A monocular camera calibration method for badminton game analysis

Abstract

The present invention discloses a monocular camera calibration method for badminton game analysis, comprising the following steps: taking a badminton court as a calibration plate, defining key points on the calibration plate, simplifying a camera intrinsic parameter representation method based on a high-end commercial camera, constructing camera intrinsic parameters according to the camera focal length based on the camera intrinsic parameter representation method, constructing a calibration equation and solving the camera extrinsic parameters, projecting key points based on the camera intrinsic and extrinsic parameters, constructing an error loss function based on the coordinates of the projection points and the coordinates on a key point graph, updating the camera focal length using an optimization algorithm with the goal of minimizing the error loss function, and simultaneously determining globally converged camera intrinsic differences and camera extrinsic parameters in conjunction with visual verification, thereby achieving calibration of the monocular camera and improving calibration accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of camera calibration, and in particular relates to a monocular camera calibration method for badminton game analysis. Background Art

[0002] In the field of artificial intelligence, especially computer vision, tasks such as 3D reconstruction and 3D pose estimation based on RGB images have attracted close attention from researchers, driven by the development of deep neural network research. Since datasets or field data used for model training and validation often lack complete camera intrinsic and extrinsic parameters, 3D vision tasks that rely solely on 2D pixel inputs from RGB images can produce less accurate 3D results even with neural network learning. However, for tasks requiring high precision, such as badminton match video analysis, any functional module that can provide additional feature input to the model will undoubtedly improve the accuracy of the model output. Therefore, camera parameter calibration is particularly important in most computer vision tasks.

[0003] In image measurement and machine vision applications, a geometric model of camera imaging must be established to determine the relationship between the 3D geometric position of a point on a spatial object's surface and its corresponding point in the image. These geometric model parameters are known as camera parameters. In most cases, these parameters must be determined through experimentation and calculation. This process of determining these parameters (intrinsic parameters, extrinsic parameters, and distortion parameters) is called camera calibration.

[0004] Classic camera calibration methods use linear calibration, which ignores camera distortion and only considers spatial coordinate transformations. Each coordinate point has two variables, X and Y, which can be expressed in two equations. The camera's intrinsic parameters have five unknowns, while the extrinsic parameters, translation and rotation, have three unknowns each, for a total of 11 variables. Therefore, at least six feature points are required to solve. For modern commercial high-end cameras, the influence of the distortion matrix is ​​increasingly reduced due to built-in distortion correction devices.

[0005] Commonly used calibration methods generally fall into the following three categories: (1) Traditional camera calibration methods, which rely on calibration objects with known calibration information, such as size determination, feature point group position determination, and three-dimensional spatial position of the calibration object. By establishing a correspondence between the three-dimensional points whose coordinates are determined a priori on the calibration object and the two-dimensional points calculated or calibrated on the image. Obtain the equation group corresponding to the calibration points, and then use the optimization algorithm to estimate the internal and external parameters of the camera. The calibration objects can be divided into three-dimensional calibration objects and planar calibration objects according to their different spatial structures. Traditional camera calibration methods always require calibration objects during the calibration process and have a strong dependence on the selection of calibration information. However, in the analysis of monocular badminton matches, it is impossible to know all the parameters of the broadcast camera, enter the venue to arrange the camera, and even more impossible to pre-make calibration objects for camera calibration. The only input information for the entire calibration process is a single video sequence, and it is impossible to add calibration objects and re-shoot. Therefore, traditional methods cannot be directly used in badminton match analysis scenarios where camera information is limited.

[0006] (2) Active vision camera calibration method, which refers to controlling the camera to perform certain specified actions without the need for calibration objects, and then using the specificity of the predicted action information to calculate the internal and external parameters of the camera. The advantage of the camera calibration method based on active vision is that the algorithm is simple and a linear solution can often be obtained, so it has high robustness. However, the disadvantages are also obvious. The selection of predefined actions greatly increases the complexity of the experiment, the requirements are very high, and the experimental equipment is expensive. It is not suitable for occasions where the position of motion parameters or cannot be controlled. This active vision calibration method relies on a set of camera action sequences with known action information, requiring the camera to move, which is impossible to achieve in badminton monocular video analysis because it is impossible to require the broadcast camera to perform the special actions we have pre-defined.

[0007] (3) Camera self-calibration method, which mainly utilizes some parallel or orthogonal information in the scene. The intersection of spatial parallel lines on the camera image plane is called the vanishing point, which is a very important feature in projective geometry. Therefore, many scholars have studied the camera self-calibration method based on the vanishing point. The self-calibration method is highly flexible and can perform online calibration of the camera. However, since it is based on an absolute quadratic curve or surface, its algorithm robustness and accuracy are very poor. Badminton game analysis requires high-precision model output results, so there are high requirements and reliance on the accuracy of camera calibration parameters. Although the advantages of the camera self-calibration method solve the camera calibration defects in badminton game analysis, its algorithm instability directly leads to the method being unable to meet the high accuracy of the estimated parameters in this scenario. Summary of the Invention

[0008] In view of the above, the object of the present invention is to provide a monocular camera calibration method for badminton game analysis to achieve accurate calibration of the monocular camera.

[0009] To achieve the above-mentioned purpose of the invention, the embodiment provides a monocular camera calibration method for badminton game analysis, comprising the following steps:

[0010] Step 1: Consider the badminton court as a calibration plate, identify key points on the calibration plate with a number greater than 11, and calculate the world 3D coordinates and the map 2D coordinates of each key point;

[0011] Step 2, initialize the camera focal length;

[0012] Step 3: After constructing the camera intrinsic parameters based on the camera focal length, the camera extrinsic parameters are solved based on the camera intrinsic parameters, the world 3D coordinates of all key points, and the 2D coordinates on the map. The key points are projected onto the map based on the camera extrinsic parameters and the camera intrinsic parameters to obtain the projected 2D coordinates of the projected points.

[0013] Step 4: construct an error loss function based on the projected 2D coordinates of the projection points and the image 2D coordinates of the key points, and use an optimization algorithm to update the camera focal length with the goal of minimizing the error loss function until the iteration termination condition is met, thereby obtaining the optimized camera focal length and determining the candidate camera intrinsic parameters and candidate camera extrinsic parameters based on the optimized camera focal length;

[0014] Step 5: Project the world 3D coordinates of all key points onto the map based on the candidate camera intrinsic parameters and candidate camera extrinsic parameters, and observe the reconstructed badminton court generated based on the projection points. When the difference between the reconstructed badminton court and the badminton court used as the calibration plate is within the preset range, the candidate camera intrinsic parameters and candidate camera extrinsic parameters are considered as the final camera intrinsic parameters and final camera extrinsic parameters, otherwise reinitialize the camera focal length and recalculate.

[0015] Preferably, 16 key points are determined on the punctuation board, namely, the 4 vertices of the badminton court, the 4 vertices of the blocking net, the 2 middle points of the two horizontal edge lines distributed on the badminton court, the 4 bisecting points of the two longitudinal edge lines, and the 2 intersection points of the line segment formed by the 2 middle points and the two line segments formed by the 4 bisecting points.

[0016] Preferably, the camera intrinsic parameter K(f) is constructed according to the camera focal length and is expressed as:

[0017]

[0018] Where f represents the focal length of the camera, W and H represent the width and height of the badminton court image.

[0019] Preferably, the camera extrinsic parameters are solved using the following formula based on the camera intrinsic parameters, the world 3D coordinates of all key points, and the 2D coordinates on the image:

[0020]

[0021] Among them, i represents the key point index, N represents the number of key points, represents the world 3D coordinate of the i-th key point, represents the 2D coordinate of the i-th key point on the map, and R is the camera extrinsic parameter to be solved.

[0022] Preferably, the error loss function adopts different distance metric functions, including the Manhattan distance and the square expectation of the Euclidean distance between the projected two-dimensional coordinates of the projection point and the two-dimensional coordinates of the key point on the graph.

[0023] Preferably, the constructed error loss function F is expressed as:

[0024]

[0025] Among them, i represents the key point index, N represents the number of key points, represents the two-dimensional coordinates of the i-th key point on the graph, Represents the projected two-dimensional coordinates of the i-th projection point.

[0026] Preferably, the optimization algorithm includes an unconstrained minimization algorithm, a bounded constrained minimization algorithm or a constrained minimization algorithm, wherein the unconstrained minimization algorithm includes BFGS and trust-ncg; the bounded constrained minimization algorithm includes Nelder-Mead and TNC; the constrained minimization algorithm includes COBYLA and SLSQP.

[0027] Preferably, when the difference between the reconstructed badminton court and the badminton court used as the calibration template is outside a preset gap range, the optimization algorithm is replaced and recalculated according to steps 3-5.

[0028] Compared with the prior art, the present invention has at least the following beneficial effects:

[0029] A badminton court is regarded as a calibration board, and key points are defined on the calibration board. Based on a high-end commercial camera, the camera intrinsic parameter representation is simplified. After constructing the camera intrinsic parameters according to the camera focal length based on the camera intrinsic parameter representation, the calibration equation is constructed and the camera extrinsic parameters are solved. The key points are projected according to the camera intrinsic and extrinsic parameters, and the error loss function is constructed based on the coordinates of the projection points and the coordinates on the key point map. The optimization algorithm is used to update the camera focal length with the goal of minimizing the error loss function. At the same time, the globally converged camera intrinsic and extrinsic parameters are determined with the help of visual verification, thus realizing the calibration of the monocular camera and improving the calibration accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0031] Figure 1 is a flow chart of a monocular camera calibration method for badminton game analysis provided in an embodiment;

[0032] Figure 2 Schematic diagram of 16 key points in a badminton court provided in an embodiment;

[0033] Figure 3 The embodiment provides a globally non-convergent reconstruction of a badminton court generated based on projection points;

[0034] Figure 4 This is a globally convergent reconstructed badminton court generated based on projection points provided by an embodiment. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0036] The principle of monocular camera calibration is as follows:

[0037]

[0038] Parameter explanation: u, v represent the pixel coordinates in the RGB image, the first matrix on the right side of the equal sign is the camera intrinsic parameter matrix and z c The ratio of , where f represents the focal length of the camera in millimeters, dx represents the width of one pixel in the x direction, dy represents the width of one pixel in the y direction, x0, y0 represent the x and y offsets of the principal point offset, z c represents the z-coordinate depth in the camera coordinate system. The units above are all in millimeters. The second matrix is ​​the camera extrinsic parameter matrix, R represents the rotation matrix, and t represents the translation vector. X, Y, and Z represent the coordinates in the world coordinate system.

[0039] In badminton match analysis, we calibrate monocular camera parameters using videos generated from live broadcast footage. While the distortion matrix estimation for broadcast camera calibration is negligible due to the camera manufacturing process, the challenge lies in the fact that the broadcast camera is a black box. Its specifications are unknown, and calibration setup is impossible at the competition venue. Therefore, the input for this task is a single video, and the goal is to calibrate the camera using only this video.

[0040] To achieve monocular camera calibration for badminton game analysis, this embodiment provides a monocular camera calibration method. By improving the traditional camera calibration method, simplifying the calibration equation and constructing a set of court key points, the camera intrinsic and extrinsic parameter matrix is ​​generated. Finally, an adaptive parameter optimization algorithm is used to estimate the camera intrinsic and extrinsic parameter matrix. By traversing the focal length f set and visually reprojecting feature points, visual accuracy verification is achieved.

[0041] Figure 1 FIG. 1 is a flow chart of a monocular camera calibration method for badminton game analysis provided in an embodiment. Figure 1 As shown, the embodiment provides a monocular camera calibration method for badminton game analysis, comprising the following steps:

[0042] Step 1: Consider the badminton court as a calibration plate, determine the key points on the calibration plate with a number greater than 11, and calculate the world 3D coordinates and the 2D coordinates on the map of each key point.

[0043] Since monocular badminton analysis can only be performed on broadcast footage, and the model of the broadcast lens is unknown, calibrating the camera's internal and external parameters using traditional methods is challenging. For example, the classic checkerboard calibration method is impractical due to the inability to set up a checkerboard calibration board on-site. The broadcast lens cannot be moved as required, and the adaptive calibration algorithm is unstable, resulting in low model accuracy. These factors make active visual calibration and self-calibration methods unsuitable for monocular badminton video analysis. While traditional methods cannot pre-place a calibration board, research and analysis revealed that broadcast lenses are typically fixed above the playing field. This offers the possibility of improving traditional methods for monocular camera calibration. Although a calibration board with known calibration parameters cannot be set up on-site, a badminton court can serve as a natural calibration board. Through discussions with professional badminton coaches, a set of key points with invariant features on the badminton court was identified. Since the calibration equation constructed has 11 variables to be solved, 11 key points are required to meet the solution requirements. In the embodiment, 16 key points are selected to be determined on the badminton court, such as Figure 1As shown in the figure, the four vertices of the badminton court, the four vertices of the net, the two midpoints of the two horizontal edge lines of the badminton court, the four bisecting points of the two vertical edge lines, and the two intersection points of the line segment formed by the two midpoints and the two line segments formed by the four bisecting points. By determining the key points on the badminton court, the problem of traditional methods that cannot deploy calibration objects on the court is solved.

[0044] In the embodiment, after the key points are determined, the world three-dimensional coordinates of the key points can be known. At the same time, the center of the badminton court is used as the coordinate origin, and the key points are marked to obtain the two-dimensional coordinates of the key points on the map.

[0045] Step 2: Initialize the camera focal length.

[0046] The camera focal length is considered to be randomly initialized and needs to be updated later in the solution process. In the embodiment, a camera focal length set can be randomly initialized to facilitate the subsequent optimization algorithm selection.

[0047] Step 3: After constructing the camera intrinsic parameters according to the camera focal length, the camera extrinsic parameters are solved according to the camera intrinsic parameters, the world 3D coordinates of all key points, and the 2D coordinates on the map. The key points are projected on the map based on the camera extrinsic parameters and the camera intrinsic parameters to obtain the projected 2D coordinates of the projection points.

[0048] In the embodiment, the ground at the center of the net is used as the origin of the three-dimensional coordinate system. Since the broadcast camera is a high-end commercial camera, the internal distortion correction component almost does not require subsequent distortion correction parameters, and relatively accurate internal and external parameter results can be obtained. Therefore, s in the camera internal parameters can be approximated to 0, and there is no need to consider the distortion correction matrix. y0 represents the position of the optical center, which can be taken as half of the image frame. For example, if the image width is W and the height is H, then x0 can be taken as W / 2 and y0 can be taken as H / 2. For the input image, x0 and y0 are both constants. The broadcast camera often uses square pixel units, that is, dx=dy. Then the estimation of the camera internal parameters can be simplified to the estimation of the camera focal length f / dx, that is, the estimation of the focal length expressed in pixels. The specific simplified formula is as follows:

[0049]

[0050] Based on simplification, the camera intrinsic parameter K(f) is constructed according to the camera focal length and is expressed as:

[0051]

[0052] Among them, f represents the focal length of the camera, and the camera intrinsic parameter K(f) is simplified from 5 parameters to 1 f / d x , constraining the optimization space.

[0053] The calibration equation constructed based on the camera intrinsic parameter K(f) is:

[0054]

[0055] Among them, i represents the key point index, N represents the number of key points, represents the world 3D coordinate of the i-th keypoint, represents the 2D coordinate of the i-th keypoint on the image, and [R / t] is the camera extrinsic parameter to be solved. Based on this calibration equation, the camera extrinsic parameters can be solved based on the camera intrinsic parameters, the world 3D coordinates of all keypoints, and the 2D coordinates on the image.

[0056] In the embodiment, the key points are projected onto the image based on the camera extrinsic parameters and the camera intrinsic parameters to obtain the projected two-dimensional coordinates of the projection points.

[0057] Step 4: Construct an error loss function based on the projected two-dimensional coordinates of the projection point and the image two-dimensional coordinates of the key point. Use an optimization algorithm to update the camera focal length with the goal of minimizing the error loss function until the iteration termination condition is met. The optimized camera focal length is obtained, and the candidate camera intrinsic parameters and candidate camera extrinsic parameters are determined based on the optimized camera focal length.

[0058] In the embodiment, the constructed error loss function adopts different distance metric functions, including the Manhattan distance, the square expectation of the Euclidean distance, etc. between the projected two-dimensional coordinates of the projection point and the two-dimensional coordinates of the key point on the graph.

[0059] Specifically, the constructed error loss function F is expressed as:

[0060]

[0061] Among them, i represents the key point index, N represents the number of key points, represents the two-dimensional coordinates of the i-th key point on the graph, Represents the projected two-dimensional coordinates of the i-th projection point.

[0062] In an embodiment, the optimization algorithm used for optimization solution includes an unconstrained minimization algorithm, a bounded constrained minimization algorithm or a constrained minimization algorithm, wherein the unconstrained minimization algorithm includes BFGS and trust-ncg; the bounded constrained minimization algorithm includes Nelder-Mead and TNC; the constrained minimization algorithm includes COBYLA and SLSQP.

[0063] The optimized camera focal length will be obtained through iterative calculation, and the candidate camera intrinsic parameters and candidate camera extrinsic parameters are calculated based on the optimized camera focal length.

[0064] Step 5: Project the world 3D coordinates of all key points onto the map based on the candidate camera intrinsic parameters and the candidate camera extrinsic parameters, and observe the reconstructed badminton court generated based on the projection points. When the difference between the reconstructed badminton court and the badminton court used as the calibration plate is within a preset range, the candidate camera intrinsic parameters and the candidate camera extrinsic parameters are considered as the final camera intrinsic parameters and the final camera extrinsic parameters. Otherwise, reinitialize the camera focal length or change the optimization algorithm to recalculate.

[0065] After obtaining the candidate camera intrinsic parameters and candidate camera extrinsic parameters, correctness verification is also required. Specifically, the accuracy of the camera internal and external parameters is verified by reprojecting the two-dimensional coordinates of the visual projection points. This step is very critical. Because a gradient descent algorithm similar to a neural network is used, the camera focal length convergence value can only be guaranteed to be a local optimal solution, not a global optimal solution. Therefore, visualization can be used to determine whether the estimated candidate camera intrinsic parameters and candidate camera extrinsic parameters are accurate, such as whether they are full rank. Specifically, the world three-dimensional coordinates of all key points are projected onto the map based on the candidate camera intrinsic parameters and candidate camera extrinsic parameters, and the reconstructed badminton court generated based on the projection points is observed. If the difference between the reconstructed badminton court and the badminton court used as the calibration plate is very small, such as Figure 4 As shown, this shows that the camera focal length solved is the global optimal solution, the candidate camera intrinsic parameters and candidate camera extrinsic parameters obtained are full rank, the candidate camera intrinsic parameters and candidate camera extrinsic parameters obtained are accurate, and can be directly output as the final camera intrinsic parameters and final camera extrinsic parameters. If the reconstructed badminton court is very different from the badminton court used as the calibration template, such as Figure 3 As shown, this shows that the solved camera focal length is a local optimal solution, and the obtained candidate camera intrinsic parameters and candidate camera extrinsic parameters are not full rank. It is necessary to reinitialize the camera focal length and loop through steps 2 to 5, or change the optimization algorithm and loop through steps 3 to 5, or reinitialize the camera focal length and change the optimization algorithm at the same time and then loop through steps 2 to 5 until the model generates a global optimal solution for camera intrinsic parameters and camera extrinsic parameters.

[0066] In the analysis of monocular badminton video matches, the above camera calibration method can be used to complete camera calibration in a nearly black-box scenario. This method requires no camera movement or knowledge of any camera parameters. By using a custom set of court key points and solving optimized calibration equations, a set of highly accurate camera intrinsic and extrinsic parameters is generated. This provides effective camera parameters for subsequent analysis of monocular badminton match videos using 3D pose estimation or ball path tracking. Based on these camera parameters, computer vision algorithms (such as 3D reconstruction and monocular 3D pose estimation) can be further applied to broadcast video analysis to determine specific players' physical parameters, stroke characteristics, and preferred scoring ranges. Finally, badminton players can be provided with opponent data or a player's technical strengths and weaknesses, achieving the goal of intelligently facilitating badminton competitions.

[0067] It should be noted that the monocular camera calibration method provided in the above embodiment is also applicable to competition venues such as weightlifting and swimming. Specifically, the weightlifting venue and swimming pool are regarded as calibration plates to determine key points.

[0068] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A monocular camera calibration method for badminton game analysis, characterized in that: The following steps are involved: Step 1: Consider the badminton court as a calibration plate, identify key points on the calibration plate with a number greater than 11, and calculate the world 3D coordinates and the map 2D coordinates of each key point; Step 2, initialize the camera focal length; Step 3: After constructing the camera intrinsic parameters based on the camera focal length, the camera extrinsic parameters are solved based on the camera intrinsic parameters, the world 3D coordinates of all key points, and the 2D coordinates on the map. The key points are projected onto the map based on the camera extrinsic parameters and the camera intrinsic parameters to obtain the projected 2D coordinates of the projected points. Step 4: construct an error loss function based on the projected 2D coordinates of the projection points and the image 2D coordinates of the key points, and use an optimization algorithm to update the camera focal length with the goal of minimizing the error loss function until the iteration termination condition is met, thereby obtaining the optimized camera focal length and determining the candidate camera intrinsic parameters and candidate camera extrinsic parameters based on the optimized camera focal length; Step 5: Project the world 3D coordinates of all key points onto the map based on the candidate camera intrinsic parameters and candidate camera extrinsic parameters, and observe the reconstructed badminton court generated based on the projection points. When the difference between the reconstructed badminton court and the badminton court used as the calibration plate is within the preset range, the candidate camera intrinsic parameters and candidate camera extrinsic parameters are considered as the final camera intrinsic parameters and final camera extrinsic parameters, otherwise reinitialize the camera focal length and recalculate.

2. The monocular camera calibration method for badminton game analysis according to claim 1, characterized in that: Determine 16 key points on the punctuation board, including the 4 vertices of the badminton court, the 4 vertices of the blocking net, the 2 middle points of the two horizontal edge lines distributed on the badminton court, the 4 bisection points of the two longitudinal edge lines, and the 2 intersection points of the line segment formed by the 2 middle points and the two line segments formed by the 4 bisection points.

3. The monocular camera calibration method for badminton game analysis according to claim 1, characterized in that: The camera intrinsic parameter K(f) is constructed according to the camera focal length and is expressed as: Where f represents the focal length of the camera, W and H represent the width and height of the badminton court image, and d x Indicates the x-width of 1 pixel.

4. The monocular camera calibration method for badminton game analysis according to claim 1, characterized in that: The following formula is used to solve the camera extrinsic parameters based on the camera intrinsic parameters, the world 3D coordinates of all key points and the 2D coordinates on the image: Among them, i represents the key point index, N represents the number of key points, represents the world 3D coordinates of the i-th key point, represents the two-dimensional coordinates of the i-th key point on the graph, R is the camera extrinsic parameter to be solved, and K(f) represents the camera intrinsic parameter.

5. The monocular camera calibration method for badminton game analysis according to claim 1, characterized in that: The error loss function adopts different distance metric functions, including the Manhattan distance and the square expectation of the Euclidean distance between the projected two-dimensional coordinates of the projection point and the two-dimensional coordinates of the key point on the graph.

6. The method for calibrating a monocular camera for badminton game analysis according to claim 5, characterized in that: The constructed error loss function F is expressed as: Among them, i represents the key point index, N represents the number of key points, represents the two-dimensional coordinates of the i-th key point on the graph, represents the projected two-dimensional coordinates of the i-th projection point, and f represents the focal length of the camera.

7. The method for calibrating a monocular camera for badminton game analysis according to claim 1, wherein: The optimization algorithm includes an unconstrained minimization algorithm, a bounded constrained minimization algorithm or a constrained minimization algorithm, wherein the unconstrained minimization algorithm includes the quasi-Newton method BFGS and trust-ncg; the bounded constrained minimization algorithm includes the heuristic rule-based optimization algorithm Nelder-Mead and the truncated Newton algorithm TNC; the constrained minimization algorithm includes COBYLA and SLSQP.

8. The monocular camera calibration method for badminton game analysis according to claim 1, characterized in that: When the difference between the reconstructed badminton court and the badminton court used as the calibration template is outside the preset gap range, the optimization algorithm is replaced and recalculated according to steps 3-5.

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