CN112150523A - Three-dimensional point cloud registration method with low overlapping rate - Google Patents

Three-dimensional point cloud registration method with low overlapping rate Download PDF

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CN112150523A
CN112150523A CN202011017246.1A CN202011017246A CN112150523A CN 112150523 A CN112150523 A CN 112150523A CN 202011017246 A CN202011017246 A CN 202011017246A CN 112150523 A CN112150523 A CN 112150523A
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张元�
李晓燕
韩燮
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North University of China
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Abstract

The invention discloses a three-dimensional point cloud registration method with low overlapping rate, and belongs to the technical field of machine vision. The method aims at the problems of high registration difficulty, low precision and the like of two pieces of point cloud with low overlapping rate. Firstly, establishing a multi-scale descriptor by utilizing the curvature characteristics of point cloud to ensure the completeness of point cloud data and minimize redundant data; secondly, carrying out corresponding relation clustering partitioning by utilizing the angle difference of the multi-scale descriptors to obtain an overlapping area of the source point cloud and the target point cloud; and finally, substituting the point clouds in the overlapped region and the corresponding relation thereof into a convex optimization problem, removing outliers and optimizing the corresponding relation, realizing coarse registration and refining by utilizing an ICP (inductively coupled plasma) algorithm. The method can narrow the useful search range of point cloud registration, reduce the registration calculation amount, and provide more advantageous registration accuracy and time efficiency for point cloud data with lower initial overlapping degree. The method can be widely applied to the fields of three-dimensional model reconstruction, cultural heritage management, robot navigation positioning and the like.

Description

Three-dimensional point cloud registration method with low overlapping rate
Technical Field
The invention belongs to the technical field of machine vision, and particularly relates to a three-dimensional point cloud registration method with low overlapping rate.
Background
In recent years, three-dimensional point cloud data is widely applied to the fields of three-dimensional model reconstruction, cultural heritage management, robot navigation positioning and the like. The rapid and accurate three-dimensional point cloud registration technology is a key technology and a research focus. The purpose of three-dimensional point cloud registration is to find the best rigid transformation that enables two input point clouds to be aligned to a common coordinate system. In practical applications, the data may be severely occluded and the overlap area between the two point clouds is small, which makes the process of finding the best rigid body transformation challenging. Therefore, finding a fast, accurate and robust registration algorithm for point clouds with smaller overlapping ranges is an active research topic today.
Currently, the hottest three-dimensional point cloud registration algorithms can be divided into two main categories: feature-based registration methods and featureless-based registration methods. The former is to extract key points and find the corresponding relation between two point clouds by using a feature descriptor which can keep unchanged under rigid body transformation, and then to carry out registration. But the quality and speed of extracting features by such methods is limited when the overlap ratio is low. The latter is a direct registration based on the original point cloud. The method identifies the abnormal-free subset by means of a bottom layer sampling strategy, so that the corresponding relation of the two subsets is established. Under the condition that noise and outlier exist, a random sampling consistency algorithm (RANSAC) is difficult to select three pairs of high-quality corresponding points required by iteration as a sample subset, and the registration effect is greatly influenced. This method can be improved using local optimization techniques. The four-point homodyne set (4PCS) algorithm adopts a strategy of enumerating all consistent subsets of 4 coplanar points, and the calculation cost is higher. The Super4PCS algorithm improves the method, and intelligent indexes are introduced, so that the complexity of the method is reduced from quadratic to linear. Le et al propose a new sampling strategy by taking a special example of the graph matching problem. The method has great advantages in running time and handling cases containing large amounts of noise and outliers by quickly searching for correspondences in a manner that solves the loose convex problem for estimating and validating assumptions.
According to the literature, when the overlapping rate of the source point cloud and the target point cloud is lower than 60%, the overlapping degree of the two point clouds is low. For point cloud data with low overlapping rate, because the amount of the point cloud data of the overlapping part is small, the extracted features are limited, and a lot of outlier subsets are generated by directly utilizing the original point cloud registration, so that the processing is time-consuming and the matching is easy to be wrong. Therefore, the point cloud registration problem of low overlap ratio is a difficult point in registration. In recent years, some researchers combine the advantages of the two main methods together, and propose a comprehensive method, which provides a new direction for the registration research of low-overlapping-rate point clouds.
Disclosure of Invention
The invention provides a three-dimensional point cloud registration method with low overlapping rate, aiming at the problems of high registration difficulty, low precision and the like of two pieces of point cloud with low overlapping rate.
In order to achieve the purpose, the invention adopts the following technical scheme:
a low-overlapping-rate three-dimensional point cloud registration method comprises the following steps:
step 1, constructing a multi-scale descriptor based on curvature features and normal vectors;
step 2, establishing the similarity degree between angle difference measurement areas based on the multi-scale descriptors, and clustering and partitioning;
and 3, judging the matching potential in the corresponding relation clustering blocks based on the SDRSAC algorithm, removing outliers, and optimizing the corresponding relation to complete registration.
Further, the step 1 further comprises the following steps:
step 1.1, for each query point P, at each neighborhood radius rlA covariance matrix is constructed,
Figure BDA0002699473010000021
wherein, the dimension L is 1.·, L; the neighborhood radius corresponding to the scale is denoted as r1＜r2＜…＜rL，SlRepresenting the distance from the query point P in the neighborhood radius rlSet S of points within rangel＝{Pi|||Pi-P||≤rl}；
Step 1.2, decomposing the formula (1) by using a singular value decomposition algorithm SVD to obtain threeCharacteristic value lambdal1≥λl2≥λl3And its corresponding feature vector nl1，nl2，nl3Feature vector n corresponding to the minimum feature valuel3I.e. the normal vector of the plane, and is marked as nl(ii) a Setting the directions of the normal vectors of the regions to be consistent, and performing negation processing on the normal vectors which do not point to the viewpoint direction to avoid the influence of the directions of the subsequent normal vectors on region blocking;
step 1.3, normalizing the characteristic value to obtain a vector dl，
Figure BDA0002699473010000031
Using difference of characteristic values Δ dl＝dl+1-dlRepresenting the variation of the point cloud patch, Δ d of L different neighborhood radii to be consideredlConnecting to construct a descriptor D based on the characteristic value;
Figure BDA0002699473010000032
merging L normal vectors n of different neighborhood radiilObtaining a descriptor N based on a normal;
N＝(n1,…,nL) (4)
and combining the descriptor D based on the characteristic value and the descriptor N based on the normal line to obtain the multi-scale descriptor (N, D) based on the characteristic value and the normal line.
Further, the step 2 further comprises the following steps:
step 2.1, performing nearest neighbor search on the source point cloud W and the target point cloud V after down-sampling according to the multi-scale descriptor to form seed matching, and sequencing the seed matching, and marking as (p)i,q1),…(pj,qn) Wherein p isi、pjRepresenting seed points in the source point cloud, qnRepresenting seed points in a target point cloud;
step 2.2, match (p) for each seedi,q1),…(pj,qn) Determining nearest neighbor search range1Calculating the minimum angular difference2Corresponding to the point, determining the distance difference between the two points3Forming n corresponding relation point cloud blocks M1,M2,…,Mn。
Further, the nearest neighbor search range is determined in the step 21The nearest neighbor searching range of the cloud center point p of the source point is determined to be alpha | | | p-piAnd determining the nearest neighbor search range of the midpoint q of the target point cloud as (beta ═ q-q)1||)∩(|β-α|＜1)。
Further, the minimum angle difference is calculated in the step 22The specific method of the corresponding point is as follows: for any point p in the neighbor search range in the source point cloud W, the descriptor and the point p are represented by a vector thetaiAngle between descriptors of (a):
θ＝(θ1,θ2,...,θL)T，
Figure BDA0002699473010000041
for any point q in the neighbor search range in the target point cloud V, the descriptor and the point q are represented by a vector psi1Angle between descriptors of (a):
ψ＝(ψ1,ψ2,...,ψL)T，
Figure BDA0002699473010000042
the difference in angle between point p and point q is expressed as:
Figure BDA0002699473010000043
the point p and the point q corresponding to the minimum Δ θ are obtained.
Further, the distance difference between the two points is judged in the step 23The specific method comprises the following steps: judging whether the point p and the point q satisfy the condition | | | Dp-Dq||＜3，3Two points of representationA threshold value of distance difference between based on the descriptor D, Dp、DqRepresenting the descriptors at point p and point q based on the feature values.
Further, the step 3 further comprises the following steps:
step 3.1 partitioning M of corresponding relation point cloud1,M2,…,MnThe point cloud in the source point cloud W is marked as PcThe point cloud set in the target point cloud V is denoted as Qc(ii) a At each iteration, from PcIn randomly selecting NsampleEach sampling point forms a point set Pc1And (3) obtaining a target point cloud Q by utilizing the corresponding relation in the corresponding relation point cloud blocks obtained in the step (2)cIs neutralized with Pc1Corresponding point set Qc1；
Step 3.2, calculating the matching potential of the point set, and removing outliers;
let A be Pc1，B＝Qc1，
Figure BDA0002699473010000051
Where H denotes the matching potential and is a symmetric matrix, a, b, c, d denote the indices of the points, ab and cd denote the indices of the rows and columns of H, AaAnd AcBelongs to a source point set A, BbAnd BdBelongs to a target point set B, and (A)a,Bb) And (A)c,Bd) Is the corresponding relation in the corresponding relation point cloud block obtained in the step 2, gamma is more than 0 and is a predefined threshold value, (A)a,Ac) Denotes the euclidean distance between two 3D point clouds, f ═ exp (- (a)a,Ac)-(Bb,Bd) |) is used to evaluate the difference in length of two segments,
solving for H, when AaAcAnd BbBdIs different by a smaller value gamma, continue to (A)a,Bb) And (A)c,Bd) The matching candidate is considered, otherwise, the corresponding relation is removed;
step 3.3 to find the optimal corresponding relation set
Figure BDA0002699473010000052
Finishing coarse registration;
let permutation matrix X be e {0,1}N×NWhen p isiE.g. A and qiBelongs to the corresponding relation set by the E B
Figure BDA0002699473010000053
The value of the element in the ith row and the j column in X is 1, otherwise, the value is 0;
the optimal solution comprises m pairs of corresponding relations, m < N, and X is obtained by stacking X columns1，
Figure BDA0002699473010000054
Problem satisfaction of searching optimal corresponding relation
Figure BDA0002699473010000055
Figure BDA00026994730100000512
The conversion is as follows:
Figure BDA0002699473010000058
order to
Figure BDA0002699473010000059
Formula (9) can be converted to:
Figure BDA00026994730100000510
when trace (Y) is m, satisfy
Figure BDA00026994730100000511
Namely convex optimization of the non-convex problem;
ensuring one point p in the source point cloud A based on the formula (10)iCan only be connected with zero or one point q in the target point cloudiMatch, but not more than one match; at the same timeTo meet the requirement of matching potential H in step 3.2, when A isaAcAnd BbBdAre different by more than a defined threshold value gamma, they are not allowed to match,
solving for X by SDP convex solver1X is divided by the linear distribution problem LP1Projecting the space X of the permutation matrix to obtain an optimized corresponding relation set
Figure BDA0002699473010000061
Step 3.4, the ICP is utilized to refine the data, the iterative process of the step 3.1, the step 3.2 and the step 3.3 is repeatedly carried out, the solution and the comparison are carried out, the highest optimal corresponding relation set in the final score is obtained, and the optimal transformation (R) is obtained*,t*) And performing registration.
Compared with the prior art, the invention has the following advantages:
according to the low-overlapping-rate three-dimensional point cloud registration algorithm, the characteristic values and the normal information of the point cloud are integrated to construct a multi-scale descriptor, corresponding-relation point cloud clustering partitioning is directly carried out according to the difference of the descriptor, the purpose of amplifying the overlapping area of the point cloud is achieved, and meanwhile, the high-quality corresponding relation between the points is kept. Meanwhile, the obtained corresponding relation is substituted into the original convex optimization point cloud registration algorithm without the corresponding relation, the search range of convex optimization registration is narrowed, a good initial value is provided for the search range, and the calculation amount is reduced. Therefore, the method has more advantageous registration accuracy and time efficiency for the registration of the three-dimensional point cloud with low overlapping rate.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a schematic diagram of the initial positions of Bunny000 and Bunny045 and the registration results;
fig. 3 is a schematic diagram of the initial positions and registration results of Bunny045 and Bunny 090;
FIG. 4 is a schematic diagram of initial positions of Dragon000 and Dragon024 and registration results;
FIG. 5 is a schematic diagram of initial positions of Dragon000 and Dragon024 and registration results;
FIG. 6 is a schematic diagram of initial positions of Happy048 and Happy096 and registration results;
fig. 7 is a schematic diagram of initial positions of Chair1 and Chair2 and registration results;
fig. 8 is a schematic diagram of the initial positions and registration results of Motobike1 and Motobike 2.
Detailed Description
Example 1
As shown in fig. 1, a three-dimensional point cloud registration method with low overlapping rate includes the following steps:
step 1, constructing a multi-scale descriptor based on curvature features and normal vectors;
step 1.1, for each query point P, at each neighborhood radius rlA covariance matrix is constructed,
Figure BDA0002699473010000071
wherein, the dimension L is 1.·, L; the neighborhood radius corresponding to the scale is denoted as r1＜r2＜…＜rL，SlRepresenting the distance from the query point P in the neighborhood radius rlSet S of points within rangel＝{Pi|||Pi-P||≤rl}；
Step 1.2, obtaining three eigenvalues lambda by using singular value decomposition algorithm SVD decomposition formula (1)l1≥λl2≥λl3And its corresponding feature vector nl1，nl2，nl3Feature vector n corresponding to the minimum feature valuel3I.e. the normal vector of the plane, and is marked as nl(ii) a Setting the directions of the normal vectors of the regions to be consistent, and performing negation processing on the normal vectors which do not point to the viewpoint direction to avoid the influence of the directions of the subsequent normal vectors on region blocking;
step 1.3, normalizing the characteristic value to obtain a vector dl，
Figure BDA0002699473010000072
Using difference of characteristic values Δ dl＝dl+1-dlRepresenting the variation of the point cloud patch, Δ d of L different neighborhood radii to be consideredlConnecting to construct a descriptor D based on the characteristic value;
Figure BDA0002699473010000073
merging L normal vectors n of different neighborhood radiilObtaining a descriptor N based on a normal;
N＝(n1,…,nL) (4)
and combining the descriptor D based on the characteristic value and the descriptor N based on the normal line to obtain the multi-scale descriptor (N, D) based on the characteristic value and the normal line.
Step 2, establishing the similarity degree between angle difference measurement areas based on the multi-scale descriptors, and clustering and partitioning;
step 2.1, performing nearest neighbor search on the source point cloud W and the target point cloud V after down-sampling according to the multi-scale descriptor to form seed matching, and sequencing the seed matching, and marking as (p)i,q1),…(pj,qn) Wherein p isi、pjRepresenting seed points in the source point cloud, qnRepresenting seed points in a target point cloud;
step 2.2, match (p) for each seedi,q1),…(pj,qn) Determining nearest neighbor search range1Calculating the minimum angular difference2Corresponding to the point, determining the distance difference between the two points3Forming n corresponding relation point cloud blocks M1,M2,…,Mn。
Further, the nearest neighbor search range is determined in the step 21The nearest neighbor searching range of the cloud center point p of the source point is determined to be alpha | | | p-piAnd determining the nearest neighbor search range of the midpoint q of the target point cloud as (beta ═ q-q)1||)∩(|β-α|＜1)。
Further, the minimum angle difference is calculated in the step 22The specific method of the corresponding point is as follows: for any point p in the neighbor search range in the source point cloud W, the descriptor and the point p are represented by a vector thetaiAngle between descriptors of (a):
θ＝(θ1,θ2,...,θL)T，
Figure BDA0002699473010000081
for any point q in the neighbor search range in the target point cloud V, the descriptor and the point q are represented by a vector psi1Angle between descriptors of (a):
ψ＝(ψ1,ψ2,...,ψL)T，
Figure BDA0002699473010000082
the difference in angle between point p and point q is expressed as:
Figure BDA0002699473010000091
the point p and the point q corresponding to the minimum Δ θ are obtained.
Further, the distance difference between the two points is judged in the step 23The specific method comprises the following steps: judging whether the point p and the point q satisfy the condition | | | Dp-Dq||＜3，3Threshold representing the difference in distance between two points based on a descriptor D, Dp、DqRepresenting the descriptors at point p and point q based on the feature values.
And 3, judging the matching potential in the corresponding relation clustering blocks based on the SDRSAC algorithm, removing outliers, and optimizing the corresponding relation to complete registration.
Step 3.1 partitioning M of corresponding relation point cloud1,M2,…,MnThe point cloud in the source point cloud W is marked as PcThe point cloud set in the target point cloud V is denoted as Qc(ii) a At each iteration, from PcIn randomly selecting NsampleEach sampling point forms a point set Pc1And (3) obtaining a target point cloud Q by utilizing the corresponding relation in the corresponding relation point cloud blocks obtained in the step (2)cIs neutralized with Pc1Corresponding point set Qc1；
Step 3.2, calculating the matching potential of the point set, and removing outliers;
let A be Pc1，B＝Qc1，
Figure BDA0002699473010000092
Where H denotes the matching potential and is a symmetric matrix, a, b, c, d denote the indices of the points, ab and cd denote the indices of the rows and columns of H, AaAnd AcBelongs to a source point set A, BbAnd BdBelongs to a target point set B, and (A)a,Bb) And (A)c,Bd) Is the corresponding relation in the corresponding relation point cloud block obtained in the step 2, gamma is more than 0 and is a predefined threshold value, (A)a,Ac) Denotes the euclidean distance between two 3D point clouds, f ═ exp (- (a)a,Ac)-(Bb,Bd) |) is used to evaluate the difference in length of two segments,
solving for H, when AaAcAnd BbBdIs different by a smaller value gamma, continue to (A)a,Bb) And (A)c,Bd) The matching candidate is considered, otherwise, the corresponding relation is removed;
step 3.3 to find the optimal corresponding relation set
Figure BDA0002699473010000093
Finishing coarse registration;
let permutation matrix X be e {0,1}N×NWhen p isiE.g. A and qiBelongs to the corresponding relation set by the E B
Figure BDA0002699473010000101
The value of the element in the ith row and the j column in X is 1, otherwise, the value is 0;
the optimal solution contains m pairs of correspondences, and m < N, stacking XIt is listed as X1，
Figure BDA0002699473010000102
Problem satisfaction of searching optimal corresponding relation
Figure BDA0002699473010000103
Figure BDA00026994730100001011
The conversion is as follows:
Figure BDA0002699473010000106
order to
Figure BDA0002699473010000107
Formula (9) can be converted to:
Figure BDA0002699473010000108
when trace (Y) is m, satisfy
Figure BDA0002699473010000109
Namely convex optimization of the non-convex problem;
ensuring one point p in the source point cloud A based on the formula (10)iCan only be connected with zero or one point q in the target point cloudiMatch, but not more than one match; at the same time, to meet the requirement of matching potential H in step 3.2, when A isaAcAnd BbBdAre different by more than a defined threshold value gamma, they are not allowed to match,
solving for X by SDP convex solver1X is divided by the linear distribution problem LP1Projecting the space X of the permutation matrix to obtain an optimized corresponding relation set
Figure BDA00026994730100001010
Step 3.4, the ICP is utilized to refine the data, the iterative process of the step 3.1, the step 3.2 and the step 3.3 is repeatedly carried out, the solution and the comparison are carried out, the highest optimal corresponding relation set in the final score is obtained, and the optimal transformation (R) is obtained*,t*) And performing registration.
Example 2
The data is derived from a three-dimensional point cloud model published by Stanford university and entity three-dimensional scanning data of geoentryhub website. The environment is a 64-bit operating system of Windows10, MATLAB 2018b development platform.
When the overlapping rate of the source point cloud and the target point cloud is lower than 60%, the overlapping degree of the two pieces of point clouds is low, and when the overlapping rate of the source point cloud and the target point cloud is higher than 60%, the overlapping degree is high. In order to prove the effectiveness of the method provided by the invention, the method is divided into two cases of high overlapping rate and low overlapping rate.
For the point cloud model, the overlapping rate of point cloud data acquired under different visual angles is reflected. And selecting representative groups of data for result display. Point cloud data with high overlapping rate: the two groups of point cloud data of Bunny000, Bunny045, Dragon000 and Dragon024 have obvious overlap, and the overlap rate is about 75%. Point cloud data with low overlapping rate: the overlap rate of the two groups of point cloud data of Bunny045, Bunny090, Dragon000 and Dragon048 is low, the overlap rate is about 50%, and the overlap rate of the two groups of data of Happy48 and Happy96 is about 40%. In addition, in order to better embody the universality of the method of the embodiment, two groups of entity three-dimensional scanning data obtained from the geometrihub website are purposely selected, which are respectively Chair1, Chair2, Motobike1 and Motobike2, and the overlapping rate is about 40%.
Point cloud registration evaluation standard
LCP (Large Common Point) maximum Common point set is used as an evaluation index of point cloud registration accuracy. LCP is related to rigid body transformation T, and represents that after rigid body transformation, points in source point cloud can find a point set with a distance within a certain fault tolerance range from the points in target point cloud. That is, LCP ═ m/n, where n represents the number of points in the target point cloud and m represents the number of points that can be found in the target point cloud that correspond to the source point cloud points. The higher the LCP, the higher the degree of optimal alignment of the source point cloud and the target point cloud, and the higher the accuracy of the registration.
Point cloud registration result analysis with high overlapping rate
For the two sets of point cloud data Bunny000, Bunny045, Dragon000 and Dragon024 with higher overlapping rate, their registration results are shown in fig. 2 and fig. 3, respectively. Figure 2Bunny000 and Bunny045 registration results. (a) An initial position; (b) registering by using a Lu J [2019] method; (c) registering by utilizing a Lei H [2017] method; (d) registering by using the method of the invention; fig. 3Dragon000 registers the results with Dragon 024. (a) An initial position; (b) registering by using a Lu J [2019] method; (c) registering by utilizing a Lei H [2017] method; (d) the registration by using the method of the invention can be seen visually from fig. 2 and fig. 3, and compared with a latest point cloud registration algorithm which is provided by army and the like in 2019 and is based on key point fusion Super4PCS and ICP, and a latest global point cloud registration algorithm which is provided by Huangan Lei and the like in 2017 and is based on quick descriptors and corresponding propagation, the registration result obtained by the method of the invention has better fit degree and better effect of two colors.
In order to evaluate the accuracy of the registration method of the present invention more accurately, LCP evaluation criteria were used for calculation, and the running time of the registration algorithm was recorded, compared with the classic Go-ICP (Global optimal ICP), the Super4PCS algorithm, and the latest fusion registration algorithm. The two fusion algorithms are respectively a point cloud registration algorithm which is provided by army et al in 2019 and is based on key point fusion Super4PCS and ICP, and a global point cloud registration algorithm which is provided by Huangan Lei et al in 2017 and is based on a quick descriptor and corresponding propagation. The two dimensions are compared in terms of registration accuracy LCP and registration time, as shown in table 1.
TABLE 1 comparison of point cloud registration results with high overlap ratio
Table 1 Comparison of point cloud registration results with high overlap rate
Figure BDA0002699473010000121
The higher the LCP, the higher the accuracy of the point cloud registration. As can be seen from Table 1, for two groups of point cloud data with higher overlapping degree, the precision value of the method is higher than that of the other four methods, and the registration time is faster than that of the three methods of Go-ICP, Super4PCS and Lei H [2017 ]. For the set of data of Bunny000 and Bunny045, the running time of the registration method of Lu J [2019] is more advantageous, because the speed of extracting the feature points by the Lu J [2019] method is much faster than that of the multi-scale descriptor of the invention, and the extraction of the feature points shortens the retrieval time of the subsequent Super4PCS algorithm.
Point cloud registration result analysis with low overlapping rate
Fig. 4, 5, and 6 show the results of registering three sets of stanford common point cloud data with low overlapping rates.
Fig. 4Bunny045 and Bunny090 registered the results. (a) An initial position; (b) registering by using a Lu J [2019] method; (c) registering by utilizing a Lei H [2017] method; (d) registering by using the method of the invention;
fig. 5Dragon000 registers the results with Dragon 048. (a) An initial position; (b) registering by using a Lu J [2019] method; (c) registering by utilizing a Lei H [2017] method; (d) registering by using the method of the invention;
fig. 6Happy048 and Happy096 registration results. (a) An initial position; (b) registering by using a Lu J [2019] method; (c) registering by utilizing a Lei H [2017] method; (d) registering by using the method of the invention;
it can be seen from the figure that the registration result obtained by the method of the invention has the lowest dislocation degree of the two point clouds and the best registration effect.
The evaluation criteria calculated LCP and recorded the run time of the registration algorithm, compared to the latest Lu J [2019], Lei H [2017] and the classical registration algorithms Go-ICP and Super4PCS, the comparison results are shown in Table 2. As can be seen from Table 2, for three groups of point cloud data with lower overlapping degree, the registration accuracy of the method is higher than that of the other four methods, and compared with Table 1, the method has a higher registration accuracy advantage in the aspect of point cloud data registration with low overlapping rate than that of the other four methods. For point cloud data with low overlapping rate, the method of the invention has higher running speed than three methods of Go-ICP, Super4PCS and Lu J [2019], and has slightly lower running speed than the Lei H [2017 ].
TABLE 2 comparison of point cloud registration results with low overlap
Table 2 Comparison of point cloud registration results with low overlap rate
Figure BDA0002699473010000131
Figure BDA0002699473010000141
From the table 1 and the table 2, the method can effectively improve the precision and the time efficiency of the three-dimensional point cloud registration, and particularly shows more precision advantages compared with other four methods in the aspect of low overlapping rate three-dimensional point cloud registration. The Go-ICP and Super4PCS algorithms are based on a featureless global point cloud registration algorithm, and the calculation cost and time for low-overlapping-rate point cloud registration are high. The method effectively reduces the registration search range of the graph matching problem, saves the calculated amount, and has higher registration effect than the latest two methods Lu J [2019] Lei H [2017] which are applicable to low overlapping rate. In addition, in order to better show the universality of the algorithm provided by the invention, the registration verification is carried out on two groups of actual three-dimensional scanning data obtained from the geometrihub website. The initial overlap of these two sets of data was about 40%. The results are shown in FIGS. 7 and 8. Fig. 7, Chair1, registers the result with Chair 2. (a) An initial point cloud 1; (b) an initial point cloud 2; (c) registering with the method herein; fig. 8Motobike1 registers the results with Motobike 2. (a) An initial point cloud 1; (b) an initial point cloud 2; (c) registering with the method herein; wherein, the images (a) and (b) are respectively initial point cloud data obtained by scanning from two different visual angles, and the image (c) is a point cloud registration result obtained by using the method of the invention. It can be seen from the figure that it can be well registered with the method of the present invention. The registration performance of the point cloud data is shown in table 3.
TABLE 3 actual three-dimensional scan data registration Performance
Table 3 Registration performance of real 3D scan data
Figure BDA0002699473010000142
In summary, the method is better in feasibility and has universality on point cloud registration with lower initial overlapping rate in comprehensive consideration of registration accuracy and registration time.
The invention provides a novel three-dimensional point cloud registration algorithm aiming at low overlapping rate. The characteristic values of the point clouds and the normal information are integrated to construct a multi-scale descriptor, corresponding relation point cloud clustering partitioning is directly carried out according to the difference of the descriptor, the purpose of amplifying the overlapping area of the point clouds is achieved, and meanwhile, the high-quality corresponding relation between the points is kept. Meanwhile, the obtained corresponding relation is substituted into the original convex optimization point cloud registration algorithm without the corresponding relation, the search range of convex optimization registration is narrowed, a good initial value is provided for the search range, and the calculation amount is reduced. The result shows that the algorithm can effectively improve the precision and time efficiency of three-dimensional point cloud registration, particularly has more obvious precision advantage in point cloud data registration with lower initial overlapping rate, and has higher registration effect compared with the latest two methods suitable for low overlapping rate; in the aspect of registration efficiency, the method has higher efficiency for point cloud registration with low overlapping rate than a point cloud registration algorithm based on key point fusion Super4PCS and ICP, and is an effective supplement for a global point cloud registration algorithm based on a fast descriptor and corresponding propagation. Registration of the actual object point cloud model with lower overlap ratio and more complex surface will be studied subsequently.
Those skilled in the art will appreciate that the invention may be practiced without these specific details. Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (7)

1. A three-dimensional point cloud registration method with low overlapping rate is characterized in that: the method comprises the following steps:
step 1, constructing a multi-scale descriptor based on curvature features and normal vectors;
step 2, establishing the similarity degree between angle difference measurement areas based on the multi-scale descriptors, and clustering and partitioning the corresponding relations;
and 3, judging the matching potential in the corresponding relation clustering blocks based on the SDRSAC algorithm, removing outliers, and optimizing the corresponding relation to complete registration.
2. The low-overlapping-rate three-dimensional point cloud registration method according to claim 1, characterized in that: the step 1 further comprises the following steps:
step 1.1, for each query point P, at each neighborhood radius rlA covariance matrix is constructed,
Figure FDA0002699471000000011
wherein, the dimension L is 1.·, L; the neighborhood radius corresponding to the scale is denoted as r1＜r2＜…＜rL，SlRepresenting the distance from the query point P in the neighborhood radius rlSet S of points within rangel＝{Pi|||Pi-P||≤rl}；
Step 1.2, obtaining three eigenvalues lambda by using singular value decomposition algorithm SVD decomposition formula (1)l1≥λl2≥λl3And its corresponding feature vector nl1，nl2，nl3Feature vector n corresponding to the minimum feature valuel3I.e. the normal vector of the plane, and is marked as nl(ii) a The directions of the normal vectors of the regions are set to be consistent, and the normal vectors which do not point to the viewpoint direction are subjected to negation processing, so that the situation that the normal vectors do not point to the viewpoint directionPartitioning the direction influence area of the subsequent normal vector;
step 1.3, normalizing the characteristic value to obtain a vector dl，
Figure FDA0002699471000000012
Using difference of characteristic values Δ dl＝dl+1-dlRepresenting the variation of the point cloud patch, Δ d of L different neighborhood radii to be consideredlConnecting to construct a descriptor D based on the characteristic value;
Figure FDA0002699471000000021
merging L normal vectors n of different neighborhood radiilObtaining a descriptor N based on a normal;
N＝(n1,…,nL) (4)
and combining the descriptor D based on the characteristic value and the descriptor N based on the normal line to obtain the multi-scale descriptor (N, D) based on the characteristic value and the normal line.
3. The low-overlapping-rate three-dimensional point cloud registration method according to claim 2, wherein: the step 2 further comprises the following steps:
step 2.1, performing nearest neighbor search on the source point cloud W and the target point cloud V after down-sampling according to the multi-scale descriptor to form seed matching, and sequencing the seed matching, and marking as (p)i,q1),…(pj,qn) Wherein p isi、pjRepresenting seed points in the source point cloud, qnRepresenting seed points in a target point cloud;
step 2.2, match (p) for each seedi,q1),…(pj,qn) Determining nearest neighbor search range1Calculating the minimum angular difference2Corresponding to the point, determining the distance difference between the two points3Forming n number ofCorrespondence point cloud partitioning M1,M2,…,Mn。
4. The low-overlap three-dimensional point cloud registration method of claim 3, wherein: determining the nearest neighbor search range in the step 21The nearest neighbor searching range of the cloud center point p of the source point is determined to be alpha | | | p-piAnd determining the nearest neighbor search range of the midpoint q of the target point cloud as (beta ═ q-q)1||)∩(|β-α|＜1)。
5. The low-overlapping-rate three-dimensional point cloud registration method according to claim 4, wherein: calculating the minimum angle difference in the step 22The specific method of the corresponding point is as follows: for any point p in the neighbor search range in the source point cloud W, the descriptor and the point p are represented by a vector thetaiAngle between descriptors of (a):
Figure FDA0002699471000000022
for any point q in the neighbor search range in the target point cloud V, the descriptor and the point q are represented by a vector psi1Angle between descriptors of (a):
Figure FDA0002699471000000031
the difference in angle between point p and point q is expressed as:
Figure FDA0002699471000000032
the point p and the point q corresponding to the minimum Δ θ are obtained.
6. The low-overlapping-rate three-dimensional point cloud registration method according to claim 5, wherein: two points are judged in the step 2Difference in distance of3The specific method comprises the following steps: judging whether the point p and the point q satisfy the condition | | | Dp-Dq||＜3，3Threshold representing the difference in distance between two points based on a descriptor D, Dp、DqRepresenting the descriptors at point p and point q based on the feature values.
7. The low-overlap three-dimensional point cloud registration method of claim 6, wherein: the step 3 further comprises the following steps:
step 3.1 partitioning M of corresponding relation point cloud1,M2,…,MnThe point cloud in the source point cloud W is marked as PcThe point cloud set in the target point cloud V is denoted as Qc(ii) a At each iteration, from PcIn randomly selecting NsampleEach sampling point forms a point set Pc1And (3) obtaining a target point cloud Q by utilizing the corresponding relation in the corresponding relation point cloud blocks obtained in the step (2)cIs neutralized with Pc1Corresponding point set Qc1；
Step 3.2, calculating the matching potential of the point set, and removing outliers;
let A be Pc1，B＝Qc1，
Figure FDA0002699471000000033
Where H denotes the matching potential and is a symmetric matrix, a, b, c, d denote the indices of the points, ab and cd denote the indices of the rows and columns of H, AaAnd AcBelongs to a source point set A, BbAnd BdBelongs to a target point set B, and (A)a,Bb) And (A)c,Bd) Is the corresponding relation in the corresponding relation point cloud block obtained in the step 2, gamma is more than 0 and is a predefined threshold value, (A)a,Ac) Denotes the euclidean distance between two 3D point clouds, f ═ exp (- (a)a,Ac)-(Bb,Bd) |) is used to evaluate the difference in length of two segments,
solving for H, when AaAcAnd BbBdIs different by a smaller value gamma, continue to (A)a,Bb) And (A)c,Bd) The matching candidate is considered, otherwise, the corresponding relation is removed;
step 3.3 to find the optimal corresponding relation set
Figure FDA0002699471000000041
Finishing coarse registration;
let permutation matrix X be e {0,1}N×NWhen p isiE.g. A and qiBelongs to the corresponding relation set by the E B
Figure FDA0002699471000000042
The value of the element in the ith row and the j column in X is 1, otherwise, the value is 0;
the optimal solution comprises m pairs of corresponding relations, m < N, and X is obtained by stacking X columns1，
Figure FDA0002699471000000043
Problem satisfaction of searching optimal corresponding relation
Figure FDA0002699471000000044
Figure FDA0002699471000000045
Figure FDA0002699471000000046
The conversion is as follows:
Figure FDA0002699471000000047
order to
Figure FDA0002699471000000048
Formula (9) can be converted to:
Figure FDA0002699471000000049
when trace (Y) is m, satisfy
Figure FDA00026994710000000410
Namely convex optimization of the non-convex problem;
ensuring one point p in the source point cloud A based on the formula (10)iCan only be connected with zero or one point q in the target point cloudiMatch, but not more than one match; at the same time, to meet the requirement of matching potential H in step 3.2, when A isaAcAnd BbBdAre different by more than a defined threshold value gamma, they are not allowed to match,
solving for X by SDP convex solver1X is divided by the linear distribution problem LP1Projecting the space X of the permutation matrix to obtain an optimized corresponding relation set
Figure FDA00026994710000000411
Step 3.4, the ICP is utilized to refine the data, the iterative process of the step 3.1, the step 3.2 and the step 3.3 is repeatedly carried out, the solution and the comparison are carried out, the highest optimal corresponding relation set in the final score is obtained, and the optimal transformation (R) is obtained*,t*) And performing registration.
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