Three-Dimensional Image Recognition of Athletes' Wrong Motions Based on Edge Detection

During the 3D visual image recognition for athlete motions, the eigenvectors of the athlete should be extracted from the images, and subjected to normalization and dimensionality reduction. On this basis, a 3D visual image recognition model needs to be established to classify and recognize these images. The specific implementation process is as follows:

First, the optimal classification and recognition function of the motion images can be defined as:

$f(x)=\operatorname{sgn}\left\{\left(\omega^{*} \cdot x\right)+a^{*}\right\}=\operatorname{sgn}\left\{\sum_{i=1}^{n} c_{i}^{*}\left(x_{1} \cdot x\right)+a^{*}\right\}$            (1)

where, sgn is a symbolic function; $c^{*}=\left(c_{1}^{*}, \ldots, c_{n}^{*}\right)$ is a Lagrange multiplier; $a^{*}$ is a classification and recognition threshold.

Next, a 3D visual image recognition model can be set up to complete the recognition of athlete motions:

$f{{(x)}^{'}}=\sum\limits_{i=1}^{n}{a_{i}^{*}f(x)K+{{b}^{*}}}$          (2)

where, K is kernel function.

Before applying the model in image recognition, the stepwise discriminant analysis should be performed to measure the contribution of each characteristic variables. The most important variables should be selected for recognition, aiming to optimize the recognition rate.

In sports training, the 3D visual motion amplitude tracking is implemented in the following procedure: locating the extreme points in the amplitude space, acquiring the direction of each amplitude feature point, computing the eigenvector of each feature point, deriving the mapping in the plane of the two cameras, and completing the amplitude tracking. The specific implementation process is as follows:

First, the extreme points in the amplitude space can be identified as:

$\text{D}(x,y,\text{ }\!\!\sigma\!\!\text{ })=\frac{\sqrt{G(x,y,\text{ }\!\!\sigma\!\!\text{ })-(x,y)}\text{ x }I(x,y)}{L(x,y,\text{ }\!\!\sigma\!\!\text{ })}$             (3)

where, $G(x, y, \sigma)$ is the space-variable Gaussian function of the motion amplitude; $(x, y)$ are the coordinates of the amplitude space; $\sigma$ is the amplitude coefficient; $I(x, y)$ are the initial coordinates of the image; $L(x, y, \sigma)$ are the coordinates of the convoluted image.

The extreme points of the 3D visual motion amplitude can be located as:

$\mu \le (R)=[a,b]\frac{R\otimes \text{Ui}}{\text{Ua,b}}\times \text{Umin}\otimes \varpi \text{(W)     }$              (4)

where, $U_{a, b}$ is the Euclidean distance between amplitude feature points a and b; $U_{\min }$ is the minimum distance between amplitude feature points; $U_{i}$ is the secondary interval of motion amplitude; $R$ is the distance threshold between the amplitude feature points; $\varpi(\mathrm{W})$ is the amplitude at the location of each feature point.

The direction of each amplitude feature point can be determined as:

$\eta (Q)=\frac{\text{E(x,y)}\otimes \text{P(x,y)}}{\mu (x,y)}\otimes \varepsilon (p)*K(i)$          (5)

where, $\mu_{(x, y)}$ is the window of cluster center of the amplitude feature points; $P_{(x, y)}$ is the cumulative gradient direction of the amplitude feature points; $E_{(x, y)}$ is the gradient square histogram of the direction of each amplitude feature point; $K_{i}$ is the normalized length of the eigenvector; $\varepsilon(p)$ is the direction vector of the feature point.

The eigenvector of each amplitude feature point can be calculated as:

${{\partial }^{\text{m}}}(x,y,z)=\frac{\varpi (p)\otimes Z(a,b,c)}{A{}^\circ B}\otimes l(o)$           (6)

where, $Z(a, b, c)$ are the feature point coordinates of the $3 \mathrm{D}$ motion space; $A \circ B$ is the azimuth of the feature point plane; $\varpi_{(p)}$ is the spatial attitude of the amplitude feature point.

The mapping in the plane of the two cameras can be obtained as:

$\text{ }\!\!\{\!\!\text{ xpr,ypr,zpr }\!\!\}\!\!\text{ }\frac{\text{Z}\otimes \text{(O1,O2)}}{f\otimes T}\times \frac{(R)}{{{R}^{T}}(\Pr )}\otimes (Tf)$      (7)

where, $O_{1}$ and $O_{2}$ are the optical centers of the two cameras, respectively; $f$ is the focal length of each camera; $\mathrm{T}$ is the focal length between the two cameras; $\mathrm{Z}$ is the distance of the motion amplitude to the plane of the two cameras; $R^{T}$ are the internal and external parameters of the left and right cameras; $P_{r}$ is the internal parameter between the two cameras; $T f$ is the distortion coefficient of each camera.

The 3D visual motion amplitude in sports training can be finalized by the following equation:

$\phi (Vx,Vy)=\frac{v(g)\otimes \{xpr,ypr,zpr\}}{{{\partial }^{m}}(x,y,z)}$             (8)

where, v(g) is the total number of elements in the set of matching points in the amplitude space.

As above, the traditional principles can complete the tracking of 3D motion amplitude in sports training, laying the basis for wrong motion recognition. However, it is impossible to obtain the complete contour feature by these principles, which dampens the recognition accuracy. To solve the problem, this paper proposes a 3D visual image recognition method based on contourlet domain edge detection, and applies it in the recognition of the wrong motions of athletes.

Before the 3D visual recognition of wrong motions, it is necessary to visually reconstruct the human motion image and analyze the visual features of human motions.

The body interaction reconstruction model [17] was established for wrong motion correction in motion recognition. The first step to model construction lies in feature extraction. When the body is in motion, each posture has its unique features. The same motion may be recognized differently with different recognition systems. Here, the visual feature acquisition method was employed to distinguish the wrong motions. The structure feature model of human motions is illustrated in Figure 1 below.

1.png

Figure 1. Structure feature model of human motions

Assuming that the human skeleton in Figure 1 has N joints, the world coordinate systems A and B were constructed based on the Denavit-Hartenberg (D-H) notation [18] for the spatial pose of the mathematical model of the kinematics chain. The D-H method can handle the key steps of the mapping from the Descartes space. The contour features of human motions can be extracted with the structural feature model. The extracted image matrix can be expressed as:

${{E}_{edge}}=[l'{{'}_{mn}}]M\times N$             (9)

To recognize the wrong motions, the characteristic variables of each posture can be calculated as:

$l_{mn}^{''}=\frac{|l_{mn}^{''}-\min \{l_{mn}^{''}\}|}{{{E}_{edge}}},(a,b)\in W$              (10)

where, W is a 3×3 window centered on the edge intensity (m, n). Through the analysis on the structural features of human motions, the background image B of an athlete (x, y)(x∈[0,W-1],y∈[0,H-1]) can be extracted from the background of the human motion image. Then, the background image B and the target image I were divided into (W/2)×(H/2) grids. Each grid can be described as:

$P(i,j)(i\in [0,\operatorname{int}({W}/{2}\;)-1],j\in [0,\operatorname{int}({H}/{2}\;)-1])$              (11)

where, W and H are the width and height of the human motion image, respectively. Each grid was imported to the structural feature model of human motions, and sorted according to the background image, thus completing the visual reconstruction process.

The visual features of the wrong motions were analyzed based on the visual reconstruction. Without changing the meaning of the parameters, the grid pheromone of the edge contour of a single frame in the human motion image can be obtained as:

$\min F(x)=\left(f_{1}(x), f_{2}(x), \ldots, f_{m}(x)\right)^{T}$

s.t. $g_{i} \leq 0, i=1,2 \ldots, q, h_{j}=0, j=1,2, \ldots, p$        (12)

where g_i and h_j are the moments of inertia of the body around the y-axis and the x-axis, respectively; q and p are the length and the width of the motion trajectory network, respectively; f_m(x) is the pixel intensity of the edge corner point.

The grid pheromones were clustered to obtain the wrong feature information of the human motion image, and the feature information was filtered to perform curve segmentation on the wrong motion features. To analyze the wrong amplitude features, it is necessary to set up the following 3D viewpoint switching equations:

$\begin{align}  & \overset{.}{\mathop{{\dot{x}}}}\,=V\cos \theta \cos \Psi ,\text{ }\overset{.}{\mathop{y}}\,=V\sin \theta  \\  & \overset{\cdot }{\mathop{z}}\,=-V\cos \theta \sin {{\Psi }_{v}} \\ \end{align}$           (13)

$\overset{\cdot }{\mathop{\vartheta }}\,={{\omega }_{y}}\sin \gamma +{{\omega }_{2}}\cos \gamma $            (14)

where, x, y, z are the centroid coordinates of the human motion image; ψ_v is the switching angle of the motion region. Figure 2 shows the process of the visual analysis on wrong motions.

2.png

Figure 2. The process of the visual analysis on wrong motions

The visual reconstruction and feature analysis pave the way for 3D visual recognition of the wrong motions of athletes. To enhance the reconstruction effect, the distribution of each modeling point should be obtained by a suitable corner matching method and the motions should be discriminated. Hence, the author proposed a 3D visual recognition method based on the contourlet domain edge detection, which is implemented as follows.

For a grayscale image on human motions g(x, y), a small sub-region $w \in g$ was extracted from the image, and the sub-region image was moved both horizontally and vertically. The displacements are respectively denoted as x and y. The square of the grayscale change through the movement can be computed as:

$g(x, y)=\left\{\begin{array}{ll}b_{0}, & f(x, y)<T \\ b_{1}, & f(x, y) \geq T\end{array}\right.$             (15)

Here, corner feature acquisition of body boundary contour is carried out through scale-invariant feature transform (SIFT). The grayscale of all frames at (x, y) can be calculated as:

$P(i, j)=\left\{\begin{array}{ll}1, & \left|\frac{1}{4}\left[B_{G}-I_{G}\right]\right|-Y_{G} \times g(x, y)>0 \\ 0, & \text { otherwise }\end{array}\right.$        (16)

Next, the contourlet domain edge detection algorithm was designed. The image contourlet domain matrix was established in the form of a Hessian matrix:

$\mathrm{D}=\left[\begin{array}{cc}I_{x}^{2} & I_{x} I_{y} \\ I_{x} I_{y} & I_{y}^{2}\end{array}\right]$           (17)

where, $I_{x}$ is the wrong feature of the human motion image; $I_{y}$ is the vertical amplitude of a motion; $I_{x} I_{y}$ is the correlation between the wrong motion and the correct motion. Through the first-order Taylor expansion, the eigenvector of the contourlet domain can be obtained as:

$\varphi (t)=\lg {{p}_{t}}(1-{{p}_{t}})+\frac{{{H}_{t}}}{{{P}_{t}}}+\frac{{{H}_{L-1}}-{{H}_{t}}}{1-{{P}_{t}}}$            (18)

${{P}_{t}}=\sum\limits_{i=0}^{t}{{{P}_{i}}}$        (19)

The following equation can be obtained from Eqns. (18) and (19):

${{H}_{t}}=-\sum\limits_{i=0}^{t}{{{p}_{i}}\lg {{p}_{i}}}$           (20)

Thus, the grayscale change of the sub-region was converted into two eigenvalues of the structural matrix M(x, y): λ₁ and λ₂. Then, the local structure matrix M was taken as a correlation function, and used to judge whether the detection point (x, y) is a corner point of the image. The judgement was made based on the two eigenvalues in the local structure matrix M. Let p_m(m) be the probability density function of the non-subsampled contourlet transform (NSCT) and p_n(n) be the probability density function of noise. Then, the relationship of the SIFT corner point of the edge feature can be obtained as:

$\frac{{{p}_{m}}(m)}{{{p}_{n}}(n)}=\frac{\partial \cdot \beta }{{{(\partial +\beta )}^{2}}}=\frac{\gamma }{{{(\gamma +1)}^{2}}}$        (21)

where,

$\frac{\gamma }{{{(\gamma +1)}^{2}}}<\frac{{{\gamma }_{0}}}{{{({{\gamma }_{0}}+1)}^{2}}}$          (22)

where, I(x, y) is the grayscale of the edge feature at (x, y); L(x, y, σ) is the information entropy space; G(x, y, σ) is the modal tracking corner information of the edge feature.

Through the above steps, the contour curve of the wrong motions was drawn by the SIFT corner detection algorithm, and the contourlet domain was smoothed, which marks the end of the 3D visual recognition of wrong motions.

This paper designs a 3D visual image recognition method based on contourlet domain edge detection, and applies it to the recognition of athlete’s wrong motions in sports training. Firstly, the visual reconstruction and feature analysis of human motions were carried out, and the edge detection features were extracted by edge detection algorithm. Then, a 3D visual motion amplitude tracking method was proposed based on improved inverse kinematics. The simulation results show that the proposed algorithm can effectively realize the recognition of 3D visual images of athlete motions, and improve the correction and judgment ability of athlete motions.