujun Wang, Lequan Yu, Caizi Li, Chi-Wing Fu, and Pheng-Ann Heng. Learning from extrinsic and intrinsicsupervisions for domain generalization. In ECCV, 2020. 2, 6 +[46] Yuan Wu, Diana Inkpen, and Ahmed El-Roby. Dual mixup regularized learning for adversarial domain adaptation. In ECCV, 2020. 3 +[47] Yanchao Yang, Dong Lao, Ganesh Sundaramoorthi, and Stefano Soatto. Phase consistent ecological domain adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9011-9020, 2020. 2 +[48] Yanchao Yang and Stefano Soatto. Fda: Fourier domain adaptation for semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4085-4095, 2020. 2, 4, 7 +[49] Hongyi Zhang, Moustapha Cisse, Yann N. Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In International Conference on Learning Representations, 2018. 2, 3, 4 +[50] Kaiyang Zhou, Yongxin Yang, Timothy M Hospedales, and Tao Xiang. Deep domain-adversarial image generation for domain generalisation. In AAAI, pages 13025-13032, 2020. 1, 2, 5, 6 +[51] K. Zhou, Yongxin Yang, Timothy M. Hospedales, and Tao Xiang. Learning to generate novel domains for domain generalization. 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Guibas +Stanford University +guibas@cs.stanford.edu + +# Abstract + +Learning pose invariant representation is a fundamental problem in shape analysis. Most existing deep learning algorithms for 3D shape analysis are not robust to rotations and are often trained on synthetic datasets consisting of pre-aligned shapes, yielding poor generalization to unseen poses. This observation motivates a growing interest in rotation invariant and equivariant methods. The field of rotation equivariant deep learning is developing in recent years thanks to a well-established theory of Lie group representations and convolutions. A fundamental problem in equivariant deep learning is to design activation functions which are both informative and preserve equivariance. The recently introduced Tensor Field Network (TFN) framework provides a rotation equivariant network design for point cloud analysis. TFN features undergo a rotation in feature space given a rotation of the input pointcloud. TFN and similar designs consider nonlinearities which operate only over rotation invariant features such as the norm of equivariant features to preserve equivariance, making them unable to capture the directional information. In a recent work entitled "Gauge Equivariant Mesh CNNs: Anisotropic Convolutions on Geometric Graphs" Hann et al. interpret 2D rotation equivariant features as Fourier coefficients of functions on the circle. In this work we transpose the idea of Hann et al. to 3D by interpreting TFN features as spherical harmonics coefficients of functions on the sphere. We introduce a new equivariant nonlinearity and pooling for TFN. We show improvements over the original TFN design and other equivariant nonlinearities in classification and segmentation tasks. Furthermore our method is competitive with state of the art rotation invariant methods in some instances. + +# 1. Introduction + +In recent years many successful deep learning architectures for 3D geometric deep learning and point cloud anal + +Analysis in particular have been developed, we refer to [14] for a comprehensive survey. Yet, most methods developed for point cloud analysis are not robust to rotations. Furthermore point cloud dataset like ModelNet [33] or ShapeNet [6] used for training and evaluating these methods often consist of synthetic pre-aligned shapes. In consequence, well established point cloud methods like [25, 27, 4, 31, 21] fail to generalise to unseen poses. An important performance gap between the aligned and unaligned or rotation augmented settings has been reported in multiple publications [11, 24, 7, 37]. Recently numerous works [12, 22, 24, 7, 37, 36, 20, 39, 28] have addressed the issue of designing rotation invariant deep learning architectures for 3D data analysis with a variety of approaches. A particularly interesting property for 3D deep learning algorithms closely related to rotation invariance is rotation equivariance. At a high level a rotation equivariant neural network produces features that undergo a rotation in feature space given a rotation of the input. The key point is that this transform only depends on the rotation applied to the input. This is a precious property for learning, guaranteeing immediate generalization to unseen poses. Many rotation equivariant designs [30, 17, 11, 32, 2] have been proposed, thanks to a well established theory of SO(3) representations. A fundamental challenge in the design of equivariant networks is the design of equivariant non-linearities. To preserve equivariance such non-linearities must commute with the rotations of equivariant features, this constraint limits the possible designs. The aforementioned methods either rely on non-linearities applied to rotation invariant quantities like the norm of equivariant features which cannot capture directional information or, consider polynomial equivariant features which can be expensive to compute and complicates training. In the recent work [9] Hann et al. introduce a non linearity for local intrinsic rotation equivariant features over surfaces by interpreting the features as Fourier coefficients of functions over the circle, composing these functions with non linear activations and getting new equivariant features by computing the Fourier coefficients of the composed functions. In this work we explore a similar ap- + +proach in the context of 3D rotation equivariant features from Tensor Field Networks [30] over point-clouds. We propose a simple yet effective design of rotation equivariant non-linearities for Tensor Field Networks. TFN relies on convolutional filters based on spherical harmonics and the resulting features share the same equivariant properties as the spherical harmonics basis. We interpret such feature vectors as the set of coefficients of a function on the unit sphere. Moving to a sphere function representation by applying inverse spherical harmonics transform we can apply non trivial activation functions or MLP's in a pointwise fashion over the sphere. We then return back to the equivariant feature representation by computing the spherical harmonics transform of the resulting function. This operation has a non trivial effect on both the norm and direction of equivariant features, allowing to capture directional information. We present the general setting of point cloud convolutions and TFN and briefly review the underlying theory in section (2). In section (3) we describe our method and specificities of our design compared to the general approach described in section (2). We present our results in section (4) where we compare our method to state of the art rotation invariant methods for shape classification and segmentation and show improvements over existing equivariant non-linearities. We believe our contribution is of general relevance to other equivariant networks like [32] sharing similar structures to TFN. + +# 2. Background and Related work + +# 2.1. Point cloud & graph convolution + +In recent years the field of point cloud processing has developed a lot thanks to many works introducing various notions of graph or point-cloud convolution [27, 21, 4, 31]. Graph convolution aggregates information over the neighbourhood of each vertex. Point cloud and graph convolutions are related as we can define a notion of point cloud convolution by considering the graph of $k$ nearest neighbours of the point cloud. More generally, it is convenient to aggregate information in the neighborhoods of points from a second point cloud, typically a sub-sampled or an upsampled point cloud, similarly to the idea of strided convolutions. The general formulation for graph convolutions is as follows: Let $\mathcal{V}$ be the set of vertices and $\mathcal{X},\mathcal{Y}\subset \mathcal{V}$ non empty subsets of $\mathcal{V}$ . Given signals $x:\mathcal{X}\to \mathbb{R}^k$ , $y:\mathcal{Y}\rightarrow \mathbb{R}^k$ and $f:\mathcal{X}\rightarrow \mathbb{R}$ and a relation kernel function $\kappa :\mathcal{X}\times \mathcal{Y}\to \mathbb{R}$ , the convolution of $f$ by $\kappa$ is the signal $g:\mathcal{Y}\to \mathbb{R}$ defined by: + +$$ +g _ {i} = c _ {i} \bigcirc_ {j \sim i} \kappa \left(x _ {j}, y _ {i}\right) f _ {j} \tag {1} +$$ + +where $\bigcirc$ is a permutation invariant operator like $\sum$ or max, $j$ ranges across the neighbours in $\mathcal{X}$ of vertex $i$ in $\mathcal{V}$ and $c_{i}$ + +is a normalization factor. We follow an approach similar to [4, 30, 24] for point cloud convolution where, $x:\mathcal{X}\to \mathbb{R}^3$ , $y:\mathcal{Y}\to \mathbb{R}^3$ are the points euclidean coordinates of point clouds $\mathcal{X}$ and $\mathcal{Y}$ and, $\kappa :\mathbb{R}^3\to \mathbb{R}$ is a kernel function: + +$$ +g _ {i} = f * _ {x, y} \kappa = c _ {i} \sum_ {j \sim i} \kappa \left(x _ {j} - y _ {i}\right) f _ {j} \tag {2} +$$ + +where $j$ ranges across the $k$ -nearest neighbours of $i$ in $\mathcal{V}$ or points in $\mathcal{V}$ within a ball of a given radius centred at $i$ . A typical choice for $c_{i}$ is to divide by the number of neighbours of $i$ , $c_{i} = \frac{1}{|\mathcal{N}(i)|}$ but in practice we will choose a different normalization as we shall see later. In deep learning applications a collection of kernel functions $\kappa_{m}$ is chosen and linear combinations of the $f *_{x,y} \kappa_{m}$ are learned. + +Feature propagation We also borrow the feature propagation layers from [27] for segmentation tasks. Feature propagation allows to transfer signals between two point clouds. Given two point clouds $x$ and $y$ and a signal $f$ over $x$ , the feature propagation of $f$ to $y$ is defined as follows: + +$$ +g _ {i} = \left(\sum_ {j \sim i} \frac {1}{\| x _ {j} - y _ {i} \| _ {2} ^ {2}}\right) ^ {- 1} \sum_ {j \sim i} \frac {f _ {j}}{\| x _ {j} - y _ {i} \| _ {2} ^ {2}} \tag {3} +$$ + +where $j$ ranges across the 3 nearest neighbors of $x_{i}$ in $y$ . Feature propagation is used in the segmentation architecture of [27] which is a variant of U-Net architecture. The network computes series of conv like layers down sampling the signal, then feature propagation layers up sample the signal to concatenate it with the output of the conv like layer of corresponding resolution and, applies a fully connected layer to the channels axis followed by a batch normalization layer and a ReLu activation. An MLP is applied to the last layer for final point classification. + +# 2.2.3D rotation equivariant CNNs + +In this subsection we describe the construction of 3D rotation equivariant CNNs and we refer to [18, 8, 16] for a more extensive view of the underlying theory. We especially consider Tensor Field Networks [30] which operate on point clouds but, our description also partly covers other works like [32, 17, 2] which also rely on equivariant convolution based on steerable kernels. 3D Rotation equivariant CNN's are built around the notion of 3D steerable kernels. A steerable kernel basis is a basis of the form: + +$$ +\kappa_ {r m} ^ {\ell} (x) = \varphi_ {r} (\| x \| _ {2}) Y _ {m} ^ {\ell} \left(\frac {x}{\| x \| _ {2}}\right) \tag {4} +$$ + +where $Y^{\ell}: x \mapsto (Y_{-\ell}^{\ell}, \ldots, Y_{\ell}^{\ell}) \in \mathbb{R}^{2\ell + 1}$ is the vector of degree $\ell \in \mathbb{N}$ spherical harmonics and $(\varphi_r: \mathbb{R} \to \mathbb{R})_r$ are the radial component of the kernels. A key property of $Y^{\ell}$ is that it undergoes a rotation in $\mathbb{R}^{2\ell + 1}$ given a rotation of its input. More precisely for any rotation $R \in \mathrm{SO}(3)$ , there + +exist a rotation matrix $D^{\ell}(R) \in \mathrm{SO}(2\ell + 1)$ associated to $R$ called the Wigner matrix (of type $\ell$ ) [8, 16, 18] such that, $Y^{\ell}(Rx) = D^{\ell}(R)Y^{\ell}(x)$ . By construction the kernel basis from Eq. (4) satisfies the same equivariance property as spherical harmonics: + +$$ +\kappa_ {r} ^ {\ell} (R x) = D ^ {\ell} (R) \kappa_ {r} ^ {\ell} (x). \tag {5} +$$ + +Many choices are possible for the radial component, we detail our exact kernel design in section (3). Given a point cloud $x \in \mathbb{R}^{n \times 3}$ and a signal $f \in \mathbb{R}^{n \times k}$ over $x$ , we say that $v(x, f) \in \mathbb{R}^{2\ell + 1}$ is a type $\ell$ equivariant feature if: + +$$ +v (R x, f) = D ^ {\ell} (R) v (x, f) \tag {6} +$$ + +Type $\ell$ vector features can be global or point-wise. Type 0 features are rotation invariant scalars. Any rotation invariant descriptor or pose independent signal can be thought of as a type 0 feature. Type 1 features undergo rotations in $\mathbb{R}^3$ (up to permutation of axes), the $yzx$ coordinates of the points are type 1 features. The convolution of a type 0 features with a type $\ell$ kernel produces type $\ell$ features: + +$$ +\begin{array}{l} \left(\kappa_ {r} ^ {e l l} * _ {R. x, R. y} f\right) _ {i} = c _ {i} \sum_ {j \sim i} \kappa_ {r} ^ {\ell} (R (x _ {j} - y _ {i})) f _ {j} \\ = D ^ {\ell} (R) \left(c _ {i} \sum_ {j \sim i} \kappa_ {r} ^ {\ell} \left(x _ {j} - y _ {i}\right) f _ {j}\right) ^ {(7)} \\ \end{array} +$$ + +Stacking convolutions with equivariant kernels involves computing convolutions between equivariant kernels and equivariant features of various types. The resulting features are linear combinations of tensor products of equivariant features. The Peter-Weyl theorem [16] implies that such tensor products can be decomposed into orthogonal sums of irreducible features of different types. More specifically, for any $k,\ell$ and any $J\in \llbracket m - \ell ,m + \ell \rrbracket$ there exists an orthogonal projection matrix $Q^{(k,l),J}$ such that $Q^{(k,l),J}u\otimes v$ is a type $J$ feature vector. The convolution of a signal $f^{\ell}$ of type $\ell$ vectors over $x$ by a type $k$ equivariant kernel $\kappa_{rk}$ is the collection of tensors: + +$$ +\left. \left(\kappa_ {r} ^ {k} * _ {x, y} f ^ {\ell}\right) _ {i p} ^ {J} := Q ^ {(k, \ell), J} \left(c _ {i} \sum_ {j \sim i} \kappa_ {r} ^ {k} \left(x _ {j} - y _ {i}\right) \otimes f _ {j p} ^ {\ell}\right) \right. \tag {8} +$$ + +For $J \in [[|l - k|, l + k]]$ , the coefficients of the matrices $Q^{(k,\ell),J}$ are given by the so-called Clebsch-Gordan coefficients [8]. TFN consists of a multi-head architecture where each head is a tensor stacking pointwise equivariant features of a given type. An equivariant convolution layer takes a collection $(f^{\ell})_{\ell}$ of such tensors as input, computes their convolution with kernels of different types, decomposes the results into irreducible features and, groups them by type + +and learns linear combinations between the resulting features: + +$$ +\sum_ {p} W _ {q p} ^ {J} \left(\kappa^ {k} * _ {x, y} f ^ {\ell}\right) _ {i p} ^ {J} + \delta_ {J 0} b _ {q}. \tag {9} +$$ + +In practice we only take decomposed features up to type 3. A bias term $b$ can be added for type 0 outputs since the bias is pose independent it is only compatible with type 0 (invariant) features. Notice that only linear combinations between vector features are taken. The reason is that the weights matrices must commute with the Wigner matrix. By a corollary of Schur's lemma [16], a linear map commutes with the Wigner matrix iff it is an homothety. Thus to preserve equivariance we can only take linear combinations of equivariant features of the same type and not between their coordinates. This is a limitation compared to traditional non-equivariant filters where we can consider any linear combinations of the basis filters. + +Equivariant Activations A major limitation in the design of rotation equivariant neural networks is the choice of activation functions. To preserve equivariance, the activation function must commute with the Wigner matrix. Equivariant non-linearities follow two trends. Works like [30, 32] multiply equivariant features by non-linear functions of invariant features. The resulting features still commute with the Wigner matrix as only their norm is affected and thus they are equivariant. However such non-linearities don't have effect on the direction of features which limits their expressivity. An other direction explored by [17] and [2] is to build equivariant features as polynomials of other equivariant features. While it has been proven in [10] that equivariant polynomial features can approximate equivariant functions, in practice they can be computationally heavy and are difficult to train as reported in section (8.1) of [2]. We now briefly review non-linearities from [30, 32, 17] and [2]. TFN [30] introduce the notion of norm non-linearities, for a multi head equivariant signal $f$ it is defined by: + +$$ +g _ {i 0 c} ^ {0} := \xi \left(f _ {i 0 c} ^ {0} + b _ {c} ^ {0}\right), \forall \ell > 0, g _ {i: c} ^ {\ell} := \xi \left(\left\| f _ {i: c} ^ {\ell} \right\| _ {2} + b _ {c} ^ {\ell}\right) \frac {f _ {i : c} ^ {\ell}}{\left\| f _ {i : c} ^ {\ell} \right\| _ {2}} \tag {10} +$$ + +Where the $\xi$ is the ReLu function and the $b^{\ell}$ 's are learnable bias terms. 3D steerable cnns [32] introduce a similar but slightly more elaborate approach called gated nonlinearities. Instead of only producing a multi head equivariant signal $f$ like in TFN, a layer also produces a rotation invariant signal $\gamma^{\ell}$ for each equivariant head $f^{\ell}$ with $\ell > 0$ (one can simply split the invariant head of the signal in two parts) the gated non linearity is defined by: + +$$ +g _ {i 0 c} ^ {0} := \xi \left(f _ {i 0 c} ^ {0} + b _ {c} ^ {0}\right), \forall \ell > 0, g _ {i m c} ^ {\ell} := \sigma \left(\gamma_ {i 0 c} ^ {\ell} + b _ {c} ^ {\ell}\right) f _ {i m c} ^ {\ell} \tag {11} +$$ + +where $\sigma$ is the sigmoid function and the $b^{\ell}$ are learnable bias vectors. On the other hand [17] and [2] consider tensor product non-linearities. The idea is to take tensor products + +of equivariant features and decompose them using the Clebsch Gordan Decomposition producing quadratic equivariant features: + +$$ +g _ {i,: c} ^ {J} := \bigoplus_ {J \in [ | \ell - k |, \ell + k ]} Q ^ {(k, \ell), J} f _ {i,: c} ^ {k} \otimes f _ {i,: c} ^ {\ell} \tag {12} +$$ + +where the $\oplus$ sign indicates concatenation on the last axis. The supplementary material of [32] also provides a description of the aforementioned non-linearities. + +# 3. Our method + +In this section we present our method and the specific changes we introduce to the pipeline presented in section (2). Our main contribution is to interpret rotation equivariant features as coefficients of functions in the spherical harmonics basis with two applications: Equivariant nonlinearities and equivariant spatial max pooling. Before detailing these points we specify our kernel design and point cloud sampling strategy. + +Our kernels and sampling strategy As explained in equation (2) of section (2) point cloud convolution requires two point clouds a first point cloud carries the signal and the second one (typically a sub-sampling or up-sampling of the first one) defines the locations at which to apply the convolution kernels. We adopt the same sampling strategy as [24], we consider point clouds whose cardinal is a power of two and index them by a balanced kd-tree, we can then sub-sample the point cloud by applying 1D average pooling with a pool size which also a power of two. This computes the means of sub-trees at a given depth. For convolutions we use a similar kernel to [30, 32, 24] but our normalization differs slightly as we empirically observed a slight improvement with the L2 normalization (14). Like [32, 24] we chose Gaussian shell functions for the radial component functions $\varphi$ of equation (4) but, we divide by the sum of the radial functions so that each point in the kernel support is assigned a mass of 1 and, we restrict the kernel support to a ball of radius $r$ . Denoting $r_j \coloneqq \frac{jr}{d}$ we define the radial component of the steerable kernel of Eq. (4) by: + +$$ +\varphi_ {r _ {j} m} (\| x \| _ {2}) := \frac {\exp \left(- \ln (2) d ^ {2} \left(\| x \| _ {2} - r _ {j}\right) ^ {2}\right)}{\sum_ {k = 0} ^ {d - 1} \exp \left(- \ln (2) d ^ {2} \left(\| x \| _ {2} - r _ {k}\right) ^ {2}\right)} \tag {13} +$$ + +We normalize the kernels at each point by their average L2 norm, leading to the following formula for the normalization factor $c_{ir\ell}$ in formula (4): + +$$ +c _ {i r \ell} = \left(\frac {1}{N} \sum_ {i = 1} ^ {N} \left(\sum_ {j \sim i} \| \kappa_ {r} ^ {\ell} \left(x _ {j} ^ {k} - x _ {i} ^ {k + 1}\right) \| _ {2} ^ {2}\right) ^ {\frac {1}{2}}\right) ^ {- 1}. \tag {14} +$$ + +Equivariant features as functions The convolution layers presented in equations (4, 8, 9) of section (2) produce + +equivariant features tensors $(f^{\ell})_{\ell}$ where the type $\ell$ ranges between 0 and $\ell_{\mathrm{max}}\geqslant 0$ , we set the same number of channels for each head. We observe that type $\ell$ rotation equivariant features as defined in equation (6) of section (2) and spherical harmonics of degree $\ell$ share the same equivariance properties, that is they are multiplied by the Wigner matrix $D^{\ell}(R)$ when their input is rotated by $R\in \mathrm{SO}(3)$ . This motivates us to interpret them as coefficients of functions in the spherical harmonics basis. For each point $i$ and channel index $c$ we can compute the inverse Spherical Harmonics Transform (SHT) resulting in a function on the unit sphere: + +$$ +\mathcal {F} ^ {+} (f) _ {i c} (x) := \sum_ {\ell = 0} ^ {\ell_ {\max }} \left\langle f _ {i: c} ^ {\ell}, Y ^ {\ell} (x) \right\rangle = \sum_ {\ell = 0} ^ {\ell_ {\max }} \sum_ {m = - \ell} ^ {\ell} f _ {i m c} ^ {\ell} Y _ {m} ^ {\ell} (x) \tag {15} +$$ + +Equivariant non-linearities The inverse SHT functional representation allows us to apply non-linearities in a pointwise fashion over the sphere by composing $\mathcal{F}^{+}(f)$ with any activation function $\xi$ and, compute the coefficients of the composition in the spherical harmonics basis using forward SHT: + +$$ +\xi (f) _ {i m c} ^ {\ell} := \mathcal {F} (\xi \circ \mathcal {F} ^ {+} (f) _ {i c}) ^ {\ell} := \int_ {\mathcal {S} _ {2}} \xi (\mathcal {F} ^ {+} (f) _ {i c} (x)) Y _ {m} ^ {\ell} (x) \mathrm {d} x \tag {16} +$$ + +Our contribution relies on the following observation: + +Theorem 3.1 Our continuous non linearity $\xi (\bullet)$ is SO(3) equivariant. That is, for any rotation $R\in \mathrm{SO}(3)$ we have $\xi (R.f)_{i:c}^{\ell} = D^{\ell}(R)\xi (f)_{i:c}^{\ell}$ . + +We refer to the supplementary material for a proof. Unfortunately there is no closed form for the integral of equation (16) so, in practice we have to rely on a discrete approximation of the SHT and its inverse. For that we consider a discrete sampling of the unit sphere given by a finite set of points $p_1, \ldots, p_N \in S_2$ , we define the discretized inverse SHT by: + +$$ +\mathcal {F} ^ {+} (f) _ {i j c} := \mathcal {F} ^ {+} (f) _ {i c} \left(p _ {j}\right) \tag {17} +$$ + +We then apply the non-linearity $\xi$ at all points $(p_j)_j$ and compute the coefficients of this discrete approximation of $\mathcal{F}^{+}(f)_{ic}$ into the spherical harmonic basis using the discretized SHT (18). Given a discrete signal $\{F_{ijk}\}$ over the points $P = (p_j)_j$ for all point $i$ of the input point cloud and all channel index $c$ we define our SHT layer by: + +$$ +\mathcal {F} (F) _ {i m c} ^ {\ell} := \frac {4 \pi}{N} \sum_ {j = 1} ^ {N} F _ {i j c} Y _ {m} ^ {\ell} \left(p _ {j}\right) \tag {18} +$$ + +We use the intermediate representation $\mathcal{F}^{+}(f)$ to apply pointwise operations at each sample $p_j$ like a dense layer over the channel axis and non-linearities or more generally + +MLP's while maintaining equivariance up to our discretization. We apply our activation function $\xi$ to $f$ by: + +$$ +\left. \xi [ f ] _ {i m c} ^ {\ell} := \mathcal {F} \left(\xi \circ \mathcal {F} ^ {+} (f)\right) _ {i m c} \right. \tag {19} +$$ + +We consider different samplings of the sphere, a first choice motivated by theorem (3.2) is to use the vertices of polyhedrons with non trivial symmetry groups. Specifically we chose the Regular dodecahedron with its 20 vertices and the Pentakis decahedron with its 32 vertices. + +Theorem 3.2 Our non linearity $\xi[\bullet]$ is equivariant w.r.t. the symmetry group of the sampling. That is, for any rotation $R \in \mathrm{SO}(3)$ in the symmetry group of the sampling $P$ we have $\xi[R.f]_{i:c}^{\ell} = D^{\ell}(R)\xi[f]_{i:c}^{\ell}$ . + +We refer to the supplementary material for a proof. We also consider the Fibonacci Sampling from [23] providing a more systematic and flexible sampling allowing to choose the number of points. + +Equivariant pooling An other benefit of our approach is that we can use our functional representation to perform max pooling. Given a sub-sampling $y$ of the point cloud $x$ we define local max pooling by: + +$$ +\mathrm {M P} (f) _ {i c} ^ {l} = \mathcal {F} \left(\max _ {i \sim j} \mathcal {F} ^ {+} (f) _ {i, \dots}\right) _ {i c} ^ {\ell} \tag {20} +$$ + +where $j$ ranges across the $k$ -nearest neighbours of $y_{i}$ in $x$ . We also define global max-pooling by: + +$$ +\operatorname {G M P} (f) _ {c} ^ {\ell} := \mathcal {F} \left(\max _ {i} \mathcal {F} ^ {+} (f) _ {i, \dots}\right) _ {c} ^ {\ell} \tag {21} +$$ + +# 3.1. Architecture and models + +In our experiments we consider a classification and a segmentation architecture. The basic brick of our architectures is our equivariant point cloud convolution layer described in figure (1). It has been shown in [10] that simply concatenate each conv layer of TFN with the $yzx$ coordinates of the underlying point clouds without applying non-linearities is enough to ensure that the resulting class of networks is a universal approximator of equivariant features (up to certain choices of radial functions in the definition of the kernels). Here we adopted this construction to compensate for the loss of information induced by the truncation of the features type. We adopt following notations to describe our layers and network architecture: + +We denote our equivariant convolution layer by $EC(K,r,d,\ell_{\max},[u_0,\ldots ,u_k])$ where: + +- $K$ is the number of centroid points at which to apply equivariant kernels. +- $r$ is the radius of the $K$ convolution windows. +- $d$ is the number of shells of the kernels. + +- $\ell_{\mathrm{max}}$ is the highest equivariant output type of the layer. +- $u_{0}$ is the number of units of the dense layers applied to the output of the equivariant convolution. +- $[u_1, \ldots, u_k]$ are the number of units of the MLP layers. + +![](images/ce9528b0e564af9be55f2a5bf272cdf88a1c4efa1aa4c6bacdbbf9b9ec5dc244.jpg) +Figure 1. Our convolution layer takes a dictionary of tensors of equivariant features $(f^{\ell ,k})_{\ell ,k}$ for $\ell \in [0,\ell_{\mathrm{max}}^{k}]$ as input. First we concatenate type 1 features with the $yzx$ coordinates of the underlying point cloud, then we perform equivariant convolution (9) and again concatenate type 1 output features with the $yzx$ coordinates of the next point cloud. We apply inverse SHT from Eq. (17) followed by a batch norm layer and ReLu activation optionally followed by an MLP. Finally we obtain a new set of equivariant features $(f^{\ell ,k + 1})_{\ell ,k}$ for $\ell \in [0,\ell_{\mathrm{max}}^{k + 1}]$ by computing SHT from Eq. (18). + +We denote by $FC(k,d)$ a fully connected layer with $k$ units followed by a batch normalization and ReLu layer and a dropout layer with dropout rate $d$ . Our classification architecture is as follows: + +$$ +\begin{array}{l} E C (2 5 6, 0. 2, 3, 3, [ 3 2, 3 2, 3 2 ]) \\ \rightarrow E C (6 4, 0. 4, 3, 3, [ 6 4, 6 4, 6 4 ]) \\ \rightarrow E C (1 6, 0. 8, 3, 3, [ 1 2 8, 1 2 8, 2 5 6 ]) \tag {22} \\ \rightarrow \mathrm {G M P} \rightarrow \mathrm {n o r m} \\ \rightarrow F C (5 1 2, 0. 5) \rightarrow F C (2 5 6, 0. 5) \rightarrow F C (K) \\ \end{array} +$$ + +It takes a point cloud with 1024 points index it by a kd-tree and computes coarser point clouds of size 256, 64 and 16 using average kd-tree pooling. Then it computes three successive equivariant convolution layers as in figure (1), taking the constant signal equal to 1 as a type 0 feature input to the first layer. After the last convolution we have equivariant tensors of types 0 to 3 representing a signal over the 16 points of the last point cloud, we apply a global max pooling layer (21), compute the norms of the resulting global features and pass them through a final two layers MLP for the class prediction. + +For segmentation we adopt a U-Net like architecture inspired by the segmentation architecture of [27]. Like our classification architecture we have three equivariant convolution layers going from a point cloud with 2048 points to a coarse point cloud of 32 points. We then up sample the + +signal back to 2048 points using feature the propagation layers from [27] described in equation (3). The output of each feature propagation layer is concatenated with the output of the convolutional layer on the corresponding point cloud if available or the $yzx$ coordinates of the input point cloud for the last feature propagation layer. Then we apply fully connected layers over the channel axis and equivariant activation as described in figure (1) (with no MLP to reduce computational cost). We denote our feature propagation layer by $FP(d)$ where $d$ is the number of units of the fully connected layers. Our segmentation architecture is as follows: + +$$ +\begin{array}{l} E C (5 1 2, 0. 2, 3, 3, [ 1 6 ]) \rightarrow E C (1 2 8, 0. 4, 3, 3, [ 3 2 ]) \\ \rightarrow E C (3 2, 0. 8, 3, 3, [ 6 4 ]) \tag {23} \\ \rightarrow F P (6 4) \rightarrow F P (3 2) \rightarrow F P (3 2) \rightarrow \mathrm {n o r m} \\ \rightarrow F C (1 2 8, 0. 1) \rightarrow F C (1 2 8, 0. 1) \rightarrow F C (K) \\ \end{array} +$$ + +# 4. Experiments and results + +We evaluate our method in point cloud classification and segmentation tasks. We consider three different experimental train / test settings: $z/z$ , $z/SO(3)$ and $SO(3)/SO(3)$ where $z$ stands for aligned data augmented by random rotations around the vertical axis and $SO(3)$ indicates data augmented by random $SO(3)$ rotations. The data is randomly rotated at each training iteration. We consider different non-linearities for TFN: 'ReLu' where we simply use a ReLu activation in our equivariant convolution layer (EC) described in Figure (1), 'mlp' where we stack a two layer mlp on top of the ReLu activation, 'norm' which is the original TFN non linearity and 'gated' which is the gated non linearity from [32]. For each non linearity $x$ we denote $\mathrm{TFN}[x]$ the TFN version based on $x$ . Thus $\mathrm{TFN}[\mathrm{norm}]$ is similar to the original TFN. We use the following abbreviations to refer to the sampling pattern: R for the regular dodecahedron, P for the Pentakis dodecahedron and F for Fibonacci sampling. + +We compare to two categories of methods: rotation sensitive and, rotation robust methods which are specifically designed for handling non aligned data. The $z / z$ case offers a baseline for rotation sensitive methods. The $z / \mathrm{SO}(3)$ setting allows to measure the robustness of a method to the observation of new poses unseen during training while, the $\mathrm{SO}(3) / \mathrm{SO}(3)$ is the most practical setting as in practice it is more representative of real world where the pose of objects is not known in advance nor consistent and, it is always possible to apply random rotation augmentation. + +For classification we consider two datasets. The ModelNet40 dataset [33] consists of 12,311 synthetic shapes in canonical pose divided into 40 categories with a 9,843/2,468 train / test split and the ScanObjectNN dataset [3] which consists of 2902 point clouds sampled from real-world objects across 15 different categories with a 2309/581 + +train test split. For segmentation we consider the ShapeNet part dataset [6] which contains 16,881 shapes from 16 classes, annotated with 50 parts labels in total. We trained all our models with a TensorFlow [1] implementation using the Adam optimizer [15] with learning rate 0.001. We used a batch size of 32 for classification reported in section (4.1) and 24 for segmentation reported in section (4.2). + +# 4.1. Classification + +Table (1) shows our results for classification on ModelNet40 and compares it to state of the art methods. We considered an alternative variant of our method using prealignment with PCA refereed to by the indication (PCA). We trained our models for 200 epochs and observed convergence in around 150 epochs. We report two different metrics, since the ModelNet40 dataset does not have an official validation set we used the test set as validation set and select the best model over training based on validation score. We average the test score over 40 randomly rotated copies of the test set to smooth the variability introduced by random rotations augmentation. We use the same best $z/z$ model for both the $z/z$ and $z/SO(3)$ scores. We refer to these results with the indication (best). We observed oscillations of validation accuracy even after convergence we included these results to indicate an upper bound of the performance of our models. For fair comparison we also report the average validation accuracy over the last 10 epochs which is more representative of actual performance. While our method is mostly robust to rotations as suggested by the $z/SO(3)$ setting, we still observe a performance drop but this is due to our pooling and activation being only approximately equivariant in practice. We notice that our PCA pre-aligned version produced more consistent results across the 3 different settings $z/z$ , $z/SO(3)$ and $SO(3)/SO(3)$ . + +Our method does not quite match the best state of the art methods yet, these methods either rely on richer input data or slightly different representation. EMVnet [12] consider a multi-view image based representation of the shapes based on renderings of meshes. LGR-Net [39] relies on surface normals, SFCNN [28] propose an original approach similar to multi-view by mapping input point-clouds to a sphere. Our results are close to GC-Conv [36] and RI-Framework [20] which both rely only on the point coordinates. + +A fundamental question is whether it is enough to stack purely invariant layers for rotation invariant tasks, it has been stated in in GC-Conv [36] that rotation invariant features are usually not as distinctive as non invariant ones. In this work we rely on equivariant layers which unlike invariant layers can transmit directional information to the next layers. Our baseline for rotation invariant layers is SPHNet [24] as we use very similar spherical harmonics based kernels in a 3 layered conv architecture, the difference is that SPHNet takes the norm of each equivariant features right + +after convolution instead of computing equivariant convolution. These observations together with our results showing a noticeable improvement over SPHNet suggest that simply stacking invariant layers is not optimal. + +We propose an ablation study of our ModelNet40 experiment in table (2) to compare our equivariant non-linearity (19) to the norm non-linearity (11) introduced in [30] and gated non linearity (12) introduced in [32]. We also study the impact of the number of samples and the sampling pattern on the performance of our non linearity. For better comparison with other non-linearities we consider TFN[ReLU] so that we only measure the effect of our new non linearity. We apply the norm and gated non linearites on top of the fully connected layers following the equivariant convolution step. To produce a global descriptor layers in our classification architecture we apply norm in a pointwise fashion, reducing equivariant features to invariant scalars, allowing to apply rotation invariant global max pooling. Results are shown in table 2, we observe a noticeable improvement over the norm and gated non-linearities baselines and interestingly the results of TFN[norm] are very close to the results of SPHNet [24] shown in table (1). Although the later uses purely invariant layers both rely on non similar linearities applied only to the norm of equivariant features. As for the effect of the number of samples we observe as expected that more samples improves robustness to rotations as shown by the $z / \mathrm{SO}(3)$ setting. We add a qualitative study of the equivariance error w.r.t. the number of samples in the supplementary material. + +We report results on ScanObjectNN [3] in table (4). We compare our method to several state of the art methods, in particular the recent SE(3)-Transformers framework [13] introducing a transformer architecture built on top of TFN. We follow the same experimental setting as [13], training our network until convergence (100 epochs) and average over 5 runs on the basic OBJ_ONLY version of the dataset with no rotation augmentation and using the $z$ coordinate as a 0 type input (indicated by $+z$ ). We achieve comparable results to SE(3)-Transf.+z [13] and noticeably better results than TFN+z. We note that SE(3)-Transf uses less input points but in (Appendix D.1.2) of [13] the authors report that increasing the number of point did not improve the performance. We also adapted the radius of our kernels(0.14, 0.28, 0.56 instead of 0.2, 0.4, 0.8 for Modelnet40. + +# 4.2. Segmentation + +For our segmentation experiment on ShapeNet [6] we used the official train/val/test split we select the best model according to the validation accuracy over a 150 epochs training which is a fair metric since validation and test sets are distinct. Table (3) compares our per class and average class intersection over union scores (IoU) to state of the art methods. Our method falls in between GC-Conv [36] and + +RI-Framework [20] which both use only $xyz$ coordinates of the point clouds as we do unlike the best performing method LGR-Net [39] which also uses normals. We again observe a noticeable improvement over other TFN non-linearities. + +
Rot-sensitive Methodsz/zz/SO(3)SO(3)/SO(3)
SubVolSup MO [26]89.545.585.0
PointNet [25]87.021.680.3
PointNet++ [27]91.828.485
PointCNN [21]92.541.284.5
DGCNN [31]92.920.081.1
ShellNet [38]93.119.987.8
PCNN [4]92.311.985.1
Rot-robust Methodsz/zz/SO(3)SO(3)/SO(3)
EMVnet [12]94.4-91.1
SPHNet [24]87.786.687.6
Spherical-CNN [11]88.976.786.9
a3S-CNN [22]89.687.988.7
ClusterNet [7]87.187.187.1
RI-Conv [37]86.586.486.4
GC-Conv [36]89.089.189.2
RI-Framework [20]89.489.489.3
LGR-Net [39]90.990.991.1
SFCNN(xyz) [28]91.484.890.1
SFCNN(xyz+n) [28]92.385.391.0
TFN[mlp] P89.487.989.0
TFN[mlp] P + PCA88.688.788.8
TFN[mlp] P (best)90.588.289.3
TFN[mlp] P + PCA (best)89.789.789.7
+ +Table 1. Test classification accuracy on the modelnet40 dataset [33] in three train / test scenarios. $z$ stands for aligned data augmented by random rotations around the vertical axis and SO(3) indicates data augmented by random SO(3) rotations. (best) stands for the best model selected over 200 training epochs. + +
Methods# samplesz/zz/SO(3)SO(3)/SO(3)time
TFN[norm]-87.786.787.227s
TFN[gated]-88.386.787.827s
TFN[ReLU] R2089.187.088.525s
TFN[ReLU] P3289.188.188.125s
TFN[ReLU] F1689.881.888.625s
TFN[ReLU] F3289.685.488.825s
TFN[ReLU] F6489.387.688.226s
TFN[norm] (b)-88.585.387.627s
TFN[gated] (b)-88.787.188.527s
TFN[ReLU] R (b)2089.686.589.025s
TFN[ReLU] P (b)3289.887.289.125s
TFN[ReLU] F (b)1690.383.488.625s
TFN[ReLU] F (b)3289.684.789.025s
TFN[ReLU] F (b)6489.987.289.226s
+ +Table 2. Comparison of equivariant non-linearities for TFN on the ModelNet40 classification dataset. ReLu is our non linearity (19), norm is the norm non linearity of Eq. (11) introduced in [30], gated is the gated non linearity of Eq. (12) introduced in [32]. (b) stands for the best model selected over 200 training epochs. Timings in seconds for 1 epoch are given for an RTX 3090gpu. + +
methodaerobagcapcarchairearph.guitarknifelamplaptopmotormugpistolrocketskatetableavg. mIoU
z/SO(3)
PointNet [25]40.448.146.324.545.139.429.242.652.736.721.255.029.726.632.135.837.8
PointNet++ [27]51.366.050.825.266.727.729.765.659.770.117.267.349.923.443.857.648.3
PointCNN [21]21.852.052.123.629.418.240.736.951.133.118.948.023.027.738.639.934.7
DGCNN [31]37.050.238.524.143.932.323.748.654.828.717.874.425.224.143.132.337.4
ShellNet [38]55.859.449.626.540.351.253.852.859.241.828.971.437.949.140.937.347.2
RI-Conv [37]80.680.070.868.886.870.387.384.777.880.657.491.271.552.366.578.475.3
GC-Conv [36]80.982.681.070.288.470.687.187.281.878.958.791.077.952.366.880.377.2
RI-Framework [20]81.482.386.375.388.572.890.382.181.381.967.592.675.554.875.178.979.2
LGR-Net [39]81.580.581.475.587.472.688.783.483.186.866.292.976.862.980.080.080.0
TFN[norm]80.176.584.771.088.167.690.180.875.879.357.692.573.958.073.678.776.8
TFN[gated]80.078.882.471.188.473.589.975.576.378.960.091.275.448.372.979.277.0
TFN[ReLU]81.177.879.874.589.177.290.882.877.778.660.393.477.054.774.479.578.1
TFN[ReLU] + PCA80.975.281.973.889.061.090.883.076.980.258.592.876.354.074.579.176.7
SO(3)/SO(3)
PointNet [25]81.668.774.070.387.668.588.980.074.983.656.577.675.253.969.479.974.4
PointNet++[27]79.571.687.770.788.864.988.878.179.294.954.392.076.450.368.481.076.7
PointCNN [21]78.080.178.268.281.270.282.070.668.980.848.677.363.250.663.282.071.4
DGCNN [31]77.771.877.755.287.368.788.785.581.881.336.286.077.351.665.380.273.3
ShellNet [38]79.079.680.264.187.471.388.881.979.195.157.291.269.855.873.079.377.1
RI-Conv [37]80.680.270.768.886.870.487.284.378.080.157.391.271.352.166.678.575.3
GC-Conv [36]81.282.681.670.288.670.686.286.681.679.658.990.876.853.267.281.677.3
RI-Framework [20]81.484.585.175.088.272.490.784.480.384.068.892.676.152.174.180.079.4
LGR-Net [39]81.778.182.575.187.674.589.486.183.086.465.392.675.264.179.880.580.1
Ours norm79.979.681.668.087.673.490.382.376.279.856.092.273.346.174.178.476.2
TFN[gated]79.677.881.271.188.475.090.281.978.077.761.292.575.452.173.278.876.9
TFN[ReLU]80.874.582.874.489.475.790.681.077.880.562.493.378.555.874.779.578.2
TFN[ReLU] + PCA80.377.382.674.788.876.390.781.777.482.460.793.279.454.374.779.678.4
+ +Table 3. Test segmentation mean per class and mean intersection over union (IoU) on the ShapeNet shape segmentation benchmark [6]. $z$ stands for aligned data augmented by random rotations around the vertical axis and SO(3) indicates data augmented by random SO(3) rotations. PCA stands for PCA pre-alignment. + +
Methods# pointstest acc
DeepSet [35]102471.4
3DmFV [5]102473.8
Set Transformer [19]102474.1
PointNet [25]102479.2
SpiderCNN [34]102479.5
TFN+z [30]12881.0
PointNet++ [27]102484.3
SE(3)-Transf.+z [13]12885.0
PointCNN [21]102485.5
DGCNN [31]102486.2
PointGLR [29]102487.2
TFN[norm] + z102480.7
TFN[norm] + z (best)102483.2
TFN[gated] + z102481.1
TFN[gated] + z (best)102483.0
TFN[MLP]+z102485.3
TFN[MLP]+z (best)102488.1
+ +Table 4. Classification accuracy on the ScanObjectNN [3] OBJ_ONLY dataset the $z$ stands for $z$ coordinate as 0 type feature input. The central column indicates the number of input points. (best) stands for the best model selected over 100 training epochs. TFN is the original TFN implementation while TFN[norm] is our implementation of TFN. + +# 5. Conclusion and future work + +In this work we highlight the importance of the design of equivariant non-linearities. We introduced a novel rotation equivariant non-linearity for Tensor Field Networks [30] based on a functional interpretation of equivariant features. In future work we would like to explore this idea further. An interesting direction would be to use equivariant features to produce rotation equivariant functions over the 3D space with potential applications such as rotation equivariant auto encoder based on implicit surface representation. In our experiments we observed that better performing methods such as [39, 28] often use point cloud normals. Tensor Field Networks are direction agnostic as they are SO(3) equivariant. Adding local direction information like normals allows to reduce the dimension of the rotation group by restricting SO(3) tor rotations around the normals which might help designing more informative and cost effective equivariant non-linearities. + +# Acknowledgements + +This work was supported by a Vannevar Bush Faculty Fellowship, a grant from the Stanford-Toyota Center for AI Research, and gifts from Adobe, Autodesk and the Amazon AWS ML program. + +# References + +[1] Martin Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. Tensorflow: A system for large-scale machine learning. In 12th {USENIX} symposium on operating systems design and implementation (\{OSDI\} 16), pages 265-283, 2016. 6 +[2] Brandon Anderson, Truong-Son Hy, and Risi Kondor. Cormorant: Covariant molecular neural networks. arXiv preprint arXiv:1906.04015, 2019. 1, 2, 3 +[3] Mikaela Angelina Uy, Quang-Hieu Pham, Binh-Son Hua, Duc Thanh Nguyen, and Sai-Kit Yeung. Revisiting point cloud classification: A new benchmark dataset and classification model on real-world data. arXiv, pages arXiv-1908, 2019. 6, 7, 8 +[4] Matan Atzmon, Haggai Maron, and Yaron Lipman. Point convolutional neural networks by extension operators. arXiv preprint arXiv:1803.10091, 2018. 1, 2, 7 +[5] Yizhak Ben-Shabat, Michael Lindenbaum, and Anath Fischer. 3dmfv: Three-dimensional point cloud classification in real-time using convolutional neural networks. IEEE Robotics and Automation Letters, 3(4):3145-3152, 2018. 8 +[6] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford University — Princeton University — Toyota Technological Institute at Chicago, 2015. 1, 6, 7, 8 +[7] Chao Chen, Guanbin Li, Ruijia Xu, Tianshui Chen, Meng Wang, and Liang Lin. Clusternet: Deep hierarchical cluster network with rigorously rotation-invariant representation for point cloud analysis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4994-5002, 2019. 1, 7 +[8] Gregory S Chirikjian, Alexander B Kyatkin, and AC Buckingham. Engineering applications of noncommutative harmonic analysis: with emphasis on rotation and motion groups. Appl. Mech. Rev., 54(6):B97-B98, 2001. 2, 3 +[9] Pim de Haan, Maurice Weiler, Taco Cohen, and Max Welling. Gauge equivariant mesh cnns: Anisotropic convolutions on geometric graphs. arXiv preprint arXiv:2003.05425, 2020.1 +[10] Nadav Dym and Haggai Maron. On the universality of rotation equivariant point cloud networks. arXiv preprint arXiv:2010.02449, 2020. 3, 5 +[11] Carlos Esteves, Christine Allen-Blanchette, Ameesh Makadia, and Kostas Daniilidis. Learning so (3) equivariant representations with spherical cnns. In Proceedings of the European Conference on Computer Vision (ECCV), pages 52–68, 2018. 1, 7 +[12] Carlos Esteves, Yinshuang Xu, Christine Allen-Blanchette, and Kostas Daniilidis. Equivariant multi-view networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 1568–1577, 2019. 1, 6, 7 +[13] Fabian B Fuchs, Daniel E Worrall, Volker Fischer, and Max Welling. Se (3)-transformers: 3d roto-translation equivariant + +attention networks. arXiv preprint arXiv:2006.10503, 2020. 7,8 +[14] Yulan Guo, Hanyun Wang, Qingyong Hu, Hao Liu, Li Liu, and Mohammed Bennamoun. Deep learning for 3d point clouds: A survey. IEEE transactions on pattern analysis and machine intelligence, 2020. 1 +[15] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. 6 +[16] Anthony W Knapp. Representation theory of semisimple groups: an overview based on examples, volume 36. Princeton university press, 2001. 2, 3 +[17] Risi Kondor, Zhen Lin, and Shubhendu Trivedi. Clebsch-gordan nets: a fully fourier space spherical convolutional neural network. arXiv preprint arXiv:1806.09231, 2018. 1, 2, 3 +[18] Leon Lang and Maurice Weiler. A wigner- Eckart theorem for group equivariant convolution kernels. arXiv preprint arXiv:2010.10952, 2020. 2, 3 +[19] Juho Lee, Yoonho Lee, Jungtaek Kim, Adam Kosiorek, Seungjin Choi, and Yee Whye Teh. Set transformer: A framework for attention-based permutation-invariant neural networks. In International Conference on Machine Learning, pages 3744-3753. PMLR, 2019. 8 +[20] Xianzhi Li, Ruihui Li, Guangyong Chen, Chi-Wing Fu, Daniel Cohen-Or, and Pheng-Ann Heng. A rotation-invariant framework for deep point cloud analysis. arXiv preprint arXiv:2003.07238, 2020.1,6,7,8 +[21] Yangyan Li, Rui Bu, Mingchao Sun, Wei Wu, Xinhan Di, and Baoquan Chen. Pointcnn: Convolution on x-transformed points. In NIPS, pages 820-830, 2018. 1, 2, 7, 8 +[22] Min Liu, Fupin Yao, Chiho Choi, Ayan Sinha, and Karthik Ramani. Deep learning 3d shapes using alt-az anisotropic 2-sphere convolution. In International Conference on Learning Representations, 2018. 1, 7 +[23] Ricardo Marques, Christian Bouville, Mickaël Ribardière, Luis Paulo Santos, and Kadi Bouatouch. Spherical fibonacci point sets for illumination integrals. In Computer Graphics Forum, volume 32, pages 134-143. Wiley Online Library, 2013. 5 +[24] Adrien Poulenard, Marie-Julie Rakotosaona, Yann Ponty, and Maks Ovsjanikov. Effective rotation-invariant point cnn with spherical harmonics kernels. In 2019 International Conference on 3D Vision (3DV), pages 47-56. IEEE, 2019. 1, 2, 4, 6, 7 +[25] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 652-660, 2017. 1, 7, 8 +[26] Charles R Qi, Hao Su, Matthias Nießner, Angela Dai, Mengyuan Yan, and Leonidas J Guibas. Volumetric and multi-view cnns for object classification on 3d data. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5648-5656, 2016. 7 +[27] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on + +point sets in a metric space. In NIPS, pages 5099-5108, 2017. 1, 2, 5, 6, 7, 8 +[28] Yongming Rao, Jiwen Lu, and Jie Zhou. Spherical fractal convolutional neural networks for point cloud recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 452-460, 2019. 1, 6, 7, 8 +[29] Yongming Rao, Jiwen Lu, and Jie Zhou. Global-local bidirectional reasoning for unsupervised representation learning of 3d point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5376-5385, 2020. 8 +[30] Nathaniel Thomas, Tess Smidt, Steven Kearnes, Lusann Yang, Li Li, Kai Kohlhoff, and Patrick Riley. Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds. arXiv preprint arXiv:1802.08219, 2018. 1, 2, 3, 4, 7, 8 +[31] Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E Sarma, Michael M Bronstein, and Justin M Solomon. Dynamic graph cnn for learning on point clouds. arXiv preprint arXiv:1801.07829, 2018. 1, 2, 7, 8 +[32] Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, and Taco Cohen. 3d steerable cnns: Learning rotationally equivariant features in volumetric data. In NIPS, pages 10381-10392, 2018. 1, 2, 3, 4, 6, 7 +[33] Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguuang Zhang, Xiaou Tang, and Jianxiong Xiao. 3d shapenets: A deep representation for volumetric shapes. In Proc. CVPR, pages 1912-1920, 2015. 1, 6, 7 +[34] Yifan Xu, Tianqi Fan, Mingye Xu, Long Zeng, and Yu Qiao. Spidercnn: Deep learning on point sets with parameterized convolutional filters. In Proceedings of the European Conference on Computer Vision (ECCV), pages 87-102, 2018. 8 +[35] Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Russ R Salakhutdinov, and Alexander J Smola. Deep sets. In Advances in neural information processing systems, pages 3391-3401, 2017. 8 +[36] Zhiyuan Zhang, Binh-Son Hua, Wei Chen, Yibin Tian, and Sai-Kit Yeung. Global context aware convolutions for 3d point cloud understanding. arXiv preprint arXiv:2008.02986, 2020. 1, 6, 7, 8 +[37] Zhiyuan Zhang, Binh-Son Hua, David W Rosen, and Sai-Kit Yeung. Rotation invariant convolutions for 3d point clouds deep learning. In 2019 International Conference on 3D Vision (3DV), pages 204–213. IEEE, 2019. 1, 7, 8 +[38] Zhiyuan Zhang, Binh-Son Hua, and Sai-Kit Yeung. Shellnet: Efficient point cloud convolutional neural networks using concentric shells statistics. In Proceedings of the IEEE International Conference on Computer Vision, pages 1607–1616, 2019. 7, 8 +[39] Chen Zhao, Jiaqi Yang, Xin Xiong, Angfan Zhu, Zhiguo Cao, and Xin Li. 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Chan + +Department of Computer Science, City University of Hong Kong + +jiawan1998@gmail.com, ziquanliu2-c@my.cityu.edu.hk, abchan@cityu.edu.hk + +# Abstract + +Previous work [40] shows that a better density map representation can improve the performance of crowd counting. In this paper, we investigate learning the density map representation through an unbalanced optimal transport problem, and propose a generalized loss function to learn density maps for crowd counting and localization. We prove that pixel-wise L2 loss and Bayesian loss [29] are special cases and suboptimal solutions to our proposed loss function. A perspective-guided transport cost function is further proposed to better handle the perspective transformation in crowd images. Since the predicted density will be pushed toward annotation positions, the density map prediction will be sparse and can naturally be used for localization. Finally, the proposed loss outperforms other losses on four large-scale datasets for counting, and achieves the best localization performance on NWPU-Crowd and UCF-QNRF. + +# 1. Introduction + +Crowd counting and localization draw increasing attention recently because of its practical usage in surveillance, transport management and business. Most of the algorithms predict a density map from a crowd image, where the summation of the density map is the crowd count [41, 4]. A density map (a smooth heat map) is an intermediate representation of the crowd – one popular method to generate the ground-truth density map is to place a Gaussian kernel on each person's dot annotation. The density map estimator is then trained as a standard pixel-wise regression problem using L2 loss [12, 40] (see Fig. 1a). In contrast to pixel-wise L2 loss, Bayesian loss (BL) [29] generates an aggregated dot prediction from the density map prediction, and uses a point-wise loss function between the ground-truth dot annotations and the aggregated dot prediction (see Fig. 1b). + +Both L2 and BL assume a fixed ground-truth representation, either Gaussian density kernels for L2 or Gaussian likelihoods for BL. Recent works [40, 43] have shown that the intermediate density map representation affects the counting performance, and a better density map representation can be learned in an end-to-end manner from the dot + +![](images/72514d63be7ff3395e26489eba623c1e925f981cbb2eb2ce489e9efb36e34e7f.jpg) +Figure 1: Loss functions for counting: (a) L2 loss generates density map as the supervision and uses a pixel-wise loss function. (b) Bayesian loss (BL) [29] computes an aggregated dot prediction and uses a point-wise loss function. We show that L2 and BL are related to an optimal transport problem using a suboptimal transport matrix. (c) Our proposed loss is based on unbalanced optimal transport, where the transport cost is fully minimized and both the pixel-wise and point-wise losses are considered. + +annotations. However, [40, 43] still use L2 loss for training, which is not appropriate in suppressing background and improving localization. In particular, with L2 loss, a unit change in density in background regions (which is a large localization error) is equivalent to a unit change in density near a dot annotation (which is a small localization error). Thus the L2 loss function is not ideal for localization or generating compact density maps, and we should prefer a loss function that has an increased penalty for errors far from the annotations, so as to improve localization and compactness. + +Considering both motivations of learning the density map representation and using localization-sensitive loss, we propose a generalized loss function based on an unbalanced optimal transport (OT) framework, which measures the transport cost between the predicted density map and the ground-truth dot annotations (see Fig. 1c). We show that the transport matrix, which is optimized to minimize the loss, is related to the intermediate density map representation. To better handle perspective changes in the image, we propose a perspective-guided transport cost function to better separate the density around people who are close together due to the camera perspective. The proposed loss function decomposes into four terms: 1) a transport loss that pushes the + +predicted density toward annotations; 2) a transport regularization term that prevents collapse onto a single annotation; 3) a pixel-wise loss that measures the difference between the predicted density map and the constructed density map (from the transport matrix); 4) a point-wise loss that ensures that all annotations are accounted for in the predicted density map. We further show that our proposed loss is a generalization of the traditional L2 loss with Gaussian density kernel and BL, i.e., they are special cases and suboptimal solutions to the unbalanced OT in our proposed loss. + +Compared to previous losses, our proposed loss function has four advantages: 1) the density map representation is learned via the optimized transport matrix; 2) it does not require any special design for background regions (such as [29, 42]), and naturally pushes predicted density away from the background and towards the annotations; 3) it produces compact density maps that can be naturally used for localization; 4) it is less sensitive to the blur factor hyperparameter (which is equivalent to the Gaussian kernel variance). In summary, the contributions of the paper are four-fold: + +1. We propose a generalized loss function, motivated by unbalanced optimal transport theory, for crowd counting and localization. We prove L2 and BL are special cases and suboptimal solutions of our loss function. +2. To handle perspective effects in crowd images, we propose a perspective-guided transport cost, which increases transport costs of density far from the camera, thus making densities in those regions more compact. +3. In extensive experiments on crowd counting, using our loss achieves better performance than traditional loss functions on three large-scale datasets, NWPU-Crowd, JHU-CROWD++, and UCF-QNRF. +4. Our low-resolution predicted density maps (1/8 image size) achieve the best localization performance on two large benchmarks NWPU-Crowd and UCF-QNRF. + +# 2. Related Works + +Traditional crowd counting Traditional methods count the number of people in an image by detecting human bodies [18] or body parts [20], which does not work well for images with high crowd density. Thus, direct regression methods are proposed based on low-level features [4, 5, 12]. + +Density map based counting Most of recent methods use a deep neural network (DNN) to predict density maps [42] from crowd images, where the sum over density map is the crowd count [19]. The DNN is trained using L2 pixel-wise loss. Various DNN structures are proposed to address scale variation [50, 33, 15], to refine the predicted density map [30, 31, 35], and to encode context information [36, 47]. To improve the generalization ability, [49] proposes a cross-scene crowd counting method. [46] proposes a synthetic dataset and a domain adaptation method to adapt DNNs trained from synthetic data to real images. [7] focuses on + +semantic consistency across different domains. Since the labeling of crowd images is time-consuming, semi-supervised and weakly-supervised methods are proposed. [26] proposes a ranking loss to utilize unlabeled data, while [38] proposes a Gaussian Process-based iterative model with limited labeled data. [28] proposes to learn generic features with self-training on surrogate tasks. Active learning is also used for crowd counting with limited supervision [51]. + +Loss functions Although most of the crowd counting methods use L2 norm as the loss function, L2 loss is sensitive to the choice of variance in the Gaussian kernel [40]. Therefore, Bayesian loss (BL) [29] is proposed with pointwise supervision. However, BL cannot well handle false positives in the background, and requires a special design for the background region. [41] proposes a generative model for spatial noise in dot annotations, and derives a novel loss function that is robust to annotation noise. + +The most related work to ours is the concurrent work of DM-count [44], which considers density maps and dot maps as probability distributions, and uses balanced OT to match the shape of the two distributions. The DM-count loss is composed of three terms: the OT loss, a total variation (TV) pixel-wise loss, and a counting loss. There are four key differences between our work and DM-count. First, DM-count normalizes the density map predictions and the dot map to compute the balanced OT between them. Since normalization removes the actual count in the two maps, an additional counting loss is required to ensure that the count (i.e., the sum of the density map) is predicted correctly. However, this counting loss provides poor supervision, since its gradient adds the same constant value to all pixels (see Supp. A). In contrast, our proposed loss is based on unbalanced OT, which preserves the count of the prediction and GT dot annotations – any mismatch in counts is penalized by our pixel-wise and point-wise loss terms, which give direct pixel-wise supervision on the erroneous predictions. Second, the TV loss used in DM-count is a pixel-wise loss between the normalized density map prediction and the normalized dot map, which is prone to over-fitting especially for the localization task. In contrast, our work contains a pixel-wise loss between the predicted density map and optimized constructed density map (via the transport matrix), which is less prone to over-fit. Third, we show that our loss is a generalization of other loss functions (L2 and BL) when a sub-optimal fixed transport matrix is used. Fourth, DM-count uses the standard squared Euclidean distance as the transport cost, while our work uses a perspective-guided transport cost to increase the separation between people's density in crowded regions, which improves localization. We compare our loss with DM-count in the ablation study. + +Crowd Localization To perform counting, density map estimation and localization simultaneously, [13] proposes a composition loss function. [23] proposes to localize crowd + +locations by a recurrent zooming network, while [22] proposes a detection-based method with RGB-D data. [32] propose to count, localize, and estimate head size simultaneously. [45] proposes a large-scale benchmark for crowd counting and localization. These works use pixel-wise losses, which are sensitive to the kernel bandwidth. In contrast, our loss pushes density towards annotation and is less sensitive to the bandwidth, and thus robust for localization. + +# 3. A Generalized Loss Function for Crowd Counting and Localization + +Recent work [40] shows that learning the intermediate density map representation yields improved performance in counting networks, which suggests the importance of directly using the ground-truth (GT) dot annotations for supervision, rather than a fixed GT density map. However, [40] uses L2 pixel-wise loss for training, which is not appropriate since small changes in background density (which are large localization errors) are equivalent to small changes in density over a person (which are small localization errors). Thus a loss function that penalizes the distance of the error to the annotation is preferred, as in optimal transport (OT) cost between the predicted density map and the dot annotations. Note that the predicted density map and GT dot annotations may not have the same count, due to mis-predictions, or annotation noise (missing/duplicate annotations). Considering these issues, we propose to use unbalanced optimal transport (UOT) as the loss function for training. This loss function both learns the density map representation (uses dot annotations as supervision), and handles count mismatches between the prediction and GT. + +# 3.1. Generalized loss function + +Formally, let the predicted density map be $\mathcal{A} = \{(a_i,\pmb {x}_i)\}_{i = 1}^n$ , where $a_{i}$ is the predicted density of pixel $\pmb {x}_i\in \mathbb{R}^2$ and $n$ is the number of pixels. We denote $\pmb {a} = [a_i]_i$ as the predicted density map. The ground-truth dot map is $\mathcal{B} = \{(b_j,\pmb {y}_j)\}_{j = 1}^m$ , where $\pmb {y}_j$ is the location of the $j$ -th annotation, $m$ is the number of annotation points, and $b_{j}$ is the number of people represented by the annotation. In this paper, we assume $\pmb {b} = [b_j]_j = 1_m$ . + +Our loss function is based on the entropic-regularized unbalanced optimal transport cost, + +$$ +\begin{array}{l} \mathcal {L} _ {\mathbf {C}} ^ {\tau} (\mathcal {A}, \mathcal {B}) = \min _ {\mathbf {P} \in \mathbb {R} _ {+} ^ {n \times m}} \left\langle \mathbf {C}, \mathbf {P} \right\rangle - \varepsilon H (\mathbf {P}) \tag {1} \\ + \tau D _ {1} (\mathbf {P} 1 _ {m} | \boldsymbol {a}) + \tau D _ {2} (\mathbf {P} ^ {\top} 1 _ {n} | \boldsymbol {b}). \\ \end{array} +$$ + +$\mathbf{C} \in \mathbb{R}_{+}^{n \times m}$ is the transport cost matrix, whose entry $C_{ij}$ measures the cost of moving the predicted density at $\pmb{x}_i$ to GT dot annotation $\pmb{y}_i$ via the cost function $C_{ij} = c(\pmb{x}_i, \pmb{y}_j)$ . $\mathbf{P}$ is the transport matrix, which (fractionally) assigns each each location $\pmb{x}_i$ from $\mathcal{A}$ to $\pmb{y}_i$ from $\mathcal{B}$ for measuring the cost. The optimal transport cost is obtained by minimizing the loss over $\mathbf{P}$ . Note that $\hat{\pmb{a}} = \mathbf{P}1_m$ is the construction + +![](images/5df5445de631f2034311f594c5f3c69b05ad8921d71e0d9b89ced3129ab1502c.jpg) +Figure 2: The relationship between density map, annotations, and transport matrix: (top) optimal transport; (bottom) fixed transport from Bayesian loss [29]. (a) predicted density maps with 81 pixels and 2 annotations; (b) transport matrix $\mathbf{P} \in \mathbb{R}^{81 \times 2}$ , where the arrow length represents the transport value, and the direction points to the assigned annotation; (c) columns of $\mathbf{P}$ ; (d,e) the transport plan for annotation $b_{0}$ and $b_{1}$ , reshaped to a map, equivalent to the ground-truth density map for each annotation. The fixed transport (bottom) assigns false positives in the background to annotations, while the optimal transport (top) only considers nearby density. The optimal transport is more sparse, which is better for localization. + +![](images/b0ee5e65af0a7f31deaf70e55236ec78234b1022024010431b8209c9e5712a8a.jpg) + +![](images/d10e48aa6522e14043d8646418c7c587a48715eecc6f03c7bf9142918dfa377e.jpg) + +![](images/4309f90229d413aedbd1e86bb3738607a65f86b7f8f0e313eb0b6c79ccf31a4b.jpg) + +of a intermediate density map representation from the GT annotations, while $\hat{\pmb{b}} = \mathbf{P}^{\top}1_{n}$ is the reconstruction of the GT dot annotations. See Fig. 2 (top) for an example. + +The loss function decomposes into four terms. The first term $\langle \mathbf{C},\mathbf{P}\rangle$ is the transport loss, which encourages prediction of density values near the annotations; it pushes the predicted density towards the annotation during training. The second term $H(\mathbf{P}) = -\sum_{ij}P_{ij}\log P_{ij}$ is the entropic regularization term, which favors partial transports between locations, resulting in spread-out (less compact) density maps. Larger values of $\varepsilon$ will yield less compact predicted density maps, and vice-versa. The third term $D_{1}(\mathbf{P}1_{m}|a)$ is the pixel-wise loss between the predicted density map $a$ and the constructed intermediate density map representation $\hat{\pmb{a}} = \mathbf{P}1_{m}$ , i.e., the "ground-truth" density map. Finally, the fourth term $D_{2}(\mathbf{P}^{\top}1_{n}|b)$ is the point-wise loss between the reconstructed annotations $\hat{\pmb{b}} = \mathbf{P}^{\top}1_{n}$ and the GT annotations. The last two terms are complementary - the pixelwise term $D_{1}$ ensures that all predicted density values have a corresponding annotation, while the point-wise term $D_{2}$ ensures that all GT annotations are accounted for (used in the transport plan). In other words, any predicted density that is not associated with an annotation is penalized, and any annotation that is not used is penalized. + +In our implementation, we use squared L2 norm for the pixel-wise term and L1-norm for the point-wise term, + +$$ +D _ {1} \left(\mathbf {P} 1 _ {m} | \boldsymbol {a}\right) = \left\| \mathbf {P} 1 _ {m} - \boldsymbol {a} \right\| _ {2} ^ {2}, \tag {2} +$$ + +$$ +D _ {2} \left(\mathbf {P} ^ {\top} 1 _ {n} | \boldsymbol {b}\right) = \| \mathbf {P} ^ {\top} 1 _ {n} - \boldsymbol {b} \| _ {1}. \tag {3} +$$ + +In Sec. 4, we show that L2 and BL are suboptimal solutions to our proposed generalized loss function, which use a fixed intermediate representation (i.e., transport matrix). + +# 3.2. Perspective-Guided Transport Cost + +We next propose a transport cost function for crowd counting. A typical cost function is the squared Euclidean distance between the two points, $L_{ij}^2 = \| \pmb{x}_i - \pmb{y}_j\|_2^2$ , which considers all distances equally throughout the image. How + +ever, due to the perspective effect in crowd images, people that are farther from the camera will appear closer together in the image, while those closer to the camera will be farther apart in the image. In order to keep the density of people in the "far" crowds from leaking together, the transport costs for those regions in the image should be higher, which will make the density for those people more compact. + +To encode perspective information in crowd images, a perspective-guided cost function is proposed to have larger penalty for the transport of density far from the camera. Formally, the cost function is defined as: + +$$ +C _ {i j} = \exp \left(\frac {1}{\eta \left(\boldsymbol {x} _ {i} , \boldsymbol {y} _ {j}\right)} \| \boldsymbol {x} _ {i} - \boldsymbol {y} _ {j} \| _ {2}\right), \tag {4} +$$ + +where $\eta (\pmb {x}_i,\pmb {y}_j)$ is an adaptive perspective factor, which is mapped between an interval based on the average height $\frac{1}{2} (h_{\pmb{x}_i} + h_{\pmb{y}_j})$ , where $h_\pmb {x}\in [0,1]$ refers to normalized height of the pixel $\pmb{x}$ in the image. We use the exponential in (4) to enhance the cost of moving densities over long distances, which makes the predicted density maps more compact. + +# 3.3. Optimization of transport matrix + +As shown in [1], the solution to (1) for the optimization of transport matrix $\mathbf{P}$ is unique, and has the form + +$$ +\mathbf {P} = \operatorname {d i a g} (\mathbf {u}) \mathbf {K} \operatorname {d i a g} (\mathbf {v}), \quad \mathbf {K} = \exp (- \mathbf {C} / \varepsilon), \tag {5} +$$ + +where $\mathbf{K}$ is the Gibbs kernel constructed from the cost matrix $\mathbf{C}$ , and $\exp$ is element-wise exponential. For the optimization of $\mathbf{P}$ in (1), we approximate $D_{1}$ and $D_{2}$ with KL divergence, since this yields an efficient algorithm. The $\mathbf{u},\mathbf{v}$ are computed with the generalized Sinkhorn iterations, + +$$ +\mathbf {u} ^ {(\ell + 1)} = \left(\frac {\boldsymbol {a}}{\mathbf {K v} ^ {(\ell)}}\right) ^ {\frac {\tau}{\tau + \epsilon}}, \quad \mathbf {v} ^ {(\ell + 1)} = \left(\frac {\boldsymbol {b}}{\mathbf {K} ^ {\top} \mathbf {u} ^ {(\ell + 1)}}\right) ^ {\frac {\tau}{\tau + \epsilon}}, \tag {6} +$$ + +where the division and exponent operations are elementwise. To compute network gradients, the optimal $\mathbf{v}^*$ is considered as a constant, and $\mathbf{u}^*$ is a function of $\pmb{a}$ , i.e., $\mathbf{P} = \mathrm{diag}(\mathbf{u}^{*}(\mathbf{a}))\mathbf{K}\mathrm{diag}(\mathbf{v}^{*})$ . + +# 3.4. Density map counting and localization + +To apply our loss function to density map counting, we learn a density map estimator $f(\mathcal{I})$ , whose input is the image $\mathcal{I}$ , and output is the density map vector $\mathbf{a}$ . The predicted density map $\mathcal{A}$ , together with the corresponding GT annotations $\mathcal{B}$ , are fed into the loss function in (1). To compute the loss, the transport matrix $\mathbf{P}$ is optimized for each input separately using (5) and the iterations in (6). Given the test image, the density map estimator predicts the density map, which is then summed to obtain the count. + +We perform localization by applying simple post-processing to the predicted density map $\pmb{a}$ . First, $\pmb{a}$ is upsampled to the image size since the density map is $\frac{1}{8}$ of the input image size (due to pooling operations). Then, a pixel is considered a candidate for a predicted location if its + +value is the local maximum in a $3 \times 3$ window centered on the pixel. Finally, the candidates with density larger than 0.05 are the final location predictions. + +# 4. Relationship with traditional losses + +In this section, we prove that the traditional L2 loss and Bayesian loss (BL) [29] are suboptimal solutions to the unbalanced OT in our loss function in (1). In particular, L2 and BL are both 2-stage approximations to solve (1), consisting of: 1) constructing a half-iteration approximate solution of the transport matrix $\mathbf{P}$ using entropic-regularized balanced OT with squared Euclidean transport cost; 2) substituting the approximate $\mathbf{P}$ into our loss in (1). Because the computed $\mathbf{P}$ is a half-iteration approximation to the minimization in (1), both L2 and BL are suboptimal approximations of our loss function. + +# 4.1. Half-iteration approximations for P + +We first derive closed-form solutions to approximate $\mathbf{P}$ under the entropic-regularized balanced OT problem. Removing the last two terms in (1), we obtain the entropic regularized OT problem, + +$$ +\mathcal {L} _ {\mathbf {C}} ^ {\varepsilon} (\mathcal {A}, \mathcal {B}) = \min _ {\mathbf {P} \in \mathbb {R} _ {+} ^ {n \times m}} \left\langle \mathbf {C}, \mathbf {P} \right\rangle - \varepsilon H (\mathbf {P}), \tag {7} +$$ + +where $\mathbf{C},\mathcal{A},\mathcal{B}$ are defined as before. As shown in [1], the solution to (7) is unique with $\mathbf{P} = [P_{ij}]_{ij}$ , + +$$ +P _ {i j} = u _ {i} K _ {i j} v _ {j}, \quad K _ {i j} = \exp (- C _ {i j} / \varepsilon), \tag {8} +$$ + +where $\mathbf{u} = [u_i]_i, \mathbf{v} = [v_j]_j$ are from the Sinkhorn iterations, + +$$ +\mathbf {u} ^ {(\ell + 1)} = \frac {\mathbf {a}}{\mathbf {K v} ^ {(\ell)}}, \quad \mathbf {v} ^ {(\ell + 1)} = \frac {\mathbf {b}}{\mathbf {K} ^ {\top} \mathbf {u} ^ {(\ell + 1)}}, \tag {9} +$$ + +where the division is element-wise. Typically, the iterations are initialized with $\mathbf{v} = 1_{m}$ . + +We next obtain 2 approximate solutions to $\mathbf{P}$ , by substituting a half Sinkhorn iteration, $\mathbf{u}^{(\ell +1)}$ or $\mathbf{v}^{(\ell +1)}$ , into (8), + +$$ +\hat {P} _ {i j} = \left[ \frac {\boldsymbol {a}}{\mathbf {K v}} \right] _ {i} K _ {i j} v _ {j}, \quad \tilde {P} _ {i j} = u _ {i} K _ {i j} \left[ \frac {\boldsymbol {b}}{\mathbf {K} ^ {\top} \mathbf {u}} \right] _ {j}. \tag {10} +$$ + +If $\mathbf{v}$ is uniform (as in the typical initialization) and the cost function $C_{ij}$ is the squared Euclidean distance, then + +$$ +\hat {P} _ {i j} = \frac {K _ {i j}}{\sum_ {j = 1} ^ {m} K _ {i j}} a _ {i} = \hat {\pi} _ {i j} a _ {i}, \quad \hat {\pi} _ {i j} = \frac {\exp (- \| \boldsymbol {x} _ {i} - \boldsymbol {y} _ {j} \| ^ {2} / \varepsilon)}{\sum_ {j = 1} ^ {m} \exp (- \| \boldsymbol {x} _ {i} - \boldsymbol {y} _ {j} \| ^ {2} / \varepsilon)}. +$$ + +Similarly, assuming $\mathbf{u}$ is initialized as uniform and $C_{ij}$ is the squared Euclidean distance, then for $\tilde{P}_{ij}$ we have + +$$ +\tilde {P} _ {i j} = \frac {K _ {i j}}{\sum_ {i = 1} ^ {n} K _ {i j}} b _ {j} = \tilde {\pi} _ {i j}, \quad \tilde {\pi} _ {i j} = \frac {\exp \left(- \| \boldsymbol {x} _ {i} - \boldsymbol {y} _ {j} \| ^ {2} / \varepsilon\right)}{\sum_ {i = 1} ^ {n} \exp \left(- \| \boldsymbol {x} _ {i} - \boldsymbol {y} _ {j} \| ^ {2} / \varepsilon\right)}, +$$ + +since $b_{j} = 1$ . Note that the difference between $\hat{\pi}_{ij}$ and $\tilde{\pi}_{ij}$ is the summation in the denominator is either over GT annotation locations $y_{j}$ or density map pixels $x_{i}$ , respectively. + +# 4.2. Relationship with L2 Loss + +We now derive the L2 loss as a special case of our loss function when using the suboptimal transport matrix $\tilde{\mathbf{P}}$ . Substituting into (1), we note that the first 2 terms, $\langle \mathbf{C},\tilde{\mathbf{P}}\rangle$ and $H(\tilde{\mathbf{P}})$ are constants w.r.t. $\pmb{a}$ , and thus do not affect the loss in terms of $\pmb{a}$ . Next, it is straightforward to show + +that $\tilde{\mathbf{P}}^{\top}1_{n} = 1_{m}$ , and therefore the fourth term in (1) is $D_{2}(\tilde{\mathbf{P}}^{\top}1_{n}|b) = 0$ . Only the third term (i.e., the pixel-wise loss) remains, and assuming $\tau = 1$ , we have the loss + +$$ +\begin{array}{l} \tilde {\mathcal {L}} (\mathcal {A}, \mathcal {B}) = D _ {1} \left(\tilde {\mathbf {P}} 1 _ {m} | \boldsymbol {a}\right) = \sum_ {i = 1} ^ {n} \left(a _ {i} - \tilde {a} _ {i}\right) ^ {2}, (11) \\ \tilde {a} _ {i} = \left[ \tilde {\mathbf {P}} 1 _ {m} \right] _ {i} = \sum_ {j = 1} ^ {m} \tilde {\pi} _ {i j} = \sum_ {j = 1} ^ {m} \frac {\exp \left(- \| \boldsymbol {x} _ {i} - \boldsymbol {y} _ {j} \| ^ {2} / \varepsilon\right)}{\sum_ {i = 1} ^ {n} \exp \left(- \| \boldsymbol {x} _ {i} - \boldsymbol {y} _ {j} \| ^ {2} / \varepsilon\right)}. (12) \\ \end{array} +$$ + +Note that $\tilde{a}_i$ is equivalent to a "ground-truth" density map value at pixel location $i$ , which places a Gaussian kernel with squared-bandwidth $\epsilon / 2$ at each annotation $y_j$ . The denominators in (12) are the normalization constants of each Gaussian. Thus from (11) and (12), our loss using the approximate transport matrix $\tilde{\mathbf{P}}$ is equivalent to L2 loss with traditional Gaussian-based density maps for supervision. + +# 4.3. Relationship with Bayesian Loss + +We next derive BL [29] as a special case of our loss using approximation $\hat{\mathbf{P}}$ . Note that $\hat{\pi}_{ij}$ is the probability of assigning the density value of the $i$ -th pixel to the $j$ -th annotation point, as defined in [29]. Since $[\hat{\mathbf{P}} 1_m]_i = \sum_{j=1}^m \hat{\pi}_{ij} a_i = a_i$ , then the third term in (1) is $D_1(\hat{\mathbf{P}} 1_m | \boldsymbol{a}) = 0$ . Assuming that $\epsilon$ is small (so that the entropy term can be ignored) and $\tau = 1$ , we have the loss + +$$ +\begin{array}{l} \hat {\mathcal {L}} (\mathcal {A}, \mathcal {B}) = \langle \mathbf {C}, \hat {\mathbf {P}} \rangle + D _ {2} \left(\hat {\mathbf {P}} ^ {\top} 1 _ {n} | \boldsymbol {b}\right) (13) \\ = \sum_ {i = 1} ^ {n} \omega_ {i} a _ {i} + \sum_ {j = 1} ^ {m} | 1 - \sum_ {i = 1} ^ {n} \hat {\pi} _ {i j} a _ {i} |, (14) \\ \end{array} +$$ + +where $\omega_{i} = \sum_{j=1}^{m} C_{ij} \hat{\pi}_{ij} = \sum_{j} ||\boldsymbol{x}_{i} - \boldsymbol{y}_{j}||^{2} \hat{\pi}_{ij}$ is a weight on the prediction $a_{i}$ . The second term in (14) is exactly the point-wise Bayesian loss defined in [29]. The first term in (14) can be interpreted as a background loss, which penalizes non-zero values of $a_{i}$ for pixels $\boldsymbol{x}_{i}$ far from any annotation (i.e., false positives). In particular, the weight $\omega_{i}$ on the i-th pixel is based on a weighted average of squared distances from the pixel to the annotations. + +We now relate the background term in (14) with the background model used in BL [29]. The background loss in [29] is based on the nearest annotation to each point $\boldsymbol{x}_i$ (details in Supp. B), + +$$ +\mathcal {L} _ {B G} = \left| 0 - \sum_ {i = 1} ^ {n} \bar {\omega} _ {i} a _ {i} \right| = \sum_ {i = 1} ^ {n} \bar {\omega} _ {i} a _ {i}, \tag {15} +$$ + +where the weight $\bar{\omega}_i = \frac{\bar{k}_i}{\bar{k}_i + \sum_{j=1}^m K_{ij}}$ and $\bar{k}_i = \exp(-(d - ||\pmb{x}_i - \pmb{y}_{\eta(i)}||)^2/\varepsilon)$ , and $\eta(i)$ is the index of the annotation nearest to $\pmb{x}_i$ . The weight can be rewritten as $\bar{\omega}_i = \exp\left(\frac{2d}{\varepsilon} ||\pmb{x}_i - \pmb{y}_{\eta(i)}|| - \frac{d^2}{\varepsilon}\right) \bar{\pi}_i$ , where $\bar{\pi}_i = \frac{K_{i,\eta(i)}}{\bar{k}_i + \sum_{j=1}^m K_{ij}}$ is the weight contribution for the nearest neighbor $\eta(i)$ . Note that (15) and the first term in (14) have the same form, but use different weight values $\bar{\omega}_i$ or $\omega_i$ . For BL, the weight $\bar{\omega}_i$ + +![](images/86c8093e64d7bf58454805e4a7533b59b4008ec65e61d23aba915920a8214450.jpg) +density map +Figure 3: Comparison of background weight maps for Bayesian Loss $(\bar{\omega})$ and approximate UOT $(\omega)$ in (14). + +![](images/3fc6c01b4ea953f409639594c19ed671d19ef6bdf358168c348603f7fe0b07c5.jpg) +Bayesian Loss + +![](images/dbff36f7a6a00d89fecc185c51a7552938e5b7cf093ad67ea4e0a4f960b0a947.jpg) +approximate UOT + +is based on the exponential distance to the nearest annotation $\eta(i)$ . In contrast, for the background term in (14), the weight $\omega_{i}$ is based on a weighted average of squared distances to all annotations. Therefore, the background model used in [29] is a special case of the background term in (14). Fig. 3 shows a visualization of the weights maps for $\bar{\omega}_{i}$ and $\omega_{i}$ . Both BL and (14) have large weights for background regions and small weights for head (annotation) regions. However, the weight map for (14) is smoother since all annotations are considered using squared distances, while the weight map for BL contains flat regions since it uses the exponential distance to only the nearest annotation. + +Thus, from (14), BL with background model is a special case of our proposed loss in (1), where the approximate transport matrix is $\hat{\mathbf{P}}$ and a single-neighbor approximation of the cost matrix $\mathbf{C}$ is used to compute the cost term (i.e., the background loss). If no background model is used, then the cost matrix is assumed to be 0. + +# 5. Experiments + +In this section, we evaluate the counting and localization performance using the proposed general loss function. + +# 5.1. Experimental setups + +Datasets: We evaluate the performance of the proposed loss function on four datasets: ShanghaiTech [50], UCFQNRF [13], JHU-CROWD++ [39], and NWPU-Crowd [45]. ShanghaiTech contains two parts: Part A (482/300 for training/testing) and Part B (716/400 for training/testing). UCF-QNRF is a large-scale dataset consists of 1,535 high-resolution crowd images (1,201/334 for training/testing). JHU-CROWD++ contains 4,317 images (2,722/500/1,600 images are for training/validation/testing). NWPU-Crowd is the largest dataset with 3,109 training images, 500 validation images, and 1,500 testing images (whose labels are not release to public for fair comparison). We report results on the NWPU-Crowd test set. + +Evaluation metrics: Mean absolute error (MAE) and root mean squared error (MSE) are used as the evaluation metric for counting performance, as in previous works [16]: + +$$ +\mathrm {M A E} = \frac {1}{N} \sum_ {i} | y _ {i} - \hat {y} _ {i} |, \mathrm {M S E} = (\frac {1}{N} \sum_ {i} (y _ {i} - \hat {y} _ {i}) ^ {2}) ^ {1 / 2}, +$$ + +where $y_{i}, \hat{y}_{i}$ are the GT and predicted counts. To evaluate the localization performance, we followed the protocols used in NWPU-Crowd and UCF-QNRF, respectively. For + +Table 1: Test results comparing different loss functions with different backbones on UCF-QNRF. + +
VGG19 [29]CSRNet [21]MCNN [50]
MAEMSEMAEMSEMAEMSE
L298.7176.1110.6190.1186.4283.6
BL [29]88.8154.8107.5184.3190.6272.3
NoiseCC [41]85.8150.696.5163.3177.4259.0
DM-count [44]85.6148.3103.6180.6176.1263.3
Ours84.3147.592.0165.7142.8227.9
+ +NWPU-Crowd, Precision, Recall and F-measure are used, and Precision, Recall and AUC are used for UCF-QNRF. + +Backbone and training: Following the experiment settings in [41], we use 3 backbone networks: VGG19 [29], CSRNet [21], and MCNN [50]. We train the counting network using our loss function in (1), where $\mathbf{P}$ is solved using the generalized Sinkhorn iterations in (6). We set $\varepsilon = 0.005$ . In practice, $\varepsilon$ -scaling heuristic is used for acceleration, which needs less than 20 iterations until converge, and the computation is calculated in log-domain for numerical stability as in [6]. In preliminary studies using the exponential transport cost, we observe that $\eta \in \{0.6, 0.8\}$ yield better performance (Fig. 4a). Thus for the perspective-guided cost, we simply map the range of image pixel y-coordinates to $\eta \in [0.6, 0.8]$ . VGG19 and CSRNet are pre-trained on ImageNet, and MCNN is trained from scratch. Adam optimizer [17] is used to train the networks with learning rate $10^{-5}$ for VGG19/CSRNet, and $10^{-4}$ for MCNN. + +# 5.2. Ablation studies + +We first conduct ablation studies on our loss function on UCF-QNRF or JHU-CROWD++. + +# 5.2.1 Comparison with different losses + +In Table 1, we compare the performance of loss functions with different backbones, including L2 pixel-wise loss, Bayesian loss (BL) [29], NoiseCC [44], which models noisy annotations, and DM-count [44], which uses balanced OT as part of their loss. Our proposed loss function achieves the lowest MAE among all loss functions. Our loss function outperforms L2 and BL since we use an optimal transport plan, instead of fixed as shown in Sec. 4, and a better transport plan (i.e., density map) can achieve better performance as shown in [43]. Compared to DM-count, our loss function achieves better performance especially for MCNN trained from scratch. Our loss function is based on unbalanced OT using exponential transport cost, while DM-count is based on balanced OT and squared-Euclidean cost. We further compare the unbalanced/balanced OT frameworks and transport cost functions in the next 2 ablation studies. + +# 5.2.2 The effect of transport cost functions + +We evaluate the effectiveness of the proposed perspective-guided transport cost by comparing with other cost functions, including Euclidean distance $(L_{ij})$ , squared Euclidean $(L_{ij}^{2})$ , and exponential of Euclidean $(e^{L_{ij}})$ . The + +test results are shown in Fig. 4a. First, the standard cost function based on Euclidean distance is less effective than the exponential cost function. The perspective-guided cost achieves the best performance, which confirms that adapting the cost function to the perspective changes is effective for crowd counting. We visualize the density maps predicted with different cost functions in Fig. 6. Using exponential cost yields a more compact density map compared to the squared Euclidean cost. Furthermore, using perspective-guided cost yields more sparsity for high-density regions, which demonstrates that its efficacy at pushing away density from background to annotations. + +Finally, TV loss used in [44] assumes the same smoothness for all annotations, which is incompatible with the perspective-guided (PG) cost that produces different smoothness for each annotation. To confirm this, we conduct an experiment by decreasing the weight of TV loss by $10\mathrm{x}$ , and the performance using PG cost improved to MAE 66, which is still worse than using exponential cost with fixed $\eta = 0.8$ (MAE 64). Thus, TV loss hinders the PG transport cost (with adaptive smoothness), but works with the exponential cost with fixed $\eta$ (i.e., fixed smoothness). + +# 5.2.3 The effect of unbalanced/balanced OT + +We next compare our unbalanced OT framework with the balanced OT of DM-count [44], using the same transport cost functions in Sec. 5.2.2. As seen in Fig. 4a, our proposed loss outperforms DM-Count when using different cost functions, which demonstrates the efficacy of unbalanced OT for the density map regression problem. Our proposed loss is based on the unbalanced OT problem, where extra/missing density is penalized using both point-wise and pixel-wise losses. In contrast, DM-count uses balanced OT, and requires an additional count loss, which is a map-wise loss that is less effective (see discussion in Sec. 2 "loss functions"). Second, the TV loss in DM-Count uses the normalized dot map for pixel-wise supervision, which is prone to overfitting. Finally, our proposed cost is more effective at pushing away density from background to annotations compare to squared Euclidean cost (see Sec. 5.2.2). + +# 5.2.4 The effect of $\varepsilon$ + +We next investigate the effect of blur factor $\varepsilon$ , which is equivalent to the Gaussian squared-bandwidth (variance) used to generate the ground-truth density maps for L2 and BL, as shown in Sec. 4.2. The results for varying $\varepsilon$ are shown in Fig. 4b. The L2 loss is sensitive to $\varepsilon$ , with MAE increasing significantly as $\varepsilon$ increases. In contrast, BL and our proposed loss are less sensitive, since the background model in BL and the transport loss in ours can push density towards annotations, always making the predicted density maps compact. The proposed loss function is generally better than BL because the BL background model only consid- + +![](images/9f1fe269c61e7eb61fd3b2117fc9f5a024fa3e819cd12a6d1ee8ec188cb2f6b0.jpg) +(a) +Figure 4: Ablation study: (a) Comparison of different transport cost functions on JHU-CROWD++, using our approach and DM-count [44]. The base cost is Euclidean distance $\mathbf{L}_{ij} = \| \pmb{x}_i - \pmb{y}_j\|_2$ . (b) The effect of $\varepsilon$ for different loss functions. $\varepsilon$ is the Gaussian bandwidth for density maps when using L2 and BL, or the blur factor for our unbalanced OT. (c) The effect of $\tau$ . (d) Comparison of divergences for point-wise and pixel-wise costs on UCF-QNRF. + +![](images/cea2ce97c58e115a9cb7fc0ffb2f9087b0b429ca40226671db6c46e93cea8243.jpg) +(b) + +![](images/49dbe5dc65ad61d7dc4346056f56dd4a176b918350eb2762753d9cea5a9e5cde.jpg) +(c) +(d) + +
175point-wise
170
165L1L2
160MAE MSEMAE MSE
155
145pixel- L188.0 149.588.7 152.1
140wise L284.3 147.588.3 160.0
135
+ +![](images/f3b4ccf1bc14985776cace6342e0f92dbfa51b02ee9159a301c4dc15f6f62728.jpg) +Figure 5: Visualization of density maps predicted from models trained with different loss functions and blur factors $\varepsilon$ . Note that the width and height of the trained images patches are normalized to 1. The sparsity is defined as the percentage of pixels with density less than 0.001, and the most sparse density map is shown in red bold. + +ers the nearest annotation, while our loss considers all annotations (see Sec. 4.3). A visualization is shown in Fig. 5. As the $\varepsilon$ increases, the density map for L2 become more blurry and inaccurate, which demonstrates that L2 is sensitive to $\varepsilon$ . BL and our loss are generally robust to the choice of $\varepsilon$ , and the network can learn a sharper density map with the proposed loss function, which is better for localization. + +# 5.2.5 The effect of $\tau$ and divergence function + +Next, we study the effect of $\tau$ and the divergence function for point-wise and pixel-wise cost functions. We try different combinations of L1 and L2 norms with $\tau = 0.5$ , and the results are presented in Fig. 4d. The best performance occurs with point-wise L1 and pixel-wise L2, which matches the common practice for the individual point-wise and pixel-wise-based losses [29, 42]. Next, using L1 and L2 for the point-wise and pixel-wise costs, we vary $\tau$ (see Fig. 4c), and visualize the learned density maps in Fig. 6. As $\tau$ decreases, the density maps become more compact (more sparse), since the transport cost dominates and + +![](images/e733324cfc23305cc4138b424ffcf6cdace35e3bc9723ed5e655eed65244fd4d.jpg) +Figure 6: Visualization of the effect of (top) transport cost functions, and (bottom) $\tau$ . The sparsity is defined as the percentage of pixels with density less than 0.001. + +Table 2: Effectiveness of terms in the loss function on UCF-QNRF. + +
ComponentCombinations
<C, P>✓✓✓✓
H(P)✓✓✓
D1(P1m|a)✓✓✓
D2(P^T 1n|b)✓✓✓
MAE91.185.485.084.3
+ +pushes the density more towards the annotations. + +# 5.2.6 The effect of terms in the loss function + +Finally, we evaluate the effect of different terms in the proposed loss function in Table 2. The most important term is entropic regularization, which controls the smoothness of the prediction to prevent over-fitting. Unbalanced OT (UOT) with either pixel-wise loss (removing $D_{2}$ ) or pointwise loss (removing $D_{1}$ ) can be effective, and is better than the corresponding approximations BL and L2 loss (85.4 vs 88.8; 85.0 vs. 98.7), which shows the effectiveness of using a better transport solution. Finally, UOT with both pixel-wise and point-wise losses further improves the model. + +# 5.3. Comparison with state-of-the-arts + +To evaluate the overall counting performance, we compare VGG19 [29] trained with our loss function with state-of-the-art methods in Table 3. First, compared with the baseline method BL and DM-Count, our method achieves significantly better performance especially for the largescale datasets NWPU-Crowd, JHU-CROWD++, and UCF-QNRF. Second, our model achieves the best MAE on the + +Table 3: Comparison with state-of-the-art crowd counting methods. + +
NWPUJHU++UCF-QNRFShTech AShTech B
MAEMSEMAEMSEMAEMSEMAEMSEMAEMSE
MCNN [50]CVPR'16232.5714.6188.9483.4277.0426.0110.2173.226.441.3
SwitchCNN [33]CVPR'17----228.0445.090.4135.021.633.4
CP-CNN [36]ICCV'17------73.6106.420.130.1
ACSCP [34]CVPR'18------75.7102.717.227.4
CSRNet [21]CVPR'18121.3387.885.9309.2110.6190.168.2115.010.616.0
CL [13]ECCV'18----132.0191.0----
SANet [3]ECCV'18190.6491.491.1320.4--67.0104.58.413.6
DSSINet [25]ICCV'19--133.5416.599.1159.260.696.06.810.3
MBTBF [37]ICCV'19--81.8299.197.5165.260.294.18.015.5
BL [29]ICCV'19105.4454.275.0299.988.7154.862.8101.87.712.7
LSCCNN [32]TPAMI'20--112.7454.4120.5218.266.5101.87.712.7
KDMG [43]TPAMI'20100.5415.569.7268.399.5173.063.899.27.812.7
RPNet [48]CVPR'20------61.296.98.111.6
ASNet [14]CVPR'20----91.6159.757.890.1--
AMSNet [10]ECCV'20----101.8163.256.793.46.710.2
AMRNet [27]ECCV'20----86.6152.261.698.47.011.0
LibraNet [24]ECCV'20----88.1143.755.997.17.311.3
DM-count [44]NeurIPS'2088.4357.668.4283.385.6148.359.795.77.411.8
NoiseCC [41]NeurIPS'2096.9534.267.7258.585.8150.661.999.67.411.3
Ours79.3346.159.9259.584.3147.561.395.47.311.7
+ +Table 4: Localization performance on NWPU-Crowd dataset. + +
PrecisionRecallF-measure
Faster RCNN [25]0.9580.0350.068
TinyFace [9]0.5290.6110.567
VGG+GPR0.5580.4960.525
RAZNet [23]0.6660.5430.599
ours0.8000.5620.660
+ +Table 5: Localization performance on UCF-QNRF dataset. + +
PrecisionRecallAUC
MCNN [50]0.5990.6350.591
ResNet [8]0.6160.6690.612
DenseNet [11]0.7020.5810.637
Encoder-Decoder [2]0.7180.6300.670
CL [13]0.7580.5980.714
DM-Count [44]0.7310.6380.692
VGG19+L20.6050.6700.623
VGG19+BL [29]0.7670.6540.720
VGG19+ours0.7820.7480.763
+ +3 largest datasets and competitive performance on ShanghaiTech, without any special design to extract multi-scale features or to handle noisy annotations. The experiment confirms the effectiveness of the proposed loss function. + +# 5.4. Localization + +Finally, since our loss function trains the model to predict compact density maps that are suitable for localization, we evaluate the localization performance on NWPU-Crowd and UCF-QNRF. We compare against other state-of-the-art that have reported results on localization, and the results are presented in Tables 4 and 5. On NWPU-Crowd, our loss achieves the overall best performance as quantified by F-measure. Faster RCNN, a detector-based approach, has the highest precision but lowest recall, which shows that it cannot handle the small objects far from the camera. In contrast, TinyFace has the highest recall, but the lowest precision, showing that it has many false-positives. Our loss yields a more balanced localization result, obtaining the best F-measure, and the 2nd best precision and recall. RAZNet also achieves better performance than the detection-based methods, via its recurrent zooming mech + +anism for handling small objects. However, our loss outperforms RAZNet, without any special design for predicting high-resolution density maps or zooming mechanism. One localization example from the NWPU-Crowd test set is shown in Fig. 7. + +On UCF-QNRF, the proposed loss outperforms other loss functions including composition loss (CL), which is designed for localization. Our loss also outperforms its baselines L2 and BL, showing the efficacy of the proposed loss over the purely pixel-wise and point-wise losses. The experiment demonstrates that the proposed loss can be naturally used for localization, since the density is encouraged to be compact around the annotations during optimization with transport loss and exponential cost. + +In Supp. D, we show a comparison of the localization results for different loss functions. For L2 loss, many false negatives appear in dense regions, and the recall is the worst, which shows that L2 loss cannot handle small objects far from the camera. BL and DM-Count have better recall, but BL has many false positives in high-density regions, and DM-Count has many false positives even in low-density regions. Our proposed loss achieves both high precision and recall, yielding the best F-measure. + +![](images/4646ef43a244fc1ce434432352afaebd1a4914cca23bef2c1a6f25d4922b7e85.jpg) +Figure 7: Example localization result on NWPU-Crowd test set. + +# 6. Conclusion + +In this paper, we propose a generalized loss function for learning density maps for crowd counting and localization, which is based on unbalanced optimal transport. We prove that traditional L2 and Bayesian loss are special cases and suboptimal solutions of our loss function. A perspective-guided cost function is proposed to handle perspective transformation in crowd images. We then conduct extensive experiments and achieve superior performance on large-scale datasets. Finally, we apply the proposed loss function to crowd localization and achieve the best performance without any special design of the architecture. + +Acknowledgments. This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11212518). + +# References + +[1] Computational optimal transport. Foundations and Trends in Machine Learning, 11(5-6):355-607, 2019. 4 +[2] Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla. Segnet: A deep convolutional encoder-decoder architecture for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(12):2481-2495, 2017. 8 +[3] Xinkun Cao, Zhipeng Wang, Yanyun Zhao, and Fei Su. Scale aggregation network for accurate and efficient crowd counting. In Proceedings of the European Conference on Computer Vision (ECCV), pages 734-750, 2018. 8 +[4] Antoni B Chan, Zhang-Sheng John Liang, and Nuno Vasconcelos. Privacy preserving crowd monitoring: Counting people without people models or tracking. In IEEE Conference on Computer Vision and Pattern Recognition, pages 1-7, 2008. 1, 2 +[5] Antoni B Chan and Nuno Vasconcelos. Bayesianoisson regression for crowd counting. In International Conference on Computer Vision, pages 545-551, 2009. 2 +[6] Jean Feydy, Thibault Séjourne, François-Xavier Vialard, Shun-ichi Amari, Alain Trouve, and Gabriel Peyre. Interpolating between optimal transport and mmd using sinkhorn divergences. In The 22nd International Conference on Artificial Intelligence and Statistics, pages 2681–2690, 2019. 6 +[7] Tao Han, Junyu Gao, Yuan Yuan, and Qi Wang. Focus on semantic consistency for cross-domain crowd understanding. In ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1848-1852. IEEE, 2020. 2 +[8] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 8 +[9] Peiyun Hu and Deva Ramanan. Finding tiny faces. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 951-959, 2017. 8 +[10] Yutao Hu, Xiaolong Jiang, Xuhui Liu, Baochang Zhang, Jungong Han, Xianbin Cao, and David Doermann. Nas-count: Counting-by-density with neural architecture search. arXiv preprint arXiv:2003.00217, 2020.8 +[11] Gao Huang, Zhuang Liu, Laurens Van Der Maaten, and Kilian Q Weinberger. Densely connected convolutional networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4700-4708, 2017. 8 +[12] H. Idrees, I. Saleemi, C. Seibert, and M. Shah. Multi-source multi-scale counting in extremely dense crowd images. In IEEE Conference on Computer Vision and Pattern Recognition, pages 2547-2554, 2013. 1, 2 +[13] Haroon Idrees, Muhammad Tayyab, Kishan Athrey, Dong Zhang, Somaya Al-Maadeed, Nasir Rajpoot, and Mubarak Shah. Composition loss for counting, density map estimation and localization in dense crowds. In Proceedings of the European Conference on Computer Vision (ECCV), pages 532-546, 2018. 2, 5, 8 +[14] Xiaoheng Jiang, Li Zhang, Mingliang Xu, Tianzhu Zhang, Pei Lv, Bing Zhou, Xin Yang, and Yanwei Pang. Attention + +scaling for crowd counting. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4706-4715, 2020. 8 +[15] Di Kang and Antoni B. Chan. Crowd counting by adaptively fusing predictions from an image pyramid. In *British Machine Vision Conference*, page 89, 2018. 2 +[16] Di Kang, Zheng Ma, and Antoni B Chan. Beyond counting: comparisons of density maps for crowd analysis task-counting, detection, and tracking. IEEE Transactions on Circuits and Systems for Video Technology, 2018. 5 +[17] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. 6 +[18] Bastian Leibe, Edgar Seemann, and Bernt Schiele. Pedestrian detection in crowded scenes. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition, volume 1, pages 878-885, 2005. 2 +[19] Victor Lempitsky and Andrew Zisserman. Learning to count objects in images. In Advances in neural information processing systems, pages 1324-1332, 2010. 2 +[20] Min Li, Zhaoxiang Zhang, Kaiqi Huang, and Tieniu Tan. Estimating the number of people in crowded scenes by mid based foreground segmentation and head-shoulder detection. In International Conference on Pattern Recognition, pages 1-4, 2008. 2 +[21] Yuhong Li, Xiaofan Zhang, and Deming Chen. Csrnet: Dilated convolutional neural networks for understanding the highly congested scenes. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1091-1100, 2018. 6, 8 +[22] Dongze Lian, Jing Li, Jia Zheng, Weixin Luo, and Shenghua Gao. Density map regression guided detection network for rgb-d crowd counting and localization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1821-1830, 2019. 3 +[23] Chenchen Liu, Xinyu Weng, and Yadong Mu. Recurrent attentive zooming for joint crowd counting and precise localization. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 1217-1226. IEEE, 2019. 2, 8 +[24] Liang Liu, Hao Lu, Hongwei Zou, Haipeng Xiong, Zhiguo Cao, and Chunhua Shen. Weighing counts: Sequential crowd counting by reinforcement learning. arXiv preprint arXiv:2007.08260, 2020. 8 +[25] Lingbo Liu, Zhilin Qiu, Guanbin Li, Shufan Liu, Wanli Ouyang, and Liang Lin. Crowd counting with deep structured scale integration network. In Proceedings of the IEEE International Conference on Computer Vision, pages 1774-1783, 2019. 8 +[26] Xialei Liu, Joost van de Weijer, and Andrew D Bagdanov. Leveraging unlabeled data for crowd counting by learning to rank. In IEEE Conference on Computer Vision and Pattern Recognition, 2018. 2 +[27] Xiyang Liu, Jie Yang, and Wenrui Ding. Adaptive mixture regression network with local counting map for crowd counting. arXiv preprint arXiv:2005.05776, 2020. 8 +[28] Yan Liu, Lingqiao Liu, Peng Wang, Pingping Zhang, and Yinjie Lei. Semi-supervised crowd counting via self-training + +on surrogate tasks. arXiv preprint arXiv:2007.03207, 2020. 2 +[29] Zhiheng Ma, Xing Wei, Xiaopeng Hong, and Yihong Gong. Bayesian loss for crowd count estimation with point supervision. In Proceedings of the IEEE International Conference on Computer Vision, pages 6142-6151, 2019. 1, 2, 3, 4, 5, 6, 7, 8 +[30] Viresh Ranjan, Hieu Le, and Minh Hoai. Iterative crowd counting. In European Conference on Computer Vision, pages 278-293, 2018. 2 +[31] Deepak Babu Sam and R. Venkatesh Babu. Top-down feedback for crowd counting convolutional neural network. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 7323-7330, 2018. 2 +[32] Deepak Babu Sam, Skand Vishwanath Peri, Mukuntha Narayanan Sundararaman, Amogh Kamath, and Venkatesh Babu Radhakrishnan. Locate, size and count: Accurately resolving people in dense crowds via detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020. 3, 8 +[33] Deepak Babu Sam, Shiv Surya, and R. Venkatesh Babu. Switching convolutional neural network for crowd counting. In IEEE Conference on Computer Vision and Pattern Recognition, pages 4031-4039, 2017. 2, 8 +[34] Zan Shen, Yi Xu, Bingbing Ni, Minsi Wang, Jianguo Hu, and Xiaokang Yang. Crowd counting via adversarial cross-scale consistency pursuit. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5245-5254, 2018. 8 +[35] Zenglin Shi, Le Zhang, Yun Liu, Xiaofeng Cao, Yangdong Ye, Ming-Ming Cheng, and Guoyan Zheng. Crowd counting with deep negative correlation learning. In IEEE Conference on Computer Vision and Pattern Recognition, pages 5382-5390, 2018. 2 +[36] Vishwanath A Sindagi and Vishal M Patel. Generating high-quality crowd density maps using contextual pyramid cnns. In IEEE International Conference on Computer Vision, pages 1879-1888, 2017. 2, 8 +[37] Vishwanath A Sindagi and Vishal M Patel. Multi-level bottom-top and top-bottom feature fusion for crowd counting. In Proceedings of the IEEE International Conference on Computer Vision, pages 1002-1012, 2019. 8 +[38] Vishwanath A Sindagi, Rajeev Yasarla, Deepak Sam Babu, R Venkatesh Babu, and Vishal M Patel. Learning to count in the crowd from limited labeled data. arXiv preprint arXiv:2007.03195, 2020. 2 +[39] Vishwanath A Sindagi, Rajeev Yasarla, and Vishal M Patel. Jhu-crowd++: Large-scale crowd counting dataset and a benchmark method. Technical Report, 2020. 5 +[40] Jia Wan and Antoni Chan. Adaptive density map generation for crowd counting. In Proceedings of the IEEE International Conference on Computer Vision, pages 1130-1139, 2019. 1, 2, 3 +[41] Jia Wan and Antoni Chan. Modeling noisy annotations for crowd counting. In Advances in Neural Information Processing Systems, to appear Dec 2020. 1, 2, 6, 8 +[42] Jia Wan, Wenhan Luo, Baoyuan Wu, Antoni B Chan, and Wei Liu. Residual regression and semantic prior for crowd + +counting. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019. 2, 7 +[43] Jia Wan, Qingzhong Wang, and Antoni B Chan. Kernel-based density map generation for dense object counting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020. 1, 6, 8 +[44] Boyu Wang, Huidong Liu, Dimitris Samaras, and Minh Hoai. Distribution matching for crowd counting. In Advances in Neural Information Processing Systems, to appear Dec 2020. 2, 6, 7, 8 +[45] Qi Wang, Junyu Gao, Wei Lin, and Xuelong Li. Nwp-crowd: A large-scale benchmark for crowd counting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020. 3, 5 +[46] Qi Wang, Junyu Gao, Wei Lin, and Yuan Yuan. Learning from synthetic data for crowd counting in the wild. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pages 8198-8207, 2019. 2 +[47] Feng Xiong, Xingjian Shi, and Dit-Yan Yeung. Spatiotemporal modeling for crowd counting in videos. In Computer Vision (ICCV), 2017 IEEE International Conference on, pages 5161-5169, 2017. 2 +[48] Yifan Yang, Guorong Li, Zhe Wu, Li Su, Qingming Huang, and Nicu Sebe. Reverse perspective network for perspective-aware object counting. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4374-4383, 2020. 8 +[49] Cong Zhang, Hongsheng Li, X. Wang, and Xiaokang Yang. Cross-scene crowd counting via deep convolutional neural networks. In IEEE Conference on Computer Vision and Pattern Recognition, pages 833-841, 2015. 2 +[50] Yingying Zhang, Desen Zhou, Siqin Chen, Shenghua Gao, and Yi Ma. Single-image crowd counting via multi-column convolutional neural network. In IEEE Conference on Computer Vision and Pattern Recognition, pages 589-597, 2016. 2, 5, 6, 8 +[51] Zhen Zhao, Miaojing Shi, Xiaoxiao Zhao, and Li Li. 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Huang1 Joachim Tesch1 David T. Hoffmann2,3* Shashank Tripathi1 Michael J. Black1 + +1Max Planck Institute for Intelligent Systems, Tübingen, Germany + +$^{2}$ University of Freiburg $^{3}$ Bosch Center for Artificial Intelligence + +{ppatel, paul.huang, jtesch, dhoffmann, stripathi, black}@tuebingen.mpg.de + +![](images/585aa37d3c2e055b64e787fc30e414f264f76c0efa26274d4d0beff007cfe5c2.jpg) +Figure 1: AGORA dataset examples. Top row: images with different scenes. Middle: SMPL-X ground-truth bodies rendered in the scene. Bottom: per-person segmentation masks including environmental occlusion (see bottom right image). + +# Abstract + +While the accuracy of 3D human pose estimation from images has steadily improved on benchmark datasets, the best methods still fail in many real-world scenarios. This suggests that there is a domain gap between current datasets and common scenes containing people. To obtain ground-truth 3D pose, current datasets limit the complexity of clothing, environmental conditions, number of subjects, and occlusion. Moreover, current datasets evaluate sparse 3D joint locations corresponding to the major joints of the body, ignoring the hand pose and the face shape. To evaluate the current state-of-the-art methods on more challenging images, and to drive the field to address new problems, we introduce AGORA, a synthetic dataset with high realism and highly accurate ground truth. Here we use 4240 commercially-available, high-quality, textured human scans in diverse poses and natural clothing; this + +includes 257 scans of children. We create reference 3D poses and body shapes by fitting the SMPL-X body model (with face and hands) to the 3D scans, taking into account clothing. We create around 14K training and 3K test images by rendering between 5 and 15 people per image using either image-based lighting or rendered 3D environments, taking care to make the images physically plausible and photoreal. In total, AGORA consists of 173K individual person crops. We evaluate existing state-of-the-art methods for 3D human pose estimation on this dataset, and find that most methods perform poorly on images of children. Hence, we extend the SMPL-X model to better capture the shape of children. Additionally, we fine-tune methods on AGORA and show improved performance on both AGORA and 3DPW, confirming the realism of the dataset. We provide all the registered 3D reference training data, rendered images, and a web-based evaluation site at https://agora.is.tue.mpg.de/. + +# 1. Introduction + +The field of 3D human pose and shape (3DHPS) estimation from images has advanced rapidly with steadily decreasing errors on standard benchmarks [17, 21, 26, 27, 36, 39, 47]. Large training datasets and benchmarks, with ground truth, enable progress and quantitative evaluation. These are difficult to obtain in the case of 3DHPS. Existing datasets have significant limitations and the rate of progress now suggests that these benchmarks are becoming saturated, making it difficult to evaluate how close the field is to fully robust and general solutions. These datasets often have limited clothing, focus on single subjects, have limited occlusion, are captured in laboratory environments, or have a limited range of ages and ethnicities. Additionally, accuracy is evaluated based on a small number of 3D joints, while the body is much more complex. To drive advances in the field, we propose a novel dataset that includes challenging scenarios neglected by earlier datasets and a more challenging evaluation protocol. + +AGORA (Avatars in Geography Optimized for Regression Analysis) is a new publicly available dataset that includes high-resolution (4K) images with ground truth 3D bodies. AGORA goes beyond previous datasets in important ways. It includes accurate 3D body pose and shape of people in varied and complex clothing. People with varied poses, ages and ethnicities appear in complex natural scenes with natural lighting. Additionally, the dataset includes person-person occlusion, environmental occlusion, camera frame occlusion, crowds, children, face and hand pose, large field of view images and people appearing at a wide range of spatial scales. To the best of our knowledge, AGORA is the only dataset that provides all these features together with highly accurate 3D ground truth. Figure 1 shows a few representative examples from the dataset. + +Since there is currently no technology to capture ground truth body shape and pose for real images of this complexity, we rely on synthetic data and a graphics rendering pipeline. Specifically, we purchased 4240 high-quality textured scans of people, which include 257 child scans from 3DPeople [1], AXYZ [2], Human Alloy [4] and Renderpeople [7]. These scans provide a rich variety of ethnicity, age, pose, and clothing variation with realistic textures. We also gathered a variety of scenes as HDRI panoramicas and 3D environments. We randomly sample 3D people and place them in scenes at random distances and orientations. We then render them realistically using a game engine optimized for high-quality output [8]. + +For every scan, we fit the SMPL-X body model [37], taking great care to accurately capture the correct body shape, pose, hand shape, and facial shape; see Fig. 1 middle row. To generate the AGORA ground truth (or reference data), we take an optimization-based approach that fits SMPL-X to each scan. Specifically, we estimate both the + +pose and body shape under clothing, similar to [10, 56]. The estimated SMPL-X fits have an average error of $5\mathrm{mm}$ , making them accurate enough to benchmark existing state-of-the-art (SOTA) methods. For backward compatibility with SMPL, we also provide ground truth in the gender-neutral SMPL format [33] used by many current methods [25, 27, 47]. + +In addition to adults, the AGORA dataset contains images of children. It is probably the only dataset of children with reference 3D pose and shape. Existing 3DHPS methods focus on adult bodies and perform poorly on images of children. With AGORA, we evaluate this performance, but go further and extend the SMPL-X shape space to capture the variation in body shape between infants and adults. Specifically, we introduce a shape dimension that interpolates between an adult SMPL-X body template and the infant SMIL template [18], which we convert to SMPL-X format. This results in an extra shape parameter that can be optimized like any other SMPL-X shape parameter. + +We make the SMPL-X fits available for all the 14529 training and 1225 validation images, enabling training with AGORA. We withhold the ground truth bodies from the 3387 test images and instead provide an evaluation server. While we cannot provide the commercial scans, we provide a "shopping list" of the training and validation scans so that others can purchase them. Purchasing the scans extends the applications of AGORA to other problems such as 3D clothing modeling, neural avatars, and shape regression. We also provide the test scripts for researchers to test their methods on the validation set. + +We use AGORA to evaluate SOTA 3DHPS methods with a novel protocol. In addition to the common 3D joint-based error measures, we provide a vertex-to-vertex error, and evaluate body, hands and face pose and shape. We also use 2D occlusion masks (Fig. 1 bottom row) to evaluate the performance of methods at varying levels of occlusion. Since our images contain multiple people, methods may detect too few as well as too many people. Consequently, we introduce an error measure that goes beyond the standard single-person measures and rewards methods for both 3DHPS and detection accuracy. We observe higher errors for SOTA methods on AGORA than on other datasets, suggesting that AGORA is more challenging. We also show that our training set can be used to improve recent 3D pose estimation methods [27] not only on AGORA but also on 3DPW [52]. This validates that the synthetic data is sufficiently real to be useful. + +In summary, we contribute a new, varied and challenging dataset to evaluate and improve the SOTA in 3D human pose and shape estimation and to push the field in new + +directions. The dataset is synthetic but diverse and realistic. We use new evaluation metrics and provide detailed analysis of limitations of current methods. We also introduce a new child model to generate better ground truth shape for children. We provide the training and validation set images with SMPL-X and SMPL ground truth and 2D masks. We also provide test images along with evaluation code and will maintain a web evaluation server: https://agna.is.tue.mpg.de/. + +# 2. Related Work + +Many datasets have been proposed for 3DHPS estimation, but each has limitations as summarized in Table 1. While there are many 2D datasets, we focus on those with 3D ground truth of one form or another. + +Datasets with real images. Unlike 2D annotation, 3D body poses are difficult for humans to annotate since the task is ambiguous and requires metric accuracy. Consequently, existing benchmarks rely on multiple synchronized cameras. For example, HumanEva [46], Human3.6M [20], and TotalCapture [48] synchronize video cameras with motion capture (mocap) systems that provide ground truth through optical markers. While providing accurate 3D pose, the image complexity is limited: lack of background variation in lab scenarios, only one subject in each image, no scene occlusions, and little clothing variety due to the attachment of markers, which, unfortunately are also visible in the images. These methods typically evaluate accuracy based on 3D joint locations. Note that, while the 3D joints are commonly treated as "ground truth", they are not directly observed, but rather are inferred by the mocap system based on an approximate skeletal body structure. + +Alternatively, several methods use marker-less motion capture, e.g. MuPoTS-3D [35], PanopticStudio [24], MPIINF-3DHP-Test [34], and HUMBI [54]. Such methods are typically less accurate than marker-based systems, but they avoid intrusive markers, allow more varied clothing, and sometimes are used in more realistic scenes e.g. outdoors. IMU sensors provide another way to measure 3D poses, which is less intrusive than mocap markers but also less accurate due to yaw drift. Von Marcard et al. [52] explicitly account for this by combining IMU data with monocular video, enabling in-the-wild capture. We consider these datasets as reference data rather than "ground truth" because the accuracy of the method is evaluated in a separate process (e.g. using mocap data) and not on the image data in the benchmark. In contrast, for AGORA we report how close the SMPL-X meshes are to these reference scans, directly indicating the fidelity of our pseudo ground truth. + +All the above are limited in the complexity of the clothing, occlusions, scene variety, ethnicity, etc. Of the above only PanopticStudio [24] and HUMBI [54] consider the face and hands together with bodies. + +Synthetic datasets. Computer graphics has the potential to synthesize large-scale image datasets, where ground truth is generated by animating parametric 3D human models such as SMPL [33], MakeHuman [5], or Mixamo [6]. The main challenge for such methods lies in creating data that is sufficiently realistic in terms of body shape, ethnicity, motion, cloth deformation, texture, and interaction with environments. In several datasets, images are created by composing 3D people on image backgrounds. MHOF [40], LTSH [19], 3DPeople [38], and SURREAL [50] render 3D people on the background image, while MPI-INF-3DHP-Train [34] and MuCo-3DHP [35] paste a segmented real human foreground on top of the background. Such composition does not faithfully reflect the local statistics of pixel intensity in real images and does not support methods that learn how humans interact with scenes. Most similar to us is SimPose [60], which poses 17 rigged commercial scans [7] and SURREAL data rendered in a 3D scene. The 3D scenes are simplistic, the scans lack diversity, there is no evaluation site, and the dataset is not public. + +A recent promising direction synthesizes realistic looking people in images [55, 59]. Zanfir et al. [55] use a learned human synthesis method to insert generated people in images such that they make sense relative to the scene geometry and lighting. While they can condition the generated person on pose and shape, the resulting images contain artifacts that are common to generative models, making the results unsuitable as ground truth. + +Other human-related datasets. There are many other datasets of real humans in images that do not contain 3D ground truth. For example, OCHuman [57] focuses on occlusion in real single-view images and provides 2D joint landmarks and human segmentation masks. Early multiview sequences e.g. Adobe data [51], MVIC [32], and MARCOonI [14] also consider 2D landmarks and silhouettes as evaluation measures. The hunger for large training corpora for deep learning motivates self-supervised strategies [25, 26, 49] that leverage 2D landmark annotations in LSP-Extended [22], COCO [31], and MPII [9]. Several recent datasets, e.g. EFT [23], STRAPS [44] and 3DOH50K [58], are generated by fitting a body model to the images, while others fit to videos of complex scenes with "frozen" people [30] using structure from motion [28] or multi-view matching [45]. Methods like EFT and SMPLy [28] provide image variety, which is good for robustness, but with unknown accuracy in body shape and pose. + +In summary, no single dataset can address all needs of the community. AGORA provides realistic textures, complex body shapes and clothing, complex varied scenes and lighting, high-resolution (4K) imagery, varied occlusion, all with high-quality 3D ground truth. This new benchmark reveals limitations of current approaches while providing novel, high-quality training data for multiple applications. + +
DatasetSub. #ImageComplexityClothingBody anno.Ground truth format
HumanEva [46]4lab1 subject, no occlusionlimitedB3D joint locations
Human3.6M [20]11lab1 subject, minor occlusionlimitedB3D joint locations
TotalCapture [48]5lab1 subject, no occlusionmocap suitB3D joint locations
PanopticStudio [24]~100labmultiple subjects & furniturevariedBFH3D joint locations
HUMBI [54]772lab1 subject, no occlusionrichBFHmeshes, SMPL
3DPW [52]18naturalmultiple subjects in the wildvariedBSMPL
MuPoTS-3D [35]8naturalmultiple subjects in the wildvariedB3D joint locations
MPI-INF-3DHP-Train [34]14both1 subject, minor occlusionvariedB3D joint locations
3DOH50K [58]n/alab1 subject, object occlusionlimitedBSMPL
EFT [23]>1000naturalmultiple subjects, in the wildvariedBSMPL
STRAPS [44]62natural1 subject, in the wildlimitedBSMPL
SMPLY [28]742naturalmultiple subjects, in the wild, frequent occlusionrichBSMPL
MuCo-3DHP [35]8composite†multiple subjects in the lablimitedB3D joint locations
MPI-INF-3DHP-Test [34]14composite†1 subject, minor occlusionvariedB3D joint locations
SURREAL [50]145composite†1 subject, no occlusiontexture¶BSMPL
3DPeople [38]80composite†1 subject, no occlusionsynthetic‡B3D joint locations
AGORA (ours)>350realistic††multiple subjects in the wild, frequent occlusionrichBFHSMPL-X, SMPL, masks
+ +Table 1: Comparison of datasets that provide images and 3D human pose annotations. Body annotation type B, F, and H correspond to body, face, and hands respectively. †: 2D foreground layers pasted on background images. ††: 3D models positioned in 3D with panoramic background or full 3D scenes. ¶: unclothed human body with clothing texture. ‡: clothed human body with texture. + +# 3. Method: Obtaining reference data + +To construct AGORA, we purchased high-quality textured 3D scans from 3DPeople [1], AXYZ [2], Human Alloy [4] and Renderpeople [7]. We selected 4240 scans for inclusion in the dataset spanning more than 350 unique subjects. A scan $S$ comprises a set of 3D points $S \subset \mathbb{R}^3$ and their connectivity $F_{S}, S = \{S, F_{S}\}$ . To each scan $S$ we fit a parametric SMPL-X body model $\mathcal{M} = \{M, F_{\mathcal{M}}\}$ , whose vertex locations $M(\theta, \beta, \psi) \subset \mathbb{R}^3$ are controlled by parameters for pose $\theta$ , shape $\beta$ , and facial expression $\psi$ [37]. $\theta$ consists of body pose $\theta_b$ and hand pose $\theta_h$ . Hand pose $\theta_h$ is a function $\theta_h(Z_h)$ of a PCA latent vector $Z_h \in \mathbb{R}^6$ . + +Fitting a SMPL-X mesh $\mathcal{M}$ to a scan $S$ amounts to solving for the optimal parameters $(\theta, \beta, \psi)$ such that $\mathcal{M}$ resembles $S$ . The fitting process takes into account that SMPL-X explains the body in minimal clothing while the scans are typically clothed. In this process we exploit the fact that a person may appear in multiple scans and their shape parameter, $\beta$ , should be the same across scans. + +We first initialize the parameters by an approach that extends the single-view SMPLify-X fitting [37] to multi-view images rendered using $C$ pre-defined virtual cameras. The initial mesh, $M$ , obtained by multi-view SMPLify-X fitting is only approximately aligned with $S$ . While sparse 2D landmarks constrain the 3D pose, they provide little information about body shape. To refine the shape and pose, we fit SMPL-X to the 3D scan surface. However, this is challenging because SMPL-X cannot model things like hair and clothing that are present in the scans. To address this, we use the idea of fitting body shape under clothing [10, 56]. + +Similar to [56], we define energy terms $E_{\mathrm{skin}}$ and $E_{\mathrm{cloth}}$ for skin and clothing, respectively. Both aim to bring the model surface close to the scan, whereas $E_{\mathrm{cloth}}$ additionally + +penalizes body vertices being outside the clothing. In other words, our objective function tries to move the model as close as possible to the scan near the visible skin while discouraging the clothing vertices from penetrating the model. We label skin and cloth vertices on scan using Graphonomy [15]. We keep the 2D landmark data term $E_{J}^{c}$ that penalizes differences between projected and observed keypoints from multi-view fitting, as they provide information complementary to $E_{\mathrm{skin}}$ and $E_{\mathrm{cloth}}$ . See Sup. Mat. for more details. + +We fit each model $M_{i}(\beta_{i},\theta_{i},\psi_{i})$ to the corresponding scan $S_{i}$ in parallel, for scans, $i$ , of the same identity. We optimize jointly for $\theta_{i}$ , $\psi_{i}$ and $\beta_{i}$ while minimizing the shape (inter-beta) distance $E_{\mathrm{ib}}$ between scans of the same identity. The objective function is: + +$$ +\begin{array}{l} E \left(\beta_ {1}, \dots , \beta_ {N}, \theta_ {1}, \dots , \theta_ {N}, \psi_ {1}, \dots , \psi_ {N}\right) = \\ \sum_ {i = 1} ^ {N} \left(\lambda_ {J} \sum_ {c = 1} ^ {C} E _ {J} ^ {c, i} + \lambda_ {\mathrm {s}} E _ {\text {s k i n}} ^ {i} + \lambda_ {\mathrm {c}} E _ {\text {c l o t h}} ^ {i} + E _ {\text {r e g}} ^ {i}\right) + \lambda_ {\mathrm {i b}} E _ {\mathrm {i b}}, \\ E _ {\mathrm {i b}} = \sum_ {i = 1} ^ {N} \sum_ {j = i + 1} ^ {N} \| \beta_ {i} - \beta_ {j} \| _ {2} ^ {2}, \\ E _ {\mathrm {r e g}} = \lambda_ {\theta_ {b}} E _ {\theta_ {b}} (\theta_ {b}) + \lambda_ {\theta_ {h}} E _ {\theta_ {h}} (\theta_ {h}) + \lambda_ {\beta} E _ {\beta} (\beta) + \lambda_ {\mathcal {E}} E _ {\mathcal {E}} (\psi), \\ \end{array} +$$ + +where $E_{\mathrm{reg}}$ contains $L_{2}$ priors used to constrain the body shape, pose and expression, as defined in [37]. Different weights denoted by $\lambda$ are used for each term. + +This approach exploits semantic information (2D landmarks, skin/clothing segmentation) as well as geometry (3D shapes) to obtain accurate fits as demonstrated in Sec. 4.1. + +# 3.1. Fitting child scans + +AGORA also contains 257 child scans. Fitting SMPL-X directly to these scans results in distorted fits as shown in + +![](images/33640d97861b121fb02f534ae38cd47c404a17714a4707134489bfcdc6d9e51e.jpg) +Scan + +![](images/c83541d4564f40badd3c3922138c86315a13b928e3aaccc0042e6113395261f6.jpg) +TA + +![](images/7233caa3d5dc9fb4e872170b58a93825c296829a30db55c5183098be036129b1.jpg) +αTA +Figure 2: Fitting child scans using an adult template $(T_A)$ , a scaled adult template $(\alpha T_A)$ , and our proposed approach, which interpolates between adult and infant templates $(\alpha T_A + (1 - \alpha)T_C)$ . + +![](images/ab3ac58ab4e2a8887a2bf37618ff362200cf4ed5b953d7ba6a8e63bf2325a152.jpg) +$\alpha T_{A} + (1 - \alpha)T_{C}$ + +![](images/eea3d3c662a00f710d24957af75384f79bf1612d8629b0dbb9276bb67997b471.jpg) +Scan & Model + +the 2nd column of Fig. 2, because SMPL-X cannot represent children. Naively scaling the adult SMPL-X template, i.e. $\alpha T_{A}$ , by optimizing for a global scale parameter $\alpha$ is better but still unnatural since children have different proportions than adults. To solve this problem, we take the mean infant body template from SMIL [18] and convert it to SMPL-X topology, $T_{C}$ . We find that interpolating between the adult SMPL-X template $T_{A}$ and the SMIL infant template $T_{C}$ approximately captures the shape of children. See Sup. Mat. Note that, while not perfect, we use the adult shape space for children and only vary the template shape. Incorporating children then involves only a minor change to the fitting process. In addition to optimizing the shape parameters, $\beta$ , we also optimize for a weight, $\alpha \in [0,1]$ , the linearly interpolates the templates. This produces more accurate body shapes for children, as shown in Fig. 2. + +# 4. AGORA Dataset + +AGORA consists of 4240 scans spanning more than 350 unique subjects, all paired with SMPL-X fits (we also supply SMPL fits for backward compatibility). While generally robust, the fitting approach fails sometimes for hands and faces. This typically happens when the hands are grasping objects. Since we want high-quality ground truth, we manually curate the results of the automatic process and create two different sets: (1) those with well aligned body, face and hands (3161, BFH); and (2) those only with well aligned bodies (1079, B). When evaluating algorithms for 3DHPS estimation, only body joints and vertices are considered for B scans, while body, hand and face joints and vertices are evaluated for BFH scans. + +We sample 1051 scans to create the test set; for these, the SMPL-X fits are withheld from public release. We make sure there are no overlapping scans between these 1051 scans and the rest, and no selected scans have been included to train previous work [43]. Our test set spans 105 subjects. We create approximately 3387 images from the test scans, including many challenging scenarios, with the goal of making them photorealistic. From the remaining scans, we sample 2930 scans as a training set and 259 scans as + +a validation set and create 14529 training and 1225 validation images, whose ground-truth SMPL-X parameters and 2D segmentation masks are included in the released dataset. Since the ground truth 3D scans are commercially available, it is possible for people to cheat by using test scans for training. We have also built in several countermeasures to detect cheating that we do not describe in this paper. + +AGORA images are rendered using perspective cameras with focal lengths $18\mathrm{mm}$ , $28\mathrm{mm}$ and $50\mathrm{mm}$ . All images are rendered using Unreal Engine [8] on a single Windows 10 PC with NVIDIA RTX 2080 graphics hardware. Renderings are generated either with image-based lighting using freely available HDR backgrounds [3] or with free and commercial 3D environments obtained from the Unreal Marketplace. The image-based lighting scenes used hardware-accelerated ray-tracing for accurate ground plane shadows. For scans in seated poses, we insert random chairs at the appropriate height so that the scans appear naturally supported. See Sup. Mat. for details of the rendering process. + +# 4.1. Fitting Accuracy + +To evaluate the accuracy of results on AGORA, and to know whether improvements are significant, we first need to know the accuracy of our ground truth2. We define accuracy relative to the high-quality 3D scans in the following ways: + +1. Skin error. For the visible skin vertices on the scan, we compute the Euclidean distance of the nearest point on the triangle of the reconstructed model $M$ . An accurate model fit should fit closely to the skin. We report the weighted mean distance as our final error value where the weight is the probability of the scan vertex belonging to skin calculated using Graphonomy [15]. +2. Penetrating clothing error. The SMPL-X fits are supposed to be fully inside the clothing. We report two values for clothing vertices on the scans: (1) the percentage of them that penetrate the body model. (2) for those penetrating vertices, we calculate their distance to the closest point on the model surface and compute the weighted avg. error. + +We consider only the scans without any large objects for the error calculation and report an average skin error of approximately $4.73\mathrm{mm}$ . Only $16\%$ of cloth vertices are inside the body with an average distance of $4.63\mathrm{mm}$ . An error of approximately $5\mathrm{mm}$ is significantly below any industry standards for the measurement of live humans and is less than the soft-tissue motion of mocap markers on the body [11]. Thus, we believe that the SMPL-X fits provide valid pseudo ground truth. + +# 4.2. Evaluation metrics + +A common practice in evaluating 3DHPS methods is applying Procrustes alignment [16] before computing the er + +
MethodMPJPE ↓MVE ↓NMJE ↓NMVE ↓F1 score↑
BLH/RHFFBBLH/RHFFBBFBBFB
SMPLHMR [25]180.5N/AN/AN/A173.6N/AN/AN/A226.0N/A217.0N/A0.80
CenterHMR [47]168.1N/AN/AN/A161.4N/AN/AN/A242.3N/A233.9N/A0.69
EFT [23]165.4N/AN/AN/A159.0N/AN/AN/A203.6N/A196.3N/A0.81
SPIN [27]175.1N/AN/AN/A168.7N/AN/AN/A223.1N/A216.3N/A0.78
SPIN-ft (ours)153.4N/AN/AN/A148.9N/AN/AN/A199.2N/A193.4N/A0.77
SMPL-XSMPLify-X [37]182.146.5/49.652.9231.8187.048.3/51.448.9236.5256.5326.5263.3333.10.71
ExPose [13]150.472.5/68.855.2215.9151.574.9/71.351.1217.3183.4263.3184.8265.00.82
Frankmocap [42]165.252.3/53.1N/AN/A168.354.7/55.7N/AN/A204.0N/A207.8N/A0.81
+ +Table 2: Comparison of SOTA 3DHPS methods on the AGORA testset. SPIN-ft is SPIN after finetuning on the AGORA training set described in Sec. 5.2. SMPL-based methods are evaluated on B+BFH and SMPL-X-based methods are evaluated on the BFH subset of AGORA. Error metrics are described in Sec. 4.2. All numbers are in millimeters. + +ror. Doing so eliminates discrepancies in scale, translation and rotation, measuring only the error in poses (PA-MPJPE) and shapes (PA-MVE/V2V). This convention is largely due to the fact that existing HPS datasets, e.g. [23, 52], contain only pose and shape annotations, and HPS methods estimate the body relative to the camera. In contrast, AGORA provides complete 3D pseudo ground truth: body parameters of each person and their spatial arrangement in the 3D scene, enabling a more comprehensive error measure. + +Consequently, we do not apply Procrustes alignment but only align at the pelvis, i.e. MPJPE and MVE/V2V, because estimating absolute depth is ambiguous. Furthermore, since AGORA has 5-15 people per image, methods may not detect every person leading to misses, i.e. false negatives. Due to occlusions, methods may also detect bodies where there are actually no people, i.e. false positives. Accuracy on AGORA means high detection performance and low error for every correct detection; consequently, we must penalize false negatives and false positives. Thus, we normalize the MPJPE and MVE/V2V error by the standard detection metric, F1 score (the harmonic mean of recall and precision), and refer to this as Normalized Mean Joint Error (NMJE) and Normalized Mean Vertex Error (NMVE). F1 score punishes both misses and false alarms so NMJE/NMVE increase the reported error for methods that make either type of mistake in detection. As a result, to reduce the overall NMJE/NMVE, the method needs to miss no one, detect no spurious bodies, and estimate accurate poses and shapes for each correct detection, making NMJE/NMVE more challenging and comprehensive than other metrics. + +We evaluate 3DHPS methods along different dimensions and also provide a combined score. For SMPL-based methods, we just evaluate on body joints and vertices using both B and BFH scans. For SMPL-X-based methods, we evaluate separately on the body, hands and face and also provide a weighted sum of the three as a full body (FB) error. SMPL-X-based methods are evaluated only for BFH scans. + +B-MPJPE is evaluated on 24 body joints of SMPL and 22 body joints of SMPL-X after aligning the pelvis. LHMPJPE, RH-MPJPE are evaluated on 15 hands joints on + +the left and right hands, respectively, after aligning the wrist joint. F-MPJPE is evaluated on 51 facial landmarks after aligning the neck joint. FB-MPJPE is a weighted sum of the above 4 errors. Since the number of hand joints and face landmarks outweigh the number of body joints, we define the FB error as $\mathrm{FB} = \mathrm{B} + (\mathrm{LH} + \mathrm{RH} + \mathrm{F}) / 3$ . + +While 3D joint error evaluates pose, it does not provide evaluation of shape, for which we have ground truth. To encourage research on body shape estimation, we also evaluate the methods on vertices. We segment the body, left hand, right hand and face vertices using SMPL [33], MANO [41] and FLAME [29] vertex indices of the SMPL-X template and calculate B-MVE, LH-MVE, RH-MVE and F-MVE respectively. FB-MVE uses the same weighted combination as joint error, FB-MPJPE. We also calculate B-NMJE, B-NMVE, FB-NMJE, FB-NMVE and penalize the methods for missed detections and false positives. + +# 4.3. Evaluation protocol + +When a method estimates a body, the matching ground truth body in AGORA is not known. Therefore, to match the predicted person with the ground truth, we project the estimated 3D keypoints to the image plane and find the closest ground-truth subject in terms of 2D joint error. If there is no match found for a particular ground truth body, we count it as a miss (see Sup. Mat. for details). Similarly, if a detection does not match any ground truth, we count it as false positive. For the correctly matched predictions, we calculate all the errors as described in Sec. 4.2. + +# 5. Experiments + +We evaluate existing methods on AGORA to determine whether the dataset provides new insights about the current SOTA. We also evaluate whether the AGORA training set can help improve the accuracy of SOTA methods by using it to fine-tune SPIN [27]. + +# 5.1. Baseline Evaluation. + +The evaluation protocol for existing methods is shown in Fig. 3. Most current methods assume that the input im + +
MethodMPJPE (mm) ↓MVE (mm) ↓
BB
SMPHMR [25]219.4209.3
CenterHMR [47]207.4198.5
EFT [23]202.7193.5
SPIN [27]203.7193.2
SPIN-ft191.7186.7
X-SMPSMPLify-X [37]208.3213.3
ExPose [13]176.6174.0
Frankmocap [42]203.7204.2
+ +![](images/85cc1852e57ba95bbffc5750ed2b711815203b3fbcb387c6d3eefef357a8ef11.jpg) +Figure 3: Baseline Evaluation. Given a test image, we detect keypoints with [12] to obtain bounding boxes centered at each detected person, followed by network inference to reconstruct a human mesh for each cropped image. We identify true positives (to compute pose error), false negatives (misses) and false positives by matching predictions and ground truth. See Sec. 4.3 for details. + +age is tightly cropped around the person [13, 23, 25, 27, 42] or require 2D keypoint detections [37]. Therefore, to fairly test prior methods on AGORA with the same input, we use OpenPose [12] to detect people and their respective keypoints and construct tight bounding boxes based on these detections. For single-stage approaches e.g. [47] we directly use the entire image as input without any cropping. + +Table 2 reports results for multiple baselines on the AGORA testset using the evaluation metrics described in Sec. 4.2. To compare our new metrics with metrics used in earlier work, we also report MPJPE and MVE without penalizing for missed detections and false positives. See Fig. 7 in Sup. Mat. for qualitative results. While SPIN fine-tuned on the AGORA training set (Sec. 5.2) outperforms other SMPL-based SOTA methods by a large margin in terms of MPJPE and MVE error, its error increases under our new NMJE and NMVE metrics because of misses and false positives. This shows that MPJPE alone is not enough to evaluate performance on multi-person images. We hope AGORA will drive research on multi-person pose estimation. + +We notice that among SMPL-X based methods, ExPose [13] performs best for the body while the optimization-based method SMPLify-X [37] beats regression based + +Table 3: Performance of SOTA methods on "AGORA kids." + +
Models3DPW (14)3DPW (24)AGORA (24)
MPJPEPA-MPJPEMPJPEPA-MPJPEMPJPE
SPIN-pt [27]96.959.395.565.5175.1
SPIN-ft-EFT [23]97.459.795.366.1173.7
SPIN-ft (ours)85.755.383.761.8153.4
+ +Table 4: Pretrained SPIN vs. SPIN finetuned with AGORA and EFT([MPII+LSPet+COCO]). Parns.: (#joints). + +methods in hand and face estimation. These errors are further analysed w.r.t. different parameters like occlusion, child shape, distance to the center of the image and orientation (Sup. Mat. for orientation). + +Occlusion. Using the ground-truth segmentation masks, Fig. 4 plots the error of SOTA methods vs. the percentage of occlusion. Since this is analyzed on ground-truth bodies in which false positives are not included, we normalize the MPJPE by recall (correctly detected and matched bodies divided by total number of bodies), denoted as recall-NMJE and we also plot it for different ranges of occlusion. As expected, the MPJPE for correct detections increases with increasing occlusion and the percentage of misses also increases as shown in the left and middle plots in Fig. 4. We observe that CenterHMR performs well for high occlusion but suffers from many misses, particularly with small people. See Fig. 7 in Sup. Mat. This shows that bottom-up methods that work on the full image are good in dealing with images of multiple people but need to improve their detection accuracy. FrankMocap and SPIN are highly sensitive to occlusion, leading to large errors as occlusion increases. We also notice that fine-tuning with AGORA improves the performance of SPIN for high occlusion cases. + +Distance from center. Most methods rely on a weak perspective camera assumption, which breaks when people occur off-center in images, as also pointed out by [53]. The large field-of-view images in AGORA facilitate the analysis of this error. We plot the B-MPJPE error of the selected SOTA methods vs. horizontal distance from the center of the image in Fig. 5. We find that error consistently increases for all methods as the distance from the center increases. This effect is less significant for CenterHMR [47], the only method that works on full images instead of crops. + +Child Shape. AGORA contains child scans with pseudo ground truth shape generated as described in Sec. 3.1. We calculate body joint and vertex error for the SOTA on a "kids" subset of AGORA. We find that performance is significantly worse for predicting child shape compared to adult shape as shown in Table 3. We hope that this, together with the child shape representation we provide, will encourage work in this direction. + +![](images/fa7263edf909bfbe0308e2ce00cfdf2e3989b5fbe8dbe2a1970b9e07a880971b.jpg) +Figure 4: SOTA evaluation: B-MPJPE for the correct predictions (left), percentage of misses (center) and B-recall-NMJE for the correct predictions (right). Evaluated on BFH subset of AGORA for 22 SMPL-X and 24 SMPL joints. + +![](images/420981a252d23e3a496b10f7fefbd8611bd99ca3f2965929d454450869efd223.jpg) + +![](images/f84c66cd79d952d02c98e6e501dae6fee730d952721585362249e47cd1e572f1.jpg) + +# 5.2. Baseline Improvement. + +To evaluate the efficacy of the AGORA training set, we fine-tune a pretrained SPIN model (SPIN-pt) using only crops from AGORA training images and refer to the fine-tuned model as SPIN-ft. We chose SPIN for the fine-tuning experiment as it uses HMR as a backbone, which is a base for many 3DHPS methods, e.g. EFT [23], VIBE [26] and FrankMocap [41]. For fair comparison, we use the same hyperparameters and loss functions as SPIN. However, unlike SPIN, we do not use SMPLify in loop, replacing that supervision with AGORA ground truth. + +While AGORA images are rendered using perspective cameras, SPIN assumes a weak perspective camera, which is unable to capture perspective warping, especially when people occur off-center in images (see Sec. 5.1). This makes the global orientation of the ground-truth 3D joints and vertices in AGORA inconsistent with SPIN predictions. During SPIN fine-tuning, we therefore set global orientation to zero before calculating all 3D losses, such that information about global orientation comes only from the 2D keypoint loss. We note that this is required only due to the weak perspective camera assumption in SPIN and we hope AGORA will encourage research with more realistic perspective camera models. + +Since SPIN reports Procrustes aligned MPJPE (PA-MPJPE) on 3DPW, we compare SPIN-pt and SPIN-ft on both MPJPE and PA-MPJPE. We also compare the AGORA training set with the EFT dataset, $\left[\mathrm{MPII} + \mathrm{LSPet} + \mathrm{COCO}\right]_{\mathrm{EFT}}$ , We call fine-tuning on EFT, SPIN-ft-EFT. We evaluate SPIN-pt, SPIN-ft-EFT and SPIN-ft on the 3DPW testset with known association and on AGORA testset without known association. Training with AGORA leads to significant improvement in performance on both datasets, with MPJPE improving by $\sim 12\%$ for 3DPW and $\sim 13\%$ for AGORA; see Table 4. Higher MPJPE on AGORA compared to 3DPW also shows that AGORA is more challenging than 3DPW. Note that we calculate the error using 14 joints to compare with original SPIN-pt results. + +![](images/63756b144731151581901c16d77972138b5f401e9d0a762b4887e9d3b8318715.jpg) +Figure 5: Horizontal distance from center of the image: B-MPJPE for selected SOTA baselines. Evaluated on the BFH subset of AGORA for 22 SMPL-X and 24 SMPL joints. + +# 6. Conclusions and Future Work + +We have presented AGORA, a new dataset that goes beyond current datasets to include challenging cases of environmental occlusion, person-person occlusion, scale variation, children, crowds, etc. AGORA is challenging and reveals limitations of existing methods. Despite being synthetic, fine-tuning on AGORA improves performance of a SOTA method on the natural 3DPW dataset. We introduce a new metric to include misses and false positives and facilitate analysis of the SOTA methods on images with multiple people. We also introduce a simple child body model and provide better 3D ground truth for images with children. Future work should include adding images of varied camera height, indoor scenes, multi-view images, larger crowds, animals, and movement. + +Acknowledgements. We thank Galina Henz, Taylor McConnell and Tsvetelina Alexiadis for the help in data labeling. Disclosure. MJB has received research gift funds from Adobe, Intel, Nvidia, Facebook, and Amazon. While MJB is a part-time employee of Amazon, his research was performed solely at, and funded solely by, Max Planck. MJB has financial interests in Amazon, Datagen Technologies, and Meshcapade GmbH. + +# References + +[1] 3DPeople, 2020. https://3dpeople.com.2,4 +[2] AXYZ, 2020. https://secure.axyz-design.com. 2,4 +[3] HDRIHaven, 2020. https://hdlhaven.com.5 +[4] HumanAlloy, 2020. https://humanalloy.com.2,4 +[5]MakeHuman, 2020. http://www.makehumancommunity.org.3 +[6] Mixamo, 2020. https://www MIXamo.com.3 +[7] Renderpeople, 2020. https://renderpeople.com.2, 3, 4 +[8] Unreal, 2020. https://www.unrealengine.com.2, 5 +[9] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. Human pose estimation: New benchmark and state of the art analysis. In IEEE Conference on Computer Vision and Pattern Recognition, pages 3686 - 3693, 2014. 3 +[10] A. Balan and M. J. Black. The naked truth: Estimating body shape under clothing., In European Conference on Computer Vision, volume 5304, pages 15-29, 2008. 2, 4 +[11] V. Camomilla, T. Bonci, and A. Cappozzo. Soft tissue displacement over pelvic anatomical landmarks during 3-D hip movements. Journal of Biomechanics, 62:14 - 20, 2017. 5 +[12] Zhe Cao, Gines Hidalgo, Tomas Simon, Shih-En Wei, and Yaser Sheikh. Openpose: Realtime multi-person 2d pose estimation using part affinity fields. IEEE Transaction on Pattern Analysis and Machine Intelligence, 43(1):172–186, 2021. 7 +[13] Vasileios Choutas, Georgios Pavlakos, Timo Bolkart, Dimitrios Tzionas, and Michael J Black. Monocular expressive body regression through body-driven attention. In European Conference on Computer Vision, pages 20-40, 2020. 6, 7 +[14] Ahmed Elhayek, *Edilson de Aguiar*, Arjun Jain, Jonathan Tompson, Leonid Pishchulin, *Mykhaylo Andriluka*, Christoph Bregler, Bernt Schiele, and Christian Theobalt. Efficient ConvNet-based marker-less motion capture in general scenes with a low number of cameras. In *IEEE Conference on Computer Vision and Pattern Recognition*, pages 3810–3818, 2015. 3 +[15] Ke Gong, Yiming Gao, Xiaodan Liang, Xiaohui Shen, Meng Wang, and Liang Lin. Graphonomy: Universal human parsing via graph transfer learning. In IEEE Conference on Computer Vision and Pattern Recognition, pages 7450-7459, 2019. 4, 5 +[16] John C Gower. Generalized procrustes analysis. Psychometrika, 40(1):33-51, 1975. 5 +[17] Riza Alp Guler and Iasonas Kokkinos. Holopose: Holistic 3D human reconstruction in-the-wild. In IEEE Conference on Computer Vision and Pattern Recognition, pages 10884-10894, 2019. 2 +[18] Nikolas Hesse, Sergi Pujades, Javier Romero, Michael J Black, Christoph Bodensteiner, Michael Arens, Ulrich G Hofmann, Uta Tacke, Mijna Hadders-Algra, Raphael Weinberger, et al. Learning an infant body model from RGB-D data for accurate full body motion analysis. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 792-800, 2018. 2, 5 + +[19] David T Hoffmann, Dimitrios Tzionas, Michael J Black, and Siyu Tang. Learning to train with synthetic humans. In German Conference on Pattern Recognition, pages 609-623, 2019. 3 +[20] Catalin Ionescu, Dragos Papava, Vlad Olaru, and Cristian Sminchisescu. Human3.6M: Large scale datasets and predictive methods for 3D human sensing in natural environments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(7):1325-1339, 2014. 3, 4 +[21] Karim Iskakov, Egor Burkov, Victor S. Lempitsky, and Yury Malkov. Learnable triangulation of human pose. In International Conference on Computer Vision, pages 7717-7726, 2019. 2 +[22] Sam Johnson and Mark Everingham. Learning effective human pose estimation from inaccurate annotation. In IEEE Conference on Computer Vision and Pattern Recognition, pages 1465-1472. IEEE, 2011. 3 +[23] Hanbyul Joo, Natalia Neverova, and Andrea Vedaldi. Exemplar fine-tuning for 3D human pose fitting towards in-the-wild 3D human pose estimation. arXiv preprint arXiv:2004.03686, 2020. 3, 4, 6, 7, 8 +[24] H. Joo, T. Simon, X. Li, H. Liu, L. Tan, L. Gui, S. Banerjee, T. Godisart, B. Nabbe, I. Matthews, T. Kanade, S. Nobuhara, and Y. Sheikh. Panoptic studio: A massively multiview system for social interaction capture. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(1):190-204, 2019. 3, 4 +[25] Angjoo Kanazawa, Michael J Black, David W Jacobs, and Jitendra Malik. End-to-end recovery of human shape and pose. In IEEE Conference on Computer Vision and Pattern Recognition, pages 7122-7131, 2018. 2, 3, 6, 7 +[26] Muhammed Kocabas, Nikos Athanasiou, and Michael J. Black. VIBE: video inference for human body pose and shape estimation. In IEEE Conference on Computer Vision and Pattern Recognition, pages 5252-5262, 2020. 2, 3, 8 +[27] Nikos Kolotouros, Georgios Pavlakos, Michael J Black, and Kostas Daniilidis. Learning to reconstruct 3D human pose and shape via model-fitting in the loop. In International Conference on Computer Vision, pages 2252-2261, 2019. 2, 6, 7 +[28] V. Leroy, Philippe Weinzaepfel, Romain Brégier, Hadrien Combaluzier, and Grégory Rogez. SMPLy benchmarking 3d human pose estimation in the wild. International Conference on 3DVision, pages 301-310, 2020. 3, 4 +[29] Tianye Li, Timo Bolkart, Michael J Black, Hao Li, and Javier Romero. Learning a model of facial shape and expression from 2D scans. ACM Trans. Graph., 36(6):194-1, 2017. 6 +[30] Zhengqi Li, Tali Dekel, Forrester Cole, Richard Tucker, Noah Snavely, Ce Liu, and William T Freeman. Learning the depths of moving people by watching frozen people. In IEEE Conference on Computer Vision and Pattern Recognition, pages 4521-4530, 2019. 3 +[31] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dólar, and C Lawrence Zitnick. Microsoft COCO: Common objects in context. In European Conference on Computer Vision, pages 740-755, 2014. 3 + +[32] Yebin Liu, Juergen Gall, Carsten Stoll, Qionghai Dai, H Seidel, and Christian Theobalt. Markerless motion capture of multiple characters using multi-view image segmentation. IEEE Transaction on Pattern Analysis and Machine Intelligence, pages 2720-2735, 2013. 3 +[33] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J. Black. SMPL: A skinned multi-person linear model. ACM Trans. Graphics (Proc. SIGGRAPH Asia), 34(6):248:1-248:16, 2015. 2, 3, 6 +[34] Dushyant Mehta, Helge Rhodin, Dan Casas, Pascal Fua, Oleksandr Sotnychenko, Weipeng Xu, and Christian Theobalt. Monocular 3D human pose estimation in the wild using improved cnn supervision. In International Conference on 3DVision, pages 506-516, 2017. 3, 4 +[35] Dushyant Mehta, Oleksandr Sotnychenko, Franziska Mueller, Weipeng Xu, Srinath Sridhar, Gerard Pons-Moll, and Christian Theobalt. Single-shot multi-person 3D pose estimation from monocular RGB. In International Conference on 3DVision, pages 120-130, 2018. 3, 4 +[36] Gyeongsik Moon, Juyong Chang, and Kyoung Mu Lee. Camera distance-aware top-down approach for 3D multiperson pose estimation from a single RGB image. In International Conference on Computer Vision, pages 10132-10141, 2019. 2 +[37] Georgios Pavlakos, Vasileios Choutas, Nima Ghorbani, Timo Bolkart, Ahmed A. A. Osman, Dimitrios Tzionas, and Michael J. Black. Expressive body capture: 3D hands, face, and body from a single image. In IEEE Conference on Computer Vision and Pattern Recognition, pages 10975-10985, 2019. 2, 4, 6, 7 +[38] Albert Pumarola, Jordi Sanchez-Riera, Gary P. T. Choi, Alberto Sanfeliu, and Francesc Moreno-Noguer. 3Dpeople: Modeling the geometry of dressed humans. In International Conference on Computer Vision, pages 2242-2251, 2019. 3, 4 +[39] Haibo Qiu, Chunyu Wang, Jingdong Wang, Naiyan Wang, and Wenjun Zeng. Cross view fusion for 3D human pose estimation. In International Conference on Computer Vision, pages 4341-4350, 2019. 2 +[40] Anurag Ranjan, David T Hoffmann, Dimitrios Tzionas, Siyu Tang, Javier Romero, and Michael J Black. Learning multi-human optical flow. International Journal of Computer Vision, pages 873-890, 2020. 3 +[41] Javier Romero, Dimitrios Tzionas, and Michael J Black. Embodied hands: Modeling and capturing hands and bodies together. ACM Transactions on Graphics (ToG), 36(6):1-17, 2017. 6, 8 +[42] Yu Rong, Takaaki Shiratori, and Hanbyul Joo. Frankmo-cap: Fast monocular 3D hand and body motion capture by regression and integration. arXiv preprint arXiv:2008.08324, 2020.6,7 +[43] Shunsuke Saito, Zeng Huang, Ryota Natsume, Shigeo Morishima, Angjoo Kanazawa, and Hao Li. Pifu: Pixel-aligned implicit function for high-resolution clothed human digitization. In International Conference on Computer Vision, pages 2304-2314, 2019. 5 +[44] Akash Sengupta, Roberto Cipolla, and Ignas Budvytis. Synthetic training for accurate 3D human pose and shape esti + +mation in the wild. In British Machine Vision Conference, 2020. 3, 4 +[45] Yeji Shen and C-C Jay Kuo. Multi-view matching (MVM): Facilitating multi-person 3D pose estimation learning with action-frozen people video. In arXiv preprint, 2020. 3 +[46] L. Sigal, A. Balan, and M. J. Black. HumanEva: Synchronized video and motion capture dataset and baseline algorithm for evaluation of articulated human motion. International Journal of Computer Vision, 87(1):4-27, 2010. 3, 4 +[47] Yu Sun, Qian Bao, Wu Liu, Yili Fu, and Tao Mei. CenterHMR: a bottom-up single-shot method for multi-person 3D mesh recovery from a single image. arXiv preprint arXiv:2008.12272, 2020. 2, 6, 7 +[48] Matt Trumble, Andrew Gilbert, Charles Malleson, Adrian Hilton, and John Collomosse. Total capture: 3D human pose estimation fusing video and inertial sensors. In 2017 British Machine Vision Conference (BMVC), 2017. 3, 4 +[49] Hsiao-Yu Tung, Hsiao-Wei Tung, Ersin Yumer, and Katerina Fragkiadaki. Self-supervised learning of motion capture. In Advances in Neural Information Processing, pages 5236-5246. Curran Associates, Inc., 2017. 3 +[50] Gül Varol, Javier Romero, Xavier Martin, Naureen Mahmood, Michael J. Black, Ivan Laptev, and Cordelia Schmid. Learning from synthetic humans. In IEEE Conference on Computer Vision and Pattern Recognition, pages 4627-4635, 2017. 3, 4 +[51] Daniel Vlasic, Ilya Baran, Wojciech Matusik, and Jovan Popovic. Articulated mesh animation from multi-view silhouettes. In ACM SIGGRAPH 2008 papers, pages 1-9. 2008. 3 +[52] Timo von Marcard, Roberto Henschel, Michael Black, Bodo Rosenhahn, and Gerard Pons-Moll. Recovering accurate 3D human pose in the wild using imus and a moving camera. In European Conference on Computer Vision, pages 614-631, 2018. 2, 3, 4, 6 +[53] Frank Yu, Mathieu Salzmann, Pascal Fua, and Helge Rhodin. PCLs: Geometry-aware neural reconstruction of 3D pose with perspective crop layers. In IEEE Conference on Computer Vision and Pattern Recognition, 2021. 7 +[54] Zhixuan Yu, Jae Shin Yoon, In Kyu Lee, Prashanth Venkatesh, Jaesik Park, Jihun Yu, and Hyun Soo Park. HUMBI: A large multiview dataset of human body expressions. In IEEE Conference on Computer Vision and Pattern Recognition, pages 2987-2997, 2020. 3, 4 +[55] Mihai Zanfir, Elisabeta Oneata, Alin-Ionut Popa, Andrei Zanfir, and Cristian Sminchisescu. Human synthesis and scene compositing. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 12749-12756, 2020. 3 +[56] Chao Zhang, Sergi Pujades, Michael J Black, and Gerard Pons-Moll. Detailed, accurate, human shape estimation from clothed 3D scan sequences. In IEEE Conference on Computer Vision and Pattern Recognition, pages 4191-4200, 2017. 2, 4 +[57] Song-Hai Zhang, Ruilong Li, Xin Dong, Paul L Rosin, Zixi Cai, Han Xi, Dingcheng Yang, Hao-Zhi Huang, and Shi-Min Hu. Pose2Seg: Detection free human instance segmentation. In IEEE Conference on Computer Vision and Pattern Recognition, pages 889-898, 2019. 3 + +[58] Tianshu Zhang, Buzhen Huang, and Yangang Wang. Object-occluded human shape and pose estimation from a single color image. In IEEE Conference on Computer Vision and Pattern Recognition, pages 7376-7385, 2020. 3, 4 +[59] Yan Zhang, Mohamed Hassan, Heiko Neumann, Michael J. Black, and Siyu Tang. Generating 3D people in scenes without people. In IEEE Conference on Computer Vision and Pattern Recognition, pages 6193-6203, 2020. 3 +[60] Tyler Zhu, Per Karlsson, and Christoph Bregler. SimPose: Effectively learning densepose and surface normals of people from simulated data. 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When developing computer vision models that can reason about compositional spatio-temporal events, we need benchmarks that can analyze progress and uncover shortcomings. Existing video question answering benchmarks are useful, but they often conflate multiple sources of error into one accuracy metric and have strong biases that models can exploit, making it difficult to pinpoint model weaknesses. We present Action Genome Question Answering (AGQA), a new benchmark for compositional spatio-temporal reasoning. AGQA contains $192M$ unbalanced question answer pairs for $9.6K$ videos. We also provide a balanced subset of $3.9M$ question answer pairs, 3 orders of magnitude larger than existing benchmarks, that minimizes bias by balancing the answer distributions and types of question structures. Although human evaluators marked $86.02\%$ of our question-answer pairs as correct, the best model achieves only $47.74\%$ accuracy. In addition, AGQA introduces multiple training/test splits to test for various reasoning abilities, including generalization to novel compositions, to indirect references, and to more compositional steps. Using AGQA, we evaluate modern visual reasoning systems, demonstrating that the best models barely perform better than non-visual baselines exploiting linguistic biases and that none of the existing models generalize to novel compositions unseen during training. + +# 1. Introduction + +People represent visual events as a composition of temporal actions, where each action encodes how an actor's relationships with surrounding objects evolves over time [44, 46, 30, 37]. For instance, people can encode the video in Figure 1 as a set of actions like putting a phone down and holding a bottle. The action holding a bottle can be further decomposed into how the actor's relationship with the bottle evolves – initially the actor may be twisting the bottle and then later shift to holding it. This ability to decompose + +![](images/5761f734584c55baebebdf5767a7e5d01fad4c1fc5860686252de9e284069297.jpg) + +Example compositional spatio-temporal questions: + +Q: What did the person hold after putting a phone somewhere? +Q: Were they taking a picture or holding a bottle for longer? +Q: Did they take a picture before or after they did the longest action? + +A: bottle + +A: holding a bottle + +A: before + +Generalization to novel compositions: + +Q: Did the person twist the bottle after taking a picture? + +A: yes + +Generalization to indirect references: + +Q: Did the person twist the bottle? + +Q: Did the person twist the object they were holding last? + +A: yes + +A: yes + +Generalization to more compositional steps: + +Q: What did they touch last before holding the bottle and after + +taking a picture, a phone or a bottle? + +A: phone + +Legend: + +objects + +relationships + +actions + +time + +Figure 1. We introduce AGQA: a new benchmark to test for compositional spatio-temporal reasoning. AGQA contains a balanced $3.9M$ and an unbalanced $192M$ question answer pairs associated with $9.6K$ videos. We design handcrafted programs that operate over spatio-temporal scene graphs to generate questions. These questions explicitly test how well models generalize to novel compositions unseen during training, to indirect references of concepts, and to more compositional steps. + +events is reflected in the language people use to communicate with one another [8, 42], so tasks involving both vision and language comprehension, such as answering questions about visual input, can test models' compositional reasoning capability. We can ask questions like "What did the person hold after putting a phone down?" and expect a model capable of compositional spatio-temporal reasoning to answer "bottle." While such behavior seems fundamental to developing vision models that can reason over events, the vision community has only developed compositional question answering benchmarks using static images [17] or synthetic worlds [31, 56] which either are not spatio-temporal or do not reflect the diversity of real-world events. + +Although questions and visual events are composed of multiple reasoning steps, existing video question answering benchmarks conflate multiple sources of model errors + +Table 1. AGQA is 3 orders of magnitude larger than all existing VideoQA benchmarks. It contains real-world videos and compositional open-answer questions with action, object, and relationship grounding. AGQA's questions focus on visual comprehension and do not require common sense or dialogue understanding. + +
DatasetVideoQuestion answersGrounding
Avg. length (s)# videos (K)Real-worldNot dialogue relatedOpen answerCompositional# questionsobjectsrelationshipsactions
MarioQA [43]3-6188✓✓188K
CLEVRER [56]520✓✓✓282K✓✓✓
Pororo-QA [27]1.416.1✓9K
MovieQA [48]202.76.77✓6.4K✓
SocialIQ [59]991.25✓7.5K
TVQA [33]76.221.8✓✓152.5K✓
TVQA+ [34]7.24.2✓✓29.4K✓✓
MovieFIB[40]4.9118.5✓✓✓349K
TGIF-QA [18]3.171.7✓✓✓165.2K
MSVD-QA [53]<101.97✓✓✓50.5K
Video-QA [61]4518.1✓✓✓175K
MSRVTT-QA [53]10-3010✓✓✓243K
ActivityNet-QA [58]1805.8✓✓✓58K
AGQA309.6✓✓✓✓192M✓✓✓
+ +into a single accuracy metric [18, 53, 40, 61, 58]. Consider this stereotypical question-answer pair, Q: “What does the bear on the right do after sitting?” A: “stand up” [18]. A model’s inability to answer such questions does not afford any deeper insights into the model’s capabilities. Did the model fail because it is unable to identify objects like bear or relationships like sitting or does it fail to reason over the temporal ordering implied by the word after? Or did the model fail for a combination of these reasons? + +Not only are failure cases difficult to analyze, but the inputs where the model correctly guesses the answer are equally difficult to dissect. Due to biases in answer distributions and the non-uniform distribution of occurrences of visual events, models may develop "cheating" approaches that can superficially guess answers without learning the underlying compositional reasoning process [36, 54]. To effectively measure how well models jointly compose spatiotemporal reasoning over objects, their relationships, and temporal actions, we need newer benchmarks with more granular control over question composition and the distribution of concepts in questions and answers. + +To measure whether models exhibit compositional spatio-temporal reasoning, we introduce Action Genome Question Answering (AGQA) $^{1}$ . AGQA presents a benchmark of $3.9M$ balanced and $192M$ unbalanced question answer pairs associated with $9.6K$ videos. We validate the accuracy of the questions and answers in AGQA using human annotators for at least 50 questions per category and find that annotators agree with $86.02\%$ of our answers. Each question is generated by a handcrafted program that outlines the necessary reasoning steps required to answer a question. The programs that create questions operate over Charades' action annotations and Action Genome's spatio-temporal scene graphs, which ground all objects with bounding boxes and actions with time stamps in the video [19, 45]. These programs also provide us with granular control over which reasoning abilities are required to answer each question. + +For example, some questions in AGQA only require understanding the temporal ordering of actions (e.g. "Did they take a picture before or after they did the longest action?") while some others require understanding actions in tandem with relationships (e.g. "What did the person hold after putting a phone somewhere?"). We control bias using rejection sampling on skewed answer distributions and across families of different compositional structures. + +With our granular control over the question generation process, we also introduce a set of new training/test splits that test for particular forms of compositional spatiotemporal desiderata: generalization to novel compositions, to indirect references, and to more compositional steps. We test whether models (PSAC, HME, and HRCN [11, 32, 35]) generalize to novel compositions unseen during training — the training set can contain the relationship twist and the object bottle separately while the test set requires reasoning over questions such as “Did the person twist the bottle after taking a picture?” with both concepts paired together in a novel composition. Similarly, we test whether models generalize to indirect references of objects by replacing objects like bottle in “Did the person twist the bottle?” with an indirect reference to make the question “Did the person twist the object they were holding last?” Finally, we test whether models generalize to questions with more reasoning steps by constraining the test set to questions with more reasoning steps than those in the training set (e.g. “What did they touch last before holding the bottle but after taking a picture, a phone or a bottle?”). + +Using AGQA, we evaluate modern visual reasoning systems (PSAC, HME, and HRCN [11, 32, 35]), and find that they barely perform better than models that purely exploit linguistic bias. The highest performing model achieves only $47.74\%$ accuracy, and HCRN performs only $0.42\%$ better than a linguistic-only version. While there is some evidence that models generalize to indirect references, all of them decrease in accuracy when the number of compositional steps increase and none of them generalize to novel compositions. + +# 2. Related Work + +Our work lies within the field of video understanding using language and is targeted towards the question answering task. We use spatio-temporal scene graphs to generate our questions, and we provide a suite of new evaluation metrics to measure compositional spatio-temporal reasoning. + +Image question answering benchmarks. A wide variety of visual question answering benchmarks have been created over the past five years [21, 17, 2, 60, 14, 29, 62, 26]. These benchmarks vary in input, from synthetic datasets [21], to cartoons [2], charts [27], or real-world images [17, 29, 62, 14, 60, 2]. They also vary in the type of questions asked, from descriptive questions (who, what, where, when, which, why, how) [62], to ones requiring commonsense reasoning [60], spatial compositional reasoning [21, 17], or spatial localization [62, 29, 17]. These benchmarks facilitated the development of many model architectures and learning algorithms that demonstrate spatial compositional reasoning abilities [39, 49, 6]. However, none of these measure temporal reasoning beyond guessing common sense actions that usually require external knowledge [60]. + +Video question answering benchmarks. As shown by the benchmarks in Table 1, there is a growing interest in measuring video reasoning capabilities using question answering [48, 33, 18, 27, 53, 40, 61, 58, 56]. Several of these prominent benchmarks rely on dialogue and plot summaries instead of a video's visual contents [33, 48, 27, 59], resulting in models with a stronger dependence on the dialogue than on the visual input and therefore reducing the benchmark's effectiveness at measuring visual reasoning [48, 33]. + +Some video-only question-answering benchmarks are synthetically generated [56, 43], which affords the granular control necessary to measure model abilities like causality [56], or counting [43]. However, these benchmarks use short video clips, utilize only a handful of objects, focus on questions that require commonsense or external knowledge (Figure 2), and lack the visual diversity of real-world videos. Other video-only benchmarks suffer from the biases and simplicity associated with human generated questions [58, 48, 18, 33] or descriptions [53, 61]. The largest human-annotated [33] and generated [40] datasets contain $152.5K$ and $349K$ questions. In comparison, our corpus is purely vision based, is three orders of magnitude larger, and evaluates complex and multi-step reasoning. + +Scene graphs. Scene graphs were first introduced as a Cognitive Science [4, 52] inspired representation for static images [29, 23]. Each scene graph encodes objects as nodes in the image and pairwise relationships between objects as directed edges connecting nodes. The Computer Vision community has utilized the scene graph representation for a variety of tasks including visual question answering [22], relationship modeling [38], object localization [28], evaluation [1], generation [20, 3], retrieval [3, 23] and few-shot + +![](images/0cd20344dce714e3d0c8349d6665fa3b77deb1a77d7f5c5616823b979ae549f9.jpg) +Figure 2. AGQA contains a variety of compositional spatiotemporal reasoning types that are absent from existing real-world video-only corpus, including duration of actions, interactions between relationships and actions, action sequencing, and logical combinations. We focus on questions that require visual understanding, so we do not have questions that require external knowledge. + +learning [7, 10]. Of particular interest to our project is how scene graphs from Visual Genome [29] were used to create GQA, a benchmark for compositional spatial reasoning over an image [17]. Our work is a generalization of GQA's pipeline. While GQA uses indirect references to objects with attributes (e.g. "red") and spatial relations (e.g. to the left of), we also use temporal localizations (e.g. before), indirect action references (e.g. the longest action), and changes in a subject's relationship with objects over time (e.g. before holding the dish). Our programs operate over Action Genome's spatio-temporal scene graphs to automatically generate question-answer-video pairs [19]. + +Compositional reasoning. While there are numerous definitions of compositionality, we in particular use what is more colloquially referred to as bottom-up compositionality — "the meaning of the whole is a function of the meanings of its parts" [9]. In our case, reasoning about the question "Was the person running or sitting for longer?" requires finding the start and end of when the person was running and sitting, subtracting the start from the end, then comparing the resulting lengths. Unfortunately, the most popular benchmarks and metrics defined to study compositional behavior have been limited to synthetic environments [25, 31, 21, 56] or to static images [17]. Recent work has argued the importance of compositionality in enabling models to generalize to new domains, categories, and logical rules [31, 49] and has discovered that current models struggle with multi-step reasoning [11]. These studies motivate a benchmark like ours that defines multiple metrics to explore compositional reasoning in real-world videos. + +![](images/f91597981cfff550960dc520c4f6f56d0f3d1c7162f2cfb8889fbb7e9f591708.jpg) +Input +Figure 3. (Left:) Our benchmark generation process expects a dataset of videos with spatio-temporal scene graphs as input. (Middle:) We handcraft programs that operate over the scene graphs to generate questions and answers. (Right:) We balance generated questions and their corresponding answers using rejection sampling to avoid biases that models can exploit. We can control the number of reasoning steps required to answer a question by either developing more complex programs or by referencing visual concepts using indirect references (e.g. referring to a specific action as the shortest action or object as the object they carried). + +# Our benchmark generation process + +Template #1: What did they