Research on contour feature extraction method of multiple sports images based on nonlinear mechanics

: This article solves the issue of long extraction time and low extraction accuracy in traditional moving image contour feature extraction methods. Here authors have explored deformable active contour model to research the image processing technology in scienti ﬁ c research and the application of multiple sports and the method. A B - spline active contour model based on dynamic program - ming method is proposed in this article. This article pro - poses a method of using it to face image processing and extracting computed tomography ( CT ) image data to estab - lish a three - dimensional model. The Lyapunov exponent, correlation dimension and approximate entropy of the non - linear dynamics algorithm were used to extract the features of eight types of motor imagination electroencephalogram ( EEG ) signals. The results show that the success rate of pose reconstruction is more than 97% when the contour extrac - tion quality is relatively ideal. The method is also robust to image noise, and the success rate of pose reconstruction can reach 94% when the video image has large noise. The execution e ﬃ ciency is sub - linear, which can basically meet the requirements of real - time processing in video - based human posture reconstruction. The proposed method has a low error rate in the calculation of curvature features, e ﬀ ectively reduces the time for extracting contour features of moving images, and improves the accuracy of feature information extraction.


Introduction
Contour extraction is an important research topic of computer vision. It has a wide application prospect in virtual reality, autonomous vehicle, robot environment analysis, object tracking, recognition in monitoring system, biomedical image processing, and industrial online automatic detection [1]. The reverse engineering technology has its domain in various fields. In the manufacturing field, reverse engineering is used for physical or model measurement to construct the geometric model of the object, and then used to improve the design and manufacturing. Reverse engineering technology is widely used in scientific research, engineering technology, and biomedical fields. This method helps in solving or helps to solve many problems such as geometric dimension measurement, deformation measurement, vibration mode testing, damage measurement, product quality monitoring, physical copy, computer aided design (CAD)/computer aided manufacturing (CAM), and medical diagnosis [2]. Deformable active contour model has brought new ideas and ways of thinking to traditional computer vision theory and application research, and has developed into one of the most active and successful research fields in computer vision and pattern recognition. Therefore, the study of image processing technology based on deformable active contour model is of great significance in scientific research and engineering application [3]. The basic steps for network parameter modification for computer vision application are provided in Figure 1 [4].

Literature review
Liu et al. used the deformable model to complete the segmentation and reconstruction of the left ventricle in 15 min, which is much less than the 1.5-2 h required by manual sketch [5]. In view of the deficiency that the traditional deformable surface could not accurately delineate the cerebral cortical groove [6], Gaur and Srivastav proposed a deforming surface based on the gradient vector flow force field for the reconstruction of the cerebral cortex, which improved the description of the cerebral cortex [7]. Rega et al. proposed a semi-automatic segmentation method combining user interaction with B-spline Snake (also known as B-Snake), which extracted hepatoma contour from ultrasound images and successfully applied it in the liver tumor surgery simulation system [8].
Nifa et al. proposed a B-spline deformable active contour model based on a dynamic programming method. The B-spline method is the most commonly used method for modeling free-form curves and surfaces, and dynamic programming is an effective method for solving discrete optimization problems. The model adopts the cubic B-spline curve segment controlled by the control point to represent the active contour, and then the control point is used to solve the dynamic programming method to realize the contour extraction of the image [9]. Anakhaev et al. stated that the model combines the advantages of the B-spline method and the dynamic programming method, and can converge to the target contour quickly and stably. The resulting B-spline profiles facilitate further surface reconstruction processing [10]. Rega et al. believed that with the continuous development of pattern recognition and image processing technology, contour feature extraction of moving images has received sufficient attention in the field of related sports [11]. Fischer and Neukamm indicated that the moving image is affected by a specific complex environment, which will cause problems such as blurred contour features and uneven curvature sign feature points [12]. Eremeyev et al. proposed that among the existing moving image contour feature extraction methods, the most widely used is the feature extraction method under threshold constraint. Setting the threshold value can quickly and accurately extract the information that the user is interested in the edge of the image, and it can automatically compensate for the inaccurate extraction caused by factors such as unclear images content [13]. Karaaal et al. proposed an image feature extraction method based on random forest algorithm, which uses the form of mathematical classification to set the threshold of the edge contour content information contained in the image, and adopts the optimized training random forest classification algorithm. The contour threshold is used for mapping and classification processing to achieve image contour feature extraction. However, this method processes the threshold in two parts, which leads to the long extraction time of the feature information of the algorithm [14]. Namnabat et al. proposed an image feature extraction method based on multi-scale fusion. The method uses a Gaussian pyramid to decompose moving images, divides the decomposition results into multi-scale spaces, and sets thresholds based on this to extract moving images' multiscale features. This method has higher recognition rate, but lower segmentation accuracy [15]. Aiming at a series of problems existing in traditional methods, Georgievskii proposed a new feature extraction methoda method for extracting contour feature information of moving images with multithreshold optimization [16]. Ruggeri et al. indicated that the feature boundaries of moving image contours are often blurred. The maximum inter-class variance method combined with the inter-class classification ability can be used to set multiple thresholds for moving image features, and the fuzzy membership function constraints are used to complete the multi-threshold calculation optimization [17]. Zhao et al. transformed the edges of moving images into image blur space according to the gray scale data space, and the moving image contour blur membership function can be replaced by a simpler linear function to obtain a fast and simple threshold [18].

Article contribution
This article solves the issue of long extraction time and low extraction accuracy in traditional moving image contour feature extraction methods. Deformable active contour is a hot research topic in the field of contour extraction. Feature extraction is a key step to ensure classification accuracy. Therefore, this work studies feature extraction methods for eight types of motor imagination tasks. Traditional analysis methods are usually difficult to ensure that data changes are within a controllable range when analyzing nonlinear systems, and at the same time, they cannot explain related problems [4].
With the continuous development of nonlinear dynamics, more and more evidences show that the brain is a nonlinear dynamic system, and the EEG signal can be regarded as its output. The introduction of nonlinear dynamics analysis method in the field of EEG signal processing can well explain the nonlinear characteristics of EEG sequence. Analysis methods of nonlinear dynamics include complexity, fractal dimension, Lyapunov exponent, correlation dimension (CD), etc., [5]. In this work, Lyapunov, CD, and approximate entropy methods were used to extract the features of eight types of motor imagination EEG signals, and the extraction effect of each method was analyzed. The execution efficiency is sub-linear and it can meet the requirements of real-time processing in video-based human posture reconstruction.

Article organization
The rest of this article is organized as: Section 2 presents the image contour features followed by experimental analysis in Section 3. Section 4 presents the concluding remarks of this article.

Methodology for image contour features
The classical snake model uses a set of discrete points to approximate the deformable contour, which will bring three obvious deficiencies. First, in the numerical calculation process, finite difference is used to directly approximate the derivation, resulting in numerical instability and reduced accuracy [19]. Second, the discrete characteristics of the model make the situation between two points on the contour uncertain, and the model lacks robustness. Third, in order to more approximately express the active contour, it is necessary to increase the number of discrete points, which will not only increase the calculation amount, but also cause "collision" between adjacent points in the convergence process, which reduces the operability of the contour [20]. The concept of B-spline was first proposed by Schoenberg in the 1940s: B-spline is a piecewise polynomial of degree K determined by a sequence u: u 0 ≤ u 1 ≤ … u i+k+1 of non-decreasing parameters u called node vector, that is, multinomial spline of degree K. Although scholars have different definition methods for B-spline, we decided to choose Clark's definition method, which has the characteristics of visual and intuitive starting from geometric concept [21]. Clark defines the starting point of B-spline as follows: first, local approximation rather than interpolation is performed on the given point; second, there is a certain continuity requirement between adjacent approximate curve segments. Let P i (t)(i = 1,2,…,n,t, ∈ [0,1]) point column A in the three-dimensional space be approximated by a sequence of curve segments P i (t)(i = 1,2,…,n,t, ∈ [0,1]), we require that the shape of each curve segment is only controlled by a number of sequential points in the point column (V 1 , V 2 ,…,V 4 ), and has the following form (1): Formula (1) is a one-time B-spline basis function [22]. If two basic functions are connected end to end, it is a oneorder B-spline, as shown in Figure 2. Lyapunov index is an important index to measure the dynamic characteristics of a system, which can measure the chaos or convergence between adjacent orbitals in phase space. When the maximum value of Lyapunov exponent is positive, the system is chaotic [23]. When Lyapunov exponents are all negative, the system converges. When the maximum Lyapunov exponent is 0, the system motion is periodic. When two or more Lyapunov exponentials are positive, the system is hyper chaotic. Lyapunov is defined as: take an n-dimensional infinitesimal sphere and let the sphere move along the trajectory with its own points as initial values [24]. Due to local deformation, the sphere will become an n-dimensional ellipsoid where P i (t) is the length of the ith spindle ellipsoid sphere axis at time T , and P i (0) is the initial radius of the ndimensional sphere. So, there is formula (3): From the above derivation, it can be concluded that with the increase in the system dimension, the calculation amount will increase exponentially when calculating Lyapunov exponent [25]. Because the amount of data needed to calculate Lyapunov is very large, the application of Lyapunov is limited to some extent. CD is an extension of traditional dimension and is used to describe the degree of freedom of a system. CD has been widely used in the analysis of nonlinear dynamics. The EEG data collected in this work are one-dimensional sequences, and the phase space of the signal should be reconstructed before the calculation of CD algorithm [26]. The specific steps are as follows: (1) Construct the state space attractor through the singletime series of the original EEG signal, set the embedding dimension to m and the time delay to τ, and then the reconstructed phase space is shown in formula (4): Xn is an element of the original multi-class imaginary EEG data, which contains sampling points [27]. The original multi-class motor imagination EEG data were reconstructed into m-dimensional vectors, and each vector X was the sample value of the original multi-class motor imagination at different moments. Each reconstructed vector forms a subset that can be approximated as the system attractor [28].
(2) Estimate the distance between attractor point pairs, taking Euclidean distance as the unit of measurement [29]. (3) Evaluate the correlation integral C r ( ). Taking a range of neighborhood radius R C r , ( ) can be calculated by the correlation integral of the logarithm of points whose attractor distance is less than r. C r ( ) is defined as formula (5): where θ represents Heaviside function, which is defined in formula (6): where ||V(i) − V(j)|| represents the Euclidean distance between two points. (4) When N approaches infinity, for each R, if the limit of C r ( ) exists, then the fractal number between all state vectors within the neighborhood radius R is formula (7): Then, the CD is defined as formula (8): When R is very small, the CD can be estimated from the slope of log C(r) over log r [30].

Experimental analysis
In this work, the trampoline exercise is chosen as a research example. We used motion capture technology, namely, VICON8, to collect the trampoline instance data of the national team's main athletes, covering all the prescribed and optional trampoline movements, and established a relatively complete trampoline standard action database [31]. In the motion database, human motion is represented by a time-varying function m t ( ), where the value of the function at a certain moment is the human posture at that moment. We used a 3D vector to represent the position of root, and unit quotations to describe the orientation information of root and each joint [32]. The human posture data in the motion database is represented in the coordinate system with root position as the origin.
Thus, in the 3D motion database, 3D human motion can be expressed as (9): , , , where P(t) ∈ R 3 and q 1 (t) ∈ S 3 , respectively, represent the position and (S 2 is the unit quaternion space) of root, and q 1 (t) ∈ S 2 represents the orientation information of each joint center, and n is the number of joint centers plus one [33].
We use contour-based method to reconstruct 3D human posture. First, we use motion segmentation method to extract 2D contour information of human body from video image. A general parameterized virtual human model is used to customize the human model according to the human in the video [34]. Then, the corresponding camera view information is extracted from the motion video, and the personalized human body model is used to conduct behavior driving and 2D projection on the motion data in the 3D motion database under the display view, so as to obtain the 2D human profile library. Finally, contour matching was performed in 2D moving contour database according to the contour similarity criterion to find the contour data with the highest similarity with the video contour to be reconstructed. The 3D attitude information corresponding to the contour is the preliminary reconstruction result. This is the basic idea of human posture reconstruction based on video in this article [35]. The processing process of human posture reconstruction is shown in Figure 3.
In order to further improve the accuracy and calculation efficiency of attitude reconstruction and achieve real-time calculation effect, we use the Earth-Mover's distance (EMD) [PWR89] method to optimize the shape matching method. Meanwhile, for the second nearest neighbor retrieval problem, we use locality-sensitive hashing (LSH) to index the database. It has been proved by practice that the precision and processing efficiency of the reconstruction results have been improved greatly after this series of optimization. Since motion capture data can be collected at a frequency of 120 frames per second, the 3D pose library containing all trampoline motion data is large. In order to ensure the efficiency of reconstruction, it is necessary to cluster the data in the 3D attitude library [36]. At the same time, there is an important characteristic of the air movement type like trampoline, that is, although the height of the center of gravity of the human body is different in many stances, the stances are similar, and such data account for a considerable proportion. We omit the height position of the center of gravity of the attitude, and do c-means clustering on the data, and those data with approximate attitude belong to the same category. In our application, the pre-set initial classification is C 50 = . In our original trampoline motion database, which was collected by our motion capture device, we included all the required and optional actions with a total length of 6,000 frames. This motion database of 6,000 frames is the data source for the 3D human posture reconstruction in this article. We apply the shape matching method based on visual invariants to 3D human pose reconstruction, and experimental results demonstrate its effectiveness. All experiments were carried out on a PC with P4 2.8 G and 512 MB memory.
As can be seen from Table 1, during the reconstruction phase, the total time taken to reconstruct 2,000 frames of data was about 811 s. The average time of single frame processing was 0.415 s. Even with the time of the entire pre-processing phase, the average time of the single frame processing is about 1.60 s. Compared with the Hu moment and AMIs method in the previous section, the computational efficiency is greatly improved.
Human posture reconstruction based on video is a key step in the overall technical framework of this article. In order to further improve the accuracy and computational efficiency of pose reconstruction, in this chapter, we improve and implement a human pose reconstruction method based on EMD.
In order to verify the motion correlation of the reconstructed motion, we extracted the Y-component (height) and the velocity component of the root position of each attitude in the above reconstructed 3D motion sequence to verify the continuity of the reconstructed motion ( Figure 4). It can be seen that the root position and velocity description curves of the reconstructed results have good smooth connectivity, indicating the good motion correlation characteristics of the reconstructed results [37]. Among them, the piecework discontinuity between the describing curves is caused by the fact that we only reconstructed the attitude data of the vacating  part, but omitted the sequence of the contact between the person and the trampoline. We use software Posers to generate the composite video data sequence, and the motion reconstruction of these composite. We added noise processing of closed operation (expansion first, corrosion later) to the contour of the synthesized data, and carried out motion reconstruction of the data after noise processing [38]. For example, we reconstructed a noisy synthesized motion sequence with a length of 440 frames, as shown in Figure 5.
Also, the comparative analysis of traditional and proposed methodology is done as shown in Figure 6 in terms of accuracy and success rate.
Experiments show that after a series of optimization processing, the success rate of pose reconstruction is stable over 97% when the contour extraction quality is relatively ideal. The method is also robust to image noise, and the success rate of pose reconstruction can reach 94% when the video image has large noise. The execution efficiency is sub-linear, which can basically meet the requirements of real-time processing in video-based human posture reconstruction.

Conclusion
The theory and application of deformable models are reviewed. The theoretical research of deformable model is carried out from three aspects: geometric model, scale space, and algorithm realization, and its applications include image segmentation and surface reconstruction. A B-spline active contour model based on DP algorithm is proposed, and the B-spline deformable model is mainly studied for face contour extraction and medical tomography image contour extraction and surface reconstruction. The B-spline active contour model based on DP algorithm can combine the advantages of the two methods, which can quickly and stably converge to the target contour, and the obtained B-spline contour is beneficial to further surface reconstruction and other processing. The Lyapunov exponent, CD, and approximate entropy of the nonlinear dynamics algorithm were used to extract the features of eight types of motor imagination EEG signals, respectively. At present, the image potential energy of the model only contains the information of the object edge. The moving image contour feature pixels extracted by the method in this article are accurate and comprehensive. There are overlapping and missing problems. The calculation error rate of the curvature feature of the method in this article is kept at about 10%, and it has high extraction accuracy. It is revealed from experimentation that the proposed article has low error rate in the calculation of curvature features, effectively reduces the time for extracting contour features of moving images, and improves the accuracy of feature information extraction.  Funding information: The authors state no funding involved.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.