Structural point cloud principal axis identification method based on adaptive weighted principal component analysis

Abstract

The invention relates to the technical field of engineering surveying and mapping, in particular to a structural point cloud principal axis identification method based on adaptive weighted principal component analysis, which comprises the following steps: acquiring a point cloud data set, initializing a weight set, and performing weighted centralization on the point cloud data set after point cloud downsampling; calculating a weighted covariance matrix according to the point cloud data set after weighted centralization, and obtaining a feature value and a normalized feature vector through the weighted covariance matrix; obtaining a distance measurement set of all point clouds; calculating an iteration weight set; and calculating the eigenvalue of the weighted covariance matrix and outputting an iterative spindle rotation angle. In the application of the method, along with the increase of the complexity of the point cloud, the advantage of adaptive weight estimation is more remarkable than that of common scale estimation, so that the high-precision rapid convergence performance when the common scale estimation is used for processing the uniform and symmetrical point cloud is reserved; and interference of outliers and environmental noise points on main shaft identification can be effectively prevented when highly non-uniform distribution point clouds are processed.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of engineering surveying and mapping, and particularly relates to a structural point cloud principal axis identification method based on adaptive weighted principal component analysis. BACKGROUND

[0002] Principal component analysis (PCA) is a core tool for identifying the principal axis of the point cloud of an engineering structure due to its mathematical simplicity, high efficiency and strong adaptability to linear structures.

[0003] However, PCA is strongly sensitive to the spatial distribution of the point cloud: when the point cloud density distribution is uneven, there are outliers or environmental noise points, the calculation result of the covariance matrix deviates from the true principal axis direction of the structure. Although for most engineering structures, the significant scale difference between the longitudinal direction (span direction) and the transverse direction (cross-section direction) helps to determine the longitudinal principal axis by the maximum variance direction, in actual calculation, various factors will interfere with accurate identification: the lack of geometric symmetry, the existence of auxiliary components and noise point clouds introduced in the point cloud acquisition process, etc. Figure 18 As shown in the box girder point cloud under complex conditions, although the main axis can be identified by the PCA method, there are still obvious local interferences, which affect the accuracy of the principal axis identification.

[0004] Ideally, the spatial point cloud of an engineering structure obtained by scanning is a uniform and symmetric point cloud. However, in the actual application scene of scanning an engineering structure, it is limited by the field of view angle of the laser scanner and the constraint of the scanning station site, resulting in unavoidable blind areas and occluded areas in the point cloud acquisition process; at the same time, the geometric complexity of the engineering structure further increases the spatial non-uniformity of the sampling density. This non-uniformity is manifested in the point cloud data as a density gradient change along the local coordinate system direction: high-density sampling point clusters are formed in the surface area facing the scanner and the structure edges, while the areas far from the scanning station, the surfaces with large incident angles and the occluded structure parts show obvious low-density distribution characteristics. This non-uniform sampling characteristic poses a severe challenge to the subsequent symmetry analysis process.

[0005] The research results of the application prove that the scale parameter of a single probability distribution model has inherent limitations in processing non-uniform symmetric point clouds, and it cannot adapt to the changing statistical characteristics of non-uniform symmetric point clouds in the iterative distance measurement process, thereby introducing adaptive scale estimation to propose a structural point cloud principal axis identification method based on adaptive weighted principal component analysis, which improves the accuracy and robustness of the algorithm in the principal axis identification of the point cloud of an engineering structure. SUMMARY

[0006] The purpose of this invention is to provide a method for identifying the principal axes of structural point clouds based on adaptive weighted principal component analysis, so as to solve the technical problems of insufficient accuracy and robustness of existing principal component analysis algorithms in identifying the principal axes of point clouds. The specific technical solution is as follows: This invention provides a method for identifying the principal axes of structural point clouds based on adaptive weighted principal component analysis, comprising the following steps: S1. Obtain the point cloud dataset, perform denoising on the point cloud dataset, and obtain the denoised point cloud dataset. S2. Perform point cloud downsampling on the denoised point cloud dataset; S3. Initialize the weight set The point cloud dataset after downsampling is then weighted and centered; among which, Point cloud The weight, Represents the set of initial weights. The code name for point clouds; S4. Based on the weighted and centered point cloud dataset, calculate the weighted covariance matrix, and obtain the eigenvalues ​​and corresponding normalized eigenvectors through the weighted covariance matrix. S5. Select the largest eigenvalue among the eigenvalues. The corresponding normalized feature vector As the direction of the principal axis of symmetry, and transformed into the principal axis rotation angle, through the eigenvectors Obtain the plane equation Then, based on the principal axis of symmetry plane equation and a reasonable angle threshold, symmetric points are searched to obtain the corresponding set of symmetric points. The nearest Euclidean distance between the symmetric points in the set is calculated to obtain the left-side point cloud segmented by the axis of symmetry. Distance metric set of all point clouds ,in This represents the matrix transpose operation. Describes the coefficients of the plane equation. Represents the constant term in the plane equation; S6, according to the first Substatistic distance metric set Calculate the iterative weight set and using the updated weight set Re-execute S3 through S6; S7. Set the spindle rotation angle convergence threshold. When the spindle rotation angles of two iterations are adjacent, the error Alternatively, if the system reaches a convergent state within a stable iteration interval, the eigenvalues ​​of the weighted covariance matrix are calculated, and the rotation angle of the iteration principal axis is output.

[0007] The improved adaptive weighted principal component analysis-based structural point cloud principal axis identification method of the application is improved in that S2 is specifically: the point cloud data set after denoising is subjected to point cloud down-sampling by using a voxel grid-based random down-sampling filtering method.

[0008] The improved adaptive weighted principal component analysis-based structural point cloud principal axis identification method of the application is improved in that the point cloud data set in S1 comprises spatial coordinates and reflection intensity information.

[0009] The improved adaptive weighted principal component analysis-based structural point cloud principal axis identification method of the application is improved in that when the point cloud data set after point cloud down-sampling is subjected to weighted centering, the calculation expression is as formula 1): 1); In the formula, is a weighted centroid of the point cloud data, s is a weight sum, is a point cloud quantity, is a three-dimensional coordinate (position vector) of the point cloud . The spatial coordinates of each dimension in the point cloud data set after point cloud down-sampling are subtracted by the weighted mean value of the corresponding dimension, wherein: the weight set is initialized, and all the weights are 1.

[0010] The improved adaptive weighted principal component analysis-based structural point cloud principal axis identification method of the application is improved in that the calculation formula of the weighted covariance matrix in S4 is as follows: 2); In the formula, is a weighted covariance matrix ， is a horizontal coordinate of the point cloud . is a vertical coordinate of the point cloud .

[0011] The improved adaptive weighted principal component analysis-based structural point cloud principal axis identification method of the application is improved in that S5 specifically comprises the following steps: S501, selecting the maximum eigenvalue in the eigenvalues calculated in step S4 as the corresponding eigenvector as the principal symmetry axis direction, and transforming into a principal axis rotation angle, obtaining a plane equation through the eigenvector . Then, based on the principal symmetry axis plane equation and a reasonable angle threshold, symmetric points are searched, the test point cloud set is segmented into symmetric point cloud sets about the initial symmetric plane through the plane equation, and the symmetric point cloud set comprises a left point cloud split by the symmetric axis and a right point cloud split by the symmetric axis. S502, adopts Calculate the point cloud normal features for each neighboring point, if the point cloud on the right... Arbitrary point cloud Unit normal vector and symmetric point cloud The unit normal vector satisfies formula 3), so this point is retained and merged into a point cloud. ,in, This represents the angle between the normal vector of a point that meets the conditions and the normal vector of a point in the symmetrical point cloud; 3); in, Represents the midpoint of a symmetrical point cloud. The normal vector, Point The normal vector, Represents the midpoint of a symmetrical point cloud. 3D coordinates (position vector), with apostrophe The normal vector represents the normal vector of a point in a symmetric point cloud. The angle threshold is represented by the neighboring points, and the nearest neighboring points are represented by the nearest neighboring points. Through a large number of experiments, researchers have found that for many common density point cloud data, 10 neighboring points can smooth noise well without losing details, and are a good "default value".

[0012] S503, Search Point Cloud Regarding symmetrical point clouds Find the nearest Euclidean distance point and calculate the nearest Euclidean distance of the corresponding point cloud. This yields the correspondence regarding distance metrics. Traverse the left-side point cloud Afterwards, information about the point cloud on the left side was obtained. Distance metric set of all point clouds ,in, Representing points in a point cloud Or a set of points, containing position and normal vector information.

[0013] The improvement of the structural point cloud principal axis identification method based on adaptive weighted principal component analysis in this invention lies in the fact that, in calculating the iterative weight set... At that time, according to the first Substatistic distance metric set ,based on The weight estimation function updates the weight set for the next iteration. The expression is as follows: 4); in, It is a time-varying equation with low complexity. This represents the nearest Euclidean distance to the corresponding point cloud. Indicates the distance threshold. It is an iterative weight set The elements in the array represent the weights of the corresponding point clouds.

[0014] The improvement of the structural point cloud principal axis identification method based on adaptive weighted principal component analysis in this invention lies in the following: The robust scaling function for the absolute deviation of the median, based on an unknown mean, is specifically formulated as follows: 5); 6); 7); in, This represents the adaptive weight estimator for the robust scaling function based on the absolute deviation of the median when the mean is unknown. For summation of the exponential weight function with unknown mean, Indicates exponent or power. These correspond to the exponential weighting function based on an unknown mean. and Summation, This represents median operations. Represents all point clouds the median of This represents the standardized residuals with an unknown mean. This represents the k-th power of the standardized residuals with an unknown mean. It represents the base of the natural logarithm.

[0015] The application of the technical solution of the present invention has the following beneficial effects: This invention discloses a method for identifying the principal axis of structural point clouds based on adaptive weighted principal component analysis. It utilizes 3D laser scanning to acquire the linear shape of engineering structures. The identification method includes the following steps: acquiring an original engineering structure point cloud dataset; downsampling the acquired point cloud; initializing a weight set; and weighting and centering the downsampled point cloud dataset. Based on the weighted and centered point cloud dataset, a weighted covariance matrix is ​​calculated. Eigenvalues ​​and normalized eigenvectors are obtained from the weighted covariance matrix. The principal axis rotation angle is obtained from the eigenvectors. Based on the obtained principal axis, the point cloud is divided into two parts: the left point cloud and the right point cloud. and the point cloud on the right Traverse the left-side point cloud For each point cloud, calculate the points during each traversal. Reflection symmetry point about the plane of symmetry If the point cloud on the right any point in the middle The unit normal vector and the symmetric point If the unit normal vector satisfies the condition, the points are retained and merged into a point cloud. Search point cloud China regarding Find the nearest Euclidean distance point and calculate the nearest Euclidean distance of the corresponding point cloud. This yields the correspondence regarding distance metrics. Traverse the left-side point cloud Afterwards, information about the point cloud on the left side was obtained. The initial distance metric set of all point clouds ; Calculate the iterative weight set; Calculate the eigenvalues ​​of the weighted covariance matrix based on the updated iterative weight set, and output the iterative principal axis rotation angle. Continue this process until the principal axis rotation angles of two iterations are adjacent. Alternatively, it may reach a convergence state when it is in a stable iteration range, and output the optimal spindle rotation angle.

[0016] Specifically, the structural point cloud principal axis identification method based on adaptive weighted principal component analysis provided in this embodiment has at least the following beneficial effects: (1) Using a three-dimensional laser scanner to perform laser scanning on the engineering structure, without direct contact with the structure, the point cloud data of the engineering structure can be obtained quickly and accurately, which greatly saves measurement time and labor costs, reduces safety risks in the measurement process, and ensures the integrity of the engineering structure. (2) By scanning the engineering structure, the appearance and model of the engineering structure under test can be obtained, which has high surveying accuracy and replaces manual surveying; (3) It is not affected by the structural shape and size of the engineering structure under test, and can be applied to engineering structures of various forms and scales. It has high versatility and applicability, and provides reliable technical support for the design, evaluation and maintenance of engineering structures. (4) As the complexity of point clouds increases, the advantages of adaptive weight estimation compared with commonly used scale estimation become more and more significant. It retains the high accuracy and fast convergence capability of commonly used scale estimation when processing uniform symmetrical point clouds, and can effectively prevent outliers and environmental noise points from interfering with the identification of principal axes when processing highly non-uniformly distributed point clouds. It solves the technical problem of insufficient accuracy and robustness of principal component analysis algorithm in point cloud principal axis identification in the prior art.

[0017] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0018] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the application and, together with the description, serve to explain the application. In the drawings: Figure 1 is a flow chart of the structural point cloud principal axis recognition method of the present application based on adaptive weighted principal component analysis; Figure 2 is a non-uniform symmetric point cloud data graph of a scanned bridge (in the figure represents the rotation angle of the laser emitting device in the horizontal plane, represents the rotation angle of the laser emitting device in the vertical plane); Figure 3 is a down-sampling point cloud graph after voxel grid with a grid resolution parameter of 0.1 m; Figure 4 is a down-sampling point cloud graph after voxel grid with a grid resolution parameter of 0.2 m; Figure 5 is a down-sampling point cloud graph after voxel grid with a grid resolution parameter of 0.3 m; Figure 6 is a searched point cloud when the angle threshold is 10° (red points are the points to be searched, and green points are the searched point cloud); Figure 7 is a searched point cloud when the angle threshold is 20° (red points are the points to be searched, and green points are the searched point cloud); Figure 8 is a searched point cloud when the angle threshold is 30° (red points are the points to be searched, and green points are the searched point cloud); Figure 9 is a searched point cloud when the angle threshold is 40° (red points are the points to be searched, and green points are the searched point cloud); Figure 10 is a point cloud initial iteration elimination effect graph (red marks are outlier points or environmental noise points); Figure 11 is a point cloud iteration outlier and environmental noise point marking graph (from iteration once to iteration twenty times to iteration forty times); Figure 12 is a point cloud outlier marking graph after 40 times of iteration in the scale estimation in the prior art; Figure 13 is a point cloud outlier marking after 40 times of iteration in adaptive weight estimation; Figure 14 is a point cloud principal axis rotation angle iteration effect; Figure 15 For point clouds Iterative effect of spindle rotation angle; Figure 16 For point clouds Iterative effect of spindle rotation angle; Figure 17 For point clouds In the periodic iteration interval of adaptive weight estimation, the yellow interval represents one cycle (where the red line represents the adaptive weight estimation factor). of The estimated principal axis iteration effect, with the black line representing the estimation factor based on a single scale. The main axis iteration effect, the blue line represents the adaptive weight estimation factor. of (Estimated spindle iteration effect); Figure 18 The PCA spindle recognition effect of bridges under complex working conditions. Detailed Implementation

[0019] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0020] See Figures 1-18 As shown, a method for identifying the principal axes of structural point clouds based on adaptive weighted principal component analysis includes the following steps: S1. Obtain the point cloud dataset of the bridge, and perform cloud noise processing on the point cloud dataset to obtain a denoised point cloud dataset. Specifically, use Cloudcompare software (an open-source 3D point cloud processing software) to manually remove obvious noise points (including point clouds of construction workers and railing components on the bridge deck); for example... Figure 1 The bridge point cloud dataset shown was acquired using a Leica ScanStation P50 long-range 3D laser scanner to obtain spatial point cloud data (arch foot + tie beam plane) of a symmetrical structure in a local part of the bridge. Preferably, the point cloud dataset is stored in pcd format (an image storage format) containing spatial coordinates and reflection intensity information.

[0021] S2. Considering the large size of the original point cloud dataset, a voxel grid-based random downsampling filtering method is used to downsample the point cloud dataset after denoising. Specifically, multiple sets of voxel grid resolution parameters were set in the experiment. (Number of point clouds: 21840) (Number of point clouds: 5641) (Number of point clouds:) Conduct comparative tests, such as Figures 3-5 As shown. After considering both the number of sampling points and the preservation of geometric information, the raster resolution was determined. The downsampled point cloud is used as the input point cloud for subsequent analysis. .

[0022] S3. Initialize the weight set The point cloud dataset after downsampling is then weighted and centered; among which, Point cloud The weight, Represents the set of initial weights. The code name for point clouds; Preferably, when performing weighted centering on the downsampled point cloud dataset, the calculation expression is as shown in Equation 1), and the updated weight set is used in each iteration. Perform the calculation: 1); In the formula, Weight the centroid of the point cloud data. The weighting coefficients assigned to the point cloud. s The sum of weights For the number of point clouds, For point clouds The three-dimensional coordinates (position vector); Subtract the weighted mean of the corresponding dimension from the spatial coordinates of each dimension in the downsampled point cloud dataset, where all weights except the initial weight set are 1.

[0023] S4. Based on the weighted and centered point cloud dataset, calculate the weighted covariance matrix, and obtain the eigenvalues ​​and corresponding normalized eigenvectors from the weighted covariance matrix; the calculation formula is as follows: 2); in, The weighted covariance matrix ， For point clouds x-axis, For point clouds The vertical axis.

[0024] S5. Select the largest eigenvalue among the eigenvalues. The corresponding normalized feature vector As the direction of the principal axis of symmetry, and transformed into the principal axis rotation angle, through the eigenvectors Obtain the plane equation Then, based on the principal symmetry axis plane equation and a reasonable angle threshold (generally within...), Search for symmetrical points (left and right) to obtain the corresponding set of symmetrical points. Calculate the nearest Euclidean distance between the symmetrical points in the set to obtain the left-side point cloud segmented by the axis of symmetry. Distance metric set of all point clouds ,in This represents the matrix transpose operation. Describes the coefficients of the plane equation. Represents the constant term in the plane equation; Furthermore, S5 specifically includes the following steps: S501. Select the largest eigenvalue from the eigenvalues ​​calculated in step S4. Corresponding feature vector As the direction of the principal axis of symmetry, and transformed into the principal axis rotation angle, through the eigenvectors Obtain the plane equation Then, based on the principal symmetry axis plane equation and a reasonable angle threshold (generally within...), (Left and right) Search for symmetric points, and divide the test point cloud into symmetric point clouds about the initial symmetric plane using the plane equation. The symmetric point clouds include the left point cloud divided by the axis of symmetry. And the right-side point cloud divided by the axis of symmetry ; S502, adopts Calculate the point cloud normal features for each neighboring point, if the point cloud on the right... Arbitrary point cloud Unit normal vector and symmetric point cloud The unit normal vector satisfies formula 3), so this point is retained and merged into a point cloud. ,in, This represents the angle between the normal vector of a point that meets the conditions and the normal vector of a point in the symmetrical point cloud; 3); in, Represents the midpoint of a symmetrical point cloud. The normal vector, Point The normal vector, Represents the midpoint of a symmetrical point cloud. 3D coordinates (position vector), with apostrophe The normal vector represents the normal vector of a point in a symmetric point cloud. Indicates the angle threshold, as studied Generally taken This avoids the noise matching phenomenon that may be introduced by a large threshold, while also overcoming the problem of insufficient coverage caused by a small threshold. Neighborhood points represent the nearest points. For many common density point cloud data, 10 neighborhood points can smooth out noise well without losing details, which is a good "default value". like Figures 6-9 Search for symmetrical point clouds for different angle thresholds (red dots are the points to be searched, and green dots are the symmetrical point clouds to be searched).

[0025] S503、search point cloud the closest Euclidean distance of the symmetric point cloud , the closest Euclidean distance of the corresponding point cloud is counted , and the corresponding relationship about the distance metric is obtained , traverse the left point cloud , and obtain the distance metric set of all point clouds in the left point cloud , the distance metric set , wherein represents a point in the point cloud or a point set, containing position and normal vector information. S6, according to the first

[0026] statistical distance metric set , calculate the iteration weight set , and re-execute S3 to S6 using the updated weight set Preferably, when calculating the iteration weight set , according to the first statistical distance metric set , based on estimate weight estimation function to update the next iteration weight set , the expression is as follows: 4); wherein is a median absolute deviation robust scale estimation function based on unknown mean, represents the closest Euclidean distance of the corresponding point cloud, represents the distance threshold, if represents if, otherwise represents otherwise. GM estimation weight refers to the correlation degree between each index and comprehensive rating calculated by grey correlation analysis method in grey system theory, and then the weight of each index is determined.

[0027] Further, is a median absolute deviation robust scale estimation function based on unknown mean, and the specific formula is as follows: 5); 6); 7); wherein represents an adaptive weight estimation factor based on a median absolute deviation robust scale estimation function based on unknown mean, is the sum of the exponential weight function based on unknown mean,​​ denotes an index or power, corresponds to the sum of the exponential weight function based on the mean unknown (counting weight) and (counting weight), denotes a median operation, denotes the median of all of the point cloud, denotes a standardized residual, denotes the k-th power based on the standardized residual of the mean unknown, denotes the base of the natural logarithm, denotes that this is the median absolute deviation centered on the median; S7, according to the weight set calculated in step S6 , the eigenvalues of the weighted covariance matrix are calculated, and the maximum eigenvalue corresponding eigenvector is selected as the principal axis direction, and is transformed into the principal axis rotation angle.

[0028] The principal axis rotation angle convergence threshold is set, and when the adjacent error of the principal axis rotation angle of two iterations is less than or equal to the convergence threshold, the convergence state is reached, and the iteration principal axis rotation angle is output. Otherwise, S1 to S6 are re-executed. As Figure 13 , the point cloud outlier marker gradually decreases with the increase of the number of iterations.

[0029] Figure 1 is the flowchart of the structure point cloud principal axis recognition method based on adaptive weighted principal component analysis of the present application, and the specific process is: obtaining a spatial point cloud with a local symmetrical structure from the input point cloud data , and preprocessing it, the preprocessing includes downsampling and denoising, obtaining an initial weight set, then calculating the point cloud features, then judging whether the principal symmetrical plane converges? If yes, output the principal axis rotation angle; if not, add the data filtered by the normal vector, search for symmetrical points, obtain the metric set of the nearest distance from the symmetrical points, then update the point cloud iteration by adaptive scale estimation, and finally return to the initial weight set.

[0030] The application is based on a structure point cloud principal axis identification method of adaptive weighted principal component analysis, obtains engineering structure line shape based on three-dimensional laser scanning, the method belongs to non-contact measurement, field measurement time is short, and point cloud data extraction automation degree is high.The application has the advantages that, with the increase of point cloud complexity, the adaptive weight estimation has more and more obvious advantages compared with the common scale estimation, the common scale estimation retains the high-precision fast convergence ability when processing uniform and symmetric point clouds, and can effectively prevent the interference of outlier points and environmental noise points on principal axis identification when processing highly non-uniformly distributed point clouds, and solves the technical problems of the insufficient precision and robustness of the principal component analysis algorithm in the prior art in point cloud principal axis identification.

[0031] Finally, in order to show the advantages of the application, the adaptive weighted principal component analysis based structure point cloud principal axis identification method of the application is compared with the detection method in the prior art.

[0032] In order to study the robustness of a single scale estimation factor in the principal axis identification of non-uniformly symmetric point clouds, without changing the significant discrete points and environmental noise points, the input point cloud is resampled, and the sampling process only simply changes the segmentation angle of the arch foot horizontal bridge point cloud as the input point cloud .

[0033] Among them, the point cloud is the spatial point cloud data (arch foot + tie beam plane) of the bridge local symmetrical structure obtained by the Leica ScanStation P50 long-range three-dimensional laser scanner in the specific embodiment; In order to study the principal axis identification effect of the improved weighted PCA algorithm based on adaptive weight estimation in non-uniformly symmetric point clouds, the application performs angle iteration test on the non-uniformly symmetric point cloud and the uniformly symmetric point cloud Armadillo, presets an upper limit of iteration and adds a common scale estimation for comparative analysis, and the result is as shown in Figures 14-16 .

[0034] Among them, the discrete experimental data set is derived from the Stanford data set: Armadillo, derived from the high-precision three-dimensional model database constructed by Stanford University; The common scale estimation of different point clouds is processed by a smoothing strategy, so that the convergence performance under the oscillation condition is comparable with the adaptive weight estimation result, and the result is as shown in Figure 15 . Under the adaptive weight estimation, there is a periodic iteration cycle interval, and the angle mean value in the interval is used as the convergence result, and the result is as shown in Figure 17 .

[0035] Finally, a systematic analysis of the angle convergence performance of the three sets of point clouds was conducted using the traditional commonly used scale estimation weighted PCA algorithm and the improved weighted PCA algorithm, respectively. The influence of different estimation methods on the convergence interval was quantified, and the statistical results are shown in Table 1.

[0036] in, Based on the mean Improved robust scaling function for median absolute bias: 8); 9); in: 10); in, Indicates based on the mean An adaptive weight estimator for the improved robust scaling function of median absolute bias. Indicates based on the mean The summation of the exponential weighting function, Indicates exponent or power. , Corresponding to the mean as The exponential weighting function in (Counting weights) and Summation of (counting weights), Indicates based on the mean Standardized residuals This indicates that the median absolute deviation is centered at zero (mean).

[0037] illustrate: When using a function, it means... In the formula Replace with Everything else remains the same, and functions and The difference between the functions is that one is based on a mean of 0, while the other is based on a mean that is unknown.

[0038] Sometimes, the principal axis rotation angle, under iterative calculation with a small-scale estimator, exhibits stable periodic oscillations near its precise value, such as... Figure 17 To assess the impact of different scale estimators on the angle convergence interval, it is necessary to determine the smaller scale estimator. The stable equilibrium value under the condition is processed using a smoothing strategy based on formula 11) to extract the central trend of the rotation angle change, so that the convergence performance under the oscillation condition is comparable to the convergence results under other scale factor conditions.

[0039] 11); 1. Initialization: The algorithm starts with the first calculated angle value, i.e. Since there is no historical data available for smoothing at this point, the first estimate is directly used. As the initial value after smoothing .

[0040] 2. Iterative smoothing: Starting with the second value (N=2), the algorithm enters the smoothing phase. Each new smoothed value... All are derived from the previous smoothing value and the newly calculated original value It is obtained by taking the arithmetic mean.

[0041] Table 1. Impact of Common Scale Estimation and Adaptive Weight Estimation on Angle Convergence Interval

[0042] In the table, This represents the principal axis rotation angle calculated using different scale estimation factors. This indicates the actual spindle rotation angle in the project. This indicates the spindle rotation angle obtained by using a smoothing strategy when the spindle rotation angle exhibits stable periodic oscillation characteristics near its precise value under iterative calculation. This represents the error between the calculated spindle rotation angle and the actual spindle rotation angle.

[0043] By analyzing three sets of input point clouds (non-uniform symmetric input point clouds) , An analysis of the angle convergence performance of the Armadillo uniform symmetric input point cloud under both the traditional commonly used scale estimation weighted PCA algorithm and the improved weighted PCA algorithm is presented. Figures 14-17 From Table 1, we can find that: (1) the convergence curve shows that, , Both common scale estimation and adaptive weight estimation can achieve stable convergence of angle iteration. Compared with common scale estimation, the adaptive weight estimation factor can achieve stable convergence. of It is estimated that the convergence speed is faster, and the point cloud Armadillo is formed from the initial angle. The point cloud converges rapidly to a stable state. from The initial angle convergence effect is obvious, and the point cloud It still maintains a good convergence trend under fluctuating conditions. (2) Compare the convergence values ​​of the three sets of point cloud iteration angles. Error with true value It was found that under uniformly symmetrical point clouds, The estimation demonstrates the same high-precision convergence capability as commonly used scaling estimates, with convergence errors of only [missing information]. ,and The estimation performance is poor; in non-uniform symmetric point clouds, the weighted PCA algorithm has a large convergence error in the iterative angle when processing two sets of input point clouds, while the estimation method has a more obvious advantage. The angle convergence error is , The angle convergence error is Compared to commonly used single-method scale estimation, the accuracy has been greatly improved, and The estimated angle convergence accuracy is poor.

[0044] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying principal axes of a structure point cloud based on adaptive weighted principal component analysis, characterized in that, The method comprises the following steps: S1, acquiring a point cloud dataset, performing denoising processing on the point cloud dataset, and obtaining a denoised point cloud dataset; S2, performing point cloud down-sampling on the denoised point cloud dataset; S3, initializing a weight set weighting and centering the down-sampled point cloud dataset; wherein, denotes a point cloud weight of the point cloud, denotes a set of initial weights, denotes a code of the point cloud; S4, calculating a weighted covariance matrix according to the weighted and centralized point cloud dataset, and obtaining eigenvalues and corresponding normalized eigenvectors through the weighted covariance matrix; S5, selecting the largest eigenvalue in the eigenvalues corresponding normalized eigenvector as the principal axis direction, and transform into the principal axis rotation angle, through the eigenvector get the plane equation Then, based on the principal axis plane equation and the reasonable angle threshold search symmetry point, get the corresponding symmetry point set, calculate the nearest Euclidean distance of the symmetry points in the symmetry point set, and obtain the left point cloud about the symmetry axis division distance metric set of all point clouds wherein denotes the transpose operation of the matrix, denotes the coefficient of the plane equation, denotes the constant term in the plane equation; S6、depending on the result of S5 a set of secondary statistical distance measures , compute a set of iteration weights and re-perform S3 to S6 using the updated set of weights ​ S7, set the principal axis rotation angle convergence threshold When the adjacent errors of the two iteration principal axis rotation angles are Or reach the convergence state in the stable iteration interval, calculate the eigenvalue of the weighted covariance matrix to output the iteration principal axis rotation angle.

2. The method of claim 1, wherein, S2 is specifically: performing point cloud down-sampling on the denoised point cloud dataset by using a random down-sampling filtering method based on a voxel grid. 3.The method of claim 1, wherein, The point cloud dataset in S1 comprises spatial coordinates and reflection intensity information.

4. The method of claim 3, wherein, When performing weighted centralization on the point cloud dataset after point cloud down-sampling, the calculation expression is as shown in formula 1): 1）； wherein is a weighted centroid of the point cloud data, s is a sum of weights, is a number of points of the point cloud, is a point cloud of three-dimensional coordinates; Subtract the weighted mean value of each dimension from the spatial coordinates of each dimension in the point cloud dataset after point cloud down-sampling, wherein: the initial weight set weight is all 1.

5. The method of claim 4, wherein, The calculation formula of the weighted covariance matrix in S4 is as follows: 2）； wherein is a weighted covariance matrix ， is a point cloud abscissa, is a point cloud ordinate.

6. The method of claim 5, wherein the method further comprises: S5 specifically comprises the following steps: S501、selecting the maximum eigenvalue among the eigenvalues calculated in step S4 corresponding eigenvector as the principal axis direction, and transform into the principal axis rotation angle, through the eigenvector get the plane equation Then, based on the principal axis plane equation and the reasonable angle threshold, search for the symmetry point, and divide the test point cloud set into the left point cloud set and the right point cloud set about the initial symmetry plane through the plane equation, the symmetry point cloud set includes the left point cloud set divided by the symmetry axis and the right point cloud set divided by the symmetry axis ; S502, adopts Calculate the point cloud normal features for each neighboring point, if the point cloud on the right... Arbitrary point cloud Unit normal vector and symmetric point cloud The unit normal vector satisfies formula 3), so this point is retained and merged into a point cloud. ,in, This represents the angle between the normal vector of a point that meets the conditions and the normal vector of a point in the symmetrical point cloud; 3）； wherein denotes a normal vector of a point in the symmetric point cloud, denotes a normal vector of a point in the symmetric point cloud, denotes a three-dimensional coordinate of a point in the symmetric point cloud, denotes an angle threshold value, with apostrophe denotes a normal vector of a point in the symmetric point cloud; S503、search point cloud the closest euclidean distance point in the symmetric point cloud statistic the closest euclidean distance of the corresponding point cloud get the corresponding relationship about distance metric traverse the left point cloud after that, get the distance metric set of all point clouds in the left point cloud wherein, the point in the point cloud or point set, contains position and normal vector information.​ 7. The method of claim 1, wherein the method is based on adaptive weighted principal component analysis. When computing the iteration weight set , the first statistical distance metric set is determined based on the first weight estimation function , the second weight estimation function is updated based on the weight estimation function , and the next iteration weight set is updated based on the second weight estimation function , and the expression is as follows: 4）； wherein, is a low-complexity time-varying equation, denotes the nearest Euclidean distance to the corresponding point cloud, denotes a distance threshold, is an element of the set of iteration weights denotes the weight of the corresponding point cloud.

8. The method of claim 7, wherein, The median absolute deviation robust scale estimation function based on the unknown mean is specifically as follows: 5）； 6）； 7）； wherein, denotes an adaptive weight estimation factor based on the median absolute deviation robust scale estimation function under unknown mean, is a sum based on the exponential weight function under unknown mean, denotes an exponential or power, is a sum based on the exponential weight function under unknown mean, respectively, and denotes a median operation, denotes the median of all of the point cloud, denotes a normalized residual based on the median absolute deviation robust scale estimation function under unknown mean, denotes the k-th power of a normalized residual based on the median absolute deviation robust scale estimation function under unknown mean, denotes the base of the natural logarithm.​

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