CN109887013B - PCA-based point cloud registration final determination method and system - Google Patents

Abstract

The invention discloses a point cloud registration final determination method and a point cloud registration final determination system based on PCA, wherein a translation matrix and a covariance orthogonal eigenvector matrix of two point clouds after the translation matrix is applied are calculated according to a classical PCA algorithm, then a coordinate system is established by respectively taking the maximum and second large vectors in the eigenvector matrix as a first main direction and a second main direction, then coordinate values of points of the two point clouds with the farthest distance from a coordinate origin in the two directions under the coordinate system are calculated, the coordinate values in the two directions are analyzed, when the multiplication of the coordinate values is less than zero, the main vectors in the directions of the two point clouds are reversed, otherwise, the final eigenvector matrix is obtained, a rotation matrix is calculated according to the final eigenvector matrix, and the point cloud registration is realized by applying the rotation matrix. By the method, whether the point cloud registration is correct or not does not need to be judged after the point cloud registration like the existing method, the final correct result can be directly determined to realize the point cloud registration, the registration operation is simplified, and the registration efficiency and the registration precision are improved.

Description

PCA-based point cloud registration final determination method and system

Technical Field

The invention relates to rough registration of point clouds, in particular to a point cloud registration final determination method and system based on PCA.

Background

With the rapid development of computer aided design, the point cloud and point cloud registration technology is a key step in industrial application. The point cloud registration is that one point cloud is overlapped with the other point cloud to the maximum extent by using coordinate transformation, and the registration speed and precision of the point cloud and the point cloud influence the subsequent other procedures. The current point cloud registration mainly comprises two forms of coarse registration and fine registration, wherein the coarse registration is the basis of the fine registration, and a PCA (principal component analysis) method in the coarse registration is the most common method. At present, point cloud registration by using a PCA method is mature, but when orthogonal feature vectors of two point clouds are obtained, the feature vectors have the possibility of reversal, and at this time, it is difficult to determine a final transformation matrix; the second method is to calculate the bounding boxes of two point clouds after the transformation matrix acts on the point clouds, finally calculate the contact ratio of the bounding boxes, determine the final transformation matrix if the contact ratio meets the requirement, or else, determine the final transformation matrix by reversing the original characteristic vector.

Disclosure of Invention

The invention mainly aims to provide a point cloud registration final determination method and a point cloud registration final determination system based on PCA (principal component analysis), so as to solve the problems of complexity and time consumption of a point cloud and point cloud registration method in the prior art.

The invention is realized by the following technical scheme:

a PCA-based point cloud registration final determination method comprises the following steps:

step 1: importing two point clouds P for registration_aAnd P_bIn which P is_bFor reference point clouds, P_aThe point cloud is to be moved;

step 2: to point cloud P_aObtaining point cloud P 'by using translation matrix T obtained by classical PCA method'_aTwo point clouds P 'after translation matrix transformation'_aAnd P_bThe centers of the two are overlapped;

and step 3: respectively calculating point cloud P'_aAnd P_bOf the covariance orthogonal eigenvector matrix M_aAnd M_bWherein M is_a＝[M_a1，M_a2，M_a1×M_a2]，M_b＝[M_b1，M_b2，M_b1×M_b2]；

And 4, step 4: the feature vector matrix M_aAnd M_bEstablishing a coordinate system by taking the maximum vector and the second large vector as a first main direction and a second main direction respectively;

and 5: respectively calculating point cloud P'_aAnd point cloud P_bThe coordinate values of the points with the maximum distance from the coordinate origin 0 in the first main direction and the second main direction in each coordinate system are respectively P'_amax1、P′_amax2And P_bmax1、P_bmax2；

Step 6: when P'_amax1*P_bmax1When < 0, — M_a1As the final M_a1Is P'_amax1*P_bmax1When > 0, M is maintained_a1Invariably, when P'_amax2*P_bmax2When < 0, — M_a2As the final M_a2Is P'_amax2*P_bmax2When > 0, M is maintained_a2The change is not changed;

and 7: m determined according to step 6_a1、M_a2Through M_a1×M_a2Determining the third direction of the coordinate system and applying M_aAnd M_bTo calculate a final rotation matrix R;

and 8: to point cloud P'_aUsing rotation matrix R to make point cloud P'_aRotate to and with point cloud P_bThe maximum overlapping is realized.

A PCA-based point cloud registration finalization system, comprising:

a point cloud importing module for importing two point clouds P for registration_aAnd P_bIn which P is_bFor reference point clouds, P_aThe point cloud is to be moved;

translation transformation module for point cloud P_aObtaining point cloud P 'by using translation matrix T obtained by classical PCA method'_aTwo point clouds P 'after translation matrix transformation'_aAnd P_bThe centers of the two are overlapped;

a feature vector matrix calculation module for calculating point cloud P'_aAnd P_bOf the covariance orthogonal eigenvector matrix M_aAnd M_bWherein M is_a＝[M_a1，M_a2，M_a1×M_a2]，M_b＝[M_b1，M_b2，M_b1×M_b2]；

A coordinate system creation module for creating the eigenvector matrix M_aAnd M_bEstablishing a coordinate system by taking the maximum vector and the second large vector as a first main direction and a second main direction respectively;

a coordinate calculation module for calculating point cloud P'_aAnd point cloud P_bThe coordinate values of the points with the maximum distance from the coordinate origin 0 in the first main direction and the second main direction in each coordinate system are respectively P'_amax1、P′_amax2And P_bmax1、P_bmax2；

A feature vector reverse module for when P'_amax1*P_bmax1When < 0, — M_a1As the final M_a1Is P'_amax1*P_bmax1When > 0, M is maintained_a1Invariably, when P'_amax2*P_bmax2When < 0, — M_a2As the final M_a2Is P'_amax2*P_bmax2When > 0, M is maintained_a2The change is not changed;

a rotation matrix calculation module for calculating M determined by the eigenvector reversal module_a1、M_a2Through M_a1×M_a2Determining the third direction of the coordinate system and applying M_aAnd M_bTo calculate a final rotation matrix R;

a registration module for registering point cloud P'_aUsing rotation matrix R to make point cloud P'_aRotate to and with point cloud P_bThe maximum overlapping is realized.

Compared with the prior art, the method and the system for finally determining the point cloud registration based on the PCA provided by the invention comprise the steps of firstly calculating a translation matrix and a covariance orthogonal eigenvector matrix of two point clouds after applying the translation matrix according to a classical PCA algorithm, then respectively taking the maximum and second large vectors in the eigenvector matrix as a first main direction and a second main direction to create a coordinate system, then calculating coordinate values of points of the two point clouds with the farthest distances from coordinate origin points in the two directions under the coordinate system, analyzing the coordinate values in the two directions, and when the multiplication of the coordinate values is less than zero, indicating that the main vectors in the directions of the two point clouds are reversed, otherwise, obtaining a final eigenvector matrix, calculating a rotation matrix according to the main vectors, and applying the rotation matrix to realize the point cloud registration. By the method, whether the point cloud registration is correct or not does not need to be judged after the point cloud registration like the existing method, the final correct result can be directly determined to realize the point cloud registration, the registration operation is simplified, and the registration efficiency and the registration precision are improved.

Drawings

FIG. 1 is a schematic flow chart of a point cloud registration final determination method based on PCA according to an embodiment of the present invention;

FIG. 2 is two raw point clouds used for registration;

FIG. 3 is two point cloud locations that have undergone a translation transformation;

FIG. 4 is a diagram of the feature vector forming coordinate system possibilities;

FIG. 5 is point cloud P'_aA point with the maximum distance from the origin of coordinates 0;

FIG. 6 is a point cloud P_bA point with the maximum distance from the origin of coordinates 0;

FIG. 7 is two point cloud locations that have undergone a rotational transformation;

fig. 8 is a schematic diagram of the principle of composition of a PCA-based point cloud registration final determination system according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the following embodiments and the accompanying drawings.

As shown in fig. 1, the method for final determination of point cloud registration based on PCA provided by the embodiment of the present invention includes:

step 1: importing two point clouds P for registration_aAnd P_bIn which P is_bFor reference point clouds, P_aThe point cloud to be moved. FIG. 2 shows the point clouds P_aAnd P_b。

Step 2: to point cloud P_aObtaining point cloud P 'by using translation matrix T obtained by classical PCA method'_aTwo point clouds P 'after translation matrix transformation'_aAnd P_bThe centers of which coincide. As shown in FIG. 3, the last two point clouds P 'of the translation matrix transformation'_aAnd P_bThe centers of (i.e., the cross symbol in fig. 3) coincide.

And step 3: respectively calculating point cloud P'_aAnd P_bOf the covariance orthogonal eigenvector matrix M_aAnd M_bWherein M is_a＝[M_a1，M_a2，M_a1×M_a2]，M_b＝[M_b1，M_b2，M_b1×M_b2]。

And 4, step 4: the feature vector matrix M_aAnd M_bThe medium maximum and second large vectors create a coordinate system as the first principal direction and the second principal direction, respectively. As shown in FIG. 4, by point cloud P'_aFor example, by means of the eigenvector matrix M_a2 x 2 possibilities for creating a coordinate system, point cloud P_bThe same is true.

And 5: respectively calculating point cloud P'_aAnd point cloud P_bThe coordinate values of the points with the maximum distance from the coordinate origin 0 in the first main direction and the second main direction in each coordinate system are respectively P'_amax1、P′_amax2And P_bmax1、P_bmax2As shown in fig. 5 and 6.

Step 6: when P'_amax1*P_bmax1When < 0, — M_a1As the final M_a1Is P'_amax1*P_bmax1When > 0, M is maintained_a1Invariably, when P'_amax2*P_bmax2When < 0, — M_a2As the final M_a2Is P'_amax2*P_bmax2When > 0, M is maintained_a2And is not changed.

And 7: m determined according to step 6_a1、M_a2Through M_a1×M_a2Determining the third direction of the coordinate system and applying M_aAnd M_bTo calculate the final rotation matrix R.

And 8: to point cloud P'_aUsing rotation matrix R to make point cloud P'_aRotate to and with point cloud P_bThe maximum overlapping is realized. As can be seen from fig. 7, after the rotation transformation, the two point clouds are overlapped to the maximum extent.

Based on the above method, an embodiment of the present invention further provides a PCA-based point cloud registration final determination system, as shown in fig. 8, the system includes:

a point cloud importing module 1 for importing two point clouds P for registration_aAnd P_bIn which P is_bFor reference point clouds, P_aThe point cloud to be moved.

A translation transformation module 2 for point cloud P_aObtaining point cloud P 'by using translation matrix T obtained by classical PCA method'_aTwo point clouds P 'after translation matrix transformation'_aAnd P_bThe centers of which coincide.

A feature vector matrix calculating module 3 for calculating point clouds P'_aAnd P_bOf the covariance orthogonal eigenvector matrix M_aAnd M_bWherein M is_a＝[M_a1，M_a2，M_a1×M_a2]，M_b＝[M_b1，M_b2，M_b1×M_b2]。

A coordinate system creation module 4 for creating a feature vector matrix M_aAnd M_bThe medium maximum and second large vectors create a coordinate system as the first principal direction and the second principal direction, respectively.

A coordinate calculation module 5 for calculating point clouds P'_aAnd point cloud P_bThe coordinate values of the points with the maximum distance from the coordinate origin 0 in the first main direction and the second main direction in each coordinate system are respectively P'_amax1、P′_amax2And P_bmax1、P_bmax2。

Feature vector inverse Module 6, for when P'_amax1*P_bmax1When < 0, — M_a1As the final M_a1Is P'_amax1*P_bmax1When is greater than 0Maintenance of M_a1Invariably, when P'_amax2*P_bmax2When < 0, — M_a2As the final M_a2Is P'_amax2*P_bmax2When > 0, M is maintained_a2And is not changed.

A rotation matrix calculation module 7 for calculating M determined by the eigenvector reversal module 6_a1、M_a2Through M_a1×M_a2Determining the third direction of the coordinate system and applying M_aAnd M_bTo calculate the final rotation matrix R.

A registration module 8 for registering the point cloud P'_aUsing rotation matrix R to make point cloud P'_aRotate to and with point cloud P_bThe maximum overlapping is realized.

Each module in the system is configured to execute each step in the method, and specific reference may be made to the description of each step in the method, which is not described herein again.

The above-described embodiments are merely preferred embodiments, which are not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (2)

1. A point cloud registration final determination method based on PCA is characterized by comprising the following steps:

step 1: importing two point clouds P for registration_aAnd P_bIn which P is_bFor reference point clouds, P_aThe point cloud is to be moved;

step 2: to point cloud P_aObtaining point cloud P 'by using translation matrix T obtained by classical PCA method'_aTwo point clouds P 'after translation matrix transformation'_aAnd P_bThe centers of the two are overlapped;

and step 3: respectively calculating point cloud P'_aAnd P_bOf the covariance orthogonal eigenvector matrix M_aAnd M_bWherein M is_a＝[M_a1，M_a2，M_a1×M_a2]，M_b＝[M_b1，M_b2，M_b1×M_b2]；

And 4, step 4: the feature vector matrix M_aCreating a coordinate system by taking the maximum vector and the second large vector as a first main direction and a second main direction respectively, and taking M as_bEstablishing a coordinate system by taking the maximum vector and the second large vector as a first main direction and a second main direction respectively;

and 5: respectively calculating point cloud P'_aAnd point cloud P_bThe coordinate values of the point with the maximum distance from the coordinate origin O in the first main direction and the second main direction in the corresponding main direction in each coordinate system are respectively P'_amax1、P′_amax2And P_bmax1、P_bmax2；

Step 6: when P'_amax1*P_bmax1<At 0, will be-M_a1As the final M_a1Is P'_amax1*P_bmax1>At 0, maintain M_a1Invariably, when P'_amax2*P_bmax2<At 0, will be-M_a2As the final M_a2Is P'_amax2*P_bmax2>At 0, maintain M_a2The change is not changed;

and 7: m determined according to step 6_a1、M_a2Through M_a1×M_a2Determining the third direction of the coordinate system and applying M_aAnd M_bTo calculate a final rotation matrix R;

and 8: to point cloud P'_aUsing rotation matrix R to make point cloud P'_aRotate to and with point cloud P_bThe maximum overlapping is realized.

2. A PCA-based point cloud registration finalization system, comprising:

a point cloud importing module for importing two point clouds P for registration_aAnd P_bIn which P is_bFor reference point clouds, P_aThe point cloud is to be moved;

translation transformation module for point cloud P_aObtaining point cloud P 'by using translation matrix T obtained by classical PCA method'_aTwo point clouds P 'after translation matrix transformation'_aAnd P_bThe centers of the two are overlapped;

feature(s)A vector matrix calculation module for calculating point cloud P'_aAnd P_bOf the covariance orthogonal eigenvector matrix M_aAnd M_bWherein M is_a＝[M_a1，M_a2，M_a1×M_a2]，M_b＝[M_b1，M_b2，M_b1×M_b2]；

A coordinate system creation module for creating the eigenvector matrix M_aCreating a coordinate system by taking the maximum vector and the second large vector as a first main direction and a second main direction respectively, and taking M as_bEstablishing a coordinate system by taking the maximum vector and the second large vector as a first main direction and a second main direction respectively;

a coordinate calculation module for calculating point cloud P'_aAnd point cloud P_bThe coordinate values of the point with the maximum distance from the coordinate origin O in the first main direction and the second main direction in the corresponding main direction in each coordinate system are respectively P'_amax1、P′_amax2And P_bmax1、P_bmax2；

A feature vector reverse module for when P'_amax1*P_bmax1<At 0, will be-M_a1As the final M_a1Is P'_amax1*P_bmax1>At 0, maintain M_a1Invariably, when P'_amax2*P_bmax2<At 0, will be-M_a2As the final M_a2Is P'_amax2*P_bmax2>At 0, maintain M_a2The change is not changed;

a rotation matrix calculation module for calculating M determined by the eigenvector reversal module_a1、M_a2Through M_a1×M_a2Determining the third direction of the coordinate system and applying M_aAnd M_bTo calculate a final rotation matrix R;

a registration module for registering point cloud P'_aUsing rotation matrix R to make point cloud P'_aRotate to and with point cloud P_bThe maximum overlapping is realized.

Images