A shot put three-dimensional space trajectory analysis and performance prediction method based on a 2D image

Abstract

The application discloses a kind of 2D image-based shot three-dimensional space trajectory analysis and result prediction method, it is related to computer vision technical field.For the fitting of multi-angle condition, 3D space curve model is established, and the difference value between the points on 3D space curve and two-dimensional image plane is calculated by projection cost function, the difference value is corrected 3D space curve using optimization algorithm, make 3D space curve 2D projection and multiple shot position coincide;In addition, the landing position is adaptively calculated in the mode of fusion of the first rebound curve and the rolling trajectory of its landing, and the relationship between physical distance and pixel is automatically calculated by relying on the formula of gravity, so as to automatically calculate the actual landing physical distance.The 2D image-based shot three-dimensional space trajectory analysis and result prediction method provided by the application realizes space curve fitting and high-precision landing point distance calculation based on 2D image, which greatly reduces the tracking cost of shot.

Description

Technical Field

[0001] This invention relates to the field of computer vision technology, and in particular to a method for analyzing the three-dimensional spatial trajectory of a shot put and predicting its performance based on 2D images. Background Technology

[0002] Against the backdrop of AI-driven sports development, using AI algorithms to calculate athletic performance and evaluate overall results has become a growing trend. For shot put, traditional manual distance measurement and performance analysis methods are difficult to implement objectively, accurately, and efficiently. Therefore, there is an urgent need for a low-cost, easily deployable solution to achieve efficient and high-precision shot put distance measurement.

[0003] Existing methods for 2D image shot put detection and trajectory prediction based on computer vision algorithms rely on target detection, target tracking, and quadratic curve fitting to predict the landing point's location in the image. These methods also rely on pre-calibration schemes, where markers are placed at multiple locations on the image after actual distance measurements are taken, allowing image processing algorithms to estimate the relationship between pixels and actual physical distances, thus calculating the physical displacement of the shot put upon landing. 3D positioning-based methods, on the other hand, require the use of three active beacons for spatial positioning based on algorithms such as RSSI and TDOA, or image processing algorithms, to achieve accurate spatial tracking and landing point prediction.

[0004] Existing 2D image-based methods cannot model 3D space. When the plane containing the trajectory of a ball thrown by an athlete is not perpendicular to the camera's normal vector, the trajectory captured by the camera appears as a non-standard quadratic function curve in the 2D image. While fitting the sampled points effectively using higher-order functions or complex multilayer perceptron (MLP) models can lead to underfitting and prediction errors in complex scenes with insufficient detection points. High-precision spatial positioning methods typically rely on triangulation algorithms such as Received Signal Strength Indicator (RSSI) or Time Difference of Arrival (TDOA). Although these methods offer high accuracy, they require precise beacon coordinate configuration, resulting in high deployment costs and excessive complexity. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method for three-dimensional spatial trajectory analysis and performance prediction of shot put based on 2D images. Based on 2D images, it realizes spatial curve fitting and high-precision calculation of landing point distance, which greatly reduces the cost of shot put tracking.

[0006] This invention provides a method for analyzing the three-dimensional spatial trajectory of a shot put and predicting its performance based on 2D images, comprising:

[0007] Target detection process: Make the camera's normal plane perpendicular to the ground, then acquire two-dimensional images of the process from the start of the shot put to the stop of the shot put's motion, detect the position of the shot put through the target detection model, and synthesize discrete trajectories with timestamps;

[0008] Space curve model fitting process: Establish a 3D space curve model, which is a cosine angle side projectile model or a space oblique projectile curve model. Calculate the difference between the 3D space curve and the points on the two-dimensional image plane using the projection cost function. Then, use an optimization algorithm to correct the 3D space curve based on this difference, so that the 2D projection of the 3D space curve coincides with the position of the shot put in multiple frames.

[0009] Landing point prediction process: Identify two inflection points in the discrete trajectory to obtain the projectile trajectory, the first bounce trajectory, and the rolling trajectory; adaptively calculate the landing point position based on the fusion method of the first bounce trajectory and the rolling trajectory.

[0010] Actual distance calculation process: Based on the gravity formula, the relationship between the actual height of the highest point and the pixels is automatically calculated, thereby automatically calculating the actual physical distance of landing.

[0011] The technical solutions provided in the embodiments of the present invention have at least the following technical effects:

[0012] By establishing a 3D spatial curve model and proposing a projection cost function to calculate the difference between points on the spatial curve and the 2D image plane, the 2D projection of the 3D spatial curve coincides with the position of the shot put in multiple frames, solving the problem that existing methods relying on 2D images cannot model 3D space. Furthermore, an auxiliary method based on the fusion of a single bounce trajectory and a rolling trajectory is proposed to model the position of the landing point on the curve and adaptively calculate the landing point position. By achieving spatial curve fitting and high-precision landing point distance calculation based on 2D images, the cost of shot put tracking is greatly reduced.

[0013] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0014] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0015] Figure 1 This is a schematic diagram showing the relationship between the actual flight trajectory of the cosine angle side-projection model and its projection onto a 2D image in an embodiment of the present invention;

[0016] Figure 2(a) shows the curve l of the spatial projectile curve model with randomly initialized parameters a, b, and c in the embodiment of the present invention, and the curve after p. xp y p z A schematic diagram of curve l' after parameter rotation;

[0017] Figure 2(b) is a schematic diagram of the projection of Figure 2(a) onto the xoy plane;

[0018] Figure 3 This is an example diagram of inflection point detection in an embodiment of the present invention;

[0019] Figure 4(a) is a schematic diagram of the calculation principle of the linear mapping relationship of pixel distance in Pix-Real coordinate mapping in an embodiment of the present invention;

[0020] Figure 4(b) is a schematic diagram illustrating the calculation principle of the actual distance d between the landing point and the launch point of the Pix-Real coordinate mapping in an embodiment of the present invention;

[0021] Figure 5 This is a schematic diagram of the overall process of the method according to an embodiment of the present invention;

[0022] Figure 6(a) is a schematic diagram of the fitting results using the traditional quadratic curve model in an embodiment of the present invention;

[0023] Figure 6(b) is a schematic diagram of the fitting results using the spatial projectile curve model in an embodiment of the present invention;

[0024] Figure 7(a) is a schematic diagram of the prediction effect of the embodiment of the present invention on a hard ground surface;

[0025] Figure 7(b) is a schematic diagram of the prediction effect of the embodiment of the present invention under the condition that the surface cannot bounce back in soft ground;

[0026] Figure 7(c) is a schematic diagram of the prediction effect in the case of occlusion in the application scenario of the present invention;

[0027] Figure 7(d) is a schematic diagram of the prediction effect when the rolling trajectory deviates due to ground potholes in an embodiment of the present invention. Detailed Implementation

[0028] This invention provides a method for analyzing the three-dimensional spatial trajectory of a shot put and predicting results based on 2D images. It achieves spatial curve fitting and high-precision calculation of the landing point distance based on 2D images, greatly reducing the cost of shot put tracking.

[0029] The overall concept of the technical solutions in the embodiments of the present invention is as follows:

[0030] Based on a target detection model trained on a shot put dataset, this paper designs and applies algorithms to obtain multi-frame shot put positions, thereby achieving high-precision calculation of landing distance. To fit multiple angles, a 3D spatial curve model is established, and a projection cost function is proposed to calculate the difference between the spatial curve and points on the 2D image plane. The Levenberg-Marquardt (LM) optimization algorithm is used to correct the 3D spatial curve, ensuring that the 2D projection of the 3D spatial curve coincides with the multi-frame shot put positions. Furthermore, the landing position is adaptively calculated by fusing the first bounce curve and the rolling trajectory, and the relationship between physical distance and pixels is automatically calculated using the gravity formula to automatically calculate the actual landing physical distance.

[0031] 1. Model Establishment

[0032] 1.1 Shot Put Detection Model

[0033] The YOLOv8 open-source detection algorithm was used as the target detection model for shot put.

[0034] 1.2 Space Curve Model

[0035] In an ideal environment, ignoring external interference factors such as air resistance, the motion of the ball is a standard projectile motion, and the trajectory is a standard quadratic curve, which can be modeled as formula (1).

[0036] y = a·x 2 +b·x+c (1)

[0037] Given that the diameter of a standard shot put is between 95mm and 130mm, the air density is a common value of 1.225kg / m³, the drag coefficient is approximately 0.4 to 0.5, and the average speed at which a shot put is thrown by an average person is approximately 10m / s to 14m / s, the air resistance of an actual shot put is approximately 0.2N to 0.7N according to the traditional quadratic curve model of formula (2). Therefore, the effect of air resistance is ignored in the modeling of this invention. Where F... d It is air resistance, C d ρ is the drag coefficient, A is the air density, A is the cross-sectional area of ​​the shot put, and v is the velocity of the shot put.

[0038]

[0039] The actual shot put court is a fan-shaped area. The angle between the plane on which the shot put trajectory is located and the camera normal plane (the plane perpendicular to the camera normal vector) is denoted as θ. When the camera normal plane is perpendicular to the ground, this invention proposes to model it as a cosine angle side-projection model, as shown in formula (3).

[0040] y = a·(x·cos(θ)) 2 +b·x·cos(θ)+c (3)

[0041] A three-dimensional Cartesian coordinate system (x, y, z) is constructed with the launch point as the origin. The angle between the plane woy containing the launch direction vector w and the plane xoy parallel to the camera's normal plane is θ. The actual flight trajectory is the oe curve, and the image obtained from the 2D image of the camera is the oe' curve. The relationship between the actual flight trajectory and the projection onto the 2D image can be obtained from formula (3), such as... Figure 1 As shown.

[0042] The cosine angle side-launch model can theoretically fit the actual trajectory of the shot put to a very high degree, but it requires ensuring that the launch point is on the y-axis. Therefore, this scheme has better fitting effect and speed, but it requires extremely high accuracy of the target detection algorithm and extremely high video frame rate to ensure the detection of the shot put release frame.

[0043] To reduce the need for shot release frame detection, a spatial oblique projectile curve model is proposed. First, a spatial initialization curve is established as shown in Equation (4), and a spatial rotation matrix R is defined. The direction of the rotation axis is known to be parallel to the y-axis, so the rotation axis normal vector is given in Equation (5). The point through which the rotation axis passes is used as the parameter to be optimized, and the detected shot release position is used as the initial value. The spatial curve can be calculated using the rotation matrix, as shown in Equation (6).

[0044]

[0045] Based on the above formula, the parameters a, b, c, and p are randomly initialized. x p y p z The resulting curves are shown in Figure 2. Figure 2(a) shows the curves l and p after random initialization of parameters a, b, and c. x p y p z The curve l' after parameter rotation, as shown in Figure 2(b), is projected onto the xoy plane.

[0046] 1.3 Landing Point Prediction Modeling

[0047] To model the landing point position, ground information needs to be provided to the model. This invention proposes an auxiliary method based on the fusion of a single bounce trajectory and a rolling trajectory to model the landing point position on a curve. Here, the spatial position sequence of the target detection from launch to stop is defined as follows: Where n represents the position of the ball in the n frames detected from the start of the ball being thrown until the ball stops moving, and 3 represents the three data points in each frame: the timestamp of the position, the horizontal position, and the vertical position.

[0048] Since the trajectory of flight in the air is parabolic, the inflection points on the trajectory are calculated using discrete second-order differentials. From Taylor's formula, we have equations (7) and (8). Solving these two equations simultaneously, we ignore higher-order terms (i.e., the Lagrange remainder O(h) in the equations). 3 )) Calculate the second-order differential as shown in formula (9).

[0049]

[0050] To obtain the inflection point where the discrete curve transforms into an upward convex curve, the position of three consecutive frames is judged using formula (10) to determine whether it is an inflection point. If the x-value of formula (10) is satisfied... i This is the inflection point. To avoid incorrect inflection point judgments caused by minor errors in the target detection model's image localization, Δ = 0.01 is used. This method is used to detect inflection points on discrete curves, such as... Figure 3 As shown.

[0051] f″(x i )>0+Δ (10)

[0052] The discrete curve is divided into three parts: the trajectory before the first inflection point is the projectile trajectory; the trajectory from one frame after the first inflection point to the second inflection point is the single-bounce trajectory; and the trajectory from the last inflection point to the stop is the rolling trajectory. The projectile trajectory and the single-bounce trajectory are fitted using a cosine angle side-projection model or a spatial projectile trajectory model, and the position C1 of the intersection point projected onto the 2D image can be calculated by combining the two curves. The rolling trajectory is subjected to linear regression, and the intersection point C2 is obtained by combining the regression line with the projectile curve.

[0053] To accommodate different ground materials, the L2 norm of coordinates C1 and C2 is calculated, and the Euclidean distance d of their L2 norm is used as the reference value. c If the value is less than the threshold, C1 is taken as the predicted landing point; otherwise, C2 is taken as the landing point.

[0054] 1.4 Modeling the mapping relationship between the Pix-Real coordinate system

[0055] To calculate the real spatial distance using the distance between two points in an image, it is necessary to model the relationship between the image coordinate system and the real coordinate system. The cosine angle projectile model and the spatial projectile curve model proposed in this invention can both calculate the quadratic coefficient, linear coefficient, and constant value of the projectile curve on its plane, and can calculate the precise position p of the highest point in its projectile trajectory. t and the precise location of the landing point p e .

[0056] Since the horizontal component of the flight direction w is uniform linear motion, p can be calculated using the relationship between displacement, velocity, and time. t Corresponding timestamp t t and p e Corresponding timestamp te As shown in Figure 4(a), the highest point p in the real environment can be calculated using the gravitational formula. t The height h relative to the ground (in meters) is given by formula (11), where g is the gravitational acceleration and is taken as 9.81 m / s². The linear mapping relationship between the actual height and the pixel distance is obtained through this formula. Therefore, the actual distance d between the landing point and the launch point can be calculated by formula (12), as shown in Figure 4(b).

[0057]

[0058]

[0059] 2. Cost Function

[0060] The data obtained by object detection is a two-dimensional point T on a plane. 2d The i-th point is denoted as [x ti ,f(x ti The fitted curve is a three-dimensional curve, and the points on the curve are denoted as P. 3d The i-th point is denoted as [x pi ,z pi ,f(x pi ,z pi Since traditional least squares and other methods cannot directly calculate the average error, this embodiment proposes a projection cost function, cost. proj (T 2d ,P 3d As shown in formula (13). Since the plane containing the image is parallel to xoy during modeling, let z pi =0 will P 3d The predicted key points are projected onto T 2d The mean square error is calculated based on the plane in which it is located.

[0061]

[0062] The Levenberg-Marquardt (LM) optimization algorithm was used to optimize the cosine angle projectile model and the spatial projectile curve model proposed in this invention, thereby fitting the curve in space. For the cosine angle projectile model, there are learnable parameters a, b, c, and θ. After LM optimization, the projection cost function cost is obtained. proj The parameters are minimized; for the spatial projectile curve model, there are learnable parameters a, b, c, θ, p. x p y p z After optimization by LM, the projection cost function cost is obtained. proj The parameter at its smallest value.

[0063] Based on the overall concept of the invention described above, this embodiment provides a method for analyzing the three-dimensional spatial trajectory of a shot put and predicting its performance based on 2D images, such as... Figure 5 As shown, it may include the following steps:

[0064] S1. Target detection process: Make the camera's normal plane perpendicular to the ground, then acquire two-dimensional images of the process from the start of the shot put to the shot put stopping, detect the position of the shot put through the target detection model, and synthesize discrete trajectories with timestamps.

[0065] S2. Spatial Curve Model Fitting Process: Establish a 3D spatial curve model, which is a cosine angle side projectile model or a spatial oblique projectile curve model. Calculate the difference between the 3D spatial curve and the points on the two-dimensional image plane using the projection cost function. Then, use an optimization algorithm to correct the 3D spatial curve based on this difference, so that the 2D projection of the 3D spatial curve coincides with the position of the shot put in multiple frames.

[0066] S3. Landing point prediction process: Determine the two inflection points in the discrete trajectory to obtain the projectile trajectory, the first bounce trajectory, and the rolling trajectory; Adaptively calculate the landing point position based on the fusion method of the first bounce trajectory and the rolling trajectory.

[0067] S4. Actual distance calculation process: Based on the gravity formula, the relationship between the actual height of the highest point and the pixels is automatically calculated, thereby automatically calculating the actual physical distance of landing.

[0068] In one possible implementation, the 3D space curve model is a cosine angle projectile model, with the following formula:

[0069] y = a·(x·cos(θ)) 2 +b·x·cos(θ)+c

[0070] Where θ is the angle between the plane containing the trajectory of the shot put and the normal plane of the camera, and a, b, and c are learnable parameters.

[0071] However, while the cosine angle side-launch model can theoretically fit the actual trajectory of the shot put to a very high degree, it requires ensuring that the launch point is on the y-axis. Therefore, this scheme is superior in terms of fitting effect and speed, but it has extremely high requirements for the accuracy of the target detection algorithm and the video frame rate to ensure the detection of the shot put release frame.

[0072] In another possible implementation, to reduce the need for release frame detection, the 3D spatial curve model is a spatial projectile curve model, with the following formula:

[0073]

[0074] Where R is the spatial rotation matrix, p = [p x ,p y ,p z ] are learnable parameters, and (x, y, z) represent the coordinates of a point in the coordinate system.

[0075] In this embodiment, the formula for the projection cost function is:

[0076]

[0077] Among them, T 2d The i-th point is denoted as [x_i] in the discrete trajectory. ti ,f(x ti )], P 3d The points represent the fitted 3D curve, and the i-th point is denoted as [x]. pi ,z pi ,f(x pi ,z pi )], where m represents the number of discrete trajectories.

[0078] The Levenberg-Marquardt optimization algorithm was used to calculate the difference value of the projection cost function.

[0079] In one possible implementation, determining the two inflection points in the discrete trajectory specifically involves calculating the inflection points using discrete second-order differentiation over three consecutive frames, where the i-th point x... i The inflection point is when the following formula is satisfied:

[0080] f″(x i )>0+Δ

[0081] in,

[0082] Where, f(x) i Let be the height of the i-th point, Δ be the error threshold (0.01 in this embodiment), and Δx be the height of x. i With x i-1 The difference between them.

[0083] In this embodiment, during the landing point prediction process, the landing point position is adaptively calculated based on the fusion of the first bounce trajectory and the rolling trajectory. Specifically, this includes: fitting a 3D spatial curve model to the projectile trajectory and the first bounce trajectory, and calculating the intersection point as the first intersection point C1 by combining the two curves; applying linear regression to the rolling trajectory, and combining the regression line with the projectile curve to obtain the second intersection point C2; calculating the L2 norm of the first intersection point C1 and the second intersection point C2, and determining the L2 norm when the Euclidean distance value d is... cIf the value is less than the threshold (set to 40 pixels in this embodiment), the first intersection point C1 is taken as the landing point; otherwise, the second intersection point C2 is taken as the landing point. (Generally, the intersection of two curves is more accurate, but the Euclidean distance d...) c A value greater than or equal to the threshold indicates that there is almost no rebound trajectory or that the rebound trajectory is incorrect; obtaining the intersection point by combining the regression line and the projectile curve is more accurate.

[0084] Preferably, the actual distance calculation process specifically includes: calculating the precise position p of the highest point in the projectile trajectory using a 3D spatial curve model. t and the precise location of the landing point p e p is calculated using the relationship between displacement, velocity, and time. t Corresponding timestamp t t and p e Corresponding timestamp t e The highest point p in real-world conditions was calculated using the gravitational formula. t The linear mapping relationship between the actual height h relative to the ground and the pixel distance is obtained. Then, the actual distance d between the landing point and the launch point is calculated based on the linear mapping relationship, as shown in the following formula:

[0085]

[0086] Among them, w e w is the pixel height of the highest point of the curve. t This is the pixel distance from the landing point to the starting point.

[0087] To verify the effectiveness of the 3D spatial curve model, the traditional quadratic curve model of formula (2) and the spatial projectile curve model of formula (6) were fitted with the same data to verify the effect, as shown in Figure 6. Figure 6(a) shows the fitting result using the traditional quadratic curve model. Although it is relatively accurate in predicting the landing point, the fitting effect is poor at the highest point and near the launch position, which will lead to errors in the modeling of the Pix-Real coordinate system mapping relationship and affect the final actual distance. Figure 6(b) shows the fitting result using the spatial projectile curve model. It can be observed that its fitting effect is better than the traditional scheme. In the figure, the red curve is the projectile curve, the yellow curve is the first bounce curve, the blue line is the rolling trajectory fitting line, the purple point is the final landing point predicted by the projectile curve and the first bounce curve, the cyan point is the final landing point predicted by the rolling trajectory and the projectile curve, and the arrow color and the point pointed to by the arrow are the final landing points predicted by the d c The final point of judgment regarding the relationship with the threshold.

[0088] To ensure that the model can be applied to complex terrain and real-world environments, different types of terrain and different real-world scenarios were selected for effect verification.

[0089] Figure 7(a) shows the prediction result on a hard surface, and Figure 7(b) shows the prediction result on a soft surface where the object cannot bounce. The validation in the environments shown in Figures 7(a) and 7(b) demonstrates the generalization ability of the proposed model for different ground scenarios. Figure 7(c) shows the prediction result when the application scenario is occluded. This figure proves that even when the target detection is lost due to complex backgrounds or occlusion, the model can still accurately predict the landing position. Figure 7(d) shows the prediction result when the rolling trajectory is deviated due to ground potholes. This figure proves that the proposed solution can maintain high-precision prediction even in complex ground environments.

[0090] 100 sets of data were sampled in different scenarios, and the verification results are shown in Table 1. The image resolution was 1920×1080. The precision of the trained YOLOv8 shot put detection model was 99.31%, and the recall was 98.62%. A high refresh rate of 120FPS was used to ensure that the landing point was captured, thus recording the pixel error of the actual image. A sampling rate of 25FPS was used to simulate the normal frame rate of the actual application scenario to ensure that the detection effect was consistent with reality. The actual ranging error is the difference between the distance measured by the ruler after landing and the distance predicted by the algorithm. The final data is the average error after 100 sets of actual sampling.

[0091] Table 1 Shot Put Distance Measurement Evaluation Table

[0092] average error Traditional quadratic curve model Spatial projectile curve model Average pixel error of the image (unit: pixels) 32.51 0.82 Average error in actual distance measurement (unit: millimeters) 81.28 2.05

[0093] This invention establishes a 3D spatial curve model and proposes a projection cost function to calculate the difference between points on the spatial curve and the two-dimensional image plane, making the 2D projection of the 3D spatial curve coincide with the position of the shot put in multiple frames, thus solving the problem that existing methods relying on 2D images cannot model three-dimensional space. It also proposes an auxiliary method based on the fusion of a single bounce trajectory and a rolling trajectory to model the position of the landing point on the curve and adaptively calculate the landing point position. By achieving spatial curve fitting and high-precision landing point distance calculation based on 2D images, the cost of shot put tracking is greatly reduced.

[0094] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0095] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0096] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0097] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0098] While specific embodiments of the present invention have been described above, those skilled in the art should understand that the specific embodiments described are merely illustrative and not intended to limit the scope of the present invention. Equivalent modifications and variations made by those skilled in the art in accordance with the spirit of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for analyzing the three-dimensional spatial trajectory of a shot put and predicting its performance based on 2D images, characterized in that, include: Target detection process: Make the camera's normal plane perpendicular to the ground, then acquire two-dimensional images of the process from the start of the shot put to the stop of the shot put's motion, detect the position of the shot put through the target detection model, and synthesize discrete trajectories with timestamps; Space curve model fitting process: Establish a 3D space curve model, which is a cosine angle side projectile model or a space oblique projectile curve model. Calculate the difference between the 3D space curve and the points on the two-dimensional image plane using the projection cost function. Then, use an optimization algorithm to correct the 3D space curve based on this difference, so that the 2D projection of the 3D space curve coincides with the position of the shot put in multiple frames. Landing point prediction process: Identify two inflection points in the discrete trajectory to obtain the projectile trajectory, the first bounce trajectory, and the rolling trajectory; adaptively calculate the landing point position based on the fusion method of the first bounce trajectory and the rolling trajectory. Actual distance calculation process: The relationship between the actual height of the highest point and the pixels is automatically calculated based on the gravity formula, thereby automatically calculating the actual physical distance of landing; The formula for the cosine angle projectile model is as follows: ； Where θ is the angle between the plane containing the trajectory of the shot put and the normal plane of the camera, and a, b, and c are learnable parameters; The formula for the spatial projectile curve model is as follows: ； Where R is the spatial rotation matrix, These are learnable parameters, where (x, y, z) represent the coordinates of a point in the coordinate system. The formula for the projection cost function is: ； Among them, T 2d The i-th point is denoted as [x_i] in the discrete trajectory. ti ,f(x ti )], P 3d The points represent the fitted 3D curve, and the i-th point is denoted as [x]. pi ,z pi ,f(x pi ,z pi )], where m represents the number of discrete trajectories; In the landing point prediction process, the landing point position is adaptively calculated based on the fusion of the first bounce trajectory and the rolling trajectory. Specifically, this includes: fitting a 3D spatial curve model to the projectile trajectory and the first bounce trajectory, and calculating the intersection point of the two curves as the first intersection point position; applying linear regression to the rolling trajectory, and combining the regression line with the projectile curve to obtain the second intersection point position; calculating the L2 norm of the first intersection point position and the second intersection point position, and taking the first intersection point position as the landing point position when the Euclidean distance value of the L2 norm is less than a threshold, otherwise taking the second intersection point position as the landing point position. The precise location p of the highest point in the projectile trajectory was calculated using a 3D spatial curve model. t and the precise location of the landing point p e p is calculated using the relationship between displacement, velocity, and time. t Corresponding timestamp t t and p e Corresponding timestamp t e The highest point p in real-world conditions was calculated using the gravitational formula. t The linear mapping relationship between the actual height h relative to the ground and the pixel distance is obtained. Then, the actual distance d between the landing point and the launch point is calculated based on the linear mapping relationship, as shown in the following formula: ； ； in, The pixel height of the highest point of the curve. This is the pixel distance from the landing point to the starting point.

2. The method according to claim 1, characterized in that: The Levenberg-Marquardt optimization algorithm was used to calculate the difference value of the projection cost function.

3. The method according to claim 1, characterized in that: Determining the two inflection points in a discrete trajectory specifically involves calculating the inflection points using discrete second-order differentiation over three consecutive frames, with the i-th point x... i The inflection point is when the following formula is satisfied: ； in, ; Where, f(x) i Let be the height of the i-th point, Δ be the error threshold, and Δx be the value of x. i With x i-1 The difference between them.

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