I Introduction
Hand pose estimation is a fundamental and challenging problem in computer vision, and it has a wide range of vision applications such as humancomputer interface (HCI) [1, 2] and augmentation reality (AR) [3]. So far, there have been a number of methods [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]
proposed on this topic, and significant progress has been made with the emergence of deep learning and lowcost depth sensors. The performance of previous RGB image based methods is limited to the clustered background, while the depth sensor is able to generate depth images in low illumination conditions, and it is simple to do hand detection and hand segmentation. Nevertheless, it is still difficult to accurately estimate 3D hand pose in the practical scenarios due to data noises, high freedom of degree for hand motion, and selfocclusions between fingers.
The typical pipeline for estimating hand joints from depth images could be separated into two stages: 1) extracting robust features from depth images; 2) regressing hand pose based on the extracted features. Current approaches concentrate on improving the different algorithms in each of the stages. Specifically, in [4]
, the features extracted by multiview CNNs are utilized for regression, then the same author in
[6] replaces the 2D CNN by 3D CNN to fully exploit 3D spatial information. Besides, hierarchical hand joint regression [10] and iterative refinement [18, 19] for hand pose are deployed in several approaches.In this paper, we propose a novel method named as CADSTN (ContextAware Deep SpatioTemporal Network) to jointly model the spatiotemporal context for 3D hand pose estimation. We adopt sliced 3D volumetric representation, which keeps the structure of the hand to explicitly model the depthaware spatial context. Moreover, motion coherence between the successive frames is exploited to enforce the smoothness of the predictions of the images in sequence. The model is able to learn the representations of the spatial information and the temporal structure in the image sequences. Moreover, the model is capable of combining the spatiotemporal properties for final prediction. As shown in Figure 1, the architecture is composed of three parts: first, we sufficiently capture the spatial information via Spatial Network; second, the dependency between frames is modeled via a set of LSTM nodes in Temporal Network; third, to exploit spatial and temporal context simultaneously, the predictions from the above two networks are utilized for the final prediction via Fusion Network. The main contributions of our work are summarized as the following two folds:

First, we propose a unified spatiotemporal context modeling approach with group input and group output, which benefits from the interimage correspondence structures between consecutive frames. The proposed approach extracts the feature representation for both unary image and successive frames, which generally leads to the performance improvement of hand pose estimation.

Second, we present an endtoend neural network model to jointly model the temporal dependency relationships among the multiple images while preserving spatial information for an individual image in a totally datadriven manner. Moreover, an adaptive fusion method is enabled to make the network dynamically adapt to the various situations.
We evaluate our proposed method on two public datasets: NYU [20] and ICVL [8]. With detailed analysis of the effects of different components of our method, and the experimental results demonstrate that most results of our method are best comparing with stateoftheart methods. Our method runs in 60fps on a single GPU that satisfies the practical requirements^{1}^{1}1A demo video is available online at https://goo.gl/tbnWse.
The rest of the paper is organized as follows. In Section II, we review some works for 3D hand pose estimation. In Section III, we introduce our proposed method. In Section IV, we present the experimental results of the comparison with stateoftheart methods and ablation study. Finally, the paper is concluded in Section V.
Ii Related Work
Iia Feature Representation Learning
Most stateoftheart performance hand pose estimation methods based on deep learning rely on visual representation learned from data. Given a depth image, different methods try to learn the sufficient context and get the robust feature. For example, in [18], the original segmented hand image is downscaled by several factors, and each scaled image is followed with a neural network to extract multiscale feature. Although increasing the number of scale factor may improve the performance, the computational complexity will also be increased. In [21], Guo et al. propose a regional feature ensemble neural network and extend it into 3D human pose estimation in [22], Chen et al. [23] propose a cascaded framework denoted as PoseREN to improve the performance of region ensemble network. In [24], various combinations of voxel and pixel representations are experimented, and finally use a voxeltovoxel prediction framework to estimate pervoxel likelihood.
Furthermore, recovering the fully 3D information catches researcher’s attention. MultiView CNN [4] is introduced for hand pose estimation, which exploits depth cues to recover 3D information of hand joints. In [5], 3D CNN and truncated signed distance function (TSDF) [25] are adopted to learn both the 3D feature and the 3D global context. Ge et al. [6] take advantage of the above two methods, and propose a multiview 3D CNN to regress the hand joint locations. In addition, data augmentation is usually considered for extracting robust feature. A synthesizer CNN is used to generate synthesized images to predict an estimate of the 3D pose by using a feedback loop in [19]. Wan et al. [26]
use two generative models, variational autoencoder (VAE)
[27] and generative adversarial network (GAN) [28], to learn the manifold of the hand pose, with an alignment operation, pose space is projected into a corresponding depth map space via a shared latent space. Our method is different from the aforementioned architectures in the following ways: 1) we deploy the sliced 3D volumetric representation to recover 3D spatial information. 2) we extract the temporal property from an image sequence to enhance the consistency between images.IiB SpatioTemporal Modeling
Towards the tasks based on the video, spatiotemporal modeling is widely used (e.g. hand tracking, human pose tracking and action recognition).
In the matters of hand tracking problems, Franziska et al. [29] propose a kinematic pose tracking energy to estimate the joint angles and to overcome the challenge occlusion cases. In [30], Oberweger et al. propose a semiautomated method to annotate the hand pose in an image sequence by exploiting spatial, temporal and appearance constraints.
In the context of human pose tracking, Fragkiadaki et al. [31] propose an EncoderRecurrentDecoder (ERD) module to predict heat maps of frames in an image sequence. More recently, Song et al. [32] introduce a spatiotemporal inference layer to perform message passing on general loopy spatiotemporal graphs.
In terms of action recognition problem, Molchanov et al. [33] employ RNN and deep 3D CNN on a whole video sequence for spatiotemporal feature extraction. Our approach is closely related to [34] who propose a twostream architecture to encode the spatial and temporal information separately. Our approach is based on the depth image, which leads us to learn spatiotemporal feature via LSTM instead of optical flow.
IiC Regression Strategies
Regression strategy has the close relationship with the performance of methods, and it can be roughly classified into three camps: 1) 2D heatmap regression and 3D recovery; 2) directly 3D hand joint coordinates regression; 3) cascaded or hierarchical regression. In
[20, 4], 2D heatmaps, which represent the 2D location for hand joints, are regressed based on the extracted feature, then the 3D positions are determined via recovery. Directly 3D hand joint coordinates regression predicts the hand locations in a single forwardpass, which exhibits superior performances comparing to the previous 2D heatmap regression [35, 6, 7, 5, 26, 21].Cascaded and hierarchical regression has shown good performance in hand pose estimation. Oberweger et al. [18] use the iterative refinement stage to increase the accuracy, and in [19], they use the generated synthesized images to correct the initial estimation by using a feedback loop. Tang et al. [36, 37] introduce hierarchical regression strategies to predict treelike topology of hand. Similarly, the strategy to first estimate hand palm and sequentially estimate the remaining joints is adopted in [8, 9]. Recently, Ye et al. [10]
combine the attention model with both cascaded and hierarchical estimation, and propose an endtoend learning framework.
Iii Hand Pose Estimation
Figure 1 illustrates the main building blocks of our method. Given an image sequence, two predictions are estimated by Temporal Network and Spatial Network, then the predictions are fused by the output from Fusion Network.
Iiia Overview
We denote a single depth image as , and the corresponding
hand joints are represented as a vector
, where is the 3D position of th joint in the depth image .Currently, most discriminative approaches concentrate on modeling a mapping function from the input image to hand pose. We define a cost function as follows:
(1) 
where calculates the norm, is the number of images. Then the expected mapping function is expressed as , where is the hypothesis space.
To obtain a robust mapping function, most approaches concentrate on the hand structure to capture features for estimation. In this paper, we capture the spatial and temporal information simultaneously to learn features for prediction. As shown in Figure 1, the architecture is separated into three parts. The first part is denoted as Spatial Network, which is applied on a single frame to learn a mapping function . Inspired by the texture based volume rendering used in the medical image [38], we slice the depth image into several layers, which makes the different joints scatter in the different layer. We feed the depth image and corresponding sliced 3D volumetric representation into the network, depth and spatial information are extracted hierarchically for hand pose estimation.
The second part is denoted as Temporal Network. This network concentrates on the time coherence property in image sequences, and learns the mapping from an image sequence to a set of hand poses. By using LSTM layer, this network takes the features from previous frames into account when estimating the pose in the current frame.
The third part is named as Fusion Network. For the sake of predicting pose via the combination of information from the individual and consecutive frames, we fuse the aforementioned two networks as an integration by adaptive fusion method, the final prediction is calculated as the summation of the different networks’ outputs. By means of employing this approach, spatial information from the individual frame and temporal property between frames are thought to have in mind as a unified scheme.
IiiB Proposed Method
In this section, we present details of our method for hand pose estimation.
Spatial Network
In an individual frame, the spatial information is critical for hand pose estimation.
By adopting 3D sliced volumetric representation and DeeplyFusion network [39], we extract features
to learn a robust mapping function.
In the original depth image , the value of the pixel encodes the depth information. We first crop the hand region out of the image, this step is same as [18]. As shown in Figure 2, the cropped depth image is resized to , and depth is represented as a function of coordinates. Previous methods represent the 3D hand in different ways. In [40], the depth image is recovered as a binary voxel grid for training. The hand surface and occluded space [41] are filled with , the free space is filled with . In [5, 6], TSDF and projective Directional TSDF (DTSDF) are adopted to encode more information in the 3D volumetric representation. However, the size of 3D volume used in these methods is commonly set as . Different from previous methods, we employ a solution that the hand surface is sliced into pieces. Then our sliced 3D volumetric representation is an voxel grid, where represents the number of sliced layers in axes. For an exact cropped depth image, the free space and occluded space are omitted, then we denote and as the depth of closest and farthest surface point, then we divide equally into pieces. So the binary sliced 3D volumetric representation is filled with if the depth value is in the range of , where . In Figure 2, from the top layer to the bottom layer, the fingertips and palm center scatter in the different layers.
Sliced 3D volumetric representation keeps the structure of the hand. To obtain the hand structure and depth information simultaneously, we input depth image and sliced 3D volumetric representation at the same time. As shown in Figure 3
, the left part extracts features from depth image, and the right part extracts features from sliced 3D volumetric representation. We denote the features from maxpooling layers as
and , then the features are hierarchically fused by DeeplyFusion Network [39] as follows:(2)  
where is elementwise mean for features, is the transformation for features learned by a fully connected layer, is the index for layer.
Owing to the adoption of several fully connected layers, the network tends to overfitting, so we use an auxiliary loss as the regularization as well as dropout. In Figure 3
, every fully connected layer is followed by a dropout layer, the nodes are dropout randomly with 30% probability. For the purpose of obtaining more representative capability for each input, the auxiliary paths are added in training stage. As shown in the green boxes, the layers in the auxiliary paths are same as the main network, the layers connected by the blue dotted line share parameters. And in the training stage, the total losses are consist of three losses, i.e. three regression losses in auxiliary paths and main network. When testing, the auxiliary paths are removed.
Temporal Network
As we know, the hand poses between successive frames are closely related (e.g. when grabbing, the joints on fingers are most likely to be closer). The temporal property in the between frames are also critical for estimating hand joints. So we extend the mapping function from single frame to a sequence of images. The sequential prediction problem could be reformulated as follows:
(3) 
where is the number of images in a sequence.
Currently, due to the feedback loop structure in the recurrent neural network (RNN), it possesses powerful "longterm dependencies" modeling capability, and is widely used in computer vision tasks. In general, RNN is difficult to train due to the vanishing gradient and error blowup problems
[42]. In this paper, we adapt LSTM [43, 44], a variant of RNN which is expressive and easy to train, to model the temporal context of successive frames. As shown in Figure 4, an image sequence is taken as input and the network gives out the estimated poses. Without loss of generality, we think about the th depth image, the image is fed into the convolution neural network and the feature
extracted from the first fully connected layer is denoted as follows:(4) 
Then we feed the features into LSTM layer, and get the hidden state as the new features.
(5)  
where
is sigmoid function,
is tanh function, is elementwise product, and matrices ( is in ) are parameters for the gates in LSTM layer. The features output from LSTM layer and the original features are concatenated, and then are fed into the last fully connected layer to regress the hand pose coordinates.Fusion Network
The aforementioned Temporal Network and Spatial Network estimate the joints by placing emphasis on
capturing spatial and temporal information, we name the predictions from these two networks as and respectively.
Due to the importance of spatial and temporal information, we jointly model the spatiotemporal properties,
which adaptively integrates different predictions for the final estimation. As shown in Figure 5,
Fusion Network
uses an activation function
after the last fully connected layer, then output and . Fusion Network fuses two predictors, and gives out the final prediction as follows:(6) 
where , and is a vector that all elements are one. The weights and are learned as the confidence of two predictions, and the final prediction is estimated as the weighted summation of each prediction.
Because Temporal Network considers the temporal information and Spatial Network extracts the spatial information, then the network infers the hand joint locations depend on spatial and temporal features.
Finally, we summarize our proposed method in Algorithm 1.
Iv Experiments
In this section, we evaluate our method on two public datasets for comparison with the stateoftheart methods. In addition, we do ablation experiments and analyse the performance of each component.
Iva Experiment Setting
IvA1 Datasets
We evaluate our method on NYU [20] and ICVL [36], details about the datasets are summarized in Table I, where Train is the number of train images, Test is the number of test images and the number in bracket is the number of sequences; Resolution is the resolution of images; Annotation is the number of annotated joints. NYU dataset is challenging because of its wider pose variation and noisy image as well as limited annotation accuracy. On ICVL dataset, the scale of image is small and the discrepancies between training and testing is large, these make the estimation difficult.
Dataset  Train  Test  Resolution  Annotation 

NYU  72k (1)  8k(2)  36  
ICVL  22k (10)  1.6k(2)  16 
IvA2 Evaluation Metrics
The evaluation follows the standard metrics proposed in [18], including accuracy, prejoint error distances and average error distance. As mentioned above, we denote as the predicted th joint location in the th frame, is the corresponding ground truth. The total number of frames is denoted as , and is the number of hand joints.
Perjoint error distance calculates the average Euclidean distance between the predicted joint location and the ground truth in 3D space.
(7) 
Average error distance computes the mean distance for all joints.
(8) 
Accuracy is the fraction of frames that all predicted joints from the ground truth in a frame below the given distance threshold .
(9) 
where is the indicator function.
IvA3 Implementation Details
We implement the training and testing with Caffe
[45] framework. The preprocess step follows [18], then the cropped image is resized to with the depth value normalized to [1, 1], and for sliced 3D volumetric representation, is set to 8 in the experiments. Moreover, we augment the dataset from the available dataset.Data augmentation On NYU dataset, we do augmentation by random rotation and flipping. On one side, we randomly rotate the images by an angle selected from and . On the other side, we flip the image vertically or horizontally. For each image in the dataset, we just generate one image by the abovementioned augmentation method. So the size of the dataset is twice as many as the original. On ICVL dataset, inplane rotation has been applied and there are 330k training samples in total, so the augmentation is not used on ICVL.
Training configuration Theoretically, training the three networks jointly is considerable, but it takes a longer training time to optimize the parameters of the three networks. Besides, we have tried to finetune the spatial and temporal network, but there is no much difference to freeze the Spatial Network and Temporal Network due to the limited size of data set. Practically, we strike a balance between training complexity and efficiency, so we adopt the simpler method as follows. We train Temporal Network and Spatial Network first, then train Fusion Network by fixing the above two networks. The training strategy is same for Spatial Network and Temporal Network, we optimize the parameters by using backpropagation and apply Adam [46] algorithm, the batch size is set as 128, the learning rate starts with 1e3 and decays every 20k iterations. Spatial Network and Temporal Network are trained from scratch with 60k iterations. Fusion Network is trained by 40k iterations with the above two networks fixed. Our training takes place on machines equipped with a 12GB Titan X GPU.
IvB Experimental Results
IvB1 Comparison with Stateoftheart
We compare our method with several stateoftheart hand pose estimation methods [20, 26, 18, 19, 35, 36, 6, 7]. What worth mentioning is that some methods provide predicted joints but some not, we calculate the metrics of some methods [20, 18, 19, 35, 36] available online and estimate the others from the figures in their papers.
NYU Dataset contains 72k training images from one subject and 8k testing images from two subjects. There are totally 36 annotated joints, and we only evaluate a subset of 14 joints as used in other papers for a fair comparison. The annotation for hand is illustrated in Figure 7.
We compare our method with several stateoftheart approaches on NYU dataset, including 3DCNN [6], DeepModel [35], Feedback [19], DeepPrior [18], Matrix [7], HeatMap [20], LieX [47].
The accuracy and the prejoint error distances are shown in Figure 6, our proposed method has a comparable performance with stateoftheart methods. In Figure (a)a, our method outperforms the majority of methods. For example, the proportion of good frames is about 10% higher than Feedback when distance threshold is 30mm. 3DCNN adopts the augmentation and projective DTSDF method, and trains a 3D convolution neural network which maps the sliced 3D volumetric representation to 3D hand pose, our method could not as accurate as 3D CNN from 1560mm due to the sufficient 3D spatial information captured by the 3D CNN. LieX infers the optimal hand pose in the manifold via a Lie group based method, it stands out over the range of 2046mm, but our method overtakes at other threshold. In Figure (c)c, the perjoint error distance for five methods and our method are illustrated.
Table II reports the average error distance for different methods. Generally, results show that our method has a comparable performance with competing methods. Our method outperforms [20, 18, 19, 35] by a large margin, and is comparing to [47].
To have an intuitive sense, we present some examples as depicted in Figure 8. Our method could get an acceptable prediction even in the extreme circumstance.
Methods  Average joint error (mm) 

HeatMap [20]  21.02 
DeepPrior [18]  19.73 
Feedback [19]  15.97 
DeepModel [35]  16.90 
LieX [47]  14.51 
CADSTN  14.83 
ICVL Dataset contains 22k training images (totally 330k by augmentation), and is separated into ten sequences. And testing dataset includes two sequences, there are 1.6k images in total.
On ICVL dataset, we compare our proposed method against five approaches: CrossingNet [26], LRF [36], DeepPrior [18], DeepModel [35] and LSN [9]. The quantitative results are shown in Figure (b)b. Our method is better than LRF, DeepPrior ^{2}^{2}2DeepPrior [18] only provides test results on the first sequence on ICVL, the accuracy curve is plotted based on the provided result., DeepModel and CrossingNet, and is roughly same as LSN. CrossingNet employs GAN and VAE for data augmentation, and our method surpasses it when the threshold is bigger than 9mm. Compared to the hierarchical regression framework LSN, our method is not as accurate from 1430mm but outperforms when the threshold is bigger than 30mm. Furthermore, Figure (d)d reveals the same case that fingertips estimation is generally worse than the palm of the hand. As summarized in Table III, the mean error distance of our method is the lowest in four methods, which obtains a 1.4mm error decrease than DeepPrior and is 0.16mm smaller than LSN.
IvB2 Ablation Study
For the sake of analyzing the effects of different parts in our method, we perform an extensive ablation experiments on NYU dataset.
Ablation Study For Feature Representation Except for Spatial Network and Temporal Network, we train two networks named Baseline Regression Network and Sliced 3D Input Network. As shown in Figure 9, these two networks are parts of Spatial Network.
We show the results in Figure 10 and Table IV. The experimental results reveal that Spatial Network and Temporal Network improve the performance by exploiting the spatial and temporal context respectively, and our final model performs best by utilizing spatiotemporal context simultaneously.
Methods  Average joint error (mm) 

Sliced 3D Input  16.56 
Baseline Regression  15.95 
Temporal  15.47 
Spatial  15.03 
CADSTN  14.83 
w  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  ours 
Average joint error (mm)  14.98  14.94  14.89  14.88  14.89  14.90  14.92  15.06  15.24  14.83 
Baseline Regression Network is a simple network composed of convolution, maxpooling, and fully connected layers. The network regresses the labels directly, and the average error distance is shown in Table IV. The results reveal that Baseline Regression Network already surpasses some methods.
Sliced 3D Input Network regresses the hand joints with the sliced 3D volumetric representation. Due to the absence of depth information, it is difficult to estimate the depth for hand joint.
Spatial Network hierarchically fuses the features from depth image input and sliced 3D volumetric representation. We could find that Sliced 3D is the worst in several competitors. In our opinion, the bad performance is because the depth information is sacrificed in sliced 3D volumetric representation. Via the DeeplyFusion network, Spatial Network borrow the spatial information from Sliced 3D branch, and it achieves a better result than Baseline Regression Network and Sliced 3D Input Network.
Temporal Network replaces the second fully connected layer with LSTM layer and concatenates the hidden output with the input features. We find that Temporal Network slightly improves the performance due to the temporal information from experimental results, and the T value for LSTM is set as 16 in training.
CADSTN is our proposed method, which integrates Spatial Network and Temporal Network by Fusion Network. Fusion Network fuses the predictions from two networks and yields the final prediction. The three networks are connected with the implicitly adaptation weights, and influence each other in the optimization process. Because of the temporal coherence and spatial information concerned, our method performs best in ablation experiments, and Figure (b)b reveals that the joint error distance for every joint is the lowest. Table IV reports that our final method decreases the average joint error by 1.12mm.
Ablation Study For Regression To demonstrate the advantage of our proposed Fusion Network, we compare Fusion Network with simple combination for the results from Spatial Network and Temporal Network on NYU dataset. And the experimental results are shown in Table V. The experimental result demonstrates our proposed Fusion Network performs better than simply combination method.
V Conclusion
In this paper, we propose a novel method for 3D hand pose estimation, termed CADSTN, which models the spatiotemporal context with three networks. The modeling of spatial context, temporal property and fusion are separately done by three parts. The proposed Spatial Network extracts depth and spatial information hierarchically. Further on making use of the temporal coherence between frames, Temporal Network gives out a sequence of joints by feeding into a depth image sequence. Then we fuse the predictions from the above two networks via Fusion Network. We evaluate our method on two publicly available benchmarks and the experimental results demonstrate that our method achieves the best or the secondbest result with stateoftheart approaches and can run in realtime on two datasets.
Acknowledgment
This work was supported in part by NSFC under Grant U1509206 and Grant 61472353, in part by the Key Program of Zhejiang Province under Grant 2015C01027, in part by the National Basic Research Program of China under Grant 2015CB352302, and in part by the AlibabaZhejiang University Joint Institute of Frontier Technologies.
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