Train-borne laser point cloud deformation correction method, system, device and medium based on cluster analysis

Abstract

The present invention discloses a cluster analysis-based method, system, device, and medium for correcting train-borne laser point cloud deformation. The method belongs to the field of laser point cloud processing technology and includes the following steps: obtaining a normal rail point cloud and a distorted rail point cloud; initializing clustering of the distorted rail point cloud, and assigning the normal rail point cloud as a cluster sample point to be assigned during the clustering process; searching for all neighboring points in the corresponding cluster for each sampling point in the distorted rail point cloud and the normal rail point cloud to construct a weighted covariance matrix descriptor for the sampling point; constructing an objective function for non-rigid cluster registration of the distorted rail point cloud and the normal rail point cloud; and iteratively updating the non-rigid displacement field, the weighted covariance matrix descriptor, and the cluster fuzzy membership matrix until the result falls below a threshold set by the objective function, thereby completing the corrected registration of the distorted rail point cloud. The present invention can address the problem of insufficient registration accuracy caused by uneven point cloud data density and noise interference.

Description

Technical Field

[0001] The present invention belongs to the technical field of laser point cloud processing, and in particular relates to a train-borne laser point cloud deformation correction method, system, equipment and medium based on cluster analysis. Background Art

[0002] As the core infrastructure of railway transportation, rails bear significant train loads and, over long-term use, are subject to varying degrees of deformation due to temperature changes, load fluctuations, and other external factors. These deformations primarily manifest as bending, wear, cracks, and gauge variations, severely impacting the stable operation of trains, increasing the risk of derailment, and significantly reducing train safety and transportation efficiency. To address this issue, railway authorities must regularly inspect and repair rails to ensure that their flatness and geometry meet standards. Consequently, rail correction technology has emerged as an essential component of railway maintenance.

[0003] In recent years, with the advancement of LiDAR technology, train-borne laser point cloud data has become an important tool for addressing this issue. Vehicle-borne LiDAR enables real-time acquisition of three-dimensional point cloud data of rail tracks, providing more accurate baseline data for track inspection and correction. However, due to the high speeds and complex environments, existing train-borne laser point cloud data often suffers from issues such as uneven density, noise interference, and point cloud registration errors. This directly impacts data quality, and consequently, affects subsequent data processing and analysis. Summary of the Invention

[0004] In response to the deficiencies in the prior art, the present invention provides a train-borne laser point cloud deformation correction method, system, device and medium based on cluster analysis, which can cope with changes in point cloud characteristics in complex dynamic environments and solve the problem of insufficient alignment accuracy caused by uneven point cloud data density and noise interference.

[0005] The present invention provides the following technical solutions:

[0006] In a first aspect, a method for correcting train-borne laser point cloud deformation based on cluster analysis is provided, comprising the following steps:

[0007] S1: Obtain normal rail point cloud and distorted rail point cloud;

[0008] S2: Initialize clustering of the distorted rail point cloud to divide the clusters, and in the process of initializing clustering, allocate the normal rail point cloud as the cluster sample points to be allocated;

[0009] S3: For each sampling point in the distorted rail point cloud and the normal rail point cloud, search for all neighboring points in its corresponding cluster and construct a weighted covariance matrix descriptor of the sampling point based on the geometric feature vectors of all neighboring points of the sampling point;

[0010] S4: Introducing the weighted covariance matrix descriptor similarity constraint to construct the objective function for non-rigid clustering registration of distorted rail point cloud and normal rail point cloud;

[0011] S5: Continuously iteratively update the non-rigid displacement field, weighted covariance matrix descriptor, and clustered fuzzy membership matrix until it falls below the set threshold of the objective function, completing the corrective registration of the distorted rail point cloud.

[0012] Optionally, a K-means clustering method is used to initialize the clustering of the distorted rail point cloud to divide the clusters.

[0013] Optionally, step S3 is specifically:

[0014] For each sampling point Search within the specified neighborhood radius All original neighborhood points within constitute the original neighborhood point set ;

[0015] The original neighborhood point set Projection to sampling point The tangent plane On the projection point network, a uniform grid cell is generated on the tangent plane according to the range of the projection point network, and the blank grid cells are interpolated to construct the interpolation neighborhood points corresponding to the blank grid cells. ;

[0016] Get neighborhood points The geometric eigenvector of and weights, where the neighborhood points Including interpolated neighborhood points and original neighborhood points;

[0017] Constructing sampling points The weighted covariance matrix descriptor of ;

[0018] ;

[0019] in, is the number of all neighboring points of the sampling point, is the mean vector of the eigenvectors of all neighborhood points, For field points The weight of .

[0020] Optionally, the neighborhood point The geometric eigenvector of There are 8 variables, specifically:

[0021] ;

[0022] in, For sampling points Normal vector With vector The angle between Neighborhood points Normal vector With vector The angle between is the normal vector and The angle between For sampling points and neighborhood points The distance between is a vector At the sampling point The L2 norm of the projection on the tangent plane, is a vector In the normal vector The L2 norm of the projection, At the sampling point The two principal curvatures at and The maximum value of The two principal curvatures and The arithmetic mean curvature.

[0023] Optionally, the method generates uniform grid cells on the tangent plane according to the range of the projected point network, and interpolates the blank grid cells to construct interpolation neighborhood points corresponding to the blank grid cells. , specifically:

[0024] For non-empty grid cells, project their corresponding original neighborhood points onto the tangent plane distance Fill in;

[0025] Calculate the weight of the original neighborhood points corresponding to each non-empty grid cell ;

[0026] ;

[0027] in, is the distance between the grid cell where the original neighborhood point is located and the blank grid cell, For the support radius, is the radial basis function;

[0028] For empty grid cells, fill distance based on adjacent non-empty grid cells and the weight of the corresponding original neighborhood points Perform distance interpolation;

[0029] ;

[0030] in, is the distance of blank grid interpolation, is the number of non-empty grid cells;

[0031] Interpolated distance from the blank grid and sampling points Normal vector , construct the interpolation neighborhood points corresponding to the blank grid cells .

[0032] Optionally, the obtaining of neighborhood points The geometric eigenvector of and weights, including: obtaining interpolation area points Weight , specifically:

[0033] ;

[0034] in, is the neighborhood radius, is the current neighborhood point, Interpolation neighborhood points With neighboring points The Euclidean distance of .

[0035] Optionally, the objective function for:

[0036] ; ;

[0037] in, is the fuzzy membership matrix, for The cluster center set of is the weighted covariance descriptor, Points of the distorted rail point cloud The displacement field, M Points of normal rail point cloud A collection of Points of the distorted rail point cloud A collection of Weighted covariance descriptor for normal rail point cloud and weighted covariance descriptor of distorted rail point cloud similarity; is the regularization term, is the regularization parameter, represents the matrix logarithm, represents the F norm of the matrix, is the index, is the fuzzy membership between each point in the distorted point cloud and the normal point cloud.

[0038] In a second aspect, a train-borne laser point cloud deformation correction system based on cluster analysis is provided, comprising:

[0039] Point cloud acquisition module: obtains normal rail point cloud and distorted rail point cloud;

[0040] Initialization clustering module: Initialize clustering of distorted rail point cloud to divide clusters, and in the process of initialization clustering, allocate normal rail point cloud as cluster sample points to be allocated;

[0041] Descriptor construction module: For each sampling point in the distorted rail point cloud and the normal rail point cloud, all neighboring points are searched in the corresponding cluster, and a weighted covariance matrix descriptor of the sampling point is constructed based on the geometric feature vectors of all neighboring points of the sampling point;

[0042] Objective function construction module: Introducing the weighted covariance matrix descriptor similarity constraint to construct the objective function for non-rigid clustering registration of distorted rail point clouds and normal rail point clouds;

[0043] Iterative registration module: It continuously iteratively updates the non-rigid displacement field, weighted covariance matrix descriptor, and clustered fuzzy membership matrix until it falls below the set threshold of the objective function, completing the corrective registration of the distorted rail point cloud.

[0044] In a third aspect, a computer device is provided, comprising a processor and a memory; wherein, when the processor executes a computer program stored in the memory, the steps of the train-borne laser point cloud deformation correction method based on cluster analysis as described in any one of the first aspects are implemented.

[0045] In a fourth aspect, a computer-readable storage medium is provided for storing a computer program; when the computer program is executed by a processor, the steps of the train-borne laser point cloud deformation correction method based on cluster analysis as described in any one of the first aspects are implemented.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The train-borne laser point cloud deformation correction method proposed in the present invention is targeted at rail deformation. Through the covariance matrix descriptor, it can capture the geometric features of the local point cloud of the rail, and more accurately reflect the curvature, normal vector and neighborhood structure characteristics of the rail deformation point, thereby significantly improving the correction accuracy; secondly, the present invention uses a weighted mechanism to process the density unevenness caused by deformation and the noise interference of the surrounding environment, thereby enhancing the robustness to complex scenes. At the same time, a clustering framework is added to optimize the non-rigid deformation field, so that the method can adapt to a larger range of nonlinear deformations. In addition, the clustering framework can decompose the alignment correction problem into local sub-problems, greatly reducing the complexity of global calculations. At the same time, the weighted covariance descriptor can also accelerate the similarity calculation through matrix logarithmic difference and normalization operations, further improving the overall efficiency. In addition, the present application also imposes constraints on the deformation field through regularization to ensure that the deformation results are reasonable, making it widely applicable to complex scenes such as high noise, occlusion and density differences. In summary, the deformation correction method of this application performs well in terms of accuracy, robustness, efficiency and applicability, and provides effective technical support for solving the problems of rail deformation and complex non-rigid point cloud registration. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flow chart of the train-borne laser point cloud deformation correction method based on cluster analysis of the present invention;

[0049] Figure 2 Schematic diagram of geometric characteristic vectors of neighborhood points of the present invention;

[0050] Figure 3 is an example of interpolation of uniform areas with non-uniform point density and data gaps of the present invention;

[0051] Figure 4 This is an example of the weighted covariance descriptor for two local surfaces with the same name in a railway scene according to the present invention;

[0052] Figure 5 This is a schematic diagram of the point cloud of the distorted railroad track in the first specific scenario before correction;

[0053] Figure 6 This is a schematic diagram of the point cloud of the distorted railroad track in the first specific scenario after correction using this application;

[0054] Figure 7 This is a schematic diagram of the point cloud of the second specific scene before the distorted railroad is corrected;

[0055] Figure 8 This is a schematic diagram of the point cloud of the distorted railroad track in the second specific scenario after correction using this application. DETAILED DESCRIPTION

[0056] The present invention will be further described below with reference to the accompanying drawings. The following examples are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. It should be noted that the term "comprising" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0057] Example 1

[0058] like Figure 1 As shown, a train-borne laser point cloud deformation correction method based on cluster analysis is provided, comprising the following steps:

[0059] S1: Obtain normal rail point cloud and distorted rail point cloud.

[0060] Both normal and distorted track point clouds can be collected using a train-mounted LiDAR scanning system and preprocessed, including denoising, point cloud density balancing, and data alignment. For this application, a bidirectional fabric simulation method can be used to effectively extract the track point cloud, ensuring the quality of the underlying data for subsequent registration.

[0061] As a specific example, six sets of overlapping train-borne laser point cloud data were processed using a bidirectional cloth simulation method to generate data with both distorted and normal rails. Taking one set as an example, the distorted and normal rail point clouds were first filtered to remove noise points, and then N and M approximately evenly distributed points were sampled.

[0062] S2: Initialize clustering of the distorted rail point cloud to divide the clusters, and in the process of initializing clustering, allocate the normal rail point cloud as the cluster sample points to be allocated.

[0063] Specifically, the K-means clustering method is used to divide the distorted rail point cloud data into a predetermined number of clusters to ensure that the points in each cluster have similar spatial characteristics. The K-means clustering method can refer to the existing technology, that is, the present application uses the distorted rail point cloud as the source point cloud and the normal rail point cloud as the target point cloud to initialize the clustering.

[0064] As a specific example, the K-means clustering method is used to process distorted rail point cloud data, dividing the data into C clusters, each with a cluster center, ensuring that the points in each cluster have similar spatial characteristics. First, the points in the distorted rail point cloud are used as initial cluster centers, and the points in the normal rail point cloud are used as sample points to be assigned. Specifically, the K-means clustering method is used to gradually assign the cluster centers formed by the distorted rail point cloud to the sample points of the normal rail point cloud. Subsequently, the membership degree of each cluster center point is calculated based on the sample points and the nearest cluster center.

[0065] S3: For each sampling point in the distorted rail point cloud and the normal rail point cloud, search for all neighboring points in its corresponding cluster, and construct a weighted covariance matrix descriptor of the sampling point based on the geometric feature vectors of all neighboring points of the sampling point.

[0066] Specifically, for each point in the source point cloud, the neighborhood points are searched, and the neighborhood point set is projected onto the tangent plane of the sampling point to obtain the projected point network. The 8-dimensional feature vectors of the projected grid cells in different cases are interpolated to construct a complete weighted covariance matrix descriptor. Similarly, for each point in the target point cloud, the neighborhood points are searched, and the weighted covariance matrix descriptor is constructed based on the geometric variables calculated according to the neighborhood points. In addition, when constructing the covariance matrix descriptor, in order to ensure the robustness and descriptiveness of the descriptor, the corresponding weights are assigned to each neighborhood point according to the point density.

[0067] Step S3 specifically includes the following sub-steps:

[0068] S31: For each sampling point Search within the specified neighborhood radius All original neighborhood points within constitute the original neighborhood point set .

[0069] The method of searching for original neighborhood points may refer to the prior art, where original neighborhood points refer to points in the distorted rail point cloud or the normal rail point cloud.

[0070] S32: The original neighborhood point set Projection to sampling point The tangent plane On the projection point network, a uniform grid cell is generated on the tangent plane according to the range of the projection point network, and the blank grid cells are interpolated to construct the interpolation neighborhood points corresponding to the blank grid cells. .

[0071] like Figure 3 As shown, Figure 3 (a) shows an example of interpolation of distorted railroad point cloud. Figure 3 (b) shows an example of interpolation of a normal rail point cloud, step S32, specifically:

[0072] S321: The original neighborhood point set Projection to sampling point The tangent plane On the projected point network , the original neighborhood points Its projection point Relationship, can be based on It is learned that, From this point to the tangent plane distance, is the normal vector of the sampling point.

[0073] S322: For the generated grid cell, if the grid cell is occupied by at least one projection point, it is a non-empty grid cell. For the non-empty grid cell, fill the grid with its corresponding original neighborhood points projected onto the tangent plane. distance .

[0074] S323: Calculate the weight of the original neighborhood point corresponding to each non-empty grid cell .

[0075] ;

[0076] in, is the distance between the grid cell where the original neighborhood point is located and the blank grid cell, For the support radius, is the radial basis function (RBF);

[0077] S324: For each blank grid cell, fill the grid cell based on the adjacent non-empty grid cells. and the weight of the corresponding original neighborhood points Perform distance interpolation;

[0078] ;

[0079] in, is the distance of blank grid interpolation, is the number of non-empty grid cells.

[0080] S325: Distance interpolated from blank grid and sampling points Normal vector , construct the interpolation neighborhood points corresponding to the blank grid cells .

[0081] S33: Get neighborhood points The geometric eigenvector of and weights, where the neighborhood points Includes interpolated neighborhood points and original neighborhood points.

[0082] Neighborhood Points The geometric eigenvector of There are 8 variables, specifically:

[0083] ;

[0084] in, For sampling points Normal vector With vector The angle between Neighborhood points Normal vector With vector The angle between is the normal vector and The angle between For sampling points and neighborhood points The distance between is a vector At the sampling point The L2 norm of the projection on the tangent plane, is a vector In the normal vector The L2 norm of the projection, At the sampling point The two principal curvatures at and The maximum value of The two principal curvatures and The arithmetic mean curvature.

[0085] The calculation method for each variable is:

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] in, represents the dot product, Second normal form of vector representation, geometric eigenvector Contains three angle measurements , three length measures and two curvature-based metrics ,like Figure 2 As shown, Figure 2 (a) in the equation is the three angle measurements of the geometric eigenvector, Figure 2 (b) in the figure represents the three length measures of the geometric eigenvectors. They are all relative variables that are invariant to spatial transformations and together fully describe the geometric properties of the local surface. It is worth noting that before assembling the variables into the eigenvectors, they are normalized within [0, 1] to ensure that they have equal ranges and ultimately form the geometric eigenvectors of the neighborhood points.

[0093] The weight of the original neighborhood point can refer to the calculation formula of step S323.

[0094] Interpolation area points Weight The calculation formula is:

[0095] ;

[0096] in, is the neighborhood radius, is the current neighborhood point, Interpolation neighborhood points With neighboring points The Euclidean distance of .

[0097] S34: Constructing sampling points The weighted covariance matrix descriptor of ;

[0098] ;

[0099] in, is the number of all neighboring points of the sampling point, is the mean vector of the eigenvectors of all neighborhood points, For field points The weight of .

[0100] Constructed covariance matrix descriptor It is an 8×8 asymmetric matrix, the diagonal entries represent the variance of each geometric feature, and the non-diagonal entries represent the covariance between different geometric features. The covariance descriptor regards multiple geometric features as samples of the joint variability distribution. The covariance matrix descriptor models the local features of each point in the distorted rail point cloud and the normal rail point cloud, captures the local structural characteristics of the point cloud and assigns it density weighting to improve its adaptability to complex scenes such as noise and uneven point density. This also takes into account the consistency of local geometric features when considering the global deformation optimization of the point cloud. Figure 4 As shown, Figure 4 The left side is a partial enlargement diagram of the example 1 of the local surface and descriptor with the same name. Figure 4 The right side of the figure is a partial enlargement diagram of the second example of the local surface and descriptor with the same name.

[0101] S4: The weighted covariance matrix descriptor similarity constraint is introduced to construct the objective function for non-rigid clustering registration of distorted rail point cloud and normal rail point cloud.

[0102] Before constructing the current function, the fuzzy clustering analysis mainly solves the following problems:

[0103]

[0104] in, is a fuzzy factor that controls the fuzziness of clustering. The goal of non-rigid registration that produces deformation is to find The optimal deformation mapping with the smallest shape deviation from X, therefore, the non-rigid registration based on cluster analysis can be expressed as:

[0105] Building on the aforementioned non-rigid registration method based on cluster analysis, this application constructs a weighted covariance matrix descriptor to calculate the descriptor similarity between the source and target point clouds. Furthermore, cluster analysis can be used to group the distribution characteristics of the rail point cloud (such as density, shape, and spatial location). Combining these grouping characteristics, geometric position distance error, and covariance matrix descriptor similarity, this application constructs an objective function to ensure accurate matching of homonymous points during the rail registration process and effectively avoid mismatching of non-homonymous points. Furthermore, regularization constraints are used to optimize the objective function, making the rail registration process more accurate and robust.

[0106] Therefore, the objective function of this application is for:

[0107] ;

[0108] ;

[0109] in, is the fuzzy membership matrix, for The cluster center set of is the weighted covariance descriptor, Points of the distorted rail point cloud The displacement field, M Points of normal rail point cloud A collection of Points of the distorted rail point cloud A collection of Weighted covariance descriptor for normal rail point cloud and weighted covariance descriptor of distorted rail point cloud similarity; is the regularization term, is the regularization parameter, represents the matrix logarithm, represents the F norm of the matrix, is the index, is the fuzzy membership between each point in the distorted point cloud and the normal point cloud.

[0110] The regularization term penalizes matches with low descriptor similarity, suppresses incorrect matches of non-homologous points, and encourages the optimization algorithm to prefer point pairs with high descriptor similarity.

[0111] In this application, a similarity metric is used to measure the similarity between the two weighted covariance matrix descriptors for the normal and distorted rail point clouds. To improve efficiency, the calculation is simplified by taking the difference of the matrix logarithms and normalizing them using an exponential function. This logarithmic difference metric approximates similarity faster because it decouples the two matrices and avoids the calculation of generalized eigenvalues. The larger the value, the greater the geometric difference between the two covariance descriptors, and vice versa. Finally, the similarity is normalized between (0,1) and written as:

[0112]

[0113] in, is the weight coefficient that increases the descriptiveness.

[0114] S5: Continuously iteratively update the non-rigid displacement field, weighted covariance matrix descriptor, and clustered fuzzy membership matrix until it falls below the set threshold of the objective function, completing the corrective registration of the distorted rail point cloud.

[0115] Continuous iterative solution The parameters are adjusted to reduce the change value of the objective function. When the change value is less than the set threshold, the algorithm is considered to have converged and the final rail registration result is output.

[0116] By introducing the similarity constraint of the covariance matrix descriptor into the clustering function, the rail point cloud can take into account the consistency of local geometric features while considering large-scale deformation, which increases the refinement of the correction. Finally, by iteratively optimizing the clustering probability matrix, non-rigid deformation field and covariance matrix descriptor, the precise alignment of the source point cloud and the target point cloud is gradually achieved, thus forming a robust and efficient train-borne laser point cloud deformation correction method with adaptive adjustment cluster analysis; Figure 5-Figure 8 From the two scenarios shown, it can be seen that the deformation correction method of the present application is accurate and stable.

[0117] Example 2

[0118] A train-borne laser point cloud deformation correction system based on cluster analysis, comprising:

[0119] Point cloud acquisition module: obtains normal rail point cloud and distorted rail point cloud;

[0120] Initialization clustering module: Initialize clustering of distorted rail point cloud to divide clusters, and in the process of initialization clustering, allocate normal rail point cloud as cluster sample points to be allocated;

[0121] Descriptor construction module: For each sampling point in the distorted rail point cloud and the normal rail point cloud, all neighboring points are searched in the corresponding cluster, and a weighted covariance matrix descriptor of the sampling point is constructed based on the geometric feature vectors of all neighboring points of the sampling point;

[0122] Objective function construction module: Introducing the weighted covariance matrix descriptor similarity constraint to construct the objective function for non-rigid clustering registration of distorted rail point clouds and normal rail point clouds;

[0123] Iterative registration module: It continuously iteratively updates the non-rigid displacement field, weighted covariance matrix descriptor, and clustered fuzzy membership matrix until it falls below the set threshold of the objective function, completing the corrective registration of the distorted rail point cloud.

[0124] For more specific details about the above method, please refer to the corresponding contents disclosed in the aforementioned embodiments, which will not be described again here.

[0125] Example 3

[0126] The present invention provides a computer device comprising a processor and a memory; wherein, when the processor executes a computer program stored in the memory, the steps of the train-borne laser point cloud deformation correction method based on cluster analysis are implemented.

[0127] For more specific details about the above method, please refer to the corresponding contents disclosed in the aforementioned embodiments, which will not be described again here.

[0128] Example 4

[0129] The present invention provides a computer-readable storage medium for storing a computer program; when the computer program is executed by a processor, the steps of the train-borne laser point cloud deformation correction method based on cluster analysis are implemented.

[0130] For more specific details about the above method, please refer to the corresponding contents disclosed in the aforementioned embodiments, which will not be described again here.

[0131] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from the other embodiments. References to the same or similar parts between the various embodiments will be sufficient. The systems, devices, and storage media disclosed in the embodiments are described briefly because they correspond to the methods disclosed in the embodiments. For relevant details, refer to the method description.

[0132] Those skilled in the art will clearly understand that the techniques in the embodiments of the present invention can be implemented using software and a necessary general-purpose hardware platform. Based on this understanding, the technical solutions in the embodiments of the present invention, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium such as ROM / RAM, a magnetic disk, or an optical disk, and includes instructions for enabling a computer device (such as a personal computer, server, or network device) to execute the methods described in various embodiments of the present invention, or portions thereof.

[0133] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A train-borne laser point cloud deformation correction method based on cluster analysis, characterized in that: The following steps are involved: S1: Obtain normal rail point cloud and distorted rail point cloud; S2: Initialize clustering of the distorted rail point cloud to divide the clusters, and in the process of initializing clustering, allocate the normal rail point cloud as the cluster sample points to be allocated; S3: For each sampling point in the distorted rail point cloud and the normal rail point cloud, search for all neighboring points in its corresponding cluster and construct a weighted covariance matrix descriptor of the sampling point based on the geometric feature vectors of all neighboring points of the sampling point; S4: Introducing the weighted covariance matrix descriptor similarity constraint to construct the objective function for non-rigid clustering registration of distorted rail point cloud and normal rail point cloud; S5: Continuously iteratively update the non-rigid displacement field, weighted covariance matrix descriptor, and cluster fuzzy membership matrix until it is lower than the set threshold of the objective function, completing the corrective registration of the distorted rail point cloud; Step S3 is specifically as follows: For each sampling point Search within the specified neighborhood radius All original neighborhood points within constitute the original neighborhood point set ; The original neighborhood point set Projection to sampling point The tangent plane On the projection point network, a uniform grid cell is generated on the tangent plane according to the range of the projection point network, and the blank grid cells are interpolated to construct the interpolation neighborhood points corresponding to the blank grid cells. ; Get neighborhood points The geometric eigenvector of and weights, where the neighborhood points Including interpolated neighborhood points and original neighborhood points; Constructing sampling points The weighted covariance matrix descriptor of ; ； in, is the number of all neighboring points of the sampling point, is the mean vector of the eigenvectors of all neighborhood points, For field points The weight of The method generates uniform grid cells on the tangent plane according to the range of the projected point network, and interpolates the blank grid cells to construct the interpolation neighborhood points corresponding to the blank grid cells. , specifically: For non-empty grid cells, project their corresponding original neighborhood points onto the tangent plane distance Fill in; Calculate the weight of the original neighborhood points corresponding to each non-empty grid cell ; ； in, is the distance between the grid cell where the original neighborhood point is located and the blank grid cell, For the support radius, is the radial basis function; For empty grid cells, fill distance based on adjacent non-empty grid cells and the weight of the corresponding original neighborhood points Perform distance interpolation; ； in, is the distance of blank grid interpolation, is the number of non-empty grid cells; Interpolated distance from the blank grid and sampling points Normal vector , construct the interpolation neighborhood points corresponding to the blank grid cells .

2. The train-borne laser point cloud deformation correction method based on cluster analysis according to claim 1, characterized in that: The K-means clustering method is used to initialize the clustering of the distorted rail point cloud to divide the clusters.

3. The train-borne laser point cloud deformation correction method based on cluster analysis according to claim 1, characterized in that: The neighborhood points The geometric eigenvector of There are 8 variables, specifically: ； in, For sampling points Normal vector With vector The angle between Neighborhood points Normal vector With vector The angle between is the normal vector and The angle between For sampling points and neighborhood points The distance between is a vector At the sampling point The L2 norm of the projection on the tangent plane, is a vector In the normal vector The L2 norm of the projection, At the sampling point The two principal curvatures at and The maximum value of The two principal curvatures and The arithmetic mean curvature.

4. The train-borne laser point cloud deformation correction method based on cluster analysis according to claim 1, characterized in that: Obtaining neighborhood points The geometric eigenvector of and weights, including: obtaining interpolation area points Weight , specifically: ； in, is the neighborhood radius, is the current neighborhood point, Interpolation neighborhood points With neighboring points The Euclidean distance of .

5. The train-borne laser point cloud deformation correction method based on cluster analysis according to claim 1, characterized in that: The objective function for: ； ； in, is the fuzzy membership matrix, for The cluster center set of is the weighted covariance descriptor, Points of the distorted rail point cloud The displacement field, M Points of normal rail point cloud A collection of Points of the distorted rail point cloud A collection of Weighted covariance descriptor for normal rail point cloud and weighted covariance descriptor of distorted rail point cloud similarity; is the regularization term, is the regularization parameter, represents the matrix logarithm, represents the F norm of the matrix, is the index, is the fuzzy membership between each point in the distorted point cloud and the normal point cloud.

6. Train-borne laser point cloud deformation correction system based on cluster analysis, characterized by: include: Point cloud acquisition module: obtains normal rail point cloud and distorted rail point cloud; Initialization clustering module: Initialize clustering of distorted rail point cloud to divide clusters, and in the process of initialization clustering, allocate normal rail point cloud as cluster sample points to be allocated; Descriptor construction module: For each sampling point in the distorted rail point cloud and the normal rail point cloud, all neighboring points are searched in the corresponding cluster, and a weighted covariance matrix descriptor of the sampling point is constructed based on the geometric feature vectors of all neighboring points of the sampling point. Specifically: For each sampling point Search within the specified neighborhood radius All original neighborhood points within constitute the original neighborhood point set ; The original neighborhood point set Projection to sampling point The tangent plane On the projection point network, a uniform grid cell is generated on the tangent plane according to the range of the projection point network, and the blank grid cells are interpolated to construct the interpolation neighborhood points corresponding to the blank grid cells. ; Get neighborhood points The geometric eigenvector of and weights, where the neighborhood points Including interpolated neighborhood points and original neighborhood points; Constructing sampling points The weighted covariance matrix descriptor of ; ； in, is the number of all neighboring points of the sampling point, is the mean vector of the eigenvectors of all neighborhood points, For field points The weight of The method generates uniform grid cells on the tangent plane according to the range of the projected point network, and interpolates the blank grid cells to construct the interpolation neighborhood points corresponding to the blank grid cells. , specifically: For non-empty grid cells, project their corresponding original neighborhood points onto the tangent plane distance Fill in; Calculate the weight of the original neighborhood points corresponding to each non-empty grid cell ; ； in, is the distance between the grid cell where the original neighborhood point is located and the blank grid cell, For the support radius, is the radial basis function; For empty grid cells, fill distance based on adjacent non-empty grid cells and the weight of the corresponding original neighborhood points Perform distance interpolation; ； in, is the distance of blank grid interpolation, is the number of non-empty grid cells; Interpolated distance from the blank grid and sampling points Normal vector , construct the interpolation neighborhood points corresponding to the blank grid cells ; Objective function construction module: Introducing the weighted covariance matrix descriptor similarity constraint to construct the objective function for non-rigid clustering registration of distorted rail point clouds and normal rail point clouds; Iterative registration module: It continuously iteratively updates the non-rigid displacement field, weighted covariance matrix descriptor, and clustered fuzzy membership matrix until it falls below the set threshold of the objective function, completing the corrective registration of the distorted rail point cloud.

7. A computer device, characterized in that: The invention comprises a processor and a memory; wherein, when the processor executes the computer program stored in the memory, the steps of the train-borne laser point cloud deformation correction method based on cluster analysis according to any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium, characterized in that Used to store computer programs; when the computer programs are executed by the processor, the steps of the train-borne laser point cloud deformation correction method based on cluster analysis according to any one of claims 1 to 5 are implemented.

Images