High-speed loop line shape fitting method based on point cloud random sampling

Abstract

The present invention discloses a method for fitting the linear shape of a high-speed ring road based on random sampling of point clouds, relating to the field of ring road repair technology. The method comprises the following steps: S1 pre-processing the original point cloud to obtain a road surface point cloud; S2 using Alphashapes to perform boundary detection on the road surface point cloud by dividing it into sections to obtain a boundary point cloud; S3 fitting the boundary of a circular curve and determining the center of the circle on the boundary point cloud based on the consistency of random sampling, and fitting the boundary of a straight line segment on the boundary point cloud based on the consistency of random sampling to determine the site boundary size; S4 inferring the length of the site transition curve and the straight line length of the site based on the site boundary size and the position of the circular curve. The present invention realizes that extracting the linear shape of a ring road using LiDAR point cloud data can significantly improve measurement accuracy and efficiency, and enhance the degree of automation.

Description

Technical Field

[0001] The present invention relates to the technical field of ring road repair, and more particularly to a high-speed ring road linear fitting method based on point cloud random sampling. Background Art

[0002] Since the construction of expressway ring roads began in the 1980s, China's expressway ring road construction has experienced rapid growth. These early expressway ring roads are now reaching the end of their lifespans, with representative examples including test sites in Hainan, Dingyuan, and Xiangyang, which have been in use for over 30 years. Due to the intensity of use, these ring roads are experiencing varying degrees of pavement damage, primarily including broken slabs, broken corners, peeling edges, cracks, and exposed surfaces. Medium-speed lanes are the most prone to these damages. Given that minor repairs are no longer sufficient to meet the needs of ring road users, major overhauls are imperative.

[0003] Unlike new ring roads, the overhaul of existing ring roads is influenced by a variety of factors, including initial design specifications, construction techniques, post-construction settlement, and road surface conditions. Therefore, the design approach must be based on basic ring road design theory while also integrating the actual conditions of existing ring roads and fully utilizing new technologies and methods to carry out engineering design for ring road overhauls. An analysis of the full life cycle costs of ring roads can provide a reference for future new construction or renovations.

[0004] Before starting the overhaul project, it is necessary to conduct preliminary engineering measurements on the existing alignment of the high-speed ring road. Due to the limitations of measurement accuracy and curved surface working conditions, the traditional measurement method of total station plus level cannot meet the measurement requirements of the high-speed ring road.

[0005] Chinese patent application CN2021112910934 provides an automated highway road unevenness repair system and method. This system, combined with the integrated design of motor vehicles, improves repair efficiency, thereby reducing highway obstructions or safety accidents caused by road surface repairs. By using two road surface models derived through two processing methods and calculating their root mean square values, the volume of filler material for the road surface to be repaired can be more accurately calculated. Filling the concave space multiple times can make the road surface smoother and of better quality. At the same time, the same concave space can be filled in layers according to different degrees of concavity, further improving the repair effect. However, existing technologies cannot provide assistance for large-scale road reconstruction, and because the camera is located on a moving motor vehicle, it cannot provide effective assistance for high-precision measurements.

[0006] Therefore, providing a method for fitting the linear shape of a high-speed loop is an urgent problem for those skilled in the art. 3D laser scanning technology can effectively solve this problem. Extracting the linear shape of a loop from LiDAR point cloud data in topographic surveying can significantly improve measurement accuracy and efficiency, while also increasing the degree of automation. Summary of the Invention

[0007] In view of this, the present invention provides a high-speed loop line fitting method based on random sampling of point clouds to achieve the purpose of measuring road conditions with high precision.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] The high-speed loop line shape fitting method based on point cloud random sampling includes the following steps:

[0010] S1 pre-processes the original point cloud to obtain a road surface point cloud. The point cloud of the highway ring road line is extracted by laser radar. The road surface point cloud includes straight segment point cloud and curved segment point cloud.

[0011] S2 uses Alpha shapes to perform boundary detection on the road surface point cloud and obtains boundary point clouds. The boundary point clouds include straight line segment boundary point clouds and curve segment boundary point clouds.

[0012] S3 performs circular curve boundary fitting and circle center determination on the boundary point cloud based on random sampling consistency, and performs straight line segment boundary fitting on the boundary point cloud based on random sampling consistency to determine the site boundary size;

[0013] S4 reversely calculates the length of the site transition curve and the site straight line based on the site boundary size and the circular curve position.

[0014] Optionally, the specific steps of S1 include:

[0015] S1.1 filters each point in the original point cloud and generates a denoised point cloud; wherein the method for filtering the original point cloud adopts statistical filtering;

[0016] S1.2 generates a road surface point cloud by segmenting and denoising the point cloud based on the road surface normal and elevation mean square error.

[0017] Optionally, the specific steps of S1.1 include:

[0018] S1.1.1 Perform a denoising operation on the original point cloud. In each denoising operation, select any point in the original point cloud as the first point, and form a point set with the first point and the N1-1 points closest to it. The denoised point cloud is generated after all points in the original point cloud are denoised, and N1 is an integer greater than 2. The point set formula is:

[0019]

[0020] Where: X represents a set of points, x1 represents the first point closest to the first point, x2 represents the second point closest to the first point, represents the third point closest to the first point, represents the first point; where the point set conforms to the normal distribution;

[0021] S1.1.2 For each Point, calculation Divide a point by a set of points The distance to any point other than point , the specific formula is:

[0022]

[0023] Where: express Divide a point by a set of points The distance to any point other than point Indicates that the point set is Any point outside

[0024] S1.1.3 In Except for point Among the distances of any point, select the kmean smallest distances to generate a distance set. The distance set formula is:

[0025]

[0026] Where: represents the distance set, express Divide by the point set The distance to the first point closest to the point outside the point, express Divide by the point set The distance to the second nearest point outside the point, express Divide by the point set The distance to the nearest kmean point outside the point; kmean is an integer greater than 1;

[0027] S1.1.4 Take the mean of the distance set as The characteristic value of the distance set is calculated as follows:

[0028]

[0029] Where: represents the distance set mean;

[0030] S1.1.5 Determine outliers based on the distance mean formula and the variance mean formula, remove outliers from the original cloud point, retain valid points, and generate a denoised point cloud; the distance mean formula is:

[0031]

[0032] Where: mean represents the mean of the distance set means of all points in the point set;

[0033] The distance variance formula is:

[0034]

[0035] Where: stddev represents the variance of the distance set mean of all points in the point set and the distance set mean of all points in the point set;

[0036] If d i1 >mean+C*stddev, then x j is an outlier; if When x j is a valid point, where the C value is the outlier degree of the point.

[0037] Optionally, the specific steps of S1.2 include:

[0038] S1.2.1 Select any point in the point cloud as the query point Through the query point The nearest k2 neighboring points are used to solve the covariance matrix A created by the k2 neighboring points. The eigenvectors and eigenvalues ​​of the covariance matrix are fitted by the least squares method to obtain the point cloud normal. The corresponding covariance matrix can be expressed as:

[0039]

[0040]

[0041]

[0042] Where: A represents the covariance matrix, k2 represents the point The number of neighboring points, P i represents the query point, represents the 3D centroid of the neighboring points, represents the j2th eigenvector of the covariance matrix, λ j2 represents the j2th eigenvalue of the covariance matrix;

[0043] S1.2.2 When λ j2 The eigenvector corresponding to the minimum eigenvalue That is the normal vector of the calculation point:

[0044]

[0045] Where: represents the point normal, represents the x-direction component of the normal, represents the y-direction component of the normal, represents the z-direction component of the normal, and T is the transposed sign;

[0046] S1.2.3 Calculate the slope value at each point. The slope value calculation formula is:

[0047]

[0048] Where: tanα1 represents the slope value;

[0049] S1.2.4 Compare the slope value with the slope threshold to determine the segmentation point and road surface point of the expressway loop line; if tanα1≤tanα2, it is a segmentation point; if tanα1>tanα2, it is a road surface point, and tanα2 represents the slope threshold;

[0050] S1.2.5 Set a local cylinder in the denoised point cloud. The elevations of the points within the local cylinder are:

[0051]

[0052] Where: Z G represents the elevation collection, z G1 represents the elevation of the first point in the local cylinder, z G2 represents the elevation of the second point in the local cylinder, represents the elevation of the N2th point in the local cylinder, where N2 represents the number of points in the local cylinder; where N2 is an integer greater than 1;

[0053] S1.2.6 Calculate the mean elevation and standard deviation of each point within the local cylinder. When the standard deviation exceeds the standard deviation limit, it can be determined as a split point. The formula for calculating the mean elevation is:

[0054]

[0055] Where: represents the mean elevation, i3 represents the i3th point in the local cylinder;

[0056] The formula for calculating the elevation standard deviation is:

[0057]

[0058] Where: represents the standard deviation of elevation; if Then each point within the local cylinder is a foreign point. Indicates the preset elevation standard deviation limit;

[0059] S1.2.7 treats the road surface points as road surface areas and segments the denoised point cloud using segmentation points to obtain a road surface point cloud.

[0060] Optionally, the specific steps of S2 include:

[0061] S2.1 Select any point in the plane projection point cloud as the point to be determined P e (x e ,y e ), according to the preset rolling circle radius α e , search the distance P from the plane projection point cloud e Point distance is less than 2α e All points in the road surface point cloud are recorded as point set Q; the method for generating the plane projection point cloud is to convert all points z e The coordinates are all set to the same constant;

[0062] S2.2 Select any point in the point set Q as point P e1 (x e1 ,y e1 ), according to point P e , click P e1 and rolling circle radius α e , calculate the coordinates of the center of the first circle O1(x o1 ,y o1 ) and the center coordinates of the second circle O2(x o2 ,y o2 ); wherein the first circle intersects with the second circle and has two intersection points, and the rolling circle radius α e is the distance between the center of the first circle and the two intersection points, and the rolling circle radius α e is the distance between the center of the second circle and the two intersection points, P e 、P e1 are the two intersection points of the first circle and the second circle respectively;

[0063] S2.3 For all points in the set Q except P e1 For each point outside the circle, calculate its distance to the center O1 and O2 respectively. When the distances of all points to O1 and O2 are greater than α e When , the mark point P e is the contour point, ending at point P e Calculation of

[0064] S2.4 When P is removed from the point set Q e1 When the distance from any point outside to the center O1 and O2 is less than or equal to α, all points in the point set Q are rotated as P e1 Point, recalculate the coordinates of the circle center, and repeat step S2.3 for point P e Make a judgment; if there is a point P e Marked as a contour point, point P can be determined eis the contour point, and all the obtained contour points are combined into the boundary point set S, otherwise the judgment point P e is a non-contour point.

[0065] Optionally, the S3 specific steps include:

[0066] S3.1 uses RANSAC to fit the boundary contour of the point cloud;

[0067] The output model obtained by S3.2 through circular curve fitting of the point cloud boundary contour in S3.1 is:

[0068] (x h -x ho ) 2 +(y h -y ho ) 2 =R h 2

[0069] Where: (x h ,y h ) represents the coordinates of a point on the circular curve, (x ho ,y ho ) represents the coordinates of the center of the circular curve, R h Indicates the radius of the circular curve.

[0070] The output model obtained by S3.3 by fitting the straight line segments of the point cloud boundary contour in S3.1 is:

[0071] k h (x h -x h1 )=(y h -y h1 )

[0072] Where: (x h ,y h ) represents the coordinates of a point on the line, (x h1 ,y h1 ) represents the coordinates of a known point on the line, y h1 Indicates that k h Represents the slope of the line.

[0073] Optionally, the specific steps of S3.1 include:

[0074] S3.1.1 Randomly select a subset s from the set of boundary points S, use the randomly selected subset s as hypothetical inliers, and fit the initial model using the inliers s;

[0075] The model parameters are estimated based on the subset s. The circular curve parameters are calculated assuming that the coordinates of the points inside the local area are (x β1 ,y β1 ),(x β2,y β2 ),(x β3 ,y β3 ) into the S3.2 circular curve model

[0076] (x β1 -x ho ) 2 +(y β1 -y ho ) 2 =R h 2

[0077] (x β2 -x ho ) 2 +(y β2 -y ho ) 2 =R h 2

[0078] (x β3 -x ho ) 2 +(y β3 -y ho ) 2 =R h 2

[0079] Solving the above equations, we get

[0080]

[0081]

[0082] R h 2 =(x β1 -x ho ) 2 +(y β1 -y ho ) 2

[0083] Calculation of line parameters, assuming that the coordinates of the point inside the bureau are (x β1 ,y β1 ),(x β2 ,y β2 ) into the S3.3 straight line model

[0084] k h (x β1 -x h1 )=(y β1 -y h1 )

[0085] k h(x β2 -x h1 )=(y β2 -y h1 )

[0086] Solving the above equations, we get

[0087] k h =(y β2 -y β1 ) / (x β2 -x β1 )

[0088] x h1 =x β1

[0089] y h1 =y β1

[0090] S3.1.2 Traverse all data in the boundary point set S except the subset s and calculate the radius R of the circular curve h Or the slope of the line k h Error, if the error is within the error limit e, it is marked as an interior point, otherwise it is marked as an exterior point;

[0091] S3.1.3 Group all the inliers obtained in S3.1.2 into a consistent set. If the number of points in the consistent set meets a given threshold T, re-estimate the model parameters using all the inliers in the consistent set and output the results. If the number of inliers in the consistent set is less than the threshold T, select a new subset s and repeat steps S3.1.1-S3.1.2.

[0092] S3.1.4 After multiple iterations of S3.1.1-S3.1.3, select a consistent set with the largest number of inliers, use all the inliers in the consistent set to re-estimate the model parameters, and output the results; where the number of iterations is an integer greater than 1.

[0093] Optionally, the specific steps of S4 include:

[0094] S4.1 The overall width and length of the expressway loop are calculated using the offset formula to obtain the longitudinal offset and transverse offset of the transition curve, respectively. The formula for the relationship between the width and length of the site and the transition curve offset is:

[0095]

[0096]

[0097]

[0098]

[0099] Where: W represents the overall width of the high-speed ring road, k1 represents the slope of the straight line, Indicates the horizontal coordinate of the point at the center of the two circles. represents the ordinate of the point at the center of the two circles, y1 represents the ordinate of the known point on the first fitting line, x1 represents the abscissa of the known point on the first fitting line, y2 represents the ordinate of the known point on the second fitting line, x2 represents the abscissa of the known point on the second fitting line, M represents the lane width adjustment value between the center line of the straight line segment and the fitting line, β represents the transition curve angle, R represents the radius of the circular curve, L y Indicates the longitudinal offset of the site transition curve, H indicates the overall site length of the high-speed ring road, X o1 Indicates the horizontal coordinate of the center of the first endpoint of the high-speed ring road, X o2 Indicates the horizontal coordinate of the center of the second endpoint of the high-speed ring road, Y o1 Indicates the vertical coordinate of the center of the first endpoint of the high-speed ring road, Y o2 represents the vertical coordinate of the center of the second end point of the high-speed ring road, L represents the straight length of the site, L x Indicates the lateral deviation of the site transition curve.

[0100] S4.2 The transition curve angle is calculated by the quadratic integral method of curvature; the transition curve angle β is calculated using the following formula:

[0101]

[0102] Where: Ls0 represents the assumed length of the transition curve, k(l) represents the function of the curvature of any point on the transition curve as the length of the transition curve changes;

[0103] The horizontal offset and vertical offset of the transition curve are calculated using the following formula:

[0104]

[0105]

[0106] S4.3 After linear fitting and correction, the error between the corresponding site width and the actual site width W is calculated using the assumed transition curve length Ls0, and the final transition curve length Ls is obtained by the approximation method. The site straight line length L is then calculated using the site length H.

[0107] Optionally, the transition curve curvature function k(l) in S4.2 adopts any one of the Bloss curve curvature function, the McConnell curve curvature function, the Grabowski curve curvature function, the Auberlen curve curvature function, and the Klein curve curvature function;

[0108] The curvature function of the Bloss curve is:

[0109]

[0110] Where: k(l) Bloss represents the curvature function of the Bloss curve;

[0111] The curvature function of the McConnell curve is:

[0112]

[0113]

[0114] Where: k(l) McConnell represents the curvature function of the McConnell curve, ψ represents the maximum superelevation angle, v represents the design speed, and g represents the acceleration of gravity;

[0115] The curvature function of the Grabowski curve is:

[0116]

[0117] Where: k(l) Grabowski represents the curvature function of the Grabowski curve;

[0118] The curvature function of the Auberlen curve is:

[0119]

[0120] Where: k(l) Auberlen represents the curvature function of the Auberlen curve;

[0121] The curvature function of the Klein curve is:

[0122]

[0123] Where: k(l) Klein Represents the Klein curve curvature function.

[0124] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a high-speed loop line shape fitting method based on random sampling of point clouds, which can achieve the following beneficial effects:

[0125] 1. Extracting the ring road alignment through LiDAR point cloud data can greatly improve measurement accuracy and efficiency, and increase the degree of automation;

[0126] 2. The segmented road surface boundary is fitted using the consistency of random sampling, eliminating the randomness of the calculation of the circle center result based on the radius of a single moving circle and improving the adaptive ability of road data fitting. BRIEF DESCRIPTION OF THE DRAWINGS

[0127] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0128] Figure 1 This is a flow chart of the high-speed loop line shape fitting method based on point cloud random sampling of the present invention;

[0129] Figure 2 This is a schematic diagram of Alpha shapes contour point extraction in the present invention;

[0130] Figure 3 This is a schematic diagram of Alpha shapes contour point judgment in the present invention;

[0131] Figure 4 This is the influence of the α value range of the Alpha shapes method of the present invention. DETAILED DESCRIPTION

[0132] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0133] like Figure 1 As shown, the embodiment of the present invention discloses a high-speed loop line shape fitting method based on point cloud random sampling, and the specific steps include:

[0134] S1 pre-processes the original point cloud to obtain a road surface point cloud. The point cloud of the highway ring road line is extracted by laser radar. The road surface point cloud includes straight segment point cloud and curved segment point cloud.

[0135] S2 uses Alpha shapes to perform boundary detection on the road surface point cloud and obtains boundary point clouds. The boundary point clouds include straight line segment boundary point clouds and curve segment boundary point clouds.

[0136] S3 performs circular curve boundary fitting and circle center determination on the boundary point cloud based on random sampling consistency, and performs straight line segment boundary fitting on the boundary point cloud based on random sampling consistency to determine the site boundary size;

[0137] S4 reversely calculates the length of the site transition curve and the site straight line based on the site boundary size and the circular curve position.

[0138] Furthermore, the specific steps of S1 include:

[0139] S1.1 filters the original point cloud and generates a denoised point cloud. Statistical filtering is used to filter the original point cloud. When collecting point cloud data via LiDAR, noise points are inevitably present due to factors such as equipment accuracy, operator experience, environmental factors, electromagnetic wave diffraction characteristics, surface property variations of the measured object, and the data stitching and registration process. Common point cloud filtering methods include direct filtering, voxel filtering, statistical filtering, and Gaussian filtering. Among these filtering methods, statistical filtering is particularly suitable for point cloud filtering of highway loops, given their overall point cloud characteristics.

[0140] S1.2 generates a road surface point cloud by segmenting and denoising the point cloud based on the road surface normal and elevation mean square error.

[0141] Furthermore, the specific steps of S1.1 include:

[0142] S1.1.1 Perform a denoising operation on the original point cloud. In each denoising operation, select any point in the original point cloud as the first point, and form a point set with the first point and the N1-1 points closest to it. The denoised point cloud is generated after all points in the original point cloud are denoised, and N1 is an integer greater than 2. The point set formula is:

[0143]

[0144] Where: X represents a set of points, x1 represents the first point closest to the first point, x2 represents the second point closest to the first point, represents the third point closest to the first point, represents the first point; where the point set conforms to the normal distribution;

[0145] S1.1.2 For each Point, calculation Divide a point by a set of points The distance to any point other than point , the specific formula is:

[0146]

[0147] Where: express Divide a point by a set of points The distance to any point other than point Indicates that the point set is Any point outside

[0148] S1.1.3 In Except for point-in Among the distances of any point, the kmean smallest distance group is selected as the distance set. The distance set formula is:

[0149]

[0150] Where: represents the distance set, express Divide by the point set The distance to the first point closest to the point outside the point, express Divide by the point set The distance to the second nearest point outside the point, express Divide by the point set The distance to the nearest kmean point outside the point; kmean is an integer greater than 1;

[0151] S1.1.4 Take the mean of the distance set as The characteristic value of the distance set is calculated as follows:

[0152]

[0153] Where: represents the distance set mean;

[0154] S1.1.5 Determine outliers based on the distance mean formula and the variance mean formula, remove outliers from the original cloud point, retain valid points, and generate a denoised point cloud; the distance mean formula is:

[0155]

[0156] Where: mean represents the mean of the distance set means of all points in the point set;

[0157] The distance variance formula is:

[0158]

[0159] Where: stddev represents the variance of the distance set mean of all points in the point set and the distance set mean of all points in the point set;

[0160] like When x j is an outlier; if When x j is a valid point, where the C value is the outlier degree of the point.

[0161] Furthermore, based on an analysis of the characteristics of the expressway ring road, we found that the point cloud on the expressway ring road is dense and the noise points on both sides are more significant. Therefore, the N value can be appropriately increased to remove more non-road points. Filtering tests show that when the number of points N>100 and the outlier degree C>1, the majority of noise points can be removed. After removing the outliers, the point cloud is smoother, suitable for the next step of point cloud clustering and segmentation, and converges more easily.

[0162] In addition to removing noise points, other road ancillary facilities, such as signs, guardrails, ditches, landscaping, and road workers and equipment, also affect the calculation and analysis of the point cloud road surface. Due to the limitations of the filtering algorithm, the processing of non-road surface point clouds requires further analysis of point cloud characteristics in combination with the characteristics of the expressway ring road. For the expressway ring road, there are significant differences in characteristics between straight and curved sections. Straight sections have a small cross slope, no superelevation, and various facilities on both sides, resulting in unclear boundary features. Curved sections have a large cross slope and only guardrails on both sides, resulting in clear boundary features.

[0163] Furthermore, the specific steps of S1.2 include:

[0164] S1.2.1 Select any point in the point cloud as the query point Through the query point The nearest k2 neighbor points are obtained by using the k-nearest neighbor search algorithm (kd-tree) to obtain the plane point set to be fitted. The plane equation to be constructed is:

[0165]

[0166] Where: represents the normal vector of the fitted plane, and D represents the distance from the origin to the plane;

[0167] Any point Distance to plane for

[0168]

[0169] The best fitting plane must satisfy the conditional function

[0170]

[0171] Get function

[0172]

[0173] Find the extreme point where the partial derivative of f with respect to D is 0

[0174]

[0175] Derived

[0176]

[0177] Where: Derived

[0178]

[0179] Where: Then use f to Find the extreme point where the partial derivative is 0

[0180]

[0181]

[0182]

[0183] Transforming the above formula, we can get

[0184]

[0185] In the formula

[0186] Solve the covariance matrix A created by k2 neighboring points, and fit the eigenvectors and eigenvalues ​​of the covariance matrix by the least squares method to obtain the point cloud normal; for each point in the point set The corresponding covariance matrix can be expressed as:

[0187]

[0188]

[0189]

[0190] Where: A represents the covariance matrix, k2 represents the point The number of neighboring points, P i represents the query point, represents the 3D centroid of the neighboring points, represents the j2th eigenvector of the covariance matrix, λ j2 represents the j2th eigenvalue of the covariance matrix;

[0191] S1.2.2 When The eigenvector corresponding to the minimum eigenvalue That is the normal vector of the calculation point:

[0192]

[0193] Where: represents the point normal, represents the x-direction component of the normal, represents the y-direction component of the normal, represents the z-direction component of the normal, and T is the transposed sign;

[0194] S1.2.3 Calculate the slope value at each point. The slope value calculation formula is:

[0195]

[0196] Where: tanα1 represents the slope value;

[0197] S1.2.4 Compare the slope value with the slope threshold to determine the segmentation point and road surface point of the expressway loop line; if tanα1≤tanα2, it is a segmentation point; if tanα1>tanα2, it is a road surface point, and tanα2 represents the slope threshold;

[0198] Based on the characteristics of the expressway ring road, the road surface slope threshold is the outer edge point of the circular curve section. The slope threshold is also the maximum superelevation of the expressway ring road and can be obtained through historical data of the expressway ring road. When historical data of the expressway ring road is lacking, the slope threshold can be determined through local statistical analysis.

[0199] S1.2.5 The slope classification method can achieve the segmentation of most road surface point clouds. However, due to the large composite slope of the highway ring road surface, the single slope separation method has inherent defects, and further analysis of the characteristics of the highway ring road surface point cloud is needed. Considering the characteristics of the highway ring road surface, the standard deviation of the local point cloud elevation can be used as a supplementary method for the road surface segmentation of the highway ring point cloud. A local cylinder is set in the denoised point cloud. The radius of the cylinder is preferably 0.05 to 0.1 meters. The elevations of each point within the local cylinder are:

[0200]

[0201] Where: Z G represents the elevation collection, z G1 represents the elevation of the first point in the local cylinder, z G2 represents the elevation of the second point in the local cylinder, represents the elevation of the N2th point in the local cylinder, where N2 represents the number of points in the local cylinder; where N2 is an integer greater than 1;

[0202] S1.2.6 Calculate the mean elevation and standard deviation of each point within the local cylinder. When the standard deviation exceeds the standard deviation limit, it can be determined as a split point. The formula for calculating the mean elevation is:

[0203]

[0204] Where: represents the mean elevation, i3 represents the i3th point in the local cylinder;

[0205] The formula for calculating the elevation standard deviation is:

[0206]

[0207] Where: represents the standard deviation of elevation; if Then each point within the local cylinder is a foreign point. Indicates the preset elevation standard deviation limit;

[0208] Similar to the slope determination method, a clear inflection point can be found on the elevation standard deviation change graph of the ordered point cloud as a basis for standard deviation determination. After point cloud pre-processing, the road surface point cloud can achieve a relatively ideal segmentation effect, with a road surface point cloud segmentation efficiency of over 99%.

[0209] S1.2.7 treats the road surface points as road surface areas and segments the denoised point cloud using segmentation points to obtain a road surface point cloud.

[0210] Furthermore, the specific steps of S2 include:

[0211] After pre-processing, the high-speed road surface point cloud needs to be further extracted to determine the outer dimensions of the high-speed ring road. Common point cloud boundary extraction algorithms include longitude and latitude scanning method, grid division method, normal estimation method, Alpha shapes algorithm, etc. Since the plane extraction of high-speed point clouds is mainly based on two-dimensional contour points, the Alpha shapes algorithm in the above methods is a relatively simple and effective algorithm for quickly extracting boundary points. This method overcomes the disadvantage of the influence of the shape of the boundary points of the point cloud and can quickly and accurately extract boundary points. The principle is that for a plane point cloud of any shape, if a circle with a radius of α rolls around it, the points formed by its rolling trajectory are contour points. When extracting the contour points of the point cloud, the points need to be projected onto a two-dimensional plane, generally a projection plane. At this time, the z coordinates of all points in the road surface point cloud are set to the same constant, that is, the z=0 plane.

[0212] S2.1 Select any point in the plane projection point cloud as the point to be determined P e (x e ,y e ), according to the preset rolling circle radius α e , search the distance P from the plane projection point cloud e Point distance is less than 2α e All points in the road surface point cloud are recorded as point set Q; the method for generating the plane projection point cloud is to convert all points z e The coordinates are all set to the same constant;

[0213] S2.2 As Figure 2 As shown, select any point in the point set Q as point P e1 (x e1 ,y e1 ), according to point P e , click P e1 and rolling circle radius α e , calculate the coordinates of the center of the first circle O1(x o1 ,y o1 ) and the center coordinates of the second circle O2(x o2 ,y o2 );like Figure 3 As shown, the first circle intersects with the second circle and has two intersection points, and the rolling circle radius α e is the distance between the center of the first circle and the two intersection points, and the rolling circle radius α e is the distance between the center of the second circle and the two intersection points, P e 、P e1 are the two intersection points of the first circle and the second circle respectively;

[0214] S2.3 For all points in the set Q except P e1 For each point outside the circle, calculate its distance to the center O1 and O2 respectively. When the distances of all points to O1 and O2 are greater than α e When , the mark point P e is the contour point, ending at point P e Calculation of

[0215] S2.4 When P is removed from the point set Q e1 When the distance from any point outside to the center O1 and to O2 is less than or equal to α, all points in the point set Q are rotated as P e1 Point, recalculate the coordinates of the circle center, and repeat step S2.3 for point P e Make a judgment; if there is a point P e Marked as a contour point, point P can be determined e is a contour point, otherwise the judgment point P e is a non-contour point.

[0216] According to the above calculation steps, it is necessary to determine a reasonable rolling circle radius α to complete the extraction of the plane contour of the high-ring point cloud. The point cloud contour calculation is as follows: Figure 4 As shown in the figure, since the radius of the moving circle α has a certain impact on the point cloud contour, the rationality of its value has a significant impact on linear fitting. When the value of α is smaller than the spacing at the point cloud boundary, the point cloud boundary cannot be extracted; when the value of α is larger than the point cloud boundary spacing and smaller than the average point cloud spacing, the extracted point cloud contains a large number of holes, affecting the fitting results; when the value of α is larger than the average point cloud spacing, the boundary point cloud gradually becomes sparse as the value of α increases, which has a significant impact on subsequent fitting.

[0217] Furthermore, the S3 specific steps include:

[0218] S3.1 uses RANSAC to fit the boundary contour of the point cloud;

[0219] The output model obtained by S3.2 through circular curve fitting of the point cloud boundary contour in S3.1 is:

[0220] (x h -x ho ) 2 +(y h -y ho ) 2 =R h 2

[0221] Where: (x h ,y h ) represents the coordinates of a point on the circular curve, (x ho ,y ho ) represents the coordinates of the center of the circular curve, R h Indicates the radius of the circular curve.

[0222] The output model obtained by S3.3 by fitting the straight line segments of the point cloud boundary contour in S3.1 is:

[0223] k h (x h -x h1 )=(y h -y h1 )

[0224] Where: (x h ,y h ) represents the coordinates of a point on the line, (x h1 ,y h1 ) represents the coordinates of a known point on the line, y h1 Indicates that k h Represents the slope of the line.

[0225] For the overall model, the RANSAC output is influenced by the boundary extraction results and the fitting threshold, and the results of a single parameter are subject to a certain degree of randomness. To reduce the impact of randomness on the results, it is necessary to reduce the impact of parameter changes on the fitting results. By analyzing the combined parameters of the moving circle radius α and the fitting threshold, and calculating the standard deviation of the calculated results for different boundary moving circle radii under the same fitting threshold, it is found that when the fitting threshold is between 0.004 and 0.006, the discreteness of the fitting results is low, and the fitting results are better.

[0226] In S3.2, for circular curves, the radius of the circle α is different from the boundary contour. b1 , α b2 ,…,αbn Calculation will give different circle centers (x bo1 ,y bo1 ), (x bo2 ,y bo2 ),…,(x bon ,y bon ), in order to eliminate the randomness of the calculation of the circle center by the radius of a single moving circle, it is advisable to take the center of gravity of different calculation circle center sets For a discrete set of circle center points, the calculation method of the barycentric coordinates is the arithmetic mean of the coordinates of each point, that is, the calculation formula of the barycentric coordinates is:

[0227]

[0228]

[0229] Where: Indicates the horizontal coordinate of the center of gravity, x boi represents the horizontal coordinate of the discrete circle center, Indicates the horizontal coordinate of the center of gravity, y boi Represents the vertical coordinate of the discrete circle center.

[0230] In S3.2, for straight lines, due to the long length of the expressway loop, when using RANSAC for linear fitting, a small fitting threshold yields high line accuracy, but the number of boundary subset points is small, the maximum distance between the fitted points is small, and the integrity of the fitted line is poor. Conversely, a large fitting threshold results in a large number of boundary subset points, a larger maximum distance between the fitted points, and lower RANSAC output model accuracy. For a complete expressway loop, there are four boundary lines between two straight segments. Due to the influence of point cloud acquisition accuracy and the widening of the entry and exit segments, the maximum length of the fitted point cloud varies for different lines. The minimum threshold at which the maximum length of the fitted points for each line reaches a stable value is used as the line fitting result.

[0231] Furthermore, the specific steps of S3.1 include:

[0232] After extracting the boundary contours of the highway loop point cloud, two corresponding fitting operations are required for both the straight line and the circular curve to obtain the linearity metrics. In step S3, the RANSAC method is used to fit the circular curve and the straight line segments separately. This method iteratively estimates the parameters of the mathematical model from a set of observations containing "outliers." This is an uncertain algorithm that can derive a reasonable result based on a certain probability. However, increasing the number of iterations is necessary to improve the probability.

[0233] The basic assumptions of RANSAC are: (1) the data consists of "inliers," i.e., the distribution of the data can be explained by some model parameters; (2) "outliers" are data that cannot fit the model; and (3) all other data is noise. Outliers can be caused by extreme noise values, incorrect measurement methods, or incorrect assumptions about the data.

[0234] The input of the RANSAC algorithm is a set of boundary data, a parameterized model that can explain or adapt to the observed data, and some parameters. RANSAC achieves its goal by repeatedly selecting a set of random subsets of the data. The selected subsets are assumed to be inliers and verified using the following method:

[0235] S3.1.1 Randomly select a subset s from the set of boundary points S, use the randomly selected subset s as hypothetical inliers, and fit the initial model using the inliers s;

[0236] The model parameters are estimated based on the subset s. The circular curve parameters are calculated assuming that the coordinates of the points inside the local area are (x β1 ,y β1 ),(x β2 ,y β2 ),(x β3 ,y β3 ) into the S3.2 circular curve model

[0237] (x β1 -x ho ) 2 +(y β1 -y ho ) 2 =R h 2

[0238] (x β2 -x ho ) 2 +(y β2 -y ho ) 2 =R h 2

[0239] (x β3 -x ho ) 2 +(y β3 -y ho ) 2 =R h 2

[0240] Solving the above equations, we get

[0241]

[0242]

[0243] R h 2 =(x β1 -x ho ) 2 +9y β1 -y ho ) 2

[0244] Calculation of line parameters, assuming that the coordinates of the point inside the bureau are (x β1 ,y β1 ),(x β2 ,y β2 ) into the S3.3 straight line model

[0245] k h (x β1 -x h1 )=(y β1 -y h1 )

[0246] k h (x β2 -x h1 )=(y β2 -y h1 )

[0247] Solving the above equations, we get

[0248] k h =(y β2 -y β1 ) / (x β2 -x β1 )

[0249] x h1 =x β1

[0250] y h1 =y β1

[0251] S3.1.2 Traverse all data in the boundary point set S except the subset s and calculate the radius R of the circular curve h Or the slope of the line k h Error, if the error is within the error limit e, it is marked as an interior point, otherwise it is marked as an exterior point;

[0252] S3.1.3 Group all the inliers obtained in S3.1.2 into a consistent set. If the number of points in the consistent set meets a given threshold T, re-estimate the model parameters using all the inliers in the consistent set and output the results. If the number of inliers in the consistent set is less than the threshold T, select a new subset s and repeat steps S3.1.1-S3.1.2.

[0253] S3.1.4 After multiple iterations of S3.1.1-S3.1.3, select a consistent set with the largest number of inliers, use all the inliers in the consistent set to re-estimate the model parameters, and output the results; where the number of iterations is an integer greater than 1.

[0254] Furthermore, the specific steps of S4 include:

[0255] S4.1 The overall width and length of the expressway loop are calculated using the offset formula to obtain the longitudinal offset and transverse offset of the transition curve, respectively. The formula for the relationship between the width and length of the site and the transition curve offset is:

[0256]

[0257]

[0258]

[0259]

[0260] Where: W represents the overall width of the high-speed ring road, k1 represents the slope of the straight line, Indicates the horizontal coordinate of the point at the center of the two circles. represents the ordinate of the point at the center of the two circles, y1 represents the ordinate of the known point on the first fitting line, x1 represents the abscissa of the known point on the first fitting line, y2 represents the ordinate of the known point on the second fitting line, x2 represents the abscissa of the known point on the second fitting line, M represents the lane width adjustment value between the center line of the straight line segment and the fitting line, β represents the transition curve angle, R represents the radius of the circular curve, L y Indicates the longitudinal offset of the site transition curve, H indicates the overall site length of the high-speed ring road, X o1 Indicates the horizontal coordinate of the center of the first endpoint of the high-speed ring road, X o2 Indicates the horizontal coordinate of the center of the second endpoint of the high-speed ring road, Y o1 Indicates the vertical coordinate of the center of the first endpoint of the high-speed ring road, Y o2 represents the vertical coordinate of the center of the second end point of the high-speed ring road, L represents the straight length of the site, L x Indicates the lateral deviation of the site transition curve.

[0261] Furthermore, the results output by the model in S3 are based on the calculation and fitting of the point cloud, but there are still differences between the actual point cloud and the design indicators. The design indicators of the circular curve part fitting cannot completely match the design indicators of the straight line fitting. As shown in the figure below, the slopes of the two straight lines are not equal to the slope of the line connecting the center of the circle, that is, V1 / U1≠V2 / U2≠(y o2 -y o1 ) / (xo2 -x o1 ). Therefore, the high loop line shape needs further fitting analysis and correction.

[0262] Among them, the indicators that need to be clarified for the fitting line shape of the expressway ring include the coordinates of the center of the circle at both ends (Xo1, Yo1), (Xo2, Yo2), the length of the site straight line L, the length of the site transition curve Ls, and the radius of the circular curve R; the coordinates of the center of the circle have been obtained through RANSAC fitting, and the radius of the circular curve can be calculated by the offset value of the boundary fitting radius and the design line, and then comprehensively determined by comparison with the original design indicators. The length of the straight line and the length of the transition curve are unknown parameters; according to the characteristics of the transition curve, the transition curve offset x, y and the transition curve angle β can be calculated when R and Ls are known, and then the overall site width W and length H of the expressway ring are derived. During the calculation, W is based on the spacing between the fitted lines on both sides, and the lane width is adjusted according to the centerline position of the straight line segment. H is determined by the distance between the center coordinates of the circle at both ends.

[0263] S4.2 The transition curve angle is calculated by the quadratic integral method of curvature; the transition curve angle β is calculated using the following formula:

[0264]

[0265] Where: Ls0 represents the assumed length of the transition curve, k(l) represents the function of the curvature of any point on the transition curve as the length of the transition curve changes;

[0266] The horizontal offset and vertical offset of the transition curve are calculated using the following formula:

[0267]

[0268]

[0269] S4.3 After linear fitting and correction, the error between the corresponding site width and the actual site width W is calculated using the assumed transition curve length Ls0, and the final transition curve length Ls is obtained through the approximation method. The site straight line length L is then calculated using the site length H. The above indicators can be obtained to complete the high-precision fitting of the loop plane linear shape.

[0270] Furthermore, the transition curve curvature function k(l) in S4.2 adopts any one of the Bloss curve curvature function, the McConnell curve curvature function, the Grabowski curve curvature function, the Auberlen curve curvature function, and the Klein curve curvature function;

[0271] The curvature function of the Bloss curve is:

[0272]

[0273] Where: k(l)Bloss represents the curvature function of the Bloss curve;

[0274] The curvature function of the McConnell curve is:

[0275]

[0276]

[0277] Where: k(l) McConnell represents the curvature function of the McConnell curve, ψ represents the maximum superelevation angle, v represents the design speed, and g represents the acceleration of gravity;

[0278] The curvature function of the Grabowski curve is:

[0279]

[0280] Where: k(l) Grabowski represents the curvature function of the Grabowski curve;

[0281] The curvature function of the Auberlen curve is:

[0282]

[0283] Where: k(l) Auberlen represents the curvature function of the Auberlen curve;

[0284] The curvature function of the Klein curve is:

[0285]

[0286] Where: k(l) Klein Represents the Klein curve curvature function.

[0287] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0288] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A high-speed loop line shape fitting method based on random sampling of point clouds, characterized in that: The specific steps include: S1 pre-processes the original point cloud to obtain a road surface point cloud. The point cloud of the highway ring road line is extracted by laser radar. The road surface point cloud includes straight segment point cloud and curved segment point cloud. S2 uses Alpha shapes to perform boundary detection on the road surface point cloud and obtains boundary point clouds. The boundary point clouds include straight line segment boundary point clouds and curve segment boundary point clouds. S3 performs circular curve boundary fitting and circle center determination on the boundary point cloud based on random sampling consistency, and performs straight line segment boundary fitting on the boundary point cloud based on random sampling consistency to determine the site boundary size; S4 reversely calculates the length of the site transition curve and the site straight line based on the site boundary size and the circular curve position; The specific steps of S1 include: S1.1 filters the original point cloud and generates a denoised point cloud; wherein the method for filtering the original point cloud adopts statistical filtering; S1.2 generates a road surface point cloud by segmenting and denoising the point cloud based on the road surface normal and elevation mean square error.

2. The high-speed loop line shape fitting method based on point cloud random sampling according to claim 1 is characterized in that: The specific steps of S1.1 include: S1.1.1 Perform a denoising operation on the original point cloud. In each denoising operation, select any point in the original point cloud as the first point, and form a point set with the first point and the N1-1 points closest to it. The denoised point cloud is generated after all points in the original point cloud are denoised, and N1 is an integer greater than 2. The point set formula is: Where: X represents a set of points, x1 represents the first point closest to the first point, x2 represents the second point closest to the first point, represents the third point closest to the first point, represents the first point; where the point set conforms to the normal distribution; S1.1.2 For each Point, calculation Divide a point by a set of points The distance to any point other than point , the specific formula is: Where: express Divide a point by a set of points The distance to any point other than point Indicates that the point set is Any point outside S1.1.3 In Except for point Among the distances of any point, select the kmean smallest distances to generate a distance set. The distance set formula is: Where: represents the distance set, express Divide by the point set The distance to the first point closest to the point outside the point, express Divide by the point set The distance to the second nearest point outside the point, express Divide by the point set The distance to the nearest kmean point outside the point; kmean is an integer greater than 1; S1.1.4 Take the mean of the distance set as The characteristic value of the distance set is calculated as follows: Where: represents the distance set mean; S1.1.5 Determine outliers based on the distance mean formula and the variance mean formula, remove outliers from the original point cloud, retain valid points, and generate a denoised point cloud; the distance mean formula is: Where: mean represents the mean of the distance set means of all points in the point set; The distance variance formula is: Where: stddev represents the variance of the distance set mean of all points in the point set and the distance set mean of all points in the point set; like When is an outlier; if When is a valid point, where the C value is the outlier degree of the point.

3. The high-speed loop line shape fitting method based on point cloud random sampling according to claim 2 is characterized in that: S1.2 The specific steps include: S1.2.1 Select any point in the point cloud as the query point Through the query point The nearest k2 neighboring points are used to solve the covariance matrix A created by the k2 neighboring points. The eigenvectors and eigenvalues ​​of the covariance matrix are fitted by the least squares method to obtain the point cloud normal. The corresponding covariance matrix can be expressed as: Where: A represents the covariance matrix, k2 represents the point The number of neighboring points, P i represents the query point, represents the 3D centroid of the neighboring points, represents the j2-th eigenvector of the covariance matrix, represents the j2th eigenvalue of the covariance matrix; S1.2.2 When The eigenvector corresponding to the minimum eigenvalue That is the normal vector of the calculation point: Where: represents the point normal, represents the x-direction component of the normal, represents the y-direction component of the normal, represents the z-direction component of the normal, and T is the transposed sign; S1.2.3 Calculate the slope value at each point. The slope value calculation formula is: Where: tanα1 represents the slope value; S1.2.4 Compare the slope value with the slope threshold to determine the segmentation point and road surface point of the expressway loop line; if tanα1≤tanα2, it is a segmentation point; if tanα1>tanα2, it is a road surface point, and tanα2 represents the slope threshold; S1.2.5 Set a local cylinder in the denoised point cloud. The elevations of the points within the local cylinder are: Where: Z G represents the elevation collection, z G1 represents the elevation of the first point in the local cylinder, z G2 represents the elevation of the second point in the local cylinder, represents the elevation of the N2th point in the local cylinder, where N2 represents the number of points in the local cylinder; where N2 is an integer greater than 1; S1.2.6 Calculate the mean elevation and standard deviation of each point within the local cylinder. When the standard deviation exceeds the standard deviation limit, it is considered a split point. The formula for calculating the mean elevation is: Where: represents the mean elevation, i3 represents the i3th point in the local cylinder; The formula for calculating the elevation standard deviation is: Where: represents the standard deviation of elevation; if Then each point within the local cylinder is a foreign point. Indicates the preset elevation standard deviation limit; S1.2.7 treats the road surface points as road surface areas and segments the denoised point cloud using segmentation points to obtain a road surface point cloud.

4. The high-speed loop line shape fitting method based on point cloud random sampling according to claim 3 is characterized in that: The specific steps of S2 include: S2.1 Select any point in the plane projection point cloud as the point to be determined P e (x e ,y e ), according to the preset rolling circle radius α e , search the distance P from the plane projection point cloud e Point distance is less than 2α e All points in the road surface point cloud are recorded as point set Q; the method for generating the plane projection point cloud is to convert all points z e The coordinates are all set to the same constant; S2.2 Select any point in the point set Q as point P e1 (x e1 ,y e1 ), according to point P e , click P e1 and rolling circle radius α e , calculate the coordinates of the center of the first circle O1(x o1 ,y o1 ) and the center coordinates of the second circle O2(x o2 ,y o2 ); wherein the first circle intersects with the second circle and has two intersection points, and the rolling circle radius α e is the distance between the center of the first circle and the two intersection points, and the rolling circle radius α e is the distance between the center of the second circle and the two intersection points, P e 、P e1 are the two intersection points of the first circle and the second circle respectively; S2.3 For all points in the set Q except P e1 For each point outside the circle, calculate its distance to the center O1 and O2 respectively. When the distances of all points to O1 and O2 are greater than α e When , the mark point P e is the contour point, ending at point P e Calculation of S2.4 When P is removed from the point set Q e1 When the distance from any point outside to the center O1 and to O2 is less than or equal to α, all points in the point set Q are rotated as P e1 Point, recalculate the coordinates of the circle center, and repeat step S2.3 for point P e Make a judgment; if there is a point P e Marked as a contour point, point P can be determined e is the contour point, and all the obtained contour points are combined into the boundary point set S, otherwise the judgment point P e is a non-contour point.

5. The high-speed loop line shape fitting method based on point cloud random sampling according to claim 4 is characterized in that: The S3 specific steps include: S3.1 uses RANSAC to fit the boundary contour of the point cloud; The output model obtained by S3.2 through circular curve fitting of the point cloud boundary contour in S3.1 is: (x h -x ho ) 2 +(y h -y ho ) 2 =R h 2 Where: (x h ,y h ) represents the coordinates of a point on the circular curve, (x ho ,y ho ) represents the coordinates of the center of the circular curve, R h Indicates the radius of the circular curve; The output model obtained by S3.3 by fitting the straight line segments of the point cloud boundary contour in S3.1 is: k h (x h -x h1 )=(and h -and h1 ) Where: (x h ,y h ) represents the coordinates of a point on the line, (x h1 ,y h1 ) represents the coordinates of a known point on the line, k h Represents the slope of the line.

6. The high-speed loop line shape fitting method based on point cloud random sampling according to claim 5 is characterized in that: S3.1 The specific steps include: S3.1.1 Randomly select a subset s from the set of boundary points S, use the randomly selected subset s as hypothetical inliers, and fit the initial model using the inliers s; The model parameters are estimated based on the subset s. The circular curve parameters are calculated assuming that the coordinates of the points inside the local area are (x β1 ,y β1 ),(x β2 ,y β2 ),(x β3 ,y β3 ) into the S3.2 circular curve model (x β1 -x ho ) 2 +(y β1 -y ho ) 2 =R h 2 (x β2 -x ho ) 2 +(y β2 -y ho ) 2 =R h 2 (x β3 -x ho ) 2 +(y β3 -y ho ) 2 =R h 2 Solving the system of equations, we get R h 2 =(x β1 -x ho ) 2 +(y β1 -y ho ) 2 Calculation of line parameters, assuming that the coordinates of the point inside the bureau are (x β1 ,y β1 ),(x β2 ,y β2 ) into the S3.3 straight line model k h (x β1 -x h1 )=(and β1 -and h1 ) k h (x β2 -x h1 )=(and β2 -and h1 ) Solving the system of equations, we get k h =(and β2 -and β1 ) / (x β2 -x β1 ) x h1 =x β1 and h1 =and β1 S3.1.2 Traverse all data in the boundary point set S except the subset s and calculate the radius R of the circular curve h Or the slope of the line k h Error, if the error is within the error limit e, it is marked as an interior point, otherwise it is marked as an exterior point; S3.1.3 Group all the inliers obtained in S3.1.2 into a consistent set. If the number of points in the consistent set meets a given threshold T, re-estimate the model parameters using all the inliers in the consistent set and output the results. If the number of inliers in the consistent set is less than the threshold T, select a new subset s and repeat steps S3.1.1-S3.1.

2. S3.1.4 After multiple iterations of S3.1.1-S3.1.3, select a consistent set with the largest number of inliers, use all the inliers in the consistent set to re-estimate the model parameters, and output the results; where the number of iterations is an integer greater than 1.

7. The high-speed loop line shape fitting method based on point cloud random sampling according to claim 5 is characterized in that: The specific steps of S4 include: S4.1 The overall width and length of the expressway loop are calculated using the offset formula to obtain the longitudinal offset and transverse offset of the transition curve, respectively. The formula for the relationship between the width and length of the site and the transition curve offset is: Where: W represents the overall width of the highway ring road, k a represents the slope of the straight line, Indicates the horizontal coordinate of the point at the center of the two circles. represents the ordinate of the point at the center of the two circles, y1 represents the ordinate of the known point on the first fitting line, x1 represents the abscissa of the known point on the first fitting line, y2 represents the ordinate of the known point on the second fitting line, x2 represents the abscissa of the known point on the second fitting line, M represents the lane width adjustment value between the center line of the straight line segment and the fitting line, β represents the transition curve angle, R represents the radius of the circular curve, L y Indicates the longitudinal offset of the site transition curve, H indicates the overall site length of the high-speed ring road, X o1 Indicates the horizontal coordinate of the center of the first endpoint of the high-speed ring road, X o2 Indicates the horizontal coordinate of the center of the second endpoint of the high-speed ring road, Y o1 Indicates the vertical coordinate of the center of the first endpoint of the high-speed ring road, Y o2 represents the vertical coordinate of the center of the second end point of the high-speed ring road, L represents the straight length of the site, L x Indicates the horizontal deviation of the site transition curve; S4.2 The transition curve angle is calculated by the quadratic integral method of curvature; the transition curve angle β is calculated using the following formula: Where: Ls0 represents the assumed length of the transition curve, k(l) represents the function of the curvature of any point on the transition curve as the length of the transition curve changes; The horizontal offset and vertical offset of the transition curve are calculated using the following formula: S4.3 After linear fitting and correction, the error between the corresponding site width and the actual site width W is calculated using the assumed transition curve length Ls0, and the final transition curve length Ls is obtained by the approximation method. The site straight line length L is then calculated using the site length H.

8. The high-speed loop line shape fitting method based on point cloud random sampling according to claim 7 is characterized in that: In S4.2, the curvature function k(l) of the transition curve is any one of the curvature functions of the Bloss curve, the McConnell curve, the Grabowski curve, the Auberlen curve, and the Klein curve; The curvature function of the Bloss curve is: Where: k(l) Bloss represents the curvature function of the Bloss curve; The curvature function of the McConnell curve is: Where: k(l) McConnell represents the curvature function of the McConnell curve, ψ represents the maximum superelevation angle, v represents the design speed, and g represents the acceleration of gravity; The curvature function of the Grabowski curve is: Where: k(l) Grabowski represents the curvature function of the Grabowski curve; The curvature function of the Auberlen curve is: Where: k(l) Auberlen represents the curvature function of the Auberlen curve; The curvature function of the Klein curve is: Where: k(l) Klein Represents the Klein curve curvature function.

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