A method for eliminating mismatched image feature points based on consistent adjacency relationships

Abstract

The present invention belongs to an image processing method, and specifically relates to a method for eliminating mismatches of image feature points based on consistent adjacency relations. The method comprises the following steps: step 1: extracting feature points; extracting feature points and constructing description vectors; step 2: matching feature points; step 3: obtaining an inner point set; step 4: constructing a neighborhood relationship; step 5: calculating; step 6: calculating the restored inner point set; step 7: obtaining a complete inner point set. The significant effects of the present invention are: (1) constructing a stable local adjacency relationship based on the Delaunay partitioning algorithm. (2) Based on the geometry of the Delaunay triangulation, the geometric constraints and stability of the consistent adjacency relationship model are enhanced. (3) A decision is added to perform pre-filtering of external points. The robustness of the algorithm is improved under non-rigid deformation and abnormally high external point rate (higher than 90%) data. (4) A global description method based on triangle similarity is proposed to improve the recall rate of the algorithm.

Description

Technical Field

[0001] The invention belongs to an image processing method, and in particular relates to a method for eliminating mismatching of image feature points based on consistent adjacency relations. Background Art

[0002] Remote sensing image registration refers to the process of aligning two remote sensing images with overlapping areas. The reasons for the misalignment between the two images to be registered are usually different perspectives, different sensors, different data acquisition times, etc. In the field of remote sensing image processing, accurate image registration is an important prerequisite for effective analysis of the observation area, and is an important pre-step for remote sensing image processing technologies such as multi-source remote sensing image fusion, change detection, and image mosaicking. Therefore, image registration plays a very important role in the remote sensing image processing process. It is one of the hot topics in the field of remote sensing information processing and is widely used in scenes that require the comprehensive use of information from multiple images. The point feature-based registration method has become the mainstream method for image registration due to its good repeatability and robustness. For image registration, it is necessary to find a sufficient number of feature points that are evenly distributed and correctly matched. Compared with ordinary images, remote sensing images often have local radiation and geometric distortion, complex and changeable textures, few overlapping areas of matching images, and different imaging perspectives due to their large scale, complex imaging process, and different ways of acquiring data, resulting in a large number of incorrect matching pairs in the initial matching results of image features. Therefore, it is very important to study a method to eliminate false matches in remote sensing images.

[0003] Image registration based on point features requires matching of point features. Point feature matching includes four steps: point feature detection, point feature description, point feature descriptor matching and mismatch elimination. At present, the main method for eliminating mismatches is the random sampling consensus (RANSAC) algorithm. This algorithm is based on the idea of ​​global geometric constraints. It randomly samples and calculates a global homography matrix multiple times, and determines the transformation model based on the number of internal points and deletes mismatched points. The algorithm is more accurate when the image satisfies the global homography matrix transformation, but when the image transformation relationship is more complex, it will cause inaccurate point selection in the local area, and it is very easy to fall into the local maximum value and fail to solve the global optimal parameter model.

[0004] Dong Yang et al. introduced the principal component analysis method to eliminate false matches in the paper "Purification Method of Matching Point Pairs Based on Principal Component Analysis". Unlike RANSAC, this method uses the entire point set as the initial input instead of the minimum point set, and robustly solves the global optimal solution through a step-by-step method. However, this method only performs better than RANSAC in data with a low to medium external point ratio, and is inferior to RANSAC in the case of a high external point ratio. This method also relies on a pre-set global transformation model, and is not applicable to non-rigid image matching where a global transformation model cannot be defined.

[0005] Ma et al. proposed a mismatch elimination method based on locality preservation (LPM) in the paper "Locality Preserving Matching". This method uses the principle of spatial variation continuity and proposes the assumption that the local adjacency relationship of the correct match remains unchanged. Based on this assumption, a local preservation model is constructed to eliminate mismatches. This method is simple and effective and does not rely on any predefined global transformation model. It is still applicable when the image undergoes non-rigid deformation. However, LPM only uses local information and adopts a weaker local geometric constraint - the adjacency relationship. Moreover, the local relationship constructed by the K nearest neighbor is less stable and is easily affected by the fact that the accuracy of LPM will drop sharply when the proportion of external points is too high.

[0006] Bian et al. proposed a grid-based motion statistics method (GMS) in the paper “GMS: Grid-based Motion Statistics for Fast, Ultra-Robust Feature Correspondence”. This method first divides the image into small grids, calculates the number of matches within the grid, and then uses statistical likelihood to distinguish between inliers and outliers. This method has achieved excellent performance in eliminating false matches in rigid images, but the geometric constraints adopted by GMS are relatively weak and rely more on the reliability of the descriptor. When the image is a complex texture or weak texture scene, the descriptor becomes unreliable, and a large number of false matches with the same motion direction are generated. GMS often fails and has poor effect in remote sensing image matching applications.

[0007] Sao et al. proposed a method for eliminating false matches based on minimum relative motion entropy (MRME) in the paper “Feature Matching Based on Minimum Relative Motion Entropy for Image Registration”. The algorithm defines the relative motion between the initial matching point and the k nearest neighbors. Based on the relative motion clustering results, the relative motion entropy is defined to find the correct match. However, the K nearest neighbor method is unstable in constructing local geometric relationships and is easily affected by external points. When the proportion of external points is too high, the clustering results become unreliable. Therefore, in the application scenario of high external point ratio data, it is very necessary to accurately estimate the transformation model of the non-rigid deformable image.

[0008] The defects of the prior art are mainly reflected in the following points:

[0009] 1. The current method of using geometric constraints to eliminate mismatches often uses the K nearest neighbor or the nearest Euclidean distance method when constructing local connections. The K nearest neighbor and Euclidean distance-based methods are difficult to determine the appropriate threshold to construct local connection relationships in unevenly distributed point sets. The constructed adjacency relationships are unevenly distributed, and there are often too many or too few local connections.

[0010] 2. LPM, which is the closest to the technology in this paper, only uses the weaker constraint of local adjacency when constructing the geometric constraint model. When the proportion of outliers is too high, LPM often fails due to the wrong belief in outliers.

[0011] 3. The method based on the consistency of local adjacency relationship does not make full use of global information. When the internal points do not meet the conditions for maintaining local adjacency relationship, the correct matching point pairs will inevitably be missed. Summary of the invention

[0012] The present invention aims at the defects of the prior art and provides a method for eliminating mismatch of image feature points.

[0013] The present invention is implemented as follows: a method for eliminating mismatching of image feature points, which includes the following steps:

[0014] Step 1: Extract feature points;

[0015] Extract feature points and construct description vectors;

[0016] Step 2: Feature point matching;

[0017] Step 3: Get the internal point set;

[0018] Step 4: Build neighborhood relationships;

[0019] Step 5: Calculation;

[0020] Step 6: Calculate the restored internal point set;

[0021] Step 7: Get the complete set of interior points.

[0022] The above-mentioned method for eliminating mismatched image feature points, wherein the step 1 comprises:

[0023] Harris corner algorithm is used to extract feature points in target image Is and matching image It respectively, and SIFT algorithm is used to construct description vectors for feature points; then go to step 2.

[0024] The above-mentioned method for eliminating mismatched image feature points, wherein the step 2 comprises:

[0025] The NNDR (Nearest Neighbor Distance Ratio) algorithm is used to match each feature point in the target image with the feature points in the matching image to obtain N pairs of initial matching results. where x i ,y i is a two-dimensional column vector representing the position of the feature point; then proceed to step 3.

[0026] The above-mentioned method for eliminating mismatching of image feature points, wherein the step 3 comprises

[0027] Use the Delaunay triangulation algorithm to locally connect the initial matching points, construct a triangulated network, and obtain the point set k in the neighborhood of the point set x and y. s , k t ; then go to step 4.

[0028] The above-mentioned method for eliminating mismatching of image feature points, wherein the step 4 comprises

[0029] The directly connected node of a node in the triangulated network is set as a directly adjacent node, and the node connected to the node through the directly adjacent node is set as a secondary adjacent node, and a neighborhood relationship is established, and then step 5 is entered.

[0030] The above-mentioned method for eliminating mismatched image feature points, wherein the step 5 comprises

[0031] Step 5.1: Calculate the loss function based on the adjacency relationship constructed by the direct neighboring nodes. Based on the assumption that the local adjacency relationship between feature points in the local area of ​​the non-rigidly deformed image remains unchanged, when there are no outliers in the two points to be matched, all the adjacency relationships in the matching point sets will remain consistent. Therefore, we use the percentage of the number of matching relationships maintained in the neighborhood to the total number of neighborhood points as a metric to determine whether the matching point pair is an inner point. The larger the percentage of the number of matching relationships maintained in the neighborhood to the total number of neighborhood points, the greater the possibility that the central point pair of the neighborhood is a correct match. The loss function is written as the sum of the percentage of the neighborhood that cannot maintain the adjacency relationship and the number of outliers:

[0032]

[0033] in, For x i and i The point set with matching relationship in the two neighborhoods with centered is obtained by step 2. x i and i is the feature point set in the neighborhood centered on the center, which is obtained by step 3. I1 is the internal point set, which is obtained by step 3. |·| is the cardinality of the set. The first term on the right side of the equation is the penalty term for the point pairs that cannot maintain a consistent matching relationship in the neighborhood of the matching point. The second term is to maximize the number of internal points by controlling the intensity through λ. i It is a binary function. Whether the number of point pairs that maintain matching relationships in the neighborhood is greater than or equal to 2 is used to determine whether the central feature point of the neighborhood is trustworthy. Untrusted connections are eliminated. i The expression is as follows:

[0034]

[0035] According to formula (1), calculate the loss function C1 based on the adjacency relationship constructed based on the direct adjacent nodes, and then go to step 5.2. λ is the input parameter, which is the threshold for judging whether it is an internal point. The threshold belongs to [0, 1]. N is the number of point pairs after the initial matching. Among them, i is the index of the i-th match. If the i-th match satisfies C, that is, the cost is less than λ, then the match is an internal point. The values ​​of parameters λ and N are directly given by the outside.

[0036] Step 5.2: Calculate the loss function for building adjacency relationships based on direct neighboring nodes and secondary neighboring nodes. The calculation formula is as follows:

[0037]

[0038] in, x iThe set of directly adjacent nodes and secondary adjacent nodes with matching relationships in the neighborhood of the center, y i The set of directly adjacent nodes and secondary adjacent nodes with matching relationships in the neighborhood of the center, x i is the set of direct adjacent nodes and secondary adjacent nodes in the neighborhood of the center, y i The set of direct adjacent nodes and the set of secondary adjacent nodes in the neighborhood of the center is I2, and I2 is the internal point set. According to formula (2), the loss function C2 of building the adjacency relationship based on the direct adjacent nodes is calculated, and then step 5.3 is entered.

[0039] Step 5.3: Calculate the final loss function C according to formula (3), and then go to step 5.4;

[0040] C=0.5*C1+0.5*C2 (3) Step 5.4: Obtain the initial interior point set I0 according to equation (4), and then proceed to step 5.5;

[0041] I0={i|C i ≤λ,i=1,…,N} (4)

[0042] λ is an input parameter, which is the threshold for determining whether it is an inlier. The threshold belongs to [0, 1]. N is the number of point pairs after the initial matching. Among them, i is the index of the i-th match. If the i-th match satisfies C, that is, the cost is less than λ, then the match is an inlier.

[0043] Step 5.5: Get the initial correct matching point set S1 and the initial incorrect matching point set S2, S1 = {x i ,y i |i=I0}, S2 is the initial mismatch point set, which is the difference between S and S1.

[0044] The above-mentioned method for eliminating mismatched image feature points, wherein step 6 comprises

[0045] Step 6.1: Calculate the similarity of the two triangles according to formula (5), where A1, A2 are a pair of matching points in set S2, B1, B2, and C1, C2 are two pairs of matching points in set S1, and then go to step 6.2;

[0046]

[0047] In formula (5), the point pairs in S1 are considered to be assumed to be correctly matched, so As a comparison benchmark, the closer the ratios of the other two groups of corresponding edges are, The more similar the two triangles are,

[0048] Step 6.2: In order to enhance the accuracy of the triangle similarity function measurement, add the angle similarity measurement to the proportional constraint of the three sides, calculate the similarity of the two triangle angles according to formula (6), and then go to step 6.3;

[0049] SimAngle=|cos(∠B1A1C1)-cos(∠B2A2C2)| (6)

[0050] Step 6.3: When the SimEdge value is less than the threshold τ and the SimAngle value is less than When the two triangles are determined to be similar, A1 and A2 are restored to be correctly matched, and the restored interior point set I r The expression of is as follows:

[0051]

[0052] The above-mentioned method for eliminating mismatching of image feature points, wherein the step 7 comprises

[0053] According to formula (8), we can get the complete interior point set I.

[0054] I r =I = I0∪I r (8)

[0055] The remarkable effects of the present invention are: first, a stable local adjacency relationship is constructed based on the Delaunay triangulation algorithm. The Delaunay triangulation has the empty circumscribed circle criterion, the maximization minimum angle criterion and the shortest distance sum criterion, and the constructed Delaunay triangulation has the excellent characteristics of optimality, regionality and uniqueness. The triangulation network constructed with the shortest distance sum as the criterion has three-point proximity, which ensures that the local node will be connected to the nearest nodes. The empty circumscribed circle criterion and the maximization minimum angle criterion ensure that each triangle in the Delaunay triangulation network tends to be an equilateral triangle as much as possible, reduces the appearance of narrow triangles, and can ensure the uniformity of the distribution of local node connection relations. Based on the Delaunay triangulation algorithm, a uniformly distributed local adjacency relationship can be constructed, while avoiding the problem that the threshold is difficult to determine when constructing the local adjacency relationship such as the K nearest neighbor algorithm.

[0056] Second, based on the geometry of the Delaunay triangulation, the geometric constraints and stability of the adjacency relationship consistency model are enhanced. The Delaunay triangulation has regional characteristics, so when a vertex is added, deleted or moved in a local area of ​​the triangulation, it will only affect the neighboring triangles. That is, the outliers in the Delaunay triangulation have little effect on non-adjacent internal points, making the adjacency relationship model constructed using the Delaunay triangulation more robust.

[0057] Third, a decision is added: whether the number of point pairs that maintain matching relationships in the neighborhood is greater than or equal to 2 is used to determine whether the central feature point of the neighborhood is trustworthy, which effectively improves the accuracy in application scenarios with high external point ratios. When the number of point pairs that maintain matching relationships in the neighborhood is n ≥ 2, they and the center point of the neighborhood form n-1 minimum triangles, which are triangles under the Delaunay subdivision criterion. At this time, a dual constraint of local topological consistency constraint and adjacency consistency is formed. When the number of point pairs that maintain matching relationships in the neighborhood is n<2, the local topological consistency constraint naturally disappears, and the above model degenerates into a weak constraint that only relies on adjacency. The success rate of simply relying on the percentage of matching relationships in the neighborhood to determine whether the point is an internal point will be reduced. Therefore, this paper uses the above decision to eliminate feature points that are difficult to confirm, increase the proportion of internal points, and thus improve the robustness of the algorithm in data with high external point ratios. Through the first to third points, the robustness of the algorithm is improved under non-rigid deformation and abnormally high external point rate (higher than 90%) data.

[0058] Fourth, a global descriptor based on triangle similarity is proposed to restore the correct matches that are missed, which can improve the recall rate while ensuring the accuracy. In the reference image, any two points in the point set filtered by the consistent adjacency model are used as the two vertices of the triangle, and any point in the eliminated point set is used as the other vertex of the triangle; in the image to be registered, the corresponding triangle is obtained. The similarity function of the two triangles is obtained by calculating the proportional difference of the corresponding sides of the two triangles and the angle value difference with the eliminated point as the vertex. When the value of the function is less than the threshold, the eliminated point is restored as an inner point. Through the proposed descriptor extended matching, the precision and recall rate are better balanced, and better false match elimination results are obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of the present application method. DETAILED DESCRIPTION

[0060] A method for eliminating mismatching of image feature points comprises the following steps:

[0061] Step 1: Use Harris corner algorithm to extract feature points in target image Is and matching image It respectively, and use SIFT algorithm to construct description vectors for feature points; then proceed to step 2;

[0062] Step 2: Use the NNDR (Nearest Neighbor Distance Ratio) algorithm to match each feature point in the target image with the feature points in the matching image to obtain N pairs of initial matching results. where xi ,y i is a two-dimensional column vector representing the position of the feature point; then proceed to step 3;

[0063] The matching in this step is to establish a corresponding relationship.

[0064] Step 3: Use the Delaunay triangulation algorithm to locally connect the initial matching points, construct a triangulated network, and obtain the point set k in the neighborhood of the point set x, y s , k t ; Then go to step 4;

[0065] Step 4: Set the directly connected node of a node in the triangulated network as the directly adjacent node, and set the node connected to the node through the directly adjacent node as the secondary adjacent node to build a neighborhood relationship. Then proceed to step 5.

[0066] Step 5 includes the following steps:

[0067] Step 5.1: Calculate the loss function for building adjacency relationships based on directly adjacent nodes. Based on the assumption that the local adjacency relationships between feature points in a local area of ​​a non-rigidly deformed image remain unchanged, when there are no outliers in the two sets of points to be matched, all the adjacency relationships in the matching point sets will remain consistent. Therefore, we use the percentage of the number of matching relationships maintained in the neighborhood to the total number of neighborhood points as a metric to determine whether a matching point pair is an inner point. The greater the percentage of the number of matching relationships maintained in the neighborhood to the total number of neighborhood points, the greater the possibility that the center point pair of the neighborhood is a correct match. Write the loss function as the sum of the percentage of points that cannot maintain adjacency relationships in the neighborhood and the number of outliers:

[0068]

[0069] in, For x i and i The point set with matching relationship in the two neighborhoods with centered is obtained by step 2. x i and i is the feature point set in the neighborhood centered on the center, which is obtained by step 3, I1 is the inlier set, which is obtained by step 3, |·| is the cardinality of the set, the first term on the right side of the equation is the penalty term for the point pairs that cannot maintain a consistent matching relationship in the neighborhood of the matching point, and the second term is to maximize the number of inliers by controlling the strength through λ. i It is a binary function that determines whether the central feature point of the neighborhood is trustworthy based on whether the number of point pairs that maintain matching relationships in the neighborhood is greater than or equal to 2, and removes untrusted connections. i The expression is as follows:

[0070]

[0071] According to formula (1), calculate the loss function C1 based on the adjacency relationship constructed based on the directly adjacent nodes. Then proceed to step 5.2. λ is the input parameter, which is the threshold for judging whether it is an inlier, and the threshold belongs to [0, 1]. N is the number of point pairs after the initial matching. Among them, i is the index of the i-th match. If the i-th match satisfies C, that is, the cost is less than λ, then the match is an inlier. The values ​​of the parameters λ and N are directly given by the outside.

[0072] Step 5.2: Calculate the loss function for building adjacency relationships based on direct neighboring nodes and secondary neighboring nodes. The calculation formula is as follows:

[0073]

[0074] in, x i The set of directly adjacent nodes and secondary adjacent nodes with matching relationships in the neighborhood of the center. y i The set of directly adjacent nodes and secondary adjacent nodes with matching relationships in the neighborhood of the center. x i is the set of direct adjacent nodes and secondary adjacent nodes in the neighborhood of the center, y i is the set of direct neighboring nodes and secondary neighboring nodes in the neighborhood of the center, and I2 is the set of internal points. According to formula (2), the loss function C2 of building adjacency relationships based on direct neighboring nodes is calculated. Then go to step 5.3.

[0075] Step 5.3: Calculate the final loss function C according to formula (3). Then proceed to step 5.4;

[0076] C=0.5*C1+0.5*C2 (3) Step 5.4: Obtain the initial interior point set I0 according to equation (4). Then proceed to step 5.5;

[0077] I0={i|C i ≤λ,i=1,…,N} (4)

[0078] λ is an input parameter, which is the threshold for determining whether it is an inlier. This threshold belongs to [0, 1]. N is the number of point pairs after the initial matching. Among them, i is the index of the i-th match. If the i-th match satisfies C, that is, the cost is less than λ, then the match is an inlier.

[0079] Step 5.5: Get the initial correct matching point set S1 and the initial incorrect matching point set S2, S1 = {x i ,yi |i=I0}, S2 is the initial mismatch point set, which is the difference between S and S1.

[0080] Step 6 includes the following steps:

[0081] Step 6.1: Calculate the similarity of the two triangles according to formula (5), where A1, A2 are a pair of matching points in set S2, B1, B2, and C1, C2 are two pairs of matching points in set S1. Then proceed to step 6.2;

[0082]

[0083] In formula (5), the point pairs in S1 are considered to be assumed to be correctly matched, so As a comparison benchmark, the closer the ratios of the other two groups of corresponding edges are, The more similar the two triangles are.

[0084] Step 6.2: In order to enhance the accuracy of the triangle similarity function measurement, add angle similarity measurement to the proportional constraint of the three sides. Calculate the similarity of the two triangle angles according to formula (6). Then proceed to step 6.3;

[0085] SimAngle=|cos(∠B1A1C1)-cos(∠B2A2C2)| (6)

[0086] Step 6.3: When the SimEdge value is less than the threshold τ and the SimAngle value is less than When , the two triangles are determined to be similar, and A1 and A2 are restored as correct matches. The restored interior point set I r The expression of is as follows:

[0087]

[0088] Step 7: Obtain the complete interior point set I according to formula (8).

[0089] I r =I = I0∪I r (8) .

Claims

1. A method for eliminating mismatching of image feature points, characterized in that: The following steps are included: Step 1: Extract feature points; Extract feature points and construct description vectors; Step 2: Feature point matching; Step 3: Get the internal point set; Step 4: Build neighborhood relationships; Step 5: Calculate the initial internal point set; Step 6: Calculate the restored internal point set; Step 7: Get the complete set of interior points; The step 1 comprises: Harris corner algorithm is used to extract feature points in target image Is and matching image It respectively, and SIFT algorithm is used to construct description vectors for feature points; then, step 2 is entered; The step 2 comprises: The NNDR (Nearest Neighbor Distance Ratio) algorithm is used to match each feature point in the target image with each feature point in the matching image to obtain N pairs of initial matching results. where x i ,y s is a two-dimensional column vector representing the position of the feature point; then proceed to step 3; The step 3 comprises: Use the Delaunay triangulation algorithm to locally connect the initial matching points, construct a triangulated network, and obtain the point set k in the neighborhood of the point set x and y. t , k i ; Then go to step 4; The step 4 comprises: Set the directly connected node of a node in the triangulated network as a directly adjacent node, set the node connected to the node through the directly adjacent node as a secondary adjacent node, build a neighborhood relationship, and then go to step 5; The step 5 comprises: Step 5.1: Calculate the loss function based on the adjacency relationship constructed by the direct neighboring nodes. Based on the assumption that the local adjacency relationship between feature points in the local area of ​​the non-rigidly deformed image remains unchanged, when there are no outliers in the two points to be matched, all the adjacency relationships in the matching point sets will remain consistent. Therefore, we use the percentage of the number of matching relationships maintained in the neighborhood to the total number of neighborhood points as a metric to determine whether the matching point pair is an inner point. The larger the percentage of the number of matching relationships maintained in the neighborhood to the total number of neighborhood points, the greater the possibility that the central point pair of the neighborhood is a correct match. The loss function is written as the sum of the percentage of the neighborhood that cannot maintain the adjacency relationship and the number of outliers: in, For x i and i The point set with matching relationship in the two neighborhoods with centered is obtained by step 2. x i and i is the feature point set in the neighborhood centered on , which is obtained by step 3. I1 is the inlier set, which obtains the optimal solution when the loss function C1 is minimized. |·| is the cardinality of the set. The first term on the right side of the equation is the penalty term for the point pairs that cannot maintain a consistent matching relationship in the neighborhood of the matching point. The second term is to maximize the number of inliers by controlling the intensity through λ. i It is a binary function. Whether the number of point pairs that maintain matching relationships in the neighborhood is greater than or equal to 2 is used to determine whether the central feature point of the neighborhood is trustworthy. Untrusted connections are eliminated. i The expression is as follows: According to formula (1), calculate the loss function C1 of building adjacency relationship based on direct adjacent nodes, and then go to step 5.2; λ in formula (1) is an input parameter, which is used as the threshold for judging the internal point. The value range of λ is [0, 1]. N in formula (1) is the number of point pairs after initial matching, and i is the index of the i-th match. If the C1 value of the i-th match is less than λ, it means that the match is an internal point. The values ​​of parameters λ and N are directly set externally; Step 5.2: Calculate the loss function for building adjacency relationships based on direct neighboring nodes and secondary neighboring nodes. The calculation formula is as follows: in, x i The set of directly adjacent nodes and secondary adjacent nodes with matching relationships in the neighborhood of the center. y i The set of directly adjacent nodes and secondary adjacent nodes with matching relationships in the neighborhood of the center. x i is the set of direct adjacent nodes and secondary adjacent nodes in the neighborhood of the center, y i The set of direct adjacent nodes and the set of secondary adjacent nodes in the neighborhood of the center is I2, and I2 is the set of internal points. According to formula (3), the loss function C2 of building adjacency relationships based on direct adjacent nodes is calculated, and then step 5.3 is entered. Step 5.3: Calculate the final loss function C according to formula (4), and then go to step 5.4; c=0.5*C1+0.5*C2 (4) Step 5.4: Obtain the initial interior point set I0 according to equation (5), and then proceed to step 5.5; I0={i|C i ≤λ,i=1,…,N}(5)λ is the input parameter, which is the threshold for determining the inliers. The value range of λ is [0, 1]; N is the number of point pairs after the initial matching, where i is the index of the i-th match. If the i-th match satisfies C, i.e., the cost is less than λ, then the match is an inlier. Step 5.5: Get the initial correct matching point set S1 and the initial incorrect matching point set S2, S1 = {x i ,y i |i=I0}, S2 is the initial mismatch point set, which is the difference between S and S1; The step 6 comprises: Step 6.1: Calculate the similarity of the two triangles according to formula (6), where A1, A2 are a pair of matching points in set S2, B1, B2, and C1, C2 are two pairs of matching points in set S1, and then go to step 6.2; In formula (6), the point pairs in S1 are considered to be assumed to be correctly matched, so As a comparison benchmark, the closer the ratios of the other two groups of corresponding edges are, The more similar the two triangles are, Step 6.2: In order to enhance the accuracy of the triangle similarity function measurement, add the angle similarity measurement to the proportional constraint of the three sides, calculate the similarity of the two triangle angles according to formula (7), and then go to step 6.3; SimAngle=|cos(∠B1A1C1)-cos(∠B2A2C2)| (7) Step 6.3: When the SimEdge value is less than the threshold τ and the SimAngle value is less than When , the two triangles are determined to be similar, and A1 and A2 are restored as correct matches. The restored interior point set I r The expression is as follows: The step 7 comprises: According to formula (9), we can get the complete interior point set I. I r =I=I0∪I r (9)。

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