Method for identifying principal axes of structural point cloud based on adaptive weighted principal component analysis

Abstract

The present application relates to the field of engineering surveying and mapping technology, and particularly relates to a structure point cloud principal axis identification method based on adaptive weighted principal component analysis, which comprises the following steps: obtaining a point cloud data set, initializing a weight set, and weighting and centralizing the point cloud data set after point cloud downsampling; calculating a weighted covariance matrix according to the weighted and centralized point cloud data set, and obtaining eigenvalues and normalized eigenvectors through the weighted covariance matrix; obtaining a distance measurement set of all point clouds; calculating an iterative weight set; and calculating the eigenvalues of the weighted covariance matrix to output an iterative principal axis rotation angle. In application, with the increase of point cloud complexity, the advantage of adaptive weight estimation is more and more significant compared with the common scale estimation, which not only retains the high-precision fast convergence ability of the common scale estimation when processing uniform and symmetric point clouds, but also effectively prevents the interference of outlier points and environmental noise points on the principal axis identification when processing highly non-uniformly distributed point clouds.

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 highly 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 scanning station layout constraint, 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 serious 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 application aims to provide a structure point cloud principal axis identification method based on adaptive weighted principal component analysis, to solve the technical problem of insufficient precision and robustness of the principal component analysis algorithm in point cloud principal axis identification in the prior art, and the specific technical solution is as follows:

[0007] The application provides a structure point cloud principal axis identification method based on adaptive weighted principal component analysis, comprising the following steps:

[0008] S1, acquiring a point cloud data set, performing denoising processing on the point cloud data set, and obtaining a denoised point cloud data set;

[0009] S2, performing point cloud down-sampling on the denoised point cloud data set;

[0010] S3, initializing a weight set , performing weighted centering on the point cloud data set after point cloud down-sampling; wherein, represents the weight of the point cloud , represents the set of initial weights, represents the code of the point cloud;

[0011] S4, calculating a weighted covariance matrix according to the point cloud data set after weighted centering, obtaining eigenvalues and corresponding normalized eigenvectors through the weighted covariance matrix;

[0012] S5, selecting the maximum eigenvalue from the eigenvalues , and selecting the corresponding normalized eigenvector as the principal symmetry axis direction, and transforming into a principal axis rotation angle, obtaining a plane equation through the eigenvector , then searching for symmetric points based on the principal symmetry axis plane equation and a reasonable angle threshold, obtaining a corresponding symmetric point set, calculating the nearest Euclidean distance of the symmetric points in the symmetric point set, and obtaining the left point cloud about the symmetric axis segmentation distance measurement set of all point clouds , wherein represents the transposition operation of a matrix, represents the coefficient of the plane equation, represents the constant term in the plane equation;

[0013] S6, according to the first distance measurement set , calculating an iterative weight set , and re-executing S3 to S6 using the updated weight set ;

[0014] S7, setting a principal axis rotation angle convergence threshold ​When the rotation angle of the iteration principal axis of two iterations is adjacent to the error Or reach the convergence state when in the stable iteration interval, the eigenvalue of the weighted covariance matrix is calculated to output the rotation angle of the iteration principal axis.

[0015] The improvement of the structure point cloud principal axis recognition method based on adaptive weighted principal component analysis of the application is 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.

[0016] The improvement of the structure point cloud principal axis recognition method based on adaptive weighted principal component analysis of the application is that the point cloud data set in S1 includes spatial coordinates and reflection intensity information.

[0017] The improvement of the structure point cloud principal axis recognition method based on adaptive weighted principal component analysis of the application is that when the point cloud data set after point cloud down-sampling is subjected to weighted centering, the calculation expression is as formula 1):

[0018] 1);

[0019] In the formula, is the weighted centroid of the point cloud data, s is the weight sum, is the number of point clouds, is the three-dimensional coordinate (position vector) of the point cloud .

[0020] 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.

[0021] The improvement of the structure point cloud principal axis recognition method based on adaptive weighted principal component analysis of the application is that the calculation formula of the weighted covariance matrix in S4 is as follows:

[0022] 2);

[0023] In the formula, is the weighted covariance matrix ， is the horizontal coordinate of the point cloud . is the vertical coordinate of the point cloud .

[0024] The improvement of the structure point cloud principal axis recognition method based on adaptive weighted principal component analysis of the application is that S5 specifically includes the following steps:

[0025] S501, select the maximum eigenvalue in the eigenvalues calculated in step S4 corresponding eigenvector As the direction of the principal axis of symmetry, and transformed into the principal axis rotation angle, through the eigenvector Obtain the planar square Then, based on the principal symmetry axis plane equation and a reasonable angle threshold, symmetric points are searched. The test point cloud is segmented into a symmetric point cloud about the initial symmetry plane using the plane equation. The symmetric point cloud includes the left-side point cloud segmented by the symmetry axis. And the right-side point cloud divided by the axis of symmetry ;

[0026] 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;

[0027] 3);

[0028] 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".

[0029] 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.

[0030] The improved adaptive weighted principal component analysis based structural point cloud principal axis identification method of the application is improved in that when calculating the iteration weight set , the first statistical distance measure set is used to update the iteration weight set of the next time based on the weight estimation function , and the expression is as follows:

[0031] 4);

[0032] wherein, the low complexity scale time-varying equation is , the nearest Euclidean distance of the corresponding point cloud is represented by , the distance threshold is represented by , the element in the iteration weight set is represented by , and the weight of the corresponding point cloud is represented by

[0033] The improved adaptive weighted principal component analysis based structural point cloud principal axis identification method of the application is improved in that , the median absolute deviation robust scale estimation function based on unknown mean is specifically as follows:

[0034] 5);

[0035] 6);

[0036] 7);

[0037] wherein, the adaptive weight estimation factor based on the median absolute deviation robust scale estimation function under unknown mean is represented by , the summation based on the exponential weight function under unknown mean is represented by , the exponent or power is represented by , the summation of the exponential weight function under unknown mean corresponding to and is represented by , the median operation is represented by , the median of all of the point cloud is represented by , the normalized residual based on unknown mean is represented by , the k-th power of the normalized residual based on unknown mean is represented by , and the base number of the natural logarithm is represented by

[0038] The technical scheme of the application has the following beneficial effects:

[0039] ​​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 all point clouds, calculate points on 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.

[0040] 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:

[0041] (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.

[0042] (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;

[0043] (3) Not affected by the structure shape and size of the engineering structure to be tested, can be applied to various forms and scales of engineering structures, has high universality and applicability, and provides reliable technical support for the design, evaluation and maintenance of engineering structures;

[0044] (4) With the increase of point cloud complexity, the adaptive weight estimation has more and more obvious advantages compared with the commonly used scale estimation, which not only retains the high-precision fast convergence ability of the commonly used scale estimation when processing uniform and symmetric point clouds, but also effectively prevents the interference of outliers and environmental noise points on the main shaft 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 point cloud main shaft identification in the prior art.

[0045] In addition to the purposes, features and advantages described above, the present application has other purposes, features and advantages. The present application will be further described below with reference to the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0046] 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 application. The embodiments of the present application illustrated in the drawings, and their description thereto, are presented to provide the practitioner with a thorough and enabling disclosure of the present application, and are included as a part of this application to convey the principles of the present application to those skilled in the art. In the drawings:

[0047] Figure 1 is a flow chart of the structure point cloud main shaft identification method of the present application based on adaptive weighted principal component analysis;

[0048] Figure 2 is a non-uniformly 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);

[0049] Figure 3 is a down-sampled point cloud graph after voxel grid with a grid resolution parameter of 0.1m;

[0050] Figure 4 is a down-sampled point cloud graph after voxel grid with a grid resolution parameter of 0.2m;

[0051] Figure 5 is a down-sampled point cloud graph after voxel grid with a grid resolution parameter of 0.3m;

[0052] Figure 6 is the searched point cloud when the angle threshold is 10° (red points are the points to be searched, and green points are the searched point clouds);

[0053] Figure 7 is the searched point cloud when the angle threshold is 20° (Red dots represent points to be searched, and green dots represent the point cloud to be searched).

[0054] Figure 8 Point cloud searched with an angle threshold of 30° (Red dots represent points to be searched, and green dots represent the point cloud to be searched).

[0055] Figure 9 Point cloud searched with an angle threshold of 40° (Red dots represent points to be searched, and green dots represent the point cloud to be searched).

[0056] Figure 10 For point clouds Initial iteration removal results (outliers or environmental noise points are marked in red);

[0057] Figure 11 For point clouds Iterative outlier and environmental noise point marking diagrams (from the first iteration to the 20th to the 40th iteration);

[0058] Figure 12 A marker map of outliers in a point cloud after 40 iterations of mesoscale estimation using existing techniques;

[0059] Figure 13 To estimate outlier markers in the point cloud after 40 iterations using adaptive weighting;

[0060] Figure 14 For point clouds Iterative effect of spindle rotation angle;

[0061] Figure 15 For point clouds Iterative effect of spindle rotation angle;

[0062] Figure 16 For point clouds Iterative effect of spindle rotation angle;

[0063] 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);

[0064] Figure 18 The PCA spindle recognition effect of bridges under complex working conditions. Detailed Implementation

[0065] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0066] 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:

[0067] 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.

[0068] 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.

[0069] 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. .

[0070] 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;

[0071] 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:

[0072] 1);

[0073] In the formula, is the weighted centroid of the point cloud data, is the weight coefficient assigned to the point cloud, s is the weight sum, is the number of point clouds, is the point cloud three-dimensional coordinates (position vector) of the point cloud;

[0074] Subtract the weighted mean value of each dimension of the point cloud data set after down-sampling the point cloud from the spatial coordinates of each dimension.

[0075] S4, according to the weighted centralized point cloud data set, calculate the weighted covariance matrix, get the eigenvalue and the corresponding normalized eigenvector through the weighted covariance matrix; the calculation formula is as follows:

[0076] 2) ;

[0077] wherein, is the weighted covariance matrix ， is the point cloud horizontal coordinate, is the point cloud vertical coordinate.

[0078] S5, select the largest eigenvalue corresponding normalized eigenvector as the principal axis direction, and transform into the principal axis rotation angle, get the plane equation through the eigenvector , then search for symmetric points based on the principal axis plane equation and reasonable angle threshold (generally left and right), get the corresponding symmetric point set, calculate the nearest Euclidean distance of the symmetric points in the symmetric point set, obtain the distance metric set of all point clouds about the left point cloud split by the symmetric axis wherein, denotes the transpose operation of the matrix, denotes the coefficient of the plane equation, denotes the constant term in the plane equation;

[0079] Further, S5 specifically includes the following steps:

[0080] S501, select the largest eigenvalue corresponding eigenvector as the principal axis direction, and transform into the principal axis rotation angle, get the plane equation through the eigenvector 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 symmetry 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 ;

[0081] 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;

[0082] 3);

[0083] 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".

[0084] 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).

[0085] 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 Distance metric set wherein, represents a point in a point cloud or a point set, containing position and normal vector information.

[0086] S6, according to the first statistical distance metric set , the iteration weight set is calculated, and the next iteration weight set is updated using the updated weight set re-executes S3 to S6;

[0087] Preferably, in the calculation of the iteration weight set , according to the first statistical distance metric set , the next iteration weight set is updated based on the weight estimation function, expressed as follows:

[0088] 4);

[0089] wherein, is a median absolute deviation robust scale estimation function based on unknown mean, represents the nearest 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.

[0090] Further, is a median absolute deviation robust scale estimation function based on unknown mean, and the specific formula is as follows:

[0091] 5);

[0092] 6);

[0093] 7);

[0094] wherein, represents an adaptive weight estimation factor based on a median absolute deviation robust scale estimation function based on unknown mean, is the sum based on an exponential weight function based on unknown mean, represents an exponential or power, corresponds to the sum of the exponential weight function based on unknown mean at (counting weight) and (counting weight), respectively, denotes a median operation, denotes all of the point cloud, denotes a standardized residual, denotes a k-th power based on the standardized residual under the mean unknown, denotes the base of the natural logarithm, denotes that this is a median absolute deviation centered on the median;

[0095] S7、according to the weight set calculated in step S6 , calculate the eigenvalue of the weighted covariance matrix, select the maximum eigenvalue corresponding eigenvector as the principal axis direction, and transform into the principal axis rotation angle.

[0096] Set the principal axis rotation angle convergence threshold , when the adjacent error of the two iterations of the principal axis rotation angle or in the stable iteration interval, reach the convergence state, output the iteration principal axis rotation angle. Otherwise, re-execute S1 to S6. As Figure 13 , with the increase of the number of iterations, the point cloud outlier point label gradually decreases.

[0097] Figure 1 is the flow chart of the structure point cloud principal axis recognition method based on adaptive weighted principal component analysis of the application, the specific process is: obtaining the spatial point cloud with local symmetrical structure from the input point cloud data , and preprocessing it, the preprocessing includes downsampling and denoising, obtaining the initial weight set, then calculating the point cloud feature, 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 the symmetrical points, obtain the metric set with the nearest distance to the symmetrical points, then update the point cloud iteration by adaptive scale estimation, and finally return to the initial weight set.

[0098] The structure point cloud principal axis recognition method based on adaptive weighted principal component analysis of the application is based on three-dimensional laser scanning to obtain engineering structure linearity, which belongs to non-contact measurement, the field measurement time is short, and the point cloud data extraction automation degree is high. And in the application, with the increase of the complexity of the point cloud, the adaptive weight estimation has more and more obvious advantages compared with the commonly used scale estimation, which not only retains the high-precision fast convergence ability of the commonly used scale estimation when processing uniform symmetrical point cloud, but also effectively prevents the interference of outliers and environmental noise points on the principal axis recognition when processing highly non-uniformly distributed point cloud, and solves the technical problems of the lack of precision and robustness of the principal component analysis algorithm in the point cloud principal axis recognition in the prior art.

[0099] Finally, in order to show the advantages of the application, the adaptive weighted principal component analysis based structure point cloud principal axis recognition method of the application is compared with the detection method in the prior art.

[0100] In order to study the robustness of a single scale estimation factor in the principal axis recognition of non-uniform symmetric point clouds, the input point cloud is resampled without changing the significant discrete points and the environmental noise points, and the sampling process only simply changes the segmentation angle of the arch foot horizontal bridge point cloud as the input point cloud . .

[0101] Among them, the point cloud is the bridge local spatial point cloud data (arch foot + tie beam plane) with symmetrical structure obtained by the Leica ScanStation P50 long-range three-dimensional laser scanner in the embodiment;

[0102] In order to study the principal axis recognition effect of the improved weighted PCA algorithm based on adaptive weight estimation in non-uniform symmetric point clouds, the application performs angle iteration test on non-uniform symmetric point clouds and uniform symmetric point clouds Armadillo, predefines an upper limit of iteration and adds a commonly used scale estimation for comparative analysis, and the results are as shown in Figures 14-16 .

[0103] 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;

[0104] The commonly used scale estimation of different point clouds is processed by a smoothing strategy, so that the convergence performance under oscillation conditions is comparable to the adaptive weight estimation result, and the results are as shown in Figure 15 . Under the adaptive weight estimation, there is a periodic iteration cycle interval, and the angle mean value in this interval is used for calculation as the convergence result, and the results are as shown in Figure 17 .

[0105] Finally, the angle convergence performance of the traditional commonly used scale estimation weighted PCA and the improved weighted PCA algorithm is analyzed for three groups of point clouds respectively, the influence of different estimation methods on the convergence interval is quantified, and the statistical results are as shown in Table 1.

[0106] Among them, is the improved median absolute deviation robust scale estimation function based on the mean .

[0107] 8);

[0108] 9);

[0109] in:

[0110] 10);

[0111] 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).

[0112] 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.

[0113] 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.

[0114] 11);

[0115] 1. Initialization:

[0116] 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 .

[0117] 2. Iterative smoothing:

[0118] From the second value (N=2), the algorithm enters the smoothing phase. Each new smoothed value is obtained by taking the arithmetic mean of the previous smoothed value and the newly computed raw value .

[0119] Table 1. Influence of scale estimation and adaptive weight estimation on the convergence interval of the angle

[0120]

[0121] In the table, denotes the principal axis rotation angle computed using different scale estimation factors, denotes the actual principal axis rotation angle in engineering practice, denotes the principal axis rotation angle obtained using the smoothing strategy when the principal axis rotation angle exhibits stable periodic oscillation characteristics near the exact value under iterative computation, denotes the error between the computed principal axis rotation angle and the true principal axis rotation angle.

[0122] By analyzing the angle convergence performance of three groups of input point clouds (non-uniform symmetric input point clouds , and uniform symmetric input point cloud Armadillo) under the traditional commonly used scale estimation weighted PCA algorithm and the improved weighted PCA algorithm, it can be found from Figures 14-17 and Table 1 that: (1) the convergence curves show that , and the commonly used scale estimation can achieve stable convergence of the iterative angle, compared with the commonly used scale estimation, the estimation based on the adaptive weight estimation factor exhibits faster convergence speed, the point cloud Armadillo converges quickly from the initial angle to a stable state, the point cloud converges significantly from the starting angle, and the point cloud still maintains a good convergence trend under fluctuation conditions. (2) By comparing the iterative angle convergence values and the true value error of the three groups of point clouds, it is found that under uniform symmetric point clouds, the estimation exhibits the same significant high-precision convergence ability as the commonly used scale estimation, with a convergence error of , while the estimation performs poorly; in non-uniform symmetric point clouds, the iterative angle convergence error of the weighted PCA algorithm processing two groups of input point clouds is large, while the estimation performs better, with an angle convergence error of , The angle convergence error of the angle is Compared with the single common scale, the estimation accuracy is greatly improved, and The estimated angle convergence accuracy is poor.

[0123] The above only describes the preferred embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

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, 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 method further comprises: 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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