CN106780524B - A 3D point cloud road boundary automatic extraction method - Google Patents

Abstract

The invention relates to the field of point cloud processing, and specifically discloses a three-dimensional point cloud road boundary automatic extraction method. Use the α-shape algorithm to extract the boundary points between adjacent non-coplanar supervoxels; S3. Use the graph cut-based energy minimization algorithm to extract the road boundary points; S4. Use the Euclidean distance clustering algorithm to remove outliers point; S5, fitting the extracted road boundary points into a smooth curve. The method of the invention can be directly run on a large-scale three-dimensional point cloud, can be used in different scenarios, has fast calculation speed, good algorithm robustness, and can quickly extract road boundaries.

Description

A 3D point cloud road boundary automatic extraction method

technical field

The invention relates to the field of point cloud processing, in particular to a method for automatically extracting road boundaries from a three-dimensional point cloud.

Background technique

As a transportation infrastructure, the digital management and construction of roads are of great significance for urban planning, traffic management, and navigation applications. As a rapidly developing high-tech surveying and mapping technology, vehicle-mounted laser scanning technology has the advantages of fast data acquisition, high data accuracy, non-contact active measurement, and strong real-time performance compared with traditional surveying and mapping methods. Obtaining detailed three-dimensional spatial information of roads and objects on both sides has obvious advantages for obtaining road information with strip distribution.

The traditional methods of obtaining road information mainly include manual measurement and digital photogrammetry. Although manual measurement can obtain more accurate road coordinates and other information, the measurement speed is slow and the update cycle of road information is long; digital photogrammetry has gradually developed and matured with the development of science and technology and the wide application of high and new technologies such as computers, but Limited by the image resolution and other reasons, the road feature information and accuracy requirements extracted from the image still need to be further improved. The vehicle-mounted laser scanning system consists of a global positioning system, an inertial navigation system, a laser scanner and a CCD camera, and has become a new means of acquiring three-dimensional spatial data. The use of vehicle-mounted laser scanning technology can effectively save measurement time, improve measurement efficiency, shorten the update cycle of road information, avoid the risk of exposure of measurement operators in the traffic environment, and provide a strong technical guarantee for the survey and planning of urban space resources.

However, the city usually has a complex environment, not only the auxiliary components are complex and numerous, but also the data is missing due to the mutual occlusion of the scanned targets, which brings challenges to the automatic extraction of road boundaries. In addition, the complexity caused by different road environments (such as vehicle stops, vegetation surrounds, fences, etc.) increases the difficulty of automatic extraction of road boundaries. Therefore, it is difficult and demanding to quickly and automatically extract road boundaries from massive point clouds, but this technology has important economic and application requirements and has always been a research hotspot at home and abroad.

At present, most of the research on vehicle laser scanning data processing focuses on the classification of ground objects and point clouds, the extraction and modeling of building facade information, and the extraction of road ancillary facilities, while the research on the extraction of road boundary information is relatively rare. It can be divided into two categories: indirect extraction and direct extraction.

The indirect extraction method generally uses the properties of the point cloud (height, intensity and wavelength, etc.) to generate a depth image, and then uses image processing methods (cropping, fitting and filtering, etc.) to detect and extract road boundaries. For the indirect extraction method, that is, converting the point cloud into a depth image, and then using the image processing method to extract the road boundary, these methods are bound to generate errors in the conversion process, and it is difficult to obtain accurate road boundary results.

The direct extraction method generally uses road features (such as planes, curbs, etc.) to detect and extract road boundaries. The commonly used method is to extract the road surface with the method based on random sampling agreement (RANSAC), and then use the linear fitting algorithm to obtain the road boundary. Use the Gaussian filtering method or the sliding window method to detect the curbs, thereby obtaining the road boundary. For the method of direct extraction, the scope of application of the scene is relatively limited. Using the method based on random sampling consensus (RANSAC) to extract road surfaces will have difficulties in the face of road undulations, and the extracted road surfaces will often lose some details. However, the method of using Gaussian filtering method or sliding window method to detect curbs often has challenges in the face of irregular road boundaries (such as walls, fences) or surrounded by vegetation.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the above-mentioned deficiencies of the prior art. The present invention provides a method for automatically extracting road boundaries from a 3D point cloud. The method can be directly run on a large-scale 3D point cloud and can be used in different scenarios. The calculation speed is fast, and the algorithm It has good robustness and can quickly extract road boundaries.

The specific technical solutions are as follows:

A three-dimensional point cloud road boundary automatic extraction method, comprising the following steps:

S1. For the entire obtained three-dimensional point cloud data set P, filter the seed points to perform super-voxel division;

S2. Use the α-shape algorithm to extract the boundary points between adjacent non-coplanar supervoxels;

S3. Use a graph cut-based energy minimization algorithm to extract road boundary points;

S4, remove outliers based on Euclidean distance clustering algorithm;

S5. Fit the extracted road boundary points into a smooth curve.

Preferably, the division process of step S1 to the supervoxel is as follows:

S11. Solve the fitting plane T _p ( _pi ):

For each input point pi of the entire 3D point cloud dataset P, its tangent plane Tp( _pi ) can be represented as a two-tuple consisting of its center point _{o i and} normal vector n _l , namely

The distance from any point p in the three-dimensional space to Tp( _pi ) can be expressed as

_{Denote the set of K nearest neighbors of pi as Nb k ( pi} ), and the best fitting plane in the sense of least squares can be obtained by solving the following formula

Then an iteratively reweighted least squares method is used to optimize the fitted plane

The optimized fitting plane Tp( _pi ) can be obtained by solving the weighted least squares equation

The above process is repeated for the plane Tp( _pi ) until the algorithm converges.

S12. Remove non-ground points:

Note that the three eigenvalues of the covariance matrix of the point set finally constituting the tangent plane Tp(pi) are λ ₁ , λ ₂ , and λ ₃ , and satisfy λ _{1 ≥λ 2} ≥λ ₃ . Then the smoothness _s ( _pi ) of point pi can be expressed as

Use the following two constraints to remove non-ground points:

A. Remove the points that are obviously higher than the road surface (z _i ≥ 5m) (z _i is the height value of point p _i );

B. Remove the points whose normal vector and the Z-axis angle are greater than 22.5°.

S13. Calculate the supervoxel f _i :

对每个种子点seed_i，令其初始的超体素f_i的初始点集为{p_i}，中心点和法向量分别是Tp(p_i).o_i和Tp(p_i).n_l。然后，采用宽度优先的原则对f_i进行区域增长。对每个候选点p_j，如果满足(1)p_j到p_i的距离小于阈值R_seed；(2)向量Tp(p_j).n_l与Tp(p_i).n_l的夹角小于22.5°；(3)p_j到Tp(p_i)的距离小于阈值∈；则将p_j加入到f_i的点集中。当f_i无法再扩展时，根据f_i.p_i使用最小二乘法拟合平面，并将f_i.n_lg更新为拟合平面的法向量。在这些初始小平面的基础上采用局部K均值聚类来将点赋值于超体素，并保证每个点到其所属的超体素的距离小于到其他超体素的距离。这里的距离函数定义为：The point set _Pg after removing the non-ground points is sorted according to the smoothness of each point, and the point with the largest smoothness is selected as the seed point first. The supervoxel is calculated by region growing from the seed point. The supervoxel f _i is formally defined as a triplet consisting of the belonging point set P _i , the center point o _i , and the normal vector n _l

For each seed point seed _i , let the initial point set of its initial supervoxel f _i be { _pi }, the center point and normal vector are Tp( _{pi ).o i and} Tp( _pi ).n respectively _l . Then, use the breadth-first principle to perform regional growth on f _i . For each candidate point p _j , if (1) the distance from p _j to p _i is less than the threshold R _seed ; (2) the angle between the vector Tp(p _j ).n _l and Tp( _pi ).n _l is less than 22.5°; (3) the distance from p _j to Tp( _pi ) is less than the threshold ∈; then add p _j to the point set of f _i . When f _i can no longer be extended, use the least squares method to fit the plane according to f _i .pi , and update _{f i .n l} g to the normal vector of the fitted plane. On the basis of these initial facets, local K-means clustering is used to assign points to supervoxels, and the distance from each point to the supervoxel to which it belongs is guaranteed to be smaller than the distance to other supervoxels. The distance function here is defined as:

where D _s , D _n and D _i are the Euclidean distance, the normal vector distance and the intensity distance, respectively. ω _s , ω _n and ω _i are the corresponding weights, respectively.

Preferably, step S2 uses the α-shape algorithm to extract the boundary points between adjacent non-coplanar supervoxels as follows:

After dividing the point cloud into supervoxels, for each supervoxel, the α-shape algorithm can be used to extract the boundary points, and at the same time, the boundary points between two supervoxels that are coplanar with each other are removed, that is, if the two If the angle between the normal vectors of the super voxels is less than 22.5°, the boundary points between the two super voxels are deleted, and the boundary points P _b at this time include road boundary points and non-road boundary points.

Preferably, step S3 uses a graph cut-based energy minimization algorithm to extract road boundary points, as follows:

The vehicle driving trajectory data is provided by the vehicle laser scanning system, and the trajectory data is used as the initial observation model of the graph cut algorithm. The energy formula is defined as:

E(f)=E _data (f)+λ·E _smooth (f)

Here P _b refers to the set of boundary points extracted in step 2. n is the potential of the point set of the _supervoxel to which pi belongs. Δd _j is the distance from the point p _j to the straight line L _pi . Δd _i refers to the average redundancy of all points in the neighborhood of point _pi to the line L _pi . σ ₁ refers to the average redundancy of all points. The straight line L _pi is defined as the direction of the trajectory line passing through the point _pi and in the direction closest to the distance _pi .

是指点p_i和p_j的欧式距离。这里

表示的是如果点p_i和p_j分配的标签一致的话，代价为零，反之代价为

(x _i , y _i , z _i ), (x _j , y _j , z _j ) are the three-dimensional coordinates of points p _i and p _j respectively,

is the Euclidean distance between points p _i and p _j . here

It means that if the labels assigned by points p _i and p _j are the same, the cost is zero, otherwise the cost is

Here σ ₂ refers to the spatial resolution of the point set P _b . Using the graph cut algorithm to obtain the minimum value of the above energy formula, the boundary points are divided into two categories, one is road boundary points, and the other is non-road boundary points.

Compared with the prior art, the scheme of the present invention has the following advantages:

(1) The present invention can directly run on a large-scale three-dimensional point cloud, and provides a fast and effective automatic solution for the extraction and positioning of road boundaries. Very few parameters need to be set manually, reducing human subjective intervention. Compared with the prior art, the present invention adopts super-voxel segmentation and a graph-cut-based energy minimization algorithm, and can still effectively extract road boundaries in a complex urban environment. It overcomes the shortcomings of point cloud data occlusion and uneven density distribution, making the results stable and robust, universal to different scenarios, and easy to use in practice.

(2) The present invention fully exploits the basic properties (spatial distance, geometric properties and intensity information) of the point cloud, performs super-voxel segmentation on the point cloud, and removes non-ground points at the same time, thereby improving the subsequent calculation efficiency. Due to the method of sorting and prioritizing the seed points, the result of super-voxel segmentation is very good to preserve the boundary information, which improves the robustness of the subsequent road boundary extraction algorithm.

(3) The present invention has carried out innovative optimization on the model algorithm, and proposed the energy minimization algorithm based on graph cut for the first time, using the trajectory data provided by the vehicle system, combined with the inherent characteristics of the road boundary to establish a graph cut model, effectively and quickly extracting to the road boundary.

Description of drawings

Fig. 1 is the schematic flow chart of the technical solution of the present invention;

Fig. 2 embodiment of the present invention original point cloud data;

Figure 3. Effect diagram after processing.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

Example

The specific implementation scheme of the road boundary extraction method based on the vehicle-mounted laser scanning point cloud data proposed by the present invention is as follows (see Figure 1 for the overall technical scheme flow):

S1, to the obtained whole three-dimensional point cloud data set P, screen seed points and carry out supervoxel division (the original point cloud data of the present embodiment can be seen in Figure 2);

Supervoxel division refers to gathering adjacent points with the same properties into a super point to reduce the complexity of data processing;

S11. Solve the fitting plane T _p ( _pi ):

For each input point pi of the entire 3D point cloud dataset P, its tangent plane Tp( _pi ) can be represented as a two-tuple consisting of its center point _{o i and} normal vector n _l , namely

The distance from any point p in the three-dimensional space to Tp( _pi ) can be expressed as

_{Denote the set of K nearest neighbors of pi as Nb k ( pi} ), and the best fitting plane in the sense of least squares can be obtained by solving the following formula

Then an iteratively reweighted least squares method is used to optimize the fitted plane

The optimized fitting plane Tp( _pi ) can be obtained by solving the weighted least squares equation

The above process is repeated for the plane Tp( _pi ) until the algorithm converges.

S12. Remove non-ground points:

Note that the three eigenvalues of the covariance matrix of the point set finally constituting the tangent plane Tp(pi) are λ ₁ , λ ₂ , and λ ₃ , and satisfy λ _{1 ≥λ 2} ≥λ ₃ . Then the smoothness _s ( _pi ) of point pi can be expressed as

Use the following two constraints to remove non-ground points:

A. Remove the points that are obviously higher than the road surface (z _i ≥ 5m) (z _i is the height value of point p _i );

B. Remove the points whose normal vector and the Z-axis angle are greater than 22.5°.

S13. Calculate the supervoxel f _i :

对每个种子点seed_i，令其初始的超体素f_i的初始点集为{p_i}，中心点和法向量分别是Tp(p_i).o_i和Tp(p_i).n_l。然后，采用宽度优先的原则对f_i进行区域增长。对每个候选点p_j，如果满足(1)p_j到p_i的距离小于阈值R_seed；(2)向量Tp(p_j).n_l与Tp(p_i).n_l的夹角小于22.5°；(3)p_j到Tp(p_i)的距离小于阈值∈；则将p_j加入到f_i的点集中。当f_i无法再扩展时，根据f_i.p_i使用最小二乘法拟合平面，并将f_i.n_lg更新为拟合平面的法向量。在这些初始小平面的基础上采用局部K均值聚类来将点赋值于超体素，并保证每个点到其所属的超体素的距离小于到其他超体素的距离。这里的距离函数定义为：Therefore, the point set P _g after removing the non-surface points is sorted according to the smoothness of each point, and the point with the largest smoothness is selected as the seed point first. The supervoxel is calculated by region growing from the seed point. The supervoxel f _i is formally defined as a triplet consisting of the belonging point set P _i , the center point o _i , and the normal vector n _l

For each seed point seed _i , let the initial point set of its initial supervoxel f _i be { _pi }, the center point and normal vector are Tp( _{pi ).o i and} Tp( _pi ).n respectively _l . Then, use the breadth-first principle to perform regional growth on f _i . For each candidate point p _j , if (1) the distance from p _j to p _i is less than the threshold R _seed ; (2) the angle between the vector Tp(p _j ).n _l and Tp( _pi ).n _l is less than 22.5°; (3) the distance from p _j to Tp( _pi ) is less than the threshold ∈; then add p _j to the point set of f _i . When f _i can no longer be extended, use the least squares method to fit the plane according to f _i .pi , and update _{f i .n l} g to the normal vector of the fitted plane. On the basis of these initial facets, local K-means clustering is used to assign points to supervoxels, and the distance from each point to the supervoxel to which it belongs is guaranteed to be smaller than the distance to other supervoxels. The distance function here is defined as:

where D _s , D _n and D _i are the Euclidean distance, the normal vector distance and the intensity distance, respectively. ω _s , ω _n and ω _i are the corresponding weights, respectively.

S2. Use the α-shape algorithm to extract the boundary points between adjacent non-coplanar supervoxels;

After segmenting the point cloud into supervoxels, for each supervoxel, an α-shape algorithm can be used to extract boundary points. At the same time, the boundary points between two supervoxels that are coplanar with each other are removed, that is, if the angle between the normal vectors of the two supervoxels is less than 22.5°, the boundary points between the two supervoxels are removed. The boundary point P _b at this time includes a road boundary point and a non-road boundary point.

The α-shape algorithm can be regarded as an extension of the closure Convex Hull. It can calculate a finer closure by adjusting the α parameter to roughly describe the shape of a group of points on a plane or space. Specifically, a circle with a fixed radius is used to cover it. A pair of points, when a pair of points both fall exactly on the circle and the circle does not contain any other points, these two points are the boundary points of the shape. By finding all the boundary points in this way, the Alpha shape is described.

S3. Use a graph cut-based energy minimization algorithm to extract road boundary points;

Next, a graph-cut based energy minimization algorithm is used to extract road boundary points. The vehicle-mounted laser scanning system provides vehicle driving trajectory data, and the observed trajectory data is basically consistent with the measured road position and direction. Therefore, the trajectory data is used as the initial observation model of the graph cut algorithm. The energy formula is defined as:

E(f)=E _data (f)+λ·E _smooth (f)

的距离。Δd_i是指点p_i邻域内所有点到直线

的平均冗余。σ₁是指所有点的平均冗余。直线

定义为经过点p_i且方向与距离p_i最近的轨迹线的方向。Here P _b refers to the set of boundary points extracted in step 2. n is the potential of the point set of the _supervoxel to which pi belongs. Δd _j is the point p _j to the line

the distance. Δd _i refers to all points in the neighborhood of point p _i to the line

average redundancy. σ ₁ refers to the average redundancy of all points. straight line

Defined as the direction of the trajectory line that passes through point _pi and whose direction is closest to _pi .

是指点p_i和p_j的欧式距离。这里

表示的是如果点p_i和p_j分配的标签一致的话，代价为零，反之代价为

(x _i , y _i , z _i ), (x _j , y _j , z _j ) are the three-dimensional coordinates of points p _i and p _j respectively,

is the Euclidean distance between points p _i and p _j . here

It means that if the labels assigned by points p _i and p _j are the same, the cost is zero, otherwise the cost is

Here σ ₂ refers to the spatial resolution of the point set P _b . Using the graph cut algorithm to obtain the minimum value of the above energy formula, the boundary points are divided into two categories, one is road boundary points, and the other is non-road boundary points.

S4, remove outliers based on Euclidean distance clustering algorithm;

Use the Euclidean distance clustering algorithm to cluster the road boundary points obtained above, and delete the category with a small number of points, that is, after clustering, if the number of points contained in a category is less than 5, then delete this category.

S5. Fit the extracted road boundary points into a smooth curve.

The remaining classes are fitted to smooth curves, respectively, and the road boundaries are obtained. Here we use Cubic Spline Interpolation to fit straight lines.

Among them, Fig. 3 is an effect diagram after processing, showing the extracted road.

The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited to this. Substitutions should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (5)

1. a three-dimensional point cloud road boundary automatic extraction method, is characterized in that: comprise the following steps: S1. For the entire obtained three-dimensional point cloud data set P, filter the seed points to perform super-voxel division; S2. Use the α-shape algorithm to extract the boundary points between adjacent non-coplanar supervoxels; S3. Use a graph cut-based energy minimization algorithm to extract road boundary points; S4, remove outliers based on Euclidean distance clustering algorithm; S5, fitting the road boundary points after removing outliers into a smooth curve; Wherein, the division process of the supervoxel in step S1 includes the following steps: S11, solve the fitting plane T _p (P _i ), wherein P _i is each input point of the entire three-dimensional point cloud data set P; S12, remove the non-ground point; S13. Calculate the supervoxel f _i ; And, the specific steps for solving the fitting plane T _p (P _i ) are as follows: For each input point P _i of the entire 3D point cloud dataset P, its tangent plane T _p (P _i ) can be represented as a two-tuple consisting of its center point o _i and normal vector n _l , namely:

in,

is the estimated value of the normal vector n _l , The distance from any point p in the three-dimensional space to T _p (P _i ) can be expressed as:

Denote the set of K nearest neighbors of P _i as Nb _K (P _i ), and the best fitting plane in the sense of least squares can be obtained by solving the following formula:

Then an iteratively reweighted least squares method is used to optimize the fitted plane:

The optimized fitting plane T _p (P _i ) can be obtained by solving the weighted least squares equation:

The above solving process is repeated for the optimized fitting plane T _p (P _i ) until the algorithm for solving the weighted least squares equation converges. 2. a kind of three-dimensional point cloud road boundary automatic extraction method according to claim 1, is characterized in that: the concrete steps that step S2 uses α-shape algorithm to extract the boundary point between adjacent non-coplanar supervoxels are: After dividing the point cloud into supervoxels, for each supervoxel, the α-shape algorithm can be used to extract the boundary points, and at the same time, the boundary points between two supervoxels that are coplanar with each other are removed, that is, if the two If the angle between the normal vectors of the supervoxels is less than 22.5°, the boundary points between the two supervoxels are deleted, and the boundary points P _b at this time include road boundary points and non-road boundary points. 3. a kind of three-dimensional point cloud road boundary automatic extraction method according to claim 1, is characterized in that: S12. The specific steps for removing non-ground points are as follows: Note that the three eigenvalues of the covariance matrix of the point set that finally constitute the fitting plane T _p (P _i ) are λ ₁ , λ ₂ , and λ ₃ , and satisfy λ ₁ ≥λ ₂ ≥λ ₃ , then the point P _i The smoothness s(P _i ) of can be expressed as:

Use the following two constraints to remove non-ground points: A. Remove the points that are obviously higher than the road surface, that is, the points where zi _i ≥ 5m, and zi _i is the height value of point P _i ; B. Remove the points whose normal vector and the Z-axis angle are greater than 22.5°. 4. a kind of three-dimensional point cloud road boundary automatic extraction method according to claim 2 is characterized in that: S13. The specific steps for calculating the supervoxel f _i are as follows: Sort the point set Pg after removing the non-ground points according to the smoothness of each point, first select the point whose smoothness is greater than the preset value as the seed point, and calculate the _supervoxel by regional growth from the seed point; A supervoxel f _i is formally defined as a triplet consisting of the belonging point P _i , the center point o _i , and the normal vector n _l

For each seed point seed _i , let the initial point set of its initial supervoxel f _i be {P _i }, the center point and the normal vector are respectively T _p (P _i ).o _i and T _p (P _i ) .n _l ; then, adopt the principle of breadth priority to carry out regional growth on f _i , for each candidate point P _j , if (1) the distance from P _j to P _i is less than the threshold R _seed at the same time; (2) the vector T _p The angle between (P _j ).n _l and T _p (P _i ).n _l is less than 22.5°; (3) the distance from P _j to T _p (P _i ) is less than the threshold ∈; then add P _j to f _i In the point set of , when f _i can no longer be extended _, use the least squares method to fit the plane according to the term _{P i} in the triple f _{i .}

this item

Update to the normal vector of the fitted plane; use local K-means clustering on the basis of all calculated f _i triples to assign points to supervoxels, and ensure that each point is the same as the supervoxel to which it belongs. The distance is less than the distance to other supervoxels, where the distance function is defined as:

where D _s , D _n and D _i are the Euclidean distance, the normal vector distance and the intensity distance, respectively, and ω _s , ω _n and ω _i are the weights corresponding to the three distance values, respectively. 5. three-dimensional point cloud road boundary automatic extraction method according to claim 4, is characterized in that: step S3 uses the energy minimization algorithm based on graph cut to extract road boundary point, is specifically as follows: The vehicle driving trajectory data provided by the vehicle laser scanning system is used as the initial observation model, and the graph cut algorithm is used to divide the boundary points into the following two categories {"road boundary points", "non-road boundary points"}, that is, the graph cut algorithm. The goal is to find a classification function f to assign a label f _p ∈ L to each point, where L is the category set {"road boundary points", "non-road boundary points"}, so that the cost is the smallest, that is, the energy formula is obtained. minimize, Here the energy formula is defined as: E(f)=E _data (f)+λ·E _smooth (f) Here E _data (f), the data item in the energy formula, refers to the error between the classification result and the initial observation model, and is the cost of assigning labels to each point in the classification process, E _smooth (f), the energy formula The smooth item in , refers to the degree of non-smoothness of the classification function f, specifically refers to the cost of inconsistency between the classification results between each point and the adjacent points in the classification process, λ is the weight of the smooth item E _smooth (f), here press experience is set to 32, where,

Here P _b refers to the set of boundary points extracted in step S2, n is the potential of the point set of the _supervoxel to which Pi belongs, and Δd _j refers to the line from point P _j to the line

The distance of Δd _i refers to all points in the neighborhood of point P _i to the line

The average redundancy of , σ ₁ refers to the average redundancy of all points in the point set P _g , the straight line

Defined as passing through point _Pi and the direction vector is consistent with the direction of the trajectory line closest to _Pi ,

is the label of _Pi ,

is the label of P _j , (x _i , y _i , z _i ), (x _j , y _j , z _j ) are the three-dimensional coordinates of points P _i and P _j , respectively,

is the Euclidean distance between points P _i and P _j , where

It means that if the labels assigned by points P _i and P _j are consistent, the cost is zero, otherwise the cost is B{P _i , P _j }, Here σ ₂ refers to the spatial resolution of the point set P _b . Using the graph cut algorithm to obtain the minimum value of the above energy formula, the boundary points are divided into two categories, one is the road boundary point, and the other is the non-road boundary point .

Images