Point cloud segmentation method and point cloud-based tilt monitoring method

Abstract

This invention relates to a point cloud cutting method and a point cloud-based tilt monitoring method. The point cloud cutting method performs point cloud cutting as follows: In the station-centered spatial coordinate system o-xyz, horizontal cross-sectional slices are made along the z-axis at set height intervals to obtain sliced ​​point cloud data. The range of each cross-sectional slice is , where is the height of the i-th layer of the cross-sectional slice, is the total number of cross-sectional slices, and is the set point cloud slice thickness. The slice thickness is set at intervals of 1% to 5% of the target object height, and at intervals of 1% to 3% of the target object height, or at intervals of 1% to 5% of the target object height. The point cloud slice thickness is set according to the measurement accuracy of the point cloud itself, the average deviation MD of the central axis fitting, or 0.5 to 1 times the standard error of the central axis fitting.

Description

[0001] This invention is a divisional application of the invention patent application filed on August 21, 2025, entitled "Tilting Monitoring Method and Device Based on Point Cloud", with application number 202511177601.4. Technical Field

[0002] This invention relates to the field of tilt monitoring and device technology, and in particular to a tilt monitoring method and device based on point clouds. Background Technology

[0003] Tall industrial relics, such as towering industrial chimneys, are prone to geometric changes due to their large size, long service life, and susceptibility to wind loads. If the tilting of a towering industrial chimney is not monitored and addressed promptly, it can lead to serious structural damage or even collapse. In patent application number 201910948237.5, entitled "A Point Cloud-Based Verticality Detection System for Building Tower Cranes," a point cloud-based system for detecting the verticality of building tower cranes is disclosed. In this patent application, multiple point cloud segments are cut from standard sections of the tower body to obtain the center points of each segment, and the verticality of the tower body is detected based on these center points. However, in cases such as tall chimneys and wind turbine towers, it is sometimes difficult to find structures similar to standard sections, thus requiring new point cloud cutting methods. Summary of the Invention

[0004] The present invention is made in view of the above-mentioned problems, in order to solve one or more defects existing in the prior art, and at least provide an advantageous alternative.

[0005] According to one aspect of the present invention, a point cloud segmentation method is provided, wherein point cloud segmentation is performed as follows: In the station-centric spatial coordinate system o-xyz, horizontal cross-sectional slices are made along the z-axis at set height intervals to obtain sliced ​​point cloud data. The range of each cross-sectional slice is [missing information]. , For the first The height of the cross-sectional slice of the layer, , The total number of cross-sectional slices. The set point cloud slice thickness, where the first... The set of point clouds contained within a slice can be represented by equation (2): (2) In the formula: For the first A collection of point cloud data slices; For the first slice Three-dimensional point cloud data, ; For the first The number of point cloud data points contained in a layer slice; Specifically, the height is set at intervals ranging from 1% to 5% of the target object's height. And use 1% to 3% of the target object's height as the slice thickness, or Set the height in intervals of 1% to 5% of the target object's height. The thickness of the point cloud slice is determined by 0.5 to 1 times the measurement accuracy of the point cloud itself, the mean deviation (MD) of the center axis fitting, or the mean square error (RMSE) of the center axis fitting. .

[0006] According to another aspect of the present invention, a tilt monitoring method based on point clouds is provided, characterized by comprising the following steps: obtaining effective point cloud data of a target object; acquiring multiple slice point cloud data from the effective point cloud data; projecting each slice point cloud data onto a plane to obtain a set of planar projected point cloud data; extracting the shape contour lines of each slice using the set of planar projected point cloud data; calculating the geometric center point coordinates of each slice shape contour line to obtain multiple geometric center point coordinates; determining the unit direction vector of the central axis based on the multiple geometric center point coordinates; and determining the tilt result of the target object based on the unit direction vector of the central axis, wherein point cloud segmentation is performed as follows: In the station-centric spatial coordinate system o-xyz, horizontal cross-sectional slices are made along the z-axis at set height intervals to obtain sliced ​​point cloud data. The range of each cross-sectional slice is [missing information]. , For the first The height of the cross-sectional slice of the layer, , The total number of cross-sectional slices. The set point cloud slice thickness, where the first... The set of point clouds contained within a slice can be represented by equation (2): (2) In the formula: For the first A collection of point cloud data slices; For the first slice Three-dimensional point cloud data, ; For the first The number of point cloud data points contained in a layer slice; Specifically, the height is set at intervals ranging from 1% to 5% of the target object's height. And use 1% to 3% of the target object's height as the slice thickness, or Set the height in intervals of 1% to 5% of the target object's height. The thickness of the point cloud slice is determined by 0.5 to 1 times the measurement accuracy of the point cloud itself, the mean deviation (MD) of the center axis fitting, or the mean square error (RMSE) of the center axis fitting. ...

[0007] The embodiments of the present invention are particularly applicable to tall chimneys and wind turbine towers exceeding 30 meters. Attached Figure Description

[0008] The invention can be better understood by referring to the accompanying drawings. The drawings are merely illustrative and are not intended to limit the scope of protection of the invention.

[0009] Figure 1 This is a schematic diagram illustrating a point cloud-based tilt monitoring method according to one embodiment of the present invention.

[0010] Figure 2 This is a schematic diagram illustrating a method for determining the unit direction vector of the central axis according to an embodiment of the present invention.

[0011] Figure 3 This is a schematic diagram illustrating a method for determining the unit direction vector of the central axis according to another embodiment of the present invention.

[0012] Figure 4 This is a schematic diagram illustrating a point cloud-based tilt monitoring device according to one embodiment of the present invention. Detailed Implementation

[0013] Specific embodiments of the present invention will now be described with reference to the accompanying drawings. These descriptions are exemplary and intended to enable those skilled in the art to implement the embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. No content essential for actual implementation but irrelevant to understanding the present invention is described in the description.

[0014] Figure 1 This is a schematic diagram illustrating a point cloud-based tilt monitoring method according to one embodiment of the present invention.

[0015] like Figure 1 As shown, firstly, in step S101, point cloud data is acquired.

[0016] According to one embodiment, a lidar remote sensing measurement device integrating BeiDou / GNSS positioning and timing, and 5G communication performs a full-circle, omnidirectional scan of a target object, such as the surface of a tall chimney, in a line-of-sight manner, collecting raw point cloud data of the chimney surface. This raw point cloud data from each station is then transmitted in real-time to a remote terminal using a 5G communication module. This remote terminal can implement the embodiments of this invention and can be a server, computer, laptop, or other device containing a processor and memory. The lidar remote sensing measurement device integrates a ground-based or airborne lidar sensor, a BeiDou / GNSS positioning and timing module, a high-precision motor, and a 5G communication module. Point cloud data can be obtained from other information sources via data communication equipment.

[0017] The point cloud data can be reconstructed in three dimensions. Based on the station location and observation epoch information provided by the BeiDou / GNSS positioning and timing module, the original point cloud data is coarsely registered station by station by a data preprocessing program on a remote terminal or other device. An improved iterative nearest point (ICP) algorithm is used to perform fine registration on the coarse registration results, and the point cloud data is transformed from the polar coordinate system to the station-centered spatial coordinate system o-xyz to obtain a complete high-precision three-dimensional point cloud. Finally, after preprocessing such as denoising, redundancy removal, and segmentation, the high-precision three-dimensional point cloud is used to obtain high-precision effective point cloud data of the target object, such as a tall chimney, in the station-centered spatial coordinate system o-xyz. The point cloud data in the station-centered spatial coordinate system o-xyz is expressed as Equation (1).

[0018] (1) In the formula: Point cloud data; This is used to measure the distance from the lidar laser beam to a target object, such as the surface of a tall chimney. This refers to the horizontal deflection angle of the lidar laser beam. This refers to the deflection angle of the laser beam in the longitudinal direction of the lidar.

[0019] Then, in step S102, multiple slice point cloud data are obtained from the point cloud data.

[0020] According to one implementation, in the station-centric spatial coordinate system o-xyz, the preprocessed target object, such as the surface point cloud of a tall chimney, is divided into horizontal cross-sectional slices along the z-axis at set height intervals to obtain sliced ​​point cloud data. The range of each cross-sectional slice is... , For the first The height of the cross-sectional slice of the layer, , The total number of cross-sectional slices. The thickness of the point cloud slice is set. Among them, the... The set of point clouds contained in a layer slice can be represented by equation (2).

[0021] (2) In the formula: For the first A collection of point cloud data slices; For the first slice Three-dimensional point cloud data, ; For the first The number of point cloud data points contained in a layer slice.

[0022] According to one implementation, the number of slices and the spatial coordinates of the point cloud contained within each slice are adaptively determined based on sliced ​​point cloud data. Preferably, the intervals can be set according to the height of the target object, such as a tall chimney, from 1% to 5%. Slice the material, and use the thickness of the slice as 1% to 3% of the height of the target object, such as a tall chimney.

[0023] According to another implementation, the height can be set at intervals of 1% to 5% of the height of the target object, such as a tall chimney. Slice the point cloud and use 0.5 to 1 times the point cloud's measurement accuracy, the mean deviation (MD) of the center axis fitting, or the mean square error (RMSE) of the center axis fitting as the slice thickness. .

[0024] For example, for a 100-meter-tall chimney, slices are horizontally divided along the z-axis at intervals of 1 to 5 meters, with the slice height set to 1 cm to 3 cm. Experiments show that slices obtained in this way can better ensure the reliability of detection and achieve a good dynamic update weight ratio for the geometric center point.

[0025] Then, in step S103, the slice point cloud data is projected onto the plane to obtain a set of planar projected point cloud data.

[0026] According to one implementation, to simplify the fitting calculation of the shape contour of each slice, the three-dimensional point cloud data within the slice is... The resulting planar projection point cloud dataset is represented by formula (3) when projected onto the xy plane.

[0027] (3) In the formula, For the first A collection of planar projection point cloud data of layer slices; The first slice within the projected slice A planar point cloud.

[0028] Various methods in the existing technology can be used to perform projection and obtain a set of planar projection point cloud data.

[0029] Then, in step S104, the outline of each slice shape is extracted using the planar projection point cloud data set.

[0030] According to one implementation, based on the outer contour design parameters of the target object (building, tall chimney, wind turbine tower, etc.), the outline of the slice shape is set to a circular outline, an elliptical outline, a spline curve outline, or a square outline, and the outline of each slice shape is extracted.

[0031] According to one embodiment, when the slice shape contour line is a circular contour line, extracting each slice shape contour line includes: Will Substituting the coordinates of the planar projected point cloud data into the following formula forms a linear system. (4) In the formula: ; ; , Let be any point on the circle; The coordinates of the center of the circle; Let be the radius of the circle. The matrix form of the linear system is shown in equation (5). (5) In the formula: ; ; , The optimal solution is obtained according to equation (6). (6) Finally, based on the obtained least squares solution The corresponding coordinates of the center of the plane circle and the radius are obtained by inverse solving, as shown in equations (7) and (8).

[0032] (7) (8) Then, in step S105, the coordinates of the geometric center point of each slice shape outline are calculated to obtain multiple geometric center point coordinates.

[0033] According to one implementation, in conjunction with the first Height range of layer slices The coordinates of the center of the circle in the two-dimensional plane Restored to the geometric center coordinates of three-dimensional space Take the middle height The z-coordinate of the geometric center of the three-dimensional spatial contour line can be expressed as Equation (9).

[0034] (9) According to equation (9). A cross-sectional slice can be obtained A shape outline, corresponding to The coordinates of the geometric center can be represented by a set as Equation (10).

[0035] (10) Then, in step S106, the unit direction vector of the central axis is determined based on the coordinates of the plurality of geometric center points. This step can be implemented using various methods of the prior art. According to one embodiment, it can be performed iteratively from top to bottom or from bottom to top according to the coordinates of the geometric center points.

[0036] Figure 2 This is a schematic diagram illustrating a method for determining the unit direction vector of the central axis according to an embodiment of the present invention.

[0037] like Figure 2 As shown, according to one embodiment, in step S201, the weighted centroid of the central axis is first calculated. C .

[0038] According to one implementation, the weighted centroid of the central axis can be calculated as follows: (11) In the formula: The weighted centroid of the geometric center points of all contour lines in the current iteration is the spatial reference point through which the line passes. For the current iteration The weight of the geometric center of each contour line; The weights of the initial state. For the number of iterations, This is the initial state.

[0039] Then, in step S202, a weighted covariance matrix is ​​constructed.

[0040] According to one implementation method, the weighted covariance matrix is ​​calculated by subtracting the three-dimensional coordinates of the weighted centroid from the coordinates of the geometric center points of each contour line, as shown in equation (12): (12) In the formula: The set of coordinates of the geometric center points of the contour line in the current iteration The weighted covariance matrix can reflect the distribution and degree of change of the geometric center point of the contour line in various directions in three-dimensional space.

[0041] Then, in step S203, the unit direction vector of the central axis is calculated based on the weighted covariance matrix.

[0042] According to one implementation, the weighted covariance matrix is ​​decomposed into eigenvalues, and the unit eigenvector corresponding to the largest eigenvalue is taken as the unit direction vector of the central axis, as shown in equations (13) and (14).

[0043] (13) (14) In the formula: The covariance matrix in the current iteration A feature vector represents the dominant distribution trend of the data in a certain direction; For the current iteration and the feature vector The corresponding eigenvalues ​​reflect the direction of the data. The degree of dispersion on; This is the unit eigenvector corresponding to the largest eigenvalue in the current iteration; This is the unit direction vector of the central axis in the current iteration.

[0044] Then, in step S204, it is determined whether the convergence condition is met.

[0045] According to one implementation, the algorithm is considered to have converged when the change in the unit direction vector of the central axis is less than a preset threshold or the number of iterations reaches the maximum value in two consecutive iterations.

[0046] The convergence conditions of the algorithm are shown in equations (15) and (16).

[0047] (15) (16) In the formula: The threshold value for the change in the unit direction vector of the central axis between two consecutive iterations; This is the maximum number of iterations set.

[0048] If the convergence condition is not met, proceed to step S205. Then, in step S205, calculate the shortest distance residual and update the weight of the geometric center of the contour line.

[0049] According to one implementation, the shortest distance residual from the geometric center of each contour line to the spatial straight line containing the central axis is calculated, and the weight is dynamically updated by the residual feedback adjustment method, as shown in Equations (17) and (18).

[0050] (17) (18) In the formula: For the current iteration The shortest distance residual from the geometric center of each contour line to the current spatial fitted line; “∥ ∥” represents the vector norm; The current iteration updates the residual based on the shortest distance inverse ratio principle. New weights for the geometric centers of the contour lines; It is a very small constant that avoids division by zero, and is a predetermined value. According to one implementation, it is set to 10. -6 .

[0051] Then, return to step S201 and recalculate the weighted centroid of the central axis. C。

[0052] Through such iterations, based on the collaborative optimization of residual feedback and dynamic weight updates, intelligent extraction of the unit direction vector of the central axis is achieved, thereby realizing high-precision extraction of the tilt information of the target object and improving the accuracy of tilt monitoring.

[0053] On the other hand, when it is determined in step S204 that the convergence condition is met, the process proceeds to step S206. In step S206, the unit direction vector of the central axis determined in step S203 is output.

[0054] Figure 3 This is a schematic diagram illustrating a method for determining the unit direction vector of the central axis according to another embodiment of the present invention.

[0055] Figure 3 The implementation method is based on Figure 2 The implementation method, and therefore with Figure 2 The same steps will not be repeated here.

[0056] like Figure 3 As shown, when the convergence condition is met in step S204, the fitting accuracy of the unit direction vector of the central axis is determined in step S301, and it is determined whether they are not greater than their respective predetermined thresholds.

[0057] According to one implementation, the average deviation and mean error of the fitting result of the central axis direction vector are calculated based on the shortest distance residual, as shown in equations (19) and (20).

[0058] (19) (20) In the formula, The average deviation is fitted to the central axis; This represents the fitting error of the central axis.

[0059] When either the average deviation of the center axis fitting or the mean error of the center axis fitting exceeds a predetermined threshold, in step S207, the geometric center point of the contour line with the largest current shortest distance residual is removed, and the process returns to step S203. This implementation effectively removes poor point cloud data or slices, improving accuracy.

[0060] When the average deviation of the center axis fitting and the mean error of the center axis fitting are both not greater than their respective predetermined thresholds, in step S206, the unit direction vector of the center axis determined in step S203 is output.

[0061] Back Figure 1 Finally, in step S107, the tilt monitoring results of the target object are evaluated based on the determined unit direction vector of the central axis.

[0062] According to one implementation, the tilt monitoring parameters for the central axis of an industrial heritage chimney are set to include tilt azimuth, tilt angle, verticality, and verticality deviation. These can be calculated as follows.

[0063] 1) Calculate the tilt azimuth angle of the central axis. In the station-centered spatial coordinate system o-xyz, the unit direction vector of the x-axis is... Central axis tilt azimuth angle It is a vector with vector The horizontal angle between them can be obtained through vector operations, as shown in equation (21).

[0064] (twenty one) 2) Calculate the tilt angle of the central axis. In the station-centered spatial coordinate system o-xyz, the unit vector of the z-axis is... Inclination angle of the central axis It is a vector with vector The longitudinal angle between them can be obtained through vector operations, as shown in equation (22).

[0065] (twenty two) 3) Calculate the perpendicularity of the central axis. According to the definition of perpendicularity, the perpendicularity of the central axis can be calculated according to equation (22). See equation (23).

[0066] (twenty three) 4) Calculate the perpendicularity deviation value of the center axis. Perpendicularity deviation value It is based on the chimneys of industrial heritage sites at a specific elevation. The horizontal offset relative to the bottom. It can be obtained from equation (23), see equation (24).

[0067] (twenty four) 5) Accuracy evaluation of tilt monitoring parameters. According to one implementation method, relative error is used as the evaluation index, and the accuracy of each tilt monitoring parameter is evaluated by comparing it with the corresponding reference value. The formula for calculating the relative error is shown in equation (25).

[0068] (25) In the formula: This is relative error; These are the calculated values ​​for each tilt attitude parameter; The corresponding reference value can be determined using traditional, known methods.

[0069] Figure 4 This is a schematic diagram illustrating a point cloud-based tilt monitoring device according to one embodiment of the present invention.

[0070] like Figure 4 As shown, according to one embodiment, a point cloud-based tilt monitoring device according to an embodiment of the present invention includes: Point cloud data acquisition unit 110 is used to obtain valid point cloud data of the target object; The slice acquisition unit 120 acquires multiple slice point cloud data from the effective point cloud data; The projection unit 130 projects each slice point cloud data onto a plane to obtain a set of planar projected point cloud data. The contour line extraction unit 140 extracts the contour lines of each slice shape using the planar projection point cloud data set; Unit 150 for obtaining geometric center point coordinates calculates the geometric center point coordinates of the outline of each slice shape, thus obtaining multiple geometric center point coordinates. The central axis unit direction vector acquisition unit 160 determines the central axis unit direction vector based on the coordinates of the plurality of geometric center points; and The tilt result acquisition unit 170 determines the tilt result of the target object based on the unit direction vector of the central axis.

[0071] For an understanding of each unit and its implementation, please refer to the previous descriptions of each step. The unit 160 for obtaining the unit direction vector of the central axis can be based on... Figure 2 and Figure 3 The described steps determine the unit direction vector of the central axis based on the coordinates of the plurality of geometric center points.

[0072] The above units can be implemented by a combination of hardware and software, or only by hardware.

[0073] The above description is merely illustrative and is not intended to limit the scope of protection of this invention. Any changes or substitutions within the scope of the concept of this invention are within the scope of protection of this invention.

Claims

1. A point cloud segmentation method, characterized in that, Point cloud segmentation is performed as follows: In the station-centric spatial coordinate system o-xyz, horizontal cross-sectional slices are made along the z-axis at set height intervals to obtain sliced ​​point cloud data. The range of each cross-sectional slice is [missing information]. , For the first The height of the cross-sectional slice of the layer, , The total number of cross-sectional slices. The set point cloud slice thickness, where the first... The set of point clouds contained within a slice can be represented by equation (2): （2） In the formula: For the first A collection of point cloud data slices; For the first slice Three-dimensional point cloud data, ; For the first The number of point cloud data points contained in a layer slice; Specifically, the height is set at intervals ranging from 1% to 5% of the target object's height. And use 1% to 3% of the target object's height as the slice thickness, or Set the height in intervals of 1% to 5% of the target object's height. The thickness of the point cloud slice is determined by 0.5 to 1 times the measurement accuracy of the point cloud itself, the mean deviation (MD) of the center axis fitting, or the mean square error (RMSE) of the center axis fitting. .

2. A tilt monitoring method based on point clouds, characterized in that, Includes the following steps: Obtain valid point cloud data of the target object; Multiple slice point cloud data are obtained from the effective point cloud data; The slice point cloud data is projected onto a plane to obtain a set of planar projected point cloud data. Using the aforementioned planar projection point cloud data set, extract the outline of each slice shape; Calculate the coordinates of the geometric center point of the outline of each slice shape to obtain multiple geometric center point coordinates; Determine the unit direction vector of the central axis based on the coordinates of the plurality of geometric center points; and The tilt result of the target object is determined based on the unit direction vector of the central axis. Point cloud segmentation is performed as follows: In the station-centric spatial coordinate system o-xyz, horizontal cross-sectional slices are made along the z-axis at set height intervals to obtain sliced ​​point cloud data. The range of each cross-sectional slice is [missing information]. , For the first The height of the cross-sectional slice of the layer, , The total number of cross-sectional slices. The set point cloud slice thickness, where the first... The set of point clouds contained within a slice can be represented by equation (2): （2） In the formula: For the first A collection of point cloud data slices; For the first slice Three-dimensional point cloud data, ; For the first The number of point cloud data points contained in a layer slice; Specifically, the height is set at intervals ranging from 1% to 5% of the target object's height. And use 1% to 3% of the target object's height as the slice thickness, or Set the height in intervals of 1% to 5% of the target object's height. The thickness of the point cloud slice is determined by 0.5 to 1 times the measurement accuracy of the point cloud itself, the mean deviation (MD) of the center axis fitting, or the mean square error (RMSE) of the center axis fitting. .

3. The method according to claim 1, characterized in that, The outline of the slice shape is set to a circular outline. Extracting the outline of each slice shape includes: Will Substituting the coordinates of the planar projected point cloud data into the following formula forms a linear system. （4） In the formula: ; ; , Let be any point on the circle; The coordinates of the center of the circle; Let be the radius of the circle. The matrix form of the linear system is shown in equation (5). （5） In the formula: ; ; , The optimal solution is obtained according to equation (6). （6） Finally, based on the obtained least squares solution The corresponding coordinates of the center of the plane circle and the radius are obtained by inverse solving, as shown in equations (7) and (8). （7） （8）。 4. The method according to claim 1, characterized in that, The unit direction vector of the central axis is determined based on the coordinates of the geometric center point as follows: (1) Calculate the weighted centroid of the central axis using the weight of the geometric center of the contour line. C ; (2) Construct the weighted covariance matrix by subtracting the three-dimensional coordinates of the weighted centroid from the coordinates of the geometric center point of each contour line, and calculate the weighted covariance matrix, as shown in equation (12): （12） In the formula: The set of coordinates of the geometric center points of the contour line in the current iteration The weighted covariance matrix; (3) Calculate the unit direction vector of the central axis: Perform eigenvalue decomposition on the weighted covariance matrix, and take the unit eigenvector corresponding to the largest eigenvalue as the unit direction vector of the central axis, as shown in equations (13) and (14): （13） （14） In the formula: The covariance matrix in the current iteration A feature vector represents the dominant distribution trend of the data in a certain direction; For the current iteration and the feature vector The corresponding eigenvalues ​​reflect the direction of the data. The degree of dispersion on; The unit eigenvector corresponding to the largest eigenvalue; This is the unit direction vector of the central axis in the current iteration; (4) Determine whether the convergence condition is met based on the following formula. （15） （16） In the formula: The threshold value for the change in the unit direction vector of the central axis between two consecutive iterations. The maximum number of iterations is set. (5) When it is determined that the convergence condition is not met, calculate the shortest distance residual, update the weight of the geometric center of the contour line, and then return to step (1).

5. The method according to claim 4, characterized in that, The weighted centroid of the central axis is calculated as follows: （11） In the formula: The weighted centroid of the geometric center points of all contour lines in the current iteration is the spatial reference point through which the line passes. For the current iteration The weight of the geometric center of each contour line; , For the number of iterations, This is the initial state.

6. The method according to claim 4, characterized in that, The shortest distance residual is calculated and the weights of the geometric center of the contour line are updated as follows: （17） （18） In the formula: For the current iteration The shortest distance residual from the geometric center of the contour line to the current spatial fitted line; "∥ ∥" represents the vector norm; For the current iteration, the number of iterations updated according to the inverse residual principle is... New weights for the geometric centers of the contour lines; It is a very small constant that avoids division by zero.

7. The method according to claim 4, characterized in that, Also includes: When step (4) determines that the convergence condition is met, the average deviation and mean error of the fitting result of the central axis direction vector are calculated based on the shortest distance residual, and it is determined whether they are not greater than their respective predetermined thresholds. When either the average deviation or the mean error is greater than a predetermined threshold, the geometric center point of the contour line with the largest current shortest distance residual is removed, and the process returns to step (3).

8. The method according to claim 7, characterized in that, The average deviation and mean error of the fitting result of the central axis direction vector are calculated based on the shortest distance residual as shown in equations (19) and (20). （19） （20）， In the formula, The average deviation is fitted to the central axis; This represents the fitting error of the central axis.

9. The method according to claim 7, characterized in that, Determining the tilt monitoring parameters of the target object includes: (1) Calculate the azimuth angle of the central axis as follows. : （21） Among them, the tilt azimuth angle of the central axis It is a vector with vector The horizontal angle between them, in the station-centered spatial coordinate system o-xyz, the unit direction vector of the x-axis is... , (2) Calculate the tilt angle of the central axis as follows. : （22） In the station-centered spatial coordinate system o-xyz, the unit vector of the z-axis is... Inclination angle of the central axis It is a vector with vector The longitudinal angle between them.

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