Train-mounted laser point cloud deformation correction method, system and equipment based on clustering analysis and medium

Abstract

The invention discloses a train-mounted laser point cloud deformation correction method, system and device based on clustering analysis and a medium, and belongs to the technical field of laser point cloud processing, and the method comprises the steps: obtaining a normal rail point cloud and a distorted rail point cloud; performing initialization clustering on the distorted rail point clouds, and distributing the normal rail point clouds as to-be-distributed clustering sample points in the clustering process; for each sampling point of the distorted rail point cloud and the normal rail point cloud, searching all neighborhood points in corresponding clusters to construct weighted covariance matrix descriptors of the sampling points; constructing a target function of non-rigid clustering registration of the distorted rail point cloud and the normal rail point cloud; and continuously iteratively updating the non-rigid displacement field, the weighted covariance matrix descriptor and the clustered fuzzy membership matrix until the values are lower than a set threshold value of an objective function, and completing correction registration of the distorted rail point cloud. According to the invention, the problem of insufficient registration precision caused by uneven point cloud data density and noise interference can be solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of laser point cloud processing, and particularly relates to a method, system, device and medium for correcting the deformation of train-borne laser point clouds based on clustering analysis. Background Art

[0002] As the core infrastructure of railway transportation, railway tracks bear a large number of train loads and are affected by temperature changes, load fluctuations and other external factors during long-term use, resulting in varying degrees of deformation. These deformations are mainly manifested as the bending, wear, cracks and gauge changes of the railway tracks, which seriously affect the stable operation of trains, increase the risk of derailment, and lead to a significant decline in the train operation safety and transportation efficiency. To solve this problem, railway departments need to regularly detect and repair railway tracks to ensure that the flatness and geometric shape of the tracks meet the standards. Therefore, the correction technology for railway tracks has emerged as the times require and has become an essential technical means in railway maintenance.

[0003] In recent years, with the development of lidar technology, train-borne laser point cloud data has gradually become an important tool for solving this problem. Through on-vehicle lidar, the three-dimensional point cloud data of railway tracks can be collected in real time, providing more accurate basic data for the detection and correction of railway tracks. However, due to the influence of high speed and complex environment, the existing train-borne laser point cloud data often has problems such as uneven density, noise interference and point cloud registration error, which directly affect the data quality and further affect the subsequent data processing and analysis results. Summary of the Invention

[0004] Aiming at the deficiencies in the prior art, the present invention provides a method, system, device and medium for correcting the deformation of train-borne laser point clouds based on clustering analysis, which can cope with the changes in the characteristics of point clouds in complex dynamic environments and solve the problem of insufficient registration accuracy caused by uneven density and noise interference of point cloud data.

[0005] The present invention provides the following technical solutions: In the first aspect, a method for correcting the deformation of train-borne laser point clouds based on clustering analysis is provided, including the following steps: S1: Obtain the normal railway track point cloud and the distorted railway track point cloud; S2: Initialize the clustering of the distorted railway track point cloud to divide clusters, and during the initialization clustering process, assign the normal railway track point cloud as the clustering sample points to be assigned; S3: For each sampling point of the distorted railway track point cloud and the normal railway track point cloud, search for all neighborhood points in its corresponding cluster, and construct a weighted covariance matrix descriptor of the sampling point based on the geometric feature vectors of all neighborhood points of the sampling point; S4: Introduce 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; S5: Continuously iterate and update the non-rigid displacement field, weighted covariance matrix descriptor, and fuzzy membership matrix of the clusters until it is lower than the set threshold of the objective function to complete the corrective registration of the distorted rail point clouds.

[0006] Optionally, use the K-means clustering method to initialize the clustering of the distorted rail point clouds to divide the clusters.

[0007] Optionally, step S3 is specifically: For each sampling point Search for all the original neighborhood points within its set neighborhood radius to form the original neighborhood point set ; Project the original neighborhood point set onto the tangent plane of the sampling point to obtain the projected point network. Generate uniform grid cells on the tangent plane according to the range of the projected point network, and interpolate the blank grid cells to construct the interpolation neighborhood points corresponding to the blank grid cells ; Obtain the geometric feature vector and weight of the neighborhood point , where the neighborhood point includes the interpolation neighborhood points and the original neighborhood points; Construct the weighted covariance matrix descriptor of the sampling point ; ; where, is the number of all neighborhood points of the sampling point, is the mean vector of the feature vectors of all neighborhood points, is the weight of the domain point .

[0008] Optionally, the geometric feature vector of the neighborhood point has 8 variables, specifically: ; where, is the angle between the normal vector of the sampling point and the vector , is the angle between the normal vector of the neighborhood point and the vector , is the normal vector and is the included angle between is the sampling point and the neighborhood point is the distance between is the vector projected onto the tangent plane at the sampling point is the L2 norm of the projection is the vector projected onto the normal vector is the L2 norm of the projection is at the sampling point are the two principal curvatures and is the maximum value of are the two principal curvatures and is the arithmetic mean curvature

[0009] Optionally, uniformly spaced grid cells are generated on the tangent plane according to the range of the projected point network, and interpolation is performed on the blank grid cells to construct interpolation neighborhood points corresponding to the blank grid cells , specifically: For non-empty grid cells, the corresponding original neighborhood points are projected onto the tangent plane The distance is filled in; Calculate the weights of the original neighborhood points corresponding to each non-empty grid cell ; ; wherein, is the distance between the grid cell where the original neighborhood point is located and the blank grid cell, is the support radius, is the radial basis function; For blank grid cells, distance interpolation is performed based on the filled distances of adjacent non-empty grid cells and the weights ; wherein, is the distance for blank grid interpolation, is the number of non-empty grid cells; According to the distance for blank grid interpolation and the normal vector of the sampling point is constructed

[0010] Optionally, obtaining the neighborhood points Geometric feature vector and weights, including: obtaining interpolation neighborhood points weights , specifically: ; wherein, is the neighborhood radius, is the current neighborhood point, is the interpolation neighborhood point and the Euclidean distance between the neighborhood point .

[0011] Optionally, the objective function is: ; ; wherein, is the fuzzy membership matrix, is set of cluster centers, is the weighted covariance descriptor, is the point displacement field of the distorted rail point cloud, M is the point set of the normal rail point cloud, is the point set of the distorted rail point cloud, is the similarity between the weighted covariance descriptor of the normal rail point cloud and the weighted covariance descriptor of the distorted rail point cloud; is the regularization term, is the regularization parameter, represents the matrix logarithm, represents the Frobenius norm of the matrix, is the exponent, is the fuzzy membership between each point of the distorted point cloud and the normal point cloud.

[0012] In a second aspect, a train-borne laser point cloud deformation correction system based on clustering analysis is provided, including: Point cloud acquisition module: acquiring a normal rail point cloud and a distorted rail point cloud; Initialization clustering module: performing initialization clustering on the distorted rail point cloud to divide clusters, and during the initialization clustering process, allocating the normal rail point cloud as the clustering sample points to be allocated; Descriptor construction module: for each sampling point of the distorted rail point cloud and the normal rail point cloud, searching for all neighborhood points in its corresponding cluster, and constructing a weighted covariance matrix descriptor of the sampling point based on the geometric feature vectors of all neighborhood points of the sampling point; Objective function construction module: Introduce 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; Iterative registration module: Continuously iterate and update the non-rigid displacement field, weighted covariance matrix descriptor, and fuzzy membership matrix of the clustering until it is lower than the set threshold of the objective function to complete the corrected registration of the distorted rail point cloud.

[0013] In a third aspect, a computer device is provided, including a processor and a memory; wherein, when the processor executes the computer program stored in the memory, the steps of the method for correcting the deformation of train-borne laser point cloud based on clustering analysis according to any one of the first aspects are implemented.

[0014] 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 method for correcting the deformation of train-borne laser point cloud based on clustering analysis according to any one of the first aspects are implemented.

[0015] Compared with the prior art, the beneficial effects of the present invention are: The method for correcting the deformation of train-borne laser point cloud proposed by the present invention, aiming at rail deformation, can capture the geometric features of the local point cloud of the rail through the covariance matrix descriptor, more accurately reflect the curvature, normal vector and neighborhood structure characteristics of the deformed rail points, thus significantly improving the correction accuracy; Secondly, the present invention processes the density non-uniformity caused by deformation and the noise interference of the surrounding environment through a weighting mechanism, enhances the robustness to complex scenes, and at the same time adds a clustering framework to optimize the non-rigid deformation field, making the method adaptable to a large range of non-linear deformations. In addition, the clustering framework can decompose the registration and correction problem into local sub-problems, greatly reducing the complexity of global calculation. 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 result is reasonable, making it widely applicable to complex scenes such as high noise, occlusion and density difference. Generally speaking, the deformation correction method of the present application performs excellently in terms of accuracy, robustness, efficiency and applicability, providing effective technical support for solving the problems of rail deformation and complex non-rigid point cloud registration. Description of the Drawings

[0016] Figure 1 is the flowchart of the method for correcting the deformation of train-borne laser point cloud based on clustering analysis of the present invention; Figure 2 is the schematic diagram of the geometric feature vector of the neighborhood points of the present invention; Figure 3 is the interpolation example of the uniform area with non-uniform point density and data gap of the present invention; Figure 4 It is an example of the weighted covariance descriptor for two identical local surfaces in the railway track scenario of the present invention; Figure 5 It is a schematic diagram of the point cloud before correcting the distorted railway tracks in the first specific scenario; Figure 6 It is a schematic diagram of the point cloud after correcting the distorted railway tracks in the first specific scenario using the present application; Figure 7 It is a schematic diagram of the point cloud before correcting the distorted railway tracks in the second specific scenario; Figure 8 It is a schematic diagram of the point cloud after correcting the distorted railway tracks in the second specific scenario using the present application. Detailed implementation manners

[0017] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and cannot be used to limit the protection scope of the present invention. It should be noted that the term "including" and any of its deformations in the description and claims of the present invention and the above accompanying drawings are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device including a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0018] Embodiment 1 As Figure 1 shown, a method for correcting the deformation of train-borne laser point clouds based on clustering analysis is provided, including the following steps: S1: Obtain the point cloud of normal railway tracks and the point cloud of distorted railway tracks.

[0019] Both the point cloud of normal railway tracks and the point cloud of distorted railway tracks can be collected by a lidar scanning system installed on the train and preprocessed, including denoising, point cloud density balancing, and data alignment. For the present application, the method of two-way cloth simulation can be used to effectively extract the point cloud of the railway track part and ensure the quality of the basic data for subsequent registration.

[0020] As a specific example, six groups of overlapping train-borne laser point cloud data are processed, and the method of two-way cloth simulation is used to obtain data with distorted railway tracks and normal railway tracks. Taking one group as an example, first, the point cloud of the distorted railway tracks and the point cloud of the normal railway tracks are respectively filtered to remove noise points, and then N and M approximately uniformly distributed points are sampled.

[0021] S2: Initialize the clustering of the point cloud of distorted railway tracks to divide clusters, and during the initialization of clustering, the point cloud of normal railway tracks is used as the clustering sample points to be assigned for assignment.

[0022] Specifically, the K-means clustering method is used to divide the distorted railway track point cloud data into a predetermined number of clusters, ensuring that the points in each cluster have similar spatial characteristics. The K-means clustering method can refer to the prior art. That is, in this application, the distorted railway track point cloud is used as the source point cloud, and the normal railway track point cloud is used as the target point cloud to initialize the clustering.

[0023] As a specific example, the K-means clustering method is used to process the distorted railway track point cloud data, and the data is divided into C clusters, with one clustering center for each cluster, ensuring that the points in each cluster have similar spatial characteristics. First, the points in the distorted railway track point cloud are used as the initial clustering centers, and the points in the normal railway track point cloud are used as the sample points to be assigned. Specifically, the k-means clustering method is used to gradually assign the clustering centers formed by the distorted railway track point cloud to the sample points of the normal railway track point cloud, and then the membership degree of each clustering center point is calculated according to the sample points and the nearest clustering center.

[0024] S3: For each sampling point of the distorted railway track point cloud and the normal railway track point cloud, search for all neighboring points in its corresponding cluster, and based on the geometric feature vectors of all neighboring points of the sampling point, construct a weighted covariance matrix descriptor for the sampling point.

[0025] Specifically, search for neighboring points for the points in each cluster of the source point cloud, project the neighboring point set onto the tangent plane of the sampling point to obtain a projected point network, interpolate the 8D feature vectors of the projected grid cells in different cases to construct a complete weighted covariance matrix descriptor; similarly, search for neighboring points for each point of the target point cloud, calculate geometric variables based on the neighboring points to construct its weighted covariance matrix descriptor. In addition, when constructing the covariance matrix descriptor, to ensure the robustness and descriptiveness of the descriptor, corresponding weights are assigned according to the point density of each neighboring point.

[0026] Step S3 specifically includes the following sub-steps: S31: For each sampling point Search for all original neighboring points within its set neighborhood radius to form an original neighboring point set .

[0027] The way to search for the original neighboring points can refer to the prior art. The original neighboring points refer to the points of the distorted railway track point cloud or the normal railway track point cloud.

[0028] S32: Project the original neighboring point set onto the tangent plane of the sampling point to obtain a projected point network, generate uniform grid cells on the tangent plane according to the range of the projected point network, and interpolate the blank grid cells to construct interpolation neighboring points corresponding to the blank grid cells .

[0029] As Figure 3 shown Figure 3 (a) shows an example of interpolating distorted rail point clouds, Figure 3 (b) shows an example of interpolating normal rail point clouds. Step S32 is specifically as follows: S321: Project the original neighborhood point set onto the tangent plane of the sampling point to obtain a projected point network . The relationship between the original neighborhood point and its projected point can be obtained according to . Among them, is the distance from this point to the tangent plane , is the normal vector of the sampling point.

[0030] S322: For the generated grid cells, if a grid cell is occupied by at least one projected point, it is a non-empty grid cell. For non-empty grid cells, fill in the distance of the corresponding original neighborhood point projected onto the tangent plane in the grid.

[0031] S323: Calculate the weight of the original neighborhood point corresponding to each non-empty grid cell.

[0032] ; Among them, is the distance between the grid cell where the original neighborhood point is located and the blank grid cell, is the support radius, is the radial basis function (RBF); S324: For each blank grid cell, perform distance interpolation based on the filling distance of the adjacent non-empty grid cells and the weight of the corresponding original neighborhood point; ; Among them, is the distance of blank grid interpolation, is the number of non-empty grid cells.

[0033] S325: According to the distance of blank grid interpolation and the normal vector of the sampling point , construct an interpolation neighborhood point corresponding to the blank grid cell.

[0034] S33: Obtain neighborhood points and their geometric feature vectors as well as weights, where the neighborhood points include interpolated neighborhood points and original neighborhood points.

[0035] The neighborhood points have 8 variables for their geometric feature vectors , specifically:[[]] ; where is the angle between the normal vector of the sampling point and the vector . is the angle between the normal vector of the neighborhood point and the vector . is the angle between the normal vectors and . is the distance between the sampling point and the neighborhood point . is the L2 norm of the projection of the vector on the tangent plane of the sampling point . is the L2 norm of the projection of the vector on the normal vector . is the maximum value of the two principal curvatures and at the sampling point . is the arithmetic mean curvature of the two principal curvatures and .

[0036] The calculation methods for each variable are as follows:[[]]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] where represents the dot product Represents the second norm of a vector, the geometric feature vector Contains three angular measures , three length measures And two curvature-based measures , as Figure 2 Shown Figure 2 In (a) is the three angular measures of the geometric feature vector, Figure 2 In (b) is the three length measures of the geometric feature vector. They are all relative variables that are invariant to spatial transformation and jointly describe the geometric properties of the local surface comprehensively. It should be noted that before each variable is assembled into the feature vector, they are normalized within [0,1] respectively to ensure that these variables have equal ranges, and finally the geometric feature vector of this neighborhood point is formed.

[0043] The weight of the original neighborhood point can refer to the calculation formula in step S323.

[0044] Interpolated neighborhood point Weight The calculation formula is: ; Among them, Is the neighborhood radius, Is the current neighborhood point, Is the interpolated neighborhood point And the neighborhood point Euclidean distance.

[0045] S34: Construct the weighted covariance matrix descriptor of the sampling point ; ; ; Among them, Is the number of all neighborhood points of the sampling point, Is the mean vector of the feature vectors of all neighborhood points, Is the weight of the neighborhood point .

[0046] The constructed covariance matrix descriptor Is an 8×8 asymmetric matrix. The diagonal entries represent the variances of each geometric feature, and the non-diagonal entries represent the covariances between different geometric features. The covariance descriptor treats multiple geometric features as samples of a joint variability distribution. The covariance matrix descriptor performs local feature modeling on each point of 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 the adaptability to complex scenarios such as noise and uneven point density. This also considers the consistency of local geometric features when considering the global deformation optimization of the point cloud. As Figure 4 ShownFigure 4 On the left side in Figure 4 is a partially enlarged schematic part, which is Example 1 of the local surface and descriptor with the same name.

[0047] S4: Introduce 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.

[0048] Before constructing the current function, the following problems need to be mainly solved for fuzzy clustering analysis:

[0049] Among them, is the fuzzy factor that controls the fuzziness of clustering. For the non-rigid registration with deformation, the goal is to find the optimal deformation mapping that minimizes the shape deviation between and X. Therefore, the non-rigid registration based on clustering analysis can be expressed as: Based on the above non-rigid registration based on clustering analysis, this application constructs a weighted covariance matrix descriptor, calculates the descriptor similarity between the source point cloud and the target point cloud, and according to the characteristics that clustering analysis can group the distribution characteristics (such as density, shape, spatial position, etc.) of the rail point cloud, combines the above grouping characteristics, geometric position distance error and covariance matrix descriptor similarity to construct the objective function to ensure that the corresponding points in the rail correction registration process can be accurately matched and effectively avoid the mis-matching of non-corresponding points. In addition, regularization constraints are used to optimize the objective function, making the rail registration and correction process more accurate and robust.

[0050] Therefore, the objective function of this application is: ; ; Among them, is the fuzzy membership matrix, is the set of cluster centers of, is the weighted covariance descriptor, is the displacement field of the point of the distorted rail point cloud, M is the set of points of the normal rail point cloud, is the set of points of the distorted rail point cloud, is the similarity between the weighted covariance descriptor of the normal rail point cloud and the weighted covariance descriptor of the distorted rail point cloud; is the regularization term, is the regularization parameter, represents the matrix logarithm, represents the Frobenius norm of the matrix, is the exponent, is the fuzzy membership degree between each point of the distorted point cloud and the normal point cloud.

[0051] The regularization term penalizes those matches with low descriptor similarity, suppresses the incorrect matches of non-homonymous points, and prompts the optimization algorithm to tend to select point pairs with high descriptor similarity.

[0052] In this application, for the two weighted covariance matrix descriptors of the normal rail point cloud and the distorted rail point cloud, a similarity metric is used to measure their similarity. To improve efficiency, the calculation is simplified by the difference of matrix logarithms, and it is normalized by an exponential function. The similarity is approximated by the logarithm difference metric, and the metric is faster because the two matrices are decoupled, avoiding 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:

[0053] where is the weight coefficient to increase the description.

[0054] S5: Continuously iterate and update the non-rigid displacement field, the weighted covariance matrix descriptor, and the clustering fuzzy membership matrix until it is lower than the set threshold of the objective function, and complete the corrected registration of the distorted rail point cloud.

[0055] Continuously iterative solution parameters, so that the change value of the objective function decreases. When the change value is less than the set threshold, the algorithm is considered to converge, and the final rail registration result is output.

[0056] Introduce the covariance matrix descriptor similarity constraint into the clustering function, so that the rail point cloud considers the consistency of local geometric features while considering large-scale deformation, increasing the refinement of the correction. Finally, through iterative optimization of the clustering probability matrix, the non-rigid deformation field, and the covariance matrix descriptor, the accurate alignment of the source point cloud and the target point cloud is gradually realized, thus forming a train-borne laser point cloud deformation correction method for adaptive adjustment clustering analysis that is both robust and efficient; as Figures 5 - 8 shown in the two scenarios, it can be seen that the deformation correction method of this application is accurate and stable.

[0057] Embodiment 2 A train-borne laser point cloud deformation correction system based on clustering analysis, including: Point cloud acquisition module: acquire normal rail point cloud and distorted rail point cloud; Initial clustering module: perform initial clustering on the distorted rail point cloud to divide clusters, and during the initial clustering process, assign the normal rail point cloud as the clustering sample points to be assigned; Descriptor construction module: for each sampling point of the distorted rail point cloud and the normal rail point cloud, search for all neighborhood points in its corresponding cluster, and construct a weighted covariance matrix descriptor of the sampling point based on the geometric feature vectors of all neighborhood points of the sampling point; Objective function construction module: introduce the similarity constraint of the weighted covariance matrix descriptor, and construct the objective function for non-rigid clustering registration of the distorted rail point cloud and the normal rail point cloud; Iterative registration module: continuously iterate and update the non-rigid displacement field, the weighted covariance matrix descriptor, and the fuzzy membership matrix of the clustering until it is lower than the set threshold of the objective function, and complete the corrected registration of the distorted rail point cloud.

[0058] For a more specific process of the above method, reference can be made to the corresponding content disclosed in the foregoing embodiments, and details will not be elaborated here.

[0059] Embodiment 3 The present invention provides a computer device, including a processor and a memory; wherein, when the processor executes the computer program stored in the memory, the steps of the above method for correcting the deformation of train-borne laser point cloud based on clustering analysis are implemented.

[0060] For a more specific process of the above method, reference can be made to the corresponding content disclosed in the foregoing embodiments, and details will not be elaborated here.

[0061] Embodiment 4 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 above method for correcting the deformation of train-borne laser point cloud based on clustering analysis are implemented.

[0062] For a more specific process of the above method, reference can be made to the corresponding content disclosed in the foregoing embodiments, and details will not be elaborated here.

[0063] In this specification, each embodiment is described in a progressive manner. The key points of each embodiment are the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the systems, devices, and storage media disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and the relevant parts can be referred to the description of the method part.

[0064] Those skilled in the art can clearly understand that the technologies in the embodiments of the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solutions in the embodiments of the present invention, in essence, or the parts that contribute 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, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0065] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A method for correcting the deformation of train-borne laser point clouds based on clustering analysis, characterized in that It includes the following steps: S1: Obtain the normal rail point cloud and the distorted rail point cloud; S2: Perform initial clustering on the distorted rail point cloud to divide clusters, and during the initial clustering process, assign the normal rail point cloud as the clustering sample points to be assigned; S3: For each sampling point of the distorted rail point cloud and the normal rail point cloud, search for all neighborhood points in its corresponding cluster, and construct a weighted covariance matrix descriptor of the sampling point based on the geometric feature vectors of all neighborhood points of the sampling point; S4: Introduce the weighted covariance matrix descriptor similarity constraint to construct the objective function for non-rigid clustering registration of the distorted rail point cloud and the normal rail point cloud; S5: Continuously iterate and update the non-rigid displacement field, the weighted covariance matrix descriptor, and the fuzzy membership matrix of the clusters until it is lower than the set threshold of the objective function, and complete the corrected registration of the distorted rail point cloud.

2. The method for correcting the deformation of train-borne laser point cloud based on clustering analysis according to claim 1, wherein Adopt the K-means clustering method to perform initial clustering on the distorted rail point cloud to divide clusters.

3. The method for correcting the deformation of train-borne laser point cloud based on clustering analysis according to claim 1, wherein, Step S3 is specifically: For each sampling point search all the original neighborhood points within its set neighborhood radius to form the original neighborhood point set ; Project the original neighborhood point set onto the tangent plane of the sampling point to obtain a projected point network. Generate uniform grid cells on the tangent plane according to the range of the projected point network, and interpolate the blank grid cells to construct interpolation neighborhood points corresponding to the blank grid cells ; Obtain neighborhood points of the geometric feature vector and weights, where the neighborhood points include interpolated neighborhood points and original neighborhood points; Construct sampling points weighted covariance matrix descriptor ; ； Among them, is the number of all neighborhood points of the sampling point, is the mean vector of the feature vectors of all neighborhood points, is the neighborhood point weight.

4. The method for correcting the deformation of train-borne laser point cloud based on cluster analysis according to claim 3, characterized in that The neighborhood points whose geometric feature vectors have 8 variables, specifically: ； Wherein, is the sampling point 's normal vector and the vector the included angle between, is the neighborhood point 's normal vector and the vector the included angle between, is the normal vector and the included angle between, is the sampling point and the neighborhood point the distance between, is the vector projected on the tangent plane of the sampling point the L2 norm of, is the vector projected on the normal vector the L2 norm of, is at the sampling point the two principal curvatures and the maximum value of, is the two principal curvatures and the arithmetic mean curvature of.

5. The method for correcting the deformation of train-borne laser point cloud based on cluster analysis according to claim 3, characterized in that Generate uniform grid cells on the tangent plane according to the range of the projection point network, and interpolate the blank grid cells to construct interpolation neighborhood points corresponding to the blank grid cells , specifically: For a non-empty grid cell, project its corresponding original neighborhood points onto the tangent plane of the distance Fill it in; Calculate the weights of the original neighborhood points corresponding to each non-empty grid cell ; ； wherein, is the distance between the grid cell where the original neighborhood point is located and the blank grid cell, is the support radius, is the radial basis function; For blank grid cells, perform distance interpolation based on the filling distances of adjacent non-blank grid cells and the weights of the corresponding original neighborhood points ; ； Among them, is the distance for blank grid interpolation, is the number of non-empty grid cells; Distance interpolated according to the blank grid and the normal vector of the sampling points to construct interpolation neighborhood points corresponding to the blank grid cells .​ 6. The method for correcting the deformation of train-borne laser point cloud based on clustering analysis according to claim 5, wherein The acquisition of neighborhood points of the geometric feature vector and weights, including: acquiring the weights of the interpolation neighborhood points , specifically: ； Among them, is the neighborhood radius, is the current neighborhood point, is the interpolation neighborhood point is the Euclidean distance between and the neighborhood point 7. The method for correcting the deformation of train-borne laser point cloud based on clustering analysis according to claim 1, wherein, The objective function is as follows: ； ； Among them, is the fuzzy membership matrix, is the set of clustering centers of is the weighted covariance descriptor, is the displacement field of the points of the distorted rail point cloud, M is the set of points of the normal rail point cloud, is the set of points of the distorted rail point cloud, is the weighted covariance descriptor of the normal rail point cloud and the weighted covariance descriptor of the distorted rail point cloud similarity; is the regularization term, is the regularization parameter, represents the matrix logarithm, represents the Frobenius norm of the matrix, is the exponent, is the fuzzy membership between each point of the distorted point cloud and the normal point cloud.

8. A train-borne laser point cloud deformation correction system based on clustering analysis, characterized in that, It includes: Point cloud acquisition module: Obtain the normal rail point cloud and the distorted rail point cloud; Initial clustering module: Perform initial clustering on the distorted rail point cloud to divide clusters, and during the initial clustering process, assign the normal rail point cloud as the clustering sample points to be assigned; Descriptor construction module: For each sampling point of the distorted rail point cloud and the normal rail point cloud, search for all neighborhood points in its corresponding cluster, and construct a weighted covariance matrix descriptor of the sampling point based on the geometric feature vectors of all neighborhood points of the sampling point; Objective function construction module: Introduce the weighted covariance matrix descriptor similarity constraint to construct the objective function for non-rigid clustering registration of the distorted rail point cloud and the normal rail point cloud; Iterative registration module: Continuously iterate and update the non-rigid displacement field, the weighted covariance matrix descriptor, and the fuzzy membership matrix of the clusters until it is lower than the set threshold of the objective function, and complete the corrected registration of the distorted rail point cloud.

9. A computer device, characterized in that, It includes a processor and a memory; wherein, when the processor executes the computer program stored in the memory, it implements the steps of the method for correcting the deformation of the train-borne laser point cloud based on clustering analysis according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, For storing a computer program; when the computer program is executed by the processor, it implements the steps of the method for correcting the deformation of the train-borne laser point cloud based on clustering analysis according to any one of claims 1-7.

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