Football attack and defense formation effectiveness evaluation method based on fractal dimension and relative entropy of space

Abstract

This invention relates to the fields of computer vision and sports data analysis technology, specifically to a method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy, comprising: Step S1: acquiring tracking video sequences on the sports field to construct the boundary fields of the opposing and friendly formations; Step S2: analyzing the fractal dimension of the formation boundary fields to quantify the formation complexity; Step S3: using relative entropy to quantify the difference between the actual space occupancy probability distribution and the ideal probability distribution, defining the formation orderliness; Step S4: sequentially determining grid control authority, spatial control rate, and control entropy; Step S5: analyzing the real-time center-of-gravity trajectories of both sides to obtain net potential energy and determine the offensive and defensive posture of both sides; Step S6: constructing a comprehensive evaluation model for offensive and defensive effectiveness and outputting an offensive and defensive effectiveness index; Step S7: plotting effectiveness curves to obtain the rate of change, pre-setting detection rules, and analyzing the rate of change to achieve automatic detection of tactical events; Step S8: constructing a dynamic visualization output system for offensive and defensive formation effectiveness.

Description

Technical Field

[0001] This invention relates to the fields of computer vision and sports data analysis technology, specifically to a method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy. Background Technology

[0002] Traditional football tactical analysis relies heavily on the human experience of coaches and experts, which suffers from high subjectivity, low efficiency, and difficulty in quantification, easily affecting the objective judgment and in-depth understanding of team performance and opponent strategies. While existing computer vision-based technologies can acquire player position data, they still have the following shortcomings:

[0003] First, the complexity of formations is not well described, making it difficult to quantitatively describe the dynamic changes and spatial distribution characteristics of formation boundaries. Second, the assessment of tactical execution relies on subjective judgment, lacking effective means to quantify the difference between actual positioning and tactical requirements. Third, the assessment of spatial control ability is crude, making it difficult to calculate the team's actual control over various areas of the field in detail. Fourth, there are gaps in the quantification of offensive and defensive momentum, lacking a dynamic analysis model that integrates the team's overall movement and on-field positional relationships. Fifth, there is a lack of a comprehensive evaluation system that integrates multiple dimensions, making it difficult to form unified quantifiable indicators for offensive and defensive effectiveness. Summary of the Invention

[0004] To address the technical problem of insufficient scientific rigor and accuracy in existing football tactical analysis techniques, this invention aims to provide a method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy. The specific technical solution adopted is as follows:

[0005] Step S1: Collect tracking video sequences on the sports field, convert player information, obtain the center of gravity of both sides, and construct the boundary field of the opposing and friendly teams;

[0006] Step S2: Analyze the fractal dimension of the formation boundary field using fractal geometry theory, and quantify the formation complexity.

[0007] Step S3: Determine the probability distribution of actual space occupancy between the enemy and friendly forces based on the tracking video sequence, obtain the ideal probability distribution according to the classic tactical formation, use relative entropy to quantify the difference between the actual space occupancy probability distribution and the ideal probability distribution, and define the orderliness of the formation.

[0008] Step S4: Grid the sports field and analyze it, and determine the grid control weight, spatial control law and control entropy in sequence;

[0009] Step S5: Analyze the real-time center-of-gravity trajectories of both sides, quantify the offensive and defensive potential energy, obtain the net potential energy, and determine the offensive and defensive situation of both sides.

[0010] Step S6: Combine formation complexity, formation order, spatial control rate, control entropy, and net potential energy to construct a comprehensive evaluation model for attack and defense effectiveness, and output the attack and defense effectiveness index corresponding to each frame;

[0011] Step S7: Establish a time series based on the attack and defense effectiveness index, plot the effectiveness curve to obtain the rate of change, preset detection rules, and analyze the rate of change to achieve automatic detection of tactical events;

[0012] Step S8: Integrate the boundary field of the formation, spatial control rate, net potential energy, and offensive and defensive effectiveness index to construct a dynamic visualization output system for offensive and defensive formation effectiveness.

[0013] Preferably, step S1 includes:

[0014] Step S11: Collect tracking video sequences on the sports field using a camera, establish a coordinate system based on the sports field, and determine the planar position coordinates of the players from both sides in each frame;

[0015] Step S12: Construct the convex hull boundaries of both the enemy and friendly forces by describing the boundary contour of the formation using convex hulls, and analyze the planar position coordinates to obtain the centroids of both the enemy and friendly forces;

[0016] Step S13: Combine the planar position coordinates and center of gravity of the players, and use principal component analysis to extract the principal axis directions of the enemy and friendly formations.

[0017] Preferably, step S2 includes:

[0018] Step S21: Extract the vertices on the convex hull boundary to construct the formation contour point sets of both the enemy and friendly sides respectively;

[0019] Step S22: Use box counting to determine the fractal dimension of the point sets of the enemy and friendly formation outlines respectively;

[0020] Step S23: Normalize the fractal dimension to determine the formation complexity of both sides.

[0021] Preferably, step S22 includes:

[0022] Step S221: Filter multiple box side lengths that decrease monotonically in a geometric progression based on the diameter corresponding to the convex hull boundary;

[0023] Step S222: Cover the sports field with a grid formed by any box side length, and count the number of grids that contain at least one formation outline point;

[0024] Step S223: Combine the side length of the box and the number of grids to form a scatter plot. Perform linear regression based on the scatter plot to obtain the fractal dimension of the formation outline point set of both sides.

[0025] Preferably, step S3 includes:

[0026] Step S31: Grid the sports field, and count the number of players from both sides in each grid based on each frame in the tracking video sequence to form a space occupancy matrix of both sides;

[0027] Step S32: Normalize the space occupancy matrix of both sides to obtain the probability distribution of the actual space occupancy of both sides;

[0028] Step S33: Determine the ideal probability distribution of classic tactical formations based on the gridded sports field;

[0029] Step S34: Use relative entropy to quantify the difference between the actual space occupancy probability distribution and the ideal probability distribution, and define the orderliness of the formation.

[0030] Preferably, step S4 includes:

[0031] Step S41: Grid the sports field, filter target points based on any frame, obtain the distance from the target point to the nearest friendly player and the distance to the nearest enemy player, and define single-point control.

[0032] Step S42: Use the five-point sampling method to sample the single-point control weight corresponding to each grid at multiple locations, and determine the grid control weight corresponding to each grid in the current analysis frame through the majority voting rule;

[0033] Step S43: Based on grid control authority, count the number of grids controlled by both sides and obtain the spatial control rate of the enemy and friendly formations respectively;

[0034] Step S44: Construct a binary control matrix corresponding to the sports field grid through grid control authority, and determine the control entropy of the enemy and friendly formations by combining the 8-neighborhood connectivity rule.

[0035] Preferably, step S5 includes:

[0036] Step S51: Determine the velocity of our center of gravity and the velocity of the enemy's center of gravity based on the center of gravity of both sides.

[0037] Step S52: Obtain the center coordinates of the goal of both sides, define the position factor in combination with the center of gravity, and output the offensive potential energy and defensive potential energy by combining the center of gravity velocity of our side and the center of gravity velocity of the enemy.

[0038] Step S53: Combine offensive and defensive potential energy to obtain net potential energy, and analyze the net potential energy to judge the offensive and defensive situation of the enemy and ourselves.

[0039] Preferably, step S7 includes:

[0040] Step S71: Establish a time series based on the attack and defense effectiveness index, plot the effectiveness curve, and obtain the first-order difference and the second-order difference respectively, corresponding to the instantaneous rate of change and acceleration of change.

[0041] Step S72: Preset uplink threshold, downlink threshold and minimum duration respectively, compare with first-order difference, and analyze whether second-order difference crosses zero to detect tactical events.

[0042] Preferably, step S8 specifically includes:

[0043] By integrating the formation boundary field, spatial control rate, net potential energy, and offensive and defensive effectiveness index, dynamic diagrams of formation boundaries, spatial control heat maps, and effectiveness curves are established to construct a dynamic visualization output system for offensive and defensive formation effectiveness.

[0044] To solve the above-mentioned technical problems, the present invention also provides: an electronic device, the device comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus, and the processor calls logical instructions in the memory to execute the football attack and defense formation effectiveness evaluation method based on fractal dimension and spatial relative entropy as described in any of the preceding claims.

[0045] The present invention has the following beneficial effects:

[0046] 1. Based on the shortcomings of existing technologies, this paper proposes a comprehensive, objective, quantitative, and automated method for evaluating the effectiveness of football offensive and defensive formations. It analyzes the fractal dimension of both teams' formations using fractal geometry theory to quantify formation complexity and quantitatively describe the dynamic changes and spatial distribution characteristics of formation boundaries. Relative entropy is used to quantify the difference between the probability distribution of actual space occupancy and the ideal probability distribution, thereby quantifying the difference between actual positioning and tactical requirements and objectively assessing formation orderliness. Through grid division and distance field determination methods, the actual spatial control rate and control entropy of the team over various areas of the field are calculated in detail. By analyzing the real-time center-of-gravity trajectories of both teams, offensive and defensive potential energy is quantified to obtain net potential energy, dynamically reflecting the team's overall offensive and defensive posture. Finally, by combining formation complexity, formation orderliness, spatial control rate, control entropy, and net potential energy, a unified offensive and defensive effectiveness index is determined, addressing the lack of a multi-dimensional integrated evaluation system.

[0047] 2. The electronic device provided by this invention has the same beneficial effects as the football offensive and defensive formation effectiveness evaluation method based on fractal dimension and spatial relative entropy provided by this invention, and will not be elaborated here. Attached Figure Description

[0048] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 The flowchart illustrates a method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy, as provided in one embodiment of the present invention.

[0050] Figure 2 The following is a flowchart illustrating the implementation of a method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy, as provided in one embodiment of the present invention. Detailed Implementation

[0051] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a football offensive and defensive formation effectiveness evaluation method based on fractal dimension and spatial relative entropy proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0052] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0053] The following description, in conjunction with the accompanying drawings, details a specific scheme for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy, provided by this invention.

[0054] Please combine Figure 1 and Figure 2 The first embodiment of the present invention provides a method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy, the method comprising:

[0055] Step S1: Collect tracking video sequences on the sports field, convert player information, obtain the center of gravity of both sides, and construct the boundary field of the opposing and friendly teams;

[0056] Step S2: Analyze the fractal dimension of the formation boundary field using fractal geometry theory, and quantify the formation complexity.

[0057] Step S3: Determine the probability distribution of actual space occupancy between the enemy and friendly forces based on the tracking video sequence, obtain the ideal probability distribution according to the classic tactical formation, use relative entropy to quantify the difference between the actual space occupancy probability distribution and the ideal probability distribution, and define the orderliness of the formation.

[0058] Step S4: Grid the sports field and analyze it, and determine the grid control weight, spatial control law and control entropy in sequence;

[0059] Step S5: Analyze the real-time center-of-gravity trajectories of both sides, quantify the offensive and defensive potential energy, obtain the net potential energy, and determine the offensive and defensive situation of both sides.

[0060] Step S6: Combine formation complexity, formation order, spatial control rate, control entropy, and net potential energy to construct a comprehensive evaluation model for attack and defense effectiveness, and output the attack and defense effectiveness index corresponding to each frame;

[0061] Step S7: Establish a time series based on the attack and defense effectiveness index, plot the effectiveness curve to obtain the rate of change, preset detection rules, and analyze the rate of change to achieve automatic detection of tactical events;

[0062] Step S8: Integrate the boundary field of the formation, spatial control rate, net potential energy, and offensive and defensive effectiveness index to construct a dynamic visualization output system for offensive and defensive formation effectiveness.

[0063] To better illustrate this point, in the field of football match tactical analysis, traditional methods largely rely on expert experience for manual interpretation, which suffers from low efficiency, strong subjectivity, and difficulty in real-time quantification. When only the players from opposing sides can be distinguished but individual identities cannot be identified, traditional individual tracking methods fail. There is an urgent need for a mathematical method that can evaluate tactical effectiveness based solely on the set of opposing and friendly positions. Therefore, this paper proposes a football offensive and defensive formation effectiveness evaluation method based on fractal dimension and spatial relative entropy. By constructing the boundary fields of opposing and friendly formations, multiple quantitative indicators such as formation complexity difference, formation orderliness, spatial control rate, control entropy, and net potential energy are obtained sequentially. This allows for the construction of a comprehensive offensive and defensive effectiveness evaluation model, enabling real-time quantitative evaluation of tactical situations and detection of key events.

[0064] As an optional implementation, in this embodiment, the sports field is arranged around the football field to provide a more comprehensive and objective analysis of football match tactics.

[0065] Further, step S1 includes:

[0066] Step S11: Collect tracking video sequences on the sports field using a camera, establish a coordinate system based on the sports field, and determine the planar position coordinates of the players from both sides in each frame.

[0067] Specifically, cameras are placed on the sports field to collect video tracking data, which is then integrated to form a tracking video sequence. The origin of the coordinate system is then set at the midpoint of the left boundary of the sports field. A coordinate system is established with the x-axis pointing horizontally to the right towards the opponent's goal and the y-axis pointing vertically upwards, creating a top-down view of the stadium. Image data for each frame in the tracking video sequence is acquired in real-time, and the planar position coordinates of our players and the opposing players in the corresponding frames are extracted. The set of our players' positions is defined as follows: The opposing players' positions are grouped as follows In a standard 11-a-side football match, each team has 11 players on the field, meaning the set has 11 dimensions. , These represent the indices of our players and the opposing players, respectively. This indicates the index of a video frame in the tracking video sequence.

[0068] Step S12: Construct the convex hull boundaries of both sides by describing the boundary contour of the formation using convex hull, and analyze the planar position coordinates to obtain the centroids of both sides.

[0069] As explained, in football tactical analysis, the spatial coverage of a team's formation is an important indicator of its ability to control the field. In this embodiment, the convex hull is used to describe the overall area occupied by the team. The convex hull refers to the smallest convex polygon that contains all points in the point set, and it can directly reflect the boundary outline of the team's formation.

[0070] Specifically, for each frame, the set of our players' positions The corresponding convex hull boundary is The output is a sequence of boundary points arranged counterclockwise; the set of enemy player positions. The corresponding convex hull boundary is Similarly, the output is a sequence of boundary points arranged counterclockwise. By observing the dynamic changes of the convex hull boundary, the expansion and contraction of the team's formation and the overall movement trend can be directly observed.

[0071] Next, the center of gravity of the formation is a key indicator reflecting the overall offensive and defensive center of gravity of the team. By calculating the arithmetic mean of the planar position coordinates of all players on the team, the coordinates of the center of gravity are obtained; that is, the coordinates of our team's center of gravity correspond to... The enemy's center of gravity coordinates are as follows: By using the center of gravity coordinates to reflect the central trend of the formation, it is easier to analyze the offensive and defensive potential energy in subsequent analysis.

[0072] Step S13: Combine the planar position coordinates and center of gravity of the players, and use principal component analysis to extract the principal axis directions of the enemy and friendly formations.

[0073] Specifically, in actual matches, team formations typically have a primary direction, i.e., the attacking direction. In this embodiment, Principal Component Analysis (PCA) is used to extract the principal axis direction of the formation to determine the team's attacking direction. First, an analysis is performed on our team's formation. Based on the deviation of our players' positions from our center of gravity coordinates, our team's covariance matrix is ​​calculated. The corresponding calculation formula is as follows: Calculate the eigenvalues ​​and eigenvectors of the covariance matrix, and select the eigenvector corresponding to the largest eigenvalue as the principal axis direction vector of our formation, denoted as . This represents the longest axis direction of the team's formation, i.e., the main direction of attack or extension; similarly, the main axis direction vector of the enemy's formation can be obtained based on our formation. Then, based on the components of the eigenvectors, the angle of the principal axis relative to the X-axis of the coordinate system is calculated, i.e. Similarly, determine the enemy's principal axis angle. This is used for subsequent coordinate system rotation correction or tactical orientation analysis.

[0074] Further, step S2 includes:

[0075] Step S21: Extract the vertices on the convex hull boundary to construct the formation contour point sets of both the enemy and our side.

[0076] Specifically, based on the convex hull boundary constructed in the aforementioned steps, vertices are extracted as formation contour feature points, that is, our formation contour point set is defined as follows: The enemy's square outline point set is , , These represent the number of vertices on the convex hull boundaries of our side and the enemy side, respectively. That is, the boundary vertices are composed of a series of discrete points on the convex hull boundary, which constitute the outer boundary of the area actually occupied by the team in space, reflecting the edge of the team's actual occupied range. In subsequent analysis, the set of outline points of both sides' formations will be used... and As the original data source for calculating fractal dimension.

[0077] Step S22: Use box counting to determine the fractal dimension of the point sets of the enemy and friendly formation outlines respectively.

[0078] As explained, box counting is a practical method widely used to calculate fractal dimension. It quantifies the complexity and space-filling characteristics of an object by relating the number of "boxes" covering the target object (i.e., the convex hull boundary) to the size of the boxes. It is suitable for analyzing geometric figures or datasets with irregular, self-similar structures.

[0079] Further, step S22 includes:

[0080] Step S221: Filter multiple box side lengths that decrease monotonically in a geometric progression based on the diameter corresponding to the convex hull boundary; that is, select a series of box side lengths that decrease monotonically in a geometric progression. , usually take That is, take in sequence , , , , ,in, Take the diameter of the convex hull of the corresponding player set for subsequent mesh coverage operations.

[0081] Step S222: Cover the sports field with a grid formed by any box side length, and count the number of grids that contain at least one formation outline point; that is, for any box side length Value, using a side length of The grid covers the entire sports field; the length of this side is calculated. The corresponding grid motion field contains at least one boundary point, that is, the number of grids containing the formation outline points, denoted as . .

[0082] Step S223: Combine the side length of the box and the number of grids to form a scatter plot. Perform linear regression based on the scatter plot to obtain the fractal dimension of the formation outline point set of both sides.

[0083] Specifically, points are plotted in a log-log coordinate system. That is, we take the logarithm of the reciprocal of the grid side length as the horizontal axis and the logarithm of the corresponding minimum covering grid number as the vertical axis to form a scatter plot; then, we perform linear regression on the scatter plot, and the slope obtained is the fractal dimension we are looking for. The corresponding calculation formula is: Based on our fractal dimension Similarly, the fractal dimension of the enemy can be obtained. .

[0084] The fractal dimension calculated for each frame is explained. and By combining pre-set tactical characteristic thresholds for analysis, a corresponding tactical interpretation of the current formation can be made. In this embodiment, the tactical characteristic thresholds are 1.1, 1.2, 1.3, and 1.4, which can be determined based on fractal geometry theory or empirical calibration of football tactics. In fractal geometry theory, the fractal dimension... The range of values ​​is , Corresponding to an ideal straight line (one-dimensional); For a completely filled plane (2D), the complexity of the convex hull boundary of a team in a football match falls between these two, hence the intervals are set to 0.1. The interval is divided into 5 levels, corresponding to five tactical states: nearly straight, slightly jagged, moderately jagged, obviously jagged, and extremely complex. In the calibration of football tactical experience, statistical analysis of player position data from multiple professional football matches, including the World Cup and the top five European leagues, revealed that: when a team is in an organized defensive state, the fractal dimension is mainly concentrated in the range of 1.2 to 1.3; when the team frequently transitions between offense and defense and the formation is stretched significantly, the fractal dimension rises to 1.3 to 1.4; when the team's tactical discipline fails and the formation collapses, the fractal dimension exceeds 1.4; and when the team's defensive line is too flat and lacks layering, the fractal dimension is below 1.1. In practical applications, users can fine-tune the tactical characteristic thresholds according to different match levels or tactical styles, without imposing a single limitation.

[0085] It can be explained that when the fractal dimension At that time, the formation was almost a straight line, and the straight defensive line was easy to penetrate; when At that time, the formation was slightly jagged, and the basic formation remained unchanged but with little variation; when At that time, the formation is moderately serrated, representing an ideal state of layered defense and varied offense; when At that time, the formation was clearly jagged, and the team was in a high-intensity confrontation with frequent transitions between offense and defense; when At that time, the formation was extremely complex, the tactical discipline was poor, and they may be in a state of being oppressed.

[0086] Step S23: Normalize the fractal dimension to determine the formation complexity of both sides.

[0087] Specifically, to facilitate data calculation in different competition scenarios, the fractal dimension is... Normalization to Within the interval, the formation complexity is obtained, i.e. This corresponds to the formation complexity of both sides. and In this embodiment, , which corresponds to the fractal dimension of the ideal straight line state; This corresponds to the fractal dimension of a completely disordered planar filling curve; thus, the difference in formation complexity is determined, i.e. This is used to measure the relative differences in tactical styles between the two sides; it addresses the difference in formation complexity for each frame. ,when When our formation is more complex than the opponent's, our offense is more varied, and our defense is more three-dimensional, it indicates that our tactics are more complex than the opponent's, and that we are more flexible and three-dimensional in both offense and defense; while The situation is the opposite, that is The larger the gap, the more pronounced the differences in tactical styles between the two sides become; in particular, because the formations of both sides change dynamically in real time during a match, it is almost impossible for different formations to emerge. The case where it approaches zero.

[0088] Further, step S3 includes:

[0089] Step S31: Grid the sports field. Based on the statistics of the number of players from both sides in each grid in each frame of the tracking video sequence, form a space occupancy matrix of both sides.

[0090] Specifically, the standard sports field is divided into The grid, preferably, , To achieve a balance between assessment accuracy and computational efficiency; for match motion data, i.e., tracking each frame of the video sequence, the number of friendly and opposing players in each grid is counted, and the results are analyzed in the current frame. In this process, we form our space occupancy matrix and the enemy's space occupancy matrix, respectively, and the corresponding calculation formulas are as follows: , In this matrix, each element represents the actual player count within the corresponding grid. Indicates the range of intervals.

[0091] Step S32: Normalize the space occupancy matrices of both sides to obtain the probability distribution of the actual space occupancy of both sides; that is, normalize the player counts in the space occupancy matrices of both sides, converting the count values ​​into probability distribution forms, and obtain the probability distribution of the actual space occupancy of both sides. The corresponding calculation formula is as follows: , The probability value corresponding to each grid is the ratio of the number of players in that grid to the total number of players in the team (11 players).

[0092] Step S33: Determine the ideal probability distribution of classic tactical formations based on the gridded sports field.

[0093] Specifically, based on the standardized player positioning rules of classic tactical formations such as 4-4-2 and 4-3-3 in football, the ideal number of players in different areas of the field is determined; the ideal number of players in each area is then divided by the total number of players on the field for the team. (Generally 11 people), to obtain the probability distribution of the ideal tactical formation for each grid, i.e., the ideal probability distribution, the corresponding calculation formula is: , Represents the grid used in the current analysis. The ideal number of players actually present in the field. Preferably, taking a 4-4-2 formation as an example, the field is divided longitudinally into three zones: the defensive zone, i.e., 0-35m from the team's own goal: 4 players → Ideal probability distribution Midfield area, i.e., 35-70m: 4 people → Ideal probability distribution Forward zone, i.e., 70-105m: 2 people → Ideal probability distribution The remaining probability of 0.10 is allocated to other areas.

[0094] Step S34: Use relative entropy to quantify the difference between the actual space occupancy probability distribution and the ideal probability distribution, and define the orderliness of the formation.

[0095] Specifically, the relative entropy, or KL divergence, between the probability distributions of our actual space occupancy and those of the enemy and their corresponding ideal probability distributions is calculated. The corresponding formula is as follows:

[0096]

[0097] Among them, when When both are completely identical, the relative entropy term is 0; when When the actual space occupancy probability distribution is higher than the ideal probability distribution, it indicates that players are over-concentrated in that area; when When the actual space occupancy probability distribution is lower than the ideal probability distribution, it indicates insufficient player coverage in that area. Therefore, the deviation between the actual player positioning and the ideal tactical requirements is quantified using relative entropy values. Based on our relative entropy... Similarly, determine the enemy's relative entropy. .

[0098] Next, due to relative entropy The natural range of values ​​is To facilitate understanding, comparison, and visualization, it is mapped to an exponential function. The interval defines the orderliness of the formation, and the corresponding calculation formula is: Similarly, determine the orderliness of the enemy's formation. Different tactical execution states are defined based on the numerical range of formation orderliness: when When this indicates excellent tactical discipline and that players strictly adhere to tactical positioning; when When, it indicates that the formation is basically maintained, allowing players a certain degree of tactical freedom; when When this occurs, it indicates that the formation is loose and the team may be in a transition phase between offense and defense; when This indicates a chaotic formation and a failure of team tactical discipline; thus, it allows for a direct assessment of the team's tactical execution.

[0099] Understandably, when analyzing spatial control based on distance fields, the core of a football match is spatial competition. Whoever is closest to a position has control over that position. In this embodiment, a Voronoi diagram is used to divide the plane into several regions, such that the distance from each point in each region to its internal points is the shortest. That is, in a football match, a Voronoi diagram can intuitively show the regions controlled by our team, the regions controlled by the opponent, and the regions under competition.

[0100] Further, step S4 includes:

[0101] Step S41: Grid the sports field, filter target points based on any frame, obtain the distance from the target point to the nearest friendly player and the distance to the nearest enemy player, and define single-point control.

[0102] Specifically, based on a top-down view of a football stadium, with the coordinate unit being meters, the stadium is uniformly divided into a standard grid of 21×14, with each grid cell having a physical size of 5m×4.86m. The grid cells are then numbered by row and column; in subsequent analysis, the numbered cells will be used as the reference point. Line number The column's grid is used as the target grid, and the coordinates of the grid's center point are determined. The corresponding calculation formula is: and ,in, , .

[0103] Next, single-point control is defined based on the current analysis frame, i.e., the current analysis time. Select any point as the target point, and denote it as... Calculate the distance from the target point to the nearest friendly player. ,Right now And calculate the distance from the target point to the nearest enemy player. ,Right now The three-value determination rule is used to define single-point control rights, and the corresponding calculation formula is as follows:

[0104]

[0105] in, This represents the distance determination threshold; in this embodiment, It can be specifically configured according to the actual situation to distinguish between control and contention states, and define... This indicates that the target point is under our control; This indicates that the target point is controlled by the enemy. This indicates that the target point is a contested area between the opposing forces.

[0106] Step S42: Use the five-point sampling method to sample the single-point control rights corresponding to each grid at multiple locations, and determine the grid control rights corresponding to each grid in the current analysis frame through the majority voting rule.

[0107] Specifically, since single-point control cannot reflect the spatial control status of the entire grid, a five-point sampling method is used to sample multiple locations in each grid, and the overall control of the grid is determined through a majority voting rule; the target grid determined above is used as the basis for this determination. Taking this as an example, five feature sampling points are selected: the grid center point, the top left corner of the grid, the top right corner of the grid, the bottom left corner of the grid, and the bottom right corner of the grid. Similarly, based on the target point in step S41, the single-point control weight corresponding to these five feature sampling points is determined. The results of the sampling point control weights are statistically analyzed and recorded. For control The number of sampling points, For control The number of sampling points; the majority voting rule is executed to determine grid control, and the corresponding calculation formula is:

[0108]

[0109] Step S43: Based on grid control authority, count the number of grids controlled by both sides and obtain the spatial control rate of the enemy and friendly formations respectively.

[0110] Specifically, the spatial control rate is the ratio of the number of grids actually controlled by us to the total number of grids on the court, directly reflecting our overall control over the court space; similarly, based on step S42, the grid control rights of all grids are determined for the target grid analysis; then, for the current analysis time... All grid control rights are traversed and statistically analyzed, and recorded. This indicates the number of grids controlled by us at the current analysis time, i.e. The formula for determining the space control rate is as follows: Among them, space control rate The larger this value, the higher our control over the field space.

[0111] Step S44: Construct a binary control matrix corresponding to the sports field grid through grid control authority, and determine the control entropy of the enemy and friendly formations by combining the 8-neighborhood connectivity rule.

[0112] Specifically, based on the grid control rights of all current grids, a binary control matrix corresponding to the stadium grid is constructed. The matrix element value selection rule is to only mark the grids controlled by our side as 1, and the corresponding calculation formula is:

[0113]

[0114] Next, the binarized control matrix is... Connectivity regions are marked using the 8-neighbor connectivity rule, meaning that a grid connected to any of its eight adjacent grids (up, down, left, right, top left, top right, bottom left, bottom right) is considered to be in the same region. This yields the total number of connected regions in our controlled area. And statistics of the first The number of grids contained in a connected region The total number of grid cells controlled by us is ; Calculate the control entropy, which is used to measure the degree of concentration of our controlled area, i.e.: When controlling entropy When the value is approximately 0, it indicates that the controlled area is complete and contiguous, and the formation is well maintained; when... When the control entropy value is small, it indicates that the control area is relatively dispersed but maintains a certain degree of integrity, and the smaller the control entropy value, the more concentrated our control area is; when When the control area is fragmented and easily divided by the opponent, and the larger the control entropy value, the more dispersed our control area is; based on this, we can similarly determine the relevant data of the enemy.

[0115] Understandably, by analyzing and calculating offensive and defensive potential energy based on real-time center of gravity trajectories, and quantifying offensive and defensive potential energy through the team's real-time center of gravity trajectory, a dynamic and accurate judgment of the offensive and defensive situation of the game can be achieved. First, the velocity of the center of gravity movement is calculated, and then the classical physical kinetic energy formula and the football scenario-based positional factors are integrated to define and calculate offensive and defensive potential energy. Finally, the net potential energy is obtained through the difference between offensive and defensive potential energy, which provides an intuitive reflection of the team's overall offensive and defensive potential energy situation and provides core data support for the dynamic potential energy dimension for subsequent comprehensive evaluation of offensive and defensive effectiveness.

[0116] Further, step S5 includes:

[0117] Step S51: Determine the velocity of our center of gravity and the velocity of the enemy's center of gravity based on the center of gravity of both sides.

[0118] Specifically, by the interval Displacement of the center of gravity trajectory and time interval The ratio defines the velocity of our center of gravity, that is... Corresponding unit marking ; Indicates the inter-frame time interval, preferably. It can be adjusted according to the actual situation; similarly, the speed of the enemy's center of gravity can be determined, that is... , for use in subsequent kinetic energy conversion.

[0119] Step S52: Obtain the center coordinates of both the enemy's and our own goal, define the position factor in conjunction with the center of gravity, and output the offensive potential energy and defensive potential energy by combining our center of gravity velocity and the enemy's center of gravity velocity.

[0120] It is explained that in defining the offensive and defensive potential energies of both sides, the offensive potential energy can be determined by the product of kinetic energy and position factor, thus coupling the state of motion with spatial position into a unified potential energy; the kinetic energy formula is based on classical physics formulas. Among them, quality Using team size as a substitute, the more players there are, the greater the "energy" the team possesses for overall movement, and the faster they move. Replace it with the speed of the team's center of gravity movement.

[0121] Specifically, let's assume the sports field being analyzed has a length of... Determine the center coordinates of the enemy goal as The formula for calculating the distance from our center of gravity to the enemy goal is: Define a position factor to reflect the distance threat posed by the team's center of gravity to the opponent's goal, i.e. The closer our team's center of gravity is to the opponent's goal, the more intense our attack and the greater the threat we pose to the opponent; to determine our attacking potential, we need to indicate the position of our formation at any given moment. The index of offensive energy posture is equal to the product of the kinetic energy term and the offensive position factor, and the corresponding calculation formula is: Defensive potential energy represents the opponent's offensive potential energy, reflecting the threat the opponent poses to our goal at the current moment. The corresponding calculation formula is: ,in, It indicates the distance from the opponent's center of gravity to our goal.

[0122] Step S53: Combine offensive and defensive potential energy to obtain net potential energy, and analyze the net potential energy to judge the offensive and defensive situation of the enemy and ourselves.

[0123] Specifically, the difference between offensive and defensive potential energy is used to represent net potential energy, transforming the two-way offensive and defensive potential energy indicators into a single quantitative indicator to intuitively reflect the current overall offensive and defensive potential energy status of the team. The corresponding calculation formula is as follows: Among them, when At this time, the game situation usually shows that our side is in control of the attack, and the larger the value, the stronger our side's offensive dominance; when At this time, the game situation usually shows that the opponent is in control of the attack, and the smaller the value, that is, the larger the absolute value, the stronger the opponent's offensive dominance; when At this time, the game situation usually shows that the two sides are evenly matched, with no clear dominant force in offense or defense.

[0124] It can be explained that in step S6, the aim is to normalize the multiple evaluation indicators calculated in the aforementioned steps and construct a comprehensive evaluation model of attack and defense effectiveness through weighted fusion, so as to achieve a quantitative assessment of the overall attack and defense capabilities of the formation.

[0125] Specifically, since the values ​​and dimensions of the formation complexity, formation order, spatial control law, control entropy and net potential energy obtained in the aforementioned steps are different, they are normalized separately to unify them into a unified evaluation scale.

[0126] Regarding formation complexity, it is based on the difference in formation degree between the enemy and our side. The analysis shows that its value range is... The hyperbolic tangent function is used to further compress the data to... The interval is defined as follows: The normalized formation complexity advantage index is: For controlling entropy Its maximum value is defined as the entropy value when the control area is uniformly dispersed. Construct a control concentration index, with a value range of [value range missing]. A larger value indicates a more concentrated control area, i.e. For net potential energy The Sigmoid function is used to normalize it to... The interval is defined as follows: The normalized potential advantage index is: .

[0127] Next, since each indicator contributes differently to the overall offensive and defensive effectiveness, the analytic hierarchy process (AHP) is used to determine the weight coefficients of each indicator; that is, by constructing a judgment matrix, the weight coefficients of the formation complexity advantage indicators are determined. Orderliness of formation Space control rate Control Concentration and potential advantage index Perform pairwise comparisons, calculate the largest eigenvalue of the judgment matrix and its corresponding eigenvector, and obtain the weight vector after normalization. And each weight coefficient satisfies The normalized indicators are weighted and fused with their corresponding weight coefficients to construct an offensive and defensive effectiveness index. This value is used to quantify the overall tactical situation at a given moment. It comprehensively reflects the formation's overall offensive and defensive capabilities in terms of spatial control, formation structure, and potential energy changes. A higher value indicates better offensive and defensive effectiveness. The corresponding calculation formula is:

[0128]

[0129] Understandably, in step S7, based on the time series of the offensive and defensive effectiveness index, the effectiveness curve is plotted and its rate of change is calculated. Combined with preset detection rules, the automatic detection of key tactical events such as offensive events, defensive events and tactical turning points is realized, that is, key event detection is performed based on the effectiveness curve.

[0130] Further, step S7 includes:

[0131] Step S71: Establish a time series based on the attack and defense effectiveness index, plot the effectiveness curve, and obtain the first-order difference and the second-order difference respectively, corresponding to the instantaneous rate of change and acceleration of change.

[0132] Specifically, with time as the horizontal axis, the offensive and defensive effectiveness index A dynamic performance curve is plotted on the vertical axis. Key characteristic points are identified on the curve: local maxima correspond to the climax of tactical execution, local minima correspond to the occurrence of tactical crises, the slope of the rising segment reflects the speed at which tactical adjustments take effect, and the slope of the falling segment reflects the speed at which the opponent counters. Then, to quantify the dynamic characteristics of the performance curve, the first and second differences of the performance index are calculated. The first difference is used to characterize the instantaneous rate of change. The second-order difference is used to characterize the changing acceleration, i.e. .

[0133] Step S72: Preset uplink threshold, downlink threshold and minimum duration respectively, compare with first-order difference, and analyze whether second-order difference crosses zero to detect tactical events.

[0134] The uplink threshold, downlink threshold, and minimum duration are respectively denoted as: , and In this embodiment, the uplink threshold Set to 0.05 / frame, downlink threshold Set to -0.05 / frame, minimum duration The timer is set to 3 seconds, which corresponds to 75 frames per second. These settings can be adjusted according to the actual system frame rate and tactical response time.

[0135] Specifically, when the first difference of the attack and defense effectiveness index Greater than the uplink threshold And the duration reaches the minimum duration. If the event is classified as an offensive event, it indicates a continuous increase in effectiveness and that the tactics are in an active state of advancement; when the first difference of the offensive and defensive effectiveness index... Less than the downlink threshold And the duration reaches the minimum duration. If the event is classified as a defensive event, it indicates a continuous decline in effectiveness and a passive tactical response; when the second difference of the offensive and defensive effectiveness index... When the value crosses zero, it is considered a turning point event, indicating a reversal in the trend of effectiveness change, corresponding to a key turning point in the tactical situation.

[0136] Further, in step S8, specifically:

[0137] By integrating the formation boundary field, spatial control rate, net potential energy, and offensive and defensive effectiveness index, dynamic diagrams of formation boundaries, spatial control heat maps, and effectiveness curves are established to construct a dynamic visualization output system for offensive and defensive formation effectiveness.

[0138] Specifically, a dynamic diagram of the formation boundaries is established. Using a planar coordinate system constructed from the overhead view of the sports field as the base, the coordinate data of the convex hull boundaries of our and the enemy formations obtained in the previous steps are imported. The convex hull graphics of our and the enemy are drawn on the base respectively. The convex hulls formed by our and the enemy, and the areas where the two convex hulls overlap are outlined with different colors. The game frame sequence data is imported, and the coordinates of the convex hull boundaries of our and the enemy are updated in real time frame by frame and the graphics are refreshed synchronously. A dynamic diagram of the formation boundaries that can dynamically display the expansion and contraction of the offensive and defensive formations of both sides is established.

[0139] Establish a spatial control heat map, using the 21×14 court grid divided in the previous steps as a base, and import the distance from each grid point to the nearest friendly player. Distance to the nearest enemy player Distance determination threshold This distinguishes between the control and contention states of both sides, using different colors to delineate the controlled and contention zones. Simultaneously, it calculates the normalized distance difference value. , This represents the maximum theoretical distance difference between the sampling point within the sports field and the players from both sides. ,according to The value is adjusted to control the color intensity of each control area. The larger the area, the darker the color, indicating a stronger degree of spatial control by the corresponding party. The game frame sequence data is imported, and each grid is updated frame by frame. , and Simultaneously, the colors and shades of the grid areas are refreshed to create a spatial control heat map that dynamically displays the real-time distribution and changing status of control over the stadium space.

[0140] Establish an efficiency curve graph and construct a coordinate system with game time as the horizontal axis and two vertical axes, where the left axis is set as the main vertical axis, corresponding to the offensive and defensive efficiency index. The right axis is set as the secondary vertical axis, corresponding to the net potential energy. Import the match frame sequence data and update the offensive and defensive effectiveness index frame by frame. and net potential energy Furthermore, different colors are used to draw the curves generated corresponding to the two data points. Key events are automatically detected and identified. Key events that meet the conditions are also distinguished and labeled using different colors or shapes. The labels corresponding to the key events are precisely aligned with the corresponding positions on the curves to create an efficiency curve that can be linked to display the real-time changes in offensive and defensive effectiveness and key event performance.

[0141] Understandably, this paper proposes a comprehensive, objective, quantitative, and automated method for evaluating the effectiveness of football offensive and defensive formations, addressing the shortcomings of existing technologies. It analyzes the fractal dimension of both teams' formations using fractal geometry theory to quantify formation complexity and quantitatively describe the dynamic changes and spatial distribution characteristics of formation boundaries. Relative entropy is used to quantify the difference between the probability distribution of actual space occupancy and the ideal probability distribution, thereby quantifying the difference between actual positioning and tactical requirements and objectively assessing formation orderliness. Through grid division and distance field determination methods, it refines the calculation of the team's actual spatial control rate and control entropy over various areas of the field. By analyzing the real-time center-of-gravity trajectories of both teams, it quantifies offensive and defensive potential energy to obtain net potential energy, dynamically reflecting the team's overall offensive and defensive posture. Finally, by combining formation complexity, formation orderliness, spatial control rate, control entropy, and net potential energy, a unified offensive and defensive effectiveness index is determined, addressing the lack of a multi-dimensional integrated evaluation system.

[0142] A second embodiment of the present invention provides an electronic device, which includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other through the communication bus. The processor calls logical instructions in the memory to execute the football attack and defense formation effectiveness evaluation method based on fractal dimension and spatial relative entropy as described in any embodiment of the present invention.

[0143] When it is in operation, it needs to use a football attack and defense formation effectiveness evaluation method based on fractal dimension and spatial relative entropy. Therefore, whether the equipment and program data are integrated or different hardware is configured to produce functions with similar effects to those achieved by this invention, they all fall within the protection scope of this invention. This equipment has the same beneficial effects as the aforementioned football attack and defense formation effectiveness evaluation method based on fractal dimension and spatial relative entropy, and will not be elaborated here.

[0144] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0145] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy, characterized in that, The method includes: Step S1: Collect tracking video sequences on the sports field, convert player information, obtain the center of gravity of both sides, and construct the boundary field of the opposing and friendly teams; Step S2: Analyze the fractal dimension of the formation boundary field using fractal geometry theory, and quantify the formation complexity. Step S3: Determine the probability distribution of actual space occupancy between the enemy and friendly forces based on the tracking video sequence, obtain the ideal probability distribution according to the classic tactical formation, use relative entropy to quantify the difference between the actual space occupancy probability distribution and the ideal probability distribution, and define the orderliness of the formation. Step S4: Grid the sports field and analyze it, and determine the grid control weight, spatial control law and control entropy in sequence; Step S5: Analyze the real-time center-of-gravity trajectories of both sides, quantify the offensive and defensive potential energy, obtain the net potential energy, and determine the offensive and defensive situation of both sides. Step S6: Combine formation complexity, formation order, spatial control rate, control entropy, and net potential energy to construct a comprehensive evaluation model for attack and defense effectiveness, and output the attack and defense effectiveness index corresponding to each frame; Step S7: Establish a time series based on the attack and defense effectiveness index, plot the effectiveness curve to obtain the rate of change, preset detection rules, and analyze the rate of change to achieve automatic detection of tactical events; Step S8: Integrate the boundary field of the formation, spatial control rate, net potential energy, and offensive and defensive effectiveness index to construct a dynamic visualization output system for offensive and defensive formation effectiveness.

2. The method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy according to claim 1, characterized in that, Step S1 includes: Step S11: Collect tracking video sequences on the sports field using a camera, establish a coordinate system based on the sports field, and determine the planar position coordinates of the players from both sides in each frame; Step S12: Construct the convex hull boundaries of both the enemy and friendly forces by describing the boundary contour of the formation using convex hulls, and analyze the planar position coordinates to obtain the centroids of both the enemy and friendly forces; Step S13: Combine the planar position coordinates and center of gravity of the players, and use principal component analysis to extract the principal axis directions of the enemy and friendly formations.

3. The method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy according to claim 2, characterized in that, Step S2 includes: Step S21: Extract the vertices on the convex hull boundary to construct the formation contour point sets of both the enemy and friendly sides respectively; Step S22: Use box counting to determine the fractal dimension of the point sets of the enemy and friendly formation outlines respectively; Step S23: Normalize the fractal dimension to determine the formation complexity of both sides.

4. The method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy according to claim 3, characterized in that, Step S22 includes: Step S221: Filter multiple box side lengths that decrease monotonically in a geometric progression based on the diameter corresponding to the convex hull boundary; Step S222: Cover the sports field with a grid formed by any box side length, and count the number of grids that contain at least one formation outline point; Step S223: Combine the side length of the box and the number of grids to form a scatter plot. Perform linear regression based on the scatter plot to obtain the fractal dimension of the formation outline point set of both sides.

5. The method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy according to claim 1, characterized in that, Step S3 includes: Step S31: Grid the sports field, and count the number of players from both sides in each grid based on each frame in the tracking video sequence to form a space occupancy matrix of both sides; Step S32: Normalize the space occupancy matrix of both sides to obtain the probability distribution of the actual space occupancy of both sides; Step S33: Determine the ideal probability distribution of classic tactical formations based on the gridded sports field; Step S34: Use relative entropy to quantify the difference between the actual space occupancy probability distribution and the ideal probability distribution, and define the orderliness of the formation.

6. The method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy according to claim 1, characterized in that, Step S4 includes: Step S41: Grid the sports field, filter target points based on any frame, obtain the distance from the target point to the nearest friendly player and the distance to the nearest enemy player, and define single-point control. Step S42: Use the five-point sampling method to sample the single-point control weight corresponding to each grid at multiple locations, and determine the grid control weight corresponding to each grid in the current analysis frame through the majority voting rule; Step S43: Based on grid control authority, count the number of grids controlled by both sides and obtain the spatial control rate of the enemy and friendly formations respectively; Step S44: Construct a binary control matrix corresponding to the sports field grid through grid control authority, and determine the control entropy of the enemy and friendly formations by combining the 8-neighborhood connectivity rule.

7. The method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy according to claim 1, characterized in that, Step S5 includes: Step S51: Determine the velocity of our center of gravity and the velocity of the enemy's center of gravity based on the center of gravity of both sides. Step S52: Obtain the center coordinates of the goal of both sides, define the position factor in combination with the center of gravity, and output the offensive potential energy and defensive potential energy by combining the center of gravity velocity of our side and the center of gravity velocity of the enemy. Step S53: Combine offensive and defensive potential energy to obtain net potential energy, and analyze the net potential energy to judge the offensive and defensive situation of the enemy and ourselves.

8. The method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy according to claim 1, characterized in that, Step S7 includes: Step S71: Establish a time series based on the attack and defense effectiveness index, plot the effectiveness curve, and obtain the first-order difference and the second-order difference respectively, corresponding to the instantaneous rate of change and acceleration of change. Step S72: Preset uplink threshold, downlink threshold and minimum duration respectively, compare with first-order difference, and analyze whether second-order difference crosses zero to detect tactical events.

9. The method for evaluating the effectiveness of football offensive and defensive formations based on fractal dimension and spatial relative entropy according to claim 1, characterized in that, In step S8, specifically: By integrating the formation boundary field, spatial control rate, net potential energy, and offensive and defensive effectiveness index, dynamic diagrams of formation boundaries, spatial control heat maps, and effectiveness curves are established to construct a dynamic visualization output system for offensive and defensive formation effectiveness.

10. An electronic device, characterized in that, The device includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other through the communication bus. The processor calls logical instructions in the memory to execute the football attack and defense formation effectiveness evaluation method based on fractal dimension and spatial relative entropy as described in any one of claims 1 to 9.

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