Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching

The literature mainly studies the posture of the human arm. The video is used to obtain the parameters of the arm's posture. The particle filter algorithm is used as the weight of the sampling points to approximate the condition density. The approximate weights are randomly updated by Monte Carlo. Next, is to predict the random motion of the particles and measure the range of particle motion to extract the posture of the human arm. The literature introduced annealing particle swarm optimisation method into the analysis of human motion posture. First, the captured 3D parameters are reduced by PCA to obtain a low-dimensional compact attitude space. Second, the fitness function is constructed using human silhouette features in low-dimensional space to measure the similarity between the model and image features. Finally, the annealing particle swarm optimisation algorithm is used to improve the analysis efficiency [5] as (1) E(yt,xt)=S×((1−β)BtBt+Yt+βRtRt+Yt) E\left( {{y_t},{x_t}} \right) = S \times \left( {\left( {1 - \beta } \right){{{B_t}} \over {{B_t} + {Y_t}}} + \beta {{{R_t}} \over {{R_t} + {Y_t}}}} \right) where R_t is the silhouette area of the human body in the calculated image, B_t is the projected area of the model and Y_t is the overlap area of the two.

This method first needs to establish a corresponding representation model of the human body, and then map the model into a 2D image, and express the similarity between the model and the image data by some evaluation function. First, in the model selection and establishment stage, a good model representation can approximate the human body in an image. For example, the human skeleton is represented by a stick figure. In the method of least square curve fitting, the law of human motion is approximated by the obtained polynomial coefficients [6]. First, calculate the function f (t) = a₀t + a₁ of the discrete coordinate data point x_i,y_i,z_i as a function of time. To determine the approximate trend of the function, expect Φ = span{φ₀t,φ₁t, ⋯ , φ_nt} to find the most suitable function f (t) in the coefficient space, that is, (2) s(t)=a0φ0t+a1φ1t+⋯+anφnt s(t) = {a_0}{\varphi _0}t + {a_1}{\varphi _1}t + \cdots + {a_n}{\varphi _n}t The closest function s(t) is the best fit to function B f (t). as shown in Figure 2. Geometrically speaking, this method is to find the sequence of given points and find the curve with the smallest sum of squared distances.

Fig. 2

This type of method does not require modelling in advance, and feature selection is the basic work of attitude analysis. The common features are points, lines, faces, blocks, corners and other more complex features. For example, the centroid of the human body is used as a pose feature to represent the orientation of the frame where it is located, and the centroid position of the person in the next frame is estimated by changing the centroid position [7].

With the continuous progress and development of computer hardware facilities, motion capture devices are becoming more and more commercialised. Different companies have relatively different configurations of motion capture devices, but in general, relatively classic capture devices often include the following components:

Sensor: In the motion capture system, the sensor is a kind of tracking equipment that is firmly set in the key part of the moving target. The motion capture device can capture the displacement, speed and angle of a moving object through the physical signals sent by the sensor. There are usually different requirements for the number of sensors for different inspection sites of different inspection objects. For example, to capture the movement of the human body, the demand for sensors is usually relatively small. For tracking research such as gesture capture, more sensors are needed [8].

This article studies the optical capture system, which is the first practical optical capture product in China—Dongfangxin DIMS9100. The system uses multiple near-infrared high-sensitivity cameras, and uses the ‘S/D three-dimensional space calibration algorithm’ developed independently to improve the real-time 3D data. The main hardware equipment of the system includes a high-speed 3D data capture workstation, a DIMS controller, a dedicated near-infrared high-sensitivity camera, a high-sensitivity marking point, a high-precision 3D static and a dynamic calibration rod, as shown in Figure 3. The main operation flow of the system is shown in Figure 4 [9].

Fig. 3

Fig. 4

In this paper, an optical motion capture system is used to achieve the acquisition of motion data, to establish a database of human motion pose models and skeleton models. The basic flow is as shown in Figure 5.

Fig. 5

Motion posture analysis is the process of tracking, capturing, acquiring and analysing the features of the human body to obtain the relevant parameters. Through the effective combination of motion analysis and teaching, the teaching system can be more personalised and special. It can also decompose the performance of the performers in detail, and gradually demonstrate each dance movement. The parameters obtained are helpful for quantitative analysis of the movement posture, providing good help for more scientific and intelligent dance teaching [10].

In order to better analyse the movement status of dance performers, a method of analysing human motion poses by using the principle of feature plane similarity matching is proposed. This method simplifies the traditional calculation of Euclidean distance based on multiple identification points to base on calculation of the feature plane feature vector and its included angle. In this paper, the identification points of 21 key parts are simplified into seven feature planes to calculate the difference and correlation of motion. After verification, this method can quickly and effectively analyse human movement posture and apply it to dance teaching to improve the efficiency of dance teaching. The specific process is as shown in Figure 6, where the main steps of the analysis process include as follows:

Step 1. Real-time acquisition of skeleton data: The optical motion capture method is used to acquire the dance action sequence in real-time, and the coordinates of each identification point of the human model in the space coordinate system are stored.

Fig. 6

The similarity matching of human poses is a measure of the pose difference or similarity between different human bodies. The most used method is the traditional Euclidean distance measurement.

The traditional 3D model similarity matching is based on Euclidean distance, and its calculation methods are as follows: (3) D=sqrt((x1−x2)2+(y1−y2)2) D = sqrt\left( {{{\left( {{x_1} - {x_2}} \right)}^2} + {{({y_1} - {y_2})}^2}} \right) (4) D=sqrt((x1−x2)2+(y1−y2)2+(z1−z2)2) D = sqrt\left( {{{\left( {{x_1} - {x_2}} \right)}^2} + {{({y_1} - {y_2})}^2} + {{({z_1} - {z_2})}^2}} \right) where X₁ = (X₁₁,X₁₂,X₁₃,⋯,X_1n), X₁ = (X₂₁,X₂₂,X₂₃,⋯,X_2n) is n-dimensional data. Every two marking points can be calculated by the formula based on the Euclidean distance. If the difference is less than the threshold, which is set by the coach, the two marking points are considered to be similar. If the difference is greater than this threshold, the two identification points are considered to be dissimilar. Comparison of the track of the same marked point between the standard action and the action are measured, as shown in Figure 7 [11].

Fig. 7

The direct comparison method based on the traditional Euclidean distance is to compare the moving trajectories of two moving targets. During the comparison of each action sequence, the corresponding distance difference is obtained, and the degree of data matching is calculated according to a preset threshold. However, this method not only has a large amount of calculation, but also depends on the inherent characteristics of the test object. When the object's body proportion, such as height, weight and weight changes, the distance between the marking points also changes accordingly and must be repeated in the settings and calculations. Therefore, the strict requirements for moving objects limit the use of traditional methods, which not only greatly reduces the computational efficiency, but also lacks universality [12].

This article uses a motion capture system to extract a human skeleton model. First, a feature plane can be determined based on three feature points, and 21 identification points on the human motion posture skeleton are converted into 7 feature planes as basic calculation planes. Each feature plane represents various parts of the human body, as shown in Figure 8. Seven feature plane normal vectors (V₁ ∼ V₇) are extracted on the feature plane to determine the difference in the overall direction of the motion pose. Second, the local normality of the motion pose plane is determined by the angle (θ₁ ∼θ₇) of the feature plane edge vector. In addition, the feature plane edge vector and the trunk included angle (θ₈ ∼ θ₁₂) in the vertical direction (V_{s tan d}) considers the local relationship between the limb and the torso. In this way, a two-tuple 〈V, θ 〉 is used as the input of the model similarity calculation, and the correlation parameter of 〈V, θ〉 is used as the output. This method effectively solves the calculation errors caused by the inherent characteristics of the object to be measured, and reduces the calculation complexity, thereby improving the efficiency and stability of the human posture analysis [13].

Fig. 8

According to the normative requirements of dance movements and the relative range of movement of the human skeleton, the feature vectors of the main movement parts of the human body and their included angles are specified as shown in Tables 1 and 2:

The movement direction of the limbs and limbs can be determined by the inner product of the limb feature plane P_m (m = 1,2,3,4), the normal vector V_m (m = 1,2,3,4) and the vertical vector V_{s tan d} of the trunk to determine the direction of movement, and the angle θ_m (m = 1,2,3,4) to accurately determine the regularity of limb movement.

The angle between the feature plane edge vector and the vertical direction is used to determine the relationship between the limbs and the trunk joints, and the connection angle is determined as shown in Table 3:

In this paper, the cosine similarity method is used as the similarity function. This method can not only measure the degree of difference between vectors, but also measure the similarity and difference between angles. According to the angle cosine of the product of the two vectors in space, the difference between the feature vectors can be measured. The calculation method is as follows: (5) θ〈i,j〉=arccos(similarity(Vi,Vj)) {\theta _{\left\langle {i,j} \right\rangle }} = \arccos \,\left( {similarity\left( {{V_i},{V_j}} \right)} \right) The effective movement range θ_〈i,j〉 between the feature vectors and the value range [θ_min,θ_max] are used to judge the standard and formativeness of the dance movement amplitude. If θ_〈i,j〉 < θ_min or θ_〈i,j〉 > θ_max, then the corresponding limb movement is wrong and the next operation cannot be performed. If θ_min ≤ θ_〈i,j〉 ≤ θ_max, then the corresponding limb movement is within the discriminable range, that is, the next operation is performed.

Because there are individual differences between human bodies, such as different problems such as height, weight and arm length, the proportion of human bodies is constant. Therefore, it is necessary to measure whether the limb's motion amplitude meets the standard through the similarity of the angles. The calculation method is as follows: (6) Corr(θ〈i,j〉)=1−(arccos(similarity(Vi,Vj))π) Corr\left( {{\theta _{\left\langle {i,j} \right\rangle }}} \right) = 1 - \left( {{{\arccos \,\left( {similarity\,\left( {{V_i},{V_j}} \right)} \right)} \over \pi }} \right) Taking the movement of the left arm of the dance trainer as an example, and taking the characteristic plane P1 of the left arm as the basic calculation plane, three discriminative parameters {Sim(V₁,V_{s tan d}),Corr (θ₁),Corr (θ₈)} can be obtained, and the overall posture of the left arm can be determined based on the above three parameters. Experiments show that the calculation error is effectively reduced. The results are shown in Table 4 [15].