Game theory-based global structure consistency image feature high-precision matching method

Abstract

The invention discloses a global structure consistency image feature high-precision matching method based on the game theory, and the method comprises the steps: obtaining feature points of two to-be-matched images through a feature detection algorithm, and constructing a group of initial rough matching sets; calculating affine transformation according to the feature information of the feature points in the matching items, solving a profit value between every two matching items under the same affine transformation, and constructing a profit matrix; a matching income problem is converted into a probability estimation problem of a mixed strategy; then calculating the expected income and the average income of the pure strategy under the mixed strategy, and searching the optimal strategy in the pure strategy set; and finally, the probability distribution of the hybrid strategy is adjusted according to the optimal strategy until a Nash equilibrium point is reached, an evolution stable strategy is obtained, and mismatching items are eliminated. The method is high in adaptability to an application environment, high in robustness and high in response speed, the complexity of matching calculation is simplified, and the matching precision and the utilization rate of calculation resources can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of computer vision technology, and in particular to a high-precision matching method for image features based on game theory and global structural consistency. Background Art

[0002] Computer vision is a key research direction in the current field of robot navigation, autonomous driving and artificial intelligence, among which image feature matching plays a vital role in core visual tasks such as estimating 3D structure and camera pose. For example, in tasks such as panorama stitching, structure from motion (SFM), simultaneous localization and mapping (SLAM), binocular stereo vision and 3D reconstruction, feature matching provides key support for building 3D models and determining camera pose.

[0003] At present, image matching methods can be roughly divided into two categories:

[0004] One is the traditional algorithm, which is mainly based on image feature matching, such as fast corner detection (FAST), scale-invariant feature transform (SIFT) and speeded up robust features (SURF). The feature matching-based method matches images by extracting feature descriptors of feature points in different images.

[0005] The other type is a deep learning-based method that automatically extracts image features through deep models such as convolutional neural networks (CNNs) and achieves high-precision image matching through feature comparison.

[0006] Compared with deep learning-based methods, feature matching-based methods do not require large data sets for training. At the same time, they can better reflect the essential structure of the image, simplify the image expression form, and improve the running speed of the algorithm.

[0007] In practical applications, due to the fluctuations of the imaging object surface, changes in the imaging viewpoint or non-rigid transformation, the geometric structure of the image of the same object in different viewpoints is distorted, making it difficult for traditional feature matching methods to ensure global one-to-one matching and structural consistency; secondly, in scenes with light changes or illumination differences, the accuracy of a single image feature descriptor in describing image features is insufficient, which may lead to mismatching problems when dealing with repeated patterns and weak texture scenes; finally, due to the combinatorial nature of feature matching, matching algorithms usually have a high time complexity and cannot take into account the matching efficiency of image feature matching with a larger amount of data. Therefore, how to maintain structural consistency while taking into account the high-precision matching of local features is an important challenge facing feature matching. Summary of the invention

[0008] The purpose of the present invention is to provide a high-precision matching method for global structural consistency image features based on game theory in view of the deficiencies of the prior art. The matching method considers the geometric structural similarity of the affine transformation of a single matching item relative to the group matching item, and selects high-precision matching items through evolutionary games, taking into account the accuracy of feature matching and the consistency of global structure to the greatest extent, so that the algorithm has stronger adaptability and can achieve high-precision image feature matching without increasing the complexity of feature descriptors.

[0009] The technical solution adopted by the present invention to solve its technical problem is:

[0010] The high-precision matching method of global structural consistency image features based on game theory includes the following steps:

[0011] Step 1), using a feature detection algorithm to obtain feature points of two images to be matched, and establishing feature descriptors and generating feature information, and constructing a set of initial rough matching sets according to the similarity of the feature descriptors in the two images;

[0012] Step 2), calculate the affine transformation based on the feature information between the source feature point and the target feature point in the matching item, find the reprojection deviation between the two matching item feature points under the same affine transformation, and then define the profit function based on the deviation to construct the profit matrix;

[0013] Step 3), transform the matching payoff problem into a probability estimation problem for the mixed strategy, and generate the initial probability distribution of the mixed strategy;

[0014] Step 4), calculate the expected return and average return of the pure strategy under the mixed strategy, and find the optimal strategy in the pure strategy set according to the Nash equilibrium condition;

[0015] Step 5), according to the optimal strategy found, the amplitude factor and response value of the hybrid strategy are calculated, and the probability distribution of the hybrid strategy is adjusted accordingly, and the dynamic adjustment mechanism composed of steps 4) to 5) is repeated to update the probability distribution of the hybrid strategy;

[0016] Step 6), while repeating steps 4)-5), calculate the Nash equilibrium point of the mixed strategy, determine whether the mixed strategy reaches an evolutionary stable state, obtain an evolutionary stable strategy, and retain the precise matching items according to the probability distribution of the evolutionary stable strategy; for the coarse matching items, repeat steps 2)-6) to obtain more precise matching items.

[0017] Advantages or beneficial effects of the present invention:

[0018] (1) The present invention can effectively deal with problems such as illumination changes, weak texture scenes and repeated patterns through the matching method of evolutionary games, thereby improving the robustness of the system;

[0019] (2) The evolutionary game matching method of the present invention seeks a balance between multiple strategies and considers the global consistency between matching items, so that the system is more stable when facing the fluctuations of the imaging object surface, changes in the imaging viewpoint or non-rigid transformation;

[0020] (3) The evolutionary game matching model can adaptively adjust the strategy using a dynamic adjustment mechanism, which can effectively reduce the mismatch rate, maintain high matching accuracy and a sufficient number of precise matches;

[0021] (4) The dynamic adjustment mechanism of the evolutionary game matching model can simplify the complexity of matching calculations, quickly calculate results in applications with large amounts of data, improve system response speed, and reduce the waste of computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Flow chart of a high-precision matching method for global structural consistency image features based on game theory in an embodiment;

[0023] Figure 2 is a binocular water surface image taken in the embodiment;

[0024] Figure 3 A schematic diagram of affine transformation and reprojection in an embodiment;

[0025] Figure 4 This is a diagram showing the matching results of the high-precision matching method for global structural consistency image features based on game theory in the embodiment. DETAILED DESCRIPTION

[0026] The present invention is described in detail below in conjunction with the accompanying drawings and embodiments, examples of which are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0027] Example:

[0028] In order to illustrate the high-precision matching method of global structural consistency image features based on game theory designed by the present invention, the water surface environment is taken as a typical scene and binocular stereo vision is taken as a typical task, but it is not limited to this scene and this task. The matching method can also be used for other scenes and other tasks.

[0029] like Figure 1 As shown in FIG. 1 , a high-precision matching method for global structural consistency image features based on game theory includes the following steps:

[0030] Step (1), using a feature detection algorithm to obtain feature points of the two images to be matched, and establishing feature descriptors and generating feature information, and constructing a set of initial rough matching sets according to the similarity of the feature descriptors in the two images;

[0031] The specific implementation method is:

[0032] For two binocular images to be matched with a pixel size of 2448×2048, the SURF (Speeded Up Robust Features) feature detection algorithm is used to extract about 2000 feature points from each image, establish feature descriptors of feature points, and generate feature information of corresponding feature points, including position coordinates p, feature scale s, and main gradient direction θ;

[0033] The left image of the binocular image is the source image, and the right image is the target image. The feature information of the source feature point is (p l ,s l ,θ l ), the feature information of the target feature point is (p r ,s r ,θ r );

[0034] Then, the K-nearest neighbor algorithm (KNN) is used to perform initial matching based on the similarity of the feature descriptors in the source image and the target image, and the obtained N matching items are constructed into a set of initial rough matching sets;

[0035] In this example, one source feature point matches three target feature points, and a total of N rough matching items are generated. The water surface image to be processed is as follows: Figure 2 As shown, finally, the rough matching items are optimized through the evolutionary game matching model constructed in steps (2) to (6);

[0036] Step (2), calculating the affine transformation based on the feature information between the source feature point and the target feature point in the matching item, finding the reprojection deviation between the two matching item feature points under the same affine transformation, and then defining the benefit function based on the deviation to construct the benefit matrix;

[0037] The specific implementation method is:

[0038] Step (2-1) calculates the affine transformation of the matching item by combining the position coordinates, feature scale and main gradient direction information of the source feature point and the target feature point. The affine transformation is shown in formula (1):

[0039]

[0040] p l For matching items (p l ,p r )’s source feature point, p r For matching items (p l ,p r )’s target feature point; l is the source feature point p l The characteristic scale, sr is the target feature point p r characteristic scale of

[0041] Obtain the source feature point p through affine transformation l and virtual point p′ r The affine relationship of is shown in formula (2):

[0042] p′ r =T(p l ,p r ) l (2)

[0043] Step (2-2), under the same affine transformation, find the reprojection deviation between the two matching items, as shown in formula (3):

[0044]

[0045] Let O = {1, 2, 3, ..., N} be the enumeration of matching sets, i∈O, j∈O; d i Represents the affine transformation T(p li ,p ri ), the target feature point p ri and virtual point p′ ri The true error distance p ri -p′ ri With the target feature point p rj and virtual point T(p li ,p ri ) lj The prediction error distance p rj -T(p li ,p ri ) lj The distance deviation between j Represents the affine transformation T(p lj ,p rj ), the target feature point p rj and virtual point p′ rj The true error distance p rj -p′ rj With the target feature point p ri and virtual point T(p lj ,p rj ) li The prediction error distance p ri -T(p lj ,p rj ) li The distance deviation between them; Formula (3) represents the distance deviation between two matching items (p li ,p ri ) and (p lj ,p rj) can be regarded as a loose geometric constraint condition. The schematic diagram of affine transformation and reprojection is shown in Figure 3 As shown;

[0046] Figure 3 In, p li and p lj The left image I l The source feature point on ri and p rj For the right image I r The target feature point on T(p li ,p ri ) is a matching item (p li ,p ri ) is an affine transformation, T(p lj ,p rj ) is a matching item (p lj ,p rj ), the black solid line is the line connecting the source feature point and the target feature point, the green and yellow points represent the virtual points obtained by the source feature point under different affine transformations, and the dotted line is the line connecting the source feature point and the virtual point; where p′ ri It's point p li In the affine transformation T(p li ,p ri ) under the virtual point, p′ ri =T(p li ,p ri ) li ; p′ rj It's point p lj In the affine transformation T(p lj ,p rj ) under the virtual point, p′ rj =T(p lj ,p rj ) lj ; T(p lj ,p rj ) li It's point p li In the affine transformation T(p lj ,p rj ) virtual point; T(p li ,p ri ) lj It's point p lj In the affine transformation T(p li ,p ri ) under the virtual point; the black arrow indicates the characteristic scale and main gradient direction of the feature point;

[0047] Step (2-3), define the benefit function of the similarity between two matching items, as shown in formula (4):

[0048]

[0049] λ is the attenuation coefficient, in this example λ=10 -5 ; Calculate the benefit value a between all matching items ij , the benefit value represents that the smaller the reprojection deviation of the two matching items, the greater the similarity, and the greater the benefit; finally, an N×N symmetric benefit matrix A=(a ij );

[0050] Step (3), transform the matching payoff problem into a probability estimation problem for mixed strategies and generate the initial probability distribution of the mixed strategies;

[0051] The specific implementation method is:

[0052] In game theory, the enumeration of matching sets O = {1, 2, 3, ..., N} is the enumeration of pure strategy sets. The probability of selecting a pure strategy is represented as a column vector x, i.e., a mixed strategy. The matching problem is converted into a probability estimation problem for the mixed strategy. The initial mixed strategy x is set to a uniform probability distribution x. i =1 / N;

[0053] The standard form of x in N-dimensional Euclidean space In the example, the support set of x∈Δ is σ(x) = {i∈O:x i >0} is a set of non-zero probability elements;

[0054] Step (4), calculate the expected return and average return of the pure strategy under the mixed strategy, and find the optimal strategy in the pure strategy set according to the Nash equilibrium condition;

[0055] The specific implementation method is:

[0056] Step (4-1), the expected return of pure strategy i under the mixed strategy is shown in formula (5):

[0057]

[0058] (Ax) i is the profit when pure strategy i is used under mixed strategy x, and the average profit is x T Ax;

[0059] Step (4-2), when adopting mixed strategy y, the average return is y T Ax; the optimal response to the mixed strategy x is the mixed strategy set β(x) = {y∈Δ:y T Ax=max z (z T Ax)}; if the optimal response strategy of mixed strategy x is itself, then x is a Nash equilibrium, that is, yT Ax≤x T Ax, or (Ax) i =x T Ax;

[0060] Step (4-3), let the strategy set τ + ={i∈O:(Ax) i >x T Ax}, τ - ={i∈O:(Ax) i <x T Ax}, τ + is the set of pure strategies whose returns of pure strategy i are higher than the average return, τ - is the set of pure strategies whose returns of pure strategy i are lower than the average return;

[0061] According to the Nash equilibrium condition, the optimal strategy is set to M(x), as shown in formula (6). The optimal strategy is the pure strategy i that maximizes the objective function value;

[0062] M(x)∈argmax{(Ax) i -x T Ax:i∈τ + (x)}∪{-(Ax) i +x T Ax:i∈τ - (x)∩σ(x)} (6)

[0063] Step (5), according to the optimal strategy found, the amplitude factor and response value of the hybrid strategy are calculated, and the probability distribution of the hybrid strategy is adjusted accordingly, and the dynamic adjustment mechanism composed of steps 4) to 5) is repeated to update the probability distribution of the hybrid strategy;

[0064] The specific implementation method is:

[0065] As shown in formula (7), y(x) is a response function. If the current strategy x is not a Nash equilibrium, the system will adjust the strategy x through the response function y(x) according to the optimal strategy, so that the strategy x gradually converges to the Nash equilibrium point, that is, x moves to e i Close, i is a standard vector with the i-th term being 1 and the rest being 0;

[0066] If M(x)∈τ + (x), the optimal strategy is in the strategy set with returns above the average level, and the update of x will completely adopt the pure strategy i; if M(x)∈τ - (x)∩σ(x), the optimal strategy is in the strategy set whose returns are below the average level and have not yet been extinct, and the system will adjust x to e iMove; In either case, the optimal strategy will be propagated, and the remaining strategies will go extinct; For strategies that do not belong to any of the above two strategy sets, the mixed strategy x will remain unchanged, where the extinct strategy refers to the probability distribution x i Pure strategy ≤0;

[0067]

[0068] δ y (x) is the amplitude factor, as shown in formula (8). Its calculation is based on the distance and benefit comparison between the current strategy x and the response strategy y. The update amplitude is adjusted according to the distance between the two strategy ratios to control the change step size of x during the update process, so that the evolution of x is reasonable and stable.

[0069] δ y (x) through (yx) T A(yx)<0 determines whether the change from strategy x to strategy y will lead to a decrease in profit. If the profit decreases, it is necessary to control the adjustment range of strategy x more carefully to avoid excessive decline in profit. If strategy y leads to an increase in profit, a larger strategy adjustment can be made.

[0070]

[0071] Update the hybrid strategy x, as shown in formula (9), and then normalize x, as shown in formula (10), where t is the number of iterations. Repeat the dynamic adjustment mechanism of steps (4) and (5) until it reaches an evolutionary stable state. In this example, t≤5000;

[0072]

[0073] Step (6), while repeating steps (4) to (5), calculate the Nash equilibrium point of the mixed strategy, determine whether the mixed strategy has reached an evolutionary stable state, obtain an evolutionary stable strategy, retain the precise matching items according to the probability distribution of the evolutionary stable strategy, and repeat steps (2) to (6) for the rough matching items, thereby obtaining more precise matching items;

[0074] The specific implementation method is:

[0075] Step (6-1), through the dynamic adjustment mechanism, while selecting the optimal strategy and updating x, calculate and determine the Nash equilibrium error Nash of the optimal strategy error Whether the evolutionary stability condition is reached Nash error →0, in this example, the evolutionary stability condition is Nash error <10 -30 , the Nash equilibrium error is shown in formula (11). When the optimal strategy goes to extinction, that is, x iWhen x slowly approaches 0 or reaches the Nash equilibrium condition, x is considered to be an evolutionary stable strategy, and x ends its evolutionary update;

[0076]

[0077] Step (6-2), let σ + ={i∈O:x i >μ*(maxx i )},σ - ={i∈O:x i ≤μ*(maxx i )}, μ is the threshold of the robust strategy, in this example μ = 0.7, σ + is the set of exact matches, σ - is a set of coarse matching items;

[0078] After obtaining the evolutionary stable strategy, for i∈σ + The matching items are retained, for i∈σ - The matching items can repeat steps (2) to (6) to obtain more i∈σ + The exact matching items; among them, after the first round of evolutionary game matching, if i∈σ + If the number of elements of is less than m, that is, the number of winning precise matches is less than m, or the number of iterations exceeds n, the evolutionary game matching iteration is terminated. m represents the minimum number of winning precise matches required after the first round of evolutionary game matching, and n represents the maximum number of iterations for evolutionary game matching. In this example, m = 20 and n = 5. In this example, if the number of winning precise matches is less than m after the first round of evolutionary game matching, it can be considered that the similarity of the matching items of the two binocular images is low, that is, the global consistency is poor, and the evolutionary game matching is terminated. The final matching result is shown in the figure below. Figure 4 shown.

[0079] Figure 4 This is the visualization matching result diagram of this embodiment, in which the yellow lines represent the matching visualization lines between the source feature points of the left image and the target feature points of the right image. From the visualization matching result diagram, in the water surface image with weak textures and repeated patterns, the connected feature points are visually similar and have corresponding positions. The connected feature point lines are distributed regularly in the overlapping area, and there are no irregular or chaotic feature point lines, which shows that they have high consistency and geometric relationship in space.

[0080] The above description is only a preferred embodiment of the present invention, which is to help readers understand the implementation method of the present invention. It should be understood that the protection scope of the present invention is not limited to such specific descriptions and embodiments. Any equivalent structure or equivalent process transformation made by using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A high-precision matching method for global structural consistency image features based on game theory, characterized in that: The steps include: Step 1), using a feature detection algorithm to obtain feature points of two images to be matched, and establishing feature descriptors and generating feature information, and constructing a set of initial rough matching sets according to the similarity of the feature descriptors in the two images; Step 2), calculate the affine transformation based on the feature information between the source feature point and the target feature point in the matching item, find the reprojection deviation between the two matching item feature points under the same affine transformation, and then define the profit function based on the deviation to construct the profit matrix; Step 3), transform the matching payoff problem into a probability estimation problem for the mixed strategy, and generate the initial probability distribution of the mixed strategy; Step 4), calculate the expected return and average return of the pure strategy under the mixed strategy, and find the optimal strategy in the pure strategy set according to the Nash equilibrium condition; Step 5), according to the optimal strategy found, the amplitude factor and response value of the hybrid strategy are calculated, and the probability distribution of the hybrid strategy is adjusted accordingly, and the dynamic adjustment mechanism composed of steps 4) to 5) is repeated to update the probability distribution of the hybrid strategy; Step 6), while repeating steps 4)-5), calculate the Nash equilibrium point of the mixed strategy, determine whether the mixed strategy reaches an evolutionary stable state, obtain an evolutionary stable strategy, and retain the precise matching items according to the probability distribution of the evolutionary stable strategy; for the coarse matching items, repeat steps 2)-6) to obtain more precise matching items.

2. The high-precision matching method of global structural consistency image features based on game theory according to claim 1 is characterized in that: Step 2) includes the following steps: Step (2-1) calculates the affine transformation of the matching item by combining the position coordinates, feature scale and main gradient direction information of the source feature point and the target feature point. The affine transformation is shown in formula (1): p l For matching items (p l ,p r )’s source feature point, p r For matching items (p l ,p r )’s target feature point; l is the source feature point p l The characteristic scale, s r is the target feature point p r characteristic scale of Obtain the source feature point p through affine transformation l and virtual point p′ r The affine relationship of is shown in formula (2): p′ r =T(p l ,p r )p l (2) Step (2-2), under the same affine transformation, find the reprojection deviation between the two matching items, as shown in formula (3): Let O = {1, 2, 3, ..., N} be the enumeration of matching sets, i∈O, j∈O; d i Represents the affine transformation T(p li ,p ri ), the target feature point p ri and virtual point p′ ri The true error distance p ri -p′ ri With the target feature point p rj and virtual point T(p li ,p ri ) lj The prediction error distance p rj -T(p li ,p ri ) lj The distance deviation between j Represents the affine transformation T(p lj ,p rj ), the target feature point p rj and virtual point p′ rj The true error distance p rj -p′ rj With the target feature point p ri and virtual point T(p lj ,p rj ) li The prediction error distance p ri -T(p lj ,p rj ) li The distance deviation between them; Formula (3) represents the distance deviation between two matching items (p li ,p ri ) and (p lj ,p rj ) between the reprojection deviations; Step (2-3), define the benefit function of the similarity between two matching items, as shown in formula (4): λ is the attenuation coefficient, in this example λ=10 -5 ; Calculate the benefit value a between all matching items ij , the benefit value represents that the smaller the reprojection deviation of the two matching items, the greater the similarity, and the greater the benefit; finally, an N×N symmetric benefit matrix A=(a ij ).

3. The high-precision matching method of global structural consistency image features based on game theory according to claim 1 is characterized in that: Step 4) comprises the following steps: Step (4-1), the expected return of pure strategy i under the mixed strategy is shown in formula (5): (Ax) i is the profit when pure strategy i is used under mixed strategy x, and the average profit is x T Ax; Step (4-2), when adopting mixed strategy y, the average return is y T Ax; the optimal response to the mixed strategy x is the mixed strategy set β(x) = {y∈Δ:y T Ax=max z (z T Ax)}; if the optimal response strategy of mixed strategy x is itself, then x is a Nash equilibrium, that is, y T Ax≤x T Ax, or (Ax) i =x T Ax; Step (4-3), let the strategy set τ + ={i∈O:(Ax) i >x T Ax}, τ - ={i∈O:(Ax) i <x T Ax}, τ + is the set of pure strategies whose returns of pure strategy i are higher than the average return, τ - is the set of pure strategies whose returns of pure strategy i are lower than the average return; According to the Nash equilibrium condition, the optimal strategy is set to M(x), as shown in formula (6). The optimal strategy is the pure strategy i that maximizes the objective function value; M(x)∈argmax{(Ax) i -x T Ax:i∈τ + (x)}∪{-(Ax) i +x T Ax:i∈τ_(x)∩σ(x)} (6)。 4. The high-precision matching method of global structural consistency image features based on game theory according to claim 1 is characterized in that: Step 5) comprises the following steps: As shown in formula (7), y(x) is a response function. If the current strategy x is not a Nash equilibrium, the system will adjust the strategy x through the response function y(x) according to the optimal strategy, so that the strategy x gradually converges to the Nash equilibrium point, that is, x moves to e i Close, i is a standard vector with the i-th term being 1 and the rest being 0; If M(x)∈τ + (x), the optimal strategy is in the strategy set with returns above the average level, and the update of x will completely adopt the pure strategy i; if M(x)∈τ - (x)∩σ(x), the optimal strategy is in the strategy set whose returns are below the average level and have not yet been extinct, and the system will adjust x to e i Move; In either case, the optimal strategy will be propagated, and the remaining strategies will go extinct; For strategies that do not belong to any of the above two strategy sets, the mixed strategy x will remain unchanged, where the extinct strategy refers to the strategy with probability distribution x i Pure strategy ≤0; δ y (x) is the amplitude factor, as shown in formula (8). Its calculation is based on the distance and benefit comparison between the current strategy x and the response strategy y. The update amplitude is adjusted according to the distance between the two strategy ratios to control the change step size of x during the update process, so that the evolution of x is reasonable and stable. δ y (x) through (yx) T A(yx)<0 determines whether the change from strategy x to strategy y will lead to a decrease in profit. If the profit decreases, it is necessary to control the adjustment range of strategy x more carefully to avoid excessive decline in profit. If strategy y leads to an increase in profit, a larger strategy adjustment can be made. Update the hybrid strategy x, as shown in formula (9), and then normalize x, as shown in formula (10), where t is the number of iterations, and repeat the dynamic adjustment mechanism of steps 4) and 5) until it reaches an evolutionary stable state; 5. The high-precision matching method of global structural consistency image features based on game theory according to claim 1 is characterized in that: Step 6) comprises the following steps: Step (6-1), through the dynamic adjustment mechanism, while selecting the optimal strategy and updating x, calculate and determine the Nash equilibrium error Nash of the optimal strategy error Whether the evolutionary stability condition is reached Nash error →0, the Nash equilibrium error is shown in formula (11). When the optimal strategy goes extinct, that is, x i When x slowly approaches 0 or reaches the Nash equilibrium condition, x is considered to be an evolutionary stable strategy, and x ends its evolutionary update; Step (6-2), let σ + ={i∈O:x i >μ*(maxx i )},σ - ={i∈O:x i ≤μ*(maxx i )}, μ is the threshold of the robust strategy, σ + is the set of exact matches, σ - is a set of coarse matching items; After obtaining the evolutionary stable strategy, for i∈σ + The matching items are retained, for i∈σ - Repeat steps 2) to 6) for the matching items, and then get more i∈σ + The exact matching items; among them, after the first round of evolutionary game matching, if i∈σ + If the number of elements is less than m, that is, the number of winning precise matches is less than m, or the number of iterations exceeds n, the evolutionary game matching iteration ends. m represents the minimum number of winning precise matches after the first round of evolutionary game matching, and n represents the maximum number of iterations for evolutionary game matching.

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