Mesh point set completion method and system based on anchor point clustering
By using an anchor-point clustering method to process the coordinate point data collected by sensors, the problems of missing data and outlier interference were solved, and a fixed number of grid point sets were completed, improving the rationality of grid distribution and completion accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHENGDU ONE CHIP BIOTECHNOLOGY CO LTD
- Filing Date
- 2025-09-16
- Publication Date
- 2026-07-21
AI Technical Summary
Existing clustering algorithms suffer from problems such as missing data, outlier interference, abnormal inter-class spacing, and difficulty in meeting fixed quantity requirements when processing coordinate point data collected by sensors, resulting in unreasonable grid distribution.
An anchor-point clustering method is adopted. The DBSCAN algorithm is used for initial grouping, anchor-point clusters are selected, virtual clusters are generated, and missing points are dynamically filled in by combining cross-direction distance verification and radius information to ensure the rationality of the number and distribution of clusters.
It achieves a robust, controllable clustering number, and high completion accuracy grid point set, which is suitable for scenarios such as sensor array calibration and image feature point repair.
Smart Images
Figure CN121167340B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of data processing and cluster analysis technology, and in particular to a grid point set completion method and system based on anchor point clustering. Background Technology
[0002] In fields such as industrial inspection and image recognition, it is often necessary to process coordinate point data (including radius information) collected by sensors or inspection equipment. This data often presents the following problems:
[0003] (1) Data missing: Some theoretical grid points were not detected, resulting in an incomplete point set.
[0004] (2) Outlier interference: There are outliers that exceed the reasonable range, which affect the accuracy of clustering.
[0005] (3) Abnormal inter-class spacing: Some points are too close (less than normal inter-class spacing) or too far apart (more than normal inter-class spacing), which disrupts the grid distribution pattern.
[0006] (4) Fixed clustering quantity requirement: In practical applications, it is often required that the grid point set be distributed in a fixed quantity (n×n). Traditional clustering algorithms have difficulty ensuring the quantity while taking into account the reasonableness of the distribution.
[0007] While existing clustering algorithms (such as K-Means and DBSCAN) can achieve basic clustering, they have limitations in handling the aforementioned problems: K-Means is sensitive to initial values, struggles to handle outliers, and cannot dynamically complete missing clusters; while DBSCAN (Density-Based Spatial Clustering of Applications with Noise) can identify outliers, it struggles to balance cluster completeness and accuracy in scenarios with a fixed number of clusters. Furthermore, existing completion methods often rely on linear interpolation, neglecting the radius information of the point set and the distance constraints in the intersection direction, resulting in limited completion accuracy.
[0008] Therefore, there is an urgent need for a point set completion method and system that can take into account anomaly handling, fixed number of clusters, and reasonable grid distribution. Summary of the Invention
[0009] The technical problem this invention aims to solve is to design a grid point set completion method and system based on anchor point clustering, for processing coordinate point sets containing radius information (in the format of...). ), output a fixed number ( The complete grid point set is suitable for scenarios that require a complete grid point set, such as sensor array calibration, image feature point repair, and point array charge distribution analysis, thereby solving existing technical problems.
[0010] To address the aforementioned technical problems, this invention provides a grid point set completion method based on anchor point clustering, specifically including the following steps:
[0011] Step S1: Obtain a set of coordinate points containing radius information, remove invalid points whose coordinates are outside the valid range, and perform feature separation.
[0012] Step S2: Use DBSCAN to cluster the X and Y coordinates respectively, obtain the clustering feature parameters of each coordinate axis, and realize the initial grouping of the point set.
[0013] Step S3: Based on the screening threshold, perform anchor point clustering screening and classification for X-axis clustering and Y-axis clustering respectively.
[0014] Step S4: Generate the complete cluster set to obtain the complete cluster along the X-axis. Complete clustering along the Y-axis Specifically, it includes the following steps:
[0015] Step S41: Based on the anchor cluster, supplement the non-anchor clusters in descending order of size to form a temporary cluster set.
[0016] Step S42: When the number of temporary clusters is less than the expected grid dimension At that time, virtual clusters are generated and populated.
[0017] Step S5: Clean up the non-anchor clusters that were not included in the complete cluster to obtain the optimized final cluster sets for the X and Y axes.
[0018] Step S6: Filter out points that simultaneously satisfy the clustering constraints of the X-axis and Y-axis to obtain the purified point set.
[0019] Step S7: Construct a grid based on complete clustering and locate missing points to obtain the final grid point set.
[0020] Furthermore, in this invention, step S1 specifically includes the following steps:
[0021] Step S11: Obtain the coordinates of each point in the point set. .
[0022] Step S12: Remove invalid points whose coordinates are outside the valid range, and retain the set of valid points. , effective range As the preset coordinate space boundary, The maximum values of the horizontal and vertical axes of the two-dimensional plane containing the point set.
[0023] Step S13: Extract the X coordinate sets respectively Y-coordinate set and radius set .
[0024] Furthermore, in step S2 of this invention, the X-coordinate clustering specifically includes: inputting an X-coordinate array. Set the neighborhood radius eps based on the radius information of the point set, and set the minimum number of samples. The DBSCAN algorithm is used to group X-coordinates that are spatially close into the same cluster, and cluster labels are output. Clustering for each X-axis Calculate the point set, its size, extrema, and center;
[0025] Y-axis clustering uses the same method as X-axis clustering, yielding a Y-axis cluster set. and the corresponding feature parameters.
[0026] Furthermore, in step S3 of this invention, the clustering and classification rules are as follows:
[0027] Anchor clustering: Clustering where the cluster size is greater than the threshold;
[0028] Non-anchor clustering: Clustering where the cluster size is less than or equal to the threshold.
[0029] X-axis anchor point clustering was obtained respectively. Clustering with non-anchor points Y-axis anchor point clustering Clustering with non-anchor points .
[0030] Furthermore, in step S3 of this invention, the formula for calculating the screening threshold is as follows: ;in, For the expected grid dimensions, This is the floor symbol.
[0031] Furthermore, in this invention, step S42 specifically includes:
[0032] The theoretical spacing is calculated by taking the median value of the points in the same row and column as the theoretical spacing.
[0033] The virtual clustering filling strategy combines gap-first filling with edge supplementation, where:
[0034] The preferred filling of the gaps includes:
[0035] Calculate the gap size of the existing cluster centers and sort them from largest to smallest gap;
[0036] In each gap, virtual clusters are inserted based on the theoretical spacing;
[0037] The gap list is dynamically updated and repeatedly populated until no gaps are available.
[0038] The edge supplement includes:
[0039] Calculate the distances between the existing cluster set and its left and right edges;
[0040] Prioritize supplementing virtual clusters to the edges of larger spatial areas;
[0041] Ensure that the virtual cluster centers do not exceed the effective range. .
[0042] In a further step of this invention, step S5 specifically includes: finding the left and right neighbors of the complete cluster for each remaining cluster, calculating the center distance and vertical distance between the remaining cluster and the neighboring clusters, and performing merging or deletion operations on the remaining clusters based on the numerical relationship between the vertical distance and the center distance.
[0043] Furthermore, in step S6 of this invention, the purification point set ,in:
[0044] X-axis constraint: The X-coordinate of a point belongs to the range of the point set in the final X-axis cluster;
[0045] Y-axis constraint: The Y-coordinate of a point belongs to the range of the point set in the final Y-axis cluster.
[0046] Furthermore, in step S7 of this invention, the specific components include:
[0047] Step S71: Calculate the X-axis boundary and Y-axis boundary, where the X-axis boundary is the midpoint of the extreme values of adjacent X clusters, and the Y-axis boundary is the midpoint of the extreme values of adjacent Y clusters, formed by the X-axis boundary and Y-axis boundary. Each grid cell.
[0048] Step S72: Calculate the grid cell to which each purification point belongs. , For X-axis index, Construct a known grid set using the Y-axis index. .
[0049] Step S73: Calculate the theoretical intersection points of all grid cells, i.e., the cluster center intersection points: The intersection points belonging to unknown grid cells are taken as missing points, and the average value of the cleaned point radius is used as the radius of the missing point to complete the grid point set.
[0050] This invention also provides a grid point set completion system based on anchor point clustering, including...
[0051] Data preprocessing module: Cleans the input set of known points, removes invalid points whose coordinates are out of range, performs feature separation, and extracts the X-coordinate set. Y-coordinate set and radius set This prepares for independent clustering.
[0052] Independent clustering analysis module: The density clustering algorithm is used to cluster the X and Y coordinates respectively, and the X-axis cluster set, Y-axis cluster set and corresponding feature parameters are obtained respectively, realizing the preliminary grouping of the point set;
[0053] Anchor point clustering filtering module: performs clustering and classification based on a filtering threshold, obtaining X-axis anchor point clusters respectively. Clustering with non-anchor points Y-axis anchor point clustering Clustering with non-anchor points ;
[0054] The complete clustering generation module is used to supplement the non-anchor clusters in descending order of size, based on the anchor clusters, to form a temporary cluster set, and to generate virtual clusters until the number of temporary clusters reaches the expected grid dimension. The final quantity was all X-axis complete clustering Complete clustering along the Y-axis .
[0055] The residual clustering optimization module is used to clean up the non-anchor clusters (residual clusters) that were not included in the complete clusters to avoid noise interference, and finally obtain the optimized X-axis final cluster set and Y-axis final cluster set.
[0056] Clean point set determination module: used to filter points that simultaneously satisfy the clustering constraints of the X-axis and Y-axis, remove noise points, and obtain the clean point set.
[0057] Mesh system construction module: used for meshing based on the calculated X-axis and Y-axis boundaries. A grid is constructed from individual grid cells, and a set of known grids is constructed based on the grid cells to which each purification point belongs.
[0058] Missing point inference module: Based on the calculated intersection of the cluster centers of all grid cells, the missing point is the intersection of unknown grid cells, and the radius of the missing point is the average of the radii of the cleaned points.
[0059] Furthermore, in this invention, each module of the anchor point clustering-based grid point set completion system operates according to the aforementioned anchor point clustering-based grid point set completion method.
[0060] Compared with the prior art, the present invention has the following beneficial effects:
[0061] (1) Robustness: It can effectively handle problems such as outliers and abnormal class spacing, and reduce false merging by checking the cross direction distance.
[0062] (2) The number of clusters is controllable: The dynamic completion mechanism ensures that the number of clusters strictly conforms to the target value (n×n) and meets the grid distribution requirements.
[0063] (3) High completion accuracy: missing points are inferred based on the intersection of cluster centers, and the original data features are preserved by combining radius information.
[0064] (4) Wide applicability: Applicable to any scenario that requires grid point set completion, such as sensor arrays, image feature points, and point charge analysis. Attached Figure Description
[0065] The specific embodiments of the present invention will be further explained below with reference to the accompanying drawings.
[0066] Figure 1 This is a flowchart of the grid point set completion method based on anchor point clustering in this invention.
[0067] Figure 2 This is a schematic diagram showing the result of using the grid point set completion method based on anchor point clustering in Example 1.
[0068] Figure 3 This is a system block diagram of the grid point set completion system based on anchor point clustering in this invention. Detailed Implementation
[0069] Example 1
[0070] Combination Figure 1 The grid point set completion method based on anchor point clustering in this embodiment specifically includes the following steps:
[0071] Step S1: Data preprocessing and feature extraction: Obtain a set of coordinate points containing radius information, remove invalid points whose coordinates are outside the valid range, and perform feature separation.
[0072] In this embodiment, step S1 preferably includes the following steps:
[0073] Step S11: Obtain the coordinates of each point in the point set. , The radius is used to characterize the spatial extent of a point.
[0074] Step S12: Data cleaning: Remove invalid points whose coordinates are outside the valid range, and retain the set of valid points. , effective range The coordinate space boundary is preset and can be adjusted according to the actual application scenario (such as image resolution, detection area size, etc.). The maximum values of the horizontal and vertical axes of the two-dimensional plane containing the point set are represented. In this embodiment, S is 512, meaning that the range in this embodiment is limited to... .
[0075] Step S13: Feature Separation: Extract the X coordinate sets separately. Y-coordinate set and radius set This prepares for independent clustering.
[0076] Step S2: Use the density clustering algorithm DBSCAN to cluster the X and Y coordinates respectively, obtain the clustering feature parameters of each coordinate axis, and realize the initial grouping of the point set.
[0077] In this embodiment, preferably, step S2, X-coordinate clustering specifically includes: inputting an X-coordinate array. , shape is The neighborhood radius eps is set based on the radius information of the point set. In this embodiment, the neighborhood radius eps is set to be less than 1.5 times the average radius of the point set, and a minimum number of samples is set. Specifically, in this embodiment, the neighborhood radius eps = 20, and the minimum number of samples is... (Retaining isolated points), the DBSCAN algorithm is used to group spatially close X-coordinates into the same cluster, and the cluster labels are output. Clustering for each X-axis Calculate the point set, size, extrema, and center.
[0078] For each cluster ,calculate:
[0079] Dot set: .
[0080] size: .
[0081] extremum: , .
[0082] center: That is, the coordinates of the cluster center.
[0083] Y-coordinate clustering uses the same method as X-coordinate clustering, specifically including: inputting an array of Y coordinates. , shape is The neighborhood radius eps is set based on the radius information of the point set. In this embodiment, the neighborhood radius eps is set to be less than 1.5 times the average radius of the point set, and a minimum number of samples is set. Specifically, in this embodiment, the neighborhood radius eps = 20, and the minimum number of samples is... (Retaining isolated points), the DBSCAN algorithm is used to group spatially close Y-coordinates into the same cluster, and the cluster labels are output. Clustering for each Y-axis Calculate the point set, size, extrema, and center.
[0084] For each cluster ,calculate:
[0085] Dot set: .
[0086] size: .
[0087] extremum: , .
[0088] center: That is, the coordinates of the cluster center.
[0089] Step S3: Anchor point clustering screening and classification: Based on the screening threshold, anchor point clustering is screened and classified for X-axis clustering and Y-axis clustering respectively. By screening out representative and stable clusters (anchor points), noise interference is reduced.
[0090] In this embodiment, preferably, the clustering classification rule in step S3 is:
[0091] Anchor clustering (statistically stable clustering): clusters where the cluster size is greater than the threshold;
[0092] Non-anchor clustering (which may be noisy or sparse point groups): Clustering with a size ≤ threshold;
[0093] X-axis anchor point clustering was obtained respectively. Clustering with non-anchor points Y-axis anchor point clustering Clustering with non-anchor points .
[0094] In this embodiment, preferably, the formula for calculating the filtering threshold in step S3 is: ;in, For the expected grid dimensions, This is the floor function. For example, when... hour, .
[0095] Step S4: Generate a complete cluster set (including virtual cluster completion) to obtain the complete X-axis cluster. Complete clustering along the Y-axis The quantities are all In this embodiment, to construct a complete clustering system that meets the expected dimensions, the following steps are specifically included:
[0096] Step S41: Based on the anchor point clustering, supplement the non-anchor point clusters in descending order of size (prioritizing the retention of non-anchor points with more points) to form a temporary cluster set.
[0097] Step S42: When the number of temporary clusters is less than the expected grid dimension At that time, virtual clusters are generated and populated.
[0098] In this embodiment, step S42 specifically includes:
[0099] Calculate the theoretical spacing: The median value of each row and column point is taken as the theoretical spacing, i.e.:
[0100] Theoretical spacing calculation in the X direction: Based on the X coordinate spacing of points in the same row (with similar Y coordinates and an error of ±10 pixels), the median value is taken as the theoretical spacing of the X axis (anti-outlier value).
[0101] The theoretical spacing calculation direction of Y-axis: Based on the Y-coordinate spacing of the same column points (with similar X coordinates and an error of ±10 pixels), the median value is taken as the theoretical spacing of the Y-axis.
[0102] In this embodiment, preferably, if the point set is sparse, a default spacing is used. .
[0103] The virtual clustering filling strategy combines gap-first filling with edge supplementation, where:
[0104] The preferred filling of the gaps includes:
[0105] Calculate the gap size of the existing cluster centers and sort them from largest to smallest gap;
[0106] In each gap, a virtual cluster is inserted based on the theoretical spacing. For example, if the gap is 100 pixels and the theoretical spacing is 30 pixels, then two virtual clusters can be inserted.
[0107] The gap list is dynamically updated and repeatedly populated until no gaps are available.
[0108] The edge supplement includes:
[0109] Calculate the distance between the existing cluster set and the boundary (0 and S=512, left and right edges) (left edge space, right edge space);
[0110] Virtual clusters are added to the edges with larger spatial dimensions first; for example, when the left edge has a spatial dimension of 50 pixels and the right edge has a spatial dimension of 80 pixels, virtual clusters are added to the right edge first.
[0111] Ensure that the virtual cluster centers do not exceed the effective range. In this embodiment, the effective range is taken as .
[0112] Step S5: Residual Clustering Optimization: The non-anchor clusters (residual clusters) that were not included in the complete clusters are purified to avoid noise interference, and the optimized X-axis and Y-axis final cluster sets are obtained.
[0113] In this embodiment, step S5 specifically includes: finding the left and right neighbors of the complete cluster for each remaining cluster (neighbor location), calculating the center distance and vertical distance between the remaining cluster and the neighboring clusters, and merging or deleting the remaining clusters based on the numerical relationship between the vertical distance and the center distance.
[0114] In this embodiment, specifically in step S5, the distance calculation method is as follows:
[0115] Center distance: The difference in center coordinates between the remaining cluster and the neighbor cluster.
[0116] Vertical distance: X-axis clustering calculates the difference in Y coordinates (to determine if they belong to the same row), and Y-axis clustering calculates the difference in X coordinates (to determine if they belong to the same column).
[0117] In this embodiment, specifically in step S5, the judgment rule for the merge / delete operation is as follows:
[0118] If the vertical distance is greater than the threshold (30 pixels in this example) and the center distance is less than the minimum cluster spacing (45 pixels in this example), then the cluster is merged into the neighbor cluster.
[0119] Otherwise, it will be classified as a noisy cluster and deleted.
[0120] This outputs the optimized X-axis and Y-axis final cluster sets.
[0121] Step S6: Filter out points that simultaneously satisfy the clustering constraints of the X-axis and Y-axis to obtain the purified point set.
[0122] In this embodiment, preferably, in step S6, the purification point set ,in:
[0123] X-axis constraint: The X-coordinate of a point belongs to the range of the point set in the final X-axis cluster;
[0124] Y-axis constraint: The Y-coordinate of a point belongs to the range of the point set in the final Y-axis cluster.
[0125] Step S7: Construct a grid based on complete clustering and locate missing points to obtain the final grid point set.
[0126] In this embodiment, step S7 specifically includes:
[0127] Step S71: Calculate the X-axis boundary and Y-axis boundary:
[0128] The X-axis boundary is the midpoint of the extreme values of adjacent X clusters, such as clusters. and Then the boundary is 125;
[0129] The Y-axis boundary is the midpoint of the extreme values of adjacent Y clusters;
[0130] Formed by dividing the boundary between the X-axis and the Y-axis Each grid cell.
[0131] Step S72: Calculate the grid cell to which each purification point belongs. , For X-axis index, Construct a known grid set using the Y-axis index. , .
[0132] Step S73: Calculate the theoretical intersection points of all grid cells, i.e., the cluster center intersection points. : The intersection points belonging to unknown grid cells are taken as missing points, and the average value of the cleaned point radius is used as the radius of the missing point to complete the grid point set.
[0133] The result of using the grid point set completion method based on anchor point clustering in this embodiment is as follows: Figure 2 As shown, Figure 2 The green dots represent known points, and outliers may exist. The algorithm finds the boundaries of each cluster along the X or Y axis, resulting in an n x n grid. Theoretically, each grid contains only one valid point. Missing points are filled in using the intersections of the cluster centers, indicated by the orange dots. Not every point in the graph is perfectly aligned with the theoretical rows and columns; some may even deviate significantly. However, manual judgment often identifies these points as belonging to that grid, while simple DBSCAN clustering might classify them as separate clusters. The algorithm in this embodiment can accurately summarize the point sets.
[0134] The anchor-point clustering-based grid completion method in this embodiment employs an anchor-point clustering mechanism, using a point count threshold to select high-confidence clusters as the grid skeleton, thereby improving clustering stability. It uses cross-directional distance verification, introducing cross-directional (X-axis clustering checks the Y-direction, Y-axis clustering checks the X-direction) distance constraints when merging remaining points to prevent the point set from becoming too dense. Dynamic clustering completion is used, combining non-anchor-point clustering screening with virtual cluster generation to ensure the number of clusters is strictly n, balancing completeness and reasonable distribution. Radius-aware missing point generation is employed, with the radius of missing points calculated based on the average radius of known points, preserving the geometric features of the original data.
[0135] Example 2
[0136] Combination Figure 3 The grid point set completion system based on anchor point clustering in this embodiment includes the following modules:
[0137] Data preprocessing module: Cleans the input set of known points, removes invalid points whose coordinates are out of range, performs feature separation, and extracts the X-coordinate set. Y-coordinate set and radius set This prepares for independent clustering.
[0138] Independent clustering analysis module: The density clustering algorithm is used to cluster the X and Y coordinates respectively, and the X-axis cluster set, Y-axis cluster set and corresponding feature parameters are obtained respectively, realizing the preliminary grouping of the point set;
[0139] Anchor point clustering filtering module: performs clustering and classification based on a filtering threshold, obtaining X-axis anchor point clusters respectively. Clustering with non-anchor points Y-axis anchor point clustering Clustering with non-anchor points ;
[0140] The complete clustering generation module is used to supplement the non-anchor clusters in descending order of size, based on the anchor clusters, to form a temporary cluster set, and to generate virtual clusters until the number of temporary clusters reaches the expected grid dimension. The final quantity was all X-axis complete clustering Complete clustering along the Y-axis .
[0141] The residual clustering optimization module is used to clean up the non-anchor clusters (residual clusters) that were not included in the complete clusters to avoid noise interference, and finally obtain the optimized X-axis final cluster set and Y-axis final cluster set.
[0142] Clean point set determination module: used to filter points that simultaneously satisfy the clustering constraints of the X-axis and Y-axis, remove noise points, and obtain the clean point set.
[0143] Mesh system construction module: used for meshing based on the calculated X-axis and Y-axis boundaries. A grid is constructed from individual grid cells, and a set of known grids is constructed based on the grid cells to which each purification point belongs.
[0144] Missing point inference module: Based on the calculated intersection of the cluster centers of all grid cells, the missing point is the intersection of unknown grid cells, and the radius of the missing point is the average of the radii of the cleaned points.
[0145] Preferably, in this embodiment, each module of the system operates according to the grid point set completion method based on anchor point clustering in Embodiment 1.
[0146] Many specific details have been set forth in the foregoing description to provide a thorough understanding of the present invention. However, the above description is merely a preferred embodiment of the present invention, and the present invention can be implemented in many other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed above. Furthermore, any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, using the methods and techniques disclosed above, without departing from the scope of the present invention. Any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, shall still fall within the protection scope of the present invention.
Claims
1. A grid point set completion method based on anchor point clustering, characterized in that: Includes the following steps: Step S1: Obtain the set of coordinate points containing radius information, remove invalid points whose coordinates are outside the valid range, and perform feature separation; Step S2: Use DBSCAN to cluster the X and Y coordinates respectively, obtain the clustering feature parameters of each coordinate axis, and realize the initial grouping of the point set; Step S3: Based on the screening threshold, perform anchor point clustering screening and classification for X-axis clustering and Y-axis clustering respectively; Step S4: Generate the complete cluster set to obtain the complete cluster along the X-axis. Complete clustering along the Y-axis Specifically, it includes the following steps: Step S41: Based on the anchor clustering, supplement the non-anchor clusters in descending order of size to form a temporary cluster set; Step S42: When the number of temporary clusters is less than the expected grid dimension At that time, virtual clusters are generated and populated. Step S5: Clean up the non-anchor clusters that were not included in the complete cluster to obtain the optimized final cluster sets for the X and Y axes; Step S6: Filter out points that simultaneously satisfy the clustering constraints of the X-axis and Y-axis to obtain the purified point set; Step S7: Construct a grid based on complete clustering and locate missing points to obtain the final grid point set.
2. The grid point set completion method based on anchor point clustering according to claim 1, characterized in that: Step S1 specifically includes the following steps: Step S11: Obtain the coordinates of each point in the point set. ; Step S12: Remove invalid points whose coordinates are outside the valid range, and retain the set of valid points. , effective range As the preset coordinate space boundary, The maximum values of the horizontal and vertical axes of the two-dimensional plane containing the point set; Step S13: Extract the X coordinate sets respectively Y-coordinate set and radius set .
3. The grid point set completion method based on anchor point clustering according to claim 1, characterized in that: In step S2, X-coordinate clustering specifically includes: inputting an array of X-coordinates. Set the neighborhood radius eps based on the radius information of the point set, and set the minimum number of samples. The DBSCAN algorithm is used to group X-coordinates that are spatially close into the same cluster, and cluster labels are output. Clustering for each X-axis Calculate the point set, its size, extrema, and center; Y-axis clustering uses the same method as X-axis clustering, yielding a Y-axis cluster set. and the corresponding feature parameters.
4. The grid point set completion method based on anchor point clustering according to claim 1, characterized in that: In step S3, the clustering classification rules are as follows: Anchor clustering: Clustering where the cluster size is greater than the threshold; Non-anchor clustering: Clustering where the cluster size is less than or equal to the threshold. X-axis anchor point clustering was obtained respectively. Clustering with non-anchor points Y-axis anchor point clustering Clustering with non-anchor points .
5. The grid point set completion method based on anchor point clustering according to claim 1, characterized in that: In step S3, the formula for calculating the filtering threshold is: ;in, For the expected grid dimensions, This is the floor symbol.
6. The grid point set completion method based on anchor point clustering according to claim 1, characterized in that: Step S42 specifically includes: The theoretical spacing is calculated by taking the median value of the points in the same row and column as the theoretical spacing. The virtual clustering filling strategy combines gap-first filling with edge supplementation, wherein the gap-first filling includes: Calculate the gap size of the existing cluster centers and sort them from largest to smallest gap; In each gap, virtual clusters are inserted based on the theoretical spacing; Dynamically update the gap list and repeatedly populate it until no gaps are available. The edge supplement includes: Calculate the distances between the existing cluster set and its left and right edges; Prioritize supplementing virtual clusters to the edges of larger spatial areas; Ensure that the virtual cluster centers do not exceed the effective range. .
7. The grid point set completion method based on anchor point clustering according to claim 1, characterized in that: Step S5 specifically includes: finding the left and right neighbors of the complete cluster for each remaining cluster, calculating the center distance and vertical distance between the remaining cluster and the neighboring clusters, and merging or deleting the remaining clusters based on the numerical relationship between the vertical distance and the center distance.
8. The grid point set completion method based on anchor point clustering according to claim 1, characterized in that: In step S6, the set of purification points ,in: X-axis constraint: The X-coordinate of a point belongs to the range of the point set in the final X-axis cluster; Y-axis constraint: The Y-coordinate of a point belongs to the range of the point set in the final Y-axis cluster.
9. The grid point set completion method based on anchor point clustering according to claim 1, characterized in that: Step S7 specifically includes: Step S71: Calculate the X-axis boundary and Y-axis boundary, where the X-axis boundary is the midpoint of the extreme values of adjacent X clusters, and the Y-axis boundary is the midpoint of the extreme values of adjacent Y clusters, formed by the X-axis boundary and Y-axis boundary. One grid cell; Step S72: Calculate the grid cell to which each purification point belongs. , For X-axis index, Construct a known grid set using the Y-axis index. ; Step S73: Calculate the theoretical intersection points of all grid cells, i.e., the cluster center intersection points: The intersection points belonging to unknown grid cells are taken as missing points, and the average value of the cleaned point radius is used as the radius of the missing point to complete the grid point set.
10. A grid point set completion system based on anchor point clustering, characterized in that: include Data preprocessing module: Cleans the input set of known points, removes invalid points whose coordinates are out of range, performs feature separation, and extracts the X-coordinate set. Y-coordinate set and radius set This prepares for independent clustering; Independent clustering analysis module: The density clustering algorithm is used to cluster the X and Y coordinates respectively, and the X-axis cluster set, Y-axis cluster set and corresponding feature parameters are obtained respectively, realizing the preliminary grouping of the point set; Anchor point clustering filtering module: performs clustering and classification based on a filtering threshold, obtaining X-axis anchor point clusters respectively. Clustering with non-anchor points Y-axis anchor point clustering Clustering with non-anchor points ; The complete clustering generation module is used to supplement the non-anchor clusters in descending order of size, based on the anchor clusters, to form a temporary cluster set, and to generate virtual clusters until the number of temporary clusters reaches the expected grid dimension. The final quantity was all X-axis complete clustering Complete clustering along the Y-axis ; The residual clustering optimization module is used to clean up non-anchor clusters that are not included in the complete clusters to avoid noise interference, and finally obtain the optimized final cluster set on the X-axis and the final cluster set on the Y-axis. Clean point set determination module: used to filter points that simultaneously satisfy the clustering constraints of the X-axis and Y-axis, remove noise points, and obtain a clean point set; Mesh system construction module: used for meshing based on the calculated X-axis and Y-axis boundaries. A grid is constructed from individual grid cells, and a set of known grids (known-grids) is constructed based on the grid cells to which each purification point belongs. Missing point inference module: Based on the calculated intersection of the cluster centers of all grid cells, the missing point is the intersection of unknown grid cells, and the radius of the missing point is the average of the radii of the cleaned points.