# Improved Deep Learning Method for Intelligent Analysis of Sports Training Posture

Authors: Xianyou Yan
Journal: Advances in Multimedia
 (2022)

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## Abstract

Motion recognition based on human bones has attracted extensive attention in recent years because of its simplicity and robustness. Considering the causality of human movement, this paper proposes an improved deep learning method for posture analysis in sports training. In order to deal with the complex situation of calculating joint torques as weights, the edge weights and convolution weights of bone maps are used as auxiliary information networks according to the causality of joint distribution. Thus, the stronger driving force of joint weights in the neural network is improved, the low importance of joint attention is reduced, and the high importance of joint attention is enhanced. Experiments on three public motion recognition datasets show that the proposed method can distinguish similar motions effectively compared with the mainstream methods. Besides, experiments on a challenging UCF (University of Central Florida) sports dataset show that the proposed method can effectively enhance the motion features and improve the accuracy of recognition.


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## Body

## 1. Introduction

To analyze the problem of motion recognition from multidata dimensions, the existing methods use visual appearance, depth information, optical flow, and even sound for fusion and auxiliary recognition. Literature [1] proposed that low redundancy and high separable joint information representation can significantly improve the performance of motion recognition. Literature [2] uses 3D joint coordinates to analyze motion pattern recognition motions, and the motion information extraction method adopted is simple and efficient. However, the spatial relationship between joints is ignored in this method; thus the accuracy is limited. To solve this problem, relative distance and angle coding joints were adopted in literature [3] to improve accuracy, but the recognition results relying only on manual features were not satisfactory. Deep learning model uses nonlinear neural network to extract deep-level motion features to improve accuracy [4]. Based on the excellent spatial feature extraction ability of CNN (convolutional neural network), the bone sequence is encoded as a pseudoimage in literature [5], and its depth features are extracted based on CNN to improve the recognition effect. However, the lack of time domain information of the encoded image results in limited improvement of accuracy. In view of this problem, RNN (recurrent neural network) [6], which has a good temporal modelling ability, can recognize motions with a high accuracy. However, the inherent defect of gradient dispersion in RNN makes it difficult to learn long-term historical information.The above recognition method based on deep network processes each image frame by frame and lacks the mining of key images and parts. However, motion sequences usually have large information redundancy, which makes the relevant methods have poor real-time performance and lack of highly separable information, resulting in limited improvement of accuracy. Based on this, a model based on spatiotemporal attention mechanism was proposed in literature [7]. It uses the space-time attention mechanism to extract bone features and assigns corresponding weights to joints based on their importance to enhance the influence of key images and parts, so as to improve the accuracy of motions [8]. However, this method only considers joint coordinates and ignores spatial topological information, so the accuracy is limited.Deep learning-based methods are used to study posture recognition in sports training from multiple perspectives, and good recognition performance is achieved [9]. However, these methods still have some limitations, such as ignoring the correlation between bone joints in the human body structure and not considering the weight changes of joints in different movements. Joints are considered to be the ends of a rigid body, and different joints play different roles in different training postures, so the key joints should have more weight in determining the type of movement. The joints of the human body are simplified to the multirigid body model, and the torques of each joint are calculated by solving partial differential equations, and then different weights are assigned to each joint according to the torques of each joint. This method is not suitable for complex graph convolutional networks because of too many equations and too much calculation. However, the main disadvantage of the local attention model is that it only uses the local variation of the motion sequence to get the attention weight, and it is difficult to get the accurate attention weight.Therefore, this paper proposes a human skeletal motion recognition method combining causality and spatiotemporal graph convolution network. Firstly, the causal coefficients of the joint are calculated according to the joint coordinate sequence, and the causal coefficient matrix is constructed. Then, the causal coefficient matrix is applied to the graph convolution network, which assigns different weights according to the importance of joints in the process of motion. In order to effectively learn dynamic features and improve the accuracy of recognition, it is necessary to pay attention to the joints with greater influence in the process of motion and ignore the joints with less influence.This paper has two main contributions:(1)
Considering the causality in human movement, a spatiotemporal graph model is constructed for bone data, and a motion recognition method combining causality and spatiotemporal graph convolution network is proposed.(2)
Aiming at the complex situation of calculating joint torques to obtain weights, a method of calculating joint weights based on causality was proposed, and edge weights were assigned to bone graph according to the causal relationship between joints. The weights are used as auxiliary information to enhance the convolutional network to improve the weights of some joints with strong driving forces in the neural network, so that the neural network can reduce the joint attention of low importance and enhance the joint attention of high importance.This paper consists of five main parts: the first part is the introduction, the second part is state of the art, the third part is methodology, the fourth part is result analysis and discussion, and the fifth part is the conclusion.


## 2. State of the Art

### 2.1. Bone-Based Training Motion Recognition

Traditional bone motion recognition based on manual features captures the dynamics of joint motion by manually designing different feature extraction methods. For example, literature [10] established time-domain hierarchical covariance matrix descriptors to represent the motion trajectories of joints. Literature [11] used the relative position of joints as features. In literature [12], rotation and translation between various parts of the body are used to extract features, and then traditional machine learning algorithms are used to classify features, so as to classify motions. Because deep neural networks can better learn feature representation, some research studies on bone-based motion recognition has shifted from manual feature design to deep learning-based methods.


### 2.2. Training Motion Recognition Method Based on Deep Learning

Deep learning-based methods are divided into two stages. In the early stage, researchers use RNN or Temporal CNN to learn the motion recognition model in an end-to-end manner. Most of these methods directly take the bone coordinate sequence as the input feature or convert the bone coordinate sequence into grayscale image and then input it into the network for classification. However, RNN and CNN cannot completely represent bone structure. According to the natural structure of the human body, the graph model is more suitable for the representation of bone data. Therefore, literature [13] first applied a graph convolution network to bone-based motion recognition and proposed an ST-GCN network model. Later, on the basis of ST-GCN, 2S-AGCN was proposed in literature [14], which improved the GCN module so that it could adaptively learn the topological structure of the graph. Besides the bone data, the bone information that had never been noticed before was also used as the second information flow to improve the recognition effect. Literature [15] used SGR component to find connectivity between joints in spatial subgroup clustering and measure correlation of joint time trajectory. Literature [16] extended the skeleton diagram structure to capture potential dependencies specific to the motion. However, the above related algorithms based on bones only consider the information of bone depth and ignore the appearance features of effective expression of training movements.


## 2.1. Bone-Based Training Motion Recognition

Traditional bone motion recognition based on manual features captures the dynamics of joint motion by manually designing different feature extraction methods. For example, literature [10] established time-domain hierarchical covariance matrix descriptors to represent the motion trajectories of joints. Literature [11] used the relative position of joints as features. In literature [12], rotation and translation between various parts of the body are used to extract features, and then traditional machine learning algorithms are used to classify features, so as to classify motions. Because deep neural networks can better learn feature representation, some research studies on bone-based motion recognition has shifted from manual feature design to deep learning-based methods.


## 2.2. Training Motion Recognition Method Based on Deep Learning

Deep learning-based methods are divided into two stages. In the early stage, researchers use RNN or Temporal CNN to learn the motion recognition model in an end-to-end manner. Most of these methods directly take the bone coordinate sequence as the input feature or convert the bone coordinate sequence into grayscale image and then input it into the network for classification. However, RNN and CNN cannot completely represent bone structure. According to the natural structure of the human body, the graph model is more suitable for the representation of bone data. Therefore, literature [13] first applied a graph convolution network to bone-based motion recognition and proposed an ST-GCN network model. Later, on the basis of ST-GCN, 2S-AGCN was proposed in literature [14], which improved the GCN module so that it could adaptively learn the topological structure of the graph. Besides the bone data, the bone information that had never been noticed before was also used as the second information flow to improve the recognition effect. Literature [15] used SGR component to find connectivity between joints in spatial subgroup clustering and measure correlation of joint time trajectory. Literature [16] extended the skeleton diagram structure to capture potential dependencies specific to the motion. However, the above related algorithms based on bones only consider the information of bone depth and ignore the appearance features of effective expression of training movements.


## 3. Methodology

As shown in Figure1, this paper proposes a human motion recognition model that integrates causality and spatiotemporal graph convolution network.Figure 1
Motion recognition model combining causality and spatiotemporal graph convolution network.Firstly, the model calculates the causality of the joint according to the joint coordinate sequence and constructs the causal coefficient matrix. Then, the matrix is applied to the ST-GCN graph convolution network to extract deep features from bone data, so as to effectively learn dynamic features and increase the accuracy of motion recognition.


### 3.1. Space-Time Map Model

Let the bone sequence space-time map beA(Q, E) with length N frames, and point set Q contains joints at all times. Edge set E consists of two subsets, one of which is the interskeleton connection Es of each frame (blue line in Figure 2). Es reflects spatial attributes. The other edge subset is EF (red line in Figure 2), which reflects temporal ownership. The top feature of A(Q, E) is the joint coordinate vector Fqnx, and the vertex qnx represents the coordinates of joint x in the nth frame.Figure 2
Schematic diagram of skeleton spatiotemporal graph.


### 3.2. Graph Convolution

By givingA(Q, E), the qnx graph is convoluted.(1)foutqnx=∑qnx∈Hqnx1Knxqnyfinqny⋅mlnxqny,where Hqnx=qny|dqny,qnx≤D is the convolution sampling region of qnx. fin is the input feature of qnx. M is the weight function that provides the weight vector for the input feature. Since the size of the traditional convolution sampling area is fixed, and the number of weight vectors is equal to the size of the sampling area, and the number of vertices in H is changing, the mapping vertices need to correspond to the weight vector in graph convolution. Mapping lnx:Hqnx⟶0,⋯,Z−1. The adjacent nodes are mapped to subset labels, and each neighbor node finds the corresponding weight vector according to subset labels. Usually, Z is set to 3, which will be divided into 3 subsets. The first subset (S1) is the vertices themselves (orange nodes in Figure 3). The second subset (S2) is a centripetal subset that contains nodes closer to the body’s center of gravity (blue nodes in Figure 3). The third subset (S3) is a centrifugal subset that contains nodes farther from the center of gravity (green nodes in Figure 3).Figure 3
Subset mapping strategy.Graph convolution network is usually composed of multilayer spatiotemporal graph convolution layers; each layer carries out spatial graph convolution and temporal graph convolution in turn to extract high-level features of the graph, and finally carries out pooling and Softmax processing.The feature ofA(Q, E) is represented by the (C, N, T) tensor, where C is the number of channels. N is the length of time, and T is the number of vertices. According to equation (1), the graph convolution formula on multidimensional tensors is shown in equations (2) and (3).(2)fout=∑qZqMzfinGz,(3)Gz=Λz−1/2G¯zΛz−1/2∈ℝT×T,where Gz is the adjacency matrix, Zq represents the convolution kernel size; its element Gzxy represents whether the vertex qy is in the subset of qx, and Mz∈ℝCopn×Cxt×1×1 is the weight vector. The matrix Gz determines whether the vertex features are computed in conjunction with the weight vectors. Since Gz is defined in advance according to the bone structure, that is, two different motion videos, as long as the structure of human skeleton extracted is the same, Gz is the same in the convolution of the graph. Since the importance of joints in different human motions is different, it is necessary to reflect the difference of joint importance in the adjacency matrix Gz. In order to solve this problem, causality is integrated into the graph convolutional network to enhance the motion recognition effect.


### 3.3. Motion Recognition Integrating Causality

The multirigid body model of the human body is modelled by the Lagrange method, and joint torques are calculated by partial differential equations. The rigid body model has linkage; one rigid body will drive other rigid bodies to move through the rotating shaft. This linkage relationship obviously has causality. When a joint with a large torque exerts force, it will drive other joints more, and the exerting joint is the “cause” of the driven joint. Because the dynamic system of the human body is very complex and there are many equations after modelling, it is too complicated to calculate the interaction degree between joints through equations. Moreover, the multirigid body model can only calculate the joint torques at a single moment, and the calculation of joint torques in continuous time is more complicated. Therefore, it is difficult to analyze the strength and causality of joint interaction through the multirigid body model.


#### 3.3.1. Calculation of Joint Causality

Convergent cross mapping (CCM) is a method to calculate the special correlation of time series in complex systems. This method is used to measure the causal relationship between the estimated value and the similarity test variable ofI. It can overcome the difficulties of complex multirigid body model modelling and high computational complexity. And it can quickly test the joint causal relationship, which has been widely used. This paper allocates edge weights based on CCM, and the steps are as follows:(1)
Build shadow flowThe e-dimensional delay vector is composed ofIn historical points of the point, which describes the change of the joint over a period of time and can be expressed as follows:(4)I˜n=In,In−τ,In−2τ,⋯,In−E−1τ.The shadow flowI˜ of joint coordinate sequence I is the set of delay vectors In of each point I, τ is the step.(2)
Find the nearest point and create the weightForI˜n, find other E+1 time points that are most similar to the joint position changes at time n and calculate the Euclidean distance between I˜n and other delay vectors. The calculation formula is shown in equation (4).(5)dx=DI˜n,I˜n^.SelectE + 1 delay vector with the smallest distance as the nearest neighbor point, and get the set of time points n˜1,n˜2,⋯,n˜E+1 and distance sets d1,d2,⋯,dE+1. Calculate the weight of I˜n for the distance set as follows:(6)mx=pxT,(7)px=e−dx/d1,(8)T=∑y=1E+1py.(3)
Calculate the estimated value ofX to Y and the correlation coefficientUsing the weight of each point, the weighted sum of each pointJn in the coordinate sequence J is carried out, thus obtaining the estimate of I to J.(9)Jn|I˜=∑x=1E+1mxJn^x.In this paper, the ability ofI historical information to estimate J is measured by calculating Pearson phase relation CJI of original coordinate sequence J and estimated value J|I˜.(10)CJI=ρJ,J|I˜2.(4)
Calculate the edge weight matrixFor a pair of jointsI and J, two correlation coefficients CIJ and CJI can be obtained, which are I estimation J and J estimation I, respectively. Assuming that the space-time graph has T joints, the causality coefficient matrix C can be obtained by calculating the causality coefficient of two joints.(11)C=∑x=0T−1∑y=0T−1corly,lx.x and y are the joint numbers. In this paper, each line of coefficient matrix C is normalized by Softmax, and the normalized coefficients are embedded as edge weights of A(Q, E).


#### 3.3.2. Edge Weight Embedding

Inspired by the attention mechanism of CNN and RNN, this paper changes the edge weight ofA(Q, E) edge set according to the causal coefficient. In order to assign different weights to different edges in A(Q, E), equation (2) is modified as follows:(12)fout=∑qZqMzfinGz⊙C^,where ⊙ represents the product of each element of the matrix. In equation (12), Gz indicates whether two vertices are connected in a subset by a matrix element value of 0 or 1/Sxz. However, in the process of movement, the strength of interarticular force is different. Since the matrix Gz was T × T, the edge weight matrix C^ was T × T, the matrix size was also T × T when C^ and Gz were applied element by element. Therefore, replacing Gz in equation (2) with Gz⊙C^ will not cause the problem of matrix size mismatch.As shown in Figure4, the weight of the upper part of the bone marked C^ corresponds to the movements of the lower part. Because the main movement part is the arm, and the movement range is large, while the movement range of the lower limb joints is small, the edge weight between the upper limb joints is correspondingly larger than the lower limb joints.Figure 4
Schematic diagram of edge weight.In this paper, the CCM method is used to test the characteristics of time variable causality and calculate the causality between each vertex. Joint causality is transformed into edge weights, and then edge weights are embedded into graph adjacency matrix by by-element product, thus reducing the joint attention of low importance and enhancing the joint attention of high importance.


#### 3.3.3. Network Structure

ST-GCN is used as the basic network in this paper. In order to apply edge weight matrix, this paper adds edge weight matrix as input and multiplies edge weight matrix with adjacent matrix element by an element before convolution operation. The convolution layer structure of space-time graph is shown in Figure5.Figure 5
Spatiotemporal graph convolutional block.


## 3.1. Space-Time Map Model

Let the bone sequence space-time map beA(Q, E) with length N frames, and point set Q contains joints at all times. Edge set E consists of two subsets, one of which is the interskeleton connection Es of each frame (blue line in Figure 2). Es reflects spatial attributes. The other edge subset is EF (red line in Figure 2), which reflects temporal ownership. The top feature of A(Q, E) is the joint coordinate vector Fqnx, and the vertex qnx represents the coordinates of joint x in the nth frame.Figure 2
Schematic diagram of skeleton spatiotemporal graph.


## 3.2. Graph Convolution

By givingA(Q, E), the qnx graph is convoluted.(1)foutqnx=∑qnx∈Hqnx1Knxqnyfinqny⋅mlnxqny,where Hqnx=qny|dqny,qnx≤D is the convolution sampling region of qnx. fin is the input feature of qnx. M is the weight function that provides the weight vector for the input feature. Since the size of the traditional convolution sampling area is fixed, and the number of weight vectors is equal to the size of the sampling area, and the number of vertices in H is changing, the mapping vertices need to correspond to the weight vector in graph convolution. Mapping lnx:Hqnx⟶0,⋯,Z−1. The adjacent nodes are mapped to subset labels, and each neighbor node finds the corresponding weight vector according to subset labels. Usually, Z is set to 3, which will be divided into 3 subsets. The first subset (S1) is the vertices themselves (orange nodes in Figure 3). The second subset (S2) is a centripetal subset that contains nodes closer to the body’s center of gravity (blue nodes in Figure 3). The third subset (S3) is a centrifugal subset that contains nodes farther from the center of gravity (green nodes in Figure 3).Figure 3
Subset mapping strategy.Graph convolution network is usually composed of multilayer spatiotemporal graph convolution layers; each layer carries out spatial graph convolution and temporal graph convolution in turn to extract high-level features of the graph, and finally carries out pooling and Softmax processing.The feature ofA(Q, E) is represented by the (C, N, T) tensor, where C is the number of channels. N is the length of time, and T is the number of vertices. According to equation (1), the graph convolution formula on multidimensional tensors is shown in equations (2) and (3).(2)fout=∑qZqMzfinGz,(3)Gz=Λz−1/2G¯zΛz−1/2∈ℝT×T,where Gz is the adjacency matrix, Zq represents the convolution kernel size; its element Gzxy represents whether the vertex qy is in the subset of qx, and Mz∈ℝCopn×Cxt×1×1 is the weight vector. The matrix Gz determines whether the vertex features are computed in conjunction with the weight vectors. Since Gz is defined in advance according to the bone structure, that is, two different motion videos, as long as the structure of human skeleton extracted is the same, Gz is the same in the convolution of the graph. Since the importance of joints in different human motions is different, it is necessary to reflect the difference of joint importance in the adjacency matrix Gz. In order to solve this problem, causality is integrated into the graph convolutional network to enhance the motion recognition effect.


## 3.3. Motion Recognition Integrating Causality

The multirigid body model of the human body is modelled by the Lagrange method, and joint torques are calculated by partial differential equations. The rigid body model has linkage; one rigid body will drive other rigid bodies to move through the rotating shaft. This linkage relationship obviously has causality. When a joint with a large torque exerts force, it will drive other joints more, and the exerting joint is the “cause” of the driven joint. Because the dynamic system of the human body is very complex and there are many equations after modelling, it is too complicated to calculate the interaction degree between joints through equations. Moreover, the multirigid body model can only calculate the joint torques at a single moment, and the calculation of joint torques in continuous time is more complicated. Therefore, it is difficult to analyze the strength and causality of joint interaction through the multirigid body model.


### 3.3.1. Calculation of Joint Causality

Convergent cross mapping (CCM) is a method to calculate the special correlation of time series in complex systems. This method is used to measure the causal relationship between the estimated value and the similarity test variable ofI. It can overcome the difficulties of complex multirigid body model modelling and high computational complexity. And it can quickly test the joint causal relationship, which has been widely used. This paper allocates edge weights based on CCM, and the steps are as follows:(1)
Build shadow flowThe e-dimensional delay vector is composed ofIn historical points of the point, which describes the change of the joint over a period of time and can be expressed as follows:(4)I˜n=In,In−τ,In−2τ,⋯,In−E−1τ.The shadow flowI˜ of joint coordinate sequence I is the set of delay vectors In of each point I, τ is the step.(2)
Find the nearest point and create the weightForI˜n, find other E+1 time points that are most similar to the joint position changes at time n and calculate the Euclidean distance between I˜n and other delay vectors. The calculation formula is shown in equation (4).(5)dx=DI˜n,I˜n^.SelectE + 1 delay vector with the smallest distance as the nearest neighbor point, and get the set of time points n˜1,n˜2,⋯,n˜E+1 and distance sets d1,d2,⋯,dE+1. Calculate the weight of I˜n for the distance set as follows:(6)mx=pxT,(7)px=e−dx/d1,(8)T=∑y=1E+1py.(3)
Calculate the estimated value ofX to Y and the correlation coefficientUsing the weight of each point, the weighted sum of each pointJn in the coordinate sequence J is carried out, thus obtaining the estimate of I to J.(9)Jn|I˜=∑x=1E+1mxJn^x.In this paper, the ability ofI historical information to estimate J is measured by calculating Pearson phase relation CJI of original coordinate sequence J and estimated value J|I˜.(10)CJI=ρJ,J|I˜2.(4)
Calculate the edge weight matrixFor a pair of jointsI and J, two correlation coefficients CIJ and CJI can be obtained, which are I estimation J and J estimation I, respectively. Assuming that the space-time graph has T joints, the causality coefficient matrix C can be obtained by calculating the causality coefficient of two joints.(11)C=∑x=0T−1∑y=0T−1corly,lx.x and y are the joint numbers. In this paper, each line of coefficient matrix C is normalized by Softmax, and the normalized coefficients are embedded as edge weights of A(Q, E).


### 3.3.2. Edge Weight Embedding

Inspired by the attention mechanism of CNN and RNN, this paper changes the edge weight ofA(Q, E) edge set according to the causal coefficient. In order to assign different weights to different edges in A(Q, E), equation (2) is modified as follows:(12)fout=∑qZqMzfinGz⊙C^,where ⊙ represents the product of each element of the matrix. In equation (12), Gz indicates whether two vertices are connected in a subset by a matrix element value of 0 or 1/Sxz. However, in the process of movement, the strength of interarticular force is different. Since the matrix Gz was T × T, the edge weight matrix C^ was T × T, the matrix size was also T × T when C^ and Gz were applied element by element. Therefore, replacing Gz in equation (2) with Gz⊙C^ will not cause the problem of matrix size mismatch.As shown in Figure4, the weight of the upper part of the bone marked C^ corresponds to the movements of the lower part. Because the main movement part is the arm, and the movement range is large, while the movement range of the lower limb joints is small, the edge weight between the upper limb joints is correspondingly larger than the lower limb joints.Figure 4
Schematic diagram of edge weight.In this paper, the CCM method is used to test the characteristics of time variable causality and calculate the causality between each vertex. Joint causality is transformed into edge weights, and then edge weights are embedded into graph adjacency matrix by by-element product, thus reducing the joint attention of low importance and enhancing the joint attention of high importance.


### 3.3.3. Network Structure

ST-GCN is used as the basic network in this paper. In order to apply edge weight matrix, this paper adds edge weight matrix as input and multiplies edge weight matrix with adjacent matrix element by an element before convolution operation. The convolution layer structure of space-time graph is shown in Figure5.Figure 5
Spatiotemporal graph convolutional block.


## 3.3.1. Calculation of Joint Causality

Convergent cross mapping (CCM) is a method to calculate the special correlation of time series in complex systems. This method is used to measure the causal relationship between the estimated value and the similarity test variable ofI. It can overcome the difficulties of complex multirigid body model modelling and high computational complexity. And it can quickly test the joint causal relationship, which has been widely used. This paper allocates edge weights based on CCM, and the steps are as follows:(1)
Build shadow flowThe e-dimensional delay vector is composed ofIn historical points of the point, which describes the change of the joint over a period of time and can be expressed as follows:(4)I˜n=In,In−τ,In−2τ,⋯,In−E−1τ.The shadow flowI˜ of joint coordinate sequence I is the set of delay vectors In of each point I, τ is the step.(2)
Find the nearest point and create the weightForI˜n, find other E+1 time points that are most similar to the joint position changes at time n and calculate the Euclidean distance between I˜n and other delay vectors. The calculation formula is shown in equation (4).(5)dx=DI˜n,I˜n^.SelectE + 1 delay vector with the smallest distance as the nearest neighbor point, and get the set of time points n˜1,n˜2,⋯,n˜E+1 and distance sets d1,d2,⋯,dE+1. Calculate the weight of I˜n for the distance set as follows:(6)mx=pxT,(7)px=e−dx/d1,(8)T=∑y=1E+1py.(3)
Calculate the estimated value ofX to Y and the correlation coefficientUsing the weight of each point, the weighted sum of each pointJn in the coordinate sequence J is carried out, thus obtaining the estimate of I to J.(9)Jn|I˜=∑x=1E+1mxJn^x.In this paper, the ability ofI historical information to estimate J is measured by calculating Pearson phase relation CJI of original coordinate sequence J and estimated value J|I˜.(10)CJI=ρJ,J|I˜2.(4)
Calculate the edge weight matrixFor a pair of jointsI and J, two correlation coefficients CIJ and CJI can be obtained, which are I estimation J and J estimation I, respectively. Assuming that the space-time graph has T joints, the causality coefficient matrix C can be obtained by calculating the causality coefficient of two joints.(11)C=∑x=0T−1∑y=0T−1corly,lx.x and y are the joint numbers. In this paper, each line of coefficient matrix C is normalized by Softmax, and the normalized coefficients are embedded as edge weights of A(Q, E).


## 3.3.2. Edge Weight Embedding

Inspired by the attention mechanism of CNN and RNN, this paper changes the edge weight ofA(Q, E) edge set according to the causal coefficient. In order to assign different weights to different edges in A(Q, E), equation (2) is modified as follows:(12)fout=∑qZqMzfinGz⊙C^,where ⊙ represents the product of each element of the matrix. In equation (12), Gz indicates whether two vertices are connected in a subset by a matrix element value of 0 or 1/Sxz. However, in the process of movement, the strength of interarticular force is different. Since the matrix Gz was T × T, the edge weight matrix C^ was T × T, the matrix size was also T × T when C^ and Gz were applied element by element. Therefore, replacing Gz in equation (2) with Gz⊙C^ will not cause the problem of matrix size mismatch.As shown in Figure4, the weight of the upper part of the bone marked C^ corresponds to the movements of the lower part. Because the main movement part is the arm, and the movement range is large, while the movement range of the lower limb joints is small, the edge weight between the upper limb joints is correspondingly larger than the lower limb joints.Figure 4
Schematic diagram of edge weight.In this paper, the CCM method is used to test the characteristics of time variable causality and calculate the causality between each vertex. Joint causality is transformed into edge weights, and then edge weights are embedded into graph adjacency matrix by by-element product, thus reducing the joint attention of low importance and enhancing the joint attention of high importance.


## 3.3.3. Network Structure

ST-GCN is used as the basic network in this paper. In order to apply edge weight matrix, this paper adds edge weight matrix as input and multiplies edge weight matrix with adjacent matrix element by an element before convolution operation. The convolution layer structure of space-time graph is shown in Figure5.Figure 5
Spatiotemporal graph convolutional block.


## 4. Result Analysis and Discussion

In this section, the experiment is firstly carried out on three public motion recognition datasets based on NTU RGB-D, Northwestern-UCLA, and SBU Interaction Dataset. The experiment was then performed on the UCF Sports dataset.


### 4.1. Experiment on General Motion Recognition Database

This experiment is based on the framework of the space-time graph convolution network. The processor is Intel Core(TM) I7-7700, main frequency 3.60 GHz, 32 GB memory, and NVIDIA Ge Force GTX 1070. The number of neurons in each layer was 128, the apparent feature extraction radius was 5 pixels, and the initial learning rate was 0.002. The equilibrium factorλ = 10–5 and the batch size is 64. Dropout = 0.45 to prevent overfitting.


#### 4.1.1. NTU RGB-D Dataset

This dataset consisted of 40 subjects using 3 Kinect V2 cameras to collect 60 kinds of movements, 56,880 video clips, and 3D bone data sequences from −45°, 0° and 45° angles. It includes individual daily training movements (such as rope skipping, running, and squatting), interactive training of characters (such as barbell training, dumbbell training, and elastic belt training), and interactive training of pairs (such as drug ball relay, double flat back stretching, and double cross high-five)In the cross-subject experiment, 40 types of subjects were divided into training and test sets, numbered as 1, 2, 4, 5, 8, 9, 13, 14, 15, 16, 17, 18, 19, 25, 27, 28, 31, 34, 35, 38, and the rest were test sets. In the cross-view experiment, the first camera was selected as the test set, and the rest were training sets.In this section, the accuracy and loss curves corresponding to the training set and test set in the iterative training of cross subject and cross view are shown in Figures6 and 7. It can be seen from Figures 6 and 7 that the accuracy of the model increases with the increase of training times and tends to be stable and the loss value converges when the iteration reaches 220 times. Based on the NTU RGB-D dataset, the accuracy of cross subjects and cross angles obtained by the proposed method and the mainstream method is shown in Table 1.Figure 6
Accuracy and loss values in cross subject.
(a)(b)Figure 7
Accuracy and loss values in cross view.
(a)(b)Table 1
Cross subject and cross view accuracy obtained by each algorithm for the dataset.
DataMethodsCross subject %Cross view %Bone sequenceLiterature [17]51.1953.87Literature [18]67.9673.69Literature [19]78.9188.44Literature [20]85.3390.82Proposed method89.8491.12From Table1, it is clear that literature [17] based on variable parameter related skeletons and dynamic skeletons based on 3D geometric relationships) does not take into account deep space-time information, resulting in low accuracy. Literature [18] mapped joints to 3D space and extracted depth features through 3D CNN, thus effectively improving accuracy to 67.96% and 73.69%. However, it does not consider the time domain information of bone recognition. Literature [19] considered the relative motion trend of interframe and intraframe joint links. However, this method only considers joint characteristics and ignores topological relations, so the accuracy is limited. Literature [20] encodes spatial relations between joints to improve accuracy. However, they lack appearance features, thus limiting recognition ability. The proposed method uses causality as auxiliary information to enhance the graph convolutional network, thus improving the accuracy to 89.84% and 91.12%. It shows that the proposed method has high accuracy in complex scenarios.


#### 4.1.2. Northwestern-UCLA Dataset

The Northwestern-UCLA dataset consisted of 1,494 sequences of 10 subjects performing 10 types of exercises: bends, presses, hard pulls, push-ups, planks, squats, pull-ups, pull-ups, dumbbell exercises, and barbell exercises. The dataset was collected from three different perspectives. The first two cameras were training data, and the rest were test data.As shown in Table2, literature [17] assumed that the skeleton was perpendicular to the ground for projection clustering discrimination, ignoring the spatial relationship of the skeleton, resulting in low accuracy. Reference [18] is better than reference [17] because it is based on variable parameter-associated skeleton to represent motions, but it ignores bone dynamic information. Literature [19] obtained 79.72% accuracy by considering the temporal characteristics of joints, but it was difficult to distinguish similar movements due to the lack of appearance information. In literature [20], multiperspective dynamic images are extracted to cope with spatial changes and take appearance features into consideration, but they lack timing features. This method integrates causality and represents important dynamic information of joint effectively, and extracts color texture information based on the heat map to obtain highly separable expression of the motion. The accuracy is improved to 87.95%, which is 8.23% and 2.85% higher than literature [19] and literature [20], respectively. It indicates that the proposed method has high recognition ability under the condition of different perspectives and diversified topics.Table 2
Experimental results of northwestern-UCLA dataset.
DataFeaturesMethodsAccuracy (%)Bone sequenceManual extractionLiterature [17]55.70Spatiotemporal graph convolution networkLiterature [18]75.40Literature [19]79.72Literature [20]85.40Combining causality and spatiotemporal graph convolution networkProposed method87.95


#### 4.1.3. SBU Interaction Dataset

The SBU interaction dataset contains the following 5 types of interaction: double squats, double single-leg squats, high-five push-ups, reverse crunches, and boxing, which are divided into 5 cross sets. Four of them were selected as training sets and the rest as test sets. The average value of the verification results of each cross set was taken as the final accuracy.See Figure8 for a comparison of the accuracy of the 5 algorithms. It shows that the accuracy of the proposed method can reach 95.46%, which is more accurate than the other four methods, indicating that the accuracy of the proposed method is relatively high under a small sample dataset.Figure 8
Experimental results of SBU interaction dataset.


#### 4.1.4. Ablation Experiment

In order to further verify the effectiveness of the proposed method, based on the above dataset, the influence of the proposed method on accuracy was studied by integrating causality and spatiotemporal graph convolution network (see Table3). As can be seen from Table 3, compared with the spatiotemporal graph convolutional network model, the accuracy of the model in this paper has been improved by 12.90%, 7.29%, 8.15% and 3.13%, respectively. In this model, causal coefficients are added as edge weights, and causality is used as auxiliary information to enhance graph convolutional networks. Therefore, it can better highlight the main joints in the process of human movement, and its effect is far better than other methods.Table 3
Experimental results of different models.
DatasetSpatiotemporal graph convolution network (%)Proposed method (%)NTU (cross subject)77.0689.96NTU (cross view)83.9591.24Northwestern-UCLA78.8186.96SBU93.5696.69


### 4.2. Experiments on the Dataset of Motion Training Posture

The UCF Sports dataset was used, which consists of eight training movements, including running, rope skipping, swimming, swallows, cycling, pull-ups, and planks. These movements are in a real moving environment, showing variations in background, lighting conditions and occlusion, making it a challenging dataset. A sample frame for each motion is shown in Figure9.Figure 9
Sample frames of each motion in the UCF motion dataset. (a) Barbell training. (b) Running. (c) Pull-ups. (d) Jumping rope. (e) Swimming. (f) Cycling. (g) Flying swallow. (h) Plank support.


## 4.1. Experiment on General Motion Recognition Database

This experiment is based on the framework of the space-time graph convolution network. The processor is Intel Core(TM) I7-7700, main frequency 3.60 GHz, 32 GB memory, and NVIDIA Ge Force GTX 1070. The number of neurons in each layer was 128, the apparent feature extraction radius was 5 pixels, and the initial learning rate was 0.002. The equilibrium factorλ = 10–5 and the batch size is 64. Dropout = 0.45 to prevent overfitting.


### 4.1.1. NTU RGB-D Dataset

This dataset consisted of 40 subjects using 3 Kinect V2 cameras to collect 60 kinds of movements, 56,880 video clips, and 3D bone data sequences from −45°, 0° and 45° angles. It includes individual daily training movements (such as rope skipping, running, and squatting), interactive training of characters (such as barbell training, dumbbell training, and elastic belt training), and interactive training of pairs (such as drug ball relay, double flat back stretching, and double cross high-five)In the cross-subject experiment, 40 types of subjects were divided into training and test sets, numbered as 1, 2, 4, 5, 8, 9, 13, 14, 15, 16, 17, 18, 19, 25, 27, 28, 31, 34, 35, 38, and the rest were test sets. In the cross-view experiment, the first camera was selected as the test set, and the rest were training sets.In this section, the accuracy and loss curves corresponding to the training set and test set in the iterative training of cross subject and cross view are shown in Figures6 and 7. It can be seen from Figures 6 and 7 that the accuracy of the model increases with the increase of training times and tends to be stable and the loss value converges when the iteration reaches 220 times. Based on the NTU RGB-D dataset, the accuracy of cross subjects and cross angles obtained by the proposed method and the mainstream method is shown in Table 1.Figure 6
Accuracy and loss values in cross subject.
(a)(b)Figure 7
Accuracy and loss values in cross view.
(a)(b)Table 1
Cross subject and cross view accuracy obtained by each algorithm for the dataset.
DataMethodsCross subject %Cross view %Bone sequenceLiterature [17]51.1953.87Literature [18]67.9673.69Literature [19]78.9188.44Literature [20]85.3390.82Proposed method89.8491.12From Table1, it is clear that literature [17] based on variable parameter related skeletons and dynamic skeletons based on 3D geometric relationships) does not take into account deep space-time information, resulting in low accuracy. Literature [18] mapped joints to 3D space and extracted depth features through 3D CNN, thus effectively improving accuracy to 67.96% and 73.69%. However, it does not consider the time domain information of bone recognition. Literature [19] considered the relative motion trend of interframe and intraframe joint links. However, this method only considers joint characteristics and ignores topological relations, so the accuracy is limited. Literature [20] encodes spatial relations between joints to improve accuracy. However, they lack appearance features, thus limiting recognition ability. The proposed method uses causality as auxiliary information to enhance the graph convolutional network, thus improving the accuracy to 89.84% and 91.12%. It shows that the proposed method has high accuracy in complex scenarios.


### 4.1.2. Northwestern-UCLA Dataset

The Northwestern-UCLA dataset consisted of 1,494 sequences of 10 subjects performing 10 types of exercises: bends, presses, hard pulls, push-ups, planks, squats, pull-ups, pull-ups, dumbbell exercises, and barbell exercises. The dataset was collected from three different perspectives. The first two cameras were training data, and the rest were test data.As shown in Table2, literature [17] assumed that the skeleton was perpendicular to the ground for projection clustering discrimination, ignoring the spatial relationship of the skeleton, resulting in low accuracy. Reference [18] is better than reference [17] because it is based on variable parameter-associated skeleton to represent motions, but it ignores bone dynamic information. Literature [19] obtained 79.72% accuracy by considering the temporal characteristics of joints, but it was difficult to distinguish similar movements due to the lack of appearance information. In literature [20], multiperspective dynamic images are extracted to cope with spatial changes and take appearance features into consideration, but they lack timing features. This method integrates causality and represents important dynamic information of joint effectively, and extracts color texture information based on the heat map to obtain highly separable expression of the motion. The accuracy is improved to 87.95%, which is 8.23% and 2.85% higher than literature [19] and literature [20], respectively. It indicates that the proposed method has high recognition ability under the condition of different perspectives and diversified topics.Table 2
Experimental results of northwestern-UCLA dataset.
DataFeaturesMethodsAccuracy (%)Bone sequenceManual extractionLiterature [17]55.70Spatiotemporal graph convolution networkLiterature [18]75.40Literature [19]79.72Literature [20]85.40Combining causality and spatiotemporal graph convolution networkProposed method87.95


### 4.1.3. SBU Interaction Dataset

The SBU interaction dataset contains the following 5 types of interaction: double squats, double single-leg squats, high-five push-ups, reverse crunches, and boxing, which are divided into 5 cross sets. Four of them were selected as training sets and the rest as test sets. The average value of the verification results of each cross set was taken as the final accuracy.See Figure8 for a comparison of the accuracy of the 5 algorithms. It shows that the accuracy of the proposed method can reach 95.46%, which is more accurate than the other four methods, indicating that the accuracy of the proposed method is relatively high under a small sample dataset.Figure 8
Experimental results of SBU interaction dataset.


### 4.1.4. Ablation Experiment

In order to further verify the effectiveness of the proposed method, based on the above dataset, the influence of the proposed method on accuracy was studied by integrating causality and spatiotemporal graph convolution network (see Table3). As can be seen from Table 3, compared with the spatiotemporal graph convolutional network model, the accuracy of the model in this paper has been improved by 12.90%, 7.29%, 8.15% and 3.13%, respectively. In this model, causal coefficients are added as edge weights, and causality is used as auxiliary information to enhance graph convolutional networks. Therefore, it can better highlight the main joints in the process of human movement, and its effect is far better than other methods.Table 3
Experimental results of different models.
DatasetSpatiotemporal graph convolution network (%)Proposed method (%)NTU (cross subject)77.0689.96NTU (cross view)83.9591.24Northwestern-UCLA78.8186.96SBU93.5696.69


## 4.1.1. NTU RGB-D Dataset

This dataset consisted of 40 subjects using 3 Kinect V2 cameras to collect 60 kinds of movements, 56,880 video clips, and 3D bone data sequences from −45°, 0° and 45° angles. It includes individual daily training movements (such as rope skipping, running, and squatting), interactive training of characters (such as barbell training, dumbbell training, and elastic belt training), and interactive training of pairs (such as drug ball relay, double flat back stretching, and double cross high-five)In the cross-subject experiment, 40 types of subjects were divided into training and test sets, numbered as 1, 2, 4, 5, 8, 9, 13, 14, 15, 16, 17, 18, 19, 25, 27, 28, 31, 34, 35, 38, and the rest were test sets. In the cross-view experiment, the first camera was selected as the test set, and the rest were training sets.In this section, the accuracy and loss curves corresponding to the training set and test set in the iterative training of cross subject and cross view are shown in Figures6 and 7. It can be seen from Figures 6 and 7 that the accuracy of the model increases with the increase of training times and tends to be stable and the loss value converges when the iteration reaches 220 times. Based on the NTU RGB-D dataset, the accuracy of cross subjects and cross angles obtained by the proposed method and the mainstream method is shown in Table 1.Figure 6
Accuracy and loss values in cross subject.
(a)(b)Figure 7
Accuracy and loss values in cross view.
(a)(b)Table 1
Cross subject and cross view accuracy obtained by each algorithm for the dataset.
DataMethodsCross subject %Cross view %Bone sequenceLiterature [17]51.1953.87Literature [18]67.9673.69Literature [19]78.9188.44Literature [20]85.3390.82Proposed method89.8491.12From Table1, it is clear that literature [17] based on variable parameter related skeletons and dynamic skeletons based on 3D geometric relationships) does not take into account deep space-time information, resulting in low accuracy. Literature [18] mapped joints to 3D space and extracted depth features through 3D CNN, thus effectively improving accuracy to 67.96% and 73.69%. However, it does not consider the time domain information of bone recognition. Literature [19] considered the relative motion trend of interframe and intraframe joint links. However, this method only considers joint characteristics and ignores topological relations, so the accuracy is limited. Literature [20] encodes spatial relations between joints to improve accuracy. However, they lack appearance features, thus limiting recognition ability. The proposed method uses causality as auxiliary information to enhance the graph convolutional network, thus improving the accuracy to 89.84% and 91.12%. It shows that the proposed method has high accuracy in complex scenarios.


## 4.1.2. Northwestern-UCLA Dataset

The Northwestern-UCLA dataset consisted of 1,494 sequences of 10 subjects performing 10 types of exercises: bends, presses, hard pulls, push-ups, planks, squats, pull-ups, pull-ups, dumbbell exercises, and barbell exercises. The dataset was collected from three different perspectives. The first two cameras were training data, and the rest were test data.As shown in Table2, literature [17] assumed that the skeleton was perpendicular to the ground for projection clustering discrimination, ignoring the spatial relationship of the skeleton, resulting in low accuracy. Reference [18] is better than reference [17] because it is based on variable parameter-associated skeleton to represent motions, but it ignores bone dynamic information. Literature [19] obtained 79.72% accuracy by considering the temporal characteristics of joints, but it was difficult to distinguish similar movements due to the lack of appearance information. In literature [20], multiperspective dynamic images are extracted to cope with spatial changes and take appearance features into consideration, but they lack timing features. This method integrates causality and represents important dynamic information of joint effectively, and extracts color texture information based on the heat map to obtain highly separable expression of the motion. The accuracy is improved to 87.95%, which is 8.23% and 2.85% higher than literature [19] and literature [20], respectively. It indicates that the proposed method has high recognition ability under the condition of different perspectives and diversified topics.Table 2
Experimental results of northwestern-UCLA dataset.
DataFeaturesMethodsAccuracy (%)Bone sequenceManual extractionLiterature [17]55.70Spatiotemporal graph convolution networkLiterature [18]75.40Literature [19]79.72Literature [20]85.40Combining causality and spatiotemporal graph convolution networkProposed method87.95


## 4.1.3. SBU Interaction Dataset

The SBU interaction dataset contains the following 5 types of interaction: double squats, double single-leg squats, high-five push-ups, reverse crunches, and boxing, which are divided into 5 cross sets. Four of them were selected as training sets and the rest as test sets. The average value of the verification results of each cross set was taken as the final accuracy.See Figure8 for a comparison of the accuracy of the 5 algorithms. It shows that the accuracy of the proposed method can reach 95.46%, which is more accurate than the other four methods, indicating that the accuracy of the proposed method is relatively high under a small sample dataset.Figure 8
Experimental results of SBU interaction dataset.


## 4.1.4. Ablation Experiment

In order to further verify the effectiveness of the proposed method, based on the above dataset, the influence of the proposed method on accuracy was studied by integrating causality and spatiotemporal graph convolution network (see Table3). As can be seen from Table 3, compared with the spatiotemporal graph convolutional network model, the accuracy of the model in this paper has been improved by 12.90%, 7.29%, 8.15% and 3.13%, respectively. In this model, causal coefficients are added as edge weights, and causality is used as auxiliary information to enhance graph convolutional networks. Therefore, it can better highlight the main joints in the process of human movement, and its effect is far better than other methods.Table 3
Experimental results of different models.
DatasetSpatiotemporal graph convolution network (%)Proposed method (%)NTU (cross subject)77.0689.96NTU (cross view)83.9591.24Northwestern-UCLA78.8186.96SBU93.5696.69


## 4.2. Experiments on the Dataset of Motion Training Posture

The UCF Sports dataset was used, which consists of eight training movements, including running, rope skipping, swimming, swallows, cycling, pull-ups, and planks. These movements are in a real moving environment, showing variations in background, lighting conditions and occlusion, making it a challenging dataset. A sample frame for each motion is shown in Figure9.Figure 9
Sample frames of each motion in the UCF motion dataset. (a) Barbell training. (b) Running. (c) Pull-ups. (d) Jumping rope. (e) Swimming. (f) Cycling. (g) Flying swallow. (h) Plank support.


## 5. Conclusion

Considering the weight of joints in human motion from the perspective of causality, this paper proposes a human motion recognition method combining causality and spatiotemporal graph convolution network. Inspired by the attention mechanism in RNN and CNN, causality is used as auxiliary information in this paper to enhance the graph convolutional network, so as to effectively improve the weight of some joints with strong driving force in the neural network. Experiments on three public motion recognition datasets show that the accuracy of the proposed method is significantly higher than that of the existing mainstream recognition methods. It is proved that the proposed method can effectively learn dynamic features and increase the accuracy of motion recognition. In the future, this paper will try to integrate other modal information, such as RGB and skeleton data, and combine skeleton-based motion recognition and pose estimation methods in a unified framework.



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*Source: 4667640-2022-08-09.xml*