CN110443836A - A kind of point cloud data autoegistration method and device based on plane characteristic - Google Patents
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Abstract
The present invention relates to a kind of point cloud data autoegistration method and device based on plane characteristic, belongs to three-dimensional laser scanning technique field.The present invention passes through plane partitioning algorithm first and divides to obtain planar chip to point cloud data progress plane, and calculate each plane properties information, then the corresponding relationship between planar chip is established by planar chip attribute information, interplanar correlation and rotation translation geometrical constraint, the corresponding flat for obtaining solving for coordinate transformation parameter is to set, coordinate transformation parameter is solved using plane parameter, it is measured according to the point cloud registering global consistency of foundation, selects optimal solution, as final registration result.This method comprehensive utilization plane properties information, interplanar constraint and space geometry constraint ensure the Accuracy and high efficiency of registration process, and additional intensity or color information are not depended on, the point cloud data obtained for various platforms can be effectively registrated, strong applicability.
Description
Technical Field
The invention relates to a point cloud data automatic registration method and device based on plane features, and belongs to the technical field of three-dimensional laser scanning.
Background
The three-dimensional point cloud is a discrete sampling of an objective world, is composed of a series of points, and can be obtained by a laser scanner, a laser radar (LiDAR), a depth camera, a stereoscopic vision and other sensors. In the field of surveying and mapping remote sensing, three-dimensional laser scanning is known as a 'live-action replication' technology, and mass point cloud data of a target can be quickly and accurately acquired, so that great attention is paid to the technology. Due to the limited effective range and view field range of the measuring instrument and the influence of shielding, in order to obtain the complete point cloud of the operation scene, the measuring instrument is often erected at a plurality of measuring stations for measurement, and then sequence registration is performed among the point clouds, as shown in fig. 1. The essence of point cloud registration is to seek a set of translation and rotation parameters to unify point clouds in the same coordinate system, so that the point clouds after coordinate conversionThe overlapping parts of the point clouds are well aligned. Describing the point cloud registration problem by using a mathematical language, and giving point cloud P to be registered as { P ═ P }i＝(xi,yi,zi) Q and the target point cloud Q ═ Qi＝(xi,yi,zi)}，Solving rigid body transformationsSuch that:
wherein R ∈ SO (3) is a rotation matrix, t is a translation vector, eijFor error measurement, C { (i, j)mDenotes a corresponding point pair set, point piCorresponding point qj。
In the last two decades, three-dimensional laser scanning has become a standard technology in many fields by virtue of its specific advantages, is extensively researched and widely applied, and particularly, with the continuous improvement of cost performance, various products are continuously updated and updated, and the three-dimensional laser scanning has been applied to the fields of three-dimensional modeling, digital factories, cultural relic protection, landslide monitoring, asset management and the like. However, the massive amount of point cloud obtained by the three-dimensional laser scanner poses a challenge to the later data processing. In general measurement operation, registration among multi-station point clouds is often realized by laying artificial targets, and by adopting the method, a target laying scheme needs to be designed in advance, secondary fine scanning needs to be carried out on the targets in the measurement process, time and labor are wasted, and extra cost needs to be paid for target purchase. In addition, in many cases (such as tall and big city building groups), the targets manually laid can only be distributed in a small space range, and good mesh constraint cannot be formed on the registration parameters, so that the coordinate conversion parameters obtained by solving have large errors; even in some cases where it is not possible or convenient to lay out the target, the registration process of the point cloud will be very annoying to the field handler. When the point cloud registration can not be realized based on the artificial target, the point cloud registration often needs to be manually carried outMore than three groups of corresponding points are selected from the Point cloud to be registered to calculate a rough initial registration result, and the final registration result is solved by using Iterative Closest Point (ICP) as an initial value, so that a great deal of energy and time are consumed in the process, and the requirement of Point cloud data automatic processing cannot be met. Meanwhile, the massive amount of the point clouds puts higher requirements on a data processing hardware platform, three-dimensional coordinate points are directly used as processing elements, when dozens of or even hundreds of groups of point clouds are processed, a large memory is occupied, and a Central Processing Unit (CPU) and a Graphic Processing Unit (GPU) with ultrahigh performance are needed. The search for automatic and efficient point cloud registration has been a hot research problem in the field of point cloud data processing,the method comprises the steps of utilizing intensity information to assist point cloud registration, firstly projecting three-dimensional point cloud into a two-dimensional intensity image, extracting feature points through the intensity image and calculating a descriptor so as to establish a corresponding relation, and solving coordinate conversion parameters. However, there is inevitable distortion in projecting the point cloud into an image, and the intensity value is greatly affected by the scanning distance and angle, and the accuracy of point cloud registration is greatly affected.
In an actual measurement scene, a large number of geometric features such as angular points, planes, straight line segments, cylinders and the like often exist, the point cloud registration can be achieved by reasonably utilizing the features, the extraction of the plane features is relatively easy to achieve, and the point cloud registration is widely distributed in an artificial scene, so that the point cloud registration based on the extracted plane features is a potential feasible method. The existing point cloud registration method based on plane features is mainly divided into the following two types: (1) an additional auxiliary device is needed, such as a chinese patent application document with application publication No. CN105571519A, which discloses an auxiliary device for point cloud stitching of a three-dimensional scanner and a stitching method thereof, the method also needs to perform scanning measurement operation according to a predetermined requirement in order to realize registration, so that data acquisition is not flexible enough, and the method is not suitable for large scenes; (2) for example, the chinese patent application publication No. CN106570823A discloses a point cloud rough stitching method based on matching of plane features, which further needs to manually select and determine corresponding planes in subsequent processing, that is, manually perform plane matching, but cannot realize automation through a program, and manually select corresponding planes to realize registration, which often only can select a few pairs of corresponding planes from a large number of plane features, and is difficult to select an optimal plane combination to participate in registration resolution, so that only a rough registration result with a large error can be calculated. In addition, when matching the corresponding planes, the existing registration method based on the plane features is usually based on a complete plane hypothesis, that is, the corresponding planes in the two groups of point clouds are required to be completely consistent, so that the requirements on the overlapping degree between the target point cloud and the point cloud to be registered and the environmental shielding are high, and when the overlapping degree between the point clouds is low or the shielding is serious, the point cloud registration is difficult to realize. Therefore, the current point cloud registration method based on the plane features has limited use scenes, the error of the registration result is large, and the automation degree needs to be improved.
Disclosure of Invention
The invention aims to provide a point cloud data automatic registration method and device based on plane features, and aims to solve the problems of large error, poor adaptability and low automation degree of the existing point cloud registration method.
The invention provides a point cloud data automatic registration method based on plane features for solving the technical problems, which comprises the following steps:
1) acquiring target point cloud data and point cloud data to be registered;
2) respectively carrying out plane segmentation on the target point cloud data and the point cloud data to be registered to obtain a target plane piece group and a plane piece group to be registered, and calculating attribute information of each plane piece in each plane group;
3) obtaining a plane pair set with consistent attributes from a target plane piece set and a plane piece set to be registered according to the attribute information of each plane piece;
4) selecting two pairs of non-parallel plane pairs from the plane pair sets with consistent attributes, and determining a rotation matrix according to the obtained two pairs of non-parallel plane pairs; selecting a non-parallel plane pair meeting rotation consistency from the remaining plane pairs of the plane pair set with consistent attributes by using a rotation matrix, taking the three selected plane pairs as a triple, acting conversion parameters corresponding to the triple on a plane of point cloud to be registered in the triple, and adding the triple into the triple set if an overlapping condition is met;
5) traversing the remaining plane pairs in the plane pair set with consistent attributes according to the mode of the step 4) to obtain a triple set, respectively acting the conversion parameters corresponding to each triple in the triple set on the cloud data of the point to be registered, calculating the overall consistency measurement, and selecting the conversion parameter of the triple with the minimum overall consistency measurement from the triple to perform point cloud registration.
The invention also provides a plane feature-based point cloud data automatic registration device, which comprises a memory, a processor and a computer program, wherein the computer program is stored on the memory and runs on the processor, the processor is coupled with the memory, and the processor realizes the plane feature-based point cloud data automatic registration method when executing the computer program.
The method comprises the steps of firstly carrying out plane segmentation on point cloud data through a plane segmentation algorithm to obtain plane pieces, calculating attribute information of each plane, then establishing a corresponding relation among the plane pieces through the attribute information of the plane pieces, the mutual relation among the planes and a rotation and translation geometric constraint to obtain a corresponding plane pair set for solving coordinate conversion parameters, solving the coordinate conversion parameters for each group of plane pairs, and selecting an optimal solution, namely a final registration result, according to the established point cloud registration overall consistency measurement. The method comprehensively utilizes the plane attribute information, the plane constraint and the space geometric constraint to ensure the accuracy and the high efficiency of the registration process, does not depend on additional strength or color information, can effectively register point cloud data acquired by various platforms, has strong applicability, and can process small-scene indoor point clouds and large-scale complex outdoor scene point clouds.
Further, in order to avoid unnecessary interference and reduce the complexity of subsequent processing, the method also comprises the step of preprocessing the target point cloud data and the to-be-registered point cloud data before plane segmentation, and removing in-vitro isolated points and outlier points from the target point cloud data and the to-be-registered point cloud data.
Further, the attribute information of each planar patch in step 2) includes a unit normal vector of the plane, a distance from the coordinate origin to the fitting plane, a mean square error of the plane fitting, an area of the planar patch, a boundary point of the planar patch, a boundary length, and a length and a width of a minimum bounding rectangle of the planar patch.
Further, the invention also provides a specific judgment mode of consistent attributes, wherein the plane pair set with consistent attributes in the step 3) refers to a plane pair which satisfies the condition that the plane area ratio is smaller than a set ratio, the difference between the plane shapes is smaller than a set shape difference and the difference between the plane fitting mean square errors is smaller than a set error in the target plane sheet set and the plane sheet set to be aligned.
Further, in order to improve the efficiency and the precision of plane extraction, the plane segmentation in the step 2) is realized by adopting an adaptive plane segmentation algorithm based on voxel growth.
Further, in order to improve the extraction efficiency, in the step 2), an incremental PCA algorithm is adopted to calculate the plane parameters after the growth of the voxels and the mean square error of plane fitting in the voxel growth process.
Further, to avoid the incremental PCA being susceptible to noise and outliers, the method further includes recalculating the planar parameters obtained using the incremental PCA algorithm by a plane fitting algorithm that accounts for the noise of the sensor measurements.
Further, in order to improve the accuracy of the rotation matrix calculation, the rotation matrix in the step 4) is calculated by using a singular value decomposition method of covariance matrix weighting.
Further, in order to improve the efficiency and robustness of matching, the method further comprises filtering the planar sheet in step 2) to remove the planar sheet with a small area, approximate line shape and poor flatness.
Drawings
FIG. 1 is a schematic diagram of point cloud registration;
FIG. 2 is a flow chart of the automatic registration method of point cloud data based on plane features according to the present invention.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
Method embodiment
The automatic point cloud data registration method based on the plane features comprises the steps of firstly, carrying out plane segmentation on target point cloud data and point cloud data to be registered to obtain a target plane piece group and a plane piece group to be registered, and calculating attribute information of each plane piece in each plane group; then according to the attribute information of each plane slice, obtaining a plane pair set with consistent attributes from the target plane slice set and the plane slice set to be registered; obtaining a corresponding plane pair set for solving coordinate conversion parameters according to the plane piece attribute information, the inter-plane correlation and the plane pair set with consistent rotation and translation geometric constraint dependency; and finally, selecting an optimal solution from the corresponding plane pair set as a final registration result according to the established point cloud registration overall consistency measurement. The implementation process of the method is shown in fig. 2, and the specific implementation steps are as follows.
1. And acquiring target point cloud data and point cloud data to be registered.
In this embodiment, the target point cloud data and the cloud data of the points to be registered are obtained through the three-dimensional laser scanner, and in order to avoid interference of some isolated points and outliers, the target point cloud data and the cloud data of the points to be registered obtained through the three-dimensional laser scanner need to be preprocessed, points far away from the origin of coordinates are removed, points within 80% of the effective measurement range of the three-dimensional laser scanner are reserved, and external isolated points and outliers are removed.
2. And performing plane segmentation on the target point cloud data and the point cloud data to be registered to obtain a target plane piece group and a plane piece group to be registered.
The plane segmentation can be realized by methods such as dynamic clustering, hough transform, Random Sample Consensus (RANSAC), voxel growth adaptive plane segmentation algorithm, and the like. In the embodiment, a self-adaptive plane segmentation algorithm based on voxel growth is adopted to automatically extract plane features in target point cloud data and point cloud data to be registered, and in order to improve efficiency in the voxel growth process, an incremental pca (principal component analysis) algorithm is adopted to calculate plane parameters after voxel growth and mean square error (a measure of flatness) of plane fitting. The specific process is as follows:
adopting a Hessian standard type to express that a plane equation is n & r ═ d, wherein r is the coordinate of a certain point on a plane, n is a unit normal vector of the plane, d is the distance from a coordinate origin to a fitting plane, and the incremental PCA plane fitting algorithm is described as follows:
two sets of point sets P1And P2Each of which includes n1And n2Point of which is indicated by riRepresenting point coordinates, m representing the center of gravity;
order matrixThe geometric information after the two sets of point sets are combined can be obtained by the following formula:
A＝A1+A2
wherein,is the eigenvector, σ, corresponding to the smallest eigenvalue of the matrix S2The mean square error of the plane fit.
3. Plane parameters are calculated for each planar patch in each plane group.
And calculating plane parameters of the series of plane slices obtained in the last step, wherein the plane parameters mainly refer to the distances from unit normal vectors and coordinate origins of the planes to the fitting plane. Because the incremental PCA adopted in the plane segmentation process is easily influenced by noise and abnormal points and the plane parameter calculation is not accurate enough, the plane parameter is recalculated by adopting a plane fitting algorithm considering the noise measured by the sensor, and the points are expressed as a homogeneous coordinate form x ═ rT,1]Let pi be [ n ]T,d]，The superscript e represents unitization, and at this time, the plane equation can be represented as pi · x — 0, and the specific calculation steps are as follows:
(1) computing matricesj ═ 1.. times, N, initialize c ═ 0, letwj1 where ρjDistance of a point from the origin of coordinates, CjIs a covariance matrix, wjIs a weight factor;
(2) calculating the matrices M and N using the following equations, respectively
Computing matricesAnd its corresponding unit eigenvector
If λ ≈ 0, returnc andotherwise, c is updated according to the following formula,and wj：
And (5) returning to the step (2) and carrying out iterative solution.
Finally, the plane parameters are found using the following formula:
order toWherein I is an identity matrix, and the covariance matrix of the plane parameters is:
in addition, the calculation of the attribute information includes the area of the planar patch, the boundary point of the planar patch, the boundary length, and the length and width of the rectangle surrounded by the planar patch. The general plane point set area and boundary point calculation method takes longer time, and the method accelerates the process by adopting a method based on a point cloud projection image. Firstly, taking the average point density as the projection resolution, projecting the point set on each plane sheet into a binary image, then carrying out mathematical morphology processing on the projected image, and utilizing an image boundary detection algorithm to be easierBoundary pixels are identified, boundary points of the plane sheet can be determined according to the mapping relation between the pixels and the points, three-dimensional boundary points can be converted into two dimensions according to the first and second main directions of the plane in the projection process, so that the calculation of plane attribute information is facilitated, and a series of two-dimensional boundary point coordinates { p) projected onto the plane are obtainedi＝(xi,yi),|i＝1,…,Nb}，NbFor the number of boundary points, the length L and width W of the bounding rectangle can be statistically determined from the coordinate values, and the plane area s and the boundary length L can be calculated by the following equations.
4. Filtering with a flat sheet.
In order to improve the efficiency of subsequent plane matching and the robustness of the algorithm, the plane slice filtering is required to be carried out, the plane slice with a smaller area is removed according to a preset parameter threshold, the plane slice with approximate linearity is removed according to the length-width ratio, and the plane slice with poor flatness, namely a larger plane fitting mean square error is removed.
5. The planar pieces are automatically matched.
Through the steps 1-4, the target point cloud data and the plane pieces corresponding to the point cloud data to be registered can be obtained respectively, wherein the target point cloud data obtains m plane pieces, and the point cloud data to be registered obtains n plane pieces which are called a target plane piece group and a plane piece group to be registered respectively.
(1) A set of attribute-consistent pairs of planes is determined.
According to the plane attribute, traversing the two plane sheet groups to obtain KacFor plane pair with consistent attributesThe superscripts t and s are used for marking the target point cloud and the point cloud to be registered, P represents a plane, and the attribute consistency refers to the following attribute measurement.
Ratio of plane area
Difference in shape
Difference of mean square error of plane fitting
The invention adopts relative quantity rather than absolute quantity for condition judgment, which is convenient for parameter setting, improves the registration success rate and enhances the robustness of the registration method to the overlapping degree change and the shielding between the point clouds. That is, if the attribute difference between the two planes is within a certain range, the algorithm will determine that the plane attributes are consistent, and store the consistent plane attributes into the consistent plane attribute set Θac。
(2) A rotation matrix is determined.
The rotation matrix only requires two pairs of non-parallel planes, thus traversing the set Θ of plane-attribute-consistent plane pairsacTwo pairs of non-parallel planar pairs are sought, the non-parallel planar pairs being pairs of planes that satisfy the following condition.
Condition 1:
condition 2:
condition 3:
wherein the two sets of corresponding planes selected by the condition 1 need to satisfy a non-parallel relation,is a non-parallel angle thresholdThe value, condition 2, indicates that the two sets of planes need to satisfy the consistency of the included angles, i.e. the included angles of the normal vectors of the two planes to which the target point cloud belongs are consistent with the included angles of the normal vectors of the two planes to which the point cloud to be registered belongs,is the corresponding angle difference threshold, condition 3 denotes the plane center of gravity (denoted r)cRepresenting) distance change needs to meet certain threshold conditions, thereby reducing the possibility of mismatching and greatly reducing the processing burden of subsequent algorithms. After two groups of corresponding planes meeting the three conditions are obtained, calculating a rotation matrix from a plane normal vector by a two-step rotation method:
(3) a triplet is determined.
Continuously traversing theta on the basis of the step (2)acIn the middle residual plane pair, searching the third group of corresponding planes meeting the conditionsTo determine the translation parameters, the set of planes need to satisfy the rotational consistency, i.e. by passing throughAfter rotation matrix transformation, to be registered in the point cloudShould be in accordance withParallel, i.e. satisfy
Where ψ is an angle threshold. The three sets of plane pairs constitute a plane-to-triplet for calculating translation parameters:
and simultaneously updating the rotation parameters:
converting parametersAndand acting on a plane of the point cloud to be registered in the triple, performing overlapping judgment by using plane boundary points and the gravity center, if the overlapping condition is met, keeping the triple as a group of possible solutions, and if not, giving up. After this step N is obtainedΠGroup triplet
(4) And determining the triple set and the corresponding coordinate conversion parameters.
Traversing the obtained triple set, and expanding each triple Π, namely judging the theta from the theta through rotation and translation consistency and overlappingacThe plane pair meeting the condition is selected to be added into pi, and the expanded triple is represented by gamma. For each Γ, a new coordinate transformation parameter may be calculated, typically using weighted least squares, where a rotation matrix (also called a rotation parameter) may be calculated by:
wherein, the matrix W is a weight matrix, and the matrix N is obtained by accumulating corresponding unit normal vectorsThis direct solution, however, may result in inaccurate results, given the presence of measurement noise. The solution is carried out by using a singular value decomposition method of covariance matrix weighting, the obtained rotation matrix is ensured to be a unit orthogonal matrix, and a correlation matrix Q is defined assNTWtN, wherein the weight is the reciprocal of the trace of the normal vector N fitting covariance matrix, and Q ═ UΛ V can be obtained by performing singular value decomposition on the traceTThe rotation matrix to be solved is:
order toThe translation vector (translation parameter) is calculated by the following formula, wherein the weight is determined by the inverse of the variance of the parameter d.
But here updated conditionally after new rotation and translation parameters are calculated.
For theAndand respectively calculating rotation consistency measures according to the plane corresponding relation provided by the gamma and the following formula:
if it isAccepting the rotation update, otherwise refusing the update, and maintaining the original value
For translationAndsimilarly, a translation consistency metric is calculated according to:
if it isAccepting translation updating, or refusing updating, and maintaining original value
(5) And selecting an optimal solution.
After the step (4) is finished, a series of feasible solutions are obtained, an optimal solution is required to be selected from the feasible solutions, for each feasible solution, the feasible solution acts on a plane to be registered, the corresponding relation is determined again by using a nearest neighbor rule, and the total consistency measure is calculated as follows:
and selecting the solution with the minimum delta value as a final registration result.
Device embodiment
The automatic registration device for point cloud data of plane features comprises a memory, a processor and a computer program which is stored on the memory and runs on the processor, wherein the processor is coupled with the memory, and the processor executes the computer program to realize the automatic registration method for point cloud data of plane features in the method embodiment.
In the plane segmentation process, the traditional point-based method is replaced by a voxel growth-based mode, and plane parameters are updated by combining an incremental PCA algorithm, so that the efficiency of extracting plane features from large-scale point clouds is greatly improved; filtering out partial non-ideal planes, limiting the number of the planes sent into the plane matching module within a certain range, and reducing the complexity of plane matching; in the plane matching process, the high efficiency of the registration process is further ensured by comprehensively utilizing the plane attribute information, the inter-plane constraint and the space geometric constraint; the whole process realizes automatic processing without manual intervention. Meanwhile, the invention only utilizes three-dimensional point coordinates, namely geometric information, and does not depend on additional intensity or color information, can effectively register point cloud data acquired by various platforms, and can process small-scene indoor point clouds and large-scale complex outdoor scene point clouds.
Claims (10)
1. A point cloud data automatic registration method based on plane features is characterized by comprising the following steps:
1) acquiring target point cloud data and point cloud data to be registered;
2) respectively carrying out plane segmentation on the target point cloud data and the point cloud data to be registered to obtain a target plane piece group and a plane piece group to be registered, and calculating attribute information of each plane piece in each plane group;
3) obtaining a plane pair set with consistent attributes from a target plane piece set and a plane piece set to be registered according to the attribute information of each plane piece;
4) selecting two pairs of non-parallel plane pairs from the plane pair sets with consistent attributes, and determining a rotation matrix according to the obtained two pairs of non-parallel plane pairs; selecting a non-parallel plane pair meeting rotation consistency from the remaining plane pairs of the plane pair set with consistent attributes by using a rotation matrix, taking the three selected plane pairs as a triple, acting conversion parameters corresponding to the triple on a plane of point cloud to be registered in the triple, and adding the triple into the triple set if an overlapping condition is met;
5) traversing the remaining plane pairs in the plane pair set with consistent attributes according to the mode of the step 4) to obtain a triple set, respectively acting the conversion parameters corresponding to each triple in the triple set on the cloud data of the point to be registered, calculating the overall consistency measurement, and selecting the conversion parameter of the triple with the minimum overall consistency measurement from the triple to perform point cloud registration.
2. The method of claim 1, further comprising the step of pre-processing the target point cloud data and the point cloud data to be registered before performing the planar segmentation, and removing isolated points and outliers from the target point cloud data and the point cloud data to be registered.
3. The method of claim 1, wherein the attribute information of each plane piece in the step 2) comprises a unit normal vector of the plane, a distance from an origin of coordinates to a fitting plane, a mean square error of plane fitting, an area of the plane piece, a boundary point of the plane piece, a boundary length, and a length and a width of a minimum bounding rectangle of the plane piece.
4. The method according to claim 3, wherein the set of plane pairs with consistent attributes in step 3) refers to the pair of planes in the target plane group and the plane group to be registered, which satisfy the condition that the area ratio of the planes is smaller than a set ratio, the difference between the plane shapes is smaller than a set shape difference, and the difference between the mean square errors of the plane fitting is smaller than a set error.
5. The method for automatically registering point cloud data based on planar features according to claim 3, wherein the planar segmentation in the step 2) is realized by adopting an adaptive planar segmentation algorithm based on voxel growth.
6. The method for automatically registering point cloud data based on plane features according to claim 5, wherein the step 2) adopts an incremental PCA algorithm to calculate plane parameters after voxel growth and mean square error of plane fitting in the voxel growth process.
7. The method of claim 6, further comprising recalculating the planar parameters from the incremental PCA algorithm by a plane fitting algorithm that accounts for sensor measurement noise.
8. The method for automatically registering point cloud data based on plane features as claimed in claim 1, wherein the rotation matrix in the step 4) is calculated by using a singular value decomposition method of covariance matrix weighting.
9. The method for automatically registering point cloud data based on plane features of any one of claims 1-8, wherein the method further comprises filtering the plane patches in step 2) to remove plane patches with small area, approximate line shape and poor flatness.
10. An apparatus for automatic registration of point cloud data based on planar features, the apparatus comprising a memory and a processor, and a computer program stored on the memory and running on the processor, the processor being coupled to the memory, the processor implementing the method for automatic registration of point cloud data of planar features according to any one of claims 1 to 9 when executing the computer program.
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