Table tennis track prediction and drop point analysis system

Abstract

The invention relates to the technical field of sports engineering, in particular to a table tennis track prediction and drop point analysis system. The system comprises a data acquisition module, a data processing module and a prediction module, the data acquisition module captures a motion image sequence through a visual sensor; the data processing module extracts a position coordinate time sequence and calculates motion parameters; the prediction module predicts a trajectory and a drop point in combination with a physical motion equation and a machine learning model. The physical motion equation comprises air resistance, gravity and Magnus effect items, and the machine learning model adopts a long short-term memory network to process time sequence data. According to the system, the tracking precision is improved through multi-sensor data fusion, model parameters are dynamically adjusted through an environment calibration module, and accurate and reliable trajectory prediction and drop point analysis are achieved.

Description

Technical Field

[0001] This invention relates to the field of sports engineering technology, and more specifically, to a system for predicting the trajectory and landing point of a table tennis ball. Background Technology

[0002] In recent years, with the development of computer vision and artificial intelligence technologies, research institutions at home and abroad have successively carried out research on vision-based sphere tracking and trajectory prediction. Early systems mainly relied on high-speed cameras and simple kinematic models, while machine learning methods have been gradually introduced in recent years to improve prediction accuracy. This field is developing from single-sensor to multi-sensor fusion, from offline analysis to real-time prediction, and from basic trajectory prediction to complex motion analysis including rotational effects.

[0003] Existing table tennis trajectory prediction technologies have significant shortcomings. While methods based on purely physical models have clear physical meaning, they struggle to accurately simulate the complex interactions between the ball and the air, particularly the Magnus effect caused by spin, which is often simplified, leading to prediction bias. Pure machine learning methods, although capable of learning complex patterns in data, require large amounts of labeled data and lack physical interpretability, exhibiting instability when encountering shot types not covered by training data. Most existing systems employ a single technical approach, failing to simultaneously guarantee prediction accuracy and adaptability. Regarding multi-sensor data fusion, the spatiotemporal registration accuracy of visual and inertial data is insufficient, resulting in cumulative errors in trajectory tracking. The impact of environmental factors such as temperature and humidity changes on air resistance is rarely considered, limiting the system's accuracy in actual stadium applications.

[0004] Therefore, a table tennis trajectory prediction and landing point analysis system is proposed to address the above problems. This system aims to solve the problems of limited prediction accuracy caused by inaccurate physical models, poor adaptability of machine learning, and insufficient consideration of environmental factors in existing table tennis trajectory prediction systems, as well as the tracking error caused by insufficient fusion of multi-source data. At the same time, it also aims to overcome the challenge of balancing real-time performance and accuracy. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a table tennis ball trajectory prediction and landing point analysis system to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a ping-pong ball trajectory prediction and landing point analysis system, the system comprising a data acquisition module, a data processing module, and a prediction module; The data acquisition module is used to capture a sequence of motion images of a ping-pong ball using a visual sensor and to obtain the ball's initial motion data. The data processing module is used to extract the position coordinate time series of the ball from the motion image sequence, and calculate the ball's motion parameters based on the position coordinate time series, including velocity vector, acceleration vector and rotation. The prediction module is used to predict the future trajectory and landing position of the ball based on the motion parameters, combined with predefined physical motion equations and machine learning models. The physical motion equations include differential equations describing the motion of the ball under the influence of air resistance, gravity, and collisions with the table. The machine learning model is trained using historical trajectory data to adaptively correct prediction results. The entire system is implemented in software and runs on computing devices, enabling automated processing from data acquisition to trajectory prediction.

[0007] Furthermore, the data acquisition module also integrates a motion sensor unit for acquiring the ball's inertial data, including angular velocity vector and linear acceleration vector; the data processing module fuses the inertial data with the image sequence captured by the vision sensor, and optimizes the ball's position tracking through a Kalman filter algorithm to generate a more accurate position coordinate time series.

[0008] Furthermore, the data processing module uses a deep learning-based object detection algorithm to identify ping-pong balls in a sequence of moving images. This includes analyzing each frame of the image using a convolutional neural network model to locate the ball and output its bounding box coordinates. Subsequently, a multi-target tracking algorithm is used to associate the ball positions in consecutive frames to generate a smooth time series of position coordinates. The multi-target tracking algorithm includes data association and motion compensation steps.

[0009] Furthermore, the rotation amount in the motion parameters is estimated by analyzing the changes in the surface texture or additional markings of the ball in the image sequence, including calculating the ball's rotation vector using optical flow or feature matching techniques; the data processing module integrates the rotation vector into the motion parameters to simulate the Magnus effect and the influence of spin on the trajectory in the physical equations of motion.

[0010] Furthermore, the physical equations of motion are solved using numerical integration methods, including the Euler method or the Runge-Kutta method, to simulate the motion of the ball in three-dimensional space; the physical equations of motion are expressed as:

[0011] Where m represents the mass of the ping-pong ball. Let t represent the velocity vector of the ping-pong ball, and t represent time. Represents gravity. Indicates air resistance, It represents Magnus force; among which, , Represents the gravitational acceleration vector; ρ represents air density, C_d represents drag coefficient, and A represents the cross-sectional area of ​​the ping-pong ball; , This represents the angular velocity vector of a ping-pong ball. The Magnus force coefficient is represented; the parameters in the equation are set according to the standard ping-pong ball specifications and can be dynamically adjusted according to environmental conditions.

[0012] Furthermore, the machine learning model is a recurrent neural network structure, specifically including long short-term memory units (LSM) for processing long-term dependencies in the time series of location coordinates; the update process of the LSM at time step t is defined by the following equation:

[0013] in, The input vector representing time step t includes the ball's position, velocity, or rotation. This represents the hidden state at time step t; Represents the cell state at time step t; , , These represent the activation values ​​of the input gate, forget gate, and output gate, respectively. Indicates the state of candidate cells; , , , Represents the weight matrix; , , , σ represents the bias vector; σ represents the sigmoid activation function, defined as... tanh represents the hyperbolic tangent activation function; This indicates that the previous hidden state will be removed. and current input The concatenated vector; the model is trained through supervised learning, with training data covering various shot types and environmental scenarios, to learn the nonlinear characteristics of the trajectory and output the probability distribution of the ball position at multiple future time steps.

[0014] Furthermore, the training process of the recurrent neural network model includes a data augmentation step, which simulates real-world changes by adding noise and changing the perspective; the model receives the location coordinate time series in real time during the inference phase and outputs the trajectory prediction results, while fine-tuning the model weights based on new data through an online learning mechanism.

[0015] Furthermore, the system also includes a calibration module for adjusting the parameters of the physical motion equations and machine learning models based on real-time environmental data; the calibration module receives external inputs, including temperature, humidity and air pressure information, and dynamically updates air density and drag coefficient based on this information.

[0016] Furthermore, the output of the prediction module includes the predicted trajectory curve and landing point coordinates of the ball, which are presented in a visual form through a graphical user interface. The interface allows users to interactively view trajectory history, real-time predictions, and landing point analysis reports, while also supporting data export and playback functions.

[0017] Furthermore, the system operates in real-time mode, where the data acquisition module captures images at a high frame rate, and the processing latency of the data processing module and the prediction module is controlled within the millisecond range, ensuring that trajectory prediction and landing point analysis are completed during the process from the ball's impact to its landing, and the results are transmitted to a remote display device through a network interface.

[0018] The technical effects and advantages of this invention are as follows: Compared to existing technologies, this invention establishes a complete physical equation of motion that includes air resistance, gravity, and the Magnus effect, and uses numerical integration to solve for the trajectory of the ball. The system acquires precise motion parameters through multi-sensor data fusion and dynamically adjusts these parameters using an environmental calibration module, achieving high-precision prediction of the ping-pong ball's trajectory. The first-principles modeling method ensures the physical rationality of the prediction results, accurately describing the complex motion characteristics of a spinning ball and maintaining stable prediction performance under different hitting conditions, providing a reliable basis for training and match analysis.

[0019] Compared to existing technologies, this invention utilizes Long Short-Term Memory (LSTM) networks in deep learning to process trajectory time series and establishes a predictive model with an encoder-decoder architecture. This system trains network parameters using a large amount of historical trajectory data, continuously optimizes model performance through online learning mechanisms, and enhances generalization ability by combining data augmentation techniques. It can automatically learn complex patterns in trajectories, adapt to different athletes' hitting styles, and improve the accuracy of predicting abnormal trajectories while ensuring real-time performance, providing a technical foundation for real-time tactical analysis.

[0020] Compared to existing technologies, this invention achieves complementary advantages of both methods in the prediction module through the deep integration of physical models and machine learning models. The system utilizes physical equations to ensure the basic rationality of the predictions, corrects model errors through machine learning, and introduces a physical constraint loss function to enhance the learning effect. This hybrid modeling approach maintains the interpretability of the physical model while leveraging the adaptability of machine learning, employing the most appropriate prediction strategy at different stages of motion, thus significantly improving the robustness and practicality of the system. Attached Figure Description

[0021] Figure 1 This is a flowchart of the trajectory prediction based on physical motion equations of the present invention.

[0022] Figure 2 This is a diagram of the trajectory prediction model based on LSTM network of the present invention.

[0023] Figure 3 This is a schematic diagram of the operation of the environmental adaptive calibration module of the present invention.

[0024] Figure 4 This is a flowchart of the multi-sensor data fusion processing of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] As attached Figures 1 to 4 The table tennis ball trajectory prediction and landing point analysis system shown below has the following specific implementation details: Example 1: Professional Training Analysis System Based on Physical Equations of Motion This embodiment details the implementation of a professional training analysis system based on physical motion equations. This system is primarily applied to the training analysis of professional table tennis teams, achieving high-precision prediction of the table tennis ball's trajectory through accurate physical modeling, thus providing data support for athletes' technical improvement.

[0027] Four to six high-speed vision sensors are deployed around the table tennis table. These sensors synchronously acquire sequences of table tennis motion images at a frame rate of 500fps. The placement of the vision sensors ensures that they cover the table tennis table and its surrounding three-dimensional space of at least 3 meters × 3 meters × 2 meters, with adjacent sensors having more than 30% overlap in their fields of view to achieve stereoscopic vision positioning. Each vision sensor is equipped with a global shutter and a polarizing filter to effectively avoid motion blur and reflection interference.

[0028] After the system starts, the data acquisition module first performs time synchronization calibration on each sensor to ensure that the time deviation of image acquisition is less than 1ms. During training, when the ping-pong ball is hit, all visual sensors are triggered synchronously to acquire a continuous sequence of motion images. The image resolution is set to 1280×1024 pixels, which can clearly capture the shape of the 40mm diameter ping-pong ball in high-speed motion.

[0029] After receiving the image sequence, the data processing module first performs image preprocessing, including background subtraction, contrast enhancement, and noise filtering. Then, a lightweight convolutional neural network based on YOLOv4 is used for ping-pong ball detection. This network, pre-trained on the COCO dataset, is fine-tuned using 5000 professionally labeled ping-pong ball images, achieving a detection accuracy of 98.7% on the test set.

[0030] For each frame of the image, the network outputs the bounding box coordinates and confidence score of the ping-pong ball. The center point of the bounding box is used as the initial position coordinates of the ball. Considering the shape changes of the ping-pong ball during high-speed movement, the system uses an ellipse fitting method to optimize the detection results and corrects the center of the bounding box to the geometric center of the ball.

[0031] After obtaining the initial position coordinate sequence, the system further associates the ball's position in consecutive frames using a multi-target tracking algorithm. A motion model-based data association strategy is employed, utilizing the inertial characteristics of the ping-pong ball's motion to establish a state transition model. Specifically, the system assumes that the ping-pong ball's motion state changes within an extremely short time interval (2ms) conforms to a uniformly accelerated motion model. The Hungarian algorithm is used to solve the inter-frame data association problem, and motion consistency checks are performed on abnormal associations. Furthermore, appearance features based on the ball's size and shape are introduced to assist in the association, effectively addressing situations such as occlusion and rapid rotation. The final smoothed position coordinate time series has a position error controlled within ±2mm.

[0032] After obtaining the precise position coordinate time series, the system calculates the ball's motion parameters using numerical differentiation. For each time point t, the velocity vector v is calculated using the central difference method. v(t) = [p(t+1) - p(t-1)] / (2Δt) Where p represents the position coordinates, and Δt is the sampling time interval of 2ms. The acceleration vector a is obtained by the difference of the velocity vector: a(t) = [v(t+1) - v(t-1)] / (2Δt). The estimation of the rotation ω adopts a method based on surface texture analysis. The system presets several optical markers on the surface of the sphere. By tracking the motion of these markers in continuous frames, the angular velocity vector is calculated using the principle of rigid body kinematics. Specifically, the system extracts the two-dimensional image coordinates of the markers at each time point, reconstructs their three-dimensional coordinates through multi-view geometry, and then calculates the rotation matrix and angular velocity.

[0033] In the prediction module, the system predicts the trajectory based on the physical equations of motion. The core differential equations of motion are as follows:

[0034] The mass m of the ping-pong ball is taken as the standard value of 2.7g. This parameter can be adjusted within the range of 2.67g-2.77g depending on the actual specifications of the ping-pong ball used. (Gravity term) The gravitational acceleration vector = (0, 0, -9.8) The coordinate system is defined with the z-axis pointing vertically upwards.

[0035] The air resistance term is calculated using the following formula:

[0036] The air density ρ was obtained in real time by an environmental sensor and was taken as 1.204 kg / m³ under standard conditions (20℃, 101.3 kPa). The drag coefficient... Based on dynamic calculations using the Reynolds number, the value is taken as 0.45-0.55 within the typical speed range of a table tennis ball (5-20 m / s). The cross-sectional area A is calculated based on a table tennis ball diameter of 40 mm, and is 1.257 × 10⁻³ m².

[0037] The Magnus force is calculated using the following formula:

[0038] The angular velocity vector ω comes from the aforementioned rotation estimation results, and the Magnus force coefficient... The empirical model, trained based on historical data, takes into account multiple factors such as rotational speed, motion speed, and spherical surface roughness, and its value ranges from 0.4 to 0.6 under typical conditions.

[0039] The system employs the fourth-order Runge-Kutta method to numerically solve the equations of motion, with a time step of 1 ms. During the solution process, the system monitors collision events between the ball and the table in real time. When the system detects that the ball's height is lower than the net height and its velocity is downward, it activates the collision detection algorithm. The collision model considers the translational and rotational energy losses of the ball, with a coefficient of restitution of 0.86-0.92 and a coefficient of friction of 0.1-0.3, the specific values ​​of which are adjusted according to the type of shot.

[0040] The trajectory prediction output includes the sphere's three-dimensional position, velocity, and rotation state for the next 2 seconds, with a time resolution of 10 ms. The system pays particular attention to impact point prediction, obtaining precise impact point coordinates and incident angles by solving equations with the sphere's height at zero. Simultaneously, the system provides trajectory analysis, simulating the impact of parameter perturbations on the prediction results using the Monte Carlo method, and providing the impact point range with a 95% confidence interval.

[0041] The calibration module dynamically adjusts physical parameters based on environmental sensor data. The temperature sensor monitors from -10℃ to 50℃ with an accuracy of ±0.5℃; the humidity sensor monitors from 0 to 100%RH with an accuracy of ±3%RH; and the barometric pressure sensor monitors from 300 to 1100 hPa with an accuracy of ±0.5 hPa. These environmental parameters are used to calculate the real-time air density: ρ = P / (R_specific * T), where P is the air pressure, T is the absolute temperature, and R_specific is the air specificity constant 287.05 J / (kg·K). Simultaneously, the system adjusts the sphere's elastic parameters based on ambient temperature and humidity to ensure the accuracy of the collision model.

[0042] The system ultimately presents the analysis results through a graphical user interface, including trajectory curves, landing point markers, time-series graphs of motion parameters, and statistical analysis reports. Coaches can replay slow-motion videos of specific shots to compare the technical characteristics of different athletes. The system also provides machine learning-based tactical analysis, automatically identifying shot types and quality assessments. All data is stored in a cloud database, supporting long-term tracking of athletes' technical development trajectories.

[0043] Example 2: Adaptive Real-Time Prediction System Based on Machine Learning Model This embodiment details the implementation of an adaptive real-time prediction system based on a machine learning model. This system is primarily used in real-time match analysis and training assistance scenarios. It utilizes deep learning technology to achieve rapid and accurate prediction of the trajectory of a ping-pong ball, meeting the demands of applications with high real-time requirements.

[0044] In a standard competition venue, the system deploys 8-12 medium-speed vision sensors, acquiring images at a frame rate of 250fps. The sensors are positioned around and above the table to provide multi-view coverage. The sensors utilize rolling shutter CMOS sensors, compensating for the rolling shutter effect through precise time synchronization. All sensors are connected to the central processing unit via Gigabit Ethernet to ensure real-time image data transmission. Automatic calibration is performed upon system startup, establishing the geometric relationships between the sensors by photographing a calibration board of known dimensions, achieving a calibration accuracy of 0.1 pixels.

[0045] The data acquisition module employs a pipelined architecture to process the input image stream. First, each frame undergoes preprocessing, including gamma correction, white balance, and lens distortion correction. Then, a lightweight SSD-MobileNet convolutional neural network is used for ping-pong ball detection. This optimized network achieves a single-frame processing time of less than 2ms on a mobile GPU, maintaining an accuracy of over 95%. Considering the small size of ping-pong balls in images (typically occupying 0.1%-0.5% of the image area), the network uses adaptive anchor boxes in the final feature layer to improve the detection performance of small objects.

[0046] After obtaining preliminary detection results, the system establishes inter-frame associations using a deep learning-based multi-target tracking algorithm. This algorithm employs a joint detection and tracking architecture, extracting the appearance features of each detected target through a re-identification branch and combining them with motion features for data association. Specifically, the system maintains a state vector x = [p_x, p_y, p_z, v_x, v_y, v_z] for each tracked target, where p represents position and v represents velocity. The system predicts the target's state in the next frame using Kalman filtering, and then uses the Hungarian algorithm to associate the predicted state with the detection results. For targets that fail to be associated, the system uses an attention-based re-identification model for recovery, effectively handling transient occlusion situations.

[0047] The data processing module organizes the tracking results into a time series format, sampling at 10ms intervals. Each time point includes the sphere's three-dimensional coordinates and confidence score. The system employs a sliding window processing strategy, with a window length of 30 time steps (corresponding to a 300ms motion trajectory) and a sliding step size of 1 time step. For each window, the system calculates a series of motion features, including the first-order difference of position (velocity), the second-order difference (acceleration), trajectory curvature, and motion energy, forming a 32-dimensional feature vector sequence.

[0048] The prediction module is based on a trajectory prediction model using a Long Short-Term Memory (LSTM) network. This model employs an encoder-decoder architecture, where the encoder processes historical trajectory sequences and the decoder generates future trajectory predictions. The specific computational process of the LSTM unit is defined by the following equation:

[0049] In the specific implementation, the input vector It includes the sphere's current 3D position coordinates, estimated velocity, rotation features, and environmental context features, with a total dimension of 40. Hidden State and cell state All dimensions are set to 256 to accommodate sufficient temporal information. Weight matrix , , , The dimensions are [256, 296], corresponding to the processing after concatenating the 256-dimensional hidden state and the 40-dimensional input vector. Bias vector. , , , The dimension is 256. The sigmoid activation function...

[0050] Used for gating signal generation, the tanh activation function is used for state updates.

[0051] The encoder consists of three LSTM layers, each containing 256 hidden units. After processing by the encoder, the final hidden state captures the contextual information of the entire historical trajectory. The decoder also consists of three LSTM layers, with the initial state initialized by the final state of the encoder. The decoder operates in an autoregressive manner, using the prediction result at each time step as the input for the next time step to generate trajectory predictions for the next 10 time steps (100ms).

[0052] The model training process employs a multi-task learning strategy, with the main tasks including trajectory regression and landing point classification. The trajectory regression loss uses a smoothed L1 loss function to optimize the mean squared error of position prediction. The landing point classification task divides the table area into a 16×8 grid, using cross-entropy loss to optimize landing point area prediction. Training data comes from 2000 hours of professional match footage, including various shot types and match scenarios. Data augmentation techniques include adding Gaussian noise, random scaling, timeline warping, and perspective transformation to improve the model's generalization ability.

[0053] When the error between the predicted trajectory and the actual observed trajectory exceeds a set threshold (positional error greater than 5 cm), the system automatically triggers the model update process. The update process employs an elastic weight consolidation method, which adjusts model parameters to adapt to new data while protecting learned knowledge through importance weights to avoid catastrophic forgetting.

[0054] The system integrates a physical knowledge constraint module, which introduces the basic principles of physical equations of motion as soft constraints into the prediction process. Specifically, a physical consistency term is added to the loss function to penalize prediction results that violate physical laws (such as energy conservation and momentum conservation). This hybrid modeling method maintains the flexibility of data-driven approaches while utilizing the rationality of physical models, thereby improving the physical interpretability of the results while ensuring prediction accuracy.

[0055] In terms of real-time performance optimization, the system adopts a multi-threaded parallel processing architecture. Image acquisition and preprocessing are performed in dedicated threads, object detection and tracking are performed in GPU-accelerated threads, and the trajectory prediction model runs in a dedicated inference thread. Through pipelined parallelism, the overall system latency is controlled within 80ms, meeting the requirements of real-time analysis. During the inference phase, the model is optimized using TensorRT to achieve half-precision floating-point calculations, with a single inference time of less than 15ms.

[0056] The calibration module acquires temperature, humidity, and air pressure data from environmental sensors. This data, after standardization, serves as additional input features for the LSTM model. Simultaneously, the calibration module adjusts the weights of physical constraints based on environmental conditions, strengthening the constraints of physical laws under extreme environmental conditions. The system also includes an anomaly detector that automatically switches to a conservative prediction mode when environmental parameters exceed normal ranges, ensuring the system's robustness.

[0057] The system outputs include trajectory prediction curves, landing probability heatmaps, and tactical analysis reports. The trajectory prediction results are presented in a 3D visualization, displaying multiple possible trajectories and their confidence levels. The landing probability heatmaps visually show the probability distribution of the ball landing in different areas, helping athletes predict incoming balls. The tactical analysis module identifies the opponent's hitting patterns and tactical tendencies based on historical data comparisons, providing support for real-time tactical adjustments. All data is pushed synchronously through the web interface and mobile applications, supporting coaches and athletes in making immediate decisions.

[0058] Finally, the following points should be noted: First, in the description of this application, it should be noted that, unless otherwise specified and limited, the terms "installation", "connection", and "linkage" should be interpreted broadly, and can be mechanical or electrical connections, or internal connections between two components, or direct connections. "Up", "down", "left", "right", etc. are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may change. Secondly: The accompanying drawings of the embodiments disclosed in this invention only involve the structures involved in the embodiments disclosed in this invention. Other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of this invention can be combined with each other. In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A table tennis trajectory prediction and point analysis system, characterized by, The system includes a data acquisition module, a data processing module, and a prediction module; the data acquisition module is used to capture a sequence of motion images of the ping pong ball through a visual sensor and obtain initial motion data of the ball; the data processing module is used to extract a time series of position coordinates of the ball from the sequence of motion images and calculate motion parameters of the ball based on the time series of position coordinates, including a velocity vector, an acceleration vector, and a rotation quantity; the prediction module is used to predict a future trajectory and a landing position of the ball according to the motion parameters, in combination with a predefined physical motion equation and a machine learning model; the physical motion equation includes a motion differential equation describing the ball under the influence of air resistance, gravity, and table collision, and the machine learning model is trained through historical trajectory data to adaptively correct the prediction result; the entire system is implemented in a software manner and runs on a computing device to realize automated processing from data acquisition to trajectory prediction.

2. The table tennis trajectory prediction and landing point analysis system according to claim 1, wherein, The data acquisition module is also integrated with a motion sensor unit for collecting inertial data of the ball, including an angular velocity vector and a linear acceleration vector; the data processing module fuses the inertial data with the image sequence captured by the visual sensor and optimizes the position tracking of the ball through a Kalman filtering algorithm to generate a more accurate time series of position coordinates.

3. The table tennis trajectory prediction and point analysis system according to claim 1, wherein, The data processing module uses a deep learning-based object detection algorithm to identify the ping pong ball in the sequence of motion images, including using a convolutional neural network model to analyze each frame of image to locate the ball and output its bounding box coordinates; subsequently, a multi-target tracking algorithm is used to associate the ball positions in consecutive frames to generate a smooth time series of position coordinates, wherein the multi-target tracking algorithm includes data association and motion compensation steps.

4. The table tennis trajectory prediction and point analysis system according to claim 1, wherein, The rotation quantity in the motion parameters is estimated by analyzing the changes of the surface texture or additional markers of the ball in the image sequence, including using an optical flow method or a feature matching technique to calculate the rotation vector of the ball; the data processing module integrates the rotation vector into the motion parameters for simulating the effects of Magnus effect and spin on the trajectory in the physical motion equation.

5. The table tennis trajectory prediction and point analysis system according to claim 1, wherein, The physical motion equation is solved by a numerical integration method, including Euler method or Runge-Kutta method, to simulate the movement of the ball in three-dimensional space; the physical motion equation is expressed as: wherein m represents the mass of the table tennis ball, v represents the velocity vector of the table tennis ball, and t represents time, g represents gravity, F represents air resistance, F represents the Magnus force; wherein , g represents the gravity acceleration vector; p represents the air density, C_d represents the resistance coefficient, and A represents the cross-sectional area of the table tennis ball; , w represents the angular velocity vector of the table tennis ball, C represents the Magnus force coefficient; the parameters in the equation are set according to the standard table tennis ball specifications and can be dynamically adjusted according to environmental conditions.

6. The table tennis trajectory prediction and point analysis system according to claim 1, wherein, The machine learning model is a recurrent neural network structure, specifically including a long short-term memory unit, for processing long-term dependencies of the time series of position coordinates; the update process of the long short-term memory unit at a time step t is defined by the following equation: wherein, represents an input vector at a time step t, including a position, a velocity or a rotation amount of the ball; represents a hidden state at the time step t; represents a cell state at the time step t; , , respectively represent activation values of an input gate, a forget gate and an output gate; represents a candidate cell state; , , , represents a weight matrix; , , , represents a bias vector; σ represents a sigmoid activation function, defined as ; tanh represents a hyperbolic tangent activation function; represents a vector obtained by concatenating a previous hidden state and a current input ; the model is trained in a supervised learning manner, training data covers multiple types of hitting and environmental scenarios, to learn nonlinear features of the trajectory, and output a probability distribution of ball positions at multiple future time steps.

7. A table tennis trajectory prediction and point analysis system as claimed in claim 6, characterized in that, The training process of the recurrent neural network model includes a data augmentation step, which simulates real-world variations by adding noise and transforming the viewing angle; the model receives the time series of position coordinates in real time during the inference stage and outputs the trajectory prediction result, while adjusting the model weights according to new data through an online learning mechanism.

8. The table tennis trajectory prediction and point analysis system according to claim 1, wherein, The system also includes a calibration module for adjusting the parameters of the physical motion equation and the machine learning model according to real-time environmental data; the calibration module receives external inputs including temperature, humidity, and air pressure information and dynamically updates the air density and drag coefficient based on these information.

9. The table tennis trajectory prediction and point analysis system according to claim 1, wherein, The output of the prediction module includes the predicted trajectory curve and landing point coordinates of the ball and is presented in a visual form through a graphical user interface; the interface allows users to interactively view trajectory history, real-time prediction, and landing point analysis reports, while supporting data export and playback functions.

10. The table tennis trajectory prediction and point analysis system according to claim 1, wherein, The system runs in real-time mode, in which the data acquisition module captures images at a high frame rate, the processing delay of the data processing module and the prediction module is controlled within the range of ms, ensuring that the trajectory prediction and landing point analysis are completed during the process from hitting to landing, and the results are transmitted to the remote display device through the network interface.

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