Multi-criteria method for extracting surface traces of jointed rock mass at tunnel face

Abstract

The present invention discloses a multi-criteria extraction method for the surface trace of the jointed rock mass of a tunnel face based on a depth sensor, comprising the following steps: S1: obtaining point cloud data of the surface of the jointed rock mass of the tunnel face; S2: for any point in the point cloud, calculating the average value q of the sum of the normal vector angles between this point and all points in its neighborhood. i ; S3: Calculate the eigenvalues ​​of the covariance matrix of this point with respect to its neighborhood and calculate the flatness coefficient; S4: Based on the mean shift algorithm, preset bandwidth h i , perform iterative operations to obtain the convergence position, and calculate the distance D between this point and the convergence position i With bandwidth h i The ratio D i / h i S5: Calculate the characteristic value of this point, determine whether this point is a trace feature point, and filter out all trace feature points; S6: Use the trace feature points to extract the trace contour line. This solves the problem that traditional joint trace extraction methods are single, low in precision, and too costly.

Description

Technical Field

[0001] The present invention belongs to the field of vision and image processing, and in particular relates to a multi-criteria extraction method for surface traces of jointed rock masses on a tunnel face based on a depth sensor. Background Art

[0002] To collect discontinuities in the jointed rock mass of a tunnel face, traditional measurement methods require manual contact measurement using tools such as a handheld geological compass and a tape measure. This is inefficient, inaccurate, and limits the measurement area. The unstable rock mass and harsh working environment also threaten the lives of surveyors.

[0003] Non-contact measurement methods, such as digital photogrammetry and 3D laser scanning, can efficiently, automatically, safely, and accurately collect information on rock mass discontinuities. However, the effectiveness of digital photogrammetry is significantly affected by the environment; the hardware cost of 3D laser scanning is prohibitively high; and traditional extraction methods using a single criterion often yield relatively simple and limited joint trace features, making them difficult to support rock mass quality assessment and stability analysis.

[0004] Therefore, there is an urgent need for an extraction method that is not affected by the environment and has lower costs, so as to extract surface characteristic traces that are more consistent with the real rock mass and further improve the degree of refinement. Summary of the Invention

[0005] The purpose of the embodiments of the present invention is to provide a multi-criteria method for extracting surface traces of jointed rock mass at a tunnel face, so as to solve the problems that traditional joint trace extraction methods are single, low in refinement and too costly.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is a multi-criteria method for extracting surface traces of jointed rock mass at a tunnel face, comprising the following steps:

[0007] S1: Obtain point cloud data of the jointed rock mass surface of the tunnel face;

[0008] S2: For any point in the point cloud, calculate the average value q of the sum of the normal vector angles between this point and all points in its neighborhood i ;

[0009] S3: Calculate the eigenvalues ​​of the covariance matrix of this point with respect to its neighborhood and calculate the flatness coefficient;

[0010] S4: Based on the mean shift algorithm, the preset bandwidth h i , perform iterative operations to obtain the convergence position, and calculate the distance D between this point and the convergence position i With bandwidth h i The ratio D i / h i ;

[0011] S5: Calculate the characteristic value of this point, determine whether this point is a trace feature point, and filter out all trace feature points;

[0012] S6: Extract the trace contour using the trace feature points.

[0013] Furthermore, the S1 includes:

[0014] S1.1: Use a depth sensor to acquire a depth image, remove floating points from the point cloud, use a neighborhood maximum filter to filter out sudden changes in the depth image, and use a straight-through filter to filter out outlier noise in the depth image.

[0015] S1.2: Use depth sensors to perform point cloud fusion to obtain complete three-dimensional point cloud data of the jointed rock mass at the tunnel face. Each point contains three-dimensional coordinates representing spatial information.

[0016] Furthermore, the S2 includes:

[0017] S2.1: For any point in the point cloud, use the k-value neighborhood search method to find its k-neighboring point set;

[0018] S2.2: Use principal component analysis (PCA) to calculate the normal vectors of all points in the k-neighborhood point set, obtain the angle between this point and the normal vectors of all points in the k-neighborhood point set, obtain the sum of all angles, and calculate the average value q of the sum of angles i .

[0019] Furthermore, the S3 includes:

[0020] S3.1: Using principal component analysis (PCA), calculate the three eigenvalues ​​of the covariance matrix of this point with respect to its k-neighborhood point set, which are a1, a2, and a3 respectively.

[0021] S3.2: Calculate the surface flatness coefficient a i , the calculation formula is:

[0022] a i =a1 / (a1+a2+a3).

[0023] Furthermore, the S4 includes:

[0024] S4.1: Set the maximum number of iterations; use the Gaussian kernel function to assign weights to all other points in the neighborhood of this point, calculate the weighted average position of these neighboring points, move this point to the calculated weighted average position, and repeat the iterations. When the maximum number of iterations is reached, this point reaches the convergence position, and calculate the distance Di from this point to the convergence position.

[0025] S4.2: Calculate distance D i With bandwidth hi The ratio D i / h i ;

[0026] Furthermore, the S5 includes:

[0027] S5.1: Calculate the feature threshold. The calculation formula of the feature threshold W is:

[0028]

[0029] Where N is the data volume of the point cloud in S1, and η is the control coefficient of the number of feature points;

[0030] S5.2: Calculate the quality value w of the point i , the calculation formula is:

[0031] w i =u1 q i +u2 a i +u3D i / h i

[0032] Among them, q i is the average value of the normal vector angle and u1 is the average value control coefficient of the normal vector angle; a i is the surface flatness coefficient, u2 is the surface flatness coefficient control parameter; D i / h i The distance D from this point to the convergence position i With bandwidth h i The ratio of u3 is the distance D from the point to the convergence position. i With bandwidth h i The ratio control parameter; and u1+u2+u3=1;

[0033] S5.3: If w i ≥W, the point is a characteristic point of the trace;

[0034] If w i <W, the point is not a trace feature point;

[0035] S5.4: Repeat S5.3 to filter out all trace feature points in the three-dimensional point cloud data. The total number of trace feature points is n.

[0036] Furthermore, the S6 includes:

[0037] S6.1: Use PCA to determine the starting point, end point, and base plane of the trace feature points;

[0038] S6.1.1: Calculate the centroid coordinates of n trace feature points. That is, calculate the average position of the n trace feature points as the centroid coordinates, and decentralize each point relative to the centroid to obtain a normalized point set.

[0039] S6.1.2: For the normalized point set, construct a covariance matrix and perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues ​​and corresponding eigenvectors;

[0040] S6.1.3: Select the two eigenvectors with the largest eigenvalues ​​as the normal vectors to the basis plane;

[0041] Determine the starting and ending points: Select the centroid coordinates from S6.1.1 as the starting point O, and move along the eigenvector corresponding to the maximum eigenvalue by a distance 10 to 50 times the length of the eigenvector to obtain the ending point B.

[0042] S6.2: Point sorting; including:

[0043] S6.2.1: Construct vector OB from start point O and end point B;

[0044] S6.2.2: For each feature point on the trajectory, calculate the projection of this point on the vector OB, calculate the ratio of the distance between the projection point and the starting point O to the length of the vector OB, and sort the points from largest to smallest according to the ratio;

[0045] S6.2.3: Finally, take point B as the last point in the sequence, obtaining the sequence C to be tested. Each point in the sequence C is a point to be tested.

[0046] S6.3: Determination of contour points and deletion of internal points; including:

[0047] S6.3.1: Calculate the distance between all points to be measured and the base plane and set a threshold value d;

[0048] S6.3.2: If the distance is less than the threshold, delete the point; if the distance is greater than or equal to the threshold d, use the test point P as the dividing point and divide the sequence into two subsequences C1 and C2.

[0049] If the distances between the test point P and points A and B are all greater than or equal to the threshold τ, then take P as the dividing point, put point A, point P, and the points between point A and point P into C1, and put the remaining points into C2; that is, C1 = {A, ...P} and C2 = {...,B}

[0050] Otherwise, put P into C2, that is, C1 = {A, ...} and C2 = {P ..., B};

[0051] S6.3.3: Use the points to be measured in sub-sequences C1 and C2 as input point clouds, and repeat S6.1.1 to S6.3.2 until no more points to be deleted can be selected from the currently processed sequence. Merge the points in the obtained separate sub-sequences to form the final trace of the jointed rock surface.

[0052] The beneficial effects of the present invention are:

[0053] 1. The existing technology uses 3D laser scanners to obtain 3D point cloud data, which is relatively expensive. The method of the present invention uses the depth camera Azure Kinect, which can generate depth maps, color maps, and infrared maps, denoise the depth maps, and then use Azure KinectDK 3D to fuse the point clouds to generate a spatial 3D point cloud set, reducing costs.

[0054] 2. Compared with the existing digital photogrammetry technology, the method of the present invention is not affected by the environment and has higher stability.

[0055] 3. The multi-criteria feature point extraction method proposed in the present invention effectively makes up for the feature points that cannot be identified by traditional single methods. It combines the advantages of multiple extraction methods. For different features, a certain criterion can be dominated by adjusting the control coefficient, which can give full play to the advantages of each method, making the trace extraction more accurate and the degree of refinement further deepened. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0057] Figure 1 It is a framework flow chart of the method of the present invention;

[0058] Figure 2 This is a flow chart of feature point set extraction of the method of the present invention.

[0059] Figure 3 This is a flow chart of trace extraction using 3RDP in the method of the present invention.

[0060] Figure 4 It is the surface trace of the jointed rock mass at the tunnel face extracted using a single criterion of flatness coefficient.

[0061] Figure 5 It is the surface trace of the jointed rock mass of the tunnel face extracted using the method of the present invention. DETAILED DESCRIPTION

[0062] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0063] See also Figure 1 , Figure 2 , Figure 3 The method of the present invention is divided into three parts: acquiring data, extracting feature point sets, and obtaining trace contours. The complete steps are as follows:

[0064] S1: Obtain 3D point cloud data of the jointed rock mass at the tunnel face.

[0065] S1.1: Use Azure Kinect's single-camera multi-frame stitching to acquire depth images, remove floating points from the point cloud, use the neighborhood maximum filtering method to filter out sudden changes in the depth map, and then use a pass filter to filter out outlier noise in the depth map.

[0066] S1.2: Utilize multiple Azure Kinect camera arrays for point cloud fusion to obtain continuous and complete 3D point cloud data of the jointed rock mass at the tunnel face. Each point contains 3D coordinates (x, y, z) representing spatial information.

[0067] S2: Based on the data information of the 3D point cloud and the change of the curvature of the 3D point cloud, calculate the average value q of the sum of the normal vector angles between the two points i .

[0068] S2.1: For any point in the point cloud, use the k-value neighborhood search method to find its k-neighborhood point set; in this embodiment, k is 10 to 30.

[0069] S2.2: Use principal component analysis (PCA) to calculate the normal vectors of all points in the neighborhood of the point, obtain the angle between the normal vector of the current point and each point in the neighborhood, calculate the sum of all the angles, and obtain the average value q of the sum of the normal vector angles i .

[0070] S3: Use the covariance matrix of principal component analysis (PCA) to calculate the three eigenvalues ​​a1, a2, and a3 of each point, calculate the flatness coefficient, and use the surface flatness coefficient a i Characterize the smoothness and local characteristics of the jointed rock surface of the entire tunnel face.

[0071] S3.1: Calculate the three eigenvalues ​​a1, a2, and a3 of the covariance matrix C of each point with respect to its k-neighborhood point set based on PCA;

[0072] S3.2: Calculate the surface flatness coefficient a i , the calculation formula is:

[0073] a i =a1 / (a1+a2+a3)

[0074] S4: Pre-set bandwidth h iThe size of; Based on the mean shift algorithm, set the maximum number of iterations and calculate the distance D between the current point and the convergence position i With bandwidth h i Here, the ratio of the distance between the current point and the convergence position to the bandwidth is used as the judgment feature value.

[0075] S4.1: For each point, assign weights to the neighboring points in the k-neighborhood using the Gaussian kernel function, calculate the weighted average position of these neighboring points, move this point to the calculated weighted average position, and repeat the iterations. When the maximum number of iterations is reached, this point will converge to a stable position, and calculate the distance Di from this point to the stable position.

[0076] S4.2: Calculate the distance D from this point to the convergence position i With bandwidth h i The ratio D i / h i .

[0077] S5: Based on the results of S2, S3, and S4, calculate the characteristic value and feature threshold of this point, and determine whether this point is a trace feature point.

[0078] S5.1: Calculate the feature threshold. The formula for calculating the feature threshold is:

[0079]

[0080] Among them, N is the data volume of the point cloud in S1, and η is the control coefficient of the number of feature points.

[0081] S5.2: Calculate the trait value of this point. The calculation formula is:

[0082] w i =u1 q i +u2 a i +u3D i / h i

[0083] Among them, q i is the average value of the normal vector angle and u1 is the average value control coefficient of the normal vector angle; a i is the surface flatness coefficient, u2 is the surface flatness coefficient control parameter; D i / h i The distance D from this point to the convergence position i With bandwidth h i The ratio of u3 is the distance D from the point to the convergence position. i With bandwidth h i The ratio control parameter is u1+u2+u3=1; generally u1=u2=u3.

[0084] If there are many edge points, sharp points, and corner points in the point cloud, the average value q of the sum of the normal vector angles is i and flatness coefficient a i It can reflect the degree of significant curvature change in the region, that is, the q of the edge points, cusps, and corner points in the region i 、a i Therefore, increasing u1 and u2 can enhance the recognition ability of edge points, sharp points, and corner points in areas where the curvature of the point cloud changes significantly. According to the experimental results, the values ​​of u1 and u2 are controlled within 0.2 to 0.5, which can fully reflect the q i 、a i It affects the recognition of edge points and sharp features while maintaining the balance and stability of the algorithm.

[0085] The ratio Di / hi can be considered a measure of a point's relative proximity to the center of its density region, reflecting the overall structure and distribution of the point cloud. Boundary points within a region are typically far from their corresponding convergence locations, meaning Di is relatively large. A larger Di / hi ratio indicates that the point is more likely to be located in the boundary region. Therefore, increasing u3 can enhance the ability to identify boundary feature points in the point cloud. Experimental results show that a u3 value of around 0.6 enhances the recognition of boundary feature points while maintaining algorithm stability.

[0086] S5.3: If w i ≥W, the point is a characteristic point of the trace;

[0087] If w i <W, the point is not a trace feature point.

[0088] S5.4: Repeat S5.3 to filter out all trace feature points in the three-dimensional point cloud data. The total number of trace feature points is n.

[0089] S6: Use the 3RDP algorithm to perform thinning and sorting operations on the trace feature points to extract clear, complete and accurate trace contour lines.

[0090] S6.1: Use PCA to determine the starting point, end point, and base plane of the trace feature points.

[0091] S6.1.1: Calculate the centroid coordinates of n trace feature points. That is, calculate the average position of the n trace feature points as the centroid coordinates, and decenter each point relative to the centroid to obtain a normalized point set.

[0092] S6.1.2: Construct a covariance matrix for the normalized point set and perform eigenvalue decomposition on the covariance matrix to obtain a series of eigenvalues ​​and their corresponding eigenvectors. The eigenvector corresponding to the largest eigenvalue represents the maximum variance of the data in that direction, which usually reflects the direction of the trace.

[0093] S6.1.3: Select the two eigenvectors with the largest eigenvalues ​​as the normal vectors to the basis plane because they correspond to the directions with the greatest data variation.

[0094] Determine the starting and ending points: Select the centroid coordinates from S6.1.1 as the starting point O. Move the point along the eigenvector corresponding to the maximum eigenvalue by a distance 10 to 50 times the length of the eigenvector to obtain the end point B. Once the starting and ending points are determined, sort the points. The multiple of the eigenvector length to be moved depends on actual needs. For applications requiring accurate identification and measurement, a larger multiple may be required; for general contour extraction and rough analysis, a smaller multiple can be used.

[0095] S6.2: Point sorting. The specific steps are as follows:

[0096] S6.2.1: Construct vector OB from start point O and end point B.

[0097] S6.2.2: For each feature point on the trajectory, calculate the projection of this point on the vector OB, calculate the ratio of the distance between the projection point and the starting point O to the length of the vector OB, and sort the points from largest to smallest according to the ratio.

[0098] S6.2.3: Finally, take point B as the last point in the sequence to obtain the test sequence C. Each point in the test sequence C is a test point.

[0099] S6.3: Determine the contour points and delete the internal points. The specific steps are as follows:

[0100] S6.3.1: Calculate the distances between all points to be measured and the base plane, and set a threshold d as needed. For applications requiring high-precision contours, a smaller distance threshold may be used to exclude possible noise points. For rough contour analysis, a larger threshold may be used.

[0101] S6.3.2: If the distance is less than the threshold, delete the point; if the distance is greater than or equal to the threshold d, use the test point P as the dividing point and divide the sequence into two subsequences C1 and C2.

[0102] If the distances between the test point P and points A and B are all greater than or equal to the threshold τ, then take P as the dividing point, put point A, point P, and the points between point A and point P into C1, and put the remaining points into C2; that is, C1 = {A, ... P} and C2 = { ..., B},

[0103] Otherwise, put P into C2, that is, C1 = {A, ...} and C2 = {P ..., B}.

[0104] S6.3.3: Use the points to be measured in sub-sequences C1 and C2 as input point clouds respectively, and repeat S6.1.1 to S6.3.2 until no more points to be deleted can be selected from the currently processed array. The multiple individual sub-sequences obtained are merged to form the final trace, forming the final trace of the jointed rock mass surface.

[0105] Figure 4 It is the surface trace of the jointed rock mass of the tunnel face extracted using the existing single criterion method. Figure 5 It is the surface trace of the jointed rock mass of the tunnel face extracted using the method of the present invention.

[0106] It can be seen that Figure 4 The extracted traces are fuzzy and many interference points appear; at the same time, non-trace areas are also identified as trace feature points, indicating that the features extracted using a single criterion are distorted.

[0107] Figure 5 Using the multi-criteria extraction method, the extracted trace feature points are clearer, more complete and continuous than those in the existing technology, and a complete trace trajectory is formed by straight line fitting.

[0108] The invention points of the present invention are:

[0109] 1. The method of the present invention uses the depth camera Azure Kinect to generate depth maps, color maps and infrared images, denoises the depth map, and then performs point cloud fusion through Azure KinectDK 3D to generate a spatial three-dimensional point cloud set.

[0110] 2. The multi-criteria feature point extraction method proposed by the present invention is based on the average value q of the sum of the normal vector angles i and flatness coefficient a i Extract edge points, cusps, and corner points from the point cloud. Extract boundary points from the point cloud based on Di / hi, effectively removing interference points. For different features, the control coefficient can be adjusted to make a certain criterion dominant, leveraging the strengths of each method.

[0111] Each embodiment in this specification is described in a related manner. Similar parts between the various embodiments can be referred to in conjunction with each other. Each embodiment focuses on the differences between the other embodiments. In particular, the system embodiment is generally similar to the method embodiment, so the description is relatively simple. For related parts, refer to the description of the method embodiment.

[0112] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A multi-criteria method for extracting surface traces of jointed rock mass at a tunnel face, characterized in that: The following steps are involved: S1: Obtain point cloud data of the jointed rock mass surface of the tunnel face; S2: For any point in the point cloud, calculate the average value q of the sum of the normal vector angles between this point and all points in its neighborhood i ; S3: Calculate the eigenvalues ​​of the covariance matrix of this point with respect to its neighborhood and calculate the flatness coefficient; The S3 includes: S3.1: Using principal component analysis (PCA), calculate the three eigenvalues ​​of the covariance matrix of this point with respect to its k-neighborhood point set, which are a1, a2, and a3 respectively. S3.2: Calculate the surface flatness coefficient a i , the calculation formula is: <h2 style=";text-align:left;direction:ltr">a<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> (a1 / (a1+a2+a3)) S4: Based on the mean shift algorithm, the preset bandwidth h i , perform iterative operations to obtain the convergence position, and calculate the distance D between this point and the convergence position i With bandwidth h i The ratio D i / h i ; S5: Calculate the characteristic value of this point, determine whether this point is a trace feature point, and filter out all trace feature points; The S5 includes: S5.1: Calculate the feature threshold. The calculation formula of the feature threshold W is: Where N is the data volume of the point cloud in S1, and η is the control coefficient of the number of feature points; S5.2: Calculate the quality value w of the point i , the calculation formula is: w i =u1 q i +u2 a i +u3D i / h i Among them, q i is the average value of the normal vector angle and u1 is the average value control coefficient of the normal vector angle; a i is the surface flatness coefficient, u2 is the surface flatness coefficient control parameter; D i / h i The distance D from this point to the convergence position i With bandwidth h i The ratio of u3 is the distance D from the point to the convergence position. i With bandwidth h i The ratio control parameter; and u1+u2+u3=1; S5.3: If w i ≥W, the point is a characteristic point of the trace; If w i <W, the point is not a trace feature point; S5.4: Repeat S5.3 to filter out all trace feature points in the 3D point cloud data. The total number of trace feature points is n. S6: Extract the trace contour using the trace feature points.

2. The multi-criteria method for extracting surface traces of jointed rock mass at a tunnel face according to claim 1, characterized in that: Said S1 comprises: S1.1: Use a depth sensor to acquire a depth image, remove floating points from the point cloud, use a neighborhood maximum filter to filter out sudden changes in the depth image, and use a straight-through filter to filter out outlier noise in the depth image. S1.2: Use depth sensors to perform point cloud fusion to obtain complete three-dimensional point cloud data of the jointed rock mass at the tunnel face. Each point contains three-dimensional coordinates representing spatial information.

3. The multi-criteria method for extracting surface traces of jointed rock mass at a tunnel face according to claim 2, characterized in that: The S2 includes: S2.1: For any point in the point cloud, use the k-value neighborhood search method to find its k-neighboring point set; S2.2: Use principal component analysis (PCA) to calculate the normal vectors of all points in the k-neighborhood point set, obtain the angle between this point and the normal vectors of all points in the k-neighborhood point set, obtain the sum of all angles, and calculate the average value q of the sum of angles i .

4. The multi-criteria method for extracting surface traces of jointed rock mass at a tunnel face according to claim 1, characterized in that: The S4 includes: S4.1: Set the maximum number of iterations; use the Gaussian kernel function to assign weights to all other points in the neighborhood of this point, calculate the weighted average position of these neighboring points, move this point to the calculated weighted average position, and repeat the iterations. When the maximum number of iterations is reached, this point reaches the convergence position, and calculate the distance Di from this point to the convergence position. S4.2: Calculate distance D i With bandwidth h i The ratio D i / h i .

5. The multi-criteria method for extracting surface traces of jointed rock mass at a tunnel face according to claim 1, characterized in that: The S6 includes: S6.1: Use PCA to determine the starting point, end point, and base plane of the trace feature points; S6.1.1: Calculate the centroid coordinates of n trace feature points. That is, calculate the average position of the n trace feature points as the centroid coordinates, and decentralize each point relative to the centroid to obtain a normalized point set. S6.1.2: For the normalized point set, construct a covariance matrix and perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues ​​and corresponding eigenvectors; S6.1.3: Select the two eigenvectors with the largest eigenvalues ​​as the normal vectors to the basis plane; Determine the starting and ending points: Select the centroid coordinates from S6.1.1 as the starting point O, and move along the eigenvector corresponding to the maximum eigenvalue by a distance 10 to 50 times the length of the eigenvector to obtain the ending point B. S6.2: Point sorting; including: S6.2.1: Construct vector OB from start point O and end point B; S6.2.2: For each feature point on the trajectory, calculate the projection of this point on the vector OB, calculate the ratio of the distance between the projection point and the starting point O to the length of the vector OB, and sort the points from largest to smallest according to the ratio; S6.2.3: Finally, take point B as the last point in the sequence, obtaining the sequence C to be tested. Each point in the sequence C is a point to be tested. S6.3: Determination of contour points and deletion of internal points; including: S6.3.1: Calculate the distance between all points to be measured and the base plane and set a threshold value d; S6.3.2: If the distance is less than the threshold, delete the point; if the distance is greater than or equal to the threshold d, use the test point P as the dividing point and divide the sequence into two subsequences C1 and C2. If the distances between the test point P and points A and B are all greater than or equal to the threshold τ, then take P as the dividing point, put point A, point P, and the points between point A and point P into C1, and put the remaining points into C2; that is, C1 = {A, ...P} and C2 = {...,B} Otherwise, put P into C2, that is, C1 = {A, ...} and C2 = {P ..., B}; S6.3.3: Use the points to be measured in sub-sequences C1 and C2 as input point clouds, and repeat S6.1.1 to S6.3.2 until no more points to be deleted can be selected from the currently processed sequence. Merge the points in the obtained separate sub-sequences to form the final trace of the jointed rock surface.

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