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3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System

Publié en ligne: 15 Jul 2022
Volume & Edition: AHEAD OF PRINT
Pages: -
Reçu: 26 Jan 2022
Accepté: 17 Mar 2022
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Format
Magazine
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2444-8656
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01 Jan 2016
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2 fois par an
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Abstract

Visualization software provides powerful numerical calculations for the 3D mathematical modeling process. This paper uses optical motion capture mathematical modeling technology to track and detect dancers' dance movements in segments in real-time. The research results found that the visual dance choreography system proposed in the article improves the efficiency of posture analysis and real-time analysis improves the quality of teaching. This has played an important role in the digital teaching of dance movements and the development of science.

Keywords

MSC 2010

Introduction

At present, motion capture technology is widely used in film and television production, medical rehabilitation, animation games, and other fields, achieving the perfect combination of three-dimensional virtual world and reality technology. In recent years, researchers have conducted extensive research on the application of motion capture. Some scholars combined motion capture technology with Chinese puppet shows and proposed technical solutions for the digitalization of puppet shows [1]. Some scholars use the motion capture system to study golfers' hip and torso movements during the swing and calculate the relationship between the torso and hip movements and the swing. This provides theoretical support for the scientific training of golf. Some scholars have developed a virtual basketball training system using motion capture technology. Users can train their free-throw courses through the system. Some scholars have proposed animation production methods and processes based on motion capture technology and elaborated on the animation synthesis and elimination of sliding steps in the animation production process [2]. According to the normal range of motion of the human joints, the motion posture of the main joints of the human body is studied. Some scholars have proposed a method of simulating human body motion posture. This method can use the human body motion data to drive the virtual human body model. Motion capture technology can facilitate coaches to correct students' movements through real-time analysis and processing of motion data. The traditional comparison method generally uses the Euclidean distance method to calculate the distance between two moving nodes to determine the similarity of the two-channel data. However, this method requires an action time sequence of equal length, and the coordinate displacement caused by the height, fat, or thinness of the students will cause the calculation result to shift greatly.

This paper uses optical motion capture mathematical modeling technology to track and detect dancers' dance movements in segments in real-time [3]. The research results found that the visual dance choreography system proposed in the article improves the efficiency of posture analysis and real-time analysis improves the quality of teaching. This has played an important role in the digital teaching of dance movements and the development of science.

3D data acquisition for motion capture

The motion capture system directly processes the data by the computer. According to the principle, motion capture can be divided into four types: mechanical motion capture, acoustic motion capture, electromagnetic motion capture, and optical motion capture. The optical motion capture system gives performers enough space to perform to their heart's content. It is not limited by space and mechanical equipment and can capture high-speed motions or objects. In this paper, an optical motion capture system is used to obtain 3D motion data, which can build models and skeleton databases [4]. It fully realizes high-precision real-time 3D motion data capture. Then we use the three-dimensional space coordinates of the key points to obtain the motion characteristics of the model and finally realize the analysis of the human body posture (Figure 1).

Figure 1

Three-dimensional motion data capture process

Near-infrared high-sensitivity digital camera captures human movement

The experimental research mainly uses an optical motion capture system. The system uses dedicated near-infrared high-sensitivity digital cameras distributed in the space to capture the performers' movements in real-time [5]. The article transfers the captured actions to the computer to generate virtual objects. This article uses eight high-precision cameras and cables to connect with the DIMS controller in the laboratory scenario. The camera resolution is 5.03 million pixels, and the maximum acquisition frequency is 120fps. The commonly used acquisition frequency is 60fps, and the gray level is 10bitparallel. Equipped with a standard 3–18mm variable focal length lens. We use a marker ball with a diameter of 25mm to capture human limbs.

Three-dimensional motion data capture

We use an optical motion capture system to acquire data. First of all, the performers must wear monochrome clothing with 21 markers on key parts and stand within the pre-set movement space. Start the high-precision 3D motion capture software and set the specified time. Volunteers filmed designated dance moves as required and used cameras to capture and track the movement of 21 marker points.

Then save the captured 3D motion data. Export the animation file to the data editing software and save it as a TRC file. Finally, use MotionBuilder to match the captured and edited human motion data of the 21 marker points with the actor model. Activate the 21 landmark data to complete the matching with the actor and save the model in FBX format. In this way, the establishment of the database of the human body motion posture can be completed.

Human body motion posture analysis based on feature vector matching

Human motion analysis is an important content in computer vision research, and it is also a frontier content that computer researchers pay attention to [6]. Simulating the movements of real performers requires data support. Demonstrate each dance movement step by step to facilitate quantitative analysis. This provides scientific assistance for sports teaching (Figure 2). The main steps of the analysis process include:

Acquire skeleton data in real-time. The dance action sequence is acquired in real-time utilizing optical motion capture, and the coordinates of the marker points of the human body model in the world coordinate system are stored.

Analysis of the different degrees of characteristic posture. Use the calculated feature correlation coefficients to analyze the differences and accuracy of dance movements among students.

Figure 2

Method flow chart

Obtain skeleton data in real-time

In this paper, feature points are used to calibrate the joint points of the human body, and the human skeleton is regarded as a multi-rigid body-connected model. The movement of the human body is a complicated process. Without considering the effects of muscles, the nervous system, etc., human motion can be abstracted as a simple chain system motion connected by a part of a rigid body (Figure 3). We use CoorJoint to represent the absolute position coordinates of the feature point in the world coordinate system [7]. The upper limb is composed of two rigid bodies connected by the elbow joint. The lower limbs are composed of two rigid bodies, the thigh and the calf connected by the hip joint. The knee joint connects the thigh and calf. The head, torso, and hips also represent a rigid body with a line of joint points.

Figure 3

Human skeleton and model diagram

Three-dimensional human action similarity matching algorithm

Similarity measurement is involved in pattern recognition and computer vision. This is used to measure the difference or similarity between different objects [8]. The movement data curve of each marked point in the movement trajectory of the mark point is independent of each other. The traditional Euclidean distance measurement method is used to calculate the similarity between the landmark points, which cannot truly reflect the accuracy of the comparison.

Traditional 3D model similarity matching

For two-dimensional and three-dimensional spaces, the calculation formulas of Euclidean distance are as follows: D=sqrt((x1x2)2+(y1y2)2) D = sqrt\left( {{{\left( {{x_1} - {x_2}} \right)}^2} + {{\left( {{y_1} - {y_2}} \right)}^2}} \right) D=sqrt((x1x2)2+(y1y2)2+(z1z2)2) D = sqrt\left( {{{\left( {{x_1} - {x_2}} \right)}^2} + {{\left( {{y_1} - {y_2}} \right)}^2} + {{\left( {{z_1} - {z_2}} \right)}^2}} \right) Among them: x1 = (x11, x12, x13, ⋯, x1n), x2 = (x21, x22, x23, ⋯, x2n) is n dimensional data. The difference between the two landmark points can be obtained through the calculation formula based on the Euclidean distance for every two landmark points. If the obtained difference is less than the threshold θsin gle (set by the coach), the two landmark points are similar. If If the difference is greater than this threshold, it is considered that the two marker points are not similar. Figure 4 compares the trajectory of the same mark point of the standard action and the action to be measured.

Figure 4

Comparison of motion trajectories in a single direction between single marker points

Similarity calculation based on feature plane matching

The similarity between the dance performer and the standard movement in this article can be attributed to the geometric shapes between objects. Three feature points are known to determine a feature plane, and the skeleton of the human body pose is mainly composed of seven feature planes (Figure 5). This paper uses the angle relationship between the vectors between the joint points to evaluate the degree of difference between the dancer's movement and the standard movement [9]. The human body uses the spine as the main axis, the spine as the z-axis of the spatial rectangular coordinate system, and the x-axis and y-axis of the horizontal plane are the ground planes of the motion capture device. The formal analysis of human motion can be simplified by comparing the similarity of the side vectors of the same plane and comparing the similarity of the normal vectors between planes.

Figure 5

Plan view of human bone features

The main postures of the human body include:

Movement of the limbs. Let's take the left arm as an example. Comparing the swing amplitude of the left arm's elbow can compare the similarity between the side vector VLLarm and the side vector VLFarm of the left arm plane P1. The swing amplitude between the arm and the body can be compared to the correlation between the vertical direction Vs tan d and the vector VLFarm. The change in the direction of rotation of the arm uses the normal plane vector V1 of the left arm and the vertical direction tan Vs tan d as the inner product.

Head movement. We compare the normal vector V5 of the plane P5 with the vertical standing direction Vs tan d. When the human body looks straight ahead, the V5 and tan Vs tan d directions are parallel.

Chest exercises. It mainly compares the transformation angle between the spine direction vector V6 and the vertical standing direction Vs tan d when making a rotating motion.

Hip movement. When the human body stands upright, the hip plane P7 remains horizontal. Its normal plane vector V7 is parallel to the vertical direction Vs tan d.

This paper uses cosine similarity as the similarity function. By measuring the cosine of the angle between the inner product of two vectors in space, the difference between them can be measured. Compared with the Euclidean distance metric, cosine similarity pays more attention to the difference in direction between two vectors. The calculation method is as follows: similarity(θi)=t=1nAt×Btt=1n(At)2×t=1n(Bt)2 similarity\left( {{\theta _i}} \right) = {{\sum\limits_{t = 1}^n {{A_t} \times {B_t}} } \over {\sqrt {\sum\limits_{t = 1}^n {{{\left( {{A_t}} \right)}^2}} } \times \sqrt {\sum\limits_{t = 1}^n {{{\left( {{B_t}} \right)}^2}} } }} θi is the joint angle. At, Bt is the edge vector of the corresponding feature plane. The calculated cosine value is [0, 1]. If the value is close to 1, the dancer's movements are consistent with the standard movements, and the dance is standard. If the value is close to 0, it indicates that the dancer's movement to be tested deviates. Cosine similarity can measure the difference in direction between vectors and measure the similarity and difference between angles. Although there are individual differences between the human body, there are different problems such as height, weight, arm length, etc., but the proportion of the human body is certain. Therefore, the similarity of the angles can also measure whether the limbs' motion amplitude meets the standard. The calculation method is as follows: corr(A,B)=1(arccos(similarity(θi))π) corr\left( {A,B} \right) = 1 - \left( {{{\arccos \left( {similarity\left( {{\theta _i}} \right)} \right)} \over \pi }} \right) According to equations (3) and (4), the correlation parameters of the main action posture at the arm are calculated. We compare the key action correlation parameters of the object to be tested with the standard action, and the results are shown in Tables 1 and 2.

Related parameters of the standard posture of the left arm.

Timing Sim (V2, Vstand) Corr (VLLarm, VLFarm) Corr (VLFarm, Vstand)
0–1s 0.6442 0.9365 0.9586
1–2s 0.7004 0.9623 0.9956
2–3s 0.7257 0.9726 0.9659
3–4s 0.7126 0.9759 0.9546
4–5s 0.6897 0.9588 0.9849
5–6s 0.6416 0.9659 0.9546
6–7s 0.5659 0.9588 0.9659
7–8s 0.7258 0.9649 0.9785
8–9s 0.6896 0.9876 0.9416
9–10s 0.6585 0.9659 0.9755

Related parameters of the left arm's posture to be measured.

Timing Sim (V2, Vstand) Corr (VLLarm, VLFarm) Corr (VLFarm, Vstand)
0–1s 0.6357 0.9433 0.9576
1–2s 0.6958 0.9613 0.9879
2–3s 0.7253 0.9715 0.9646
3–4s 0.711 0.9698 0.9559
4–5s 0.6906 0.8399 0.9848
5–6s 0.6506 0.9648 0.9547
6–7s 0.5998 0.9498 0.9646
7–8s 0.7199 0.965 0.9689
8–9s 0.6826 0.9798 0.9398
9–10s 0.6595 0.9698 0.9698
Calculation of the difference between feature poses

In this experiment, dance music is performed under the same rhythm to ensure that the two groups complete the same dance moves in the same period [10]. First, two groups of people complete an action simultaneously and calculate the correlation coefficient corr for each part of the action. Secondly, the relative error method is used to calculate the correlation coefficient error. The calculation method is as follows: Δcorrt=|corricorrj|corri% \Delta cor{r_t} = {{\left| {cor{r_i} - cor{r_j}} \right|} \over {cor{r_i}}}\% t is the time point of the dance movement. corr is the relative coefficient of the standard dance movement. corrj is the relative coefficient of the dance moves to be tested. The basis for judging the action standard is to calculate the relative error of the correlation coefficient. The condition for error convergence is ΔcorrtC \Delta cor{r_t} \le C C is the selected error threshold. It can modify the corresponding error threshold according to the teacher's requirements for dance movements. According to formula (5), the relative error is calculated to indicate the degree of deviation of the dance movements of the test objects from the standard movements. The calculation results are shown in Table 3.

The relative error/% of the main action posture of the object to be tested.

Timing Sim(V2,Vstand) Corr(VLLarm,VLFarm) Corr(VLFarm,Vstand)
0–1s 1.32 0.72 0.11
1–2s 0.65 0.10 0.77
2–3s 0.05 0.11 0.13
3–4s 0.22 0.63 0.14
4–5s 0.13 12.54 0.01
5–6s 1.41 0.11 0.01
6–7s 5.65 0.95 0.13
7–8s 0.82 0.01 0.99
8–9s 1.02 0.79 0.19
9–10s 0.15 0.40 0.58
Analysis of experimental results

The movement database created in this experiment contains 18 sets of dance movement clips. Each set of dance moves is about 600 frames. The subjects of the experiment were randomly selected, college students. The subjects all have a dance foundation. First of all, the subjects were asked to imitate the standard movements of the dance teacher and make corresponding dance movements under the optical motion capture system. We extracted the motion characteristics of the joint points of the subject's left arm [11]. We take a local motion sequence captured in real-time as an example to analyze the difference between the main motion changes of the object to be measured and the standard motion. This article mainly compares the final movement of the left arm in a single dance movement (within 0~10s).

In the experiment, the error threshold is set to. The part that does not meet the threshold is screened out by comparing the feature posture difference degree. The subject's elbow bending in the 4th to 5th interval and the swing amplitude of the left arm in the 6th to 7th interval was significantly different from the normal movement [12]. This paper uses the characteristic plane as the basic calculation plane to calculate three discriminant parameters. Figure 6 shows the difference comparison chart of the left arm movement posture. The figure shows that the difference between the action to be tested and the standard action can be seen.

Figure 6

Timing diagram of related parameters of left arm motion (0~10s)

The two data groups are directly compared with the traditional three-dimensional model similarity comparison method based on Euclidean distance. Persons under the test of different heights, fats, thinners, and different human body proportions will have deviations in the model's displacement self. If the movement position of the person to be measured is not specified, it will often lead to excessive spatial displacement deviation. The motion posture analysis method based on feature plane similarity matching can clearly and efficiently detect the differences and norms between moving objects. It has high robustness. This provides scientific theoretical support for dance scientific training.

Conclusion

This paper proposes a human pose analysis method based on similarity matching between feature planes. First, an optical motion capture system collects the dance performer's motion sequence in real-time. In this way, the human skeleton data is obtained, and the human motion model is established. Then use the feature plane similarity matching method to calculate the correlation matching degree of the motion data. Finally, this method is used to realize the real-time analysis of the posture of the moving human body and effectively apply it to dance teaching. The experimental data verifies that the method has good accuracy for real-time analysis of human posture and is of great significance to the realization of digital dance teaching. At the same time, this also laid a good foundation for the next step of data retrieval of dance movements.

Figure 1

Three-dimensional motion data capture process
Three-dimensional motion data capture process

Figure 2

Method flow chart
Method flow chart

Figure 3

Human skeleton and model diagram
Human skeleton and model diagram

Figure 4

Comparison of motion trajectories in a single direction between single marker points
Comparison of motion trajectories in a single direction between single marker points

Figure 5

Plan view of human bone features
Plan view of human bone features

Figure 6

Timing diagram of related parameters of left arm motion (0~10s)
Timing diagram of related parameters of left arm motion (0~10s)

Related parameters of the left arm's posture to be measured.

Timing Sim (V2, Vstand) Corr (VLLarm, VLFarm) Corr (VLFarm, Vstand)
0–1s 0.6357 0.9433 0.9576
1–2s 0.6958 0.9613 0.9879
2–3s 0.7253 0.9715 0.9646
3–4s 0.711 0.9698 0.9559
4–5s 0.6906 0.8399 0.9848
5–6s 0.6506 0.9648 0.9547
6–7s 0.5998 0.9498 0.9646
7–8s 0.7199 0.965 0.9689
8–9s 0.6826 0.9798 0.9398
9–10s 0.6595 0.9698 0.9698

Related parameters of the standard posture of the left arm.

Timing Sim (V2, Vstand) Corr (VLLarm, VLFarm) Corr (VLFarm, Vstand)
0–1s 0.6442 0.9365 0.9586
1–2s 0.7004 0.9623 0.9956
2–3s 0.7257 0.9726 0.9659
3–4s 0.7126 0.9759 0.9546
4–5s 0.6897 0.9588 0.9849
5–6s 0.6416 0.9659 0.9546
6–7s 0.5659 0.9588 0.9659
7–8s 0.7258 0.9649 0.9785
8–9s 0.6896 0.9876 0.9416
9–10s 0.6585 0.9659 0.9755

The relative error/% of the main action posture of the object to be tested.

Timing Sim(V2,Vstand) Corr(VLLarm,VLFarm) Corr(VLFarm,Vstand)
0–1s 1.32 0.72 0.11
1–2s 0.65 0.10 0.77
2–3s 0.05 0.11 0.13
3–4s 0.22 0.63 0.14
4–5s 0.13 12.54 0.01
5–6s 1.41 0.11 0.01
6–7s 5.65 0.95 0.13
7–8s 0.82 0.01 0.99
8–9s 1.02 0.79 0.19
9–10s 0.15 0.40 0.58

Lara, R., & Bengochea, A. A Restricted Four-body Problem for the Figure-eight Choreography. Regular and Chaotic Dynamics., 2021; 26(3): 222–235 LaraR. BengocheaA. A Restricted Four-body Problem for the Figure-eight Choreography Regular and Chaotic Dynamics 2021 26 3 222 235 10.1134/S1560354721030023 Search in Google Scholar

Ryu, K. H., Kim, B., Heo, S., Chang, Y. K., & Lee, J. H. Mathematical Modeling of Microalgal Internal Metabolic Behaviors under Heterotrophic Conditions and Its Application. Industrial & Engineering Chemistry Research., 2019; 59(4): 1631–1645 RyuK. H. KimB. HeoS. ChangY. K. LeeJ. H. Mathematical Modeling of Microalgal Internal Metabolic Behaviors under Heterotrophic Conditions and Its Application Industrial & Engineering Chemistry Research 2019 59 4 1631 1645 10.1021/acs.iecr.9b05948 Search in Google Scholar

Portnova, T. V. Spatial function of light in staging of contemporary choreography. Nexo Revista Científica., 2021; 34(01): 346–355 PortnovaT. V. Spatial function of light in staging of contemporary choreography Nexo Revista Científica 2021 34 01 346 355 10.5377/nexo.v34i01.11311 Search in Google Scholar

Zavala, E., Wedgwood, K. C., Voliotis, M., Tabak, J., Spiga, F., Lightman, S. L., & Tsaneva-Atanasova, K. Mathematical modelling of endocrine systems. Trends in Endocrinology & Metabolism., 2019; 30(4): 244–257 ZavalaE. WedgwoodK. C. VoliotisM. TabakJ. SpigaF. LightmanS. L. Tsaneva-AtanasovaK. Mathematical modelling of endocrine systems Trends in Endocrinology & Metabolism 2019 30 4 244 257 10.1016/j.tem.2019.01.008642508630799185 Search in Google Scholar

García, C. Vortex patches choreography for active scalar equations. Journal of Nonlinear Science., 2021; 31(5): 1–31 GarcíaC. Vortex patches choreography for active scalar equations Journal of Nonlinear Science 2021 31 5 1 31 10.1007/s00332-021-09729-x Search in Google Scholar

Autili, M., Chen, L., Englund, C., Pompilio, C., & Tivoli, M. Cooperative Intelligent Transport Systems: Choreography-Based Urban Traffic Coordination. IEEE Transactions on Intelligent Transportation Systems., 2021; 22(4): 2088–2099 AutiliM. ChenL. EnglundC. PompilioC. TivoliM. Cooperative Intelligent Transport Systems: Choreography-Based Urban Traffic Coordination IEEE Transactions on Intelligent Transportation Systems 2021 22 4 2088 2099 10.1109/TITS.2021.3059394 Search in Google Scholar

Gao, L. & Wang, M. The sloshing law of liquid surface for ground rested circular RC tank under unidirectional horizontal seismic action. Applied Mathematics and Nonlinear Sciences., 2021; 6(1): 293–306 GaoL. WangM. The sloshing law of liquid surface for ground rested circular RC tank under unidirectional horizontal seismic action Applied Mathematics and Nonlinear Sciences 2021 6 1 293 306 10.2478/amns.2021.2.00013 Search in Google Scholar

Chuan, M., Jiajia, L., Guangfu, C. & Manglink, R. Evaluation and optimization of insulation status test for primary heating network. Applied Mathematics and Nonlinear Sciences., 2021; 6(1): 181–188 ChuanM. JiajiaL. GuangfuC. ManglinkR. Evaluation and optimization of insulation status test for primary heating network Applied Mathematics and Nonlinear Sciences 2021 6 1 181 188 10.2478/amns.2021.1.00031 Search in Google Scholar

Trad, A. The Business Transformation Framework and Enterprise Architecture Framework for Managers in Business Innovation: An Applied Holistic Mathematical Model. International Journal of Service Science, Management, Engineering, and Technology (IJSSMET)., 2021;12(1): 142–181 TradA. The Business Transformation Framework and Enterprise Architecture Framework for Managers in Business Innovation: An Applied Holistic Mathematical Model International Journal of Service Science, Management, Engineering, and Technology (IJSSMET) 2021 12 1 142 181 10.4018/IJSSMET.20210101.oa1 Search in Google Scholar

Lee, J. S., & Lee, S. H. Automatic path generation for group dance performance using a genetic algorithm. Multimedia Tools and Applications., 2019; 78(6): 7517–7541 LeeJ. S. LeeS. H. Automatic path generation for group dance performance using a genetic algorithm Multimedia Tools and Applications 2019 78 6 7517 7541 10.1007/s11042-018-6493-4 Search in Google Scholar

Doroshenko, A., Tulika, E., & Yatsenko, O. Enhancing parallelism of distributed algorithms with the actor model and a smart data movement technique. International Journal of Parallel, Emergent and Distributed Systems., 2021; 36(6): 565–578 DoroshenkoA. TulikaE. YatsenkoO. Enhancing parallelism of distributed algorithms with the actor model and a smart data movement technique International Journal of Parallel, Emergent and Distributed Systems 2021 36 6 565 578 10.1080/17445760.2021.1971665 Search in Google Scholar

Rallis, I., Bakalos, N., Doulamis, N., Doulamis, A., & Voulodimos, A. Bidirectional long short-term memory networks and sparse hierarchical modeling for scalable educational learning of dance choreographies. The Visual Computer., 2021; 37(1): 47–62 RallisI. BakalosN. DoulamisN. DoulamisA. VoulodimosA. Bidirectional long short-term memory networks and sparse hierarchical modeling for scalable educational learning of dance choreographies The Visual Computer 2021 37 1 47 62 10.1007/s00371-019-01741-3 Search in Google Scholar

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