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+# 2D or not 2D? 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 stage<sup>2</sup>.
+
+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.
+
+<table><tr><td rowspan="2"></td><td colspan="4">FCVID</td><td colspan="4">ACTIVITYNET</td><td colspan="4">MINI-KINETICS</td></tr><tr><td>mAP</td><td>GFLOPs</td><td>#3D</td><td>#Frame</td><td>mAP</td><td>GFLOPs</td><td>#3D</td><td>#Frame</td><td>Acc</td><td>GFLOPs</td><td>#3D</td><td>#Frame</td></tr><tr><td colspan="13">8-frame per clip</td></tr><tr><td>Upper</td><td>82.1</td><td>58.6</td><td>5.0</td><td>8.0</td><td>82.6</td><td>58.6</td><td>5.0</td><td>8.0</td><td>79.0</td><td>58.6</td><td>5.0</td><td>8.0</td></tr><tr><td>Random</td><td>78.1</td><td>36.1</td><td>2.2</td><td>5.8</td><td>79.2</td><td>42.9</td><td>3.0</td><td>6.6</td><td>74.0</td><td>42.2</td><td>2.0</td><td>6.9</td></tr><tr><td>Random FT</td><td>80.7</td><td>36.1</td><td>2.2</td><td>5.8</td><td>81.1</td><td>42.9</td><td>3.0</td><td>6.6</td><td>77.4</td><td>41.5</td><td>1.9</td><td>6.8</td></tr><tr><td>Ours</td><td>81.9</td><td>35.6</td><td>2.2</td><td>5.7</td><td>82.6</td><td>42.2</td><td>3.1</td><td>6.6</td><td>78.9</td><td>42.4</td><td>1.9</td><td>6.9</td></tr><tr><td colspan="13">16-frame per clip</td></tr><tr><td>Upper</td><td>84.4</td><td>117.3</td><td>5.0</td><td>16.0</td><td>84.4</td><td>117.3</td><td>5.0</td><td>16.0</td><td>79.6</td><td>117.3</td><td>5.0</td><td>16.0</td></tr><tr><td>Random</td><td>79.2</td><td>63.2</td><td>2.1</td><td>10.3</td><td>80.4</td><td>73.3</td><td>3.0</td><td>11.2</td><td>75.2</td><td>75.8</td><td>2.9</td><td>11.8</td></tr><tr><td>Random FT</td><td>82.0</td><td>65.3</td><td>2.1</td><td>10.6</td><td>82.8</td><td>71.3</td><td>3.0</td><td>11.1</td><td>78.2</td><td>78.0</td><td>2.9</td><td>12.0</td></tr><tr><td>Ours</td><td>84.3</td><td>66.6</td><td>2.1</td><td>10.7</td><td>84.0</td><td>70.1</td><td>3.0</td><td>11.1</td><td>79.2</td><td>73.8</td><td>2.9</td><td>11.8</td></tr></table>
+
+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  $\gamma$ .
+
+<table><tr><td></td><td>Van → Ada</td><td>Van → Ada</td><td>Van → Ada</td></tr><tr><td>#Clip</td><td>3.0 → 2.9</td><td>5.0 → 4.2</td><td>10.0 → 7.4</td></tr><tr><td>mAP</td><td>77.8 → 78.1</td><td>80.3 → 80.5</td><td>81.9 → 82.0</td></tr></table>
+
+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.  
+
+<table><tr><td>Method</td><td>Acc</td><td>GFLOPs</td><td>#3D</td><td>#Frame</td></tr><tr><td>Upper</td><td>73.1</td><td>58.6</td><td>5.0</td><td>8.0</td></tr><tr><td>Ours</td><td>72.8</td><td>43.7</td><td>2.3</td><td>6.9</td></tr></table>
+
+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.  
+
+<table><tr><td>Method</td><td>mAP</td><td>GFLOPs</td><td>#3D</td><td>#Frame</td></tr><tr><td>Upper</td><td>82.6</td><td>54.5</td><td>2.0</td><td>8.0</td></tr><tr><td>Ours</td><td>82.4</td><td>42.1</td><td>1.3</td><td>6.6</td></tr><tr><td>Upper</td><td>83.5</td><td>109.1</td><td>2.0</td><td>16.0</td></tr><tr><td>Ours</td><td>83.4</td><td>61.8</td><td>1.4</td><td>9.5</td></tr></table>
+
+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
+
+<table><tr><td colspan="3">FCVID</td><td colspan="2">ACTIVITYNET</td></tr><tr><td>Tr FT</td><td>mAP</td><td>GFLOPs</td><td>mAP</td><td>GFLOPs</td></tr><tr><td>Upper</td><td>78.1</td><td>58.6</td><td>76.4</td><td>58.6</td></tr><tr><td></td><td>72.3</td><td>36.1</td><td>71.1</td><td>42.9</td></tr><tr><td>✓</td><td>75.9</td><td>34.7</td><td>74.3</td><td>38.1</td></tr><tr><td>✓</td><td>76.5</td><td>34.9</td><td>75.1</td><td>37.6</td></tr><tr><td>✓</td><td>77.8</td><td>35.6</td><td>76.1</td><td>42.2</td></tr></table>
+
+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.  
+
+<table><tr><td colspan="3">FCVID</td><td colspan="2">ACTIVITYNET</td></tr><tr><td>3D Frame</td><td>mAP</td><td>GFLOPs</td><td>mAP</td><td>GFLOPs</td></tr><tr><td>Upper</td><td>78.1</td><td>58.6</td><td>76.4</td><td>58.6</td></tr><tr><td></td><td>75.5</td><td>35.6</td><td>74.3</td><td>42.3</td></tr><tr><td>✓</td><td>76.8</td><td>35.3</td><td>75.3</td><td>41.1</td></tr><tr><td>✓</td><td>76.3</td><td>35.5</td><td>74.8</td><td>43.5</td></tr><tr><td>✓</td><td>77.8</td><td>35.6</td><td>76.1</td><td>42.2</td></tr></table>
+
+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.
+
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+# 3D AffordanceNet: A Benchmark for Visual Object Affordance Understanding
+
+Shengheng Deng $^{1,\ast}$ , Xun Xu $^{2,\ast}$ , Chaozheng Wu $^{1}$ , Ke Chen $^{1,4}$  and Kui Jia $^{1,3,4,\dagger}$ $^{1}$ South China University of Technology,  $^{2}$ I2R, A-STAR  
+ $^{3}$ Pazhou Laboratory,  $^{4}$ Peng Cheng Laboratory
+
+# Abstract
+
+The ability to understand the ways to interact with objects from visual cues, a.k.a. visual affordance, is essential to vision-guided robotic research. 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
+
+<table><tr><td>Affordance</td><td>Object</td><td>Question</td></tr><tr><td>Lay</td><td>Bed</td><td>If you were to lie on this bed, which points would you lie on the bed?</td></tr><tr><td>Grasp</td><td>Earphone</td><td>If you want to grab this earphone, where will your palm position be?</td></tr><tr><td>Lift</td><td>Bag</td><td>If you want to lift this bag, at which points are your finger most likely to carry the bag?</td></tr><tr><td>Sit</td><td>Chair</td><td>If you were sitting on this chair, on which points would you sit?</td></tr><tr><td>Move</td><td>Table</td><td>If you want to move this table, at which points on this table will you exert your strength?</td></tr><tr><td>Open</td><td>Trash Can</td><td>If you want to open the lid of this trash can, from which points on the trash can you open it?</td></tr><tr><td>Pour</td><td>Bottle</td><td>Suppose 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?</td></tr><tr><td>Press</td><td>Laptop</td><td>If you want to press keys on a computer keyboard, which points on the keyboard would you press?</td></tr><tr><td>Contain</td><td>Microwave</td><td>If you put something in the microwave, at which points in the microwave would you put the object?</td></tr><tr><td>Support</td><td>Table</td><td>If you want to put something on the table, at which points on the table would you put the object?</td></tr></table>
+
+![](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.  
+
+<table><tr><td>Object</td><td>Affordance</td><td>Num</td></tr><tr><td>Bag</td><td>grasp, lift, contain, open</td><td>125</td></tr><tr><td>Bed</td><td>lay, sit, support</td><td>181</td></tr><tr><td>Bowl</td><td>contain, wrap-grasp, pour</td><td>187</td></tr><tr><td>Clock</td><td>display</td><td>524</td></tr><tr><td>Dishwasher</td><td>open, contain</td><td>166</td></tr><tr><td>Display</td><td>display</td><td>887</td></tr><tr><td>Door</td><td>open, push, pull</td><td>220</td></tr><tr><td>Earphone</td><td>grasp, listen</td><td>223</td></tr><tr><td>Faucet</td><td>grasp, open</td><td>628</td></tr><tr><td>Hat</td><td>grasp, wear</td><td>222</td></tr><tr><td>Storage Furniture</td><td>contain, open</td><td>2186</td></tr><tr><td>Keyboard</td><td>press</td><td>156</td></tr><tr><td>Knife</td><td>grasp, cut, stab</td><td>314</td></tr><tr><td>Laptop</td><td>display, press</td><td>421</td></tr><tr><td>Microwave</td><td>open, contain, support</td><td>184</td></tr><tr><td>Mug</td><td>contain, pour, wrap-grasp, grasp</td><td>190</td></tr><tr><td>Refrigerator</td><td>contain, open</td><td>185</td></tr><tr><td>Chair</td><td>sit, support, move</td><td>6113</td></tr><tr><td>Scissors</td><td>grasp, cut, stab</td><td>68</td></tr><tr><td>Table</td><td>support, move</td><td>7990</td></tr><tr><td>Trash Can</td><td>contain, pour, open</td><td>315</td></tr><tr><td>Vase</td><td>contain, pour, wrap-grasp</td><td>1048</td></tr><tr><td>Bottle</td><td>contain, open, wrap-grasp, grasp, pour</td><td>411</td></tr></table>
+
+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
+
+<table><tr><td></td><td>Support</td><td>Move</td><td>Sit</td><td>Contain</td><td>Open</td><td>Grasp</td><td>Pour</td><td>Display</td><td>Wrap-Grasp</td></tr><tr><td>#Annot</td><td>14848</td><td>14540</td><td>6516</td><td>5155</td><td>4506</td><td>2253</td><td>2086</td><td>1914</td><td>1889</td></tr><tr><td></td><td>Press</td><td>Cut</td><td>Stab</td><td>Wear</td><td>Listen</td><td>Pull</td><td>Push</td><td>Lay</td><td>Lift</td></tr><tr><td>#Annot</td><td>588</td><td>393</td><td>393</td><td>231</td><td>228</td><td>225</td><td>225</td><td>194</td><td>123</td></tr></table>
+
+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
+
+<table><tr><td>Full-shape</td><td>Avg</td><td>Grasp</td><td>Lift</td><td>Contain</td><td>Open</td><td>Lay</td><td>Sit</td><td>Support</td><td>Wrap.</td><td>Pour</td><td>Display</td><td>Push</td><td>Pull</td><td>Listen</td><td>Wear</td><td>Press</td><td>Move</td><td>Cut</td><td>Stab</td></tr><tr><td>P_mAP</td><td>48.0</td><td>43.4</td><td>75.1</td><td>56.9</td><td>46.6</td><td>63.0</td><td>81.1</td><td>52.5</td><td>19.0</td><td>46.9</td><td>59.3</td><td>20.5</td><td>37.9</td><td>41.6</td><td>20.4</td><td>31.4</td><td>35.3</td><td>41.1</td><td>90.9</td></tr><tr><td>P_AUC</td><td>87.4</td><td>82.8</td><td>97.1</td><td>89.3</td><td>90.6</td><td>92.6</td><td>96.0</td><td>89.7</td><td>72.6</td><td>89.2</td><td>90.6</td><td>83.1</td><td>85.3</td><td>85.9</td><td>67.9</td><td>90.9</td><td>79.0</td><td>91.4</td><td>98.8</td></tr><tr><td>P_alOU</td><td>19.3</td><td>15.7</td><td>41.2</td><td>22.2</td><td>20.2</td><td>30.0</td><td>38.1</td><td>17.5</td><td>4.0</td><td>18.2</td><td>25.6</td><td>6.5</td><td>12.7</td><td>14.0</td><td>6.5</td><td>11.2</td><td>8.5</td><td>15.2</td><td>40.9</td></tr><tr><td>P_MSE</td><td>0.059</td><td>0.003</td><td>0.0001</td><td>0.006</td><td>0.003</td><td>0.0005</td><td>0.005</td><td>0.012</td><td>0.002</td><td>0.002</td><td>0.0007</td><td>0.0007</td><td>0.0002</td><td>0.0006</td><td>0.0005</td><td>0.0006</td><td>0.021</td><td>0.0003</td><td>0.0001</td></tr><tr><td>D_mAP</td><td>46.4</td><td>43.9</td><td>85.2</td><td>57.6</td><td>51.8</td><td>12.3</td><td>80.9</td><td>54.0</td><td>20.7</td><td>47.7</td><td>65.5</td><td>20.5</td><td>40.5</td><td>36.0</td><td>18.3</td><td>34.2</td><td>35.5</td><td>40.2</td><td>91.4</td></tr><tr><td>D_AUC</td><td>85.5</td><td>82.5</td><td>98.7</td><td>89.9</td><td>91.6</td><td>50.1</td><td>96.1</td><td>90.2</td><td>74.6</td><td>89.2</td><td>92.1</td><td>85.0</td><td>89.7</td><td>86.1</td><td>61.9</td><td>91.8</td><td>78.9</td><td>91.7</td><td>98.7</td></tr><tr><td>D_alOU</td><td>17.8</td><td>13.9</td><td>40.2</td><td>21.6</td><td>25.4</td><td>1.0</td><td>34.9</td><td>18.8</td><td>5.6</td><td>17.7</td><td>32.1</td><td>5.5</td><td>11.8</td><td>11.9</td><td>5.9</td><td>14.8</td><td>9.9</td><td>14.5</td><td>35.4</td></tr><tr><td>D_MSE</td><td>0.08</td><td>0.003</td><td>0.0001</td><td>0.007</td><td>0.003</td><td>0.0006</td><td>0.006</td><td>0.013</td><td>0.007</td><td>0.005</td><td>0.002</td><td>0.002</td><td>0.0006</td><td>0.002</td><td>0.002</td><td>0.0007</td><td>0.025</td><td>0.0002</td><td>0.0001</td></tr><tr><td>U_mAP</td><td>47.4</td><td>42.6</td><td>75.7</td><td>56.6</td><td>45.9</td><td>60.6</td><td>80.8</td><td>53.7</td><td>19.1</td><td>45.0</td><td>61.5</td><td>19.7</td><td>36.5</td><td>37.4</td><td>20.4</td><td>33.9</td><td>35.2</td><td>39.8</td><td>89.0</td></tr><tr><td>U_AUC</td><td>86.3</td><td>79.8</td><td>94.3</td><td>88.8</td><td>88.5</td><td>88.2</td><td>95.8</td><td>89.7</td><td>72.9</td><td>87.1</td><td>90.2</td><td>81.4</td><td>84.0</td><td>82.9</td><td>70.3</td><td>91.6</td><td>79.2</td><td>90.8</td><td>98.5</td></tr><tr><td>U_alOU</td><td>19.7</td><td>13.7</td><td>41.2</td><td>22.4</td><td>20.8</td><td>29.4</td><td>37.3</td><td>18.6</td><td>4.7</td><td>18.3</td><td>32.4</td><td>6.2</td><td>13.0</td><td>13.1</td><td>4.4</td><td>14.5</td><td>9.2</td><td>14.2</td><td>41.5</td></tr><tr><td>U_MSE</td><td>0.063</td><td>0.003</td><td>0.0003</td><td>0.006</td><td>0.003</td><td>0.0006</td><td>0.005</td><td>0.014</td><td>0.002</td><td>0.002</td><td>0.002</td><td>0.0006</td><td>0.0002</td><td>0.0007</td><td>0.0003</td><td>0.0008</td><td>0.021</td><td>0.0002</td><td>0.0001</td></tr><tr><td>Partial</td><td>Avg</td><td>Grasp</td><td>Lift</td><td>Contain</td><td>Open</td><td>Lay</td><td>Sit</td><td>Support</td><td>Wrap.</td><td>Pour</td><td>Display</td><td>Push</td><td>Pull</td><td>Listen</td><td>Wear</td><td>Press</td><td>Move</td><td>Cut</td><td>Stab</td></tr><tr><td>P_mAP</td><td>45.7</td><td>43.2</td><td>80.6</td><td>41.9</td><td>48.5</td><td>52.6</td><td>69.8</td><td>45.5</td><td>20.0</td><td>47.0</td><td>52.5</td><td>24.1</td><td>36.5</td><td>42.1</td><td>15.3</td><td>30.7</td><td>37.8</td><td>43.3</td><td>92.6</td></tr><tr><td>P_AUC</td><td>85.2</td><td>81.2</td><td>96.2</td><td>83.3</td><td>87.9</td><td>86.7</td><td>95.0</td><td>86.5</td><td>71.3</td><td>88.4</td><td>85.2</td><td>84.9</td><td>86.1</td><td>84.2</td><td>64.1</td><td>84.7</td><td>79.6</td><td>90.2</td><td>98.8</td></tr><tr><td>P_alOU</td><td>16.9</td><td>14.4</td><td>45.6</td><td>13.2</td><td>21.6</td><td>25.2</td><td>31.0</td><td>11.2</td><td>3.6</td><td>17.8</td><td>19.3</td><td>5.7</td><td>11.5</td><td>13.4</td><td>2.4</td><td>12.4</td><td>6.2</td><td>13.5</td><td>37.8</td></tr><tr><td>P_MSE</td><td>0.062</td><td>0.003</td><td>0.0001</td><td>0.005</td><td>0.003</td><td>0.0006</td><td>0.004</td><td>0.013</td><td>0.002</td><td>0.002</td><td>0.002</td><td>0.0002</td><td>0.0001</td><td>0.0007</td><td>0.0004</td><td>0.0006</td><td>0.025</td><td>0.0003</td><td>0.0001</td></tr><tr><td>D_mAP</td><td>42.2</td><td>40.1</td><td>83.8</td><td>38.5</td><td>44.5</td><td>46.6</td><td>67.3</td><td>43.9</td><td>19.6</td><td>44.8</td><td>50.3</td><td>15.7</td><td>28.6</td><td>19.9</td><td>17.7</td><td>26.9</td><td>35.6</td><td>43.3</td><td>92.1</td></tr><tr><td>D_AUC</td><td>83.7</td><td>80.3</td><td>97.0</td><td>80.8</td><td>86.8</td><td>82.6</td><td>94.6</td><td>87.0</td><td>70</td><td>86.8</td><td>81.7</td><td>83.6</td><td>86.0</td><td>75</td><td>64.1</td><td>83.0</td><td>78.5</td><td>90.0</td><td>99.1</td></tr><tr><td>D_alOU</td><td>13.8</td><td>13.3</td><td>37.9</td><td>8.6</td><td>16.0</td><td>15.5</td><td>27.2</td><td>13.5</td><td>3.2</td><td>13.9</td><td>13.8</td><td>3.9</td><td>4.3</td><td>8.4</td><td>5.2</td><td>5.7</td><td>8.2</td><td>13.3</td><td>36.8</td></tr><tr><td>D_MSE</td><td>0.069</td><td>0.005</td><td>0.0002</td><td>0.005</td><td>0.004</td><td>0.0006</td><td>0.004</td><td>0.013</td><td>0.003</td><td>0.002</td><td>0.002</td><td>0.001</td><td>0.001</td><td>0.002</td><td>0.003</td><td>0.0004</td><td>0.022</td><td>0.0004</td><td>0.0001</td></tr><tr><td>U_mAP</td><td>43.0</td><td>40.8</td><td>73.2</td><td>41.2</td><td>47.6</td><td>44.6</td><td>68.9</td><td>45.3</td><td>18.5</td><td>45.2</td><td>53.2</td><td>19.5</td><td>29.6</td><td>38.9</td><td>11.1</td><td>29.6</td><td>36.7</td><td>39.1</td><td>90.8</td></tr><tr><td>U_AUC</td><td>83.2</td><td>78.9</td><td>94.6</td><td>81.7</td><td>87.1</td><td>80.4</td><td>94.5</td><td>87.0</td><td>69.3</td><td>87.5</td><td>84.4</td><td>80.9</td><td>79.2</td><td>84.2</td><td>56.4</td><td>84.9</td><td>77.7</td><td>89.3</td><td>98.7</td></tr><tr><td>U_alOU</td><td>16.8</td><td>14.7</td><td>38.1</td><td>15.0</td><td>21.1</td><td>20.8</td><td>33.5</td><td>14.4</td><td>4.3</td><td>18.9</td><td>20.4</td><td>5.3</td><td>8.2</td><td>10.9</td><td>1.0</td><td>14.7</td><td>9.0</td><td>15.9</td><td>35.8</td></tr><tr><td>U_MSE</td><td>0.065</td><td>0.003</td><td>0.0002</td><td>0.006</td><td>0.003</td><td>0.001</td><td>0.006</td><td>0.012</td><td>0.003</td><td>0.003</td><td>0.002</td><td>0.0003</td><td>0.0002</td><td>0.0003</td><td>0.0006</td><td>0.0008</td><td>0.022</td><td>0.0007</td><td>0.0002</td></tr><tr><td>Rotate z</td><td>Avg</td><td>Grasp</td><td>Lift</td><td>Contain</td><td>Open</td><td>Lay</td><td>Sit</td><td>Support</td><td>Wrap.</td><td>Pour</td><td>Display</td><td>Push</td><td>Pull</td><td>Listen</td><td>Wear</td><td>Press</td><td>Move</td><td>Cut</td><td>Stab</td></tr><tr><td>P_mAP</td><td>47.3</td><td>43.1</td><td>85.7</td><td>58.1</td><td>39.6</td><td>62.7</td><td>80.6</td><td>53.8</td><td>20.4</td><td>47.5</td><td>47.2</td><td>21.8</td><td>34.8</td><td>39.7</td><td>19.0</td><td>28.1</td><td>36.3</td><td>40.4</td><td>91.9</td></tr><tr><td>P_AUC</td><td>87.0</td><td>82.0</td><td>97.9</td><td>89.5</td><td>86.2</td><td>91.1</td><td>95.9</td><td>90.1</td><td>74.2</td><td>89.4</td><td>87.1</td><td>85.4</td><td>87.9</td><td>84.3</td><td>67.0</td><td>88.5</td><td>80.3</td><td>91.5</td><td>98.5</td></tr><tr><td>P_alOU</td><td>18.7</td><td>15.5</td><td>45.4</td><td>22.4</td><td>17.6</td><td>26.0</td><td>38.0</td><td>18.3</td><td>4.6</td><td>19.5</td><td>17.4</td><td>7.0</td><td>10.5</td><td>13.9</td><td>6.9</td><td>9.2</td><td>8.8</td><td>14.8</td><td>40.6</td></tr><tr><td>P_MSE</td><td>0.06</td><td>0.003</td><td>0.0001</td><td>0.006</td><td>0.003</td><td>0.0006</td><td>0.005</td><td>0.012</td><td>0.002</td><td>0.002</td><td>0.003</td><td>0.001</td><td>0.0003</td><td>0.0007</td><td>0.0007</td><td>0.0005</td><td>0.02</td><td>0.0003</td><td>0.0001</td></tr><tr><td>D_mAP</td><td>44.8</td><td>42.2</td><td>82.9</td><td>58.2</td><td>45.2</td><td>17.3</td><td>78.8</td><td>52.4</td><td>20.3</td><td>46.7</td><td>58.5</td><td>21.6</td><td>45.2</td><td>28.5</td><td>16.8</td><td>29.6</td><td>35.0</td><td>36.4</td><td>90.8</td></tr><tr><td>D_AUC</td><td>84.9</td><td>80.8</td><td>98.2</td><td>89.9</td><td>87.9</td><td>54.9</td><td>95.8</td><td>89.9</td><td>74.0</td><td>89.5</td><td>90.6</td><td>84.7</td><td>89.4</td><td>81.0</td><td>64.4</td><td>89.2</td><td>79.7</td><td>90.6</td><td>98.4</td></tr><tr><td>D_alOU</td><td>16.1</td><td>13.6</td><td>36.1</td><td>19.6</td><td>21.2</td><td>1.0</td><td>29.2</td><td>18.5</td><td>3.4</td><td>13.6</td><td>25.3</td><td>5.7</td><td>13.6</td><td>11.3</td><td>5.7</td><td>13.1</td><td>9.7</td><td>13.6</td><td>36.3</td></tr><tr><td>D_MSE</td><td>0.074</td><td>0.003</td><td>0.0001</td><td>0.007</td><td>0.003</td><td>0.0006</td><td>0.007</td><td>0.013</td><td>0.005</td><td>0.004</td><td>0.002</td><td>0.003</td><td>0.0008</td><td>0.002</td><td>0.002</td><td>0.0009</td><td>0.021</td><td>0.0004</td><td>0.0001</td></tr><tr><td>U_mAP</td><td>46.1</td><td>42.7</td><td>74.4</td><td>56.1</td><td>40.4</td><td>58.4</td><td>81.2</td><td>54.9</td><td>18.5</td><td>44.7</td><td>56.4</td><td>20.7</td><td>35.3</td><td>36.8</td><td>17.4</td><td>31.6</td><td>35.6</td><td>36.2</td><td>88.8</td></tr><tr><td>U_AUC</td><td>86.1</td><td>81.2</td><td>95.8</td><td>87.5</td><td>85.9</td><td>88.4</td><td>95.8</td><td>90.2</td><td>72.2</td><td>87.6</td><td>87.9</td><td>85.1</td><td>87.9</td><td>83.2</td><td>63.1</td><td>90.0</td><td>78.9</td><td>90.3</td><td>98.4</td></tr><tr><td>U_alOU</td><td>18.9</td><td>15.5</td><td>39.6</td><td>21.8</td><td>18.4</td><td>24.7</td><td>38.4</td><td>18.9</td><td>4.5</td><td>18.6</td><td>26.9</td><td>6.6</td><td>12.2</td><td>14.5</td><td>5.1</td><td>14.1</td><td>9.9</td><td>12.1</td><td>37.7</td></tr><tr><td>U_MSE</td><td>0.06</td><td>0.003</td><td>0.0001</td><td>0.006</td><td>0.003</td><td>0.0004</td><td>0.005</td><td>0.013</td><td>0.002</td><td>0.002</td><td>0.002</td><td>0.0007</td><td>0.0002</td><td>0.0008</td><td>0.0004</td><td>0.0008</td><td>0.021</td><td>0.0003</td><td>0.0001</td></tr><tr><td>Rotate SO(3)</td><td>Avg</td><td>Grasp</td><td>Lift</td><td>Contain</td><td>Open</td><td>Lay</td><td>Sit</td><td>Support</td><td>Wrap.</td><td>Pour</td><td>Display</td><td>Push</td><td>Pull</td><td>Listen</td><td>Wear</td><td>Press</td><td>Move</td><td>Cut</td><td>Stab</td></tr><tr><td>P_mAP</td><td>41.8</td><td>40.5</td><td>78.5</td><td>42.4</td><td>32.7</td><td>38.4</td><td>74.5</td><td>48.3</td><td>19.4</td><td>41.7</td><td>41.1</td><td>19.7</td><td>30.3</td><td>39.4</td><td>17.6</td><td>21.5</td><td>34.6</td><td>41.1</td><td>90.6</td></tr><tr><td>P_AUC</td><td>83.3</td><td>79.0</td><td>93.6</td><td>81.1</td><td>81.3</td><td>79.6</td><td>93.9</td><td>87.4</td><td>71.6</td><td>85.4</td><td>83.7</td><td>83.1</td><td>84.0</td><td>84.2</td><td>64.8</td><td>78.2</td><td>78.6</td><td>91.0</td><td>99.4</td></tr><tr><td>P_alOU</td><td>15.2</td><td>12.8</td><td>38.3</td><td>12.2</td><td>13.1</td><td>9.6</td><td>33.6</td><td>16.5</td><td>3.8</td><td>16.1</td><td>13.7</td><td>3.0</td><td>11.1</td><td>14.8</td><td>5.5</td><td>8.8</td><td>8.9</td><td>14.4</td><td>37.2</td></tr><tr><td>P_MSE</td><td>0.072</td><td>0.003</td><td>0.0001</td><td>0.008</td><td>0.003</td><td>0.0007</td><td>0.007</td><td>0.015</td><td>0.003</td><td>0.003</td><td>0.003</td><td>0.0002</td><td>0.0001</td><td>0.0006</td><td>0.002</td><td>0.0009</td><td>0.022</td><td>0.0006</td><td>0.0001</td></tr><tr><td>D_mAP</td><td>37.3</td><td>37.9</td><td>70.7</td><td>37.3</td><td>34.2</td><td>9.7</td><td>73.9</td><td>46.8</td><td>17.6</td><td>40.2</td><td>46.8</td><td>19.1</td><td>37.4</td><td>6.9</td><td>11.8</td><td>22.3</td><td>30.9</td><td>41.4</td><td>86.4</td></tr><tr><td>D_AUC</td><td>78.9</td><td>79.1</td><td>95.6</td><td>79.4</td><td>81.4</td><td>36.3</td><td>93.9</td><td>87.2</td><td>71.2</td><td>85.6</td><td>85.7</td><td>82.3</td><td>88.8</td><td>43.5</td><td>60.3</td><td>82.7</td><td>76.9</td><td>91.9</td><td>99.1</td></tr><tr><td>D_alOU</td><td>12.8</td><td>13.6</td><td>32.5</td><td>7.8</td><td>13.9</td><td>1.0</td><td>35.4</td><td>14.4</td><td>4.9</td><td>16.4</td><td>19.3</td><td>4.5</td><td>11.0</td><td>0.003</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>D_MSE</td><td>0.08</td><td>0.004</td><td>0.0002</td><td>0.007</td><td>0.003</td><td>0.0006</td><td>0.007</td><td>0.015</td><td>0.005</td><td>0.004</td><td>0.005</td><td>0.002</td><td>0.0005</td><td>0.0004</td><td>0.0006</td><td>0.009</td><td>0.022</td><td>0.0007</td><td>0.0002</td></tr><tr><td>U_mAP</td><td>37.9</td><td>37.0</td><td>61.2</td><td>38.0</td><td>29.8</td><td>34.0</td><td>77.4</td><td>49.9</td><td>16.4</td><td>39.3</td><td>42.6</td><td>14.8</td><td>24.7</td><td>35.7</td><td>8.6</td><td>20.1</td><td>31.8</td><td>36.9</td><td>83.3</td></tr><tr><td>U_AUC</td><td>80.9</td><td>76.9</td><td>90.5</td><td>79.5</td><td>77.7</td><td>78.1</td><td>94.1</td><td>87.8</td><td>67.9</td><td>82.7</td><td>81.9</td><td>78.1</td><td>83.5</td><td>83.7</td><td>52.5</td><td>76.6</td><td>77.1</td><td>89.6</td><td>99.0</td></tr><tr><td>U_alOU</td><td>12.0</td><td>15.3</td><td>8.2</td><td>10.8</td><td>10.7</td><td>5.4</td><td>35.8</td><td>16.2</td><td>2.7</td><td>12.7</td><td>15.8</td><td>1.0</td><td>4.3</td><td>12.3</td><td>1.0</td><td>7.3</td><td>7.9</td><td>11.9</td><td>35.8</td></tr><tr><td>U_MSE</td><td>0.07</td><td>0.005</td><td>0.0001</td><td>0.008</td><td>0.003</td><td>0.0005</td><td>0.006</td><td>0.013</td><td>0.003</td><td>0.003</td><td>0.004</td><td>0.0002</td><td>0.0001</td><td>0.0004</td><td>0.0004</td><td>0.0008</td><td>0.022</td><td>0.0003</td><td>0.0001</td></tr></table>
+
+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.  
+
+<table><tr><td></td><td>mAP</td><td>AUC</td><td>aIOU</td><td>MSE</td><td>Loss</td><td></td><td>mAP</td><td>AUC</td><td>aIOU</td><td>MSE</td><td>Loss</td></tr><tr><td>P Train</td><td>52.3</td><td>89.8</td><td>21.7</td><td>0.054</td><td>8.75</td><td>D Train</td><td>51.7</td><td>89.1</td><td>21.2</td><td>0.061</td><td>8.83</td></tr><tr><td>P Val</td><td>48.2</td><td>88.0</td><td>19.2</td><td>0.057</td><td>8.81</td><td>D Val</td><td>47.8</td><td>85.8</td><td>17.5</td><td>0.075</td><td>8.91</td></tr><tr><td>P Test</td><td>48.0</td><td>87.4</td><td>19.3</td><td>0.059</td><td>8.83</td><td>D Test</td><td>46.4</td><td>85.5</td><td>17.8</td><td>0.08</td><td>8.93</td></tr></table>
+
+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.
+
+<table><tr><td>VAT</td><td>Avg</td><td>Grasp</td><td>Lift</td><td>Contain</td><td>Open</td><td>Lay</td><td>Sit</td><td>Support</td><td>Wrap.</td><td>Pour</td><td>Display</td><td>Push</td><td>Pull</td><td>Listen</td><td>Wear</td><td>Press</td><td>Move</td><td>Cut</td><td>Stab</td></tr><tr><td>mAP</td><td>36.6</td><td>34.8</td><td>78.8</td><td>44.3</td><td>22.6</td><td>34.9</td><td>64.8</td><td>41.4</td><td>13.3</td><td>41.5</td><td>58.9</td><td>13.5</td><td>8.3</td><td>20.5</td><td>8.5</td><td>29.5</td><td>19.4</td><td>33.1</td><td>90.2</td></tr><tr><td>AUC</td><td>78.8</td><td>75.8</td><td>95.3</td><td>78.4</td><td>79.2</td><td>71.2</td><td>92.4</td><td>86.7</td><td>56.5</td><td>83.7</td><td>89.9</td><td>69.0</td><td>74.8</td><td>74.1</td><td>51.4</td><td>88.8</td><td>62.7</td><td>89.3</td><td>99.1</td></tr><tr><td>aIOU</td><td>11.2</td><td>12.7</td><td>20.3</td><td>14.2</td><td>4.8</td><td>6.4</td><td>16.9</td><td>7.7</td><td>5.1</td><td>17.6</td><td>30.2</td><td>2.5</td><td>1.1</td><td>8.4</td><td>3.6</td><td>12.8</td><td>2.9</td><td>9.5</td><td>24.3</td></tr><tr><td>MSE</td><td>0.155</td><td>0.007</td><td>0.0001</td><td>0.02</td><td>0.006</td><td>0.0007</td><td>0.012</td><td>0.023</td><td>0.023</td><td>0.007</td><td>0.008</td><td>0.0003</td><td>0.0001</td><td>0.002</td><td>0.002</td><td>0.005</td><td>0.034</td><td>0.004</td><td>0.0003</td></tr><tr><td>Full-Shape</td><td>Avg</td><td>Grasp</td><td>Lift</td><td>Contain</td><td>Open</td><td>Lay</td><td>Sit</td><td>Support</td><td>Wrap.</td><td>Pour</td><td>Display</td><td>Push</td><td>Pull</td><td>Listen</td><td>Wear</td><td>Press</td><td>Move</td><td>Cut</td><td>Stab</td></tr><tr><td>mAP</td><td>34.3</td><td>34.5</td><td>77.9</td><td>42.3</td><td>18.2</td><td>36.5</td><td>62.9</td><td>38.8</td><td>11.2</td><td>38.9</td><td>53.3</td><td>13.4</td><td>7.3</td><td>9</td><td>6.7</td><td>24.5</td><td>17.4</td><td>35.8</td><td>89.5</td></tr><tr><td>AUC</td><td>77.5</td><td>75.4</td><td>94.8</td><td>78.1</td><td>75.7</td><td>73.3</td><td>92.1</td><td>85.8</td><td>54.4</td><td>82.1</td><td>87.5</td><td>74.5</td><td>77.4</td><td>61.6</td><td>46.7</td><td>83.4</td><td>64.1</td><td>89.8</td><td>98.9</td></tr><tr><td>aIOU</td><td>9.8</td><td>11.2</td><td>28.1</td><td>14.3</td><td>2.5</td><td>10.0</td><td>23.4</td><td>9.8</td><td>2.2</td><td>7.5</td><td>19.9</td><td>1.9</td><td>1.0</td><td>1.6</td><td>1.6</td><td>6.8</td><td>2.3</td><td>5.6</td><td>26.5</td></tr><tr><td>MSE</td><td>0.105</td><td>0.009</td><td>0.0002</td><td>0.013</td><td>0.003</td><td>0.001</td><td>0.013</td><td>0.021</td><td>0.004</td><td>0.003</td><td>0.003</td><td>0.0002</td><td>0.0001</td><td>0.0004</td><td>0.001</td><td>0.0008</td><td>0.031</td><td>0.0007</td><td>0.0001</td></tr></table>
+
+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).
+
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+# 3DCaricShop: A Dataset and A Baseline Method for Single-view 3D Caricature Face Reconstruction
+
+Yuda Qiu
+
+Xiaojie  $\mathbf{X}\mathbf{u}^{1}$
+
+Lingteng Qiu
+
+Yan Pan
+
+Yushuang Wu
+
+Weikai Chen
+
+Xiaoguang Han $^{1,*}$
+
+$^{1}$ SRIBD, The Chinese University of Hong Kong, Shenzhen†  $^{2}$ Tencent Game AI Research Center
+
+# Abstract
+
+Caricature is an artistic representation that deliberately exaggerates the distinctive features of a human face to convey humor or sarcasm. 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.
+
+<table><tr><td>Dataset</td><td>Global</td><td>Eye</td><td>Nose</td><td>Mouth</td><td>Ear</td><td>Cheek</td><td>Face</td></tr><tr><td>FWH</td><td>3.41</td><td>0.71</td><td>0.61</td><td>2.60</td><td>4.41</td><td>1.43</td><td>3.40</td></tr><tr><td>FaceScape</td><td>2.17</td><td>0.36</td><td>0.15</td><td>2.63</td><td>5.57</td><td>1.24</td><td>2.27</td></tr><tr><td>Aug. FWH</td><td>5.06</td><td>1.98</td><td>6.29</td><td>2.07</td><td>9.38</td><td>5.26</td><td>5.10</td></tr><tr><td>Ours</td><td>8.26</td><td>4.68</td><td>3.04</td><td>10.90</td><td>9.02</td><td>8.27</td><td>6.95</td></tr></table>
+
+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
+
+<table><tr><td>Methods</td><td>P2S</td><td>Methods</td><td>P2S</td></tr><tr><td>3DMMhuman</td><td>0.295</td><td>PiFuhead</td><td>0.153</td></tr><tr><td>3DMMcari</td><td>0.104</td><td>PiFuface</td><td>0.126</td></tr><tr><td>DF2Net</td><td>0.273</td><td>Ourshead</td><td>0.065</td></tr><tr><td>AliveCaric-DL</td><td>0.067</td><td>Oursface</td><td>0.037</td></tr></table>
+
+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)
+
+<table><tr><td>Methods</td><td>MPJPE</td><td>Methods</td><td>MPJPE</td></tr><tr><td rowspan="2">w/o GCN Refinement V2V [22]</td><td>0.451</td><td>Global only</td><td>0.373</td></tr><tr><td>0.407</td><td>w/o G2L</td><td>0.358</td></tr><tr><td></td><td></td><td>Basic</td><td>0.291</td></tr></table>
+
+![](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.  
+
+<table><tr><td>Methods</td><td>P2S</td></tr><tr><td>Ours w/o Landmark</td><td>0.074</td></tr><tr><td>Ours w/o PCA projection</td><td>0.076</td></tr><tr><td>Ours</td><td>0.065</td></tr></table>
+
+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.
+
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+# 3D CNNs with Adaptive Temporal Feature Resolutions
+
+Mohsen Fayyaz $^{1,\ast}$ , Emad Bahrami $^{1,\ast}$ , Ali Diba $^{2}$ , Mehdi Noroozi $^{3}$ , Ehsan Adeli $^{4}$ , Luc Van Gool $^{2,5}$ , Juergen Gall $^{1}$ $^{1}$ University of Bonn,  $^{2}$ KU Leuven,  $^{3}$ Bosch Center for Artificial Intelligence,  $^{4}$ Standford University,  $^{5}$ ETH Zürich  
+{lastname}@iai.uni-bonn.de, emadbahramirad@gmail.com, {firstname_lastname}@kuleuven.be, mehdi.noroozi@de.bosch.de, eadeli@stanford.edu
+
+# Abstract
+
+While state-of-the-art 3D Convolutional Neural Networks (CNN) achieve very good results on action recognition datasets, they are computationally very expensive and require many GFLOPs. 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.<sup>1</sup>
+
+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.
+
+<table><tr><td>Similarity</td><td>Magnitude</td><td>Angular</td><td>Spherical</td></tr><tr><td>top1</td><td>69.6</td><td>68.5</td><td>68.7</td></tr><tr><td>top5</td><td>88.8</td><td>87.8</td><td>88.1</td></tr></table>
+
+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  $(\%)$ .  
+
+<table><tr><td>Kernel</td><td>Linear</td><td>Kronecker</td></tr><tr><td>top1</td><td>69.6</td><td>68.9</td></tr><tr><td>top5</td><td>88.8</td><td>88.6</td></tr></table>
+
+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.  
+
+<table><tr><td>L</td><td>1</td><td>4</td><td>8</td><td>16</td></tr><tr><td>top1</td><td>67.3</td><td>68.4</td><td>69.6</td><td>64.7</td></tr><tr><td>top5</td><td>87.7</td><td>88.1</td><td>88.8</td><td>86.1</td></tr></table>
+
+Table 3: Impact of the dimensionality  $L$  of the similarity space.  
+
+<table><tr><td rowspan="3">model</td><td rowspan="3">input frames</td><td rowspan="3">GFLOPs</td><td colspan="2">top1</td><td colspan="2">top5</td></tr><tr><td colspan="4">stride</td></tr><tr><td>1</td><td>2</td><td>1</td><td>2</td></tr><tr><td rowspan="2">SlowFast-8x8-ResNet18</td><td>32</td><td>30.9</td><td>67.5</td><td>69.7</td><td>87.1</td><td>89.1</td></tr><tr><td>64</td><td>61.8 (2.0)</td><td>72.1</td><td>74.6</td><td>89.9</td><td>91.9</td></tr><tr><td rowspan="2">R(2+1)D</td><td>32</td><td>46.5</td><td>67.4</td><td>69.3</td><td>86.2</td><td>87.5</td></tr><tr><td>64</td><td>93.1 (2.0)</td><td>70.8</td><td>73.7</td><td>88.8</td><td>91.5</td></tr><tr><td rowspan="2">R(2+1)D+ATFR</td><td>32</td><td>32.3</td><td>67.4</td><td>69.3</td><td>86.4</td><td>87.6</td></tr><tr><td>64</td><td>54.9 (1.7)</td><td>71.4</td><td>73.8</td><td>88.6</td><td>90.7</td></tr><tr><td rowspan="2">3DResNet-18+ATFR</td><td>32</td><td>14.0</td><td>67.3</td><td>69.6</td><td>87.2</td><td>89.0</td></tr><tr><td>64</td><td>21.1 (1.5)</td><td>72.1</td><td>74.8</td><td>89.8</td><td>91.4</td></tr></table>
+
+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
+
+<table><tr><td>Lowest Temporal Resolution</td><td>Highest Temporal Resolution</td></tr><tr><td>presenting weather forecast stretching leg playing didgeridoo playing clarinet golf putting</td><td>passing American football (in game) swimming breast stroke playing ice hockey pushing cart gymnastics tumbling</td></tr></table>
+
+Table 5: The 5 action classes with lowest and highest required adaptive temporal resolution for 3DResNet-50 + ATFR on Mini-Kinetics.  
+
+<table><tr><td>Stage</td><td>No SGS</td><td>First Conv</td><td>Res2</td><td>Res3</td></tr><tr><td>top1</td><td>77.9</td><td>77.8</td><td>78.0</td><td>78.0</td></tr><tr><td>GFLOPs</td><td>1.9</td><td>0.9</td><td>1.1</td><td>1.3</td></tr></table>
+
+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.  
+
+<table><tr><td>model</td><td>backbone</td><td>GFLOPs</td><td>top1</td><td>top5</td></tr><tr><td>Fast-S3D [32]</td><td>-</td><td>43.5</td><td>78.0</td><td>-</td></tr><tr><td>SlowFast 8x8</td><td>ResNet18</td><td>40.4</td><td>77.5</td><td>93.3</td></tr><tr><td>SlowFast 8x8</td><td>ResNet50</td><td>65.7</td><td>79.3</td><td>94.2</td></tr><tr><td>R(2+1)D</td><td>ResNet50</td><td>101.8</td><td>78.7</td><td>93.4</td></tr><tr><td>R(2+1)D+ATFR</td><td>ResNet50</td><td>67.3</td><td>78.2</td><td>92.9</td></tr><tr><td>I3D</td><td>ResNet50</td><td>148.4</td><td>79.3</td><td>94.4</td></tr><tr><td>I3D+ATFR</td><td>ResNet50</td><td>105.2</td><td>78.8</td><td>93.6</td></tr><tr><td>X3D-S</td><td>-</td><td>1.9</td><td>77.9</td><td>93.4</td></tr><tr><td>X3D-S+ATFR</td><td>-</td><td>1.1</td><td>78.0</td><td>93.5</td></tr><tr><td>3DResNet</td><td>ResNet50</td><td>40.8</td><td>79.2</td><td>94.6</td></tr><tr><td>3DResNet+ATFR</td><td>ResNet50</td><td>23.4</td><td>79.3</td><td>94.6</td></tr></table>
+
+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.
+
+<table><tr><td>model</td><td>GFLOPs</td><td>top1</td><td>top5</td><td>Param</td></tr><tr><td>I3D*[3]</td><td>108× N/A</td><td>71.1</td><td>90.3</td><td>12.0M</td></tr><tr><td>I3D+SCSampler*[15]</td><td>108×10+N/A</td><td>75.1</td><td>N/A</td><td>N/A</td></tr><tr><td>Two-Stream I3D*[3]</td><td>216×N/A</td><td>75.7</td><td>92.0</td><td>25.0M</td></tr><tr><td>Two-Stream S3D-G*[32]</td><td>143×N/A</td><td>77.2</td><td>-</td><td>23.1M</td></tr><tr><td>TSM R50*[18]</td><td>65×10</td><td>74.4</td><td>N/A</td><td>24.3M</td></tr><tr><td>HATNET[5]</td><td>N/A</td><td>77.2</td><td>N/A</td><td>N/A</td></tr><tr><td>STC[4]</td><td>N/A</td><td>68.7</td><td>88.5</td><td>N/A</td></tr><tr><td>Two-Stream I3D[3]</td><td>216×N/A</td><td>75.7</td><td>92.0</td><td>25.0M</td></tr><tr><td>R(2+1)D[25]</td><td>152×115</td><td>72.0</td><td>90.0</td><td>63.6M</td></tr><tr><td>Two-Stream R(2+1)D[25]</td><td>304×115</td><td>73.9</td><td>90.9</td><td>127.2M</td></tr><tr><td>FASTER32[20]</td><td>67.7×8</td><td>75.3</td><td>N/A</td><td>N/A</td></tr><tr><td>SlowFast8×8,R101+NL[9]</td><td>116×30</td><td>78.7</td><td>93.5</td><td>59.9M</td></tr><tr><td>SlowFast16×8,R101+NL[9]</td><td>234×30</td><td>79.8</td><td>93.9</td><td>59.9M</td></tr><tr><td>X3D-Lα[8]</td><td>18.3×10</td><td>76.8</td><td>92.5</td><td>6.1M</td></tr><tr><td>X3D-Lβ[8]</td><td>24.8×30</td><td>77.5</td><td>92.9</td><td>6.1M</td></tr><tr><td>SlowFast4×16,R50[9]</td><td>36.1×30</td><td>75.6</td><td>92.1</td><td>34.40M</td></tr><tr><td>SlowFast4×16,R50+ATFR</td><td>20.8×30 (↓42%)</td><td>75.8</td><td>92.4</td><td>34.40M</td></tr><tr><td>X3D-Sα[8]</td><td>1.9×10</td><td>72.9</td><td>90.5</td><td>3.79M</td></tr><tr><td>X3D-S+ATFRα</td><td>1.0×10 (↓47%)</td><td>73.5</td><td>91.2</td><td>3.79M</td></tr><tr><td>X3D-XLα[8]</td><td>35.8×10</td><td>78.4</td><td>93.6</td><td>11.09M</td></tr><tr><td>X3D-XL+ATFRα</td><td>20×10 (↓44%)</td><td>78.6</td><td>93.9</td><td>11.09M</td></tr><tr><td>X3D-XLβ[8]</td><td>48.4×30</td><td>79.1</td><td>93.9</td><td>11.09M</td></tr><tr><td>X3D-XL+ATFRβ</td><td>26.3×30 (↓45%)</td><td>79.3</td><td>94.1</td><td>11.09M</td></tr></table>
+
+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.
+
+<table><tr><td>model</td><td>pretrain</td><td>GFLOPs</td><td>top1</td><td>top5</td></tr><tr><td>Oct-I3D+NL[3]</td><td>ImageNet</td><td>25.6×30</td><td>76.0</td><td>N/A</td></tr><tr><td>HATNET[5]</td><td>HVU</td><td>N/A</td><td>81.6</td><td>N/A</td></tr><tr><td>HATNET[5]</td><td>-</td><td>N/A</td><td>80.2</td><td>N/A</td></tr><tr><td>I3D[3]</td><td>-</td><td>108× N/A</td><td>71.9</td><td>90.1</td></tr><tr><td>SlowFast16×8,R101+NL[9]</td><td>-</td><td>234×30</td><td>81.8</td><td>95.1</td></tr><tr><td>SlowFast4×16,R50[9]</td><td>-</td><td>36.1×30</td><td>78.8</td><td>94.0</td></tr><tr><td>X3D-M[8]</td><td>-</td><td>6.2×30</td><td>78.8</td><td>94.5</td></tr><tr><td>X3D-M+ATFR</td><td>-</td><td>3.3×30 (↓ 46%)</td><td>79.0</td><td>94.9</td></tr><tr><td>X3D-XL[8]</td><td>-</td><td>48.4×30</td><td>81.9</td><td>95.5</td></tr><tr><td>X3D-XL+ATFR</td><td>-</td><td>25.6×30 (↓ 47%)</td><td>82.1</td><td>95.6</td></tr></table>
+
+Table 9: Comparison to the state-of-the-art on Kinetics-600.  
+
+<table><tr><td>model</td><td>pretrain</td><td>GFLOPs</td><td>top1</td><td>top5</td></tr><tr><td>SlowFast-R50 [27]</td><td>Kinetics400</td><td>132.8</td><td>61.7</td><td>87.8</td></tr><tr><td>SlowFast-R50+ATFR</td><td>Kinetics400</td><td>87.8 (↓ 33%)</td><td>61.8</td><td>87.9</td></tr></table>
+
+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
+
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+# 3D Graph Anatomy Geometry-Integrated Network for Pancreatic Mass Segmentation, Diagnosis, and Quantitative Patient Management
+
+Tianyi Zhao\*1,2, Kai Cao\*3, Jiawen Yao $^{1}$ , Isabella Nogues $^{4}$ , Le Lu $^{1}$ , Lingyun Huang $^{5}$ , Jing Xiao $^{5}$ , Zhaozheng Yin $^{2}$ , Ling Zhang $^{1}$
+
+<sup>1</sup> PAII Inc., <sup>2</sup>Stony Brook University, <sup>3</sup>Changhai Hospital, <sup>4</sup>Harvard University, <sup>5</sup>Ping An Technology
+
+# Abstract
+
+The pancreatic disease taxonomy includes ten types of masses (tumors or cysts) [20, 8]. 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.  
+
+<table><tr><td></td><td>Metric</td><td>PDAC</td><td>NonPDAC</td><td>AC</td><td>CP</td><td>DC</td><td>IPMN</td><td>MCN</td><td>PNET</td><td>RARE</td><td>SCN</td><td>SPT</td><td>micro</td><td>macro</td></tr><tr><td rowspan="2">nnUNet[13]</td><td>Average Dice</td><td>0.734</td><td>0.478</td><td>0.423</td><td>0.533</td><td>0.001</td><td>0.151</td><td>0.924</td><td>0.514</td><td>0.849</td><td>0.585</td><td>0.762</td><td>0.618</td><td>0.548</td></tr><tr><td>Detection rate</td><td>0.959</td><td>0.693</td><td>0.7</td><td>0.778</td><td>0.0</td><td>0.308</td><td>1.0</td><td>0.833</td><td>1.0</td><td>0.8</td><td>1.0</td><td>0.838</td><td>0.738</td></tr><tr><td rowspan="2">SMCN(Ours)</td><td>Average Dice</td><td>0.738</td><td>0.611</td><td>0.438</td><td>0.668</td><td>0.006</td><td>0.602</td><td>0.924</td><td>0.514</td><td>0.824</td><td>0.666</td><td>0.801</td><td>0.681</td><td>0.618</td></tr><tr><td>Detection rate</td><td>0.972</td><td>0.887</td><td>0.8</td><td>0.889</td><td>0.0</td><td>1.0</td><td>1.0</td><td>1.0</td><td>1.0</td><td>0.8</td><td>1.0</td><td>0.934</td><td>0.846</td></tr></table>
+
+Table 2. PDAC segmentation under different CT phases: non-contrast (N), arterial (A), arterial-early (AE), arterial-late (AL), venous (V), and delay (D).  
+
+<table><tr><td>Methods</td><td>CT Phases</td><td>Average Dice</td></tr><tr><td colspan="3">Reported from their original papers</td></tr><tr><td>Zhang et al. [32]</td><td>N+A+V</td><td>0.709</td></tr><tr><td>DDT [23]</td><td>V</td><td>0.634</td></tr><tr><td>Xia et al. [27]</td><td>A+V</td><td>0.644</td></tr><tr><td>Ours</td><td>AE</td><td>0.646</td></tr><tr><td>Ours</td><td>AL</td><td>0.730</td></tr><tr><td>Ours</td><td>V</td><td>0.675</td></tr><tr><td>Ours</td><td>D</td><td>0.562</td></tr><tr><td>Ours</td><td>N+AE+V+D</td><td>0.696</td></tr><tr><td>Ours</td><td>N+AE+AL+V+D</td><td>0.738</td></tr></table>
+
+# 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.  
+
+<table><tr><td>Methods</td><td>Accuracy</td><td>Sensitivity</td><td>Specificity</td></tr><tr><td>Radiomics [21]</td><td>0.857</td><td>0.853</td><td>0.868</td></tr><tr><td>DeepTexture [28]</td><td>0.770</td><td>0.827</td><td>0.697</td></tr><tr><td>ResNet3D [9]</td><td>0.720</td><td>0.788</td><td>0.633</td></tr><tr><td>SMCN w PV</td><td>0.913</td><td>0.945</td><td>0.875</td></tr><tr><td>SMCN w VV</td><td>0.920</td><td>0.945</td><td>0.891</td></tr><tr><td>SMCN w GC</td><td>0.927</td><td>0.945</td><td>0.906</td></tr><tr><td>Expert radiologists</td><td>-</td><td>~0.94</td><td>~0.90</td></tr></table>
+
+# 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].  
+
+<table><tr><td>CompCyst [20]</td><td>Discharge</td><td>Monitoring</td><td>Surgery</td><td>Ours</td><td>Discharge</td><td>Monitoring</td><td>Surgery</td></tr><tr><td>Discharge (n=53)</td><td>32 (60%)</td><td>14 (26%)</td><td>7 (13%)</td><td>(n=46)</td><td>28 (61%)</td><td>10 (22%)</td><td>8 (17%)</td></tr><tr><td>Monitor (n=140)</td><td>1 (1%)</td><td>68 (49%)</td><td>71 (51%)</td><td>(n=104)</td><td>11 (11%)</td><td>65 (63%)</td><td>27 (26%)</td></tr><tr><td>Surgery (n=152)</td><td>0 (0%)</td><td>14 (9%)</td><td>138 (91%)</td><td>(n=440)</td><td>6 (1%)</td><td>16 (4%)</td><td>418 (95%)</td></tr></table>
+
+Table 5. Experimental Results for Patient Management. PV: pixel voting; VV: vertex-based voting; GC: global classification.  
+
+<table><tr><td>Methods</td><td>Accuracy</td><td>Average Recall</td></tr><tr><td>Radiomics [21]</td><td>0.854</td><td>0.667</td></tr><tr><td>DeepTexture [28]</td><td>0.743</td><td>0.557</td></tr><tr><td>ResNet3D [9]</td><td>0.737</td><td>0.607</td></tr><tr><td>SMCN w PV</td><td>0.832</td><td>0.735</td></tr><tr><td>SMCN w VV</td><td>0.839</td><td>0.656</td></tr><tr><td>SMCN w GC</td><td>0.865</td><td>0.746</td></tr></table>
+
+![](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
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+# 3D Human Action Representation Learning via Cross-View Consistency Pursuit
+
+Linguo Li $^{1,2*}$  Minsi Wang $^{1,2*}$  Bingbing Ni $^{1,2**}$  Hang Wang $^{1,2}$  Jiancheng Yang $^{1,2}$  Wenjun Zhang $^{1}$ $^{1}$ Shanghai Jiao Tong University, Shanghai 200240, China  
+ $^{2}$ MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University mswang1994@gmail.com, {LLG440982, nibingbing, zhangwenjun}@sjtu.edu.cn
+
+# Abstract
+
+In this work, we propose a Cross-view Contrastive Learning framework for unsupervised 3D skeleton-based action Representation (CrosCLR), by leveraging multiview complementary supervision signal. 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.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">View</td><td colspan="2">NTU-60 (%)</td></tr><tr><td>xsub</td><td>xview</td></tr><tr><td>SkeletonCLR</td><td>Joint</td><td>68.3</td><td>76.4</td></tr><tr><td>SkeletonCLR</td><td>Motion</td><td>53.3</td><td>50.8</td></tr><tr><td>SkeletonCLR</td><td>Bone</td><td>69.4</td><td>67.4</td></tr><tr><td>2s-SkeletonCLR</td><td>Joint + Motion</td><td>70.5</td><td>77.9</td></tr><tr><td>3s-SkeletonCLR</td><td>Joint + Motion + Bone</td><td>75.0</td><td>79.8</td></tr><tr><td>CrosCLR</td><td>Joint</td><td>72.9</td><td>79.9</td></tr><tr><td>CrosCLR</td><td>Motion</td><td>72.7</td><td>77.6</td></tr><tr><td>CrosCLR</td><td>Bone</td><td>75.2</td><td>78.8</td></tr><tr><td>2s-CrosCLR</td><td>Joint + Motion</td><td>74.5</td><td>82.1</td></tr><tr><td>3s-CrosCLR</td><td>Joint + Motion + Bone</td><td>77.8</td><td>83.4</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2">top-K</td><td colspan="2">NTU-60 (%)</td></tr><tr><td>xsub</td><td>xview</td></tr><tr><td>0</td><td>70.5</td><td>77.4</td></tr><tr><td>1</td><td>74.5</td><td>82.1</td></tr><tr><td>3</td><td>73.7</td><td>79.9</td></tr><tr><td>5</td><td>72.4</td><td>79.2</td></tr><tr><td>7</td><td>73.0</td><td>78.6</td></tr><tr><td>10</td><td>64.4</td><td>69.9</td></tr></table>
+
+Table 2. Results of pretraining 2s-CrosSCLR with various  $K$  in knowledge miner  $\Gamma$  
+
+<table><tr><td colspan="2">Augmentation</td><td colspan="2">NTU-60 (%)</td></tr><tr><td>Shear β</td><td>Crop γ</td><td>xsub</td><td>xview</td></tr><tr><td>0</td><td>0</td><td>33.3</td><td>26.2</td></tr><tr><td>0.2</td><td>0</td><td>62.7</td><td>67.7</td></tr><tr><td>0.5</td><td>0</td><td>66.3</td><td>68.8</td></tr><tr><td>1.0</td><td>0</td><td>62.0</td><td>66.8</td></tr><tr><td>0.5</td><td>4</td><td>67.6</td><td>76.3</td></tr><tr><td>0.5</td><td>6</td><td>68.3</td><td>76.4</td></tr><tr><td>0.5</td><td>8</td><td>69.1</td><td>74.7</td></tr></table>
+
+Table 3. Ablation study on different data augmentations for Skeleton-CLR (joint).  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Views of Pre-training</td><td colspan="2">NTU-60 (%)</td></tr><tr><td>xsub</td><td>xview</td></tr><tr><td>SkeletonCLR</td><td>Joint</td><td>68.3</td><td>76.4</td></tr><tr><td>SkeletonCLR + LKM</td><td>Joint</td><td>69.3</td><td>77.4</td></tr><tr><td>CrossSCLR w/o. EC</td><td>Joint + Motion</td><td>71.4</td><td>78.5</td></tr><tr><td>CrossSCLR</td><td>Joint + Motion</td><td>72.9</td><td>79.9</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Encoder</td><td rowspan="2">Classifier</td><td colspan="2">NTU-60 (%)</td></tr><tr><td>xsub</td><td>xview</td></tr><tr><td>LongT GAN [65]</td><td>GRU</td><td>FC</td><td>39.1</td><td>48.1</td></tr><tr><td>MS2L [26]</td><td>GRU</td><td>GRU</td><td>52.6</td><td>-</td></tr><tr><td>AS-CAL [39]</td><td>LSTM</td><td>FC</td><td>58.5</td><td>64.8</td></tr><tr><td>P&amp;C [47]</td><td>GRU</td><td>KNN</td><td>50.7</td><td>76.3</td></tr><tr><td>SeBiReNet [34]</td><td>GRU</td><td>LSTM</td><td>-</td><td>79.7</td></tr><tr><td>3s-CrosSCLR (LSTM)</td><td>LSTM</td><td>FC</td><td>62.8</td><td>69.2</td></tr><tr><td>3s-CrosSCLR (LSTM)</td><td>LSTM</td><td>LSTM</td><td>70.4</td><td>79.9</td></tr><tr><td>3s-CrosSCLR‡</td><td>ST-GCN</td><td>FC</td><td>72.8</td><td>80.7</td></tr><tr><td>3s-CrosSCLR</td><td>ST-GCN</td><td>FC</td><td>77.8</td><td>83.4</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Supervision</td><td colspan="2">NTU-120 (%)</td></tr><tr><td>xsub</td><td>xset</td></tr><tr><td>Part-Aware LSTM [40]</td><td>Supervised</td><td>25.5</td><td>26.3</td></tr><tr><td>Soft RNN [15]</td><td>Supervised</td><td>36.3</td><td>44.9</td></tr><tr><td>TSRJI [2]</td><td>Supervised</td><td>67.9</td><td>62.8</td></tr><tr><td>ST-GCN [57]</td><td>Supervised</td><td>79.7</td><td>81.3</td></tr><tr><td>AS-CAL [39]</td><td>Unsupervised</td><td>48.6</td><td>49.2</td></tr><tr><td>3s-CrossCLR (LSTM)</td><td>Unsupervised</td><td>53.9</td><td>53.2</td></tr><tr><td>3s-CrossCLR</td><td>Unsupervised</td><td>67.9</td><td>66.7</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Label Fraction</td><td colspan="2">NTU-60 (%)</td></tr><tr><td>xsub</td><td>xview</td></tr><tr><td>LongT GAN [65]</td><td>1%</td><td>35.2</td><td>-</td></tr><tr><td>MS²L [26]</td><td>1%</td><td>33.1</td><td>-</td></tr><tr><td>3s-CrosCLR</td><td>1%</td><td>51.1</td><td>50.0</td></tr><tr><td>LongT GAN [65]</td><td>10%</td><td>62.0</td><td>-</td></tr><tr><td>MS²L [26]</td><td>10%</td><td>65.2</td><td>-</td></tr><tr><td>3s-CrosCLR</td><td>10%</td><td>74.4</td><td>77.8</td></tr></table>
+
+Table 7. Linear classification with fewer labels on NTU-60.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">NTU-60 (%)</td><td colspan="2">NTU-120 (%)</td></tr><tr><td>xsub</td><td>xview</td><td>xsub</td><td>xset</td></tr><tr><td>3s-ST-GCN* [57]</td><td>85.2</td><td>91.4</td><td>77.2</td><td>77.1</td></tr><tr><td>3s-CrossCLR‡ (FT)</td><td>85.6</td><td>92.0</td><td>-</td><td>-</td></tr><tr><td>3s-CrossCLR (FT)</td><td>86.2</td><td>92.5</td><td>80.5</td><td>80.4</td></tr></table>
+
+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).
+
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+# 3DIOUMatch: Leveraging IoU Prediction for Semi-Supervised 3D Object Detection
+
+He Wang $^{1*}$  Yezhen Cong $^{2*}$  Or Litany $^{3}$  Yue Gao $^{2}$  Leonidas J. 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.
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Model</td><td colspan="2">5%</td><td colspan="2">10%</td><td colspan="2">20%</td><td colspan="2">100%</td></tr><tr><td>mAP @0.25</td><td>mAP @0.5</td><td>mAP @0.25</td><td>mAP @0.5</td><td>mAP @0.25</td><td>mAP @0.5</td><td>mAP @0.25</td><td>mAP @0.5</td></tr><tr><td rowspan="5">ScanNet</td><td>VoteNet</td><td>27.9±0.5</td><td>10.8±0.6</td><td>36.9±1.6</td><td>18.2±1.0</td><td>46.9±1.9</td><td>27.5±1.2</td><td>57.8</td><td>36.0</td></tr><tr><td>SESS reported</td><td>\</td><td>\</td><td>39.7±0.9</td><td>18.6</td><td>47.9±0.4</td><td>26.9</td><td>62.1</td><td>38.8</td></tr><tr><td>SESS</td><td>32.0±0.7</td><td>14.4±0.7</td><td>39.5±1.8</td><td>19.8±1.3</td><td>49.6±1.1</td><td>29.0±1.0</td><td>61.3</td><td>39.0</td></tr><tr><td>Ours</td><td>40.0±0.9</td><td>22.5±0.5</td><td>47.2±0.4</td><td>28.3±1.5</td><td>52.8±1.2</td><td>35.2±1.1</td><td>62.9</td><td>42.1</td></tr><tr><td>Abs. improve.</td><td>+8.0</td><td>+8.1</td><td>+7.7</td><td>+8.5</td><td>+3.2</td><td>+6.2</td><td>+1.6</td><td>+3.1</td></tr><tr><td rowspan="5">SUN-RGBD</td><td>VoteNet</td><td>29.9±1.5</td><td>10.5±0.5</td><td>38.9±0.8</td><td>17.2±1.3</td><td>45.7±0.6</td><td>22.5±0.8</td><td>58.0</td><td>33.4</td></tr><tr><td>SESS reported</td><td>\</td><td>\</td><td>42.9±1.0</td><td>14.4</td><td>47.9±0.5</td><td>20.6</td><td>61.1</td><td>37.3</td></tr><tr><td>SESS</td><td>34.2±2.0</td><td>13.1±1.0</td><td>42.1±1.1</td><td>20.9±0.3</td><td>47.1±0.7</td><td>24.5±1.2</td><td>60.5</td><td>38.1</td></tr><tr><td>Ours</td><td>39.0±1.9</td><td>21.1±1.7</td><td>45.5±1.5</td><td>28.8±0.7</td><td>49.7±0.4</td><td>30.9±0.2</td><td>61.5</td><td>41.3</td></tr><tr><td>Abs. improve.</td><td>+4.8</td><td>+8.0</td><td>+3.4</td><td>+7.9</td><td>+2.6</td><td>+6.4</td><td>+1.0</td><td>+3.2</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2">Obj&amp;Cls Filter</td><td rowspan="2">IoU Filter</td><td rowspan="2">Train-time Suppression</td><td rowspan="2">Test-time Suppression</td><td rowspan="2">Test-time IoU opt.</td><td colspan="2">ScanNet 10%</td><td colspan="2">SUN-RGBD 5%</td></tr><tr><td>mAP@0.25</td><td>mAP@0.5</td><td>mAP@0.25</td><td>mAP@0.5</td></tr><tr><td></td><td></td><td></td><td>Obj-NMS</td><td></td><td>38.4</td><td>19.8</td><td>32.9</td><td>12.5</td></tr><tr><td>✓</td><td></td><td></td><td>Obj-NMS</td><td></td><td>44.5</td><td>24.7</td><td>36.9</td><td>17.5</td></tr><tr><td>✓</td><td></td><td>Obj-NMS</td><td>Obj-NMS</td><td></td><td>44.2</td><td>25.2</td><td>37.1</td><td>17.4</td></tr><tr><td>✓</td><td>✓</td><td>IoU-NMS</td><td>Obj-NMS</td><td></td><td>45.9</td><td>26.8</td><td>37.4</td><td>18.7</td></tr><tr><td>✓</td><td>✓</td><td>IoU-LHS</td><td>Obj-NMS</td><td></td><td>46.5</td><td>26.9</td><td>37.9</td><td>18.5</td></tr><tr><td>✓</td><td>✓</td><td>IoU-LHS</td><td>IoU-NMS</td><td></td><td>47.0</td><td>28.2</td><td>38.8</td><td>20.8</td></tr><tr><td>✓</td><td>✓</td><td>IoU-LHS</td><td>IoU-NMS</td><td>✓</td><td>47.2</td><td>28.3</td><td>39.0</td><td>21.1</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2"></td><td colspan="3">1%</td><td colspan="3">2%</td><td colspan="3">100%</td></tr><tr><td>Car</td><td>Ped.</td><td>Cyc.</td><td>Car</td><td>Ped.</td><td>Cyc.</td><td>Car</td><td>Ped.</td><td>Cyc.</td></tr><tr><td>PVR.</td><td>77.3</td><td>47.8</td><td>62.9</td><td>80.4</td><td>47.1</td><td>63.5</td><td>83.0</td><td>57.9</td><td>73.1</td></tr><tr><td>Ours</td><td>80.7</td><td>54.4</td><td>67.3</td><td>82.0</td><td>54.6</td><td>69.5</td><td>84.8</td><td>60.2</td><td>74.9</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2"></td><td colspan="3">Car</td><td colspan="3">Pedestrian</td><td colspan="3">Cyclist</td></tr><tr><td>Easy</td><td>Mod.</td><td>Hard</td><td>Easy</td><td>Mod.</td><td>Hard</td><td>Easy</td><td>Mod.</td><td>Hard</td></tr><tr><td>PVR.</td><td>89.6</td><td>77.3</td><td>74.1</td><td>54.9</td><td>47.8</td><td>42.3</td><td>80.4</td><td>62.9</td><td>58.7</td></tr><tr><td>naive psd.-lb.</td><td>91.1</td><td>78.8</td><td>76.1</td><td>58.9</td><td>51.3</td><td>45.4</td><td>82.6</td><td>65.5</td><td>60.8</td></tr><tr><td>cls. thres. only</td><td>90.8</td><td>79.7</td><td>76.8</td><td>63.2</td><td>55.0</td><td>49.7</td><td>84.9</td><td>65.0</td><td>61.2</td></tr><tr><td>Ours</td><td>91.6</td><td>80.7</td><td>78.1</td><td>63.3</td><td>54.4</td><td>49.5</td><td>86.5</td><td>67.3</td><td>62.8</td></tr></table>
+
+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.
+
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+# 3D-MAN: 3D Multi-frame Attention Network for Object Detection
+
+Zetong Yang $^{1*}$  Yin Zhou $^{2}$  Zhifeng Chen $^{3}$  Jiquan Ngiam $^{3}$ $^{1}$ The Chinese University of Hong Kong  $^{2}$ Waymo LLC  $^{3}$ Google Research, Brain Team  
+tomztyang@gmail.com yinzhou@waymo.com {zhifengc, jngiam}@google.com
+
+# Abstract
+
+3D object detection is an important module in autonomous driving and robotics. 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.
+
+<table><tr><td>IoU threshold</td><td>0.3</td><td>0.5</td><td>0.7</td></tr><tr><td>AP (%)</td><td>94.72</td><td>88.97</td><td>63.27</td></tr></table>
+
+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
+
+<table><tr><td>Model</td><td>Stationary (%)</td><td>Slow (%)</td><td>Medium (%)</td><td>Fast (%)</td></tr><tr><td>1-frame</td><td>60.01</td><td>66.64</td><td>65.02</td><td>71.90</td></tr><tr><td>4-frames</td><td>62.4</td><td>67.39</td><td>66.68</td><td>77.99</td></tr><tr><td>8-frames</td><td>63.7</td><td>67.98</td><td>66.29</td><td>72.30</td></tr></table>
+
+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-
+
+<table><tr><td rowspan="2">Difficulty</td><td rowspan="2">Method</td><td colspan="4">3D AP (IoU=0.7)</td><td colspan="4">3D APH (IoU=0.7)</td></tr><tr><td>Overall</td><td>0-30m</td><td>30-50m</td><td>50m-Inf</td><td>Overall</td><td>0-30m</td><td>30-50m</td><td>50m-Inf</td></tr><tr><td rowspan="10">LEVEL_1</td><td>StarNet [15]</td><td>55.11</td><td>80.48</td><td>48.61</td><td>27.74</td><td>54.64</td><td>79.92</td><td>48.10</td><td>27.29</td></tr><tr><td>PointPillars [12]</td><td>63.27</td><td>84.90</td><td>59.18</td><td>35.79</td><td>62.72</td><td>84.35</td><td>58.57</td><td>35.16</td></tr><tr><td>MVF [36]</td><td>62.93</td><td>86.30</td><td>60.02</td><td>36.02</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>AFDet [7]</td><td>63.69</td><td>87.38</td><td>62.19</td><td>29.27</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>RCD [1]</td><td>68.95</td><td>87.22</td><td>66.53</td><td>44.53</td><td>68.52</td><td>86.82</td><td>66.07</td><td>43.97</td></tr><tr><td>PV-RCNN [18]</td><td>70.30</td><td>91.92</td><td>69.21</td><td>42.17</td><td>69.49</td><td>91.34</td><td>68.53</td><td>41.31</td></tr><tr><td>3D-MAN (Ours)</td><td>69.03</td><td>87.99</td><td>66.55</td><td>43.15</td><td>68.52</td><td>87.57</td><td>65.92</td><td>42.37</td></tr><tr><td>PointPillars* [12]</td><td>65.41</td><td>85.58</td><td>61.51</td><td>39.51</td><td>64.88</td><td>85.02</td><td>60.95</td><td>38.91</td></tr><tr><td>ConvLSTM* [10]</td><td>63.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>3D-MAN* (Ours)</td><td>74.53</td><td>92.19</td><td>72.77</td><td>51.66</td><td>74.03</td><td>91.76</td><td>72.15</td><td>51.02</td></tr><tr><td rowspan="6">LEVEL_2</td><td>StarNet [15]</td><td>48.69</td><td>79.67</td><td>43.57</td><td>20.53</td><td>48.26</td><td>79.11</td><td>43.11</td><td>20.19</td></tr><tr><td>PointPillars [12]</td><td>55.18</td><td>83.61</td><td>53.01</td><td>26.73</td><td>54.69</td><td>83.08</td><td>52.46</td><td>26.24</td></tr><tr><td>PV-RCNN [18]</td><td>65.36</td><td>91.58</td><td>65.13</td><td>36.46</td><td>64.79</td><td>91.00</td><td>64.49</td><td>35.70</td></tr><tr><td>3D-MAN (Ours)</td><td>60.16</td><td>87.10</td><td>59.27</td><td>32.69</td><td>59.71</td><td>86.68</td><td>58.71</td><td>32.08</td></tr><tr><td>PointPillars* [12]</td><td>57.28</td><td>84.31</td><td>55.41</td><td>29.71</td><td>56.81</td><td>83.79</td><td>54.90</td><td>29.24</td></tr><tr><td>3D-MAN* (Ours)</td><td>67.61</td><td>92.00</td><td>67.20</td><td>41.38</td><td>67.14</td><td>91.57</td><td>66.62</td><td>40.84</td></tr></table>
+
+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].  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">LEVEL_1</td><td colspan="2">LEVEL_2</td></tr><tr><td>3D AP</td><td>3D APH</td><td>3D AP</td><td>3D APH</td></tr><tr><td>StarNet [15]</td><td>68.32</td><td>60.89</td><td>59.32</td><td>52.76</td></tr><tr><td>PointPillars [12]</td><td>68.88</td><td>56.57</td><td>59.98</td><td>49.14</td></tr><tr><td>MVF [36]</td><td>65.33</td><td>-</td><td>-</td><td>-</td></tr><tr><td>3D-MAN (Ours)</td><td>71.71</td><td>67.74</td><td>62.58</td><td>59.04</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Vehicle</td><td colspan="2">Pedestrians</td></tr><tr><td>3D AP</td><td>3D APH</td><td>3D AP</td><td>3D APH</td></tr><tr><td>SECOND [28]</td><td>50.11</td><td>49.63</td><td>-</td><td>-</td></tr><tr><td>StarNet [15]</td><td>63.51</td><td>63.03</td><td>67.78</td><td>60.10</td></tr><tr><td>PointPillars [12]</td><td>68.62</td><td>68.08</td><td>67.96</td><td>55.53</td></tr><tr><td>SA-SSD [8]</td><td>70.24</td><td>69.54</td><td>57.14</td><td>48.82</td></tr><tr><td>RCD [1]</td><td>71.97</td><td>71.59</td><td>-</td><td>-</td></tr><tr><td>3D-MAN (Ours)</td><td>78.71</td><td>78.28</td><td>69.97</td><td>65.98</td></tr></table>
+
+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.  
+
+<table><tr><td></td><td>Mask</td><td>Centeredness</td><td>Hungarian Matching</td></tr><tr><td>Ped. (%)</td><td>64.7</td><td>67.1</td><td>70.2</td></tr><tr><td>Veh. (%)</td><td>44.5</td><td>63.7</td><td>64.8</td></tr></table>
+
+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
+
+<table><tr><td>Method</td><td>Baseline</td><td>Concat</td><td>Relation</td><td>MVAA</td></tr><tr><td>AP (%)</td><td>68.2</td><td>70.5</td><td>70.1</td><td>72.5</td></tr></table>
+
+Table 7. Mini-validation AP comparison on class Vehicle among different multi-frame fusion approaches.  
+
+<table><tr><td>Supervision Method</td><td>None</td><td>Correspondence Loss</td><td>CV Loss</td></tr><tr><td>AP (%)</td><td>70.7</td><td>71.4</td><td>72.5</td></tr></table>
+
+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.  
+
+<table><tr><td>Frames</td><td>1</td><td>4</td><td>7</td><td>10</td><td>13</td><td>16</td></tr><tr><td>AP (%)</td><td>68.2</td><td>72.5</td><td>73.4</td><td>73.5</td><td>73.8</td><td>74.3</td></tr></table>
+
+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.  
+
+<table><tr><td>Model</td><td>Stationary (%)</td><td>Slow (%)</td><td>Medium (%)</td><td>Fast (%)</td></tr><tr><td>4-frames</td><td>69.5</td><td>68.6</td><td>67.1</td><td>78.3</td></tr><tr><td>16-frames</td><td>73.2</td><td>70.4</td><td>68.9</td><td>79.2</td></tr></table>
+
+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.
+
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