A bridge nonlinear geometric component alignment identification method based on three-dimensional laser scanning

Abstract

This invention relates to a method for identifying the linear shape of nonlinear geometric components of bridges based on three-dimensional laser scanning, comprising: acquiring overall point cloud data of the bridge; correcting the spatial pose of the bridge point cloud; initially fitting the approximate axis of the component point cloud; acquiring the contour point cloud of the control section; calculating the local density standard deviation of the point cloud within each slice; iteratively optimizing the slice angle to obtain the optimal slice; constructing a standard point cloud model of the feature section; performing global shape matching between the measured optimal slice and the standard point cloud model; extracting the centroid coordinates of the feature section point cloud; and extracting the three-dimensional coordinate sequence of all centroid points along the bridge span direction, which is the identified bridge linear shape. This invention achieves accurate identification of the linear shape of curved components in bridge point clouds, has a high degree of automation in linear shape data extraction, and exhibits strong robustness to data with severe local point cloud deficiencies. It can be applied to the accurate linear shape detection of straight bridges, skew bridges, and curved bridges with nonlinear geometric components.

Description

Technical Field

[0001] This invention belongs to the field of bridge appearance inspection technology in bridge engineering, and specifically relates to a method for linear identification of nonlinear geometric components of bridges based on three-dimensional laser scanning. Background Technology

[0002] Bridge alignment is a crucial evaluation indicator for bridge appearance inspection during construction and service. It reflects the bridge's mechanical response to different load effects under its current condition. Bridges whose alignment deviates significantly from the original design alignment may already be in an unhealthy operational state. Therefore, identifying the alignment of the main bridge components is one of the key aspects of appearance inspection.

[0003] Currently, conventional inspection methods such as total stations and levels are inefficient and can only acquire information from a limited number of discrete points, failing to provide a complete understanding of bridge spatial information. Unlike traditional sensors used to monitor displacement at specific locations on a bridge, 3D point cloud data allows laser scanners to act as millions of sensors simultaneously. This eliminates the need for structural repairs or damage to any part of the structure before or after monitoring, providing a highly efficient and convenient linear inspection solution.

[0004] However, in practice, when bridge components have nonlinear geometric characteristics (such as arch ribs of arch bridges and main cables of suspension bridges), the orthogonality between the cross-sectional normal direction of the displacement detection point and the principal curvature direction of the target point is difficult to calculate accurately. This causes the point cloud cross-sectional contour line to deviate from the ideal normal projection of the actual geometric characteristics. This deviation causes the topological structure of the cross-sectional point set to be distorted, thereby increasing the discreteness of the displacement feature point extraction error. In addition, the nonlinear geometric characteristics of bridge components are often accompanied by self-occlusion effect and anisotropy of point cloud density, further increasing the difficulty of solving for the optimal cross-sectional angle.

[0005] Therefore, there is an urgent need to propose an effective method for accurate identification of the line shape of the entire bridge point cloud for straight bridges, skew bridges, and curved bridges with nonlinear geometric components, so as to eliminate the problem of multiple solutions in the extraction results of the same feature point in long-term bridge monitoring. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings and deficiencies of existing technologies by providing a method for identifying the linear shape of nonlinear geometric components of bridges based on three-dimensional laser scanning. This method utilizes the golden section method to dynamically solve for the optimal angle of point cloud slices and combines Protodyakonov analysis theory to optimize the spatial coordinate calculation process, thereby improving the accuracy of bridge linear shape extraction.

[0007] The technical problem solved by this invention is achieved through the following technical solution: A method for identifying the linear shape of nonlinear geometric components of bridges based on three-dimensional laser scanning, the method comprising the following steps: S1. A ground-based laser scanner combined with a target is used to perform sub-station scanning of the entire bridge. Based on the target, the point cloud data of multiple measurement stations is registered to the same coordinate system. The measured point cloud data is analyzed using Cyclone software, and its Constraints (Target) function is used to achieve the registration of the point cloud data of multiple measurement stations by constraining the target. Finally, the registered point cloud is saved in a common format of .txt or .las to obtain the bridge point cloud data. S2. Use principal component analysis to calibrate the spatial pose of the bridge point cloud data so that the spatial pose of the bridge body is orthogonal to the rectangular coordinate system. S3. Project the point cloud of the bridge component orthogonally onto the normal plane of the local principal curvature direction, and use polynomial fitting to fit the projected point cloud to obtain the approximate axis curve of the entire component. S4. Select a slicing location point on the approximate axis curve, determine the initial slicing direction by calculating the slope of the axis at that point, and simultaneously set the slicing thickness. All control points are sliced, with a slice thickness of [missing information]. The value is determined by both local point cloud density and local curvature, and is greater than 10 times the point cloud spacing, but less than the radius of curvature of the component axis. A local coordinate system is formed using the tangent vector and the corresponding normal plane. The extracted point cloud segment is projected onto the normal plane to obtain the cross-sectional point cloud of that point. Finally, the contour point cloud of the control section is obtained. S5. Using the intersection of the initial slice center and the initial axis of the component as the rotation center, set the rotation range based on the initial slice angle to establish a search space. Within this range, use the golden section method to subdivide the search space to generate potential optimal slices as candidate angle values. S6. Calculate the standard deviation of local point cloud density for all candidate slice sections. Based on this, determine whether the current slice angle meets the accuracy requirements. If the requirements are not met, the inferior solution interval is eliminated, the search interval is shrunk, and the golden section method is used again to approximate the optimal slice angle; otherwise, it is extracted as the optimal cross-sectional point cloud. S7. Filter the optimal cross-sectional point cloud of all control points, and extract the cross-section with the smallest local point cloud density standard deviation as the standard point cloud model of the feature cross-section. S8. Use Protodyakonov's analysis theory to perform global shape matching between the measured slice point cloud and the standard point cloud model to maximize the overlap between the two point clouds. S9. Calculate the theoretical centroid coordinates of the standard point cloud model, and use the coordinate transformation parameters obtained by global shape matching to map them to the measured cross-sectional profile to determine the centroid coordinates of the control section. S10. Integrate the centroid coordinate extraction results of all control section contour point clouds to obtain complete bridge full-bridge linear feature points.

[0008] Furthermore, the calibration of S2 specifically includes: 1) Calculate the covariance matrix of the point cloud and solve for its eigenvalues ​​and eigenvectors. Before solving for the covariance matrix, first decenter the 3D coordinate matrix of the point cloud. The formula for calculating the covariance matrix of a point cloud is: ; in: The coordinate data is the decentralized version of the point cloud. For matrix The transpose of the matrix, The number of point clouds; The decentralized calculation formula is: ; in: For matrix The Line number Column elements; 2) Take the eigenvectors corresponding to the two largest eigenvalues. and As basis vectors of the point cloud, the other principal directions satisfy: ; 3) Transfer point cloud data , The coordinates are transformed along the principal axis direction, and the first principal axis direction is used as the coordinate axis after transformation. Direction, the direction of the second principal axis as Direction, the third principal axis direction as direction.

[0009] Furthermore, the S5 method of subdividing the search space using the golden ratio is specifically as follows: 1) Calculate the local density standard deviation of all point clouds in the current slice. Determine if the slice angle meets the accuracy requirements. , If the threshold set by the user is met, proceed to the next step; otherwise, directly calculate the centroid coordinates of the measurement point. 2) Using the intersection of the slice center and the component axis as the rotation center, based on the initial slice angle... Set rotation range To establish a search space The search space is subdivided using the golden section method within the interval to generate potential optimal slices as candidate angle values. The subdivision points are as follows: ; in: The golden ratio is . and These are the interior points of the section determined by the golden ratio. and These are the boundary points of the angle search space; 3) Calculate the local density standard deviation of the point cloud in all potential optimal slices, including boundary points and segmentation points, and determine it according to the method in 1); 4) By comparing the minimum local point cloud density standard deviation among all candidate slices Compared with the preset accuracy threshold The algorithm determines whether to shrink the search area. If there is a candidate angle that meets the cross-sectional accuracy requirements, the iteration is terminated and the optimal slice angle is output. Otherwise, the search area is updated based on the golden ratio, the inferior angle area with the largest standard deviation is removed, and the optimal slice is searched again in the new area until a slice angle that meets the accuracy requirements is found. 5) Repeat the above steps until the optimal slice for all measuring points is determined.

[0010] Furthermore, the formula for calculating the standard deviation of the local point cloud density of all data points in the sliced ​​point cloud in S6 is as follows: ; in: The standard deviation of the local point cloud density of a data point in a slice. For local point cloud density, for The mean, The number of point clouds; The formula for calculating the local surface density of the point cloud of the cross-sectional profile is: ; in: For local point cloud density, For the current point Nearby point, From the current point to the farthest point The distance between them; The formula for calculating the mean local point cloud density of all data points in a sliced ​​point cloud is as follows: ; in: for The mean.

[0011] Furthermore, the S8 method uses Protodyakonov analysis theory to perform global shape matching between the measured slice point cloud and the standard point cloud model, specifically as follows: Given containing A matrix of points and , representing the coordinates on the standard point cloud model and the measured cross-sectional profile, respectively. This represents the dimension used in coordinate transformation calculations; to achieve matching, the matrix needs to be... Perform coordinate transformation to make it correspond to the matrix to the greatest extent possible. : ; in: It is a rotation matrix, for An orthogonal identity matrix, representing a matrix Coordinate transformation involving rotation around the origin of the coordinate system; It is a translation vector, which is The column vectors represent the matrix. Along vector Perform coordinate transformations for translation; ; Here is the error matrix. The shift parameter with the smallest square of the L2 norm and The following formula is used: ; Wherein: Based on the properties of orthogonal matrices, the obtained... Singular value decomposition can be performed using the following formula: ; in: , and for The coordinate transformation parameters of the matrix obtained by singular value decomposition can be calculated using the following formula: ; .

[0012] Furthermore, the theoretical centroid coordinate calculation formula for the S9 standard point cloud model is as follows: ; in: The theoretical centroid coordinates of the standard point cloud model. The number of points in a standard point cloud model. The mean of the coordinate values; The formula for mapping the centroid coordinates of the measured cross-section profile is: ; in: These are the true centroid coordinates of each measured optimal slice.

[0013] The advantages and beneficial effects of this invention are as follows: 1. This invention can automatically extract the linear parameters of key components from measured bridge point cloud data, overcoming the problem of poor stability of feature point coordinate reconstruction caused by the difficulty in establishing the orthogonal relationship between the cross-section normal direction and the principal curvature of the target point in the prior art; 2. This invention dynamically shrinks the search space by analyzing the discreteness of the local density of the point cloud, which solves the problem of non-uniform distortion of the cross-sectional point cloud caused by the slicing angle error of the curved component, thereby avoiding the multiple solutions of feature point extraction results in long-term monitoring. 3. This invention proposes a standard point cloud model construction method for bridge cross sections, and significantly improves the feature extraction accuracy and stability in missing point cloud cross sections by combining Protodyakonov analysis theory to solve the spatial coordinates of the measurement points. 4. The method for identifying the linearity of nonlinear geometric components of bridges based on three-dimensional laser scanning proposed in this invention is applicable to various bridge types with nonlinear geometric components, such as straight bridges, skew bridges, and curved bridges. It has strong versatility and can be promoted and applied in various bridge engineering projects. Attached Figure Description

[0014] Figure 1 This is a flowchart of the present invention; Figure 2 This is a preliminary cross-sectional image obtained by using the slicing method to extract cross-sections from the point cloud of bridge arch ribs in this invention. Figure 3 This is a schematic diagram illustrating the application of the golden section method to shrink the search space for slice angles in this invention. Figure 4 This is a point cloud diagram of the cross-sections of each slice of the main beam of the bridge in this invention at the optimal angle; Figure 5 This is a schematic diagram of the global shape matching process of bridge cross sections based on a standard point cloud model according to the present invention. Detailed Implementation

[0015] The present invention will be further described in detail below through specific embodiments. The following embodiments are merely descriptive and not limiting, and should not be used to limit the scope of protection of the present invention.

[0016] like Figure 1 As shown, a method for identifying the linear shape of nonlinear geometric components of bridges based on three-dimensional laser scanning is innovative in that the method comprises the following steps: Step 1: Distribute the monitoring stations evenly according to the terrain of the bridge location and set up targets to collect point cloud data from each station. Then, import the data into Cyclone software for analysis. Use its Constraints (Target) function to register the point clouds of multiple monitoring stations by constraining the targets. Finally, save the registered point cloud as a .txt or .las file to obtain the full bridge point cloud. Step 2: Use principal component analysis to calibrate the spatial pose of the bridge point cloud, ensuring that the spatial pose of the bridge body is orthogonal to the Cartesian coordinate system. The specific steps for spatial pose calibration are as follows: Step 2.1: Calculate the covariance matrix of the point cloud and solve for its eigenvalues ​​and eigenvectors. Before solving for the covariance matrix, the three-dimensional coordinate matrix of the point cloud is first decentered. Step 2.2: Take the eigenvectors corresponding to the two largest eigenvalues. and As basis vectors of the point cloud, the other principal directions satisfy: ; Step 2.3: Transfer the point cloud data , The coordinates are transformed along the principal axis direction, and the first principal axis direction is used as the coordinate axis after transformation. Direction, the direction of the second principal axis as Direction, the third principal axis direction as direction.

[0017] In step 2, the point cloud decentralization processing formula is as follows: ; in, For matrix The Line number The elements of the column.

[0018] In step 2, the formula for calculating the covariance matrix of the point cloud is as follows: ; in, The coordinate data is the decentralized version of the point cloud. For matrix The transpose of the matrix, This represents the number of point clouds.

[0019] Step 3: Orthogonally project the component point cloud onto the normal plane of the local principal curvature direction, and use polynomial fitting to fit the projected point cloud to obtain the approximate axis curve of the entire component. See Figure 2 ; Step 4: Select a slicing location point on the approximate axis, determine the initial slicing direction by calculating the slope of the axis at that point, set the slicing thickness, and perform slicing processing on all control points to obtain the contour point cloud of the control section; In step 4, the slice thickness The specific principles for setting up control points and the method for slicing control points are: slice thickness. Determined by both local point cloud density and local curvature, it is recommended The value should be greater than 10 times the point cloud spacing and less than the radius of curvature of the component axis. A local coordinate system is formed by the tangent vector and the corresponding normal plane. The extracted point cloud segment is projected onto the normal plane to obtain the cross-sectional point cloud of that point.

[0020] Step 5: Using the intersection of the initial slice center and the initial axis of the component as the rotation center, set the rotation range based on the initial slice angle to establish a search space. Within this range, subdivide the search space using the golden section method to generate potential optimal slices as candidate angle values. The specific process of subdividing the search space using the golden section method is as follows: Step 5.1: Calculate the local density standard deviation of all point clouds in the current slice. Determine if the slice angle meets the accuracy requirements. ( If the threshold set by the user is met, proceed to the next step; otherwise, directly calculate the centroid coordinates of the measurement point. Step 5.2: Using the intersection of the slice center and the component axis as the rotation center, based on the initial slice angle... Set rotation range To establish a search space ,See Figure 3 The search space is subdivided using the golden section method within the interval to generate potential optimal slices as candidate angle values. The subdivision points are as follows: ; in, The golden ratio is . and These are the interior points of the section determined by the golden ratio. and These are the boundary points of the angle search space; Step 5.3: Calculate the local density standard deviation of the point cloud in all potential optimal slices (including boundary points and segmentation points), and determine it according to the method in Step 1; Step 5.4: Compare the minimum local point cloud density standard deviation among all candidate slices. Compared with the preset accuracy threshold The algorithm determines whether to shrink the search area. If there is a candidate angle that meets the cross-sectional accuracy requirements, the iteration is terminated and the optimal slice angle is output. Otherwise, the search area is updated based on the golden ratio, the inferior angle area with the largest standard deviation is removed, and the optimal slice is searched again in the new area until a slice angle that meets the accuracy requirements is found. Step 5.5: Repeat the above steps until the optimal slice for all measuring points is determined. See [link to step 5]. Figure 4 .

[0021] Step 6: Calculate the standard deviation of local point cloud density for all candidate slice sections. Based on this, determine whether the current slice angle meets the accuracy requirements. If the requirements are not met, the inferior solution interval is eliminated, the search interval is shrunk, and the golden section method is used again to approximate the optimal slice angle; otherwise, it is extracted as the optimal cross-sectional point cloud. In step 6, the formula for calculating the standard deviation of the local point cloud density of all data points in the sliced ​​point cloud is as follows: ; in, The standard deviation of the local point cloud density of a data point in a slice. For local point cloud density, for The mean, This represents the number of point clouds.

[0022] In step 6, the formula for calculating the local surface density of the cross-sectional profile point cloud is as follows: ; in, For local point cloud density, For the current point Nearby point, From the current point to the farthest point The distance is close.

[0023] In step 6, the formula for calculating the mean local point cloud density of all data points in the sliced ​​point cloud is as follows: ; in, for The mean.

[0024] Step 7: Filter the optimal cross-sectional point cloud of all control points, and extract the cross-section with the smallest local point cloud density standard deviation as the standard point cloud model of the feature cross-section; Step 8: Use Protodyakonov analysis theory to perform global shape matching between the measured slice point cloud and the standard point cloud model to maximize the overlap between the two point clouds. See [link to relevant documentation]. Figure 5 The specific steps are as follows: Step 8.1: Given a string containing A matrix of points and , representing the coordinates on the standard point cloud model and the measured cross-sectional profile, respectively. This represents the dimension used in coordinate transformation calculations. To achieve matching, the matrix needs to be... Perform coordinate transformation to make it correspond to the matrix to the greatest extent possible. : ; in, It is a rotation matrix, for An orthogonal identity matrix, representing a matrix Coordinate transformation involving rotation around the origin of the coordinate system. It is a translation vector, which is The column vectors represent the matrix. Along vector Perform coordinate transformations for translation. . Here is the error matrix. The shift parameter with the smallest square of the L2 norm and The following formula is used: ; Step 8.2: Based on the properties of orthogonal matrices, the obtained matrix can be... Singular value decomposition can be performed using the following formula: ; Step 8.3: By analyzing... The matrix obtained by performing singular value decomposition is , and The coordinate transformation parameters can be calculated using the following formula: ; ; Step 9: Calculate the theoretical centroid coordinates of the standard point cloud model, and use the coordinate transformation parameters obtained by global shape matching to map them to the measured cross-sectional profile, thereby determining the centroid coordinates of the control section; In step 9, the theoretical centroid coordinates of the standard point cloud model are calculated using the following formula: ; in, The theoretical centroid coordinates of the standard point cloud model. The number of points in a standard point cloud model. This is the mean of the coordinate values.

[0025] In step 9, the mapping formula for the centroid coordinates of the measured cross-section profile is as follows: ; in, These are the true centroid coordinates of each measured optimal slice.

[0026] Step 10: Integrate the centroid coordinate extraction results of all control section contour point clouds to obtain complete full bridge linear feature points.

[0027] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A bridge nonlinear geometric component alignment identification method based on three-dimensional laser scanning, characterized in that: The steps of the method are as follows: S1. A ground-based laser scanner combined with a target is used to perform sub-station scanning of the entire bridge. Based on the target, the point cloud data of multiple measurement stations is registered to the same coordinate system. The measured point cloud data is analyzed using Cyclone software, and its Constraints (Target) function is used to achieve the registration of the point cloud data of multiple measurement stations by constraining the target. Finally, the registered point cloud is saved in a common format of .txt or .las to obtain the bridge point cloud data. S2. Use principal component analysis to calibrate the spatial pose of the bridge point cloud data so that the spatial pose of the bridge body is orthogonal to the rectangular coordinate system. S3. Project the point cloud of the bridge component orthogonally onto the normal plane of the local principal curvature direction, and use polynomial fitting to fit the projected point cloud to obtain the approximate axis curve of the entire component. S4, select the slice position point on the approximate axis curve, determine the initial slice direction by calculating the slope of the axis at the point, and set the slice thickness and slice all control points with the slice thickness The value is determined by the local point cloud density and the local curvature, which is greater than 10 times the point cloud spacing and less than the curvature radius of the component axis A local coordinate system is formed by the tangent vector and the corresponding normal plane, the intercepted point cloud segment is projected onto the normal plane to obtain the cross-section point cloud of the point; finally, the profile point cloud of the control section is obtained; S5. Using the intersection of the initial slice center and the initial axis of the component as the rotation center, set the rotation range based on the initial slice angle to establish a search space. Within this range, use the golden section method to subdivide the search space to generate potential optimal slices as candidate angle values. S6、Calculate the local point cloud density standard deviation of all candidate slice sections According to this, it is judged whether the current slice angle meets the accuracy requirement. If not, the poor solution interval is eliminated, the search interval is contracted, and the golden section method is used again to approximate the optimal slice angle, otherwise, it is extracted as the optimal cross-section point cloud. S7. Filter the optimal cross-sectional point cloud of all control points, and extract the cross-section with the smallest local point cloud density standard deviation as the standard point cloud model of the feature cross-section. S8. Use Protodyakonov's analysis theory to perform global shape matching between the measured slice point cloud and the standard point cloud model to maximize the overlap between the two point clouds. S9. Calculate the theoretical centroid coordinates of the standard point cloud model, and use the coordinate transformation parameters obtained by global shape matching to map them to the measured cross-sectional profile to determine the centroid coordinates of the control section. S10. Integrate the centroid coordinate extraction results of all control section contour point clouds to obtain complete bridge full-bridge linear feature points.

2. The bridge nonlinear geometric component alignment identification method based on three-dimensional laser scanning according to claim 1, characterized in that: The calibration of S2 is specifically as follows: 1) Calculate the covariance matrix of the point cloud and solve for its eigenvalues ​​and eigenvectors. Before solving for the covariance matrix, first decenter the 3D coordinate matrix of the point cloud. The formula for calculating the covariance matrix of a point cloud is: ； wherein: is the coordinate data of the point cloud after decentralization, is a matrix is the transpose matrix of is the number of point clouds; The decentralized calculation formula is: ； wherein: is the element of matrix in row and column ; 2) Take the eigenvectors corresponding to the two largest eigenvalues. and As basis vectors of the point cloud, the other principal directions satisfy: ; 3) Transfer point cloud data , The coordinates are transformed along the principal axis direction, and the first principal axis direction is used as the coordinate axis after transformation. Direction, the direction of the second principal axis as Direction, the third principal axis direction as direction.

3. The method for identifying the linear shape of nonlinear geometric components of bridges based on three-dimensional laser scanning according to claim 1, characterized in that: The S5 method of subdividing the search space using the golden ratio is as follows: 1) Calculate the local density standard deviation of all point clouds in the current slice. Determine if the slice angle meets the accuracy requirements. , If the threshold set by the user is met, proceed to the next step; otherwise, directly calculate the centroid coordinates of the measurement point. 2) Using the intersection of the slice center and the component axis as the rotation center, based on the initial slice angle... Set rotation range To establish a search space The search space is subdivided using the golden section method within the interval to generate potential optimal slices as candidate angle values. The subdivision points are as follows: ； in: The golden ratio is . and These are the interior points of the section determined by the golden ratio. and These are the boundary points of the angle search space; 3) Calculate the local density standard deviation of the point cloud in all potential optimal slices, including boundary points and segmentation points, and determine it according to the method in 1); 4) By comparing the minimum local point cloud density standard deviation among all candidate slices Compared with the preset accuracy threshold The algorithm determines whether to shrink the search area. If there is a candidate angle that meets the cross-sectional accuracy requirements, the iteration is terminated and the optimal slice angle is output. Otherwise, the search area is updated based on the golden ratio, the inferior angle area with the largest standard deviation is removed, and the optimal slice is searched again in the new area until a slice angle that meets the accuracy requirements is found. 5) Repeat the above steps until the optimal slice for all measuring points is determined.

4. The method for identifying the linear shape of nonlinear geometric components of bridges based on three-dimensional laser scanning according to claim 1, characterized in that: The formula for calculating the standard deviation of the local point cloud density of all data points in the sliced ​​point cloud in S6 is as follows: ； in: The standard deviation of the local point cloud density of a data point in a slice. For local point cloud density, for The mean, The number of point clouds; The formula for calculating the local surface density of the point cloud of the cross-sectional profile is: ； in: For local point cloud density, For the current point Nearby point, From the current point to the farthest point The distance between them; The formula for calculating the mean local point cloud density of all data points in a sliced ​​point cloud is as follows: ； in: for The mean.

5. The method for identifying the linear shape of nonlinear geometric components of bridges based on three-dimensional laser scanning according to claim 1, characterized in that: Specifically, S8 uses Protodyakonov analysis theory to perform global shape matching between the measured slice point cloud and the standard point cloud model: Given containing A matrix of points and , representing the coordinates on the standard point cloud model and the measured cross-sectional profile, respectively. This represents the dimension used in coordinate transformation calculations; to achieve matching, the matrix needs to be... Perform coordinate transformation to make it correspond to the matrix to the greatest extent possible. : ； in: It is a rotation matrix, for An orthogonal identity matrix, representing a matrix Coordinate transformation involving rotation around the origin of the coordinate system; It is a translation vector, which is The column vectors represent the matrix. Along vector Perform coordinate transformations for translation; ; Here is the error matrix. The shift parameter with the smallest square of the L2 norm and The following formula is used: ； Wherein: Based on the properties of orthogonal matrices, the obtained... Singular value decomposition can be performed using the following formula: ； in: , and for The coordinate transformation parameters of the matrix obtained by singular value decomposition can be calculated using the following formula: ； 。 6. The method for identifying the linear shape of nonlinear geometric components of bridges based on three-dimensional laser scanning according to claim 1, characterized in that: The theoretical centroid coordinate calculation formula for the S9 standard point cloud model is as follows: ； in: The theoretical centroid coordinates of the standard point cloud model. The number of points in a standard point cloud model. The mean of the coordinate values; The mapping formula for the centroid coordinates of the measured cross-section profile is: ； in: These are the true centroid coordinates of each measured optimal slice.

Images