Human pose estimation (HPE) is a fundamental task in computer vision, which can be adopted to many applications such as action recognition, human behavior analysis, virtual reality and so on. Estimating 3D pose of human body joints from2D joint locations is an under-constrained problem. However, since human joints are connected by rigid bodies, the search space of 3D pose is limited to the range of joints. Therefore, it is able to learn 3D structures from 2D positions, and numerous studies on 2D-to-3D mapping of human body have been conducted. Recently, Martinez et al.(2017)Martinez, Hossain, Romero, and Little proved that a simple fully connected neural network that accepts raw 2D positions as an input gives surprisingly accurate results. Inspired by this result, we designed a network that accepts 2D positions of joints as inputs and generates 3D positions based on them.
Human body can be divided into arms, legs, a head, and a torso, each of which has distinctive behaviors and movements. We designed the network so that it learns the relations among different body parts. The relational modules for the neural networks proposed in [Santoro et al.(2017)Santoro, Raposo, Barrett, Malinowski, Pascanu,
Battaglia, and Lillicrap] provided a way to learn relations between the components within a neural network architecture. We adopt this relational modules for 3D HPE with a little modification. Specifically, the body joints are divided into several groups, and the relations between them are learned via relational networks. The features from all pairs of groups are averaged to generate the feature vectors which are
the feature vectors which areused for 3D pose regression. We found this simple structure outperforms the baseline which uses a fully connected network. Moreover, we propose a method that can impose robustness to the missing points during the training. The proposed method, named as relational dropout, randomly drops one of the pair features when they are averaged, which simulates the case that certain groups of joints are missing during the training. To capture the relations among joints within a group, we also designed a hierarchical relational network, which further allows robustness to wrong 2D joint inputs. Lastly, we discovered that the proposed structure of the network modified from [Martinez et al.(2017)Martinez, Hossain, Romero, and Little] and the finetuning schemes improve the performance of HPE. The proposed method achieved state-of-the-art performance in 3D HPE on Human 3.6M dataset [Ionescu et al.(2014)Ionescu, Papava, Olaru, and Sminchisescu], and the network can robustly estimate 3D poses even when multiple joints are missing using the proposed relational dropout scheme.
2 Related Work
Early stage studies on 3D HPE from RGB images used hand-crafted features such as local shape context [Agarwal and Triggs(2006)], histogram of gradients [Rogez et al.(2008)Rogez, Rihan, Ramalingam, Orrite, and Torr, Onishi et al.(2008)Onishi, Takiguchi, and Ariki], or segmentation results [Ionescu et al.(2011)Ionescu, Li, and Sminchisescu]. From those features, 3D poses were retrieved via regression using relevance vector machine [Agarwal and Triggs(2006)], randomized trees [Rogez et al.(2008)Rogez, Rihan, Ramalingam, Orrite, and Torr], structured SVMs [Ionescu et al.(2011)Ionescu, Li, and Sminchisescu], KD-trees [Yasin et al.(2016)Yasin, Iqbal, Kruger, Weber, and Gall]
or Bayesian non-parametric models[Sanzari et al.(2016)Sanzari, Ntouskos, and Pirri].
Recent advancements in neural networks boosted the performance of 3D HPE. li20143d
firstly applied convolutional neural networks (CNNs) to 3D HPE. Since then, various models that capture structured representation of human bodies have been combined with CNNs using, for instance, denoising autoencoders[Tekin et al.(2016)Tekin, Katircioglu, Salzmann, Lepetit, and Fua], maximum-margin cost function [Li et al.(2015)Li, Zhang, and Chan], and pose priors from 3D data [Bogo et al.(2016)Bogo, Kanazawa, Lassner, Gehler, Romero, and Black, Lassner et al.(2017)Lassner, Romero, Kiefel, Bogo, Black, and Gehler, Rogez et al.(2017)Rogez, Weinzaepfel, and Schmid].
It has been proven that 2D pose information acts a crucial role for 3D pose estimation. park_eccvw_2016 directly propagated 2D pose estimation results to the 3D pose estimation part in a single CNN. pavlakos2017coarse proposed a volumetric representation that gradually increases the resolution of the depth from heatmaps of 2D pose. mehta2017vnect similarly regressed the position of each coordinate using heatmaps. There are a couple of works that directly regress 3D pose from an image using constraints on human joints [Sun et al.(2017)Sun, Shang, Liang, and Wei] or combining weaklyZhou et al.(2017)Zhou, Huang, Sun, Xue, and Wei]. tome2017lifting lifted 2D pose heatmaps to 3D pose via probabilistic pose models. Tekin_2017_ICCV combined features from both RGB images and 2D pose heatmaps which were used for 3D pose estimation.
While 3D pose estimation from images have shown impressive performance, there is another approach that infers a 3D pose directly from the result of 2D pose estimation. It usually has a two-stage procedure: 1) 2D pose estimation using CNNs and 2) 3D pose inference via neural networks using the estimated 2D pose. Chen_2017_CVPR found that a non-parametric nearest neighbor model that estimates a 3D pose from a 2D pose showed comparable performance when the precise 2D pose information is provided. moreno20173d proposed a neural network that outputs 3D Euclidean distance matrices from 2D inputs. Martinez_2017_ICCV proposed a simple neural network that directly regresses a 3D pose from raw 2D joint positions. The network consists of two residual modules [He et al.(2016a)He, Zhang, Ren, and Sun]
with batch normalization[Ioffe and Szegedy(2015)] and dropout [Srivastava et al.(2014)Srivastava, Hinton, Krizhevsky, Sutskever, and Salakhutdinov]. The method showed state-of-the-art performance despite its simple structure. The performance has been further improved by recent works. fang2017learning proposed a pose grammar network that incorporates a set of knowledge learned from human body, which was designed as a bidirectional recurrent neural network. yang20183d used adversarial learning to implicitly learn geometric configuration of human body. cha2018pose developed a consensus algorithm that generates a 3D pose from multiple partial hypotheses which are based on a non-rigid structure from motion algorithm [Lee et al.(2016)Lee, Cho, and Oh]. The method is similar to our method in that they divided the body joints into multiple groups. However, our proposed method integrates the features of all groups within the network rather than generating a 3D pose from each group as in cha2018pose.
There are a few approaches that exploit temporal information using various methods such as overcomplete dictionaries [Zhou et al.(2016)Zhou, Zhu, Leonardos, Derpanis, and Daniilidis, Zhou et al.(2018)Zhou, Zhu, Pavlakos, Leonardos, Derpanis, and Daniilidis], 3D CNNs [Grinciunaite et al.(2016)Grinciunaite, Gudi, Tasli, and den Uyl], sequence-to-sequence networks [Hossain and Little(2017)], and multiple-view settings [Pavlakos et al.(2017a)Pavlakos, Zhou, Derpanis, and Daniilidis]. In this paper, we focus on the case that both training and testing are conducted on a single image.
. (c) The structure of the RN for 3D HPE. Features extracted from all pairs of groups are averaged to produce features for pose estimation. Each Resblock in the figure has the same structure shown in (b).
3.1 Relational Networks for 3D Human Pose Estimation
Relation networks (RN) proposed in [Santoro et al.(2017)Santoro, Raposo, Barrett, Malinowski, Pascanu, Battaglia, and Lillicrap] consists of two parts, one that does relational reasoning and the other that performs a task-specific inference. The output of the RN is formulated as follows:
where and are functions that are represented as corresponding neural networks, and is the set of objects. Pairs of different objects , are fed to the network , and the relation of all pairs are summed together to generate features that capture relational information.
We adopt the concept and the structure of the RN to 3D human pose estimation. The network proposed in this paper takes -dimensional vectors as inputs and outputs -dimensional vectors where and are the number of 2D and 3D joints respectively. For 2D inputs, we used coordinates of detected joints in RGB images whereas relative positions of coordinates from the root joint are estimated for 3D pose estimation. In the original RN [Santoro et al.(2017)Santoro, Raposo, Barrett, Malinowski, Pascanu, Battaglia, and Lillicrap], a neural network module that generates a pairwise relation, , shares weights across all pairs of objects. This weight sharing makes the network learn order-invariant relations. However, this scheme is not applied to our 2D-to-3D regression of human pose as the following reasons. While original RN tries to capture the holistic relations that does not depend on the position of the objects or order of pairs, the groups on human body represent different parts where order of pairs matters. For instance, if the 2D positions of the left arm and the right arm are switched, the 3D pose should also be changed accordingly. However, the relational features generated will be the same for both cases if the order of pair is not considered. For these reasons, we did not use weight sharing for relational models. The 3D HPE algorithm proposed in this paper is formulated as
where is the number of pairs, , represents 3D and 2D shape of human body joints respectively, and corresponds to the subsets of 2D input joints belonging to group . We divide the input 2D joints to non-overlapping five groups as illustrated in Fig. 1(a). Total 16 joints are given as an input to the proposed network. Each joint group contains 3 or 4 joints, which we designed so that each group has a small range of variations. Each group represents a different part of a human body in this configuration. In other words, the groups contain joints from left/right arms, left/right legs, or the rest (a head and a torso). Thus, the relational network captures how different body parts are related with each other. All pairs of such that are fed to the network and generates features of the same dimension. The mean of the relational features is passed to the next network module that is denoted as in Eq. 2. We empirically found that using the mean of the relational features instead of the sum stabilizes training.
We used ResNet structures proposed in [He et al.(2016b)He, Zhang, Ren, and Sun] for neural network modules that are used for relation extraction and 3D pose estimation. The structure of a single module is illustrated in Fig. 1(b). A fully connected layer is firstly applied to increase the input dimension to that of a feature vector. Then, a residual network consisting of two sets of batch normalization [Ioffe and Szegedy(2015)], dropout [Srivastava et al.(2014)Srivastava, Hinton, Krizhevsky, Sutskever, and Salakhutdinov], aReLU activation function, and a fully connected layer is applied. The overall structure of the proposed network for 3D HPE is illustrated in Fig. 1(c).
It can be advantageous if we are able to capture the relations of pairs of individual joints. However, in this case, there are total pairs which makes the network quite large. Instead, we designed a hierarchical relational network in which relations between two joints in a group are extracted within the group. The feature of each group is generated as
where is the number of pairs in group , and correspond to 2D joints that belong to group . The generated features are used as an input to the next relational network which is formulated as Eq. 2. Empirically, we observe that the hierarchical representation does not outperform a single level relational network, but the structure is advantageous if the relational dropout is applied as described in Section 3.2.
3.2 Relational Dropout
In this section, we propose a regularization method, which we call ‘relational dropout’, that can be applied to relational networks. Similar to dropout [Srivastava et al.(2014)Srivastava, Hinton, Krizhevsky, Sutskever, and Salakhutdinov], we randomly drop the relational feature vectors that contain information on a certain group. In this paper, we restrict the number of dropping element to be at most 1. Thus, when the number of groups is , among the pairs, relational feature vectors are dropped and replaced with zero vectors when relational dropout is applied. After the mean of the feature vectors are calculated, it is divided by the portion of non-dropping vectors to maintain the scale of the feature vector as in the general dropout method. Concretely, when group is selected to be dropped, the formulation becomes
Dropping features of a certain group simulates the case that the 2D points belonging to the dropping group are missing. Hence, the network learns to estimate the 3D pose not only when all the 2D joints are visible but also when some of them are invisible
. The relational dropout is applied with the probability ofduring the training. Since at most one group is dropped, the combinational variability of missing joints is limited. To alleviate the problem, we applied the proposed relational dropout to hierarchical relational networks. In this case, we are able to simulate the case when a certain joint in a group is missing and to simulate various combinations of missing joints. At test time, we simply apply relational dropout to the groups that contain missing points.
3.3 Implementation Details
For the networks used in the experiments, the pose estimator in the relational networks has fully connected layers of 2,048 dimensions with a dropout probability of 0.5. For the modules that generates relational feature vector of the pairs and , 1,024 dimensional fully connected layers with a dropout probability of 0.25 are used. Lastly, for the hierarchical relational networks, the modules that generate relations from the pairs of 2D joints consist of 256 dimensional fully connected layers with a dropout probability of 0.1. When the relational dropout is applied during the training, is set to 0.2 for the case that one of the groups of joints is dropped, and it is set to 0.1 when the relational dropout is applied to the hierarchical relational units to drop a single joint.
We used stacked hourglass network [Newell et al.(2016)Newell, Yang, and Deng] to infer 2D joint positions from training and test images. We finetuned the network pre-trained on MPII human pose dataset [Andriluka et al.(2014)Andriluka, Pishchulin, Gehler, and Schiele] using the frames of Human3.6M dataset. Mean subtraction is the only pre-processing applied to both 2D and 3D joint positions.
The proposed network is trained using ADAM optimizer [Kingma and Ba(2014)] with a starting learning rate of 0.001. The batch size is set to 128, and the learning rate is halved for every 20,000 iterations. The network is trained for 100,000 iterations.
As a final note, we found that finetuning the trained model to each sequence of Human 3.6M dataset improves the estimation performance. During the finetuning, batch normalization statistics are fixed and the dropout probability is set to 0.5 in all modules.
4 Experimental Results
We used Human 3.6M dataset [Ionescu et al.(2014)Ionescu, Papava, Olaru, and Sminchisescu] to validate the proposed algorithm. The dataset is the largest dataset for 3D HPE, and it consists of 15 action sequences which were performed by 7 different persons. Following the previous works, we used 5 subjects (S1, S5, S6, S7, S8) for training and 2 subjects (S9, S11) for testing. Mean per-joint position error (MPJPE) is used as anevaluation metric. We reported MPJPE for two types of alignments: aligning the root joints of the estimated pose and the ground truth pose denoted as Protocol 1, and aligning via Procrustes analysis including scaling, rotation, and translation denoted as Protocol 2. The proposed method is compared to the recently proposed methods that estimates 3D pose from a single image [Pavlakos et al.(2017b)Pavlakos, Zhou, Derpanis, and Daniilidis, Martinez et al.(2017)Martinez, Hossain, Romero, and Little, Fang et al.(2017)Fang, Xu, Wang, Liu, and Zhu, Cha et al.(2018)Cha, Lee, Cho, and Oh, Yang et al.(2018)Yang, Ouyang, Wang, Ren, Li, and Wang, Moreno-Noguer(2017), Zhou et al.(2017)Zhou, Huang, Sun, Xue, and Wei, Tekin et al.(2017)Tekin, Marquez-Neila, Salzmann, and Fua].
To compare the performance of the proposed algorithm to the network that does not use relational networks, we designed a baseline network containing only fully connected layers. The baseline network consists of two consecutive ResBlocks of 2,048 dimensions. Dropout with probability of 0.5 is applied.
The MPJPE of various algorithms using Protocol 1 is provided in Table 1. It can be seen that the baseline network already outperforms most of the existing methods, which validates the superiority of the proposed residual modules. The relational networks are trained without applying relational dropouts. The proposed relational network (RN) gains 0.7 mm improvements over the baseline on average, and it is further improved when the network is finetuned on each sequence (RN-FT), which achieves state-of-the-art performance. Therefore, it is verified that capturing relations between different groups of joints improves the pose estimation performance despite its simpler structure and training procedures than the compared methods. Hierarchical relational networks (RN-hier) does not outperform RN although it has bigger number of parameters than RN. We conjecture the reason to be that it is hard to capture the useful relations in a small number of joints which leads to output poorer features than the ones using the raw 2D positions.
The MPJPE using the alignment Protocol 2 is provided in Table 2. When shape aligning via Procrustes analysis is applied, our method RN-FT showed superior performance to the existing methods except [Yang et al.(2018)Yang, Ouyang, Wang, Ren, Li, and Wang].
Next, we discuss the effectiveness of the relational dropout for the case of missing joints. MPJPE for all sequences with various types of missing joints are measured and provided in Table 3. We simulated 3 types of missing joints following [Moreno-Noguer(2017)], which are 2 random joints (Rand 2), left arm (L Arm), and right leg (R Leg). We consider 3 missing joints for the latter 2 cases including shoulder or hip joints. Note that [Moreno-Noguer(2017)] used different training schemes for experiments on missing joints where six subjects were used for training. For the baseline method that can be applied to the fully connected network, we assign zero to the value of input 2D joints with the probability of 0.1, which is denoted as FC-drop. It imposes robustness to the missing joints compared to the FC baseline in which random drop is not applied. When relational dropout is applied to the relational network (RN-drop), the model outperforms FC-drop in all cases. The model successfully estimates 3D pose when one of the groups in the relational network is missing. Therefore, it shows smaller MPJPE when the left arm or the right leg is not visible. However, when two joints belonging to different groups are missing, the two groups are dropped at the same time, which is not simulated during the training. Thus, RN-drop shows poor performance for the case that random two joints are missing. This problem can be handled when relational dropout is applied to the hierarchical relational network. When one joint is missing in a group, relational dropout is applied to hierarchical relational unit within the group. In the case that two or more joints are missing in a group, relational dropout is applied to the group. This model (RN-hier-drop) showed impressive performance in all types of missing joints. Another advantage of the relational dropout is that it does not degrade the performance of the case of all-visible joints. It can be inferred that the robustness on missing joints increases as various combinations of missing joints are simulated during the training.
Qualitative results on Human 3.6M dataset are provided in Figure 2. Each row simulates different cases of missing joints, none, right leg, left arm, and random 2 joints. The results of RN, FC-drop, RN-drop, RN-hier-drop is displayed with ground truth poses. When all joints are visible, all models generate similar poses that are close to the ground truth. On the other hand, RN generates inaccurate poses when 2D inputs contain missing points. RN-drop provides more accurate results than FC-drop, but the model fails when joints of two different groups are missing. It can be seen that RN-hier-drop outputs 3D poses that are similar to the ground truth poses in all cases. More results can be found on the supplementary materials.
Lastly, we displayed qualitative results on real world images. We used MPII human pose dataset [Andriluka et al.(2014)Andriluka, Pishchulin, Gehler, and Schiele] which is designed for 2D human pose estimation. 3D pose estimation results for the relational network (RN) and the hierarchical relational network with relational dropouts (RN-hier-drop) are provided in Figure 3. We first generate 2D pose results for the images and the joints whose maximum heatmap value is less than 0.4 are treated as missing joints for RN-hier-drop. As it can be seen in the second and third rows of Figure 2, RN-hier-drop generates more plausible poses than RN when some 2D joints are wrongly detected. The last row shows failure cases which contain noisy 2D inputs or an unfamiliar 3D pose that is not provided during the training.
In this paper, we propose a novel method for 3D human pose estimation. The relational network designed for 3D pose estimation showed state-of-the-art performance despite its simple structure. We also proposed the relational dropout which is fitted for the relational network. The relational dropout successfully impose the robustness to the missing points while maintaining the performance of the original network. The proposed network is flexible in that it allows lots of variations in terms of its structure, group organization, and the policy of the relational dropout. The relational dropout can also be applied to other tasks that use relational networks.
This work was supported by Next-Generation Information Computing Development Program through the National Research Foundation of Korea (2017M3C4A7077582).
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