Low-overlap Point Cloud Registration Method and System

Abstract

An embodiment of the present invention discloses a low-overlap point cloud registration method and system, and the method includes: obtaining an initial reference point cloud and an initial source point cloud; performing feature extraction on the initial reference point cloud and the initial source point cloud to obtain a first feature vector and a second feature vector; calculating a rough alignment rotation matrix according to the first feature vector and the second feature vector; calculating a first complemented point cloud and a second complemented point cloud according to the rough alignment matrix, the first feature vector and the second feature vector; performing pre-registration on the initial reference point cloud and the initial source point cloud respectively according to the initial transformation matrix to obtain a first complete point cloud and a second complete point cloud; optimizing the first complemented point cloud and the second complemented point cloud according to the first complemented point cloud, the second complemented point cloud, the first complete point cloud and the second complete point cloud; calculating a final transformation matrix according to the optimized first complemented point cloud and the second complemented point cloud, and registering and splicing the first complemented point cloud and the second complemented point cloud according to the final transformation matrix. The registration accuracy is improved.

Description

Technical Field

[0001] The present invention relates to the field of computer vision, and in particular, to a method and system for registering low-overlap point clouds. Background Art

[0002] Three-dimensional point cloud data can be obtained through various means such as depth cameras, lidars, structured light, etc. During the acquisition process of three-dimensional point cloud data in natural scenes, due to factors such as occlusion of the scanned object at certain angles or the limited field of view of the laser scanning device, only point cloud data within a limited field of view can be obtained in a single scan. If a complete point cloud of the target is desired, point cloud data needs to be collected from multiple perspectives in the scene, and then the three-dimensional point cloud registration technology is used to stitch multiple point clouds together. Point cloud registration aims to predict a rigid transformation to align input point clouds with different poses to the same coordinate system, and this rigid transformation consists of a rotation angle and a translation distance transformation.

[0003] Most traditional point cloud registration algorithms estimate the rigid transformation parameters based on point correspondences, mainly including two stages: coarse registration and fine registration. Coarse registration is mainly used to determine the approximate position and pose relationship between point clouds, providing an initial estimate for subsequent fine registration. Fine registration further optimizes to obtain more accurate transformation parameters, making the connection of point clouds more natural. Although traditional two-stage point cloud registration algorithms have a certain degree of robustness, their registration results will be greatly affected when facing problems such as noise and data loss, and traditional point cloud registration algorithms cannot handle low-overlap point clouds well. Compared with the traditional two-stage registration method, the deep learning-based point cloud registration method can better capture the details in point cloud data and can extract useful features even under the influence of noise and outliers. When using deep learning to process point clouds with a small overlapping area, they can be input into a completion model, and after reconstructing the complete point cloud structure, registration is performed. This method can effectively increase the size of the overlapping area and improve the registration accuracy. However, currently, most point cloud completion models infer the complete point cloud structure based on partially visible point clouds. If the visible part lacks recognizable features, the inferred complete structure is often unclear, which will seriously affect the subsequent registration work.

[0004] Aiming at the problem of poor registration accuracy in the low-overlap point cloud scenario in the prior art, there is currently no effective solution. Summary of the Invention

[0005] To solve the above problems, the present invention provides a method and system for registering low-overlap point clouds. After complementing local point clouds with low overlap according to their respective features, a transformation matrix is determined based on the complemented point clouds to complete the point cloud registration and stitching, so as to solve the problem of poor registration accuracy in the prior art.

[0006] To achieve the above object, the present invention provides a low-overlap point cloud registration method, including: S1, obtaining an initial reference point cloud and an initial source point cloud; S2, performing feature extraction on the initial reference point cloud according to keypoint convolution to obtain a first feature vector; performing feature extraction on the initial source point cloud according to keypoint convolution to obtain a second feature vector; calculating a rough alignment rotation matrix according to the first feature vector and the second feature vector; S3, rotating the initial reference point cloud according to the rough alignment rotation matrix to obtain a rotated reference point cloud, extracting a third feature vector of the rotated reference point cloud and a fourth feature vector of the initial source point cloud, and calculating a first complementary point cloud according to the third feature vector and the fourth feature vector; S4, rotating the initial source point cloud according to the rough alignment rotation matrix to obtain a rotated source point cloud, extracting a fifth feature vector of the rotated source point cloud and a sixth feature vector of the initial reference point cloud, and calculating a second complementary point cloud according to the fifth feature vector and the sixth feature vector; S5, pre-registering the initial reference point cloud and the initial source point cloud respectively according to an initial transformation matrix to obtain a first complete point cloud and a second complete point cloud; optimizing the first complementary point cloud and the second complementary point cloud according to the first complementary point cloud, the second complementary point cloud, the first complete point cloud and the second complete point cloud; S6, calculating a final transformation matrix according to the optimized first complementary point cloud and the second complementary point cloud by using the random sample consensus algorithm, and registering and splicing the first complementary point cloud and the second complementary point cloud according to the final transformation matrix.

[0007] Further optionally, calculating the rough alignment rotation matrix according to the first feature vector and the second feature vector includes: S201, calculating a first fusion feature vector by cascading and element-wise subtracting the first feature vector and the second feature vector; S202, calculating the rough alignment rotation matrix according to the first fusion feature vector.

[0008] Further optionally, calculating the first complementary point cloud according to the third feature vector and the fourth feature vector includes: S301, performing feature fusion on the third feature vector and the fourth feature vector to obtain a second fusion feature vector; S302, calculating the first complementary point cloud by the second fusion feature vector.

[0009] Further optionally, optimizing the first and second complementary point clouds according to the first complementary point cloud, the second complementary point cloud, the first complete point cloud, and the second complete point cloud includes: S501. Inputting the first complementary point cloud, the second complementary point cloud, the first complete point cloud, and the second complete point cloud into a neural network, and calculating the first Earth Mover's Distance (EMD) loss between the first complementary point cloud and the second complementary point cloud, the second EMD loss between the first complementary point cloud and the first complete point cloud, and the third EMD loss between the second complementary point cloud and the second complete point cloud; S502. Establishing a distance loss function according to the first EMD loss, the second EMD loss, and the third EMD loss, and optimizing the first complementary point cloud and the second complementary point cloud according to the distance loss function until the distance loss function converges or the number of iterations reaches a predetermined value.

[0010] Further optionally, calculating the final transformation matrix according to the optimized first complementary point cloud and the second complementary point cloud using the Random Sample Consensus (RANSAC) algorithm includes: S601. Randomly selecting at least three non - collinear target points from the first complementary point cloud, and determining approximate points in the second complementary point cloud according to the target points; S602. Calculating the covariance matrix according to the target points and the approximate points, performing singular value decomposition on the covariance matrix to obtain the latest transformation matrix; S603. Transforming the first complementary point cloud using the latest transformation matrix to obtain a transformed complementary point cloud, calculating the distance between each point in the transformed complementary point cloud and the corresponding point in the second complementary point cloud, and taking the points with distances less than a preset distance threshold as inliers. When the number of inliers is greater than the number of inliers of the optimal transformation matrix, taking the latest transformation matrix as the optimal transformation matrix; repeating steps S601 - S603 until the number of iterations reaches a predetermined number, and taking the current optimal transformation matrix as the final transformation matrix.

[0011] On the other hand, the present invention also provides a low-overlap point cloud registration system, which is characterized by comprising: a point cloud acquisition module for acquiring an initial reference point cloud and an initial source point cloud; a rough alignment rotation matrix calculation module for performing feature extraction on the initial reference point cloud according to keypoint convolution to obtain a first feature vector; performing feature extraction on the initial source point cloud according to keypoint convolution to obtain a second feature vector; calculating a rough alignment rotation matrix according to the first feature vector and the second feature vector; a first point cloud completion module for rotating the initial reference point cloud according to the rough alignment rotation matrix to obtain a rotated reference point cloud, extracting a third feature vector of the rotated reference point cloud and a fourth feature vector of the initial source point cloud, and calculating a first completed point cloud according to the third feature vector and the fourth feature vector; a second point cloud completion module for rotating the initial source point cloud according to the rough alignment rotation matrix to obtain a rotated source point cloud, extracting a fifth feature vector of the rotated source point cloud and a sixth feature vector of the initial reference point cloud, and calculating a second completed point cloud according to the fifth feature vector and the sixth feature vector; an optimization module for pre-registering the initial reference point cloud and the initial source point cloud respectively according to an initial transformation matrix to obtain a first complete point cloud and a second complete point cloud; optimizing the first completed point cloud and the second completed point cloud according to the first completed point cloud, the second completed point cloud, the first complete point cloud and the second complete point cloud; a registration module for calculating a final transformation matrix according to the optimized first completed point cloud and the second completed point cloud by using the random sample consensus algorithm, and registering and splicing the first completed point cloud and the second completed point cloud according to the final transformation matrix.

[0012] Further optionally, the rough alignment rotation matrix calculation module includes: a first feature fusion sub-module for calculating a first fusion feature vector by cascading and element-wise subtracting the first feature vector and the second feature vector; a matrix conversion sub-module for calculating a rough alignment rotation matrix according to the first fusion feature vector.

[0013] Further optionally, the first point cloud completion module includes: a second feature fusion sub-module for performing feature fusion according to the third feature vector and the fourth feature vector to obtain a second fusion feature vector; a completed point cloud determination sub-module for calculating a first completed point cloud through the second fusion feature vector.

[0014] Further optionally, the optimization module includes: a distance calculation sub-module, configured to input the first completed point cloud, the second completed point cloud, the first complete point cloud, and the second complete point cloud into a neural network, and calculate a first earth mover's distance loss between the first completed point cloud and the second completed point cloud, a second earth mover's distance loss between the first completed point cloud and the first complete point cloud, and a third earth mover's distance loss between the second completed point cloud and the second complete point cloud; an optimization sub-module, configured to establish a distance loss function according to the first earth mover's distance loss, the second earth mover's distance loss, and the third earth mover's distance loss, and optimize the first completed point cloud and the second completed point cloud according to the distance loss function until the distance loss function converges or the number of iterations reaches a predetermined value.

[0015] Further optionally, the registration module includes: a point selection sub-module, configured to randomly select at least three non-collinear target points from the first completed point cloud, and determine approximate points in the second completed point cloud according to the target points; a solution sub-module, configured to calculate a covariance matrix according to the target points and the approximate points, perform singular value decomposition on the covariance matrix to obtain a latest transformation matrix; a final transformation matrix determination sub-module, configured to transform the first completed point cloud by using the latest transformation matrix to obtain a transformed completed point cloud, calculate the distance between each point in the transformed completed point cloud and the corresponding point in the second completed point cloud, use the points with a distance less than a preset distance threshold as inlier points, and when the number of inlier points is greater than the number of inlier points of the optimal transformation matrix, use the latest transformation matrix as the optimal transformation matrix; repeat the steps of the point selection sub-module, the solution sub-module, and the final transformation matrix determination sub-module until the number of iterations reaches a predetermined number, and use the current optimal transformation matrix as the final transformation matrix.

[0016] The above technical solution has the following beneficial effects: Using one point cloud as the completion reference target for another point cloud, enabling the two local point clouds to use each other as references, making both parts of the point cloud targets visible, avoiding the ambiguity introduced when predicting the invisible part, and improving the registration accuracy; constructing a loss function based on the difference between the completed point cloud and the complete point cloud to accurately measure the matching situation between point clouds, and adjusting accordingly to improve the accuracy of the completed point cloud, thereby improving the registration accuracy; calculating an accurate transformation matrix based on the two completed point clouds to improve the registration accuracy. Description of the Drawings

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0018] Figure 1It is a flowchart of the low-overlap point cloud registration method provided by an embodiment of the present invention;

[0019] Figure 2 It is a flowchart of the rough alignment rotation matrix calculation method provided by an embodiment of the present invention;

[0020] Figure 3 It is a flowchart of the first complementary point cloud calculation method provided by an embodiment of the present invention;

[0021] Figure 4 It is a flowchart of the complementary point cloud optimization method provided by an embodiment of the present invention;

[0022] Figure 5 It is a flowchart of the final transformation matrix calculation method provided by an embodiment of the present invention;

[0023] Figure 6 It is a schematic structural diagram of the low-overlap point cloud registration system provided by an embodiment of the present invention;

[0024] Figure 7 It is a schematic structural diagram of the rough alignment rotation matrix calculation module provided by an embodiment of the present invention;

[0025] Figure 8 It is a schematic structural diagram of the first point cloud completion module provided by an embodiment of the present invention;

[0026] Figure 9 It is a schematic structural diagram of the optimization module provided by an embodiment of the present invention;

[0027] Figure 10 It is a schematic structural diagram of the registration module provided by an embodiment of the present invention.

[0028] Reference numerals: 100 - point cloud acquisition module; 200 - rough alignment rotation matrix calculation module; 2001 - first feature fusion sub-module; 2002 - matrix conversion sub-module; 300 - first point cloud completion module; 3001 - second feature fusion sub-module; 3002 - complementary point cloud determination sub-module; 400 - second point cloud completion module; 500 - optimization module; 5001 - distance calculation sub-module; 5002 - optimization sub-module; 600 - registration module; 6001 - point selection sub-module; 6002 - solution sub-module; 6003 - final transformation matrix determination sub-module. Detailed implementation manners

[0029] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0030] To solve the problem of inaccurate point cloud registration in the prior art, an embodiment of the present invention provides a method for registering low-overlap point clouds. Figure 1 It is a flowchart of the method for registering low-overlap point clouds provided by an embodiment of the present invention. As Figure 1 shown, the method includes:

[0031] S1. Obtain an initial reference point cloud and an initial source point cloud;

[0032] The point cloud is obtained by scanning with a lidar, a depth camera, structured light, etc. The point cloud is a set of points in three-dimensional space. Each point in the point cloud usually includes spatial coordinates, and may also include additional attributes such as color, normal vector, intensity, etc.

[0033] Initial reference point cloud As the reference point cloud for registration, the initial source point cloud Is the point cloud that needs to be registered into the coordinate system of the reference point cloud, and may have different poses due to different positions of the acquisition device. Multiple point clouds to be registered belong to the same target, and this situation is effective in most point cloud registration scenarios.

[0034] S2. Extract features from the initial reference point cloud according to keypoint convolution to obtain a first feature vector; extract features from the initial source point cloud according to keypoint convolution to obtain a second feature vector; calculate a rough alignment rotation matrix according to the first feature vector and the second feature vector;

[0035] Extract features from the initial reference point cloud and the initial source point cloud respectively through keypoint convolution to obtain a first feature vector and a second feature vector. The working principle of keypoint convolution (KPConv) is as follows:

[0036] For any point cloud , let the features of all its points be . Taking a key point in the point cloud as the center of the sphere, as the radius, determine a sphere. The points falling within this sphere will be used as the neighbor points of the point and participate in the feature calculation of . The neighbor points of

[0037] are defined as:

[0038] The sphere is defined as:

[0039] ;

[0040] Within the sphere, find Points, as kernel points. The kernel points are not the points in the point cloud, but some special positions calculated by specific rules. Definition of kernel points: ;

[0041] For each kernel point , there is a corresponding weight matrix . In the sphere range defined above , for the points falling within this range (points in the point cloud), the distance relative to can be obtained. For any , the kernel function is defined as:

[0042] ;

[0043] It can be intuitively seen that is equivalent to a weighted sum of weight matrices. The weight coefficient is defined as:

[0044] ;

[0045] It can be seen that the coefficient of each weight matrix is determined by the relative distance from to the corresponding kernel point to . The smaller the relative distance, the larger the weight, with a maximum of 1; the larger the relative distance, the smaller the weight, with a minimum of 0. Intuitive explanation: The closer the distance, the greater the correlation and the larger the result; vice versa. It can be regarded as: calculating a weight matrix specifically for . Based on the above, the convolution of the kernel point at point is defined as, for the feature of each neighbor point , after being transformed by the matrix respectively, and then accumulated:

[0046] ;

[0047] Calculate the first eigenvector corresponding to the initial source point cloud and the second eigenvector corresponding to the initial reference point cloud in the above way respectively.

[0048] Compare the first eigenvector with the second eigenvector After performing fusion post - processing, a rough alignment matrix is obtained , which is used to perform a rough spatial alignment on the point cloud to be registered, so as to enhance the mutual information between point clouds.

[0049] S3. Rotate the initial reference point cloud according to the rough alignment rotation matrix to obtain a rotated reference point cloud. Extract the third eigenvector of the rotated reference point cloud and the fourth eigenvector of the initial source point cloud, and calculate the first completed point cloud based on the third eigenvector and the fourth eigenvector;

[0050] Since the low - overlap point cloud does not have enough point - to - point correspondence relationships, the generated rough alignment rotation matrix can only help the point cloud perform a rough spatial alignment and cannot provide reliable mutual reference information for subsequent completion tasks. Therefore, it is necessary to further improve the mutual information extraction ability by aligning the feature representations between some point clouds in the feature space, so as to optimize the point cloud completion effect.

[0051] Rotate the initial reference point cloud through the rough alignment matrix to obtain a rotated reference point cloud , and obtain its third eigenvector through feature extraction . In addition, extract the fourth eigenvector of the initial source point cloud . The feature extraction method here can also use the keypoint convolution feature extraction method. At this time, the fourth eigenvector of the initial source point cloud can directly use the above - mentioned first eigenvector to improve the calculation speed.

[0052] Calculate the completion feature through the residual between the third eigenvector and the fourth eigenvector , and then convert the completion feature into the first completed point cloud .

[0053] S4. Rotate the initial source point cloud according to the rough alignment rotation matrix to obtain a rotated source point cloud. Extract the fifth eigenvector of the rotated source point cloud and the sixth eigenvector of the initial reference point cloud, and calculate the second completed point cloud based on the fifth eigenvector and the sixth eigenvector;

[0054] Rotate the initial source point cloud through the rough alignment matrix to obtain a rotated source point cloud , and obtain its fifth eigenvector through feature extraction . In addition, extract the sixth eigenvector of the initial reference point cloud . The feature extraction method here can also use the keypoint convolution feature extraction method. At this time, the initial reference point cloud​​​ The sixth eigenvector The above-mentioned second eigenvector can be directly used to improve the calculation speed.

[0055] Through the fifth eigenvector and the sixth eigenvector calculate and complete the features based on the residuals, and then convert them into the second completed point cloud according to the completed features .

[0056] S5. Perform pre-registration on the initial reference point cloud and the initial source point cloud respectively according to the initial transformation matrix to obtain the first complete point cloud and the second complete point cloud; optimize the first complete point cloud and the second complete point cloud according to the first completed point cloud, the second completed point cloud, the first complete point cloud and the second complete point cloud;

[0057] The initial reference point cloud and the initial source point cloud The ground truth pose between them is defined as , where is the rotation matrix, is the translation vector. The rotation matrix and the translation vector together constitute the initial transformation matrix, and the initial transformation matrix can be determined in advance according to the parameters of the scanning device.

[0058] Through the initial transformation matrix, the initial reference point cloud is registered relative to the initial source point cloud to obtain the first complete point cloud , and the registration process is as follows:

[0059] ;

[0060] Similarly, the initial source point cloud is combined with the initial reference point cloud after matrix transformation to obtain the second complete point cloud .

[0061] By measuring the difference between the first completed point cloud and the second completed point cloud , the difference between the first completed point cloud and the first complete point cloud , and the difference between the second completed point cloud and the second complete point cloud , and optimizing the first completed point cloud and the second completed point cloud according to the difference to make the completion result as accurate as possible.

[0062] S6. Calculate the final transformation matrix using the optimized first-completed point cloud and the second-completed point cloud with the random sample consensus algorithm, and register and splice the first-completed point cloud and the second-completed point cloud according to the final transformation matrix.

[0063] Use the optimized first-completed point cloud and the second-completed point cloud to solve for the final transformation matrix, i.e., the rotation matrix and the translation vector .

[0064] Perform coordinate system transformation on the second-completed point cloud and splice it with the first-completed point cloud to obtain the registration and splicing result.

[0065] As an alternative implementation Figure 2 is the flowchart of the rough alignment rotation matrix calculation method provided by the embodiments of the present invention. As Figure 2 shown, calculating the rough alignment rotation matrix based on the first eigenvector and the second eigenvector includes:

[0066] S201. Calculate the first fused eigenvector by concatenating and element-wise subtracting the first eigenvector and the second eigenvector;

[0067] Concatenate the first eigenvector and the second eigenvector and merge them into the first fused eigenvector through the following formula:

[0068] ;

[0069] where represents the concatenation operation, represents the element-wise subtraction operation.

[0070] S202. Calculate the rough alignment rotation matrix based on the first fused eigenvector.

[0071] Send the obtained first fused eigenvector to a multi-layer perceptron (MLP) to generate a rough rotation matrix . The MLP is a general function approximator with strong fitting ability and rotation matrix representation. The fused point cloud features input into the MLP contain the global features of the two input point clouds and the difference information between them. These information provide sufficient context information for the MLP. Through a large amount of training data, the MLP can learn the mapping relationship from the fused features to the rotation matrix, and thus output a rough alignment rotation matrix .

[0072] As an alternative implementation, Figure 3 is a flowchart of the first point cloud completion method provided by an embodiment of the present invention. As shown in Figure 3 it is shown, calculating the first completed point cloud according to the third feature vector and the fourth feature vector includes:

[0073] S301. Perform feature fusion on the third feature vector and the fourth feature vector to obtain a second fused feature vector;

[0074] By calculating the residual between the third feature vector and the fourth feature vector to fuse a new feature containing completion information, that is, the second fused feature :

[0075] ;

[0076] Similarly, the third fused feature is obtained through the same above operations on the fifth feature vector and the sixth feature vector.

[0077] S302. Calculate the first completed point cloud through the second fused feature vector.

[0078] Input the second fused feature vector into the decoder to generate the completed first completed point cloud ;

[0079] Input the third fused feature vector into the decoder to generate the completed second completed point cloud ;

[0080] As an alternative implementation, the decoding process of the decoder can be the inverse process of feature extraction.

[0081] As an alternative implementation, Figure 4 is a flowchart of the point cloud completion optimization method provided by an embodiment of the present invention. As shown in Figure 4 it is shown, optimizing the first completed point cloud and the second completed point cloud according to the first completed point cloud, the second completed point cloud, the first complete point cloud, and the second complete point cloud includes:

[0082] S501. Input the first completed point cloud, the second completed point cloud, the first complete point cloud, and the second complete point cloud into a neural network, and calculate the first Earth Mover's Distance loss between the first completed point cloud and the second completed point cloud, the second Earth Mover's Distance loss between the first completed point cloud and the first complete point cloud, and the third Earth Mover's Distance loss between the second completed point cloud and the second complete point cloud;

[0083] S502. Establish a distance loss function according to the first bulldozer distance loss, the second bulldozer distance loss and the third bulldozer distance loss, and optimize the first completed point cloud and the second completed point cloud according to the distance loss function until the distance loss function converges or the number of iterations reaches a predetermined value.

[0084] In order to improve the completion quality of the model, it is necessary to optimize the corresponding distance between low-overlap point clouds. In this embodiment, the Earth Mover's Distance (EMD) is used to measure the difference between point clouds. The Earth Mover's Distance (EMD) is a metric used to measure the difference between two point sets (such as point clouds), which is particularly suitable for situations where the distribution is uneven and point-to-point matching cannot be accurate.

[0085] The first and second completed point clouds are optimized through deep learning algorithms and supervised by loss functions.

[0086] The Earthmoving Distance (EMD) loss is calculated by finding a bijective function , maps points in point cloud p to points in point cloud g, and minimizes the average distance between points to measure the difference between point clouds, which is defined as follows:

[0087] ;

[0088] Among them, the bijective function The solution can be approximated by the auction algorithm.

[0089] The loss function corresponding to the deep learning neural network consists of two parts: (1) completion loss: completion result and Should be as close as possible to the complete point cloud after registration and Matching; (2) Mutual reference loss: completion result and The points should be matched as much as possible to avoid inconsistencies between multiple results of the same object. The purpose of these two criteria is to improve the mutual information between point clouds and thus improve the completion effect. The distance loss function is defined as:

[0090] ;

[0091] In the above formula, is the EMD loss, is the distance loss of the first bulldozer, is the distance loss of the second bulldozer, Distance loss for the third bulldozer.

[0092] The neural network continues to complete the first result Adjust the distribution of the second completion result until the loss function converges (the function value gradually approaches a certain fixed value) or reaches the preset number of iterations, and use the first completion result and the second completion result at this time as the optimized result.

[0093] As an alternative implementation Figure 5 is a flowchart of the final transformation matrix calculation method provided by the embodiments of the present invention. As Figure 5 shown, calculate the final transformation matrix according to the optimized first completed point cloud and the second completed point cloud by using the random sample consensus algorithm, including:

[0094] S601. Randomly select at least three non-collinear target points from the first completed point cloud, and determine approximate points according to the target points in the second completed point cloud;

[0095] S602. Calculate the covariance matrix according to the target points and the approximate points, and perform singular value decomposition on the covariance matrix to obtain the latest transformation matrix;

[0096] S603. Use the latest transformation matrix to transform the first completed point cloud to obtain a transformed completed point cloud, calculate the distance between each point in the transformed completed point cloud and the corresponding point in the second completed point cloud, and use the points with a distance less than the preset distance threshold as inliers. When the number of inliers is greater than the number of inliers of the optimal transformation matrix, use the latest transformation matrix as the optimal transformation matrix; repeat steps S601 - S603 until the number of iterations reaches the predetermined number, and use the current optimal transformation matrix as the final transformation matrix.

[0097] First, randomly select N (at least 3) non-collinear target points in the completed first completed point cloud , and then find the N approximate points with the most similar features in the second completed point cloud , and calculate the centroid of the point cloud according to their coordinates:

[0098] ;

[0099] Subtract the centroid of each point in the two point clouds from their respective centroids to obtain a decentralized point set, and at the same time calculate the covariance matrix H of the centralized point set:

[0100] ;

[0101] Next, perform singular value decomposition on the covariance matrix H:

[0102] ;

[0103] In the above formula, U and V are orthogonal matrices, is a diagonal matrix. The rotation matrix in the latest transformation matrix and the translation vector can be calculated by the following formula:

[0104] ;

[0105] Then, apply the estimated latest transformation matrix to the first completed point cloud , and calculate the distance between the transformed points and the corresponding points in the second completed point cloud . If the distance between a point and its corresponding point is less than the preset distance threshold, mark the point as an inlier. If the number of inliers exceeds the number of inliers of the optimal transformation matrix, update the best model, that is, use the latest transformation matrix as the optimal transformation matrix. Repeat the above steps until the predetermined number of iterations is reached or a good enough model is found, and use the final optimal transformation matrix as the final transformation matrix, that is, use the transformation matrix with the largest number of inliers as the final transformation matrix.

[0106] An embodiment of the present invention also provides a low-overlap point cloud registration system Figure 6 is a schematic structural diagram of the low-overlap point cloud registration system provided by the embodiment of the present invention, as Figure 6 shown, the system includes:

[0107] A point cloud acquisition module 100, configured to acquire an initial reference point cloud and an initial source point cloud;

[0108] The point cloud is obtained by scanning with a lidar, a depth camera, structured light, etc. The point cloud is a set of points in three-dimensional space. Each point in the point cloud usually includes spatial coordinates, and may also include additional attributes such as color, normal vector, intensity, etc.

[0109] The initial reference point cloud serves as the reference point cloud for registration, and the initial source point cloud is the point cloud that needs to be registered into the coordinate system of the reference point cloud, and may have different poses due to different positions of the acquisition devices. Multiple point clouds to be registered belong to the same target, and this situation is effective in most point cloud registration scenarios.

[0110] A rough alignment rotation matrix calculation module 200, configured to extract features from the initial reference point cloud according to keypoint convolution to obtain a first feature vector; extract features from the initial source point cloud according to keypoint convolution to obtain a second feature vector; calculate a rough alignment rotation matrix according to the first feature vector and the second feature vector;

[0111] Extract features from the initial reference point cloud and the initial source point cloud respectively through keypoint convolution to obtain a first feature vector and a second feature vector. The working principle of keypoint convolution (KPConv) is as follows:

[0112] For any point cloud , let the features of all its points be . Taking a key point in the point cloud as the center of a sphere and as the radius, a sphere is determined. The points falling within this sphere will be used as the neighbor points of point and participate in feature calculation. The neighbor points of are defined as:

[0113] ;

[0114] The sphere is defined as:

[0115] ;

[0116] Within the sphere, find points as the kernel points. The kernel points are not the points in the point cloud but some special positions calculated by specific rules. The definition of kernel points: ;

[0117] For each kernel point , there is a corresponding weight matrix . In the sphere range defined above , for the points (points in the point cloud) falling within this range, the distance from them to can be obtained. For any , the kernel function is defined as:

[0118] ;

[0119] It can be intuitively seen that is equivalent to the weighted sum of weight matrices. The weight coefficient is defined as:

[0120] ;

[0121] It can be seen that the coefficient of each weight matrix is determined by the relative distance from the corresponding kernel point to to . The smaller the relative distance, the larger the weight, with a maximum of 1; the larger the relative distance, the smaller the weight, with a minimum of 0. Intuitive explanation: The closer the distance, the greater the correlation and the larger the result; vice versa. It can be regarded as: specifically for A weight matrix is calculated. Based on the above, the core point convolution at point is defined as, for each neighbor point 's feature , after being transformed by the matrix respectively, they are accumulated:

[0122] ;

[0123] The first eigenvector corresponding to the initial source point cloud is calculated respectively in the above way, and the second eigenvector corresponding to the initial reference point cloud . .

[0124] The first eigenvector and the second eigenvector are fused and post-processed to obtain a rough alignment matrix , which is used to perform a rough spatial alignment on the point cloud to be registered to enhance the mutual information between point clouds.

[0125] The first point cloud completion module 300 is used to rotate the initial reference point cloud according to the rough alignment rotation matrix to obtain a rotated reference point cloud, extract the third eigenvector of the rotated reference point cloud and the fourth eigenvector of the initial source point cloud, and calculate the first completed point cloud according to the third eigenvector and the fourth eigenvector;

[0126] Since the low-overlap point cloud does not have enough point-to-point correspondence relationships, the generated rough alignment rotation matrix can only help the point cloud perform rough spatial alignment and cannot provide reliable mutual reference information for subsequent completion tasks. Therefore, it is necessary to further improve the mutual information extraction ability by aligning the feature representations between some point clouds in the feature space, so as to optimize the point cloud completion effect.

[0127] The initial reference point cloud is rotated through the rough alignment matrix to obtain a rotated reference point cloud , and its third eigenvector is obtained through feature extraction. In addition, the fourth eigenvector of the initial source point cloud is extracted. The feature extraction method here can also use the core point convolution feature extraction method. At this time, the fourth eigenvector of the initial source point cloud can directly use the above first eigenvector to improve the calculation speed.

[0128] Through the third eigenvector and the fourth eigenvector Calculate the residual to complete the feature, and then convert the completed feature into the first completed point cloud .

[0129] The second point cloud completion module 400 is used to rotate the initial source point cloud according to the rough alignment rotation matrix to obtain the rotated source point cloud, extract the fifth feature vector of the rotated source point cloud and the sixth feature vector of the initial reference point cloud, and calculate the second completed point cloud according to the fifth feature vector and the sixth feature vector;

[0130] Rotate the initial source point cloud through the rough alignment matrix to obtain the rotated source point cloud , and obtain its fifth feature vector through feature extraction . In addition, extract the initial reference point cloud of the sixth feature vector . The feature extraction method here can also use the keypoint convolution feature extraction method. At this time, the sixth feature vector of the initial reference point cloud can directly use the above-mentioned second feature vector to improve the calculation speed. .

[0131] Calculate the residual of the fifth feature vector and the sixth feature vector to complete the feature, and then convert the completed feature into the second completed point cloud .

[0132] The optimization module 500 is used to pre-register the initial reference point cloud and the initial source point cloud according to the initial transformation matrix to obtain the first complete point cloud and the second complete point cloud; optimize the first complete point cloud and the second complete point cloud according to the first completed point cloud, the second completed point cloud, the first complete point cloud and the second complete point cloud;

[0133] The initial reference point cloud and the initial source point cloud The ground truth pose between them is defined as , where is the rotation matrix, is the translation vector. The rotation matrix and the translation vector together form the initial transformation matrix, and the initial transformation matrix can be determined in advance according to the parameters of the scanning device.

[0134] Register the initial reference point cloud relative to the initial source point cloud through the initial transformation matrix to obtain the first complete point cloud , and the registration process is as follows:

[0135] ;

[0136] Similarly, the initial source point cloud is combined with the initial reference point cloud after matrix transformation to obtain the second complete point cloud .

[0137] By measuring the difference between the first completed point cloud and the second completed point cloud , the difference between the first completed point cloud and the first complete point cloud , and the difference between the second completed point cloud and the second complete point cloud , and optimizing the first completed point cloud and the second completed point cloud according to the difference, the completion result is made as accurate as possible.

[0138] The registration module 600 is configured to calculate the final transformation matrix according to the optimized first completed point cloud and the second completed point cloud by using the random sample consensus algorithm, and register and splice the first completed point cloud and the second completed point cloud according to the final transformation matrix.

[0139] Using the optimized first completed point cloud and the second completed point cloud , the final transformation matrix, i.e., the rotation matrix and the translation vector , are solved by using the random sample consensus algorithm.

[0140] The coordinate system of the second completed point cloud is transformed by the final transformation matrix and spliced with the first completed point cloud to obtain the registration and splicing result.

[0141] As an optional implementation manner Figure 7 is a schematic structural diagram of the rough alignment rotation matrix calculation module provided by an embodiment of the present invention. As shown in Figure 7 , the rough alignment rotation matrix calculation module 200 includes:

[0142] The first feature fusion sub-module 2001 is configured to calculate the first fusion feature vector by cascading and element-wise subtracting the first feature vector and the second feature vector;

[0143] The first fusion feature vector is calculated by cascading and element-wise subtracting the first feature vector and the second feature vector;

[0144] The first feature vector and the second feature vector are cascaded and element-wise subtracted and combined into the first fusion feature vector , which is implemented by the following formula:

[0145] ;

[0146] Among them, represents a cascaded operation, represents an element-wise subtraction operation.

[0147] The matrix conversion sub-module 2002 is used to calculate a rough alignment rotation matrix according to the first fusion feature vector.

[0148] The obtained first fusion feature vector is sent into a multi-layer perceptron (MLP) to generate a rough rotation matrix . The MLP is a general function approximator with strong fitting ability and rotation matrix representation. The point cloud fusion features input into the MLP contain the global features of the two input point clouds and the difference information between them. These information provide sufficient context information for the MLP. Through a large amount of training data, the MLP can learn the mapping relationship from the fusion features to the rotation matrix, so as to output a rough alignment rotation matrix .

[0149] As an alternative implementation manner, Figure 8 is a schematic structural diagram of the first point cloud completion module provided by the embodiments of the present invention. As shown in Figure 8 , the first point cloud completion module 300 includes:

[0150] The second feature fusion sub-module 3001 is used to perform feature fusion on the third feature vector and the fourth feature vector to obtain a second fusion feature vector;

[0151] By calculating the residual of the third feature vector and the fourth feature vector to fuse a new feature containing completion information, that is, the second fusion feature :

[0152] ;

[0153] Similarly, the third fusion feature is obtained according to the fifth feature vector and the sixth feature vector through the above same operations.

[0154] The completed point cloud determination sub-module 3002 is used to calculate the first completed point cloud through the second fusion feature vector.

[0155] Input the second fusion feature vector into the decoder to generate the completed first completed point cloud .

[0156] Input the third fusion feature vector Input to the decoder can generate the second completed point cloud after completion. .

[0157] As an alternative implementation, the decoding process of the decoder can be the inverse process of feature extraction.

[0158] As an alternative implementation, Figure 9 is a schematic structural diagram of the optimization module provided by the embodiments of the present invention. As shown in Figure 9 , the optimization module 500 includes:

[0159] A distance calculation sub-module 5001, configured to input the first completed point cloud, the second completed point cloud, the first complete point cloud, and the second complete point cloud into a neural network, and calculate a first Earth Mover's Distance (EMD) loss between the first completed point cloud and the second completed point cloud, a second EMD loss between the first completed point cloud and the first complete point cloud, and a third EMD loss between the second completed point cloud and the second complete point cloud;

[0160] An optimization sub-module 5002, configured to establish a distance loss function according to the first EMD loss, the second EMD loss, and the third EMD loss, and optimize the first completed point cloud and the second completed point cloud according to the distance loss function until the distance loss function converges or the number of iterations reaches a predetermined value.

[0161] To improve the completion quality of the model, it is necessary to optimize the corresponding distances between point clouds with low overlap. In this embodiment, the Earth Mover's Distance (EMD) is used to measure the difference between point clouds. The Earth Mover's Distance (EMD) is a metric for measuring the difference between two point sets (such as point clouds), and is particularly suitable for cases where the distribution is uneven and point-to-point exact matching is not possible.

[0162] The first completed point cloud and the second completed point cloud are optimized through a deep learning algorithm and supervised by a loss function.

[0163] The Earth Mover's Distance (EMD) loss measures the difference between point clouds by finding a bijective function , mapping the points in point cloud p to the points in point cloud g, and minimizing the average distance between points. Its definition is as follows:

[0164] ;

[0165] where the bijective function can be approximately solved by the Auction Algorithm.

[0166] The loss function corresponding to the deep learning neural network includes two parts: (1) Completion loss: The completion result and should be matched with the complete registered point cloud as much as possible and match; (2) Mutual reference loss: The completion result and should be matched as much as possible to avoid inconsistency between multiple results of the same object. The purpose of these two criteria is to increase the mutual information between the point clouds, thereby improving the completion effect. Its distance loss function is defined as:

[0167] ;

[0168] In the above formula, is the EMD loss, is the first Earth Mover's Distance loss, is the second Earth Mover's Distance loss, is the third Earth Mover's Distance loss.

[0169] The neural network continuously adjusts the distributions of the first completion result and the second completion result until the loss function converges (the function value gradually approaches a certain fixed value) or reaches the preset number of iterations, and takes the first completion result and the second completion result at this time as the optimized results.

[0170] As an alternative implementation manner, Figure 10 is a schematic structural diagram of the registration module provided by an embodiment of the present invention. As shown in Figure 10 , the registration module 600 includes:

[0171] A point selection sub-module 6001, configured to randomly select at least three non-collinear target points from the first completion point cloud, and determine approximate points according to the target points in the second completion point cloud;

[0172] A solution sub-module 6002, configured to calculate a covariance matrix according to the target points and the approximate points, perform singular value decomposition on the covariance matrix, and obtain the latest transformation matrix;

[0173] A final transformation matrix determination sub-module 6003, configured to transform the first completion point cloud by using the latest transformation matrix to obtain a transformed completion point cloud, calculate the distance between each point in the transformed completion point cloud and the corresponding point in the second completion point cloud, take the points with a distance less than a preset distance threshold as inliers, and when the number of inliers is greater than the number of inliers of the optimal transformation matrix, take the latest transformation matrix as the optimal transformation matrix; repeat the steps of the point selection sub-module, the solution sub-module, and the final transformation matrix determination sub-module until the number of iterations reaches a predetermined number, and take the current optimal transformation matrix as the final transformation matrix.

[0174] First, in the completed first completion point cloud Randomly select N (at least 3) non - collinear target points Then, for the second complementary point cloud find N approximate points with the most similar features and calculate the centroid of the point cloud based on their coordinates:

[0175] ;

[0176] Subtract the centroid of each point in the two point clouds from the points themselves to obtain a decentralized point set, and at the same time calculate the covariance matrix H of the centralized point set:

[0177] ;

[0178] Next, perform singular value decomposition on the covariance matrix H:

[0179] ;

[0180] In the above formula, U and V are orthogonal matrices, is a diagonal matrix. The rotation matrix and the translation vector in the latest transformation matrix can be calculated by the following formula:

[0181] ;

[0182] After that, apply the estimated latest transformation matrix to the first complementary point cloud and calculate the distance between the transformed points and the corresponding points in the second complementary point cloud If the distance between a certain point and the corresponding point is less than the preset distance threshold, mark this point as an inlier. If the number of inliers exceeds the number of inliers of the optimal transformation matrix, update the best model, that is, take the latest transformation matrix as the optimal transformation matrix. Repeat the above steps until the predetermined number of iterations is reached or a good enough model is found, and take the final optimal transformation matrix as the final transformation matrix, that is, take the transformation matrix with the largest number of inliers as the final transformation matrix.

[0183] The above technical solution has the following beneficial effects: Using one point cloud as the complementary reference target for another point cloud enables the two local point clouds to refer to each other, making both parts of the point cloud targets visible, avoiding the ambiguity introduced when predicting the invisible part, and improving the registration accuracy; constructing a loss function based on the difference between the complementary point cloud and the complete point cloud to accurately measure the matching situation between the point clouds, and adjusting accordingly to improve the accuracy of the complementary point cloud, thereby improving the registration accuracy; calculating an accurate transformation matrix based on the two complementary point clouds to improve the registration accuracy.

[0184] The specific implementation manners of the above invention further elaborate on the purpose, technical solution and beneficial effects of the present invention. It should be understood that the above content is only the specific implementation manners of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A low-overlap point cloud registration method, characterized in that: include: S1, obtaining the initial reference point cloud and the initial source point cloud; S2, extracting features from the initial reference point cloud according to core point convolution to obtain a first feature vector; extracting features from the initial source point cloud according to core point convolution to obtain a second feature vector; and calculating a coarse alignment rotation matrix according to the first feature vector and the second feature vector; S3, rotating the initial reference point cloud according to the coarse alignment rotation matrix to obtain a rotated reference point cloud, extracting a third eigenvector of the rotated reference point cloud and a fourth eigenvector of the initial source point cloud, and calculating a first complement point cloud according to the third eigenvector and the fourth eigenvector; S4, rotating the initial source point cloud according to the coarse alignment rotation matrix to obtain a rotated source point cloud, extracting a fifth eigenvector of the rotated source point cloud and a sixth eigenvector of the initial reference point cloud, and calculating a second complement point cloud according to the fifth eigenvector and the sixth eigenvector; S5, pre-registering the initial reference point cloud and the initial source point cloud respectively according to the initial transformation matrix to obtain a first complete point cloud and a second complete point cloud; optimizing the first completed point cloud and the second completed point cloud according to the first completed point cloud, the second completed point cloud, the first complete point cloud and the second complete point cloud; S6. Calculate a final transformation matrix using a random sampling consistency algorithm based on the optimized first complement point cloud and the second complement point cloud, and align and splice the first complement point cloud and the second complement point cloud based on the final transformation matrix.

2. The low overlap point cloud registration method according to claim 1, characterized in that: The calculating of a coarse alignment rotation matrix according to the first eigenvector and the second eigenvector includes: S201, calculating a first fused feature vector by concatenating and element-by-element subtraction between the first feature vector and the second feature vector; S202: Calculate a coarse alignment rotation matrix according to the first fused feature vector.

3. The low overlap point cloud registration method according to claim 1, characterized in that: The calculating the first completed point cloud according to the third eigenvector and the fourth eigenvector includes: S301, performing feature fusion according to the third feature vector and the fourth feature vector to obtain a second fused feature vector; S302: Calculate a first completed point cloud using the second fused feature vector.

4. The low-overlap point cloud registration method according to claim 1, characterized in that: The optimizing the first completed point cloud and the second completed point cloud according to the first completed point cloud, the second completed point cloud, the first complete point cloud and the second complete point cloud comprises: S501, inputting the first complement point cloud, the second complement point cloud, the first complete point cloud and the second complete point cloud into the neural network, calculating the first bulldozer distance loss between the first complement point cloud and the second complement point cloud, the second bulldozer distance loss between the first complement point cloud and the first complete point cloud, and the third bulldozer distance loss between the second complement point cloud and the second complete point cloud; S502. Establish a distance loss function according to the first bulldozer distance loss, the second bulldozer distance loss and the third bulldozer distance loss, and optimize the first completed point cloud and the second completed point cloud according to the distance loss function until the distance loss function converges or the number of iterations reaches a predetermined value.

5. The low-overlap point cloud registration method according to claim 1, characterized in that: The method of calculating the final transformation matrix using a random sampling consistency algorithm according to the optimized first complement point cloud and the second complement point cloud includes: S601, randomly selecting at least three non-collinear target points from the first completed point cloud, and determining approximate points in the second completed point cloud according to the target points; S602, calculating a covariance matrix according to the target point and the approximate point, performing singular value decomposition on the covariance matrix, and obtaining a latest transformation matrix; S603. Use the latest transformation matrix to transform the first completed point cloud to obtain a transformed completed point cloud, calculate the distance between each point in the transformed completed point cloud and the corresponding point in the second completed point cloud, and use the points whose distance is less than a preset distance threshold as inliers. When the number of inliers is greater than the number of inliers of the optimal transformation matrix, use the latest transformation matrix as the optimal transformation matrix; repeat steps S601-S603 until the number of iterations reaches a predetermined number, and use the current optimal transformation matrix as the final transformation matrix.

6. A low-overlap point cloud registration system, characterized in that: include: Point cloud acquisition module, used to obtain initial reference point cloud and initial source point cloud; A coarse alignment rotation matrix calculation module is used to perform feature extraction on the initial reference point cloud according to core point convolution to obtain a first eigenvector; perform feature extraction on the initial source point cloud according to core point convolution to obtain a second eigenvector; and calculate a coarse alignment rotation matrix according to the first eigenvector and the second eigenvector; A first point cloud completion module is used to rotate the initial reference point cloud according to the coarse alignment rotation matrix to obtain a rotated reference point cloud, extract a third eigenvector of the rotated reference point cloud and a fourth eigenvector of the initial source point cloud, and calculate a first completed point cloud according to the third eigenvector and the fourth eigenvector; A second point cloud completion module is used to rotate the initial source point cloud according to the coarse alignment rotation matrix to obtain a rotated source point cloud, extract the fifth eigenvector of the rotated source point cloud and the sixth eigenvector of the initial reference point cloud, and calculate a second completed point cloud according to the fifth eigenvector and the sixth eigenvector; An optimization module is used to pre-register the initial reference point cloud and the initial source point cloud according to the initial transformation matrix to obtain a first complete point cloud and a second complete point cloud; and optimize the first completed point cloud and the second completed point cloud according to the first completed point cloud, the second completed point cloud, the first complete point cloud and the second complete point cloud; The registration module is used to calculate a final transformation matrix according to the optimized first completed point cloud and the second completed point cloud using a random sampling consistency algorithm, and to align and splice the first completed point cloud and the second completed point cloud according to the final transformation matrix.

7. The low overlap point cloud registration system according to claim 6, characterized in that: The coarse alignment rotation matrix calculation module includes: A first feature fusion submodule, used for calculating the first fused feature vector by cascading and element-by-element subtraction of the first feature vector and the second feature vector; The matrix conversion submodule is used to calculate the coarse alignment rotation matrix according to the first fused feature vector.

8. The low overlap point cloud registration system according to claim 6, characterized in that: The first point cloud completion module includes: A second feature fusion submodule is used to perform feature fusion according to the third feature vector and the fourth feature vector to obtain a second fused feature vector; The completed point cloud determination submodule is used to calculate the first completed point cloud through the second fused feature vector.

9. The low overlap point cloud registration system according to claim 6, characterized in that: The optimization module includes: a distance calculation submodule, for inputting the first complement point cloud, the second complement point cloud, the first complete point cloud and the second complete point cloud into the neural network, and calculating a first bulldozer distance loss between the first complement point cloud and the second complement point cloud, a second bulldozer distance loss between the first complement point cloud and the first complete point cloud, and a third bulldozer distance loss between the second complement point cloud and the second complete point cloud; The optimization submodule is used to establish a distance loss function according to the first bulldozer distance loss, the second bulldozer distance loss and the third bulldozer distance loss, and optimize the first completed point cloud and the second completed point cloud according to the distance loss function until the distance loss function converges or the number of iterations reaches a predetermined value.

10. The low overlap point cloud registration system according to claim 6, characterized in that: The registration module comprises: A point selection submodule, configured to randomly select at least three non-collinear target points from the first completed point cloud, and determine approximate points in the second completed point cloud according to the target points; A solution submodule, used for calculating a covariance matrix according to the target point and the approximate point, performing singular value decomposition on the covariance matrix, and obtaining a latest transformation matrix; The final transformation matrix determination submodule is used to use the latest transformation matrix to transform the first completed point cloud to obtain a transformed completed point cloud, calculate the distance between each point in the transformed completed point cloud and the corresponding point in the second completed point cloud, and take the points whose distance is less than a preset distance threshold as internal points. When the number of internal points is greater than the number of internal points of the optimal transformation matrix, the latest transformation matrix is ​​used as the optimal transformation matrix; repeat the steps of the point selection submodule, the solution submodule and the final transformation matrix determination submodule until the number of iterations reaches a predetermined number, and take the current optimal transformation matrix as the final transformation matrix.

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