# Precise Recognition Method of Local Fuzzy Features in Sprint Video Images

Authors: Xin Chen
Journal: Advances in Multimedia
 (2022)

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## Abstract

In the acceleration phase, sprinters need to have enough strength to support to better complete technical movements. In order to improve the recognition effect of local features in sprint video images, this paper analyzes the sprint process based on the accurate recognition method of local fuzzy features in video images. Moreover, this paper discusses the camera calibration method, and improves the calibration method according to the camera placement and the problems and requirements in field use to obtain an engineered fast calibration method. According to the simulation research, the accurate identification method of local fuzzy features in sprint video images proposed in this paper can play a certain role in sprint video image recognition.


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## Body

## 1. Introduction

One of the kinematic features of sprint is the presence of air, which means that the athlete needs forward and upward force when kicking off the ground. For the lower body, quick-stretch compound exercises are designed to promote vertical or horizontal acceleration in the athlete. In the current study, we found that different fast-stretching compound training methods have different effects on the rapid strength development of athletes. Some studies have found that because the movement direction of sprint is horizontal, it is inconsistent with the force-generating mode of deep jump practice, and cannot improve the athlete’s straight-line sprint ability. Whether the rapid strength obtained by the athletes through the rapid stretching compound training can be effectively transformed into the ability required for sports, and which exercise methods can more effectively affect the sports performance of sprinters are controversial and worthy of research.Athletes consume a lot of physical energy in the accelerated sprint state, so reducing energy consumption during exercise is the focus of core strength training for sprinters. The human body mainly stores energy in the core area, and the acquisition of swinging power of the upper and lower limbs requires the transmission of energy through the core area of the body. Therefore, through scientific core strength training, the energy transfer time of athletes in the starting stage can be shortened, the instantaneous explosive power can be enhanced, and the athletes can smoothly transition to the mid-running stage. At the same time, stable and strong core muscles can help athletes reduce the energy consumption caused by unnecessary joint swings, and use this energy to generate pace, thereby improving the athlete’s competitive level.Sprinting is the basic project of track and field, and good stability is the key for athletes to achieve excellent results. In the four technical movements of sprinting (starting, accelerating, midway, and sprinting), each stage has a greater impact on stability. High requirements, the core muscle group is an important support for the stability of the body, so core strength training is particularly important. Through training to stimulate the muscles of the trunk, pelvis, and hip joints and various small muscle groups, the core muscle strength of athletes can be enhanced, the stability of the body is also improved [1]. The improvement of stability can enable athletes to maintain body balance during exercise, promote the optimization of force transmission and control, and thus achieve the purpose of improving the level of competition [2].Due to the high intensity of sprint training and competition, it is inevitable that there will be excessive force or insufficient body control, which will lead to sports injuries [3]. According to the survey, injuries of sprinters often occur in the ankle joints, knees, waist, and back, among which the waist and back are in the core area of the body. In the daily training process of sprinting, good core strength training can enhance the strength of the muscles in the core area, maintain the balance and stability of the body, and play a full role with other muscles and joints during running, avoiding the burden of supporting the whole body falling on bones, joints, and skin, and it reduces the likelihood of falls [4]. In addition, core strength training for sprinters can not only improve the contraction strength and speed of the athletes’ body muscles but also activate the deep muscle groups of the athletes to ensure that the athletes are in the best state when they exert force during running. Physical injuries such as sprains, strains, etc., are caused by excessive gravity on a certain part during sports [5].Literature [6] believes that rapid strength is affected by two factors: intramuscular coordination and rapid mobilization of motor units. The proficiency of sports movements is also an influencing factor, and it is necessary to grasp the coordination ability between muscles and within muscles. Literature [7] states that the decisive factor for fast strength is the speed of muscle contraction, and the maximum strength, muscle type, and coordination ability between muscles, and external stimuli affect the maximum muscle contraction speed per unit time. Literature [8] believes that the coordination between muscles in the motor center, high-frequency stimulation, the composition of H-type fibers, and the energy supply of phosphate are the physiological factors that determine the rapid force. Literature [9] concluded in the study of improving the explosive power of long jumpers that absolute muscle strength and movement center regulation are the main factors affecting explosive power, and jumping and deep jumping exercises are an effective training method for developing explosive power.In the above studies, most scholars have found the importance of intramuscular coordination and rapid recruitment of motor units. The fast-stretching compound training can not only increase the rapid recruitment of motor units but also improve the control ability of the neuromuscular system and improve the coordination ability between muscles. It is an effective means to develop the rapid strength of athletes.Literature [10] believes that the absorption and utilization of elastic energy and the regulation of neural reflexes by muscles are the key factors affecting fast strength. Therefore, the key for athletes to improve fast strength is whether they can make full use of elastic energy to exert their best sports performance. In addition, the main influencing factors of training are: training method, training load, interval time, etc. Literature [11] believes that age, gender, hormone effects, strength training, etc., are all important factors affecting fast strength. Literature [12] believes that fast strength is related to physiological factors such as muscle type and innervation, and training factors such as training practice skills, practice time, and training methods. Literature [13] believes that the body can increase the mobilization and activation frequency of motor units during high-load training, which is beneficial for the improvement of neural adaptability. Therefore, in rapid strength training, training methods with higher load intensity should be used.Sports injury is a dilemma that every athlete will encounter in training and competition. Once a sports injury occurs, it will delay training or competition, and will cause certain damage to the athlete’s own body function, which will affect the athlete’s future career development and daily life [14]. Through further research, the problem of sports injuries in athletes is analyzed, so that the muscle layer is not further trained during the training process. However, in the sprint running part of the sprint competition, the lack of coordination between the athlete’s own psychology and body will lead to the problem of insufficient sprint running ability, which is likely to cause injury to the athlete [15]. The reason is that the previous sprint training mode lacked core strength training for athletes, resulting in injuries to athletes. The core strength training is applied to the training of sprinters. Through further training, the muscle layer of the athlete is consciously impacted, so that the muscle layer of the athlete can generate more power after stimulation. It provides strength to achieve movement completion while enabling athletes to avoid sports injuries. At the same time, in core strength training, sprinters can master the training methods and methods, enhance the core ability of athletes, help athletes’ own sprint movement patterns, and make athletes’ sprint training and competition more enjoyable [16].This paper analyzes the process of sprint by combining the method of accurate identification of local fuzzy features of video images, which provides technical support for sprinters to better participate in competitions and training.


## 2. Recognition of Local Fuzzy Features in Video Images

### 2.1. Research on Fast Calibration Method

The establishment and calibration of the camera model is an important step for coordinate positioning measurement using the principle of binocular vision.According to the pinhole camera model, the mapping relationship between the image plane coordinate system, the camera coordinate system, and the world coordinate system is expressed as a formula by using the method of transmission matrix. Among them, the rotation matrixR and the translation matrix T are expressed by formulas. For the convenience of analysis, the above formula can be comprehensively expressed as(1)ZC⋅uv1=MXWYWZW1.Among them,M is the projection matrix, which is a matrix of 4×4, and it can be expressed as(2)M=m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44,M is substituted into formula (1), and after sorting and eliminating ZC, a linear equation system can be obtained as shown in formula (3):(3)um34+uXWm31+uYWm32−uZWm33=XWm11+YWm12+ZWm13−m14,vm44+vXWm41+vYWm42−vZWm43=XWm21+YWm22+ZWm23−m24.It can be known from formula (3) that when the matrix M is determined, the mapping relationship w between the feature points (u,v) on the image surface and the coordinate XW,YW,ZW in the space can be determined. M is the product of the three matrices in the formula, which depends on the internal and external parameters of the camera. We can obtain these parameters by observing the multiplied matrix in the formula, including the physical size of the image plane center coordinate u0,v0 pixel in the axial direction dx, dy, and the focal length of the camera f, which are the internal parameters of the camera. It also includes three translation vectors Sx,Sy,Sz that determine the translation matrix and three rotation angles α,β,γ that determine the rotation matrix, which are the external parameters of the camera.


### 2.2. Simplified Measurement Model Based on Actual Usage Conditions

The formula gives a universal model for any camera placement. There are many unknown parameters in the calibration process, and the calibration is difficult. In the process of practical application, certain angles can be fixed by the limitation of mechanical structures and other devices, so that the measurement model is simplified. The coordinate positioning system mentioned in this paper is equipped with a three-point rotary leveling device. By leveling, the pitch angleβ and the tilt angle γ of the camera can be approximately 0. At this point, the rotation matrix R can be simplified as(4)R=cosα0−sinα010sinα0cosβ.The transformation relationship between coordinate systems can be further expressed as(5)ZC⋅XY1=f0000f000010⋅cosα0−sinαcosαSx−sinαSz010Sysinα0cosαsinαSx+cosαSz0001⋅XWYWZW1.Among them,X, Y are the coordinates of the coordinates in the image plane coordinate system, which can be expressed as(6)X=u−u0×dx,Y=v−v0×dy..At this time, the determination of the camera measurement model is only related to the camera’s internal parameter focal lengthf, external parameter selection angle α, and translation vector Sx,Sy,Sz.


### 2.3. Calibration Equation Derivation

The above simplified measurement model is expanded, and the following equations can be obtained:(7)fcosαXw−fsinαZw+fcosαSx−sinαSz=zcX,fYW+fSy=zcY,sinαXw+cosαZw+sinαSx−cosαSz=Zc.The first equation is combined with the third equation, and the following equation can be obtained by eliminatingZc:(8)f−XtgαXw−ftgα+XZw+f−XtgαSx−ftgα+XSz=0.The unknown model parameters in this equation include the horizontal rotation angleα and the camera focal length f. When the image surface feature points and space objects and their coordinates determined by the two mapping relationships are known, the unknown parameters can be solved in the form of simultaneous equations.Two objects with known geodetic coordinates are used to obtain unknown parameters of the camera. Within the monitoring area, two targets are placed as known points. Its geodetic coordinates are represented asXW1,ZW1,XW2,ZW2, the corresponding abscissas of the image plane are x1,x2 and x1〈x2, and the expression equation of the parameters to be calibrated is shown in formula (9):(9)f=−a1a2+b1b2x1−x2+a1a2+b1b22x1−x22−4a1b2−a2b12×x1×x22×a1b2−a2b1,α=−a1a2−b1b2x1−x2+a1a2−b1b22x1−x22−4a1b2−a2b12×x1×x22×a1b2−a2b1.Among them, there isa1=Xw1−Sxb1=Zw1−Sz,a2=Xw2−Sxb2=Zw2−Sz.In order to realize the camera calibration in the above derivation, the photoelectric target needs to be placed in a suitable position in the monitoring area. As a known point, the optimal position of the target is selected by using the principle of error analysis. Among them, the translation vector is obtained by measuring with a total station after adding a triangular prism directly above the camera lens. At the same time, the camera parameters are calibrated by substituting formula (9).It has been known that the clever choice of points can determine the ease of calibration. The origin of the geodetic coordinate system as a known point can make the calibration equation the simplest. In order to facilitate the description of the position of the object, we take the center of the monitoring area as the origin, and the true north direction as the positive direction of theX-axis to establish a geodetic coordinate system. XW=ZW=0 can be obtained. We set the coordinates of the monitoring area center in the image as u, and the coordinates of the monitoring area center in the image plane coordinate system are read. We set x0=u−u0, formula (8) is simplified to formula (10):(10)f−x0tgαSx−ftgα+x0Sz=0.Then, the expression of the horizontal rotation angleα is shown in formula (11)(11)α=fSx−x0SzfSz+x0Sx.According to formula (11), the simplified calibration method only needs to measure the two translation vectors of the camera relative to the center of the monitoring area and the image plane coordinates of the center of the monitoring area to complete the calibration. Compared with the method of using two targets to calibrate the horizontal declination angle of the optical axis of the camera and the focal length of the camera, this calibration method is simpler and easier to implement. However, a coordinate positioning error caused by a focus error occurs. Since the calibration method before the improvement has a higher level of accuracy, in the following, the calibration method is called fine calibration, and the improved calibration method is called fast calibration method.


### 2.4. Translation Vector Measurement Method

In order to realize the improved calibration method, the translation vector in the calibration equation needs to be measured. In the early stage of the system’s use, a method of measuring the translation vector with a reflective prism and a geodetic instrument was proposed. We install a triangular reflector above the camera at the front-end measuring station, the geodetic instrument is placed in the center of the monitoring area, the reflector is aimed, and the translation vector is measured.When it is used in the field, it is found that it is difficult to realize the method of measuring the translation vector by using the reflective prism with the geodetic instrument. On the one hand, the long distance makes it difficult to aim, and it is easy to produce human error. On the other hand, the use of reflective prisms is limited due to the strong on-site light. In order to overcome the problems brought by the environment of the system, a method for solving the translation vector using GPS is proposed in this paper. The method uses GPS receiver to measure the longitude and latitude information of the front-end measuring station and the center of the monitoring area, and substitutes the longitude and latitude coordinates into the angle and distance calculation formula to obtain the translation vector.For the convenience of calculation, a Cartesian coordinate system as shown in Figure1 is established with the true north direction as the positive direction of the X-axis. C1,C2 is the location of the camera, L is the distance between the camera and the center of the monitoring area, and θ is the angle between the camera and the center of the monitoring area and the X-axis. Then, the translation vector can be expressed as:(12)Sx=L×cosθ,Sz=L×sinθ.Figure 1
Schematic diagram of translation vector.After the latitude and longitude coordinates of the front-end measurement station and the center of the monitoring area are obtained by GPS, the distance between the camera and the center of the monitoring area and the angle between the line connecting the camera and the center of the monitoring area and the true north direction are calculated by using the longitude and latitude coordinates of the two points, and the translation vector can be obtained. We set the latitude and longitude coordinates of the center of the monitoring area and the camera as (lato, lono), (latc, lonc), the distance asL and the included angle as θ, as shown in formula (13):(13)L=R×arccossinlato×sinlatc×coslono−lonc+coslato×coslatc.Among them,R is the average radius of the Earth.(14)A=arccoscoslato×coslatc+sinlato×sinlatc×coslonc−lono,θ=arccoscoslatc−coslato×cosAsinlatc×sinA.According to the format and characteristics of GPS data transmission, the process of data acquisition is shown in Figure2:Figure 2
Flow chart of GPS data acquisition.The longitude and latitude information measured by the GPS is exchanged with the all-in-one computer through the serial port. The all-in-one computer collects and processes the data obtained by the serial port by loading the serial port communication program. At the same time, the remote wireless transmission of data is carried out to the upper monitoring and control computer through the GPRS module.


### 2.5. Accuracy Analysis and Verification of Rapid Calibration Method

During model simplification, we assume that the camera level isγ=0. However, in fact, although the front-end measuring station is equipped with a leveling device for the camera, it cannot guarantee the absolute level of the camera. The positional relationship between the actual image plane coordinate system X′OY′ and the coordinate system XOY used in the calculation is shown in Figure 3. The ideal and actual coordinates of any point P on the image plane are x,y,x′,y′, respectively. From the geometric relationship, it can be known that the relationship between the two sets of coordinates is as shown in the formula:(15)y=xtanγ+y′cosγx′=y′tanγ+x′cosγ.Figure 3
Schematic diagram of the positional relationship between the ideal coordinate system and the actual coordinate system.After finishing, the image plane error caused by assumptionγ=0 is:(16)Δx=x1−cosγ+ysinγ,Δy=y1−cosγ+xsinγ.It can be seen from the above formula that the size of this error is related to the position of pointP. The closer to the center of the image plane, the smaller the error, and the largest at the four corners of the image. For the camera x<4.22mm,y<3.54mm used in this system, when γ<1° is guaranteed, the maximum error on the axis is Δymax<Δxmax<0.64μm, which is about 1/5 pixel. In this system, a single-lens reflex camera is used, and the coordinates are distributed in the paraxial position of the center of the image plane. At the same time, the three-point rotation leveling device equipped with the system is considered, and the error introduced when γ=0 is set in the solution model can be ignored.During the simplification of the measurement model,β=0 is set, which also introduces theoretical errors. If the angle between the object-image connection line and the optical axis is θ, the errors in the x-axis and y-axis directions can be calculated as:(17)Δx=ytanθsinβ,Δy=y1−cosβ.Among them,θ is related to the size of the monitoring area and the distance between the front-end measurement station and the monitoring area. In the system environment used in this paper, there is tanθ<0.2, and it is not difficult to see from the above formula that the image plane error caused by setting β to 0 is mainly related to the longitudinal coordinate. The smaller this error is. When there is β<1°, there is Δxmax<14.69μm and Δymax<0.71μm. Since the system is equipped with a leveling device, and the coordinate position obtained in the actual image is close to the x-axis, the error caused by the simplification of the pitch angle of the measurement model can be ignored.Since the establishment of the coordinate axis is determined by the use requirements, its direction is changed, and theXW,ZW coordinate value will also change, but the eccentricity of the coordinate relative to the center of the monitoring area is fixed. Therefore, the calibration method proposed in this paper is evaluated by analyzing the influence of f on the eccentricity dW=XW2+ZW2, and compared with the calibration method before the simplification.The millimeter-level error in the focal length value is considered, the limit error value of the focal length is substituted into the error analysis equation, andδf1=δf2=2mm is taken to analyze the influence of δf1,δf2 in the simplified calibration method on the measurement results of the eccentricity of each point in the monitoring area. In order to simplify the analysis process, the distance between the two visual sensing units and the center of the monitoring area is set as L1=L2=2000m, and the rotation angle is set as α1=45°,α2=135°. According to the principle of error analysis, it is not difficult to know that the influence of δf1,δf2 on the eccentricity can be expressed as:(18)δZWfi=∂FZ∂fi⋅δfi,δXWfi=∂FX∂fi⋅δfi,δdWfi=∂dW∂XW⋅δXWfi+∂dW∂ZW⋅δZWfi,DdWfi=δdWf12+δdWf22.XW,ZW varies within the range of −200, 200 meters and −400, 400 meters on both sides of the center of the monitoring area, respectively. The eccentricity error δdw caused by δf in the whole monitoring area is not more than 0.5 m, the error of the four corners of the monitoring area is large, and the difference between the points in the whole area is small.From the calibration formula (11), it is not difficult to see that the factors affecting the calibration accuracy also include the measurement error of the distance L and the included angle θ. This error is caused by GPS latitude and longitude measurement errors. The specific parameters of GPS are shown in Table 1. In the case of static measurement, its plane positioning error does not exceed 5 mm. The RTK plane positioning error does not exceed 1 cm, and the coordinate equivalence error caused by the distance L measurement error is expressed by formula (19):(19)δZWLi=∂FZ∂Li⋅δLi,δXWLi=∂FX∂Li⋅δLi,δdWLi=∂dW∂XW⋅δXWLi+∂dW∂ZW⋅δZWLi,DdWLi=δdWL12+δdWL22.Table 1
Accurate recognition effect of local fuzzy features in sprint video images.
NumberFrame recognitionNumberFrame recognition186.391088.67290.851190.60386.531286.56488.101387.77587.651490.47687.131588.50790.091687.19890.611787.33990.641886.69The distance measurement error between the front-end measurement station and the center of the monitoring area has little effect on the coordinate positioning error. In the monitoring area, the center measurement error is the smallest, and the four corner measurement error is the largest. However, when the measurement error ofL is 300 mm, the coordinate positioning error does not exceed 15 mm, and the measurement error of L in this system does not exceed 10 mm. Therefore, the coordinate positioning error caused by the distance measurement error is negligible. The positioning error caused by the included angle can be expressed by formula (20):(20)δZWθi=∂FZ∂θi⋅δθi,δXWθi=∂FX∂θi⋅δθi.(21)δdWθi=∂dW∂XW⋅δXWθi+∂dW∂ZW⋅δZWθi,DdWθi=δdWθ12+δdWθ22.The coordinate positioning error caused by the angle positioning error does not change much in the whole measurement area. When the angle error is less than0.1°, the maximum coordinate positioning error in the monitoring area is less than 10 mm. When the GPS plane distance measurement error is less than 10 mm, the angular positioning accuracy is much higher than 0.1°. Therefore, the coordinate positioning error caused by the angle measurement error can be ignored.According to the principle of error analysis, the above error factors affecting the coordinate positioning accuracy are synthesized, as shown in formulas (4)–(8):(22)δXW2=∂FX∂f12⋅δf12+∂FX∂f22⋅δf22+∂FX∂L12⋅δL12+∂FX∂L22⋅δL22+∂FX∂θ12⋅δθ12+∂FX∂θ22⋅δθ22,δZW2=∂FZ∂f12⋅δf12+∂FZ∂f22⋅δf22+∂FZ∂L12⋅δL12+∂FZ∂L22⋅δL22+∂FZ∂θ12⋅δθ12+∂FZ∂θ22⋅δθ22,DdW=∂DW∂XW2⋅δXW2+∂DW∂ZW2⋅δZW2.In the above, the influence of each factor on the coordinate positioning accuracy is analyzed. Among them, the error caused byL,θ is negligible. Therefore, the error synthesis result in formula (22) is only related to the f error.


## 2.1. Research on Fast Calibration Method

The establishment and calibration of the camera model is an important step for coordinate positioning measurement using the principle of binocular vision.According to the pinhole camera model, the mapping relationship between the image plane coordinate system, the camera coordinate system, and the world coordinate system is expressed as a formula by using the method of transmission matrix. Among them, the rotation matrixR and the translation matrix T are expressed by formulas. For the convenience of analysis, the above formula can be comprehensively expressed as(1)ZC⋅uv1=MXWYWZW1.Among them,M is the projection matrix, which is a matrix of 4×4, and it can be expressed as(2)M=m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44,M is substituted into formula (1), and after sorting and eliminating ZC, a linear equation system can be obtained as shown in formula (3):(3)um34+uXWm31+uYWm32−uZWm33=XWm11+YWm12+ZWm13−m14,vm44+vXWm41+vYWm42−vZWm43=XWm21+YWm22+ZWm23−m24.It can be known from formula (3) that when the matrix M is determined, the mapping relationship w between the feature points (u,v) on the image surface and the coordinate XW,YW,ZW in the space can be determined. M is the product of the three matrices in the formula, which depends on the internal and external parameters of the camera. We can obtain these parameters by observing the multiplied matrix in the formula, including the physical size of the image plane center coordinate u0,v0 pixel in the axial direction dx, dy, and the focal length of the camera f, which are the internal parameters of the camera. It also includes three translation vectors Sx,Sy,Sz that determine the translation matrix and three rotation angles α,β,γ that determine the rotation matrix, which are the external parameters of the camera.


## 2.2. Simplified Measurement Model Based on Actual Usage Conditions

The formula gives a universal model for any camera placement. There are many unknown parameters in the calibration process, and the calibration is difficult. In the process of practical application, certain angles can be fixed by the limitation of mechanical structures and other devices, so that the measurement model is simplified. The coordinate positioning system mentioned in this paper is equipped with a three-point rotary leveling device. By leveling, the pitch angleβ and the tilt angle γ of the camera can be approximately 0. At this point, the rotation matrix R can be simplified as(4)R=cosα0−sinα010sinα0cosβ.The transformation relationship between coordinate systems can be further expressed as(5)ZC⋅XY1=f0000f000010⋅cosα0−sinαcosαSx−sinαSz010Sysinα0cosαsinαSx+cosαSz0001⋅XWYWZW1.Among them,X, Y are the coordinates of the coordinates in the image plane coordinate system, which can be expressed as(6)X=u−u0×dx,Y=v−v0×dy..At this time, the determination of the camera measurement model is only related to the camera’s internal parameter focal lengthf, external parameter selection angle α, and translation vector Sx,Sy,Sz.


## 2.3. Calibration Equation Derivation

The above simplified measurement model is expanded, and the following equations can be obtained:(7)fcosαXw−fsinαZw+fcosαSx−sinαSz=zcX,fYW+fSy=zcY,sinαXw+cosαZw+sinαSx−cosαSz=Zc.The first equation is combined with the third equation, and the following equation can be obtained by eliminatingZc:(8)f−XtgαXw−ftgα+XZw+f−XtgαSx−ftgα+XSz=0.The unknown model parameters in this equation include the horizontal rotation angleα and the camera focal length f. When the image surface feature points and space objects and their coordinates determined by the two mapping relationships are known, the unknown parameters can be solved in the form of simultaneous equations.Two objects with known geodetic coordinates are used to obtain unknown parameters of the camera. Within the monitoring area, two targets are placed as known points. Its geodetic coordinates are represented asXW1,ZW1,XW2,ZW2, the corresponding abscissas of the image plane are x1,x2 and x1〈x2, and the expression equation of the parameters to be calibrated is shown in formula (9):(9)f=−a1a2+b1b2x1−x2+a1a2+b1b22x1−x22−4a1b2−a2b12×x1×x22×a1b2−a2b1,α=−a1a2−b1b2x1−x2+a1a2−b1b22x1−x22−4a1b2−a2b12×x1×x22×a1b2−a2b1.Among them, there isa1=Xw1−Sxb1=Zw1−Sz,a2=Xw2−Sxb2=Zw2−Sz.In order to realize the camera calibration in the above derivation, the photoelectric target needs to be placed in a suitable position in the monitoring area. As a known point, the optimal position of the target is selected by using the principle of error analysis. Among them, the translation vector is obtained by measuring with a total station after adding a triangular prism directly above the camera lens. At the same time, the camera parameters are calibrated by substituting formula (9).It has been known that the clever choice of points can determine the ease of calibration. The origin of the geodetic coordinate system as a known point can make the calibration equation the simplest. In order to facilitate the description of the position of the object, we take the center of the monitoring area as the origin, and the true north direction as the positive direction of theX-axis to establish a geodetic coordinate system. XW=ZW=0 can be obtained. We set the coordinates of the monitoring area center in the image as u, and the coordinates of the monitoring area center in the image plane coordinate system are read. We set x0=u−u0, formula (8) is simplified to formula (10):(10)f−x0tgαSx−ftgα+x0Sz=0.Then, the expression of the horizontal rotation angleα is shown in formula (11)(11)α=fSx−x0SzfSz+x0Sx.According to formula (11), the simplified calibration method only needs to measure the two translation vectors of the camera relative to the center of the monitoring area and the image plane coordinates of the center of the monitoring area to complete the calibration. Compared with the method of using two targets to calibrate the horizontal declination angle of the optical axis of the camera and the focal length of the camera, this calibration method is simpler and easier to implement. However, a coordinate positioning error caused by a focus error occurs. Since the calibration method before the improvement has a higher level of accuracy, in the following, the calibration method is called fine calibration, and the improved calibration method is called fast calibration method.


## 2.4. Translation Vector Measurement Method

In order to realize the improved calibration method, the translation vector in the calibration equation needs to be measured. In the early stage of the system’s use, a method of measuring the translation vector with a reflective prism and a geodetic instrument was proposed. We install a triangular reflector above the camera at the front-end measuring station, the geodetic instrument is placed in the center of the monitoring area, the reflector is aimed, and the translation vector is measured.When it is used in the field, it is found that it is difficult to realize the method of measuring the translation vector by using the reflective prism with the geodetic instrument. On the one hand, the long distance makes it difficult to aim, and it is easy to produce human error. On the other hand, the use of reflective prisms is limited due to the strong on-site light. In order to overcome the problems brought by the environment of the system, a method for solving the translation vector using GPS is proposed in this paper. The method uses GPS receiver to measure the longitude and latitude information of the front-end measuring station and the center of the monitoring area, and substitutes the longitude and latitude coordinates into the angle and distance calculation formula to obtain the translation vector.For the convenience of calculation, a Cartesian coordinate system as shown in Figure1 is established with the true north direction as the positive direction of the X-axis. C1,C2 is the location of the camera, L is the distance between the camera and the center of the monitoring area, and θ is the angle between the camera and the center of the monitoring area and the X-axis. Then, the translation vector can be expressed as:(12)Sx=L×cosθ,Sz=L×sinθ.Figure 1
Schematic diagram of translation vector.After the latitude and longitude coordinates of the front-end measurement station and the center of the monitoring area are obtained by GPS, the distance between the camera and the center of the monitoring area and the angle between the line connecting the camera and the center of the monitoring area and the true north direction are calculated by using the longitude and latitude coordinates of the two points, and the translation vector can be obtained. We set the latitude and longitude coordinates of the center of the monitoring area and the camera as (lato, lono), (latc, lonc), the distance asL and the included angle as θ, as shown in formula (13):(13)L=R×arccossinlato×sinlatc×coslono−lonc+coslato×coslatc.Among them,R is the average radius of the Earth.(14)A=arccoscoslato×coslatc+sinlato×sinlatc×coslonc−lono,θ=arccoscoslatc−coslato×cosAsinlatc×sinA.According to the format and characteristics of GPS data transmission, the process of data acquisition is shown in Figure2:Figure 2
Flow chart of GPS data acquisition.The longitude and latitude information measured by the GPS is exchanged with the all-in-one computer through the serial port. The all-in-one computer collects and processes the data obtained by the serial port by loading the serial port communication program. At the same time, the remote wireless transmission of data is carried out to the upper monitoring and control computer through the GPRS module.


## 2.5. Accuracy Analysis and Verification of Rapid Calibration Method

During model simplification, we assume that the camera level isγ=0. However, in fact, although the front-end measuring station is equipped with a leveling device for the camera, it cannot guarantee the absolute level of the camera. The positional relationship between the actual image plane coordinate system X′OY′ and the coordinate system XOY used in the calculation is shown in Figure 3. The ideal and actual coordinates of any point P on the image plane are x,y,x′,y′, respectively. From the geometric relationship, it can be known that the relationship between the two sets of coordinates is as shown in the formula:(15)y=xtanγ+y′cosγx′=y′tanγ+x′cosγ.Figure 3
Schematic diagram of the positional relationship between the ideal coordinate system and the actual coordinate system.After finishing, the image plane error caused by assumptionγ=0 is:(16)Δx=x1−cosγ+ysinγ,Δy=y1−cosγ+xsinγ.It can be seen from the above formula that the size of this error is related to the position of pointP. The closer to the center of the image plane, the smaller the error, and the largest at the four corners of the image. For the camera x<4.22mm,y<3.54mm used in this system, when γ<1° is guaranteed, the maximum error on the axis is Δymax<Δxmax<0.64μm, which is about 1/5 pixel. In this system, a single-lens reflex camera is used, and the coordinates are distributed in the paraxial position of the center of the image plane. At the same time, the three-point rotation leveling device equipped with the system is considered, and the error introduced when γ=0 is set in the solution model can be ignored.During the simplification of the measurement model,β=0 is set, which also introduces theoretical errors. If the angle between the object-image connection line and the optical axis is θ, the errors in the x-axis and y-axis directions can be calculated as:(17)Δx=ytanθsinβ,Δy=y1−cosβ.Among them,θ is related to the size of the monitoring area and the distance between the front-end measurement station and the monitoring area. In the system environment used in this paper, there is tanθ<0.2, and it is not difficult to see from the above formula that the image plane error caused by setting β to 0 is mainly related to the longitudinal coordinate. The smaller this error is. When there is β<1°, there is Δxmax<14.69μm and Δymax<0.71μm. Since the system is equipped with a leveling device, and the coordinate position obtained in the actual image is close to the x-axis, the error caused by the simplification of the pitch angle of the measurement model can be ignored.Since the establishment of the coordinate axis is determined by the use requirements, its direction is changed, and theXW,ZW coordinate value will also change, but the eccentricity of the coordinate relative to the center of the monitoring area is fixed. Therefore, the calibration method proposed in this paper is evaluated by analyzing the influence of f on the eccentricity dW=XW2+ZW2, and compared with the calibration method before the simplification.The millimeter-level error in the focal length value is considered, the limit error value of the focal length is substituted into the error analysis equation, andδf1=δf2=2mm is taken to analyze the influence of δf1,δf2 in the simplified calibration method on the measurement results of the eccentricity of each point in the monitoring area. In order to simplify the analysis process, the distance between the two visual sensing units and the center of the monitoring area is set as L1=L2=2000m, and the rotation angle is set as α1=45°,α2=135°. According to the principle of error analysis, it is not difficult to know that the influence of δf1,δf2 on the eccentricity can be expressed as:(18)δZWfi=∂FZ∂fi⋅δfi,δXWfi=∂FX∂fi⋅δfi,δdWfi=∂dW∂XW⋅δXWfi+∂dW∂ZW⋅δZWfi,DdWfi=δdWf12+δdWf22.XW,ZW varies within the range of −200, 200 meters and −400, 400 meters on both sides of the center of the monitoring area, respectively. The eccentricity error δdw caused by δf in the whole monitoring area is not more than 0.5 m, the error of the four corners of the monitoring area is large, and the difference between the points in the whole area is small.From the calibration formula (11), it is not difficult to see that the factors affecting the calibration accuracy also include the measurement error of the distance L and the included angle θ. This error is caused by GPS latitude and longitude measurement errors. The specific parameters of GPS are shown in Table 1. In the case of static measurement, its plane positioning error does not exceed 5 mm. The RTK plane positioning error does not exceed 1 cm, and the coordinate equivalence error caused by the distance L measurement error is expressed by formula (19):(19)δZWLi=∂FZ∂Li⋅δLi,δXWLi=∂FX∂Li⋅δLi,δdWLi=∂dW∂XW⋅δXWLi+∂dW∂ZW⋅δZWLi,DdWLi=δdWL12+δdWL22.Table 1
Accurate recognition effect of local fuzzy features in sprint video images.
NumberFrame recognitionNumberFrame recognition186.391088.67290.851190.60386.531286.56488.101387.77587.651490.47687.131588.50790.091687.19890.611787.33990.641886.69The distance measurement error between the front-end measurement station and the center of the monitoring area has little effect on the coordinate positioning error. In the monitoring area, the center measurement error is the smallest, and the four corner measurement error is the largest. However, when the measurement error ofL is 300 mm, the coordinate positioning error does not exceed 15 mm, and the measurement error of L in this system does not exceed 10 mm. Therefore, the coordinate positioning error caused by the distance measurement error is negligible. The positioning error caused by the included angle can be expressed by formula (20):(20)δZWθi=∂FZ∂θi⋅δθi,δXWθi=∂FX∂θi⋅δθi.(21)δdWθi=∂dW∂XW⋅δXWθi+∂dW∂ZW⋅δZWθi,DdWθi=δdWθ12+δdWθ22.The coordinate positioning error caused by the angle positioning error does not change much in the whole measurement area. When the angle error is less than0.1°, the maximum coordinate positioning error in the monitoring area is less than 10 mm. When the GPS plane distance measurement error is less than 10 mm, the angular positioning accuracy is much higher than 0.1°. Therefore, the coordinate positioning error caused by the angle measurement error can be ignored.According to the principle of error analysis, the above error factors affecting the coordinate positioning accuracy are synthesized, as shown in formulas (4)–(8):(22)δXW2=∂FX∂f12⋅δf12+∂FX∂f22⋅δf22+∂FX∂L12⋅δL12+∂FX∂L22⋅δL22+∂FX∂θ12⋅δθ12+∂FX∂θ22⋅δθ22,δZW2=∂FZ∂f12⋅δf12+∂FZ∂f22⋅δf22+∂FZ∂L12⋅δL12+∂FZ∂L22⋅δL22+∂FZ∂θ12⋅δθ12+∂FZ∂θ22⋅δθ22,DdW=∂DW∂XW2⋅δXW2+∂DW∂ZW2⋅δZW2.In the above, the influence of each factor on the coordinate positioning accuracy is analyzed. Among them, the error caused byL,θ is negligible. Therefore, the error synthesis result in formula (22) is only related to the f error.


## 3. Accurate Recognition Method of Local Fuzzy Features in Sprint Video Images

The attitude measurement system is mainly divided into three modules: first, the data acquisition module; second, the data processing module; and third, the upper computer software module. The data acquisition module is mainly composed of the Optitrack system. Its main function is to collect the coordinate information of the marker points pasted on the model for subsequent attitude calculation, etc., and can output the collected marker point information in real time to realize the dynamic measurement of the model state. The data processing module mainly processes the data collected by the Optitrack system, and converts the collected coordinate information of the marked points into the rudder surface declination angle, attitude angle, attack angle and sideslip angle of the model. The upper computer software module is mainly responsible for managing the attitude measurement system, ensuring the safety of the system, realizing the real-time output of the data collected by the Optitrack system by communicating with the Motive software, and realizing the real-time display of the model parameters processed by the data processing module. The overall design of the system is shown in Figure4.Figure 4
Overall design scheme of the system.In order to make the system run stably and the experimental results accurate, the experiments are carried out through the following steps. First of all, this paper starts the video acquisition system to start shooting the venue, selects the picture with better lighting conditions and less noise as the background image, and then sets a time stamp to mark the target image of the athlete. Flowchart of moving target detection is shown in Figure5.Figure 5
Flowchart of moving target detection.By deploying the network cloud platform, the system allows users to access the web server to watch the game online through the PC and mobile phones installed with browsers. Considering the security of game data, the system deploys the server behind the firewall, and deploys the online service system in a distributed manner to ensure the experience of multiplayer online viewing and the stable operation of the server. The deployment of the back-end database server can be flexibly arranged according to actual needs. When the system is used by coaches and athletes to discuss and analyze game strategies, it can be deployed in the local area network, which not only reduces the cost of updating and maintaining servers and data but also ensures the security of game data. The architecture diagram of the network cloud platform is shown in Figure6.Figure 6
Architecture diagram of the network cloud platform.On the basis of the above system, this paper applies the system to the accurate recognition of local fuzzy features in sprint video images. In this paper, the motion video of sprint is obtained through the network (Figure7), and it is used as input into the simulation platform of this paper, and the feature recognition image is obtained as shown in Figure 8.Figure 7
Motion video frame extraction of sprint.Figure 8
Motion video feature recognition of sprint.Based on the above analysis, this paper verifies the effect of the accurate recognition method of local fuzzy features in sprint video images proposed in this paper, and the results shown in Table1 and Figure 9 are obtained through multiple sets of simulations.Figure 9
Statistical diagram of accurate recognition effect of local fuzzy features in sprint video images.It can be seen from the above research that the accurate identification method of local fuzzy features in sprint video images proposed in this paper can play a certain role in sprint video image recognition.


## 4. Conclusion

The training mode of sprinters is dominated by the explosive core strength training mode. This mode stimulates certain muscle groups to enhance the explosive power of sprinters, allowing sprinters to start and sprint better with explosive power. In particular, in sprint running, the athlete can win the sprint race through the input of strength. When an athlete performs an accelerated sprint, the core muscle group needs to work in coordination. The stronger the core muscle group, the more stable it is, and the faster it can be achieved when running on the ground. Core strength training can improve the physical function of sprinters, increase the strength of core muscle groups, and improve the athletic level of athletes. This paper analyzes the sprint process by combining the accurate recognition method of local fuzzy features of video images. The research shows that the accurate identification method of local fuzzy features in sprint video images proposed in this paper can play a certain role in sprint video image recognition.



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*Source: 7037814-2022-07-06.xml*