CN114463396A - Point cloud registration method using plane shape and topological graph voting - Google Patents

Point cloud registration method using plane shape and topological graph voting Download PDF

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CN114463396A
CN114463396A CN202210012942.6A CN202210012942A CN114463396A CN 114463396 A CN114463396 A CN 114463396A CN 202210012942 A CN202210012942 A CN 202210012942A CN 114463396 A CN114463396 A CN 114463396A
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CN114463396B (en
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谢洪
闫利
韦朋成
陈长军
李瑶
戴集成
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Wuhan University WHU
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Abstract

The invention discloses a point cloud registration method for voting by utilizing a plane shape and a topological graph, which comprises the following steps of: step 1, roughly dividing a point cloud into plane elements by adopting a voxelized point cloud plane division algorithm, and calculating accurate plane parameters by using a RANSAC plane fitting method; step 2, selecting a plane shape as a characteristic of plane matching, and designing a plane shape descriptor to carry out same-name plane matching; step 3, constructing a topological graph according to the matched homonymy plane position and normal vector included angle relation, and rejecting planes which are matched in error based on a homonymy plane side voting strategy; and 4, selecting optimal groups of homonymy planes to calculate a transformation matrix of the point clouds of the two stations to complete the registration of the point clouds. The invention designs an HIA-TCD plane shape descriptor, which takes the hole on the plane and the partial shielding phenomenon in the scanning process into consideration and can improve the robustness of plane matching.

Description

Point cloud registration method using plane shape and topological graph voting
Technical Field
The invention relates to a point cloud automatic coarse registration algorithm based on plane shape matching and topological map voting, belonging to the field of remote sensing mapping.
Background
In recent years, with the development of 3D Lidar technology, point clouds are widely applied in urban scenes, such as building three-dimensional reconstruction, urban planning, indoor navigation, etc., and the point clouds are proved to be one of the most suitable data sources for drawing the urban scenes. Due to the limitation of the scanning distance and the scanning mode of the three-dimensional laser scanner, complete scene data can not be obtained through one-station scanning, the data integrity and quality are improved through a multi-angle, multi-platform, multi-station and multi-time equal method, and point clouds of different stations need to be unified to the same coordinate system through a registration technology, so that point cloud registration plays an important role in laser radar research and is an important basis of other point cloud processing technologies. The research is widely distributed in the fields of computer vision, photogrammetry, forest survey, robotics and the like.
Point cloud registration is always a research hotspot in the field of three-dimensional laser, and the process of point cloud registration is to calculate a rigid transformation parameter between two station clouds, take one station cloud as a target point cloud, and convert the other station (source point cloud) into the same coordinate system with the target point cloud. A rigid transformation is a low-dimensional entity that can be uniquely recovered as long as the correct correspondence is known between the three point pairs. The fine registration algorithm represented by the ICP algorithm is one of effective methods for solving the registration problem, and the algorithm repeatedly selects corresponding relation point pairs and calculates the optimal rigid body transformation until the convergence precision requirement of correct registration is met. But the algorithm needs to give an initial value to the rotation matrix, otherwise it is easy to get into local optima. Therefore, a coarse registration of the two-site cloud is required to obtain the initial value. The point cloud rough registration technology is divided into a point-based method, a line-based method and a surface-based method according to different elements extracted by characteristics. The point-based method is low in efficiency and accuracy and is easily affected by noise points. Although the line-based method can improve efficiency, the homonym primitives are difficult to match, and the use scenarios are limited. The point cloud registration algorithm based on the plane can greatly reduce the number of matched elements, can accelerate the matching efficiency of elements with the same name, and on the other hand, the characteristics of the plane are more stable, after the Xiao et al divides the plane by using the region growing algorithm, the area of the plane is calculated, then two groups of planes with approximately equal areas are found to calculate the rotation amount, if the rotation is real, the third group of planes are found, the consistency is judged according to the normal, and finally the transformation parameters are calculated. The Dold et al performs matching based on the area of the plane, the boundary length, the boundary frame, and the average length as descriptors. Li et al look for a corresponding match in the two-station point cloud through a special angle between the three planes. However, under the influence of the scanning position, the building plane point cloud obtained by the laser scanner is usually blocked, and the homonymous plane matching constrained by the characteristics of the plane area, the bounding box, the vector included angle and the like is not reliable.
Disclosure of Invention
The invention mainly solves the technical problems that: an accurate and robust descriptor is designed for plane features to be used for matching a same-name plane, and therefore the problem of point cloud registration of large data volume in an urban scene is solved.
Aiming at the problems, the invention provides a method for solving the rough registration of the urban scene point cloud based on plane shape and topological graph voting. In the human perception rule, whether two planes in an urban scene are homonymous planes is generally judged according to plane shape similarity and a position relation between the planes, according to the principle, the plane shape is used as a feature of geometric matching, plane shape descriptors are designed to match the homonymous planes, then, in the matched homonymous planes, a topological graph is constructed according to the position and normal direction features of the planes, and error matching is eliminated according to a voting principle. And finally, calculating rigid transformation parameters between two station clouds by selecting three pairs of optimal matching planes.
In order to achieve the purpose, the invention provides the technical scheme that:
step 1, roughly dividing point cloud into plane elements by adopting a voxelized point cloud plane division algorithm, and calculating accurate plane parameters by using a RANSAC plane fitting method;
step 2, selecting a plane shape as a characteristic of plane matching, and designing a plane shape descriptor to carry out same-name plane matching;
step 3, constructing a topological graph according to the matched homonymy plane position and normal vector included angle relation, and eliminating planes which are in error matching based on a homonymy plane side voting strategy;
and 4, selecting optimal groups of homonymous planes to calculate a transformation matrix of the two-station point clouds to complete the registration of the point clouds.
Further, in step 1, firstly, constructing a binary coding octree to complete the voxelization of the point cloud, then calculating the characteristics of each voxel, and on the basis, adopting a region growing strategy to segment the plane: selecting voxels with obvious plane characteristics as seeds, then combining adjacent voxels with similar plane characteristics to the seeds into a cluster, and thinning the non-segmented voxels to improve the segmentation result; finally, obtaining accurate plane parameters by using a RANSAC plane fitting method;
further, the specific implementation of step 2 includes the following sub-steps;
step 2.1, calculating context of the shape of the interior angle HIA considering the vertical face hole;
step 2.2, calculating the shape context of the triangle centroid distance TCD;
step 2.3, calculating the HIA-TCD shape descriptor by combining the internal angle and the triangle centroid distance;
step 2.4, calculating the similarity of the shapes of the two plane profiles based on the HIA-TCD shape descriptor;
and 2.5, carrying out homonymous plane matching based on the plane shape similarity.
Further, the specific implementation manner of step 2.1 is as follows;
for a given planar shape O, the segmented plane is first rotated to xoyAnd (3) plane and contour extraction, including outer contour and hole contour, uniformly sampling the number of points of the contour, and obtaining an outer contour sampling point set P ═ P1,p2,...,pnGet two arbitrary points pi,pjThe internal angle HIA between these two points, which takes into account the hole, is defined as: contour point piSum of profile tangents of (1) and (p)iTo pjShortest path Ψ (p)i,pjAngle between O) directions Ang (p)i,pj) Shortest path Ψ (p)i,pjO) is defined as that firstly, the inner part of the plane contour is not capable of passing through holes on the plane, and routes from each point to other points can be obtained through an SPFA shortest path query algorithm; the method for extracting the contour comprises the following steps: and setting edge constraints by using a divide-and-conquer Delaunay algorithm to construct a triangular mesh, and respectively finding out the outline and the hole outline according to the characteristic that the outline edge is connected with only one triangle in sequence.
Further, the specific implementation manner of step 2.2 is as follows;
given plane outer contour sampling point set P ═ P1,p2,...,pnIn which p isi＝(xi,yi,zi) Representing points and three-dimensional coordinates thereof, wherein n represents the number of sampling points, and the sampling points are sorted according to a reverse clock; first, the point set center G ═ x (x) is calculatedG,yG,zG) For each contour point pi＝(xi,yi,zi) ( i 1, 2.., N), where N is the number of points, another point p on the contour point set can be foundj＝(xj,yj,zj) (j ═ 1, 2., N, i ≠ j), which, together with the contour center point, form a triangle Δ piGpjThen using any two points p on the contouri、pjForm a triangle delta p with the contour central point GiGpjThen calculating the center point of the triangle
Figure BDA0003459682390000031
The calculation is as follows:
Figure BDA0003459682390000032
for each contour point piN-1 triangles can be obtained and then the point p is calculatediAnd a central point gijIs a distance of
Figure BDA0003459682390000033
This feature is referred to as the three-dimensional triangle centroid distance.
Further, the specific implementation manner of step 2.3 is as follows;
given plane outer contour sampling point set P ═ P1,p2,...,pnN is the number of points on the contour, for a certain point p on the contouriFirstly, calculating the internal angle HIA and the triangle centroid distance TCD which are formed by the point and other points and take into account the hole:
Figure BDA0003459682390000034
further, the characteristics of the HIAs and TCDs of all contour points of a certain plane O can be obtained as follows:
Figure BDA0003459682390000041
Figure BDA0003459682390000042
wherein TCDs (O) is a matrix of (N-1). times.N, and the ith column is a sample point piTCDs features formed with other points; since the shape description taken in terms of distance is not scale invariant, tcds (o) is normalized by dividing by the maximum absolute value of each row, as follows:
Figure BDA0003459682390000043
among them, Dist' (p)i,gij) Representing normalized point piAnd a central point gijThe distance of (d); for point piIn constructing the HIA-TCD shape context descriptor histogram hiWhen using naRepresenting the statistical number of histogram bins of HIA as the x-axis, ntThe number of the counting square lattices representing the TCD is taken as the y axis; combine the two into a 2D histogram, according to piHIA (p) of dotsi) And normalized TCD (p)i) Calculating each valueAnd counting the number m of each interval according to the indexes falling in the histogram intervals, and obtaining the value of two-dimensional histogram bins according to m/(N-1).
Further, the specific implementation manner of step 2.4 is as follows;
let p beiIs a point on the first plane profile, qjIs a point on the second plane contour, the shape context similarity C of the two pointsij＝C(pi,qj) According to χ2Test statistics were calculated as follows:
Figure BDA0003459682390000044
wherein h isP,i(k) As a contour point P of the plane PiHIA-TCD shape context descriptor histogram of (h)Q,j(k) Contour point Q being a plane QjThe HIA-TCD shape context descriptor histogram of (1), K represents the number of histogram bins; the shape matching cost formula is as follows:
Figure BDA0003459682390000051
wherein pi (i) represents the number of points successfully matched, the matching pi of the plane profiles P and Q is a mapping from 1,2, 1, n to 1,2, 1, m, if pi (i) ≠ 0 represents PiAnd q isπ(i)And matching, wherein the optimal matching is defined as pi so that the matching cost H (pi) is minimum, and the number of points successfully matched is obtained by using a dynamic programming matching algorithm.
Further, the specific implementation manner of step 2.5 is as follows;
two-station point clouds S and T are known, wherein S is a source point cloud, T is a target point cloud, and a plane set obtained after segmentation is S ═ S { (S)1,s2,...,smT ═ T1,t2,...,tnT is equal to { T }1,t2,...,tnPlane t iniAnd S ═ S1,s2,...,smPlane s injThe matching generation of the two can be obtained by calculation according to the matching cost formulaCostijAnd the number of successfully matched points NmatchedCorresponding to H (pi) and pi (i) in step 2.4, respectively; as can be seen from the matching results, the higher the similarity of the two plane profiles is, the matching cost of the two plane profiles isijThe smaller the size; matching point cost pcostmatched＝costij/NmatchedSelecting the optimal corresponding plane as the comparison value, and selecting S ═ S1,s2,...,smIn with tiMatching point least costly plane tjTo obtain the same name plane pair (t)i,sj) And finally calculating T ═ T1,t2,...,tnThe homonymous planes of all the planes in the plan form a homonymous plane set M { (t)i,si)|ti∈T；si∈S；i＝1,2,...n}。
Further, the specific implementation manner of step 3 is as follows;
firstly, according to a homonymous plane set M { (t)i,si)|ti∈T；siE is S; n } constructing a topological graph GS(VS,ES) And GT(VT,ET) (ii) a Wherein, VS(VT) Are nodes of a topological graph, each node representing a plane s in Mi(ti) Whose properties are represented by the plane si(ti) Coordinate of center point of
Figure BDA0003459682390000052
Representing, the properties of an edge include two parts: distance of two nodes:
Figure BDA0003459682390000053
and the normal angle between the planes represented by the two nodes
Figure BDA0003459682390000054
Wherein
Figure BDA0003459682390000055
Refers to the coordinates of two nodes, ni，njRefers to the normal of the plane;
since M is the same asThe set of name planes, and therefore,
Figure BDA0003459682390000056
correspond a set for the node, if
Figure BDA0003459682390000057
And
Figure BDA0003459682390000058
are correctly matched, then their edge pairs
Figure BDA0003459682390000059
Is also a correct match and ideally
Figure BDA0003459682390000061
Where V represents a set of nodes, V represents a node in the set, E represents a set of edges, E represents an element in the set of edges, E represents a node in the set of nodes, E represents a node in the set of nodes, E(i,j)Representing the edge connecting nodes i and j; wherein the content of the first and second substances,
Figure BDA0003459682390000062
represents
Figure BDA0003459682390000063
The length of (a) of (b),
Figure BDA0003459682390000064
represents
Figure BDA0003459682390000065
I.e. the angle between the two planes, if not satisfied
Figure BDA0003459682390000066
And
Figure BDA0003459682390000067
the relationship of (A) is represented in
Figure BDA0003459682390000068
And
Figure BDA0003459682390000069
at least one of which is a false match; in practice, as long as
Figure BDA00034596823900000610
And
Figure BDA00034596823900000611
is small, the two are considered to be a correct match.
If it is used
Figure BDA00034596823900000612
If the corresponding edge set is correct, the corresponding edge set is considered to be correct
Figure BDA00034596823900000613
And
Figure BDA00034596823900000614
the two groups of corresponding homonymous planes are correctly matched, and then the node sets corresponding to the two groups of planes are
Figure BDA00034596823900000615
And
Figure BDA00034596823900000616
each vote is 1, and the principle is called as a plane relation side voting strategy; it is obvious that a certain node pair
Figure BDA00034596823900000617
Number of votes
Figure BDA00034596823900000618
The more, the more robust the set of homonymic plane correspondences; if the number of votes for a node is less than NεThe node is considered to be a wrong homonym plane match and is changed from M { (t)i,si)|ti∈T；siE is S; and (i) removing 1,2,. n), and finally sorting the nodes in the M according to the votes of each node.
Further, the specific implementation manner of step 4 is as follows:
selecting three groups of optimal matching planes for calculation, selecting the ground as a first group of homonymous planes according to the constraint condition of maximum area or maximum point number or minimum Z coordinate of a central point in the plane point cloud, and then setting the homonymous plane set M { (t) passing through a voting strategyi,si)|ti∈T；siE is S; and (3) selecting two groups of non-parallel planes to form three groups of homonymous planes by the nodes in the i-1, 2, the.. n } according to the vote number from large to small, and finally finishing point cloud registration by using a closed form solution estimation rigid body transformation method according to the plane parameters of the three groups of homonymous planes.
Compared with the prior art, the invention has the advantages and beneficial effects that:
1) a new method for coarse registration of plane elements is designed. The plane shape descriptor is matched with the homonymous plane, so that compared with a descriptor (descriptor) of point characteristics, the plane shape descriptor is less influenced by noise, and the characteristics are more stable; compared with other registration algorithms based on plane features, plane attributes such as area and bounding box are selected as descriptions to be more robust.
2) In order to improve the matching capability of an incomplete plane, the invention designs an HIA-TCD plane shape descriptor, which considers the hole on the plane and the partial shielding phenomenon in the scanning process and can improve the robustness of plane matching.
3) In order to select an optimal matching plane, the optimal matching problem is converted into an edge matching problem based on a topological graph representation. The invention establishes a mathematical model of edge correspondence maximization. On the basis of the matched homonymous planes, a topological graph is constructed according to the positions of the planes and the normal vector relation, a side voting strategy is used, error matching is eliminated, and three groups of optimal matching are selected to calculate a rigid body transformation matrix.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of calculation of the inner distance and the inner angle of the vertical-face hole according to the embodiment of the present invention.
FIG. 3 is a schematic diagram illustrating the calculation of the centroid distance of a triangle according to an embodiment of the present invention.
Fig. 4 is a diagram illustrating the matching result between two plane shape contour points according to an embodiment of the present invention.
Detailed Description
The technical solution of the present invention is further explained with reference to the drawings and the embodiments.
Three steps in the plane-based registration method are most critical:
(1) how to extract a plane quickly and accurately, in the current plane-based registration, RANSAC or a variant of RANSAC is mostly used for extracting a plane in a scene, but the method has low efficiency of plane segmentation and is not suitable for a point cloud plane segmentation task of a large urban scene. Other plane segmentation methods such as region growing and hough transform based segmentation algorithms can also be used for plane segmentation, but their efficiency is difficult to meet the requirement of large scene plane segmentation, and the over-segmentation phenomenon affects the accuracy of plane parameter calculation. The voxel-based plane segmentation algorithm can efficiently complete the task of plane segmentation of large scene point clouds, but a jagged under-segmentation result is generated at the edge of a plane.
(2) Extracting plane features and matching the corresponding relation. The key to the plane-based registration method is the correct matching of the homonym planes. In the existing registration method based on plane features, plane attributes such as area, bounding box or special angle between plane normals are generally selected as descriptors to find corresponding matching in two-station point clouds. These descriptors are not robust against occlusion.
(3) And (4) rejecting the same name planes which are in error matching. There are many similar, symmetrical or repetitive structures in urban scenes, which can easily cause mismatching between planes to some extent. The existing method generally utilizes an exhaustive search method to establish the corresponding relation between different scanning planes and eliminates incorrect homonymous planes, and the algorithm complexity of the method is too high. Or a similar point-based mismatch elimination method, which eliminates the mismatch by using RANSAC algorithm, is not stable enough.
The invention aims to design a point cloud registration algorithm suitable for urban scenes. Secondly, a robust plane descriptor is designed, has better robustness, and can be accurately matched with a plane with the same name in two-station scanning even under the condition that point cloud has occlusion. And finally, according to the geometric relation of the matched planes, eliminating the homonymous planes which are mismatched according to the human perception rule, and selecting three optimal groups of homonymous planes to finish point cloud registration.
The invention generally comprises three steps: firstly, in order to improve the efficiency of plane segmentation and the accuracy of parameter estimation, a binary coding octree high-efficiency voxelized point cloud plane segmentation algorithm is used for roughly segmenting the point cloud into plane elements and calculating accurate plane parameters by using a RANSAC plane fitting method. And secondly, selecting a plane shape as a characteristic of plane matching, and providing a space plane shape descriptor with an internal angle combined with a triangle centroid distance (HIA-TCD), wherein the descriptor can be correctly matched with a plane of the same name even if the plane contour is incomplete. And finally, constructing a topological graph according to the matched homonymous plane position and normal vector included angle relation, designing a homonymous plane side voting strategy, eliminating planes which are in error matching, and selecting the optimal three groups of homonymous planes to calculate a transformation matrix of two-station point clouds to complete coarse registration of the point clouds. The whole technical process is shown in the following figure
Step 1, roughly dividing point cloud into plane elements by adopting a voxelized point cloud plane division algorithm and calculating accurate plane parameters by using a RANSAC plane fitting method;
in order to improve the efficiency of large-scale point cloud segmentation, the invention uses an efficient plane segmentation algorithm based on coding voxels to roughly segment the point cloud into planes. Firstly, constructing a binary coding octree to complete the voxelization of the point cloud, and then calculating the characteristics of each voxel. On the basis, a region growing strategy is adopted to divide the plane: voxels with significant planar features are selected as seeds and neighboring voxels with similar planar features to the seeds are merged into one cluster. And finally, thinning the non-segmented voxels to improve the segmentation result. In voxel-based planar segmentation, setting larger voxel nodes may improve the efficiency of planar segmentation, but at the expense of accuracy of planar parameters. The invention uses RANSAC plane fitting method to improve parameter precision. And obtaining an inner point of the fitting model by setting a smaller fitting distance, and then iteratively estimating optimal plane parameters. Because the plane is re-fitted on the basis of the segmented rough plane, the RANSAC iteration times are less, and the overall segmentation efficiency is still higher.
Step 2, selecting the plane shape as the characteristic of plane matching, and carrying out homonymy plane matching based on the plane shape descriptor
The plane in the structural building can be regarded as a 3d shape with 2d characteristics, and the key of shape matching is to construct a shape descriptor which has rich characteristic information and has rotation, translation, scale invariance and the like and meets the matching requirements. In addition to the aforementioned requirements, the holes and partial shading of the building floor are also taken into account. The HIA-TCD shape descriptor fusing the angles in the contour and the distances of the centers of mass of the triangles is designed according to the requirements.
Step 2.1, calculating and considering the context of the internal angle (HIA) shape of the vertical face hole
First, the definition of the inner distance is given: given the outer contour sampling point set P ═ { P of plane shape O1,p2,...,pnGet two points pi,pjThe inner distance between two points is defined as the shortest path Ψ (p) connecting the nodes inside the shape Oi,pjLength of O) by d (p)i,pjO). The present invention defines the internal angle as, in terms of the definition of the internal distance: contour point piAnd the corresponding point pjShortest path Ψ (p)i,pjO) the angle between the directions. As shown in fig. 2 (f). The specific calculation method considering the inner distance (HID) and the inner angle (HIA) of the facade hole is shown in fig. 2, and the specific steps are as follows:
(1) firstly, the segmented plane is rotated to the xoy plane, then the edge constraint is set by using the divide-and-conquer Delaunay algorithm to construct a triangular mesh, and the outline and hole outline results are respectively found out in sequence according to the characteristic that the outline edge is only connected with one triangle, as shown in figure 2 (b).
(2) After the contour is found, the number of points of the contour is uniformly sampled, the number of sampling points of the contour is set to be 100, and the number of sampling points of the contour of the hole is 50 as shown in fig. 2 (c).
(3) According to the sampling result of the outer contour, a graph structure considering the inner holes is constructed, and two aspects are considered during construction: one is the contour point piAnd pjThe connecting line of (a) is inside the plane contour, and the connecting line between two points can not pass through the hole on the vertical surface as shown in figure 2 (d). In order to improve the shortest path query efficiency, an SPFA shortest path query algorithm is used for acquiring the routes from each point to other points and calculating an internal angle Ang (p)i,pj)。
Step 2.2, calculate Triangle Centroid Distance (TCD) shape context
The invention designs a space Triangle Centroid Distance (TCD) shape context to improve the matching performance of a partially shielded shape, and the construction method comprises the following steps: as shown in fig. 3, given a set of in-plane outline sample points P ═ P1,p2,...,pnIn which p isi＝(xi,yi,zi) And representing points and three-dimensional coordinates thereof, wherein n represents the number of sampling points, and the sampling points are sorted according to a reverse clock. First, the point set center G ═ x (x) is calculatedG,yG,zG) For each contour point pi＝(xi,yi,zi) ( i 1, 2.., N), another point p on the contour point set may be foundj＝(xj,yj,zj) (j ═ 1, 2., N, i ≠ j), which, together with the contour center point, form a triangle Δ piGpjThen calculating the center point of the triangle
Figure BDA0003459682390000091
The calculation is as follows:
Figure BDA0003459682390000092
for each contour point piN-1 triangles can be obtained and then the point p is calculatediAnd a central point gijIs a distance of
Figure BDA0003459682390000093
This feature is referred to as the three-dimensional triangle centroid distance.
Step 2.3, combining the internal angle (HIA) and the Triangle Centroid Distance (TCD), calculating the HIA-TCD shape descriptor
Because the distance and angle combination mode is more beneficial to describing the shape, the HIA-TCD shape context descriptor is designed by combining the triangle centroid distance and the interior angle considering the hole, so that the HIA-TCD shape context descriptor has the matching capability on the global characteristic, the local characteristic, the hole, the shielding and the like of a spatial plane. The construction method comprises the following steps:
given plane outer contour sampling point set P ═ P1,p2,...,pnN is the number of points on the contour, for a certain point p on the contouriFirstly, calculating the internal angle HIA and the triangle centroid distance TCD which are formed by the point and other points and take into account the hole:
Figure BDA0003459682390000101
further, the characteristics of the HIAs and TCDs of all contour points of a certain plane O can be obtained as follows:
Figure BDA0003459682390000102
Figure BDA0003459682390000103
wherein TCDs (O) is a matrix of (N-1). times.N, and the ith column is a sampling point piTCDs features formed with other points. Since the shape description obtained from the distance is not scale-invariant, it is divided by the maximum absolute value of each rowTCDs (O) are normalized as follows:
Figure BDA0003459682390000104
among them, Dist' (p)i,gij) Representing normalized point piAnd a central point gijThe distance of (d); for point piIn constructing the HIA-TCD shape context descriptor histogram hiWhen using naStatistical histogram bins (bins) quantity representing HIA (1D) (fixed value n)a12) as x-axis, ntIndicates the number of bins of TCD (1D) (taking a fixed value of n)t5) as the y-axis. Combine the two into a 2D histogram, according to piHIA (p) of dotsi) And normalized TCD (p)i) And calculating the index of each value falling in the histogram interval, counting the number m of each interval, and obtaining the value of the two-dimensional histogram bins according to m/(N-1).
Step 2.4, calculating the similarity of two plane shape contours based on HIA-TCD shape descriptors
Let p beiIs a point on the first plane profile, qjIs a point on the second plane contour, the shape context similarity C of the two pointsij＝C(pi,qj) According to χ2The test statistics were calculated as follows:
Figure BDA0003459682390000105
wherein h isP,i(k) As a contour point P of the plane PiOf the shape context descriptor histogram, hQ,j(k) Contour point Q being a plane QjK denotes the number of histogram bins. In a general feature matching algorithm, an optimal matching algorithm is usually applied to obtain optimal matching, minimum cost is obtained by solving, and finally, all shape matching costs can be obtained based on the optimal matching obtained by solving, wherein a shape matching cost formula is as follows:
Figure BDA0003459682390000111
the matching pi (i) of planes P and Q is a mapping from 1,2, 1, n to 1,2, m, if pi (i) ≠ 0, meaning PiAnd q isπ(i)Are matched. The best match is defined as pi (i) such that the matching cost H (pi) is minimal. Aiming at project specific problems, when the shape contour sequence information is known, the Dynamic Programming (DP) algorithm is used for carrying out ordered contour matching more accurately and efficiently, so that in order to solve the matching problem, the dynamic programming matching algorithm is used for solving a shape matching cost function, and the point number pi (i) of successful matching is obtained. The matching result of the two plane shapes is shown in fig. 4.
Step 2.5, carrying out homonymous plane matching based on plane shape similarity
Two point clouds S (source point cloud) and T (target point cloud) are known, and the set of segmented planes is S ═ S1,s2,...,smT ═ T1,t2,...,tnT ═ T } ═ T1,t2,...,tnPlane t iniAnd S ═ S1,s2,...,smPlane s injThe matching cost of the two can be calculated according to the matching cost formulaijAnd the number of successfully matched points NmatchedCorresponding to H (pi) and pi (i) in step 2.4, respectively, and the matching result shows that the higher the similarity of the two plane profiles is, the matching cost of the two plane profiles isijThe smaller. The invention compares the matching point cost pcost with the matching point cost pcostmatched＝costij/NmatchedAnd selecting the optimal corresponding plane as a comparison value. Selecting S ═ S1,s2,...,smIn with tiPlane t with minimum matching point costjTo obtain the same name plane pair (t)i,sj) And finally calculating T ═ T1,t2,...,tnThe homonymous planes of all the planes in the plan form a homonymous plane set M { (t)i,si)|ti∈T；si∈S；i＝1,2,...n}。
Step 3, according to the matched homonymy plane position and normal vector clipThe angle relation constructs a topological graph, and based on a same-name plane edge voting strategy, the planes which are mismatched are rejected because a large number of plane elements are contained in urban market sight clouds, the shapes of some planes are very similar, and generally, the planes are of repeated structures and have parallel relations, and the planes are very easy to cause mismatching, so that the wrong same-name planes are rejected, and the most stable same-name planes are selected for registration. Firstly, according to a homonymous plane set M { (t)i,si)|ti∈T；siE is S; i-1, 2,. n } constructing a topological graph GS(VS,ES) And GT(VT,ET) Where V represents a set of nodes (nodes), V represents a node in the set, E represents a set of graph edges (edge), E represents an element in the set of edges, and an edge connects two nodes, so E is used(i,j)And (4) showing. Wherein, VS(VT) Are nodes of a topological graph, each node representing a plane s in Mi(ti) Whose properties are represented by the plane si(ti) Coordinate of center point of
Figure BDA0003459682390000112
Indicating that only x, y coordinates are used in order to reduce the effects of noise and point cloud loss; eS(ET) For an edge of a topology graph, the attribute of the edge includes two parts: distance of two nodes
Figure BDA0003459682390000121
And the angle between two nodes
Figure BDA0003459682390000122
Wherein
Figure BDA0003459682390000123
Refers to the coordinates of two nodes, ni，njRefers to the normal of the plane.
Since M is a set of homonym planes, therefore,
Figure BDA0003459682390000124
as a pair of nodesShould be collected if
Figure BDA0003459682390000125
And
Figure BDA0003459682390000126
are correctly matched, then their edge pairs
Figure BDA0003459682390000127
Is also a correct match and ideally
Figure BDA0003459682390000128
Wherein the content of the first and second substances,
Figure BDA0003459682390000129
represents
Figure BDA00034596823900001210
The length of (a) of (b),
Figure BDA00034596823900001211
represents
Figure BDA00034596823900001212
I.e. the angle between the two planes. If not satisfied
Figure BDA00034596823900001213
And
Figure BDA00034596823900001214
the relationship of (A) is represented in
Figure BDA00034596823900001215
And
Figure BDA00034596823900001216
at least one of which is a false match.
The above principle is based on the fact that two sets of planes with the same name are completely equal, and in practice, the principle is only required to be implemented when the two sets of planes with the same name are completely equal
Figure BDA00034596823900001217
And
Figure BDA00034596823900001218
is small, the two are considered to be a correct match. If it is not
Figure BDA00034596823900001219
If the corresponding edge set is correct, the corresponding edge set is considered to be correct
Figure BDA00034596823900001220
And
Figure BDA00034596823900001221
the two groups of corresponding homonymous planes are correctly matched, and then the node sets corresponding to the two groups of planes are
Figure BDA00034596823900001222
And
Figure BDA00034596823900001223
each vote is 1, and this principle is called a flat relationship edge voting strategy. It is obvious that a certain node pair
Figure BDA00034596823900001224
Number of votes
Figure BDA00034596823900001225
The more, the more robust the set of homonym plane correspondences. If the number of votes for a node is less than NεThe node is considered to be a wrong homonym plane match and is changed from M { (t)i,si)|ti∈T；siE is S; and (i) removing 1,2,. n), and finally sorting the nodes in the M according to the votes of each node.
Step 4, selecting the optimal three groups of homonymous planes to calculate the transformation matrix of the two-station point cloud to complete the rough registration of the point cloud
The transformation between the two point clouds S and T is usually composed of a 3D rotation parameter R and a 3D translation parameter T, forPlane-based registration methods generally require three sets of exact homonymous planes to directly calculate the transformation parameters R and t. In order to reduce the number of the homonymous planes to adapt to the situation that the number of planes in a scene is small, three groups of optimal matching planes are selected for calculation. In an urban scene, the ground is a plane with stable characteristics and easy identification, so that ground points are selected as a first group of homonymous planes, the ground is selected from the segmented planes easily, and available characteristics such as the largest area, the largest number of points, the lowest Z coordinate of a central point and the like are obtained. Then, the set M { (t) of the homonymous planes which have already passed the voting strategy is definedi,si)|ti∈T；siE is S; the nodes in the i-1, 2, the.. n } select two groups of non-parallel planes from large to small according to the vote number, and the nodes form three groups of planes with the same name with the ground. And finally, estimating rigid body transformation by using a closed form solution according to the plane parameters of the three groups of homonymous planes[1]And finishing point cloud registration.
[1].Khoshelham,K.."Closed-form solutions for estimating a rigid motion from plane correspondences extracted from point clouds."Isprs Journal of Photogrammetry&Remote Sensing 114.Apr.(2016):78-91.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (10)

1. A point cloud registration method using plane shape and topological map voting is characterized by comprising the following steps:
step 1, roughly dividing point cloud into plane elements by adopting a voxelized point cloud plane division algorithm, and calculating accurate plane parameters by using a RANSAC plane fitting method;
step 2, selecting a plane shape as a characteristic of plane matching, and designing a plane shape descriptor to carry out same-name plane matching;
step 3, constructing a topological graph according to the matched homonymy plane position and normal vector included angle relation, and eliminating planes which are in error matching based on a homonymy plane side voting strategy;
and 4, selecting optimal groups of homonymous planes to calculate a transformation matrix of the two-station point clouds to complete the registration of the point clouds.
2. The point cloud registration method using plane shape and topological map voting according to claim 1, wherein: in the step 1, firstly, binary coding octree is constructed to complete the voxelization of point cloud, then the characteristics of each voxel are calculated, and on the basis, a region growing strategy is adopted to segment a plane: selecting voxels with obvious plane characteristics as seeds, then combining adjacent voxels with similar plane characteristics to the seeds into a cluster, and thinning the non-segmented voxels to improve the segmentation result; and finally, acquiring accurate plane parameters by using a RANSAC plane fitting method.
3. The point cloud registration method using plane shape and topological map voting according to claim 1, wherein: the specific implementation of the step 2 comprises the following substeps;
step 2.1, calculating context of the shape of the interior angle HIA considering the vertical face hole;
step 2.2, calculating the shape context of the triangle centroid distance TCD;
step 2.3, calculating the HIA-TCD shape descriptor by combining the internal angle and the triangle centroid distance;
step 2.4, calculating the similarity of the shapes of the two plane profiles based on the HIA-TCD shape descriptor;
and 2.5, carrying out homonymous plane matching based on the plane shape similarity.
4. A method of point cloud registration using planform and topological map voting as claimed in claim 3, wherein: the specific implementation of step 2.1 is as follows;
for a given planar shape O, the segmented plane is first rotated to the xoy plane andthe method comprises the steps of taking a contour, uniformly sampling the number of points of the contour, and obtaining an outer contour sampling point set P ═ P1,p2,...,pnGet two arbitrary points pi,pjThe internal angle HIA between these two points, which takes into account the hole, is defined as: contour point piSum of profile tangents of (1) and (p)iTo pjShortest path Ψ (p)i,pjAngle between O) directions Ang (p)i,pj) Shortest path Ψ (p)i,pjO) is defined as that firstly, the inner part of the plane contour is not capable of passing through holes on the plane, and routes from each point to other points can be obtained through an SPFA shortest path query algorithm; the method for extracting the contour comprises the following steps: and setting edge constraints by using a divide-and-conquer Delaunay algorithm to construct a triangular mesh, and respectively finding out the outline and the hole outline according to the characteristic that the outline edge is connected with only one triangle in sequence.
5. The method of point cloud registration by plane shape and topological map voting of claim 4, wherein: the specific implementation of step 2.2 is as follows;
given plane outer contour sampling point set P ═ P1,p2,...,pnIn which p isi＝(xi,yi,zi) Representing points and three-dimensional coordinates thereof, wherein n represents the number of sampling points, and the sampling points are sorted according to a reverse clock; first, the point set center G ═ x (x) is calculatedG,yG,zG) For each contour point pi＝(xi,yi,zi) (i 1, 2.., N), where N is the number of points, another point p on the contour point set can be foundj＝(xj,yj,zj) (j ═ 1, 2., N, i ≠ j), which, together with the contour center point, form a triangle Δ piGpjThen using any two points p on the contouri、pjForm a triangle delta p with the contour central point GiGpjThen calculating the center point of the triangle
Figure FDA0003459682380000021
The calculation is as follows:
Figure FDA0003459682380000022
for each contour point piN-1 triangles can be obtained and then the point p is calculatediAnd a central point gijOf (2) is
Figure FDA0003459682380000023
This feature is referred to as the three-dimensional triangle centroid distance.
6. The method of point cloud registration using planform and topological map voting according to claim 5, wherein: the specific implementation manner of the step 2.3 is as follows;
given plane outer contour sampling point set P ═ P1,p2,...,pnN is the number of points on the contour, for a certain point p on the contouriFirstly, calculating the internal angle HIA and the triangle centroid distance TCD which are formed by the point and other points and take into account the hole:
Figure FDA0003459682380000024
further, the characteristics of the HIAs and TCDs of all contour points of a certain plane O can be obtained as follows:
Figure FDA0003459682380000025
Figure FDA0003459682380000031
wherein TCDs (O) is a matrix of (N-1). times.N, and the ith column is a sampling point piTCDs features formed with other points; since the shape description obtained from the distance is not scale invariantThus, tcds (o) is normalized by dividing by the maximum absolute value of each row, as follows:
Figure FDA0003459682380000032
among them, Dist' (p)i,gij) Representing normalized point piAnd a central point gijThe distance of (d); for point piIn constructing the HIA-TCD shape context descriptor histogram hiWhen using naRepresenting the statistical number of histogram bins of HIA as the x-axis, ntThe number of the counting square lattices representing the TCD is taken as the y axis; combine the two into a 2D histogram, according to piHIA (p) of dotsi) And normalized TCD (p)i) And calculating the index of each value falling in the histogram interval, counting the number m of each interval, and obtaining the value of the two-dimensional histogram bins according to m/(N-1).
7. The method of point cloud registration using plane shape and topology voting according to claim 6, wherein: the specific implementation manner of the step 2.4 is as follows;
let p beiIs a point on the first plane profile, qjIs a point on the second plane contour, the shape context similarity C of the two pointsij＝C(pi,qj) According to χ2Test statistics were calculated as follows:
Figure FDA0003459682380000033
wherein h isP,i(k) As a contour point P of the plane PiHIA-TCD shape context descriptor histogram of (h)Q,j(k) Contour point Q being a plane QjThe HIA-TCD shape context descriptor histogram of (1), K represents the number of histogram bins; the shape matching cost formula is as follows:
Figure FDA0003459682380000034
wherein, pi (i) represents the point number of successful matching, if pi (i) ≠ 0 represents piAnd q isπ(i)And matching, wherein the optimal matching is defined as pi (i) so that the matching cost H (pi) is minimum, and the number of points successfully matched is obtained by using a dynamic programming matching algorithm.
8. The method of point cloud registration using plane shape and topology voting according to claim 7, wherein: the specific implementation of step 2.5 is as follows;
two-station point clouds S and T are known, wherein S is a source point cloud, T is a target point cloud, and a plane set obtained after segmentation is S ═ S { (S)1,s2,...,smT } and T ═ T1,t2,...,tnN and m are the numbers of planes in the plane set S and the plane set T respectively, and T is equal to { T }1,t2,...,tnPlane t iniAnd S ═ S1,s2,...,smPlane s injThe matching cost of the two can be calculated according to the matching cost formulaijAnd the number of successfully matched points NmatchedCorresponding to H (pi) and pi (i) in step 2.4, respectively; as can be seen from the matching results, the higher the similarity of the two plane profiles is, the matching cost of the two plane profiles isijThe smaller; matching point cost pcostmatched＝costij/NmatchedSelecting the optimal corresponding plane as the comparison value, and selecting S ═ S1,s2,...,smIn with tiPlane t with minimum matching point costjTo obtain the same name plane pair (t)i,sj) And finally calculating T ═ T1,t2,...,tnThe homonymous planes of all the planes in the plan form a homonymous plane set M { (t)i,si)|ti∈T；si∈S；i＝1,2,...n}。
9. The method of point cloud registration using plane shape and topology voting according to claim 8, wherein: the specific implementation manner of the step 3 is as follows;
firstly, according to a homonymous plane set M { (t)i,si)|ti∈T；siE is S; n } constructing a topological graph GS(VS,ES) And GT(VT,ET) (ii) a Wherein, VS(VT) Are nodes of a topological graph, each node representing a plane s in Mi(ti) Whose properties are represented by the plane si(ti) Coordinate of center point of
Figure FDA0003459682380000041
Representing, the properties of an edge include two parts: distance of two nodes:
Figure FDA0003459682380000042
and the normal angle between the planes represented by the two nodes
Figure FDA0003459682380000043
Wherein
Figure FDA0003459682380000044
Refers to the coordinates of two nodes, ni，njRefers to the normal of the plane;
since M is a set of homonym planes, therefore,
Figure FDA0003459682380000045
correspond a set for the node, if
Figure FDA0003459682380000046
And
Figure FDA0003459682380000047
are correctly matched, then their edge pairs
Figure FDA0003459682380000048
Is also a correct match and ideally
Figure FDA0003459682380000049
Where V represents a set of nodes, V represents a node in the set, E represents a set of edges, E represents an element in the set of edges, E represents a node in the set of nodes, E represents a node in the set of nodes, E(i,j)Representing the edge connecting nodes i and j; wherein the content of the first and second substances,
Figure FDA0003459682380000051
represents
Figure FDA0003459682380000052
The length of (a) of (b),
Figure FDA0003459682380000053
represents
Figure FDA0003459682380000054
I.e. the angle between the two planes, if not satisfied
Figure FDA0003459682380000055
And
Figure FDA0003459682380000056
the relationship of (A) is represented in
Figure FDA0003459682380000057
And
Figure FDA0003459682380000058
at least one of which is a false match; in practice, as long as
Figure FDA0003459682380000059
And
Figure FDA00034596823800000510
is small, the two are considered to be a correct match.
If it is not
Figure FDA00034596823800000511
If the corresponding edge set is correct, the corresponding edge set is considered to be correct
Figure FDA00034596823800000512
And
Figure FDA00034596823800000513
the two groups of corresponding homonymous planes are correctly matched, and then the node sets corresponding to the two groups of planes are
Figure FDA00034596823800000514
And
Figure FDA00034596823800000515
each vote is 1, and the principle is called as a plane relation side voting strategy; it is obvious that a certain node pair
Figure FDA00034596823800000516
Number of votes
Figure FDA00034596823800000517
The more, the more robust the set of homonymic plane correspondences; if the number of votes for a node is less than NεThe node is considered to be a wrong homonym plane match and is changed from M { (t)i,si)|ti∈T；siE is S; and (3) removing i-1, 2,. n } and finally sorting the nodes in the M according to the votes of all the nodes.
10. A method of point cloud registration using planform and topological map voting as claimed in claim 9, wherein: the specific implementation manner of the step 4 is as follows:
selecting three groups of optimal matching planes for calculation, selecting the ground as a first group of homonymous planes according to the constraint condition of maximum area or maximum point number or minimum Z coordinate of a central point in the point cloud of the planes, and votingPolicy set of homonymous planes M { (t)i,si)|ti∈T；siE is S; and (3) selecting two groups of non-parallel planes to form three groups of homonymous planes by the nodes in the i-1, 2, the.. n } according to the vote number from large to small, and finally finishing point cloud registration by using a closed form solution estimation rigid body transformation method according to the plane parameters of the three groups of homonymous planes.
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