CN113902779B - Point cloud registration method based on tensor voting method - Google Patents
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Abstract
The invention provides a point cloud registration method based on a tensor voting method, which belongs to the field of machine vision target gesture recognition and comprises the following steps of: acquiring two groups of point cloud data of a target object; filtering noise from the two sets of point cloud data; tensor encoding is carried out on the two groups of point cloud data after pretreatment; tensor voting is carried out on the two groups of encoded point cloud data; SVD decomposition is carried out on the tensor matrix after voting is completed; comparing the characteristic values obtained by processing the two groups of point clouds, creating a similarity function fatter, and taking a group of points with the minimum fatter value as a tensor registration result; and calculating the mathematical relationship of the two groups of point cloud feature matrixes to obtain a rotation matrix and a translation vector. The invention solves the problems of low efficiency, long time consumption and large error in the existing research method.
Description
Technical Field
The invention relates to the field of machine vision target gesture recognition, in particular to a point cloud registration method based on a tensor voting method.
Background
With the continuous development of machine vision technology and three-dimensional stereoscopic operation technology, researchers are exploring a more advanced technology to make the computer more suitable for the working mode of human brain. Registration is one of the important research topics in the study of machine vision. The application range of the registration technology is very wide, and a high-efficiency accurate registration technology is needed to replace people in various industries, so that the purpose of freeing labor force is achieved.
In the field of machine vision, the registration of the point sets adopts an automatic registration mode, and the offset between the two point sets is calculated by a computer through a certain algorithm or statistical rule, so that the effect of automatic registration of the two point sets is achieved, and the fact is that the data point sets measured in different coordinate systems are subjected to coordinate system transformation to obtain an integral data model.
In 1981, there is a method based on a random sampling consistent algorithm framework, which is a global registration algorithm, the method utilizes overlapping areas among point cloud data to determine corresponding points, solves rigid transformation relations among point clouds to be matched according to the corresponding points, repeatedly votes candidate bases, and finally determines the candidate base with highest probability as an optimal solution, but the algorithm has low stability and is easy to match with wrong corresponding points. In 2009, RUSU et al proposed computing geometric features of feature points by three-dimensional shape descriptors, identifying pairs of points with most similar features from different point clouds as corresponding points, solving transformation parameters, and such algorithms are susceptible to noise points. In 2008, AIGER et al propose a four-point congruent set algorithm 4PCS, the theoretical basis of which is affine invariance of the coplanar 4-point pairs, and by using a wide area base, the searching complexity is reduced, and the algorithm has better robustness to noise and outliers. In 2016, SUN et al propose a local shape descriptor-region curvature map with strong discriminant, search matching strategies based on RCM subregions are adopted to search three-dimensional corresponding points, and rough registration is realized by utilizing geometric consistency, so that the method has higher registration efficiency. In 2019 Zhao Mingfu et al proposed the registration of point clouds with widely different initial positions by fusion sampling consistency and ICP algorithm.
The above work has achieved some achievement to a different extent, but has some disadvantages:
1. The algorithm itself has low calculation efficiency;
2. the method for realizing registration by utilizing the geometric features is easily influenced by noise, and the accuracy of registration is influenced;
3. The ICP algorithm cannot solve the problem of partially overlapped point cloud registration, and is easy to fall into local optimization; 4. the global registration method is easy to match with wrong corresponding points and has low stability.
Disclosure of Invention
The invention aims to solve the technical problems of low efficiency, long time consumption and large error in the existing research method by providing a point cloud registration method based on a tensor voting method.
In order to solve the technical problems, the invention adopts the following technical scheme:
A point cloud registration method based on a tensor voting method comprises the following steps:
S1, acquiring two groups of point cloud data of a target object, wherein one group is used as an original point cloud, and the other group is used as a target point cloud;
s2, preprocessing two groups of point cloud data, and filtering noise by adopting a radius filtering method;
S3, performing tensor coding on the two groups of preprocessed point cloud data, and respectively representing the two groups of point cloud data of the input data as a series of sparse tensors according to known position information in the two groups of point cloud data, wherein the series of sparse tensors are represented by a positive definite symmetric matrix;
S4, tensor voting is carried out on the two groups of encoded point cloud data;
s5, SVD decomposition is carried out on the tensor matrix after voting is completed, and feature mathematical representation of two groups of point clouds is obtained;
S6, comparing the characteristic values obtained by processing the two groups of point clouds, creating a similarity function delta, and taking a group of points with the minimum delta value as a tensor registration result;
And S7, calculating mathematical relations of the two groups of point cloud feature matrixes according to the feature mathematical representations of the two groups of point clouds obtained in the S5, and obtaining a rotation matrix and a translation vector.
The technical scheme of the invention is further improved as follows: in S1, the two groups of point cloud data are obtained by rigidly transforming the target object, and the rigidly transforming ensures that the distance between the points is unchanged and the included angle between the lines is unchanged.
The technical scheme of the invention is further improved as follows: in S1, the two sets of acquisition tools of point cloud data include a monocular imaging system and a binocular imaging system, the monocular imaging system including a depth camera.
The technical scheme of the invention is further improved as follows: s2, when the number of points around a point is less than m, the point is considered as an outlier, and noise is included in the data set, and the point is filtered; m is an integer between 4 and 10.
The technical scheme of the invention is further improved as follows: s3, the known position information comprises tangential direction information and normal direction information; when the point cloud has no tangential direction information, the point cloud is encoded into a spherical tensor; when the point cloud only has tangential direction information, the point cloud is encoded into a plate tensor; when the point cloud has normal information, the point cloud is encoded into a rod tensor.
The technical scheme of the invention is further improved as follows: in S4, in the tensor voting stage, sparse voting and dense voting are performed, respectively.
The technical scheme of the invention is further improved as follows: s5, SVD decomposition is carried out on the tensor matrix, and the method specifically comprises the following steps:
In a three-dimensional space, decomposing the components into a rod tensor component, a plate tensor component and a sphere tensor component, and obtaining each tensor component and significance thereof;
The decomposition results: eigenvalue lambda 1、λ2、λ3 of original point cloud tensor matrix, eigenvector e 1、e2、e3 of tensor matrix; eigenvalue λ '1、λ′2、λ′3 of the target point cloud tensor matrix, eigenvector e' 1、e′2、e′3 of the target point cloud tensor matrix.
The technical scheme of the invention is further improved as follows: in S6, the create similarity function Δ is:
Δ＝(λ1-λ′1)2+(λ2-λ′2)2+(λ3-λ′3)2.
The technical scheme of the invention is further improved as follows: s7, obtaining a rotation matrix and a translation vector, which specifically comprises the following steps:
On the basis of obtaining the coordinates of two groups of similar points, calculating the mathematical relationship between a feature matrix E formed by E 1、e2、e3 and a feature matrix E 'formed by E' 1、e′2、e′3 to obtain a rotation matrix R and a translation vector T; the mathematical coordinate relationship of the set of corresponding point pairs is expressed as the following equation:
E＝R×E′+T
E, E' are tensor matrices composed of feature vectors of a group of corresponding points of the target point cloud matrix and the original point cloud matrix respectively;
converting E and E' into the form of homogeneous matrices by transposition:
E＝[e1 e2 e3 1]T,E′＝[e′1 e′2 e′3 1]T
the deduction process comprises the following steps:
let the registration matrix
From e=ae':
As a result of:
Let the registration vector
Constraint vector
ThenTherefore, 10-dimensional tensor voting is needed in the registration process, namely, the dimensionality of the tensor matrix is 10;
and EE' -1＝AE′E′-1;
registration matrix a=ee' -1.
By adopting the technical scheme, the invention has the following technical progress:
1. the invention adopts a tensor coding mode to store the effective position information of the point cloud data in a tensor matrix, thereby facilitating the subsequent calculation processing;
2. According to the method, abstract features are materialized through matrix singular value decomposition, so that the digital expression of the features of the point cloud is realized, and the feature similarity can be measured through function calculation;
3. According to the method, the size of the similarity can be calculated by setting a reasonable function, the problem of difficulty in measuring the similarity of two groups of point cloud data is solved, and two groups of corresponding points with the highest similarity are selected, so that a point cloud registration result is obtained; compared with the ICP method, the registration method ensures the registration efficiency, has better robustness on noise points, and can also avoid the algorithm from being trapped into local optimization.
Drawings
FIG. 1 is a flow chart of one way of solving the point cloud registration problem using tensor voting; FIG. 2 is a schematic diagram of a voting domain calculation method
FIG. 3 is a graph saliency map of tensor voting;
fig. 4 is a visual result of voting for one rod tensor in 3D space.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and examples:
as shown in fig. 1, a point cloud registration method based on a tensor voting method specifically includes the following steps:
S1, acquiring two groups of point cloud data of a target object, wherein one group is used as an original point cloud, and the other group is used as a target point cloud.
The two groups of point clouds are obtained by rigidly transforming the target object, namely, the shape of the target object is not transformed, and only rotation transformation and translation are carried out in European space. The rigid transformation ensures that the distance between the points is constant and the angle between the lines is constant. The point cloud data can be acquired by a depth camera, and can also be acquired by other monocular imaging systems or binocular imaging systems, and common depth cameras are Kinect and TOF cameras.
S2, preprocessing the two groups of point cloud data, and filtering noise by adopting a radius filtering method.
Specifically, a denoising algorithm is adopted for each point in the space three-dimensional point set, the point number n in the adjacent space with r as the radius is calculated, radius filtering is adopted in the denoising method, and when the point number around a certain point is smaller than m, the point is considered to be an outlier, and the outlier is removed.
Wherein m is an integer of 4 to 10, and m in this embodiment has a value of 4.
S3, performing tensor coding on the preprocessed two groups of point cloud data, and respectively representing the two groups of point cloud data of the input data as a series of sparse tensors according to known position information in the two groups of point cloud data, wherein the series of sparse tensors are represented by a positive definite symmetric matrix.
Specifically, the encoding process is to convert position information, normal information and the like of the point cloud into a matrix form, and according to the known position information, the point cloud of the input data is expressed as a series of sparse tensors and is expressed by a positive definite symmetric matrix; when the input points have no directional information, the points are encoded as ball tensors; if there is only tangential direction, it is encoded as a sheet tensor; if there is information about the normal of the point, it is encoded as a rod tensor.
S4, tensor voting is carried out on the encoded point cloud data, and sparse voting and dense voting are respectively carried out in the tensor voting stage.
The voting mechanism is the same, and the difference is that: the sparse voting is to vote on the positions where the data points exist in the original data set, and ball voting is carried out by regarding all the points as isolated points so as to improve the accuracy of tensor information; the dense voting is to vote on regular grid points in the distribution space of the data set to form a dense tensor field, which serves the subsequent structural feature reasoning;
Specifically, the voting field is calculated first, and the voting field can be regarded as a preferred direction of transmitting each vector to its neighborhood, as shown in fig. 2, according to the continuum in Gestalt theory, the best line between two points is considered as an arc, and the voting process has proximity, and the tensor effect of being close is larger, and the tensor effect of being far is smaller.
The relationship between the distance d between the voted points P and Q and the diameter l of the circular arc, and the central angle θ is:
The curvature of the arc is:
the arc length between the connection points P and Q is:
The size of the voted spot for P spots and surrounding spots is represented by the intensity, the decay function of the voting intensity being:
Where F is the voting strength of the voting domain, σ is the voting scale parameter, s is the arc length, k is the curvature, c is a function of the voting scale σ, and the voting strength is affected by adjusting the distance and curvature. The longer the path, the farther apart the two points are, the less intense the vote.
When voting, the voted point is the center of the voting domain, after the voting is finished, the position information obtained by the voted point through other points is integrated, the orientation information of the voted point can be expressed in a vector form, and after the voting is finished, the number and the size of the votes of the points are accumulated to form a new tensor T.
Wherein: t ij＝ei·T·ej
T＝{tij ei ej}
Wherein T is a tensor matrix obtained after voting, T ij is a numerical value of the j-th column of the i-th row in the tensor matrix, e i is a unit vector of the i-th row, and e j is a unit vector of the j-th row.
S5, performing singular value decomposition, SVD (singular value decomposition) for short, on the tensor matrix after voting is completed, and performing feature mathematical representation on the obtained two groups of point clouds.
In the tensor SVD decomposition stage, the decomposition and the coding are inverse processes.
Specifically, SVD decomposition is carried out on each tensor matrix after voting, and in a three-dimensional space, the tensor matrix is decomposed into a rod tensor component, a plate tensor component and a sphere tensor component, so that each tensor component and the significance thereof are obtained, as shown in fig. 3, and then structural reasoning is carried out according to the tensor significance;
rod tensors were defined as T S, plate tensors as T p, and sphere tensors as T B. Defining the tensor T as:
T＝TS+TP+TB
Wherein:
Wherein λ 1、λ2、λ3 is a eigenvalue of the original point cloud tensor matrix, e 1、e2、e3 is a eigenvector of the tensor matrix, λ '1、λ′2、λ′3 is a eigenvalue of the target point cloud tensor matrix, and e' 1、e′2、e′3 is a eigenvector of the target point cloud tensor matrix. After SVD decomposition, λ 1、λ2、λ3 and λ' 1、λ′2、λ′3 are ordered from small to large. Further, according to the comparison of the magnitudes of the decomposed eigenvalues, namely the comparison of the magnitudes of the coefficients of the tensors of various types in the formula, the component with the largest coefficient is the most obvious characteristic of the point: the plate tensor significantly describes the point as being on a plane, the plate tensor significantly describes the point as being on a straight line, and the ball tensor significantly describes the point as being an isolated point.
As shown in fig. 4, when λ1 and λ2 are almost 1, λ3=0, the rod tensor is significant, indicating that the tensor normal direction is determined, and the tensor is estimated as a curve of e 1; if λ1 and λ2 and λ3 are almost equal to 1, then it is explained that the sphere tensor is the dominant component, with no orientation preference. This process represents the point cloud data by tensors.
And S6, comparing the characteristic values obtained by processing the two groups of point clouds, creating a similarity function delta, and taking a group of points with the minimum delta value as a tensor registration result.
Specifically, this step aims at obtaining two portions with the highest feature similarity in the two point sets as a result of registration by comparing the feature values after tensor decomposition. After tensor decomposition, the features of the points can be represented digitally, and the feature system at each input point is typically used to calculate different salient features: the intersection is characterized by lambda 3, the curve is characterized by lambda 2-λ3, and the plane is characterized by lambda 1-λ2. The essence of finding the point with the highest feature similarity is to find the point pair with the least difference in feature values of the tensor matrix. To achieve this, a similarity function Δ is created, defined as follows:
Δ＝(λ1-λ′1)2+(λ2-λ′2)2+(λ3-λ′3)2
When the value of the similarity function Δ is smaller, it is explained that the feature values of the two points are closer, that is, the feature similarity of the two points is higher.
And S7, calculating mathematical relations of the two groups of point cloud feature matrixes according to the feature mathematical representations of the two groups of point clouds obtained in the S5, and obtaining a rotation matrix and a translation vector.
Specifically, on the basis of obtaining the coordinates of two groups of similar points, a rotation matrix R and a translation vector T are obtained by calculating the mathematical relationship between a feature matrix E composed of E 1、e2、e3 and a feature matrix E 'composed of E' 1、e′2、e′3. The mathematical coordinate relationship of the set of corresponding point pairs is expressed as the following equation:
E＝R×E′+T
wherein E, E' are tensor matrices composed of eigenvectors of a set of corresponding points of the target point cloud matrix and the original point cloud matrix, respectively.
Converting E and E' into the form of homogeneous matrices by transposition:
E＝[e1 e2 e3 1]T,E′＝[e′1 e′2 e′3 1]T
the deduction process comprises the following steps:
let the registration matrix
From e=ae':
As a result of:
Let the registration vector
Constraint vector
ThenTherefore, 10-dimensional tensor voting is needed in the registration process, namely, the dimensionality of the tensor matrix is 10;
and EE' -1＝AE′E′-1;
registration matrix a=ee' -1.
In summary, the invention adopts a tensor coding mode to store the effective position information of the point cloud data in a tensor matrix, thereby facilitating the subsequent calculation processing; the abstract features are materialized through matrix singular value decomposition, so that the digital expression of the features of the point cloud is realized, and the feature similarity is measured through function calculation; by setting a reasonable function, the similarity can be calculated, the difficulty in measuring the similarity of two groups of point cloud data is solved, and two groups of corresponding points with the highest similarity are selected, so that a point cloud registration result is obtained; compared with the ICP method, the registration method ensures the registration efficiency, has better robustness on noise points, and can also avoid the algorithm from being trapped into local optimization.
Claims (9)
1. A point cloud registration method based on a tensor voting method is characterized by comprising the following steps of: the method comprises the following steps:
S1, acquiring two groups of point cloud data of a target object, wherein one group is used as an original point cloud, and the other group is used as a target point cloud;
s2, preprocessing two groups of point cloud data, and filtering noise by adopting a radius filtering method;
S3, performing tensor coding on the two groups of preprocessed point cloud data, and respectively representing the two groups of point cloud data of the input data as a series of sparse tensors according to known position information in the two groups of point cloud data, wherein the series of sparse tensors are represented by a positive definite symmetric matrix;
S4, tensor voting is carried out on the two groups of encoded point cloud data;
s5, SVD decomposition is carried out on the tensor matrix after voting is completed, and feature mathematical representation of two groups of point clouds is obtained;
S6, comparing the characteristic values obtained by processing the two groups of point clouds, creating a similarity function delta, and taking a group of points with the minimum delta value as a tensor registration result;
And S7, calculating mathematical relations of the two groups of point cloud feature matrixes according to the feature mathematical representations of the two groups of point clouds obtained in the S5, and obtaining a rotation matrix and a translation vector.
2. The point cloud registration method based on the tensor voting method according to claim 1, wherein: in S1, the two groups of point cloud data are obtained by rigidly transforming the target object, and the rigidly transforming ensures that the distance between the points is unchanged and the included angle between the lines is unchanged.
3. The point cloud registration method based on the tensor voting method according to claim 1, wherein: in S1, the two sets of acquisition tools of point cloud data include a monocular imaging system and a binocular imaging system, the monocular imaging system including a depth camera.
4. The point cloud registration method based on the tensor voting method according to claim 1, wherein: s2, when the number of points around a point is less than m, the point is considered as an outlier, and noise is included in the data set, and the point is filtered; m is an integer between 4 and 10.
5. The point cloud registration method based on the tensor voting method according to claim 1, wherein: s3, the known position information comprises tangential direction information and normal direction information; when the point cloud has no tangential direction information, the point cloud is encoded into a spherical tensor; when the point cloud only has tangential direction information, the point cloud is encoded into a plate tensor; when the point cloud has normal information, the point cloud is encoded into a rod tensor.
6. The point cloud registration method based on the tensor voting method according to claim 1, wherein: in S4, in the tensor voting stage, sparse voting and dense voting are performed, respectively.
7. The point cloud registration method based on the tensor voting method according to claim 1, wherein: s5, SVD decomposition is carried out on the tensor matrix, and the method specifically comprises the following steps:
In a three-dimensional space, decomposing the components into a rod tensor component, a plate tensor component and a sphere tensor component, and obtaining each tensor component and significance thereof;
The decomposition results: eigenvalue lambda 1、λ2、λ3 of original point cloud tensor matrix, eigenvector e 1、e2、e3 of tensor matrix; eigenvalue λ 'i、λ′2、λ′3 of the target point cloud tensor matrix, eigenvector e' 1、e′2、e′3 of the target point cloud tensor matrix.
8. The point cloud registration method based on the tensor voting method according to claim 1, wherein: in S6, the create similarity function Δ is:
Δ＝(λ1-λ′1)2+(λ2-λ′2)2+(λ3-λ′3)2.
9. The point cloud registration method based on the tensor voting method according to claim 1, wherein: s7, obtaining a rotation matrix and a translation vector, which specifically comprises the following steps:
On the basis of obtaining the coordinates of two groups of similar points, calculating the mathematical relationship between a feature matrix E formed by E 1、e2、e3 and a feature matrix E 'formed by E' 1、e′2、e′3 to obtain a rotation matrix R and a translation vector T; the mathematical coordinate relationship of the set of corresponding point pairs is expressed as the following equation:
E＝R×E′+T
E, E' are tensor matrices composed of feature vectors of a group of corresponding points of the target point cloud matrix and the original point cloud matrix respectively;
converting E and E' into the form of homogeneous matrices by transposition:
E＝[e1 e2 e3 1]T,E′＝[e′1 e′2 e′3 1]T
the deduction process comprises the following steps:
let the registration matrix
From e=ae':
As a result of:
Let the registration vector
Constraint vector
ThenTherefore, 10-dimensional tensor voting is needed in the registration process, namely, the dimensionality of the tensor matrix is 10;
and EE' -1＝AE′E′-1;
registration matrix a=ee' -1.
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