In recent years, computer image processing capabilities have been continuously improved. The development of computer vision is also maturing. Computer vision application to action recognition in aerobics video images has multiple implications. It can accurately and comprehensively recognize the movement posture of the aerobics in the video. This makes it easy to evaluate it objectively to make suggestions for improvement for the aerobics. Action recognition has gone through a long development process. Gesture recognition, body motion recognition, etc., belong to the low-level human motion analysis. The essence of action recognition in aerobics video images is motion recognition. It belongs to the advanced stage of human motion analysis [1]. The purpose is to analyze, judge, or extract the motion in the video. It can create personalized teaching, training, and virtual simulation systems. Action recognition in aerobics video images is more complex. Our simple limb localization algorithm does not accurately reflect the movements in the aerobics video images. So we need to use mathematical models to help us solve the above problems. The Lagrangian mathematical model can help us establish a model of the body movement characteristics of aerobics athletes.

Suppose we know the trajectories of the end segments of the aerobics in the workspace. At this point, we solve the kinematic parameters of each joint of the aerobics, which is the inverse kinematics problem [2]. The inverse kinematics problem can be regarded as a nonlinear mapping from the workspace to the joint space. The movement speed

^{N}^{6×N} is the Jacobian matrix of the calisthenics body. According to the geometric topology of the body of the aerobics, we can get:

_{L}^{3×N} and _{A}^{3×N} are the linear velocity and angular velocity transfer matrices, respectively. _{j}_{−1} is the unit vector of the

This paper simplifies the human body of aerobics in EVA into four segments: trunk, upper arm, forearm, and hand. The aerobics system has four rotating joints of hip, shoulder, elbow, and wrist rotating joints. The corresponding joint angular displacements are _{1}, _{2}, _{3}, and _{4}, respectively. _{L}_{1}, _{L}_{2}, _{L}_{3}, and _{L}_{4}, according to formula (2) and the calculated spatial pose.

In this way, the Jacobian matrix of this system can be obtained. The joint angular velocity can be obtained by solving equation (1) when the hand's is known.
_{i}_{i}_{i}

The Lagrangian function

_{i}_{i}

_{i}_{ij}_{ij}

The images in the aerobics videos are mostly in color. If we feed the image directly into the computer vision system, it will increase the amount of information in the image input. This will increase the number of subsequent operations [4]. The principle of grayscale processing of color images is to reduce the dimensionality of the three-dimensional channels of the color space RGB. We make it into one dimension. The grayscale process of color images is shown in Figure 1.

There are many methods for grayscale transformation of images, such as single-component method, maximum value method, global mapping method, etc. Different methods apply to different processing objects. Our use of an inappropriate grayscale transformation method will likely result in an unsatisfactory grayscale effect [5]. Therefore, this paper adopts a hybrid grayscale processing method based on image fusion. We use Plass weighting to calculate the local transformation sum of each channel input of R, G, and B. We use the global contrast weighted mapping method to establish the objective function through elements such as gray value and color distance difference. Then this paper obtains the grayscale result by minimizing the objective function. In this paper, this hybrid method can preserve the image's global structural information and local contrast information to the greatest extent. This paper uses this method to grayscale the images in the aerobics video. The effect is shown in Figure 2.

The essence of image thresholding is to segment aerobics images. Its purpose is to compress the data volume of color images and simplify the image analysis steps. It divides the set of pixels according to the grayscale set. Each subset of this set corresponds to an individual aerobics move. Determining an appropriate threshold is critical when we threshold aerobics video images. Because it relates to where the pixels in the image belong [6], only a reasonable threshold can produce a more accurate binary image. The threshold is generally expressed in the following form.

We segment aerobics video images to change the aerobics image representation. This makes the image easier to understand and analyze by computer vision systems. This allows each pixel in the image to have its unique label. The image finally forms a multi-pixel collection [7]. After thresholding the aerobics action image, we need to separate the dancer's motion area from the whole scene to obtain the binary image. This requires segmenting the dancer's motion area, and after determining the appropriate threshold, the edge of the dancer's human silhouette can be found. Assuming that the current moment is

In this paper, a Gaussian mixture model is selected to achieve background subtraction based on the particularity of aerobics video images [8]. The principle is to use K Gaussian models to represent the features of each pixel in the aerobics video image.

Assuming that the value of the pixel at time _{t}

_{i}_{,j} represents the weight of the _{t}_{i}_{t}, _{i}_{,t}) represents its corresponding probability density function. _{i,t}_{i,t}

Assuming that the pixel value of a new input frame of image is _{t}

If this formula condition can be satisfied, it can be judged that the pixel point matches the model. It is the background point, and if it cannot be satisfied, it can be judged that it does not match the model. It is the fore spot [9]. We obtain the effect of background subtraction through the Gaussian model, as shown in Figure 3.

It can be seen from the background removal effect diagram of the Gaussian model that there is noise around the foreground, which will cause interference pulses for the computer vision system to recognize the edge of the target image. Therefore, we can achieve the purpose of protecting the edge of the dancer's body image through the noise reduction operation. In this paper, the median filter method is used to reduce noise. First, we move the template in the aerobics video image until the center of the template coincides with the center pixel in the aerobics video during the movement [10]. This pixel can be used as the center of the window. We use this center to build windows of different shapes, such as squares and circles. Second, we read the grayscale values of all pixels in the window under the template. Then we sort the grayscale values. We are generally arranged in order from smallest to largest. Finally, we calculate the median value of the gray value of the pixel arrangement and use it as the pixel's gray value at the center point of the window. The calculation formula of the output pixel gray value after median filter noise reduction follows.

There is a big difference between the aerobics movements and the daily movements of an ordinary person. When selecting the target area for background recognition, we must master the dancer's whole body movement information to identify its movements accurately. Dancer's action recognition can be divided into several categories: Static features. The main form of expression is the size, color, body contour, depth, etc., of the dancer's human target [11]. We can derive the current basic shape of the dancer through the outline features dynamic features. It is mainly manifested in the dancer's movement, speed, direction, and trajectory. These can reflect the movement path of the dancer. These feature recognition can calculate the movement direction characteristics of the dancer. This creates the conditions for modeling. The spatiotemporal features are mainly represented as shapes, points of interest, etc. Defining features include the scene where the dancer is located, surrounding objects, pose, etc.

When we use the pose feature extraction method, we can use the pose estimation sensor. It can determine the direction of the dancer's movement [12]. In this way, the dancer's joint coordinates area can be obtained. The shadowing and influence of the dancer's clothing and other factors on the dancer's movement can be eliminated. The dancer pose feature map is shown in Figure 4.

The Kinect method regards the human body as a coordinate axis composed of 25 joint point coordinates. We use these joint points to establish the dancer's human skeleton structure to obtain the dancer's human skeleton model (Figure 5).

The joints of dancers are mainly distributed in the limbs. The head, neck, spine, and shoulder center have an articulation point. The most concentrated distribution of joint points is located in the upper limbs. The left upper limb has joints such as the left shoulder, left elbow, left wrist, and left finger. The right upper limb has joints such as the right shoulder, right elbow, right wrist, and right fingers [13]. The left lower limb has joints such as the left hip, left knee, left ankle, and left foot. The right lower extremity has critical points: the right hip, right knee, right ankle, and right foot. The principle is to accurately record the movement of each joint point in the process of dancers doing various movements. In this way, each dancer's movement can be accurately identified to output the correct dancer's motion skeleton. The dancer motion skeleton model can significantly improve dancer movements’ recognition accuracy and efficiency by computer vision systems. The whole identification process is shown in Figure 6.

Aerobics video image recognition should consider the influence of aerobics background, clothing, etc., on action recognition. At the same time, we also need to consider the problem of occlusion and self-occlusion in the aerobics’ movements. We adopt an action recognition technology that can accurately and completely record and reflect the aerobics’ movement information. In this way, the aerobics body's static and action information is obtained. This paper proposes a specific identification method based on the existing research. These methods fit the dancer's movement characteristics. The algorithm proposed in this paper is of great value for video action analysis of aerobics and other applications.

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