A ground point cloud segmentation method, storage medium and electronic device

Abstract

The present disclosure provides a ground point cloud segmentation method, storage medium and electronic device, and relates to the field of point cloud data processing technology. The original point cloud is obtained by a laser radar on a vehicle; the radiation range data of each original point cloud is obtained, and the noise point of the original point cloud is filtered based on the data to obtain a first point cloud; the target area is determined, and the target area is divided to obtain multiple sub-areas; the multiple sub-areas are filtered according to the number of the first point clouds distributed in each sub-area, and multiple target sub-areas and the second point clouds therein are obtained; the second point cloud in each target sub-area is highly screened to obtain a candidate point cloud; singular value decomposition is performed according to the candidate point cloud, and plane fitting is performed according to the singular value decomposition result to obtain a candidate plane; the plane state quantity corresponding to the candidate plane is calculated, and the point cloud is screened according to the plane state quantity to obtain a ground point cloud and a non-ground point cloud; plane fitting filtering is performed again to obtain a ground point cloud segmentation result. Improve the accuracy of ground point cloud segmentation.

Description

Background Art

[0002] With the development of autonomous driving technology, the importance of LiDAR in the field of intelligent driving has become increasingly prominent. In the autonomous driving of ports, effective obstacle detection is the focus of the self-driving perception system, and LiDAR is the main sensor for detection.

[0003] However, due to various factors such as ambient light interference and terrain complexity, lidar point cloud data often contains a lot of noise, which reduces the accuracy of ground detection. Accurate ground detection is one of the prerequisites for effective identification of autonomous driving. Ground detection errors will affect the vehicle's understanding of the surrounding environment and its ability to plan paths.

[0004] Therefore, how to effectively and accurately extract ground information from lidar point clouds and improve detection accuracy is a key issue that needs to be solved urgently.

[0005] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to ordinary technicians in the field. Summary of the invention

[0006] The purpose of the present disclosure is to provide a ground point cloud segmentation method, a storage medium and an electronic device, which at least to some extent overcome the problem of low ground information extraction accuracy due to related technologies.

[0007] Other features and advantages of the present disclosure will become apparent from the following detailed description, or may be learned in part by the practice of the present disclosure.

[0008] According to one aspect of the present disclosure, a method for segmenting a ground point cloud is provided, wherein an original point cloud is acquired by a laser radar on a vehicle;

[0009] Acquire radiation range data of each of the original point clouds, and perform noise filtering on the original point clouds according to the radiation range data to obtain a first point cloud;

[0010] Determine a target area, and divide the target area into a plurality of sub-areas, wherein the sub-areas are in a fan shape or a fan ring shape;

[0011] Filtering the plurality of sub-regions according to the number of the first point clouds distributed in each sub-region to obtain a plurality of target sub-regions and second point clouds therein;

[0012] Performing a high degree screening on the second point cloud in each of the target sub-regions to obtain a candidate point cloud;

[0013] Performing singular value decomposition according to the candidate point cloud, and performing plane fitting according to the singular value decomposition result to obtain a candidate plane;

[0014] Calculate the plane state quantity corresponding to the candidate plane, and perform point cloud screening according to the plane state quantity to obtain ground point cloud and non-ground point cloud;

[0015] Plane fitting and filtering are performed according to the ground point cloud and the non-ground point cloud to obtain a ground point cloud segmentation result.

[0016] In one embodiment of the present disclosure, the obtaining of the radiation range data of each of the original point clouds, and filtering the original point clouds according to the radiation range data to obtain the first point cloud, includes:

[0017] Determine the distance from each original point cloud to the laser radar;

[0018] Calculating the angle between each original point cloud and the laser radar according to the distance;

[0019] The original point clouds whose angles are greater than a first preset angle or whose point cloud intensities are less than a preset intensity are filtered to obtain the first point cloud.

[0020] In one embodiment of the present disclosure, the determining of the target area and dividing the target area into a plurality of sub-areas includes:

[0021] Determine the target area with the laser radar as the center according to a preset distance, wherein the target area is a circular area;

[0022] Divide the target area according to the preset distance to obtain a plurality of first areas;

[0023] Dividing each of the first regions again according to a preset processing ratio to obtain a plurality of second regions;

[0024] The second area is divided according to a second preset angle to obtain the multiple sub-areas.

[0025] In one embodiment of the present disclosure, the highly screening the second point cloud in each of the target sub-areas to obtain a candidate point cloud includes:

[0026] Sorting the second point clouds in each target sub-area that are below the installation height of the laser radar;

[0027] According to the sorting results, a preset number of third point clouds with the lowest heights in each target sub-area are respectively selected;

[0028] Computing the point cloud average height of each target sub-area according to the third point cloud;

[0029] Determine a first height threshold according to the average height of the point cloud;

[0030] Screening the third point cloud to obtain the candidate point cloud below the first height threshold; or

[0031] The second height threshold corresponding to each target sub-area is determined according to the actual road condition, and a third point cloud below the second height threshold is selected to obtain the candidate point cloud.

[0032] In one embodiment of the present disclosure, performing singular value decomposition according to the candidate point cloud and performing plane fitting according to the singular value decomposition result to obtain the candidate plane includes:

[0033] The point cloud centroid coordinates of each target sub-region are calculated based on the candidate point cloud;

[0034] Obtaining a centralized point cloud matrix according to the point cloud centroid coordinates;

[0035] Calculate the covariance matrix according to the centralized point cloud matrix;

[0036] Performing singular value decomposition on the covariance matrix to obtain eigenvalues ​​and eigenvectors;

[0037] Determine an initial plane equation according to the eigenvalue and the coordinates of the point cloud centroid;

[0038] Obtaining a plane candidate point cloud according to the initial plane equation, and using the plane candidate point cloud to replace the candidate point cloud;

[0039] Plane iteration is performed according to the plane candidate point cloud to obtain a plane equation and the candidate plane corresponding to it.

[0040] In one embodiment of the present disclosure, calculating the plane state quantity corresponding to the candidate plane, screening the point cloud according to the plane state quantity, and obtaining the ground point cloud and the non-ground point cloud includes:

[0041] Determine the verticality of the plane according to the angle between the normal vector of the candidate plane and the preset vector;

[0042] Determining the flatness of the plane according to the minimum eigenvalue obtained by singular value decomposition of the candidate plane;

[0043] Calculating the point cloud centroid of the candidate plane and determining the plane centroid height;

[0044] Use the preset loss height as the plane loss height;

[0045] Determining plane linearity according to eigenvalues ​​obtained by singular value decomposition of the candidate plane;

[0046] If the verticality of the plane is less than a third preset angle, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane;

[0047] If the plane flatness is less than a preset flatness, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane;

[0048] If the plane centroid height is less than the preset maximum centroid height, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane;

[0049] If the target plane is not obtained, the ground point cloud and the non-ground point cloud are obtained according to the preset lost height.

[0050] In one embodiment of the present disclosure, it also includes:

[0051] When the plane verticality is less than a third preset angle, if the current plane flatness of the corresponding target plane is less than the corresponding preset flatness, saving the current plane flatness as a candidate flatness;

[0052] When the plane verticality is less than the third preset angle, if the corresponding current plane centroid height of the target plane is less than the preset highest centroid height, the current plane centroid height is saved as a candidate highest centroid height;

[0053] Calculate a flatness mean and a flatness variance according to the candidate flatness;

[0054] Obtaining the flatness probability value according to the flatness mean and the flatness variance;

[0055] If the plane linearity is less than a preset linearity, and the flatness probability value is less than a preset probability value, obtaining the ground point cloud and the non-ground point cloud according to the corresponding target plane;

[0056] Calculate the mean value and variance of the centroid height according to the candidate highest centroid height;

[0057] updating the preset flatness according to the flatness mean and the flatness variance;

[0058] The preset maximum center of mass height is updated according to the center of mass height mean and the center of mass height variance.

[0059] In one embodiment of the present disclosure, performing plane fitting filtering according to the ground point cloud and the non-ground point cloud to obtain a ground point cloud segmentation result includes:

[0060] Filtering the ground point cloud according to the installation position of the laser radar to obtain a fourth point cloud;

[0061] Perform the above singular value decomposition and plane fitting according to the fourth point cloud to obtain a current plane corresponding to the current plane equation;

[0062] If the angle between the current plane equation and the preset normal vector is less than a fourth preset angle, obtaining a current distance from the non-ground point cloud to the current plane;

[0063] Point clouds that meet a distance threshold are screened according to the current distance to obtain the ground point cloud segmentation result.

[0064] According to another aspect of the present disclosure, there is provided an electronic device, including:

[0065] Processor; and

[0066] A memory, configured to store executable instructions of the processor;

[0067] The processor is configured to execute any one of the above-mentioned ground point cloud segmentation methods by executing the executable instructions.

[0068] According to another aspect of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the ground point cloud segmentation method described in any one of the above is implemented.

[0069] The ground point cloud segmentation method provided by the embodiment of the present disclosure. The original point cloud is obtained by the laser radar on the vehicle; the radiation range data of each of the original point clouds is obtained, and the original point cloud is filtered according to the radiation range data to obtain the first point cloud; first, the point cloud is filtered for ghost noise to remove the noise that does not meet the requirements. Then the target area is determined, and the target area is divided to obtain multiple sub-areas, wherein the sub-areas are fan-shaped or fan-shaped; the target area to be detected is divided into small sub-areas, which can better process point clouds in different distance ranges. According to the number of the first point clouds distributed in each sub-area, the multiple sub-areas are filtered to obtain multiple target sub-areas and the second point clouds therein; the sub-areas with sparse point clouds are filtered out for the accuracy of subsequent processing. Then the second point cloud in each of the target sub-areas is highly screened to obtain a candidate point cloud; and the point cloud located at the low point is further found. Singular value decomposition is performed according to the candidate point cloud, and plane fitting is performed according to the singular value decomposition result to obtain a candidate plane; the plane fitting iterative method improves the robustness and stability of ground detection. Calculate the plane state quantity corresponding to the candidate plane, screen the point cloud according to the plane state quantity, and obtain the ground point cloud and non-ground point cloud; screen the candidate planes, and comprehensively evaluate multiple ground features to achieve more accurate ground detection in complex environments. Perform plane fitting filtering based on the ground point cloud and the non-ground point cloud to obtain the ground point cloud segmentation result. On the basis of the above, further filter out the noise points, filter out the noise points to the greatest extent, improve the ground detection capability in complex environments, and improve the accuracy of the ground point cloud segmentation results.

[0070] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0072] Figure 1 A schematic diagram of a process flow of a ground point cloud segmentation method in an embodiment of the present disclosure is shown;

[0073] Figure 2 A radiation schematic diagram of a laser radar in an embodiment of the present disclosure is shown;

[0074] Figure 3 A schematic diagram showing a flow chart of another method for segmenting ground point clouds in an embodiment of the present disclosure is shown;

[0075] Figure 4 A schematic diagram showing a flow chart of another method for segmenting ground point cloud in an embodiment of the present disclosure is shown;

[0076] Figure 5 A structural block diagram of a computer device in an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0077] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0078] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0079] Reference Figure 1 As shown, in one embodiment, a method for segmenting a ground point cloud is provided, comprising:

[0080] S101, obtaining the original point cloud through the laser radar on the vehicle;

[0081] Optionally, the laser radar is installed on the roof or the edge of the vehicle body. Mechanical and non-mechanical laser radars can be used. Preferably, a 32 / 16-line mechanical laser radar can be used. Figure 2 Shown is a radiation diagram of a 16-line mechanical laser radar.

[0082] S102, obtaining radiation range data of each of the original point clouds, and filtering noise points of the original point clouds according to the radiation range data to obtain a first point cloud;

[0083] Specifically, due to the characteristics of the laser itself, there are some ghost noise points, which need to be filtered out in advance to avoid interference with subsequent recognition and detection errors. Therefore, it is necessary to first process the original point cloud, that is, the point cloud in the laser radar coordinate system, calculate the point cloud radiation range data, and then directly filter the ghost noise points of the point cloud according to the radiation range data, remove the noise points that do not meet the requirements, and obtain the first processed point cloud. The radiation range data includes the angle and distance between each original point cloud and the laser radar, as well as information such as the point cloud intensity.

[0084] In a specific example, step S102 includes:

[0085] Determine the distance from each original point cloud to the laser radar;

[0086] Specifically, the distance from the point cloud to the laser radar is calculated using the following formula 1:

[0087] r = sqrt(x*x + y * y+z*z). Formula 1

[0088] Among them, the coordinates (x, y, z) of the point cloud are in the laser radar coordinate system and can be obtained by the laser radar, and r is the distance from the original point cloud to the laser radar.

[0089] Calculating the angle between each original point cloud and the laser radar according to the distance;

[0090] Specifically, the angle between the point cloud and the laser radar is calculated using the following formula 2:

[0091] vertical_angle = atan(z,r) Formula 2

[0092] The original point clouds whose angles are greater than a first preset angle or whose point cloud intensities are less than a preset intensity are filtered to obtain the first point cloud.

[0093] Among them, the preset angle is set according to actual needs. For example, the preset angle is preferably set to a value of 15 degrees. The preset strength is pre-set according to actual needs. For example, the preset strength is set to a value of 2, and the point cloud strength can be obtained by the lidar. The preset angle and the preset strength can adjust the value of the preset angle according to actual conditions. In the specific example, if the angle vertical_angle is greater than 15 degrees, the original point cloud is filtered, and if the intensity threshold is less than 2, the original point cloud is filtered. After the original point cloud is filtered, it meets the above conditions and is the first point cloud. Remove ghost noise in advance to avoid interference with subsequent recognition results.

[0094] S103, determining a target area, dividing the target area into a plurality of sub-areas, wherein the sub-areas are in a sector shape or a sector ring shape;

[0095] Specifically, it is necessary to determine the target area for subsequent processing. The target area is the area within a certain distance around the laser radar. The first point cloud within the range is processed by ground point cloud removal and plane fitting. The target area to be detected does not consider point clouds that are too far away from the laser radar. This can save computing power and improve the efficiency of ground point cloud detection. In order to better process point cloud data within different distance ranges, the point cloud is divided into blocks according to distance. It can be divided according to distance or angle. Figure 3 The figure shows a schematic diagram of the structure of partial area division, in which three divisions are performed, two divisions are based on distance areas, and one division is based on angles. The origin is the position of the laser radar, and the sub-area M is a fan-shaped final result of a division. The shape of the sub-area is a fan-shaped in the innermost circle and the rest are fan-shaped.

[0096] In a specific example, step S103 includes:

[0097] Determine the target area with the laser radar as the center according to a preset distance, wherein the target area is a circular area;

[0098] Specifically, the target area can be a circular area centered on the laser radar, and the maximum radius is a preset distance, such as Figure 3 The radius OD point shown is a preset distance. For example, if the preset distance is 32m, the target area is a circular area with a radius of 32m centered on the laser radar.

[0099] Divide the target area according to the preset distance to obtain a plurality of first areas;

[0100] Specifically, Figure 3 As shown, the preset distance is divided into multiple radius intervals, and points A, B, C and D are distributed in the radial direction of the radius. If the preset distance value is 32m, the position of point A represents a radius of 4m, the position of point B represents a radius of 8m, the position of point C represents a radius of 16m, and the position of point D represents a radius of 32m. Then the preset distance interval [0-32m] is divided into four first areas: the first area OA corresponds to the distance interval 0-4m, the first area AB corresponds to the distance interval 4m-8m, the first area BC corresponds to the distance interval 8m-16m, and the first area CD corresponds to the distance interval 16m-32m. The first area can be circular or annular. Specifically, the first area OA is a circular area with a radius of 4m, and the first area AB, the first area BC, and the first area BC are respectively annular areas. The above division according to the preset distance can be set according to the actual distribution of the point cloud, and is not limited here.

[0101] Dividing each of the first regions again according to a preset processing ratio to obtain a plurality of second regions;

[0102] Further division, the preset processing ratio can be set in advance based on experience, and the preset ratio can further divide each first area into multiple smaller second areas. For example, the processing ratios of each part are [2,4,4,4]. Further subdivision: For example, the preset processing ratio of the first area OA is 2, which is divided into two second areas of 0-2m and 2m-4m. Within the distance range of the first area AB, the corresponding processing ratio is 4, that is, the distance interval 4m-8m is divided into 4 blocks, and the point cloud is further divided into four second areas of 4m-5m, 5m-6m, 6m-7m, and 7m-8m according to the distance. After the division, except for the second area 0-2m which is a circular area, the other second areas are all in the shape of a ring, and the reference division is more refined. Figure 3 The division result of the first area CD is shown in FIG. , and the dotted line indicates the process of proportional division. Further finer circular or annular areas are obtained.

[0103] The second area is divided according to a second preset angle to obtain the multiple sub-areas.

[0104] Specifically, further divided according to the angle, the first preset angle is 2π / 4, for example, divided into 16 sector-shaped areas at 90 degrees along the angle direction, specifically: the first area OA corresponds to 8 sub-areas, and the other first areas AB, BC, and CD are all 16 sub-areas, among which the innermost sub-area is sector-shaped, and the other sub-areas are all sector-shaped. Figure 3 , the division result of the second area CD is shown in FIG. 1 , wherein each fan-shaped area is a sub-area, and the division of other areas is not shown.

[0105] S104, filtering the multiple sub-regions according to the number of the first point clouds distributed in each sub-region to obtain multiple target sub-regions and the second point clouds therein;

[0106] Specifically, it is necessary to filter out the areas where the number of point clouds in each sub-region is less than a certain number, that is, the areas with sparse point clouds. Optionally, the areas where the number of first point clouds distributed in each sub-region is less than 15 points are filtered out, and the number of point clouds in the retained target sub-regions reaches a certain number. And the second point clouds in each retained target sub-region can be sorted according to height to facilitate the subsequent plane fitting operation of each target sub-region. The ground point cloud can be fully and effectively segmented.

[0107] S105, highly screening the second point cloud in each of the target sub-areas to obtain a candidate point cloud;

[0108] In order to further find the point cloud located at the low point, it is necessary to perform height screening on the second point cloud to determine the point cloud located at the low point. The height of the candidate point cloud is less than the low position point cloud of the preset condition, as follows.

[0109] In a specific example, step S105 includes:

[0110] Sorting the second point clouds in each target sub-area that are below the installation height of the laser radar;

[0111] As an optional example, if the installation height of the laser radar is 1.6 m, based on the previously obtained target sub-areas, directly select the second point cloud that is 1.6 m lower than the installation height for each sub-area and sort them by height.

[0112] According to the sorting results, a preset number of third point clouds with the lowest heights in each target sub-area are respectively selected;

[0113] The preset number can be set according to actual needs, and different target sub-areas can be set to the same or different preset number values, which is not limited here. For example, the preset number is set to 20, and the lowest 20 points are selected according to the height sorting, and these 20 points are the third point cloud.

[0114] Computing the point cloud average height of each target sub-area according to the third point cloud;

[0115] Determine a preset first height threshold according to the average height of the point cloud;

[0116] Screening the third point cloud to obtain the candidate point cloud below the preset first height threshold;

[0117] Specifically, the average height height_average of the third point cloud is calculated. A height error range threshold can be preset, for example, the height error range threshold is 0.3m, the first height threshold is height_average+0.3, and the point cloud with a height lower than height_average+0.3 is selected from the third point cloud as a candidate point cloud.

[0118] Or in another optional manner, the second height threshold corresponding to each target sub-area is determined according to actual road conditions, and a third point cloud below the second height threshold is selected to obtain the candidate point cloud.

[0119] Optionally, the height threshold for height screening is determined according to the actual road conditions. If the road surface on which the vehicle is traveling is flat, the second height threshold corresponding to each target sub-area is determined according to the road conditions, and point clouds below the second height threshold are directly selected for each target sub-area. For example, the initial value of the second height threshold is 0.8m, and point clouds below 0.8m are screened in the third point cloud. The value can be set based on experience, and the initial value will be continuously updated iteratively later. The amount of calculation can be further reduced according to the regional step-by-step over-filtering. The second height thresholds corresponding to the above-mentioned target sub-areas are different. For example, the second height threshold is set to 0.4m for the area within 10m, 0.6m for 10m-25m, and 0.8m for 25-32m. Among them, the value of the second height threshold will be continuously updated iteratively later, and the second height threshold candidate_height can be adjusted according to the actual situation in the subsequent processing process.

[0120] S106, performing singular value decomposition according to the candidate point cloud, and performing plane fitting according to the singular value decomposition result to obtain a candidate plane;

[0121] Specifically, singular value decomposition (SVD) is used to process the candidate point cloud, and then the singular value decomposition results can be obtained: eigenvalues ​​and eigenvectors. Optionally, the relevant direct solution function in the eign library can be directly called, and the existing solution method can be referred to. Then the eigenvalues ​​and eigenvectors can be used to calculate the initial plane equation. After obtaining the initial plane equation, the plane equation is iterated to obtain a relatively stable plane equation. The fitting plane corresponding to the plane equation is the candidate plane. The above-mentioned area division and plane fitting iteration method improves the robustness and stability of ground detection.

[0122] Reference Figure 4 As shown, in a specific example, step S106 includes:

[0123] S401, computing the point cloud centroid coordinates of each target sub-region based on the candidate point cloud;

[0124] Specifically, the point cloud is firstly centralized: the coordinates of the point cloud centroid of each target sub-region are calculated.

[0125] S402, obtaining a centralized point cloud matrix according to the point cloud centroid coordinates.

[0126] Then the point cloud centroid coordinates are subtracted from each candidate point cloud coordinate to obtain the centered point cloud matrix.

[0127] S403, calculating a covariance matrix according to the centralized point cloud matrix;

[0128] The covariance matrix is ​​calculated using the centered point cloud matrix. The covariance matrix reflects the degree of variation of the point cloud in all directions.

[0129] S404, performing singular value decomposition on the covariance matrix to obtain eigenvalues ​​and eigenvectors;

[0130] The covariance matrix is ​​subjected to singular matrix decomposition, and the singular value decomposition result includes eigenvalues ​​and eigenvectors, which are 3 eigenvalues ​​and eigenvectors.

[0131] S405, determining an initial plane equation according to the eigenvalues ​​and the coordinates of the centroid of the point cloud;

[0132] Specifically, the eigenvector corresponding to the minimum eigenvalue is the plane normal vector, because the direction corresponding to the minimum eigenvalue indicates that the candidate point cloud has the smallest change in this direction, that is, the direction in which the point cloud is flattest, which is also the normal vector of the plane. If the component of the normal vector on the z-axis is less than 0, the direction of the normal vector is opposite, but it does not affect the extraction of the plane point cloud. Calculate the initial plane equation, the expression of the initial plane equation is: ax+by+cz+d=0, and the coordinate values ​​of the above normal vectors correspond to the values ​​of the plane equations a, b, and c respectively. The point cloud centroid coordinates pass through the plane, and the value of d in the initial plane equation can be further obtained by obtaining the coordinates of the regional point cloud centroid. Thus, the initial plane equation is obtained. The initial plane equation will be subsequently subjected to plane iteration to obtain a more stable plane equation.

[0133] S406, obtaining a plane candidate point cloud according to the initial plane equation, and using the plane candidate point cloud to replace the candidate point cloud;

[0134] Specifically, after obtaining the initial plane equation, the plane candidate point cloud is obtained according to the initial plane equation. Optionally, according to the plane equation obtained above, the candidate point clouds in each target sub-area are calculated to have a distance to the plane less than a set threshold of 0.1m, which is a plane candidate point cloud that satisfies the requirement. Then, the plane candidate point cloud obtained after screening replaces the above candidate point cloud for subsequent iterative calculations.

[0135] S407, performing plane iteration according to the plane candidate point cloud to obtain a plane equation and the candidate plane corresponding to it.

[0136] Among them, the number of plane iterations can be set in advance. Optionally, the number of iterations is set to 3 times. After replacing the candidate point cloud with the plane candidate point cloud, the above singular value decomposition and determination of the plane equation are repeated, that is, steps S401 to S406 are repeated. After repeating three times, a relatively stable plane equation and the candidate plane corresponding to the plane equation can be obtained.

[0137] S107, calculating the plane state quantity corresponding to the candidate plane, and performing point cloud screening according to the plane state quantity to obtain a ground point cloud and a non-ground point cloud;

[0138] Specifically, after obtaining the candidate planes, the candidate planes need to be screened to obtain plane point clouds and non-plane point clouds, that is, ground point clouds and non-ground point clouds. Calculate the plane state quantities corresponding to the candidate planes, which include: plane verticality, plane flatness, plane centroid height, plane loss height, and plane linearity, as described below. With the help of a comprehensive evaluation mechanism of multiple ground features, more accurate ground detection can be achieved in complex environments.

[0139] In a specific example, step S107 includes:

[0140] Determine the verticality of the plane according to the angle between the normal vector of the candidate plane and the preset vector;

[0141] The preset vector is the vector (0, 0, 1), and the angle between the normal vector and the preset vector is calculated as the perpendicularity of the plane.

[0142] Determining the flatness of the plane according to the minimum eigenvalue obtained by singular value decomposition of the candidate plane;

[0143] After the above plane iterative calculation, the SVD decomposition result of the plane equation corresponding to the candidate plane can be obtained, and the singular value can be obtained. The minimum value among the singular values ​​is selected as the plane flatness. The smaller the flatness, the flatter the candidate plane.

[0144] Calculating the point cloud centroid of the candidate plane and determining the plane centroid height;

[0145] Among them, to solve the point cloud centroid of the candidate plane, the plane centroid height can be obtained by averaging the point cloud coordinates in the candidate plane.

[0146] A loss height threshold is preset as the plane loss height;

[0147] The candidate planes obtained above may be 0, 1 or more, depending on the actual situation. The missing height threshold can be set based on experience as the minimum tolerance of the plane. If the plane screening cannot obtain a candidate plane that meets the conditions, when the point cloud is higher than the missing height threshold, it is considered to be a non-ground point cloud.

[0148] Determining plane linearity according to eigenvalues ​​obtained by singular value decomposition of the candidate plane;

[0149] Among them, plane linearity is used to describe the linear characteristics of the plane, and is used to filter out point cloud clusters close to a straight line. It can be obtained by dividing the second largest eigenvalue by the first largest eigenvalue. After solving the above SVD, three eigenvalues ​​and eigenvectors can be obtained, and the first and second largest eigenvalues ​​can be obtained by sorting.

[0150] The above plane state quantities are then used to comprehensively detect and output ground point clouds and non-ground point clouds. The details are as follows:

[0151] If the verticality of the plane is less than a third preset angle, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane;

[0152] Among them, the value range of the second preset angle is 70 degrees-80 degrees. In an example, the third preset angle is set to 75 degrees. If the verticality of the plane meets the set threshold of 75 degrees, the target plane that meets the plane verticality condition is obtained based on the candidate plane screening, and the ground and non-ground point clouds can be directly output according to the target plane that meets the condition. Optionally, the distance to the target plane can be set separately when selecting the ground point cloud. The distance limits of the four different first areas from the inside to the outside are adjusted to [0.1m, 0.1m, 0.2m, 0.2m] respectively. For example, the target plane in the first area OA can select the plane point cloud with a distance to the target equation less than 0.1m as the ground point cloud, and the rest are non-ground point clouds; the target plane in the first area BC can select the plane point cloud with a distance to the corresponding target plane equation less than 0.2m as the ground point cloud, and the rest are non-ground point clouds.

[0153] If the plane flatness is less than a preset flatness, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane;

[0154] Specifically, if the plane flatness of the candidate plane is less than the preset flatness, a target plane that meets the conditions can be obtained, and the initial values ​​of the preset flatness can be set to [0.01, 0.01, 0.01, 0.01] respectively, and different preset flatness values ​​are set from the inside to the outside for four different first areas, respectively, according to the different areas to which the target plane belongs, to achieve more accurate detection.

[0155] If the plane centroid height is less than the preset maximum centroid height, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane;

[0156] Specifically, if the point cloud centroid of the candidate plane is lower than the preset highest centroid height, it is considered that the plane equation corresponding to the target plane meets the requirements. Similarly, different threshold ranges are set according to the four first regions. For example, they are set to [0.05, 0.05, 0.1, 0.1] in the radial direction. The initial threshold of the preset highest centroid height also needs to be adjusted in combination with the actual situation, and continuously adjusted to further improve the accuracy of detection.

[0157] If the target plane is not obtained, the ground point cloud and the non-ground point cloud are obtained according to the preset lost height.

[0158] If the target plane is not obtained by screening, the point cloud is screened using the preset loss height. When the point cloud is higher than the loss height threshold, it is considered to be a non-ground point cloud, and lower than the preset loss height threshold, it is considered to be a ground point cloud. Optionally, different threshold ranges [0.1, 0.15, 0.25, 0.3] can be set for different first areas, and the initial threshold can also be adjusted in combination with the actual situation.

[0159] In another specific example, if the above conditions cannot be met, further determining the probability value of being a plane also includes:

[0160] When the plane verticality is less than a third preset angle, if the current plane flatness of the corresponding target plane is less than the corresponding preset flatness, saving the current plane flatness as a candidate flatness;

[0161] When the plane verticality is less than the third preset angle, if the corresponding current plane centroid height of the target plane is less than the preset highest centroid height, the current plane centroid height is saved as a candidate highest centroid height;

[0162] Specifically, if the plane verticality satisfies the third preset angle of 75 degrees, if the plane flatness of the candidate plane is less than the preset flatness of the corresponding first region, the current plane flatness is saved as the candidate flatness of the region, and a maximum of 100 candidate flatnesses are stored. And if the current plane centroid height is less than the preset highest centroid height, the current plane centroid height is saved as the candidate highest centroid height, and a maximum of 100 candidate highest centroid heights are stored. The initial values ​​of the preset flatness and the preset highest centroid height are subsequently calculated and updated accordingly.

[0163] Obtaining the flatness probability value according to the flatness mean and the flatness variance;

[0164] Specifically, the mean flat_mean and the variance flat_std are calculated to obtain the flatness probability value, and the flatness probability value flat_pro = 1 / (1+exp((flatness of the current area block - (flat_mean + 1.2flat_std)) / ((flat_mean + 1.2flat_std) / 10)) ), where the flatness of the current area block is the flatness of the current plane, and the constant 1.2 can be appropriately adjusted according to the actual ground flatness. And if the number of point clouds in the area exceeds the set number threshold, for example, the number of point clouds in the first area AB exceeds 1000 points, and the flatness of the area is less than 0.04, then flat_pro=1.

[0165] If the plane linearity is less than the preset linearity, and the flatness probability value is greater than the preset probability value, obtaining the ground point cloud and the non-ground point cloud according to the corresponding target plane;

[0166] For example, the preset linearity is set to 5 and the preset probability value is set to 0.7. If the plane linearity is less than 5 and the flatness probability value is greater than 0.7, the plane is considered to be the ground, and the ground and non-ground point clouds can also be directly output.

[0167] Calculate the mean value and variance of the centroid height according to the candidate highest centroid height;

[0168] updating the preset flatness according to the flatness mean and the flatness variance;

[0169] The preset maximum center of mass height is updated according to the center of mass height mean and the center of mass height variance.

[0170] Specifically, the preset highest centroid height and the preset flatness are updated, the centroid height mean centroid_mean and the centroid height variance centroid_std are calculated for the highest centroid height of the target plane, and the preset highest centroid height is iteratively updated to centroid_mean+2centroid_std, the second height threshold candidate_height is synchronously updated = centroid_mean+3centroid_std, the flatness mean flat_mean and the flatness variance flat_std are calculated for the candidate flatness, and the preset flatness is iteratively updated to flat_mean+2flat_std. Update the initial value set for the corresponding first region.

[0171] S108, performing plane fitting filtering according to the ground point cloud and the non-ground point cloud to obtain a ground point cloud segmentation result.

[0172] The above operations basically filter out most of the ground point cloud, but there are still some noise points, so another plane fitting filter is needed. This improves the robustness and stability of ground detection.

[0173] In a specific example, performing plane fitting filtering according to the ground point cloud and the non-ground point cloud to obtain a ground point cloud segmentation result includes:

[0174] Filtering the ground point cloud according to the installation position of the laser radar to obtain a fourth point cloud;

[0175] The ground point cloud obtained above is selected within a certain distance near the installation location of the laser radar, for example, within the range of plus or minus 5m of the installation location of the laser radar. This range can be adjusted appropriately according to the actual scene. Narrow the range to select the point cloud close to the installation location of the laser radar, and directly use a close-range large plane to filter it again to filter out the noise points to the greatest extent.

[0176] Perform the above singular value decomposition and plane fitting according to the fourth point cloud to obtain a current plane corresponding to the current plane equation;

[0177] Specifically, in order to filter the final noise points, the plane equation calculation needs to be performed again. The singular value decomposition and plane equation determination in the above plane fitting step are repeated to obtain the current plane equation and the corresponding current plane.

[0178] If the angle between the current plane equation and the preset normal vector is less than a fourth preset angle, obtaining a current distance from the non-ground point cloud to the current plane;

[0179] Point clouds that meet a distance threshold are screened according to the current distance to obtain the ground point cloud segmentation result.

[0180] The above angle is greater than or equal to the fourth preset angle. If the angle is too large, it means that the probability that the current plane is not the ground is very high. The current plane solution is incorrect, so the noise will not be filtered based on the wrong plane. Otherwise, it means that it is necessary to continue filtering. The fourth preset angle can be set to 15 degrees.

[0181] For the non-ground point cloud obtained above, calculate the current distance from the point cloud to the current plane, set the distance threshold range to 0.1, and include plane points if the condition is less than 0.1, and include non-plane points if it does not meet the condition. At this point, the plane and the plane point cloud required are the ground segmentation results. Directly using a close-range large plane to filter out noise points again can basically filter out all noise points, improve the ground detection capability in complex environments, and improve the accuracy of ground point cloud segmentation results.

[0182] In another exemplary embodiment, an electronic device is provided, comprising:

[0183] Processor; and

[0184] A memory, configured to store executable instructions of the processor;

[0185] The processor is configured to execute any one of the above-mentioned ground point cloud segmentation methods by executing the executable instructions.

[0186] It will be appreciated by those skilled in the art that various aspects of the present invention may be implemented as a system, method or program product. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software, which may be collectively referred to herein as a "circuit", "module" or "system".

[0187] Refer to the following Figure 5 The electronic device 500 according to this embodiment of the present invention is described. Figure 5 The electronic device 500 shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present invention.

[0188] like Figure 5 As shown, the electronic device 500 is in the form of a general computing device. The components of the electronic device 500 may include but are not limited to: at least one processing unit 510, at least one storage unit 520, and a bus 530 connecting different system components (including the storage unit 520 and the processing unit 510).

[0189] The storage unit stores program codes, which can be executed by the processing unit 510, so that the processing unit 510 performs the steps according to various exemplary embodiments of the present invention described in the above “Exemplary Method” section of this specification. For example, the processing unit 510 can perform the following steps: Figure 1 The segmentation method of the ground point cloud shown in .

[0190] The storage unit 520 may include a readable medium in the form of a volatile storage unit, such as a random access storage unit (RAM) 5201 and / or a cache storage unit 5202 , and may further include a read-only storage unit (ROM) 5203 .

[0191] The storage unit 520 may also include a program / utility 5204 having a set (at least one) of program modules 5205, such program modules 5205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0192] Bus 530 may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0193] The electronic device 500 may also communicate with one or more external devices 600 (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 600, and / or communicate with any device that enables the electronic device 500 to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication may be performed through an input / output (I / O) interface 550. In addition, the electronic device 500 may also communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) through a network adapter 560. As shown, the network adapter 560 communicates with other modules of the electronic device 500 through a bus 530. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 500, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0194] Through the description of the above implementation, it is easy for those skilled in the art to understand that the example implementation described here can be implemented by software, or by software combined with necessary hardware. Therefore, the technical solution according to the implementation of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes a number of instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to the implementation of the present disclosure.

[0195] In another exemplary embodiment of the present disclosure, a computer-readable storage medium is provided, on which a program product capable of implementing the above method of the present specification is stored. When the computer program is executed by a processor, the ground point cloud segmentation method described in any one of the above is implemented.

[0196] In some possible implementations, various aspects of the present invention may also be implemented in the form of a program product, which includes program code. When the program product is run on a terminal device, the program code is used to enable the terminal device to execute the steps of various exemplary implementations of the present invention described in the above “Exemplary Method” section of this specification.

[0197] A program product for implementing the above method according to an embodiment of the present invention is described, which can adopt a portable compact disk read-only memory (CD-ROM) and include program code, and can be run on a terminal device, such as a personal computer. However, the program product of the present invention is not limited thereto, and in this document, a readable storage medium can be any tangible medium containing or storing a program, which can be used by or in combination with an instruction execution system, an apparatus or a device.

[0198] The program product may be any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination thereof. More specific examples (non-exhaustive list) of readable storage media include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof.

[0199] Computer readable signal media may include data signals propagated in baseband or as part of a carrier wave, in which readable program code is carried. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Readable signal media may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0200] The program code embodied on the readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the foregoing.

[0201] Program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0202] It should be noted that, although several modules or units of the device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. On the contrary, the features and functions of one module or unit described above can be further divided into multiple modules or units to be embodied.

[0203] In addition, although the steps of the method in the present disclosure are described in a specific order in the drawings, this does not require or imply that the steps must be performed in this specific order, or that all the steps shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step, and / or one step may be decomposed into multiple steps, etc.

[0204] Through the description of the above implementation, it is easy for those skilled in the art to understand that the example implementation described here can be implemented by software, or by combining software with necessary hardware. Therefore, the technical solution according to the implementation of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a mobile terminal, or a network device, etc.) to execute the method according to the implementation of the present disclosure.

[0205] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A ground point cloud segmentation method, characterized in that: include: Obtain the original point cloud through the laser radar on the vehicle; Acquire radiation range data of each of the original point clouds, and perform noise filtering on the original point clouds according to the radiation range data to obtain a first point cloud; Determine a target area, and divide the target area into a plurality of sub-areas, wherein the sub-areas are in a fan shape or a fan ring shape; Filtering the plurality of sub-regions according to the number of the first point clouds distributed in each sub-region to obtain a plurality of target sub-regions and second point clouds therein; Performing a high degree screening on the second point cloud in each of the target sub-regions to obtain a candidate point cloud; Performing singular value decomposition according to the candidate point cloud, and performing plane fitting according to the singular value decomposition result to obtain a candidate plane; Calculating the plane state quantity corresponding to the candidate plane, screening the point cloud according to the plane state quantity, and obtaining the ground point cloud and the non-ground point cloud; specifically including: Determine the verticality of the plane according to the angle between the normal vector of the candidate plane and the preset vector; Determining the flatness of the plane according to the minimum eigenvalue obtained by singular value decomposition of the candidate plane; Calculating the point cloud centroid of the candidate plane and determining the plane centroid height; Use the preset loss height as the plane loss height; Determining plane linearity according to eigenvalues ​​obtained by singular value decomposition of the candidate plane; If the verticality of the plane is less than a third preset angle, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane; If the plane flatness is less than a preset flatness, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane; If the plane centroid height is less than the preset maximum centroid height, a corresponding target plane is determined, and the ground point cloud and the non-ground point cloud are obtained according to the target plane; If the target plane is not obtained, obtaining the ground point cloud and the non-ground point cloud according to the preset lost height; When the plane verticality is less than a third preset angle, if the current plane flatness of the corresponding target plane is less than the corresponding preset flatness, saving the current plane flatness as a candidate flatness; When the plane verticality is less than the third preset angle, if the corresponding current plane centroid height of the target plane is less than the preset highest centroid height, the current plane centroid height is saved as a candidate highest centroid height; Calculate a flatness mean and a flatness variance according to the candidate flatness; Obtain a flatness probability value according to the flatness mean and the flatness variance; wherein, the flatness probability value=1 / (1+exp((current plane flatness-(flatness mean+1.2 flatness variance)) / ((flatness variance+1.2 flatness variance) / 10))); If the plane linearity is less than a preset linearity, and the flatness probability value is less than a preset probability value, obtaining the ground point cloud and the non-ground point cloud according to the corresponding target plane; Calculate the mean value and variance of the centroid height according to the candidate highest centroid height; updating the preset flatness according to the flatness mean and the flatness variance; Update the preset maximum center of mass height according to the center of mass height mean and the center of mass height variance; Performing plane fitting and filtering according to the ground point cloud and the non-ground point cloud to obtain a ground point cloud segmentation result specifically includes: Filtering the ground point cloud according to the installation position of the laser radar to obtain a fourth point cloud; Perform the above singular value decomposition and plane fitting according to the fourth point cloud to obtain a current plane corresponding to the current plane equation; If the angle between the current plane equation and the preset normal vector is less than a fourth preset angle, obtaining a current distance from the non-ground point cloud to the current plane; Point clouds that meet a distance threshold are screened according to the current distance to obtain the ground point cloud segmentation result.

2. The ground point cloud segmentation method according to claim 1, characterized in that: The step of obtaining the radiation range data of each of the original point clouds and filtering the original point clouds according to the radiation range data to obtain a first point cloud includes: Determine the distance from each original point cloud to the laser radar; Calculating the angle between each original point cloud and the laser radar according to the distance; The original point clouds whose angles are greater than a first preset angle or whose point cloud intensities are less than a preset intensity are filtered to obtain the first point cloud.

3. The ground point cloud segmentation method according to claim 1, characterized in that: The determining of the target area and dividing the target area into a plurality of sub-areas includes: Determine the target area with the laser radar as the center according to a preset distance, wherein the target area is a circular area; Divide the target area according to the preset distance to obtain a plurality of first areas; Dividing each of the first regions again according to a preset processing ratio to obtain a plurality of second regions; The second area is divided according to a second preset angle to obtain the multiple sub-areas.

4. The ground point cloud segmentation method according to claim 1, characterized in that: The highly screening the second point cloud in each of the target sub-areas to obtain a candidate point cloud comprises: Sorting the second point clouds in each target sub-area that are below the installation height of the laser radar; According to the sorting results, a preset number of third point clouds with the lowest heights in each target sub-area are respectively selected; Computing the point cloud average height of each target sub-area according to the third point cloud; Determine a first height threshold according to the average height of the point cloud; Screening the third point cloud to obtain the candidate point cloud below the first height threshold; or The second height threshold corresponding to each target sub-area is determined according to the actual road condition, and a third point cloud below the second height threshold is selected to obtain the candidate point cloud.

5. The ground point cloud segmentation method according to claim 3, characterized in that: The step of performing singular value decomposition according to the candidate point cloud and performing plane fitting according to the singular value decomposition result to obtain a candidate plane includes: The point cloud centroid coordinates of each target sub-region are calculated based on the candidate point cloud; Obtaining a centralized point cloud matrix according to the point cloud centroid coordinates; Calculate the covariance matrix according to the centralized point cloud matrix; Performing singular value decomposition on the covariance matrix to obtain eigenvalues ​​and eigenvectors; Determine an initial plane equation according to the eigenvalue and the coordinates of the point cloud centroid; Obtaining a plane candidate point cloud according to the initial plane equation, and using the plane candidate point cloud to replace the candidate point cloud; Plane iteration is performed according to the plane candidate point cloud to obtain a plane equation and the candidate plane corresponding to it.

6. An electronic device, characterized in that: include: processor; as well as A memory, configured to store executable instructions of the processor; The processor is configured to execute the ground point cloud segmentation method according to any one of claims 1 to 5 by executing the executable instructions.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the ground point cloud segmentation method described in any one of claims 1 to 5 is implemented.

Images