A point cloud-based tilt monitoring method and device

Abstract

The present application relates to a kind of based on point cloud's inclination monitoring method and device, the method comprises: obtaining the effective point cloud data of target object;From the effective point cloud data, obtain multiple slice point cloud data;Each slice point cloud data is projected on plane, and obtains the set of plane projection point cloud data;Using the set of plane projection point cloud data, extract each slice shape contour line;The geometric center point coordinates of each slice shape contour line are calculated, and multiple geometric center point coordinates are obtained;According to the multiple geometric center point coordinates, determine the central axis unit direction vector;And according to central axis unit direction vector, determine the inclination result of target object.

Description

Technical Field

[0001] 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

[0002] Tall industrial sites, 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 these chimneys is not monitored and addressed promptly, it can lead to serious structural damage or even collapse. Traditional tilt monitoring methods, such as theodolites, plumb bobs, and ruler measurements, are limited in accuracy, efficiency, and lack of global awareness and automation, making them unsuitable for current industrial site tilt monitoring needs. Therefore, achieving high-precision, non-contact, and globally perceptive tilt monitoring for targets like towering industrial chimneys and wind turbine towers is crucial for safety assessment, risk warning, and life extension management of tall structures. Summary of the Invention

[0003] 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.

[0004] According to one 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 coordinates of the geometric center points 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.

[0005] According to another aspect of the present invention, a tilt monitoring device based on point clouds is provided, comprising: a point cloud data acquisition unit for acquiring effective point cloud data of a target object; a slice acquisition unit for acquiring multiple slice point cloud data from the effective point cloud data; a projection unit for projecting each slice point cloud data onto a plane to obtain a set of planar projected point cloud data; a contour line extraction unit for extracting the contour lines of each slice shape using the set of planar projected point cloud data; a geometric center point coordinate acquisition unit for calculating the geometric center point coordinates of each slice shape contour line to obtain multiple geometric center point coordinates; a central axis unit direction vector acquisition unit for determining the central axis unit direction vector based on the multiple geometric center point coordinates; and a tilt result acquisition unit for determining the tilt result of the target object based on the central axis unit direction vector.

[0006] According to one embodiment, the central axis unit direction vector acquisition unit determines the central axis unit direction vector based on the coordinates of the geometric center point as follows:

[0007] (1) Calculate the weighted centroid of the central axis C ;

[0008] (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 (14):

[0009] (12)

[0010] In the formula: The set of coordinates of the geometric center points of the contour line in the current iteration The weighted covariance matrix;

[0011] (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):

[0012] (13)

[0013] (14)

[0014] 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.

[0015] (4) Determine whether the convergence condition is met based on the following formula:

[0016] (15)

[0017] (16)

[0018] 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.

[0019] (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).

[0020] The embodiments of the present invention are particularly applicable to tall chimneys and wind turbine towers exceeding 30 meters. Attached Figure Description

[0021] 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.

[0022] Figure 1 This is a schematic diagram illustrating a point cloud-based tilt monitoring method according to one embodiment of the present invention.

[0023] 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.

[0024] 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.

[0025] 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

[0026] 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.

[0027] Figure 1 This is a schematic diagram illustrating a point cloud-based tilt monitoring method according to one embodiment of the present invention.

[0028] like Figure 1 As shown, firstly, in step S101, point cloud data is acquired.

[0029] 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.

[0030] 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).

[0031] (1)

[0032] 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 is the deflection angle of the laser beam in the longitudinal direction of the lidar.

[0033] Then, in step S102, multiple slice point cloud data are obtained from the point cloud data.

[0034] 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).

[0035] (2)

[0036] 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.

[0037] 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.

[0038] 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. .

[0039] 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.

[0040] Then, in step S103, the slice point cloud data is projected onto the plane to obtain a set of planar projected point cloud data.

[0041] 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.

[0042] (3)

[0043] 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.

[0044] Various methods in the existing technology can be used to perform projection and obtain a set of planar projection point cloud data.

[0045] Then, in step S104, the outline of each slice shape is extracted using the planar projection point cloud data set.

[0046] 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.

[0047] According to one embodiment, when the slice shape outline is a circular outline, extracting each slice shape outline includes:

[0048] Will Substituting the coordinates of the planar projected point cloud data into the following formula forms a linear system.

[0049] (4)

[0050] 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.

[0051] The matrix form of the linear system is shown in equation (5).

[0052] (5)

[0053] In the formula: ; ; ,

[0054] The optimal solution is obtained according to equation (6).

[0055] (6)

[0056] 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).

[0057] (7)

[0058] (8)

[0059] 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.

[0060] 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).

[0061] (9)

[0062] 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).

[0063] (10)

[0064] 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.

[0065] 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.

[0066] like Figure 2 As shown, according to one embodiment, in step S201, the weighted centroid of the central axis is first calculated. C .

[0067] According to one implementation, the weighted centroid of the central axis can be calculated as follows:

[0068] (11)

[0069] 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.

[0070] Then, in step S202, a weighted covariance matrix is ​​constructed.

[0071] 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):

[0072] (12)

[0073] 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.

[0074] Then, in step S203, the unit direction vector of the central axis is calculated based on the weighted covariance matrix.

[0075] 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).

[0076] (13)

[0077] (14)

[0078] 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.

[0079] Then, in step S204, it is determined whether the convergence condition is met.

[0080] 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.

[0081] The convergence conditions of the algorithm are shown in equations (15) and (16).

[0082] (15)

[0083] (16)

[0084] 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.

[0085] 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.

[0086] 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).

[0087] (17)

[0088] (18)

[0089] 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 .

[0090] Then, return to step S201 and recalculate the weighted centroid of the central axis. C。

[0091] 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.

[0092] 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.

[0093] 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.

[0094] Figure 3 The implementation method is based on Figure 2 The implementation method, and therefore with Figure 2The same steps will not be repeated here.

[0095] 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.

[0096] 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).

[0097] (19)

[0098] (20)

[0099] In the formula, The average deviation is fitted to the central axis; This represents the fitting error of the central axis.

[0100] 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.

[0101] 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.

[0102] 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.

[0103] 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.

[0104] 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).

[0105] (twenty one)

[0106] 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).

[0107] (twenty two)

[0108] 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).

[0109] (twenty three)

[0110] 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).

[0111] (twenty four)

[0112] 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).

[0113] (25)

[0114] 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.

[0115] Figure 4 This is a schematic diagram illustrating a point cloud-based tilt monitoring device according to one embodiment of the present invention.

[0116] 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:

[0117] Point cloud data acquisition unit 110 is used to obtain valid point cloud data of the target object;

[0118] The slice acquisition unit 120 acquires multiple slice point cloud data from the effective point cloud data;

[0119] The projection unit 130 projects each slice point cloud data onto a plane to obtain a set of planar projected point cloud data.

[0120] The contour line extraction unit 140 uses the planar projection point cloud data set to extract the contour lines of each slice shape;

[0121] Unit 150 for obtaining geometric center point coordinates calculates the geometric center point coordinates of the outline of each slice shape, and obtains multiple geometric center point coordinates.

[0122] 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

[0123] The tilt result acquisition unit 170 determines the tilt result of the target object based on the unit direction vector of the central axis.

[0124] 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.

[0125] The above units can be implemented by a combination of hardware and software, or only by hardware.

[0126] 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 based tilt monitoring method, characterized in that, The method comprises the following steps: obtaining effective point cloud data of a target object; obtaining a plurality of slice point cloud data from the effective point cloud data; projecting each of the slice point cloud data onto a plane to obtain a set of planar projection point cloud data; extracting a contour line of each slice shape using the set of planar projection point cloud data; calculating a geometric center point coordinate of each contour line of the slice shape to obtain a plurality of geometric center point coordinates; determining a central axis unit direction vector according to the plurality of geometric center point coordinates; and determining a tilt result of the target object according to the central axis unit direction vector, wherein the central axis unit direction vector is determined according to the geometric center point coordinate as follows: (2) constructing a weighted covariance matrix, each contour line geometric center point coordinate is subtracted from a three-dimensional coordinate of a weighted centroid, and the weighted covariance matrix is calculated, as shown in formula (12): (1) Utilizing the weight of the geometric center of the contour line to calculate the weighted centroid of the center axis C ; (3) calculating the central axis unit direction vector: performing eigenvalue decomposition on the weighted covariance matrix, and taking a unit eigenvector corresponding to the maximum eigenvalue as the central axis unit direction vector, as shown in formula (13) and formula (14): （12） In the formula: is a weighted covariance matrix of the set of contour geometric center point coordinates in the current iteration is a weighted covariance matrix of the set of contour geometric center point coordinates in the current iteration (4) judging whether a convergence condition is met according to the following formula （13） （14） wherein: is a principal eigenvector of the covariance matrix in the current iteration, representing the main distribution trend of the data in a certain direction; is the corresponding eigenvalue of the principal eigenvector in the current iteration, reflecting the dispersion degree of the data in the direction ; is the unit eigenvector corresponding to the maximum eigenvalue; is the unit directional vector of the central axis in the current iteration; (5) when it is judged that the convergence condition is not met, calculating a shortest distance residual, and updating the weight of the contour line geometric center, and then returning to step (1). （15） （16） In the formula: is the central axis unit direction vector change threshold for two consecutive iterations, is the maximum number of iterations set; When the contour line of the slice shape is a circular contour line, the step of extracting each contour line of the slice shape comprises:

2. The method of claim 1, wherein, the matrix form of the linear system is shown in formula (5) The coordinates of the planar projection point cloud data are substituted into the following formula to form a linear system, （4） wherein: ; ; , is an arbitrary point on the circle; is the center coordinate of the circle; is the radius of the circle, the optimal solution is obtained according to formula (6) （5） In the formulae: ; ; , the central axis weighted centroid is calculated as follows: （6） Finally, based on the least square solution obtained , the corresponding plane circle center coordinates and radius are solved inversely, see equation (7) and equation (8), （7） （8）。 3. The method of claim 1, wherein, the shortest distance residual is calculated and the weight of the contour line geometric center is updated as follows: （11） wherein: is the weighted centroid of all the geometric center points of the contour lines in the current iteration, i.e. the spatial reference point through which the straight line passes, is the weight of the geometric center of the contour line in the current iteration; , is the number of iterations, is the initial state.

4. The method of claim 1, wherein, Further comprising: （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.

5. The method of claim 1, wherein, when it is judged in step (4) that the convergence condition is met, calculating an average deviation and a mean error of the central axis direction vector fitting result according to the shortest distance residual, and judging whether they are not greater than predetermined respective thresholds, when one of the average deviation and the mean error is greater than the predetermined respective threshold, eliminating the contour line geometric center point with the largest shortest distance residual, and returning to step (3). The average deviation and the mean error of the central axis direction vector fitting result are calculated according to the shortest distance residual as follows, as shown in formula (19) and formula (20) 6. The method of claim 5, wherein, determining a tilt monitoring parameter of the target object comprises: （19） （20） wherein is the mean deviation of the central axis fitted; is the mean error of the central axis fitted.

7. The method of claim 5, wherein, 8. A point cloud-based tilt monitoring device, comprising: (1) The center axis tilt azimuth angle is calculated as follows : （21） Wherein the central axis is inclined by an azimuth angle is the horizontal included angle between the vector and the vector In the geocentric space coordinate system o-xyz, the unit directional vector of the x-axis is (2) The center axis tilt angle is calculated as follows : （22） Wherein, in the station center space coordinate system o-xyz, the unit vector of z axis is , the center axis inclination angle is the longitudinal angle between the vector and the vector . a point cloud data acquisition unit configured to obtain effective point cloud data of a target object; a slice acquisition unit configured to obtain a plurality of slice point cloud data from the effective point cloud data; a projection unit configured to project each of the slice point cloud data onto a plane to obtain a set of planar projection point cloud data; a contour line extraction unit configured to extract a contour line of each slice shape using the set of planar projection point cloud data; a geometric center point coordinate acquisition unit configured to calculate a geometric center point coordinate of each contour line of the slice shape to obtain a plurality of geometric center point coordinates; a central axis unit direction vector acquisition unit configured to determine a central axis unit direction vector according to the plurality of geometric center point coordinates; and a tilt result acquisition unit configured to determine a tilt result of the target object according to the central axis unit direction vector, ​ The center axis unit direction vector acquisition unit determines the center axis unit direction vector according to the geometric center point coordinates as follows: (1) Utilizing the weight of the geometric center of the contour line to calculate the weighted centroid of the center axis C ; (2) Construct a weighted covariance matrix, subtract the three-dimensional coordinates of the weighted centroid from each contour line geometric center point coordinate, and calculate the weighted covariance matrix, as shown in equation (12): （12） In the formula: is the weighted covariance matrix of the set of contour line geometric center point coordinates in the current iteration is the weighted covariance matrix of the set of contour line geometric center point coordinates in the current iteration (3) Calculate the center axis unit direction vector: perform eigenvalue decomposition on the weighted covariance matrix, and take the unit eigenvector corresponding to the maximum eigenvalue as the center axis unit direction vector, as shown in equations (13) and (14): （13） （14） wherein: is a principal eigenvector of the covariance matrix in the current iteration, representing the main distribution trend of the data in a certain direction; is the eigenvalue corresponding to the eigenvector in the current iteration, reflecting the dispersion degree of the data in the direction ; is the unit eigenvector corresponding to the largest eigenvalue; is the unit directional vector of the central axis in the current iteration; (4) Determine whether the convergence condition is met according to the following formula （15） （16） In the formula: is the central axis unit direction vector change threshold for two consecutive iterations, is the maximum number of iterations set; (5) When it is determined that the convergence condition is not met, calculate the shortest distance residual error, update the weight of the contour line geometric center, and then return to step (1).

Images