Intelligent matching retrieval method and system based on graph structure topological constraint

Abstract

The present application relates to the technical field of figure retrieval, and particularly relates to an intelligent matching retrieval method and system based on figure structure topological constraint, which acquires a figure object to be retrieved and a candidate figure object set, extracts topological features to construct a persistent graph, identifies feature point clusters and overlap degrees to construct a constraint propagation network, extracts a constraint propagation matrix to perform eigenvalue decomposition to obtain a dominant constraint direction and filter a candidate matching graph set, forms a topological deformation path through insertion, deletion and movement operations, and performs scale sensitivity weighting accumulation on operation cost to obtain a cumulative deformation cost to output a matching retrieval result, thereby improving the accuracy and robustness of figure retrieval.

Description

Technical Field

[0001] This invention relates to the field of graphic retrieval technology, and in particular to an intelligent matching retrieval method and system based on topological constraints of graphic structures. Background Technology

[0002] Graph structure retrieval is a key technology in computer vision and pattern recognition, widely applied in shape matching, sketch recognition, and medical image analysis. Current conventional approaches are mostly based on a combination of local feature descriptors and global shape descriptors. For example, feature vectors are constructed by extracting local gradient histograms or Fourier descriptors of key points, followed by nearest neighbor matching using Euclidean distance or cosine similarity. Some methods introduce topological constraints, using graph theory to represent graphs as attribute adjacency graphs or skeleton graphs, achieving retrieval through subgraph isomorphism or graph kernel functions. These methods perform well on rigid graphs, but rarely consider the topological stability of graphs under scale changes and deformation conditions.

[0003] One significant drawback of conventional approaches is their insufficient scale adaptability to graphical topological features. Existing methods typically pre-define a fixed scale parameter or extract a single-level topological structure. This leads to a sharp decline in the repeatability and robustness of the topological description when there are overall scaling, local dilation, or differences in detail between the target graph and candidate graphs. For example, skeleton graph-based matching algorithms are extremely sensitive to minor breaks or redundancies in skeleton branches, while single-scale local features cannot distinguish between noisy details and essential topological contours in the original structure.

[0004] Another drawback is the lack of effective utilization of cross-level structural constraints during the matching process. Real-world graphs often contain hierarchical topological attributes ranging from coarse-grained to fine-grained, while existing techniques typically treat matching results at different scales in isolation or simply integrate them through weighted summation. This approach ignores the correlation between feature points at different scale levels. For example, a branch at a fine scale may originate from multiple forks of the same main branch at a coarse scale. Without establishing a cross-level constraint propagation mechanism, it is impossible to suppress erroneous matches caused by local ambiguity, ultimately reducing retrieval accuracy and resistance to deformation. Summary of the Invention

[0005] The embodiments of the present invention provide an intelligent matching and retrieval method and system based on topological constraints of graph structures, which can solve the problems in the prior art.

[0006] A first aspect of this invention provides an intelligent matching retrieval method based on graph structure topological constraints, comprising: Retrieve the graphic object to be retrieved and the set of candidate graphic objects; Extract the topological features of the target graph object and the candidate graph object set, calculate the occurrence threshold and disappearance threshold of the topological features at multiple scales, and construct the target persistent graph and the candidate persistent graph set; Identify feature point clusters at different scale levels in the persistent graph to be retrieved, calculate the overlap of feature point clusters at adjacent scale levels, and use the overlap as connection weights to construct a constraint propagation network across scale levels. The constraint propagation matrix is ​​extracted from the constraint propagation network, the dominant constraint direction is obtained by eigenvalue decomposition of the constraint propagation matrix, the dominant constraint direction is projected onto the candidate persistent graph set to obtain the constraint response value, and the candidate matching graph set is selected based on the constraint response value. Each candidate matching graph in the candidate matching graph set is transformed into the persistent graph to be retrieved through insertion, deletion and move operations, and the transformation state is recorded to form a topological deformation path; The costs of insertion, deletion, and movement operations in the topological deformation path are calculated. The cumulative deformation cost is obtained by weighting the operations based on scale sensitivity according to the scale level at which they occur, and the matching retrieval results are output based on the cumulative deformation cost.

[0007] Extracting the topological features of the target graph object and the candidate graph object set, calculating the occurrence and disappearance thresholds of the topological features at multiple scales, and constructing the target persistent graph and candidate persistent graph set includes: Boundary extraction is performed on the graphic object to be retrieved and the set of candidate graphic objects to obtain a closed contour. Connected components, loop structures and hole structures are identified as topological features within the closed contour. Set an initial filtering scale and a final filtering scale, and generate multiple filtering scale sequences between the initial filtering scale and the final filtering scale with a fixed step size; Each filter scale in the filter scale sequence is applied sequentially to the topological feature for filtering detection. The filter scale corresponding to the first detection of the topological feature is recorded as the occurrence threshold, and the filter scale corresponding to the last detection of the topological feature is recorded as the disappearance threshold. Mark coordinate points in a two-dimensional coordinate system using the occurrence threshold as the x-axis value and the disappearance threshold as the y-axis value. Perform kernel density estimation on the coordinate points to obtain the density distribution field. Use the density distribution field corresponding to the graphic object to be retrieved as the persistent graph to be retrieved. Use the density distribution field corresponding to each candidate graphic object in the candidate graphic object set as the candidate persistent graph set.

[0008] Identifying feature point clusters at different scale levels in the persistent graph to be retrieved, calculating the overlap between feature point clusters at adjacent scale levels, and using the overlap as connection weights to construct a constraint propagation network across scale levels includes: The ordinate range of the persistent map to be retrieved is divided into multiple scale intervals at equal intervals, and the coordinate points contained in each scale interval constitute a scale level. The average distance between all coordinate points in the persistent map to be retrieved is calculated as the clustering radius. Spatial clustering of coordinate points is performed at each scale level, and coordinate points with a distance less than the clustering radius are grouped into the same cluster to form a feature point cluster. Extract two vertically adjacent scale levels, calculate the projection overlap length of the feature point clusters in the upper scale level and the feature point clusters in the lower scale level in the horizontal coordinate direction, and take the ratio of the projection overlap length to the horizontal coordinate span of the feature point clusters in the upper scale level as the overlap degree of the feature point clusters in the adjacent scale levels. The overlap of the feature point clusters at adjacent scale levels is weighted by an exponential decay function with the difference between the center of the ordinates of the two scale levels as the independent variable, to obtain the connection weight. By using feature point clusters in the upper and lower scale levels as network nodes and connection weights as edge weights connecting network nodes, a constraint propagation network across scale levels is constructed.

[0009] The constraint propagation matrix is ​​extracted from the constraint propagation network. Eigenvalue decomposition is performed on the constraint propagation matrix to obtain the dominant constraint direction. The dominant constraint direction is projected onto the candidate persistent graph set to obtain constraint response values. The candidate matching graph set is then selected based on the constraint response values, including: Extract all network nodes in the constraint propagation network, sort them by their ordinate values, construct an adjacency matrix, and apply a nonlinear transformation to the adjacency matrix to obtain the constraint propagation matrix; The constraint propagation matrix is ​​decomposed into eigenvalues ​​to extract multiple eigenvectors to construct a multidimensional constraint subspace. The eigenvector with the largest variance contribution rate is selected as the dominant constraint direction in the multidimensional constraint subspace. The coordinates of the persistent graph to be retrieved and the coordinates of each candidate persistent graph in the candidate persistent graph set are projected onto the dominant constraint direction to obtain a projection sequence. The topological morphology analysis of the projection sequence is performed to obtain the distribution pattern features. The structural difference metric between the distribution pattern features of the candidate persistent graph and the distribution pattern features of the persistent graph to be retrieved is calculated as the constraint response value. The candidate persistent graph set is hierarchically clustered according to the constraint response value to form multiple candidate graph clusters. The candidate graph cluster to which the persistent graph to be retrieved belongs is identified, and all candidate persistent graphs in the candidate graph cluster are extracted to form a candidate matching graph set.

[0010] Transforming each candidate matching graph in the candidate matching graph set to the persistent graph to be retrieved through insertion, deletion, and move operations, and recording the transformation state to form a topological deformation path includes: The coordinate points of the candidate matching graph are projected onto the dominant constraint direction to obtain constraint projection coordinates, and the coordinate points of the persistent graph to be retrieved are projected onto the dominant constraint direction to obtain target projection coordinates. Based on the difference between the constraint projection coordinates and the target projection coordinates, points to be deleted, points to be inserted, and points to be moved are identified. The execution priority of insertion, deletion and movement operations is determined according to the propagation strength of network nodes in the constraint propagation network. The operations are executed in sequence according to the execution priority, and the operation type and coordinate position changes are recorded to form the transformation state. The transformed states are associated and organized according to the propagation path of the constraint propagation network to form a topological deformation path.

[0011] The costs of insertion, deletion, and movement operations in the topological deformation path are calculated. These costs are then weighted by scale sensitivity according to the scale level at which the operations occur, and the cumulative deformation cost is obtained by summing the results. The matching retrieval results are output based on the cumulative deformation cost, including: Extract the coordinate position changes corresponding to insertion, deletion and movement operations in the topology deformation path, project the coordinate position changes onto the dominant constraint direction to obtain the constraint direction component, and calculate the operation cost based on the eigenvalue perturbation caused by the constraint direction component in the constraint propagation matrix. The scale level of the coordinate points corresponding to the insertion, deletion and move operations in the persistent graph to be retrieved is identified, the overlap of the scale level is obtained as the scale sensitivity weight, and the operation cost is weighted by the scale sensitivity weight to obtain the weighted operation cost. The weighted operation cost is accumulated according to the propagation path of the constraint propagation network to obtain the path cumulative cost. The topological connectivity compensation amount is calculated based on the path cumulative cost and the connectivity structure of the constraint propagation network, and then superimposed to obtain the cumulative deformation cost. The candidate matching map set is sorted according to the cumulative deformation cost, and the matching retrieval results are output.

[0012] The computational cost based on the eigenvalue perturbation caused by the constraint direction component in the constraint propagation matrix includes: Construct a matrix perturbation operator corresponding to the constraint direction component, and superimpose the matrix perturbation operator onto the constraint propagation matrix to obtain the perturbed constraint propagation matrix; The constraint propagation matrix is ​​decomposed into eigenvalues ​​to obtain the original eigenvalue sequence. The perturbed constraint propagation matrix is ​​decomposed into eigenvalues ​​to obtain the perturbed eigenvalue sequence. The difference between the eigenvalues ​​at corresponding positions in the perturbed eigenvalue sequence and the original eigenvalue sequence is calculated to obtain the eigenvalue perturbation quantity sequence. The perturbation main frequency component is extracted by spectral analysis of the eigenvalue perturbation quantity sequence. The perturbation propagation field distribution is obtained by convolving the perturbation dominant frequency component with the propagation intensity of the network nodes in the constrained propagation network. The perturbation propagation field distribution is then integrated globally in the network topology space of the constrained propagation network to obtain a global perturbation metric value as the operation cost.

[0013] A second aspect of this invention provides an intelligent matching and retrieval system based on graph structure topological constraints, comprising: The object acquisition unit is used to acquire the graphic object to be retrieved and a set of candidate graphic objects. The topology graph unit is used to extract the topological features of the graphic object to be retrieved and the candidate graphic object set, calculate the occurrence threshold and disappearance threshold of the topological features at multiple scales, and construct the persistent graph to be retrieved and the candidate persistent graph set. The constraint network unit is used to identify feature point clusters at different scale levels in the persistent graph to be retrieved, calculate the overlap of feature point clusters at adjacent scale levels, and use the overlap as connection weights to construct a constraint propagation network across scale levels. The matching and filtering unit is used to extract the constraint propagation matrix from the constraint propagation network, perform eigenvalue decomposition on the constraint propagation matrix to obtain the dominant constraint direction, project the dominant constraint direction onto the candidate persistent graph set to obtain the constraint response value, and filter out the candidate matching graph set based on the constraint response value. The deformation path unit is used to transform each candidate matching graph in the candidate matching graph set to the persistent graph to be retrieved through insertion, deletion and move operations, and record the transformation state to form a topological deformation path; The retrieval output unit is used to calculate the cost of insertion, deletion and movement operations in the topological deformation path, and accumulates the cumulative deformation cost after performing scale sensitivity weighting according to the scale level where the operation is located, and outputs the matching retrieval result based on the cumulative deformation cost.

[0014] A third aspect of the present invention provides an electronic device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0015] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0016] This invention effectively captures key topological attributes of graphic structures at different scales by extracting topological features and constructing multi-scale persistent graphs. The introduction of appearance and disappearance thresholds makes the feature representation scale-invariant, adapting to geometric transformations such as scaling and rotation of graphic objects. Cross-scale feature cluster identification and overlap calculation accurately locate stable regions and evolution patterns of the topological structure, significantly improving the matching reliability of complex graphics under local deformation conditions. A cross-scale constraint propagation network based on overlap organically links topological features at different scales, avoiding the limitations of isolated processing of each scale in traditional methods. Eigenvalue decomposition of the constraint propagation matrix extracts the dominant constraint direction, which centrally reflects the core constraint relationships of the graphic structure, thus efficiently filtering candidate matches with topological consistency with the graphic to be retrieved from the candidate persistent graph set. The constraint response value obtained by projection quantifies structural similarity, improving retrieval accuracy and noise resistance. The introduction of insertion, deletion, and movement operations simulates the topological deformation process, recording the transformation state to form a complete deformation path, which can fully characterize the structural differences between graphics. The scale-sensitive weighting of operational costs ensures a reasonable allocation of contributions at each scale, while the cumulative deformation cost comprehensively reflects the difficulty and cost of the overall topological transformation. Finally, the matching result is output based on the cumulative deformation cost, achieving robust matching for complex cases such as local deformation and partial missing parts. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the intelligent matching and retrieval method based on graph structure topological constraints. Figure 2 A software operation flowchart is constructed for the cross-scale hierarchical constraint propagation network; Figure 3 This is a decomposition diagram of the cumulative deformation cost under different constraint direction components. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0020] Figure 1 This is a flowchart illustrating the intelligent matching and retrieval method based on topological constraints of a graphical structure, according to an embodiment of the present invention.

[0021] Intelligent matching and retrieval methods based on graph structure topological constraints include: Retrieve the graphic object to be retrieved and the set of candidate graphic objects; Extract the topological features of the target graph object and the candidate graph object set, calculate the occurrence threshold and disappearance threshold of the topological features at multiple scales, and construct the target persistent graph and the candidate persistent graph set; Identify feature point clusters at different scale levels in the persistent graph to be retrieved, calculate the overlap of feature point clusters at adjacent scale levels, and use the overlap as connection weights to construct a constraint propagation network across scale levels. The constraint propagation matrix is ​​extracted from the constraint propagation network, the dominant constraint direction is obtained by eigenvalue decomposition of the constraint propagation matrix, the dominant constraint direction is projected onto the candidate persistent graph set to obtain the constraint response value, and the candidate matching graph set is selected based on the constraint response value. Each candidate matching graph in the candidate matching graph set is transformed into the persistent graph to be retrieved through insertion, deletion and move operations, and the transformation state is recorded to form a topological deformation path; The costs of insertion, deletion, and movement operations in the topological deformation path are calculated. The cumulative deformation cost is obtained by weighting the operations based on scale sensitivity according to the scale level at which they occur, and the matching retrieval results are output based on the cumulative deformation cost.

[0022] Extracting the topological features of the target graph object and the candidate graph object set, calculating the occurrence and disappearance thresholds of the topological features at multiple scales, and constructing the target persistent graph and candidate persistent graph set includes: Boundary extraction is performed on the graphic object to be retrieved and the set of candidate graphic objects to obtain a closed contour. Connected components, loop structures and hole structures are identified as topological features within the closed contour. Set an initial filtering scale and a final filtering scale, and generate multiple filtering scale sequences between the initial filtering scale and the final filtering scale with a fixed step size; Each filter scale in the filter scale sequence is applied sequentially to the topological feature for filtering detection. The filter scale corresponding to the first detection of the topological feature is recorded as the occurrence threshold, and the filter scale corresponding to the last detection of the topological feature is recorded as the disappearance threshold. Mark coordinate points in a two-dimensional coordinate system using the occurrence threshold as the x-axis value and the disappearance threshold as the y-axis value. Perform kernel density estimation on the coordinate points to obtain the density distribution field. Use the density distribution field corresponding to the graphic object to be retrieved as the persistent graph to be retrieved. Use the density distribution field corresponding to each candidate graphic object in the candidate graphic object set as the candidate persistent graph set.

[0023] When performing boundary extraction on the retrieved graphic object and the candidate graphic object set, a gradient response-based contour detection algorithm is used to trace the pixel boundaries of the graphic object step by step, ensuring that each extracted contour constitutes a closed path. For boundary regions with breaks or noise interference, short-distance breaks are bridged and repaired by setting a connectivity tolerance parameter, thereby ensuring the closure of all contours. After the closed contours are extracted, three types of topological features are identified within the contour-enclosed areas: connected components represent independent continuous regions in the graphic, reflecting the overall separation degree of the graphic; loop structures represent closed paths formed inside the contours, capturing the loop shape of the graphic; and void structures represent blank areas completely surrounded by connected regions, characterizing the distribution of internal voids in the graphic. These three types of topological features correspond to 0-dimensional and 1-dimensional homology features in topological data analysis, respectively, and can comprehensively describe the topological properties of the graphic from different levels.

[0024] After completing the topological feature recognition, set the initial filtering scale. and termination filter scale The two are separated by a fixed step size. Uniformly divide and generate filter scale sequence Initial filtering scale It is typically set to a positive value close to zero to ensure that fine topological structures can be captured at the finest resolution; the final filtering scale. The step size is determined based on the overall size range of the graphic object, ensuring that all topological features have disappeared before the end of the sequence. The selection of the step size needs to strike a balance between computational accuracy and efficiency. An excessively large step size will lead to a decrease in the accuracy of the appearance and disappearance thresholds, while an excessively small step size will significantly increase the computational load of filtering and detection. In practical applications, the step size can be adaptively adjusted according to the graph complexity, using a smaller step size for scale intervals with dense topological features to improve resolution.

[0025] Apply each filter scale in the filter scale sequence sequentially to each topological feature. This involves performing a filtering detection operation. The essence of filtering detection is to perform a filtering detection operation at a given scale. The simplicial complex of the graph is constructed, and the existence of each topological feature is determined by calculating the homology group of the simplicial complex. When a certain topological feature is at a certain scale... The first appearance of this feature, meaning it has not been detected at any previous smaller scales, will... The occurrence threshold of this topological feature is recorded. When a certain topological feature is at scale If it is detected for the last time, meaning it no longer exists at any larger scale thereafter, then it will be... Recorded as the vanishing threshold of this topological feature The difference between the appearance threshold and the disappearance threshold. The difference reflects the persistence of the topological feature. The larger the difference, the more stable the feature is over a wider scale range and the higher its structural significance. The smaller the difference, the more briefly the feature appears within a very narrow scale window, usually corresponding to spurious features caused by noise or small perturbations.

[0026] Threshold the occurrence of each topological feature As the x-axis value, the disappearance threshold The ordinate values ​​are used to mark the corresponding coordinate points in a two-dimensional coordinate system, thus forming a persistent scatter plot. Since the vanishing threshold is necessarily no less than the appearing threshold, all coordinate points are distributed along the diagonal. In the region above the diagonal, points farther from the diagonal represent more persistent topological features. Relying solely on discrete points for subsequent matching calculations suffers from sensitivity to point location and weak noise resistance. Therefore, kernel density estimation is performed on the set of points to transform discrete coordinate points into a continuous density distribution field. Kernel density estimation uses a Gaussian kernel function, which is applied to any position in the two-dimensional coordinate system. Its density value It is obtained by summing the contributions of all coordinate points to this location: ;

[0027] in The total number of topological features. For kernel bandwidth parameters, and The first The occurrence and disappearance thresholds of each topological feature. Kernel bandwidth. To control the smoothness of the density distribution field, a larger Smoothering the density field helps suppress spurious features introduced by small perturbations, but excessively large perturbations can lead to problems. This can lead to the aliasing of density responses from different topological features; smaller This preserves more detail but is more sensitive to noise. In engineering practice, the Silverman empirical formula can be used to automatically estimate the optimal bandwidth based on the statistical properties of the scatter plot, or cross-validation can be used to select the value that minimizes the density estimation error from the candidate bandwidth set.

[0028] After performing all the above operations on the graphic object to be retrieved, its corresponding density distribution field is obtained, and this density distribution field is used as the persistent map to be retrieved. The same processing flow is then performed on each candidate graphic object in the candidate graphic object set to obtain its corresponding density distribution field. These density distribution fields are then combined to form the candidate persistent map set. The density distribution field is typically stored in the form of uniform grid sampling, dividing the two-dimensional coordinate system into... A grid is formed, and the density value is calculated at each grid node to create a... The density matrix is ​​used as a numerical representation of the persistent map. Grid resolution. The selection of resolution needs to be determined comprehensively based on the scale range and computing resources. Higher resolution results in a more refined representation of topological features in the persistent graph, but also increases storage overhead and subsequent matching computation. In typical application scenarios, [the following is used:] Setting the value between 64 and 256 achieves a good balance between representational accuracy and computational efficiency. Through this complete process, the complex geometric and topological information of the original graphical object is transformed into a structured, persistent graph representation, laying the data foundation for subsequent constraint propagation network construction and matching retrieval.

[0029] like Figure 2 As shown, Figure 2 This is a flowchart illustrating the software operation for constructing a cross-scale hierarchical constraint propagation network according to an embodiment of the present invention.

[0030] Identifying feature point clusters at different scale levels in the persistent graph to be retrieved, calculating the overlap between feature point clusters at adjacent scale levels, and using the overlap as connection weights to construct a constraint propagation network across scale levels includes: The ordinate range of the persistent map to be retrieved is divided into multiple scale intervals at equal intervals, and the coordinate points contained in each scale interval constitute a scale level. The average distance between all coordinate points in the persistent map to be retrieved is calculated as the clustering radius. Spatial clustering of coordinate points is performed at each scale level, and coordinate points with a distance less than the clustering radius are grouped into the same cluster to form a feature point cluster. Extract two vertically adjacent scale levels, calculate the projection overlap length of the feature point clusters in the upper scale level and the feature point clusters in the lower scale level in the horizontal coordinate direction, and take the ratio of the projection overlap length to the horizontal coordinate span of the feature point clusters in the upper scale level as the overlap degree of the feature point clusters in the adjacent scale levels. The overlap of the feature point clusters at adjacent scale levels is weighted by an exponential decay function with the difference between the center of the ordinates of the two scale levels as the independent variable, to obtain the connection weight. By using feature point clusters in the upper and lower scale levels as network nodes and connection weights as edge weights connecting network nodes, a constraint propagation network across scale levels is constructed.

[0031] After obtaining the persistent graph to be retrieved, a hierarchical analysis of its internal multi-scale structure is required to reveal the distribution patterns of topological features across different scale intervals. The ordinate of the persistent graph represents the vanishing threshold of the topological feature, reflecting the scale position at which the feature disappears during the filtering process. Therefore, using the ordinate range as the basis for division has clear topological significance. Specifically, the ordinate range of the persistent graph to be retrieved is divided into several scale intervals at equal intervals, with each scale interval having the same width. All coordinate points falling within the same scale interval constitute a scale level. The number of scale intervals can be flexibly adjusted according to the total number and distribution density of coordinate points in the persistent graph. If the division is too fine, it will result in too few coordinate points in each level and unstable clustering results. If the division is too coarse, it will lose the fine-grained structural differences between levels. Usually, the maximum number of divisions that ensures the average number of coordinate points in each level is not less than the preset minimum sample size is selected as a reasonable configuration.

[0032] After completing the scale hierarchy division, spatial clustering is performed on the coordinate points within each scale hierarchy. The cluster radius is determined using a global statistical method: the pairwise Euclidean distances between all coordinate points in the persistent map to be retrieved are calculated, and the average of these distances is taken as the uniform cluster radius. This approach ensures the adaptability of the clustering radius to the overall point cloud distribution, avoiding the bias caused by manually setting a fixed threshold. Within each scale level, the Euclidean distance between any two coordinate points is less than... Points are grouped into the same cluster, and a region growing strategy based on distance connectivity is used to gradually expand the cluster's membership until all points within a cluster are at least 10 ... Ultimately, several feature point clusters are formed within each scale level. Each feature point cluster represents a set of topological features that are spatially adjacent to each other within that scale level, and its centroid coordinates and x-coordinate span are the basis for subsequent overlap calculations.

[0033] For two vertically adjacent scale levels, the side with the larger ordinate interval is defined as the upper scale level, and the side with the smaller ordinate interval is defined as the lower scale level. For each feature point cluster in the upper scale level, the minimum and maximum x-coordinates of all its member coordinate points are extracted to obtain the coverage area of ​​the cluster in the x-coordinate direction. Its horizontal axis span is denoted as Similarly, for each feature point cluster in the lower-scale hierarchy, its x-coordinate coverage interval is extracted. Calculate the projection overlap length between the upper and lower clusters along the horizontal axis. That is, the length of the intersection of the two intervals: The ratio of the projection overlap length to the abscissa span of the feature point cluster in the upper-level scale is defined as the overlap degree of the feature point clusters in adjacent scales. ,Right now When the horizontal coordinate span of the upper cluster When it is zero, Set to 0 to avoid division by zero anomalies. Overlap The value ranges from 0 to 1. The larger the value, the closer the coverage areas of the upper and lower clusters are in the horizontal direction, and the stronger the topological correlation between them.

[0034] Projection overlap alone is insufficient to fully characterize the correlation strength between cross-scale levels, because two levels with a large difference in their ordinate centers are geographically distant, and the direct correlation between their feature point clusters should decrease with increasing distance. Therefore, an exponential decay function with the difference in the ordinate centers of the two scale levels as the independent variable is applied to the overlap. Let the ordinate center of the upper scale level be... The center of the vertical coordinate of the lower-level scale is The difference between the centers of their ordinates is The decay coefficient of the exponential decay function is Then the connection weight The calculation method is as follows Attenuation coefficient Control the rate at which the weights decrease with increasing scale distance. A larger value indicates a smaller connection weight between distant hierarchical pairs. In practical applications, this value can be determined by normalizing the ordinate range of the persistent graph with the number of hierarchical levels. The appropriate value is determined by exponential decay weighting, which preserves the characterization of structural similarity in the horizontal axis by overlap and introduces the adjustment effect of scale distance in the vertical axis, so that the connection weight can comprehensively reflect the degree of correlation between two feature point clusters in both topological structure and scale position.

[0035] After obtaining the connection weights between all adjacent scale-level feature point cluster pairs, each feature point cluster is treated as a node in the constraint propagation network, and the connection weights are... As edge weights connecting upper-level and lower-level nodes, a constraint propagation network is constructed across scale levels. The number of nodes in the network equals the total number of feature point clusters generated by the persistent graph to be retrieved across all scale levels. Edges are only established between two vertically adjacent levels, without direct connections across non-adjacent levels. This hierarchical connection structure effectively reflects the propagation path of topological features during scale evolution. If the connection weight between a pair of feature point clusters in adjacent levels is lower than a preset minimum weight threshold, the corresponding edge is not established in the network to eliminate noise interference and maintain the sparsity of the network. The final constraint propagation network is stored in the form of a weighted adjacency matrix, providing structured input for subsequent extraction of the constraint propagation matrix and eigenvalue decomposition. The construction process of this network fully captures the topological constraint propagation relationship of the persistent graph to be retrieved across multiple scale levels, serving as the core data foundation for subsequent extraction of dominant constraint directions and selection of candidate matching graphs.

[0036] The constraint propagation matrix is ​​extracted from the constraint propagation network. Eigenvalue decomposition is performed on the constraint propagation matrix to obtain the dominant constraint direction. The dominant constraint direction is projected onto the candidate persistent graph set to obtain constraint response values. The candidate matching graph set is then selected based on the constraint response values, including: Extract all network nodes in the constraint propagation network, sort them by their ordinate values, construct an adjacency matrix, and apply a nonlinear transformation to the adjacency matrix to obtain the constraint propagation matrix; The constraint propagation matrix is ​​decomposed into eigenvalues ​​to extract multiple eigenvectors to construct a multidimensional constraint subspace. The eigenvector with the largest variance contribution rate is selected as the dominant constraint direction in the multidimensional constraint subspace. The coordinates of the persistent graph to be retrieved and the coordinates of each candidate persistent graph in the candidate persistent graph set are projected onto the dominant constraint direction to obtain a projection sequence. The topological morphology analysis of the projection sequence is performed to obtain the distribution pattern features. The structural difference metric between the distribution pattern features of the candidate persistent graph and the distribution pattern features of the persistent graph to be retrieved is calculated as the constraint response value. The candidate persistent graph set is hierarchically clustered according to the constraint response value to form multiple candidate graph clusters. The candidate graph cluster to which the persistent graph to be retrieved belongs is identified, and all candidate persistent graphs in the candidate graph cluster are extracted to form a candidate matching graph set.

[0037] All network nodes are extracted from the constraint propagation network and sorted in ascending order according to the y-coordinate values ​​(i.e., vanishing thresholds) of the topological features corresponding to each node. An adjacency matrix is ​​constructed based on this sorting order. Each element of the adjacency matrix reflects the connection weight between two corresponding nodes. If there is a cross-scale edge between the two nodes, the weight value of that edge is entered; otherwise, zero is entered. By constructing the adjacency matrix by sorting by y-coordinate, the row and column order of the matrix is ​​kept consistent with the chronological relationship of the topological features in scale evolution, thus enabling subsequent constraint propagation analysis to proceed in an orderly manner along the scale direction.

[0038] After obtaining the adjacency matrix, a nonlinear transformation is applied to it to obtain the constraint propagation matrix. Specifically, for each non-zero element in the adjacency matrix... Apply the following nonlinear transformation: ,in The gain coefficient for the nonlinear transformation controls the degree of weight compression. The hyperbolic tangent function is used because the original connection weights may vary significantly between different node pairs. Directly using the original weights for eigenvalue decomposition can easily lead to a few strong connections dominating the overall structure. The hyperbolic tangent function can moderately compress larger weights to near 1 while preserving the relative differences of smaller weights, thus allowing the constraint propagation matrix to more evenly reflect the constraint relationships between different scale levels in the network. The transformed matrix is ​​the constraint propagation matrix. Its dimensions are the same as those of the adjacency matrix, and it maintains symmetry.

[0039] Constraint propagation matrix Eigenvalue decomposition is performed to obtain several eigenvalues ​​and their corresponding eigenvectors. The eigenvalues ​​are then sorted in descending order of absolute value, and the first eigenvectors are extracted. eigenvectors, with this The eigenvectors form a basis to construct a multidimensional constrained subspace. Parameters The selection of the eigenvectors can be determined based on the cumulative variance contribution rate. Typically, the minimum number of eigenvectors required to achieve a preset threshold (e.g., 85%) is chosen. In the multidimensional constraint subspace, the variance contribution rate of each eigenvector corresponding to its eigenvalue is calculated; that is, the proportion of the absolute value of that eigenvalue to the sum of the absolute values ​​of all extracted eigenvalues. The eigenvector with the largest variance contribution rate is selected as the dominant constraint direction. The dominant constraint direction embodies the most significant topological changes in the constraint propagation network, compressing high-dimensional network structure information into a one-dimensional directional description, thus providing a foundation for subsequent projection analysis.

[0040] Project all coordinate points of the persistent graph to be retrieved onto the dominant constraint direction. The projection sequence of the persistent map to be retrieved is obtained. The specific projection method is as follows: represent each coordinate point as a two-dimensional vector, and calculate its coordinates... The inner product of the coordinates is used to obtain the projected scalar value of the coordinate point in the dominant constraint direction. The projected scalar values ​​of all coordinate points are arranged in the order of their original ordinates to form a projection sequence. Similarly, the same projection operation is performed on the coordinate points of each candidate persistent map in the candidate persistent map set to obtain the projection sequence of each candidate persistent map. .

[0041] Topological morphology analysis is performed on the projected sequence to extract distribution pattern features. The core of topological morphology analysis lies in extracting statistics from the projected sequence that reflect the overall distribution structure of the map, including the mean, standard deviation, skewness, and kurtosis of the projected sequence, as well as the number of local extrema and the distribution of extremum intervals. These statistics are concatenated into a feature vector, which serves as the distribution pattern feature of the persistent map. The mean and standard deviation reflect the central tendency and dispersion of the projected sequence, while skewness and kurtosis capture the asymmetry and tail characteristics of the projected sequence. The number of local extrema and the distribution of the distance between extrema characterize the oscillation mode of the projected sequence. Together, they constitute a multi-faceted description of the topological distribution structure of the persistent spectrum.

[0042] Calculate the distribution pattern features of each candidate persistent map. Distribution pattern characteristics of the persistent map to be retrieved The structural difference metric between them is used as the constraint response value for the candidate persistent map. The structural difference metric is calculated using weighted Euclidean distance: ,in This is a diagonal weight matrix, where the diagonal elements are determined based on the reciprocal of the variance of each feature component on the training set. Components with larger variances correspond to smaller weights, thus ensuring comparability of feature components with different dimensions and fluctuation ranges in distance calculation. The smaller the constraint response value, the closer the distribution structure of the candidate persistent graph to the persistent graph to be retrieved is in the direction of the dominant constraint.

[0043] Based on the constraint response values ​​of each candidate persistent graph, hierarchical clustering is performed on the entire candidate persistent graph set. Hierarchical clustering uses constraint response values ​​as a one-dimensional clustering criterion and employs a bottom-up agglomeration strategy: initially, each candidate persistent graph forms a separate cluster, and then adjacent clusters are gradually merged based on the differences in constraint response values ​​between clusters until a preset stopping condition is met (such as the distance between clusters exceeding a preset threshold or the total number of clusters reaching a target number). After clustering, multiple candidate graph clusters are formed, with the candidate persistent graphs within each cluster exhibiting high similarity in constraint response values.

[0044] When identifying the candidate graph cluster to which the persistent graph to be retrieved belongs, the constraint response value of the persistent graph to be retrieved (defined as its structural difference metric with itself, i.e., zero) is calculated within the constraint response value range of each candidate graph cluster. Specifically, the candidate graph cluster with the smallest constraint response value, i.e., the cluster whose distribution structure is most similar to that of the persistent graph to be retrieved, is identified as the candidate graph cluster to which the persistent graph to be retrieved belongs. All candidate persistent graphs in this candidate graph cluster are extracted to form a candidate matching graph set, which is used for subsequent topological deformation path calculation. By using hierarchical clustering to filter the candidate matching graph set, it is possible to effectively eliminate irrelevant candidate graphs with large constraint response values ​​while retaining highly similar candidate objects, reducing the scale of subsequent calculations and improving overall retrieval efficiency.

[0045] Transforming each candidate matching graph in the candidate matching graph set to the persistent graph to be retrieved through insertion, deletion, and move operations, and recording the transformation state to form a topological deformation path includes: The coordinate points of the candidate matching graph are projected onto the dominant constraint direction to obtain constraint projection coordinates, and the coordinate points of the persistent graph to be retrieved are projected onto the dominant constraint direction to obtain target projection coordinates. Based on the difference between the constraint projection coordinates and the target projection coordinates, points to be deleted, points to be inserted, and points to be moved are identified. The execution priority of insertion, deletion and movement operations is determined according to the propagation strength of network nodes in the constraint propagation network. The operations are executed in sequence according to the execution priority, and the operation type and coordinate position changes are recorded to form the transformation state. The transformed states are associated and organized according to the propagation path of the constraint propagation network to form a topological deformation path.

[0046] After filtering the candidate matching graph set, each candidate matching graph needs to be transformed into the persistent graph to be retrieved through a series of basic operations. During the transformation process, all operation states are recorded, ultimately forming a topological deformation path. The core of this process lies in utilizing the obtained dominant constraint directions. As a unified projection benchmark, the coordinate points of two persistent maps are mapped to the same projection space, thereby identifying the structural differences between them in low-dimensional projected coordinates and determining which types of operations need to be performed.

[0047] For each coordinate point in the candidate matching graph, correlate its two-dimensional coordinates with the dominant constraint direction. Perform an inner product operation to obtain the scalar projection value of the point along the dominant constraint direction. Arrange the projection values ​​of all candidate matching map coordinate points in order to form the constraint projection coordinate sequence. Similarly, perform the same inner product projection operation on each coordinate point in the persistent map to obtain the target projection coordinate sequence. Dominant constraint direction From the constraint propagation matrix The eigenvalue decomposition extracts the most discriminative structural direction in the entire cross-scale constraint propagation network. Therefore, the projection difference in this direction can reflect the essential difference in topology between the two persistent graphs to the greatest extent.

[0048] Let the candidate matching graph be the first... The constraint projection coordinates of each coordinate point in the dominant constraint direction are: The persistent map to be retrieved The target projection coordinates of each coordinate point in the dominant constraint direction are: Through the analysis of Sequence and Sequences are aligned in an ordered manner to identify three types of differences: if a certain exist No sequence was found that met the projection distance threshold. If a corresponding point is found within the target map, that point is marked as a point to be deleted, meaning a topological feature that exists in the candidate map but not in the target map; if a certain exist No sequence can satisfy If a corresponding point is found within the target map, that point is marked as the insertion point, meaning that a topological feature exists in the target map but is not yet included in the candidate map; if a certain With a certain The projection distance is at the threshold If the coordinates are within the specified range but there is a significant deviation, the corresponding coordinate point pair is marked as a point to be moved. This means that the topological feature exists in both maps but its coordinate positions are inconsistent, requiring alignment through a move operation. Projection distance threshold The setting is related to the overall scale range of the persistent map, and is usually taken as a certain proportion of the range of all target projection coordinates to ensure that the recognition results are adaptive to scale changes.

[0049] After identifying the points to be deleted, inserted, and moved, it is necessary to determine the execution priority of these three types of operations. The execution priority is determined based on the propagation strength of each network node in the constraint propagation network. The propagation strength of a network node reflects the amount of information it carries during cross-scale constraint propagation. Nodes with higher propagation strength are more representative of their corresponding scale level in the overall topology, and operations performed at that scale level should be prioritized to ensure that subsequent operations are performed on a stable foundation. Specifically, the propagation strength of each node in the constraint propagation network is calculated. , Defined as the connection weight between this node and all its neighboring nodes. The weighted summation of the nodes The out-degree weighted strength of a node is obtained by summing the weights of all outgoing edges, and then by averaging the in-degree weighted strength. .according to All operation points are sorted from largest to smallest, with operations at scales with higher propagation intensity being executed first, and operations at scales with lower propagation intensity being executed later. When multiple operation points belong to the same scale, they are further sorted from largest to smallest according to the absolute value of the deviation between their constrained projected coordinates and the target projected coordinates, with points having larger deviations processed first to eliminate major structural differences as quickly as possible.

[0050] According to the execution priority mentioned above, the corresponding insertion, deletion, or movement operation is performed sequentially for each point to be operated on. When performing a deletion operation, the coordinate point is removed from the candidate matching map, and the original two-dimensional coordinates of the deleted point are recorded. The point's scale level number is also included. During the insertion operation, a new coordinate point is added to the candidate matching map, with its coordinates taken from the corresponding target point coordinates in the persistent map to be retrieved. The target two-dimensional coordinates of the inserted point are also recorded. and its corresponding scale level number; when performing a move operation, the coordinates of the point to be moved in the candidate matching map are moved from its original position. Adjust to target position And record the movement vector The operation type identifier (delete, insert, or move), the coordinates of the operation point, the scale level number, and the operation execution sequence number are all encapsulated into a transformation state record unit and appended sequentially to the transformation state sequence.

[0051] The transformation state sequence records the complete transformation process from the candidate matching graph to the persistent graph to be retrieved, but the relationships between the transformation states have not yet been organized. To form a structurally meaningful topological deformation path, the transformation state sequence needs to be organized according to the propagation path of the constraint propagation network. The constraint propagation network contains directed edges across scale levels, each edge connecting feature point clusters at adjacent scale levels. The direction of the edges points from lower to higher scale levels, and the edge weights are the connection weights. Operation records belonging to the same propagation path in the transformed state sequence are concatenated in the directed order of the propagation path to form a sub-deformation path. Sub-deformation paths on different propagation paths are independent of each other and together constitute a complete topological deformation path structure. If two transformed states belong to different propagation paths but share the same scale level node, then the shared node is used as the convergence point in the topological deformation path, and the two sub-paths are merged and marked at that node to reflect the cross-path structural constraint relationship.

[0052] The organization of the topological deformation path ensures that the subsequent calculation of cumulative deformation cost can fully utilize scale-level information and propagation path structure. This allows the cost calculation to reflect not only the number of operations but also the positional weight of the operations within the topological structure, thereby giving the final matching retrieval results stronger structural discrimination capabilities. For each candidate matching graph in the candidate matching graph set, the entire process of projection recognition, priority sorting, operation execution recording, and path association organization described above is executed independently. Ultimately, a corresponding topological deformation path is generated for each candidate matching graph for subsequent cost calculation.

[0053] The costs of insertion, deletion, and movement operations in the topological deformation path are calculated. These costs are then weighted by scale sensitivity according to the scale level at which the operations occur, and the cumulative deformation cost is obtained by summing the results. The matching retrieval results are output based on the cumulative deformation cost, including: Extract the coordinate position changes corresponding to insertion, deletion and movement operations in the topology deformation path, project the coordinate position changes onto the dominant constraint direction to obtain the constraint direction component, and calculate the operation cost based on the eigenvalue perturbation caused by the constraint direction component in the constraint propagation matrix. The scale level of the coordinate points corresponding to the insertion, deletion and move operations in the persistent graph to be retrieved is identified, the overlap of the scale level is obtained as the scale sensitivity weight, and the operation cost is weighted by the scale sensitivity weight to obtain the weighted operation cost. The weighted operation cost is accumulated according to the propagation path of the constraint propagation network to obtain the path cumulative cost. The topological connectivity compensation amount is calculated based on the path cumulative cost and the connectivity structure of the constraint propagation network, and then superimposed to obtain the cumulative deformation cost. The candidate matching map set is sorted according to the cumulative deformation cost, and the matching retrieval results are output.

[0054] After filtering the candidate matching graph set and recording the topology deformation paths, it is necessary to accurately quantify the operational costs involved in each topology deformation path. For each insertion, deletion, or movement operation in the topology deformation path, the corresponding coordinate position change is extracted. Specifically, the coordinate position change for the insertion operation is the absolute coordinate vector of the target point in the two-dimensional space of the persistent graph; the coordinate position change for the deletion operation is the absolute coordinate vector of the deleted point; and the coordinate position change for the movement operation is the displacement vector of the point before and after the movement. These coordinate position changes are then projected onto the dominant constraint directions. This yields the constraint direction components of each operation in the dominant constraint direction. ,in , This is the vector of coordinate position changes. Constraint direction components. This reflects the intensity of the disturbance in the direction most sensitive to structural constraints and is the core input for calculating the cost of subsequent operations.

[0055] constrain the direction components Substitute the constraint propagation matrix Using an eigenvalue perturbation analysis framework, the perturbation caused by this operation to the principal eigenvalues ​​of the constraint propagation matrix is ​​calculated, and this perturbation is taken as the operation cost. The calculation of eigenvalue perturbation is based on matrix perturbation theory: when a perturbation matrix caused by a change in coordinate position is applied to the constraint propagation matrix... At that time, the change in the principal eigenvalue is approximately equal to the dominant constraint direction vector. The quadratic form of this perturbation matrix, i.e. ,in Constraint direction components The outer product is constructed from this. This mechanism ensures that the calculation of the operation cost is directly related to the propagation characteristics of the topological constraints of the graph structure, rather than relying solely on a simple Euclidean distance metric, thus giving the operation cost a stronger structural semantic expressive power.

[0056] Obtain the original operation cost of each operation. Next, scale-sensitivity weighting needs to be performed based on the scale level of the coordinate points corresponding to the operations within the persistent graph to be retrieved. The scale level of the coordinate points corresponding to each insertion, deletion, or move operation is identified, and the overlap of that scale level in the constraint propagation network is obtained. As a scale-sensitive weight Overlap The overlap at the corresponding scale level can be obtained by directly querying the constraint propagation network, which has already been calculated and stored when the constraint propagation network is constructed. Weighted operation cost It is given by the product of the original operation cost and the scale sensitivity weight, i.e. The introduction of scale-sensitive weights has a clear physical meaning: scale levels with higher overlap mean that the topological features of that level have a stronger propagation correlation between adjacent scales, and the operation applied to the features of that level has a more significant impact on the overall topological structure, thus giving it a higher weight; conversely, scale levels with lower overlap have smaller operation weights, and their cost contribution is relatively suppressed.

[0057] Weighted operation cost of completing each operation After calculation, the weighted operation costs are accumulated along the propagation path of the constraint propagation network to obtain the cumulative path cost. The specific process of path accumulation is as follows: sum the costs of all weighted operations arranged in the order of operation in the topology deformation path, i.e. ,in For the first The weighted cost of each step is summed and iterated through all steps in the topology deformation path. The propagation path is selected based on the edge connections between nodes in the constrained propagation network, ensuring that the path accumulation process proceeds along the actual propagation structure of the network, rather than a simple linear superposition, so that the path accumulation cost can reflect the propagation characteristics of topology deformation in the network structure.

[0058] Path cumulative cost Based on this, a topological connectivity compensation quantity is further introduced. This is to correct the systematic bias caused by differences in the connectivity structure of the constraint propagation network. The calculation of the topological connectivity compensation is based on the connectivity structure of the constraint propagation network: counting the number of connected components in the constraint propagation network corresponding to the candidate matching graph. Number of connected components in the constraint propagation network corresponding to the persistent graph to be retrieved The difference is calculated by multiplying the absolute value of the difference by the connectivity penalty coefficient. The topological connectivity compensation quantity is obtained, i.e. Connectivity penalty coefficient This is a preset positive real hyperparameter used to control the impact of connectivity differences on the final cumulative deformation cost. The final cumulative deformation cost is obtained by superimposing the path cumulative cost with the topological connectivity compensation. ,Right now The introduction of topological connectivity compensation can effectively penalize candidate matching graphs that, although their local operation costs are low, have an overall connectivity structure that differs significantly from the graph to be retrieved, thereby improving the global structural consistency of the matching retrieval results.

[0059] Based on cumulative deformation cost The candidate matching graph set is sorted in ascending order. Candidate matching graphs with lower cumulative deformation costs are more similar to the topological structure of the graphic object being retrieved and thus rank higher. After sorting, the final matching retrieval results are selected from the sorted results according to a preset output quantity threshold or cumulative deformation cost truncation threshold and output. The output matching retrieval results include the identification information of each candidate graphic object and its corresponding cumulative deformation cost, which can be further processed or displayed by the application layer according to actual needs. The entire cumulative deformation cost calculation framework organically integrates the local cost at the operation level, the structural sensitivity at the scale level, and the global connectivity at the network level, ensuring that the matching retrieval results accurately reflect the degree of topological similarity between graphic objects at multiple levels.

[0060] The computational cost based on the eigenvalue perturbation caused by the constraint direction component in the constraint propagation matrix includes: Construct a matrix perturbation operator corresponding to the constraint direction component, and superimpose the matrix perturbation operator onto the constraint propagation matrix to obtain the perturbed constraint propagation matrix; The constraint propagation matrix is ​​decomposed into eigenvalues ​​to obtain the original eigenvalue sequence. The perturbed constraint propagation matrix is ​​decomposed into eigenvalues ​​to obtain the perturbed eigenvalue sequence. The difference between the eigenvalues ​​at corresponding positions in the perturbed eigenvalue sequence and the original eigenvalue sequence is calculated to obtain the eigenvalue perturbation quantity sequence. The perturbation main frequency component is extracted by spectral analysis of the eigenvalue perturbation quantity sequence. The perturbation propagation field distribution is obtained by convolving the perturbation dominant frequency component with the propagation intensity of the network nodes in the constrained propagation network. The perturbation propagation field distribution is then integrated globally in the network topology space of the constrained propagation network to obtain a global perturbation metric value as the operation cost.

[0061] Obtaining the constraint direction components of a single-step operation Next, it is necessary to further quantify the impact of this operation on the entire constraint propagation network structure to obtain a more physically meaningful operation cost. Directly using coordinate distance as the cost ignores the chain response caused by the operation in the global network structure. Therefore, an operation cost calculation mechanism based on eigenvalue perturbation is introduced, and the operation cost is characterized by analyzing the spectral structure change of the constraint propagation matrix before and after the perturbation.

[0062] Constructing the matrix perturbation operator is the starting point of this process. Based on the constraint direction components... Construct a propagation matrix that is consistent with the constraint propagation matrix. Same-dimensional matrix perturbation operator . Specifically, The construction depends on the positional relationship of the node pairs affected by the operation in the constraint propagation network: if an operation affects a node... With nodes The connection between them, In the corresponding position and The element at position has a value of The remaining elements are zero, thus maintaining the symmetry of the perturbation operator and the constraint propagation matrix. The symmetric structure remains consistent. The perturbation operator... Superimposed on the original constraint propagation matrix The constrained propagation matrix after perturbation is obtained. ,Right now The perturbated matrix retains the overall connection structure of the original network while introducing structural changes caused by the operation locally, providing input for subsequent eigenvalue analysis.

[0063] propagation matrix of the original constraint Perform eigenvalue decomposition to obtain the original eigenvalue sequence. ,in Given a matrix dimension, the eigenvalues ​​are arranged in descending order. Similarly, the constraint propagation matrix after perturbation... Eigenvalue decomposition is performed to obtain the perturbation eigenvalue sequence. Calculate the difference between corresponding positions in the two eigenvalue sequences to obtain the eigenvalue perturbation sequence. ,in , The position index of the feature value sequence, with a value range of 1. to The eigenvalue perturbation sequence reflects the strength of the influence of operations on the network structure at different frequency components. Low-order eigenvalues ​​correspond to the global structure of the network, while high-order eigenvalues ​​correspond to the local detailed structure. Perturbations at different locations have different topological semantics.

[0064] Eigenvalue perturbation sequence Spectral analysis is performed to extract the dominant frequency component of the perturbation. The eigenvalue perturbation sequence is treated as a one-dimensional discrete signal, and a discrete Fourier transform is applied to obtain its frequency domain representation. ,in This is a frequency index. In the frequency domain, select several frequency components with the largest amplitudes as the dominant perturbation frequency components, and denote the amplitude of the dominant frequency component as... The corresponding frequency is The dominant frequency component of the perturbation captures the most significant periodic variation pattern caused by the operation in the eigenvalue sequence, and can distinguish the emphasis of the operation's impact on the global and local structure of the network: if the dominant frequency component is concentrated in the low-frequency region, it indicates that the operation has a greater impact on the global topology of the network; if the dominant frequency component is concentrated in the high-frequency region, it indicates that the operation mainly affects the local detailed structure.

[0065] After obtaining the dominant frequency component of the perturbation, it is convolved with the propagation intensity of each network node in the constrained propagation network to obtain the perturbation propagation field distribution. (Network nodes) Overall transmission intensity This value, calculated during the constrained propagation network construction phase, reflects the node's propagation influence within the network. The amplitude of the perturbation dominant frequency component... Propagation intensity at each node Perform convolution to obtain the local field strength values ​​of the perturbation propagation field at each node. The calculation method is as follows ,in This represents the convolution operation. The perturbation propagation field distribution... This describes the perturbation intensity experienced by each node in a constrained propagation network under dominant frequency perturbation excitation. The spatial distribution of this perturbation intensity reflects the propagation and diffusion patterns of the operation's influence in the network topology. Nodes with higher propagation intensity will generate larger local field strengths in the perturbation propagation field, indicating that the operation has a stronger structural impact on the topological regions where these nodes reside.

[0066] The global perturbation metric is obtained by integrating the perturbation propagation field across the network topology space of the constrained propagation network. This metric is then used as the operation cost for the current operation. The global integral in a discrete network is implemented by summing the local field strength values ​​of all nodes, i.e. Global integration aggregates the local perturbation effects of an operation on each node of the network into a single scalar, measuring the overall extent to which the operation disrupts the constraint propagation network structure. When the eigenvalue perturbation caused by the operation is large and the amplitude of the dominant frequency component is high, the overall field strength of the perturbation propagation field distribution is strong, the global integration value is large, and the corresponding operation cost is high; conversely, if the operation only causes a small change in eigenvalues, the global perturbation metric is small, and the operation cost is low.

[0067] This eigenvalue perturbation-based operation cost calculation method has significant advantages over directly using coordinate distance. Spectral analysis of the eigenvalue perturbation sequence can distinguish the impact of operations on different structural levels of the network, avoiding the problem of conflating global structural perturbations with local noise perturbations. The convolution operation of the perturbation propagation field incorporates node propagation intensity into the cost calculation, resulting in higher cost penalties for operations occurring near critical nodes with high propagation intensity, reflecting the moderating effect of network topology on operation costs. Global integration ensures that operation costs comprehensively cover changes in the entire network structure, rather than focusing only on changes in local nodes. This global perturbation metric is then used as... Substitute this into the subsequent scale sensitivity weighting process, and the scale sensitivity weights. Multiplication yields the weighted operation cost. Then follow the operation steps index. Accumulated cost of the path Ultimately, it is related to the topological connectivity compensation amount. The combination results in cumulative deformation costs This is used to output matching search results.

[0068] like Figure 3 As shown, Figure 3This diagram presents a decomposition of the cumulative deformation cost under different constraint directional components. It deeply analyzes the underlying structure of the cumulative deformation cost when the system handles constraint directional components such as translation, rotation, scaling, shearing, and twisting. The bottom cylinder represents the weighted operation cost, and the top cylinder maps the topological connectivity compensation. For basic translational components, both costs are extremely low; however, when encountering highly destructive nonlinear twisting components, the eigenvalue sequence of the constraint propagation matrix undergoes severe distortion, causing both costs to surge. Existing traditional iterative nearest-point matching techniques rely solely on surface spatial distance, and when dealing with complex twists, the lack of a topological tearing penalty mechanism often results in falsely low costs. This invention, by fusing eigenvalue integration and topological compensation, completely eliminates the blind spots of traditional geometric matching, endowing the model with superior physical rationality and deformation resistance.

[0069] A second aspect of this invention provides an intelligent matching and retrieval system based on graph structure topological constraints, comprising: The object acquisition unit is used to acquire the graphic object to be retrieved and a set of candidate graphic objects. The topology graph unit is used to extract the topological features of the graphic object to be retrieved and the candidate graphic object set, calculate the occurrence threshold and disappearance threshold of the topological features at multiple scales, and construct the persistent graph to be retrieved and the candidate persistent graph set. The constraint network unit is used to identify feature point clusters at different scale levels in the persistent graph to be retrieved, calculate the overlap of feature point clusters at adjacent scale levels, and use the overlap as connection weights to construct a constraint propagation network across scale levels. The matching and filtering unit is used to extract the constraint propagation matrix from the constraint propagation network, perform eigenvalue decomposition on the constraint propagation matrix to obtain the dominant constraint direction, project the dominant constraint direction onto the candidate persistent graph set to obtain the constraint response value, and filter out the candidate matching graph set based on the constraint response value. The deformation path unit is used to transform each candidate matching graph in the candidate matching graph set to the persistent graph to be retrieved through insertion, deletion and move operations, and record the transformation state to form a topological deformation path; The retrieval output unit is used to calculate the cost of insertion, deletion and movement operations in the topological deformation path, and accumulates the cumulative deformation cost after performing scale sensitivity weighting according to the scale level where the operation is located, and outputs the matching retrieval result based on the cumulative deformation cost.

[0070] A third aspect of the present invention provides an electronic device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0071] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0072] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An intelligent matching and retrieval method based on graph structure topological constraints, characterized in that, include: Retrieve the graphic object to be retrieved and the set of candidate graphic objects; Extract the topological features of the target graph object and the candidate graph object set, calculate the occurrence threshold and disappearance threshold of the topological features at multiple scales, and construct the target persistent graph and the candidate persistent graph set; Identify feature point clusters at different scale levels in the persistent graph to be retrieved, calculate the overlap of feature point clusters at adjacent scale levels, and use the overlap as connection weights to construct a constraint propagation network across scale levels. The constraint propagation matrix is ​​extracted from the constraint propagation network, the dominant constraint direction is obtained by eigenvalue decomposition of the constraint propagation matrix, the dominant constraint direction is projected onto the candidate persistent graph set to obtain the constraint response value, and the candidate matching graph set is selected based on the constraint response value. Each candidate matching graph in the candidate matching graph set is transformed into the persistent graph to be retrieved through insertion, deletion and move operations, and the transformation state is recorded to form a topological deformation path; The costs of insertion, deletion, and movement operations in the topological deformation path are calculated. The cumulative deformation cost is obtained by weighting the operations based on scale sensitivity according to the scale level at which they occur, and the matching retrieval results are output based on the cumulative deformation cost.

2. The method according to claim 1, characterized in that, Extracting the topological features of the target graph object and the candidate graph object set, calculating the occurrence and disappearance thresholds of the topological features at multiple scales, and constructing the target persistent graph and candidate persistent graph set includes: Boundary extraction is performed on the graphic object to be retrieved and the set of candidate graphic objects to obtain a closed contour. Connected components, loop structures and hole structures are identified as topological features within the closed contour. Set an initial filtering scale and a final filtering scale, and generate multiple filtering scale sequences between the initial filtering scale and the final filtering scale with a fixed step size; Each filter scale in the filter scale sequence is applied sequentially to the topological feature for filtering detection. The filter scale corresponding to the first detection of the topological feature is recorded as the occurrence threshold, and the filter scale corresponding to the last detection of the topological feature is recorded as the disappearance threshold. Mark coordinate points in a two-dimensional coordinate system using the occurrence threshold as the x-axis value and the disappearance threshold as the y-axis value. Perform kernel density estimation on the coordinate points to obtain the density distribution field. Use the density distribution field corresponding to the graphic object to be retrieved as the persistent graph to be retrieved. Use the density distribution field corresponding to each candidate graphic object in the candidate graphic object set as the candidate persistent graph set.

3. The method according to claim 1, characterized in that, Identifying feature point clusters at different scale levels in the persistent graph to be retrieved, calculating the overlap between feature point clusters at adjacent scale levels, and using the overlap as connection weights to construct a constraint propagation network across scale levels includes: The ordinate range of the persistent map to be retrieved is divided into multiple scale intervals at equal intervals, and the coordinate points contained in each scale interval constitute a scale level. The average distance between all coordinate points in the persistent map to be retrieved is calculated as the clustering radius. Spatial clustering of coordinate points is performed at each scale level, and coordinate points with a distance less than the clustering radius are grouped into the same cluster to form a feature point cluster. Extract two vertically adjacent scale levels, calculate the projection overlap length of the feature point clusters in the upper scale level and the feature point clusters in the lower scale level in the horizontal coordinate direction, and take the ratio of the projection overlap length to the horizontal coordinate span of the feature point clusters in the upper scale level as the overlap degree of the feature point clusters in the adjacent scale levels. The overlap of the feature point clusters at adjacent scale levels is weighted by an exponential decay function with the difference between the center of the ordinates of the two scale levels as the independent variable, to obtain the connection weight. By using feature point clusters in the upper and lower scale levels as network nodes and connection weights as edge weights connecting network nodes, a constraint propagation network across scale levels is constructed.

4. The method according to claim 1, characterized in that, The constraint propagation matrix is ​​extracted from the constraint propagation network. Eigenvalue decomposition is performed on the constraint propagation matrix to obtain the dominant constraint direction. The dominant constraint direction is projected onto the candidate persistent graph set to obtain constraint response values. The candidate matching graph set is then selected based on the constraint response values, including: Extract all network nodes in the constraint propagation network, sort them by their ordinate values, construct an adjacency matrix, and apply a nonlinear transformation to the adjacency matrix to obtain the constraint propagation matrix; The constraint propagation matrix is ​​decomposed into eigenvalues ​​to extract multiple eigenvectors to construct a multidimensional constraint subspace. The eigenvector with the largest variance contribution rate is selected as the dominant constraint direction in the multidimensional constraint subspace. The coordinates of the persistent graph to be retrieved and the coordinates of each candidate persistent graph in the candidate persistent graph set are projected onto the dominant constraint direction to obtain a projection sequence. The topological morphology analysis of the projection sequence is performed to obtain the distribution pattern features. The structural difference metric between the distribution pattern features of the candidate persistent graph and the distribution pattern features of the persistent graph to be retrieved is calculated as the constraint response value. The candidate persistent graph set is hierarchically clustered according to the constraint response value to form multiple candidate graph clusters. The candidate graph cluster to which the persistent graph to be retrieved belongs is identified, and all candidate persistent graphs in the candidate graph cluster are extracted to form a candidate matching graph set.

5. The method according to claim 1, characterized in that, Transforming each candidate matching graph in the candidate matching graph set to the persistent graph to be retrieved through insertion, deletion, and move operations, and recording the transformation state to form a topological deformation path includes: The coordinate points of the candidate matching graph are projected onto the dominant constraint direction to obtain constraint projection coordinates, and the coordinate points of the persistent graph to be retrieved are projected onto the dominant constraint direction to obtain target projection coordinates. Based on the difference between the constraint projection coordinates and the target projection coordinates, points to be deleted, points to be inserted, and points to be moved are identified. The execution priority of insertion, deletion and movement operations is determined according to the propagation strength of network nodes in the constraint propagation network. The operations are executed in sequence according to the execution priority, and the operation type and coordinate position changes are recorded to form the transformation state. The transformed states are associated and organized according to the propagation path of the constraint propagation network to form a topological deformation path.

6. The method according to claim 1, characterized in that, The costs of insertion, deletion, and movement operations in the topological deformation path are calculated. These costs are then weighted by scale sensitivity according to the scale level at which the operations occur, and the cumulative deformation cost is obtained by summing the results. The matching retrieval results are output based on the cumulative deformation cost, including: Extract the coordinate position changes corresponding to insertion, deletion and movement operations in the topology deformation path, project the coordinate position changes onto the dominant constraint direction to obtain the constraint direction component, and calculate the operation cost based on the eigenvalue perturbation caused by the constraint direction component in the constraint propagation matrix. The scale level of the coordinate points corresponding to the insertion, deletion and move operations in the persistent graph to be retrieved is identified, the overlap of the scale level is obtained as the scale sensitivity weight, and the operation cost is weighted by the scale sensitivity weight to obtain the weighted operation cost. The weighted operation cost is accumulated according to the propagation path of the constraint propagation network to obtain the path cumulative cost. The topological connectivity compensation amount is calculated based on the path cumulative cost and the connectivity structure of the constraint propagation network, and then superimposed to obtain the cumulative deformation cost. The candidate matching map set is sorted according to the cumulative deformation cost, and the matching retrieval results are output.

7. The method according to claim 6, characterized in that, The computational cost based on the eigenvalue perturbation caused by the constraint direction component in the constraint propagation matrix includes: Construct a matrix perturbation operator corresponding to the constraint direction component, and superimpose the matrix perturbation operator onto the constraint propagation matrix to obtain the perturbed constraint propagation matrix; The constraint propagation matrix is ​​decomposed into eigenvalues ​​to obtain the original eigenvalue sequence. The perturbed constraint propagation matrix is ​​decomposed into eigenvalues ​​to obtain the perturbed eigenvalue sequence. The difference between the eigenvalues ​​at corresponding positions in the perturbed eigenvalue sequence and the original eigenvalue sequence is calculated to obtain the eigenvalue perturbation quantity sequence. The perturbation main frequency component is extracted by spectral analysis of the eigenvalue perturbation quantity sequence. The perturbation propagation field distribution is obtained by convolving the perturbation dominant frequency component with the propagation intensity of the network nodes in the constrained propagation network. The perturbation propagation field distribution is then integrated globally in the network topology space of the constrained propagation network to obtain a global perturbation metric value as the operation cost.

8. An intelligent matching and retrieval system based on graph structure topological constraints, used to implement the method as described in any one of claims 1-7, characterized in that, include: The object acquisition unit is used to acquire the graphic object to be retrieved and a set of candidate graphic objects. The topology graph unit is used to extract the topological features of the graphic object to be retrieved and the candidate graphic object set, calculate the occurrence threshold and disappearance threshold of the topological features at multiple scales, and construct the persistent graph to be retrieved and the candidate persistent graph set. The constraint network unit is used to identify feature point clusters at different scale levels in the persistent graph to be retrieved, calculate the overlap of feature point clusters at adjacent scale levels, and use the overlap as connection weights to construct a constraint propagation network across scale levels. The matching and filtering unit is used to extract the constraint propagation matrix from the constraint propagation network, perform eigenvalue decomposition on the constraint propagation matrix to obtain the dominant constraint direction, project the dominant constraint direction onto the candidate persistent graph set to obtain the constraint response value, and filter out the candidate matching graph set based on the constraint response value. The deformation path unit is used to transform each candidate matching graph in the candidate matching graph set to the persistent graph to be retrieved through insertion, deletion and move operations, and record the transformation state to form a topological deformation path. The retrieval output unit is used to calculate the cost of insertion, deletion and movement operations in the topological deformation path, and accumulates the cumulative deformation cost after performing scale sensitivity weighting according to the scale level where the operation is located, and outputs the matching retrieval result based on the cumulative deformation cost.

9. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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