Coarse-to-fine cross-scale three-dimensional point cloud registration method

Abstract

The invention discloses a coarse-to-fine cross-scale three-dimensional point cloud registration method, and the method comprises the steps: starting from an input source point cloud and a target point cloud, firstly carrying out the down-sampling of point clouds through employing a mode of combining a global voxel structure and local farthest point sampling, and maintaining the isotropy and geometric consistency of the point clouds while simplifying the point clouds; then roughly estimating a scale factor on the sampled point cloud, and transforming the source point cloud; in the coarse registration stage, point cloud coarse registration is carried out by using a guiding type three-point sampling algorithm through feature extraction and matching, and a good initial pose is provided for fine registration while the registration speed is increased; in the fine registration stage, a scale-adaptive nearest point iterative algorithm is used, translation and scaling are jointly optimized after optimal rotation is applied to each iteration, and the registration precision of the algorithm is improved. The method does not need any training process, can effectively process cross-scale point cloud data with different resolutions, and has strong generalization ability.

Description

Technical Field

[0001] The present invention belongs to the field of computer vision technology, and in particular relates to a coarse-to-fine cross-scale three-dimensional point cloud registration method. Background Art

[0002] Point cloud registration has important application value in three-dimensional data processing and computer vision. With the development of sensing technologies such as lidar, structured light, and stereo vision, it has become easier to obtain high-density three-dimensional point cloud data. However, due to differences in the performance of point cloud acquisition equipment itself (such as scanning distance, viewing angle, etc.), acquisition scenarios (such as lighting, target distance), and acquisition time, the acquired point cloud data has significant differences in scale, resolution, viewing angle, and quality. At present, most point cloud registration studies are mainly aimed at point cloud data without scale differences, and existing traditional methods often rely on matching geometric features or feature descriptors between point clouds, which makes it difficult to deal with scale differences that cause point cloud data distribution changes and spatial misalignment. Therefore, cross-scale point cloud registration has far-reaching research significance and research value, so as to better integrate point cloud data from different sources and achieve more accurate and robust three-dimensional reconstruction and environmental perception.

[0003] Cross-scale point cloud registration is one of the difficulties in the current research on point cloud registration. It not only needs to solve the problem of rotation transformation and translation transformation, but also the problem of scale mismatch between different point cloud data. In recent years, researchers have proposed some innovative methods and technologies for the problem of point cloud registration with scale differences. For example, learning the feature representation of point clouds through machine learning methods, or introducing prior knowledge and sensor information to estimate and adjust scale differences; by constructing a multi-resolution representation of point clouds, such as a pyramid structure, and performing registration optimization step by step. At present, cross-scale optimization algorithms and cross-scale registration methods based on deep learning are still in the initial exploration and research stage. However, the existing cross-scale registration methods cannot effectively realize the registration of partially overlapping point clouds, have low efficiency in large-scale data processing, and are prone to fall into local optimality. In order to better solve the problem of cross-scale point cloud registration, it is necessary to find an efficient and robust cross-scale point cloud registration algorithm. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a coarse-to-fine cross-scale three-dimensional point cloud registration method, starting from the input source point cloud and the target point cloud, firstly, a global voxel structure and a local farthest point sampling method are used to downsample the point cloud, while simplifying the point cloud, the isotropy and geometric consistency of the point cloud are maintained; then, the scale factor is roughly estimated on the sampled point cloud, and the source point cloud is transformed; in the coarse registration stage, a guided three-point sampling algorithm is used through feature extraction and matching to perform coarse point cloud registration, while improving the registration speed, providing a good initial pose for fine registration; in the fine registration stage, a scale-adaptive nearest point iteration algorithm is used, and after each iteration, the translation and scaling are jointly optimized to improve the registration accuracy of the algorithm. The method of the present invention does not require any training process, can effectively process cross-scale point cloud data with different resolutions, and has strong generalization ability.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] Step 1: Input the source point cloud and the target point cloud, and perform point cloud downsampling by combining the global voxel structure and the local farthest point sampling;

[0007] Step 2: Calculate the centroids of the sampled source point cloud and target point cloud to obtain the initial value of the translation matrix, and calculate the initial scale factor to perform translation transformation and scale correction on the sampled source point cloud;

[0008] Step 3: Extract and match the features of the downsampled target point cloud and the source point cloud after scale correction and translation transformation, use guided three-point sampling to obtain the optimal rotation and translation matrix, and complete the rough registration of the point cloud;

[0009] Step 4: Based on the coarse registration, the scale-adaptive closest point iteration algorithm is iterated to jointly optimize the translation and scaling factors based on the obtained rotation transformation to perform fine registration;

[0010] Step 5: Apply the scale ratio, rotation transformation, and translation transformation of steps 2 to 4 to the unsampled source point cloud in sequence to obtain the final registration result.

[0011] Furthermore, the process of downsampling the point cloud in step 1 includes:

[0012] Step 1-1: Set the source point cloud Target point cloud Segment the input point cloud into a voxel structure consisting of voxel blocks of the same proportion;

[0013]

[0014] where p i ,q jRepresents the 3D point coordinates of the source point cloud and the target point cloud respectively, N and M represent the number of source point cloud and target point cloud respectively, V S 、V T Respectively represent the voxel size of the source point cloud S and the target point cloud T, L S , L T The longest sides of the bounding boxes of the source point cloud S and the target point cloud T respectively;

[0015] Step 1-2: Use local farthest point sampling to sample the point clouds in different voxel blocks in parallel; finally, combine the sampling results in different voxel blocks to obtain the final downsampled source point cloud S s , target point cloud T s :

[0016]

[0017] Where N V 、M V The number of point clouds per voxel block of the source point cloud S and the target point cloud T, respectively, N' V , M' V It represents the number of point clouds in each voxel block of the source point cloud S and the target point cloud T after sampling. k is the sampling rate, which controls the number of point clouds after final downsampling.

[0018] Furthermore, the process of performing translation transformation and scale correction on the sampled source point cloud in step 2 includes:

[0019] Step 2-1: Calculate the sampled source point cloud S respectively s , target point cloud T s The average position of all points gives the centroid And according to the centroid C S , C T Calculate the source point cloud S s To the target point cloud T s The initial value of the translation matrix

[0020]

[0021] Trans init =C T -C S (5)

[0022] Among them, p si ,q sj Respectively represent the three-dimensional point coordinates of the source point cloud and the target point cloud after sampling, N S 、M T Respectively represent the source point cloud S after sampling s , target point cloud T s The number of point clouds;

[0023] Step 2-2: Transform the target point cloud T s To the centroid C T The average distance With the source point cloud S s To the centroid C S The average distance The ratio of is used as the initial scale factor Scale init :

[0024]

[0025] Step 2-3: Source point cloud S s Perform translation transformation and scale correction to get S s ':

[0026]

[0027] p' si =C T +(p si +Trans init -C T )×Scale init (10)

[0028] Among them, p' si Represents the point cloud S after translation transformation and scale correction s ' is a three-dimensional point coordinate.

[0029] Furthermore, the specific process of performing point cloud coarse registration in step 3 includes:

[0030] Step 3-1: Use Harris3D to extract point cloud key points and remove invalid key points;

[0031] Step 3-2: Then use the SHOT descriptor to describe the local geometric features around the key points and calculate the source point cloud S s 'With the target point cloud T s Feature similarity, get the corresponding matching point set;

[0032] Step 3-3: Take the corresponding point set ranked TopK, and use the guided three-point sampling method to represent the matching point pairs and the corresponding relationship in the form of a graph, that is, a node in the graph represents a set of matching points, and the corresponding relationship is represented by the distance approximation between the matching point pairs. Then, the compatible triangles formed are sorted according to the degree of the node;

[0033] Step 3-4: Sample three points of the top-ranked compatible triangles and calculate the optimal rotation transformation Translation Transformation For the source point cloud S s'Transform to obtain the rough registration result S s ”:

[0034] p' s ' i =R 0 p' si +Trans 0 (11)

[0035]

[0036] Among them, p' s ' i Represents the point cloud S after rough registration s " is a three-dimensional point coordinate in .

[0037] Furthermore, the specific process of performing point cloud precise registration in step 4 includes:

[0038] Step 4-1: Roughly register the source point cloud S s "Search target point cloud T s Middle distance p' s ' i The nearest point sj , forming N S Matching point pairs, the rotation matrix is ​​obtained by singular value decomposition For the source point cloud S s "Perform rotation transformation;

[0039]

[0040] Where n represents the number of iterations, R k , Respectively represent the rotation matrix and the transformed point cloud obtained at the kth iteration, express The coordinates of a three-dimensional point in Represents the point cloud after the k-1th iterative transformation;

[0041] Step 4-2: Rotate the source point cloud Jointly optimize the translation vector and the scaling factor by minimizing the error E(Scale k ,Trans k ), get the scaling factor Scale k , translation vector

[0042]

[0043] Among them, Scale k 、Trans kThey represent the scaling factor and translation vector obtained at the kth iteration, respectively. Indicates the matching points of the target point cloud corresponding to the source point cloud in the kth iteration;

[0044] Step 4-3: Use the scaling factor Scale calculated in step 4-2 k , translation vector Trans k Source point cloud Perform the transformation, and then calculate the mean square error RMSE between the two point clouds after the transformation;

[0045]

[0046] Among them, RMSE k represents the root mean square error obtained at the kth iteration;

[0047] Step 4-4: When the mean square error of two consecutive iterations is less than the threshold or reaches the set number of iterations n, stop the iteration, otherwise repeat steps 4-1 to 4-3.

[0048] The beneficial effects of the present invention are as follows:

[0049] 1. The method of the present invention does not require any training process, can effectively process point cloud data with different resolutions, and has strong generalization ability.

[0050] 2. The method of the present invention designs an efficient optimization strategy. For the partial overlap point cloud registration with scale differences, the algorithm is more efficient and more robust. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 The figure is a flow chart of the method of the present invention.

[0052] Figure 2 A point cloud is input for an embodiment of the present invention.

[0053] Figure 3 This is the downsampling result of the embodiment of the present invention.

[0054] Figure 4 This is the result of the downsampled point cloud translation transformation and initial scale correction according to an embodiment of the present invention.

[0055] Figure 5 This is the rough registration result of the downsampled point cloud according to the embodiment of the present invention.

[0056] Figure 6 This is the precise registration result of the downsampled point cloud according to the embodiment of the present invention.

[0057] Figure 7 This is the final original point cloud registration result of the embodiment of the present invention. DETAILED DESCRIPTION

[0058] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0059] In order to solve the problem that existing methods are difficult to achieve good registration effects for partially overlapping point clouds due to scale differences and resolution differences, the present invention proposes a cross-scale three-dimensional point cloud registration method from coarse to fine. Starting from the input source point cloud and the target point cloud, the point cloud is first downsampled using a combination of a global voxel structure and local farthest point sampling, which simplifies the point cloud while maintaining the isotropy (global uniform density) and geometric consistency of the point cloud; then the scale factor is roughly estimated on the sampled point cloud to transform the source point cloud; in the coarse registration stage, a guided three-point sampling algorithm is used through feature extraction and matching to perform coarse point cloud registration, which improves the registration speed and provides a good initial pose for fine registration; in the fine registration stage, a scale-adaptive nearest point iterative algorithm is used, and after applying the optimal rotation in each iteration, the translation and scaling are jointly optimized to improve the registration accuracy of the algorithm.

[0060] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0061] S1: Input source point cloud and target point cloud, and perform point cloud downsampling by combining global voxel structure and local farthest point sampling;

[0062] S2: Calculate the centroid of the sampled source point cloud and target point cloud to obtain the initial value of the translation matrix, and calculate the initial scale factor to perform translation transformation and scale correction on the sampled source point cloud;

[0063] S3: Extract and match the features of the downsampled target point cloud and the source point cloud after scale correction and translation transformation, use guided three-point sampling to obtain the optimal rotation and translation matrix, and complete the rough registration of the point cloud;

[0064] S4: Based on the coarse registration, the scale-adaptive closest point iteration algorithm is used iteratively to jointly optimize the translation and scaling factors based on the obtained rotation transformation for fine registration;

[0065] S5: Apply the scale ratio, rotation transformation, and translation transformation of S2 to S4 to the unsampled source point cloud in sequence to obtain the final registration result.

[0066] In detail, the process of downsampling the point cloud in S1 includes:

[0067] S11: Set source point cloud Target point cloud Segment the input point cloud into a voxel structure consisting of voxel blocks of the same proportion;

[0068]

[0069] where p i ,q j Represents the 3D point coordinates of the source point cloud and the target point cloud respectively, N and M represent the number of source point cloud and target point cloud respectively, V S 、V T Respectively represent the voxel size of the source point cloud S and the target point cloud T, L S , L T The longest sides of the bounding boxes of the source point cloud S and the target point cloud T respectively;

[0070] S12: Use local farthest point sampling to sample the point clouds in different voxel blocks in parallel. Finally, combine the sampling results in different voxel blocks to obtain the final downsampled source point cloud S s , target point cloud T s .

[0071]

[0072] Where N V 、M V The number of point clouds per voxel block of the source point cloud S and the target point cloud T, respectively, N' V , M' V It represents the number of point clouds in each voxel block of the source point cloud S and the target point cloud T after sampling. k is the sampling rate, which controls the number of point clouds after final downsampling.

[0073] In detail, the process of performing translation transformation and scale correction on the sampled source point cloud in S2 includes:

[0074] S21: Calculate the sampled source point cloud S respectively s , target point cloud T s The average position of all points gives the centroid And according to the centroid C S , C T Calculate the source point cloud S s To the target point cloud T s The initial value of the translation matrix

[0075]

[0076] Trans init =C T -C S (5)

[0077] Among them, p si ,q sj Respectively represent the source point cloud S after sampling s , target point cloud T s The coordinates of a three-dimensional point, N S、M T Respectively represent the source point cloud S after sampling s , target point cloud T s The number of point clouds;

[0078] S22: The target point cloud T s To the centroid C T The average distance With the source point cloud S s To the centroid C S The average distance The ratio of is used as the initial scale factor Scale init :

[0079]

[0080] S23: Source point cloud S s Perform translation transformation and scale correction to get S s ':

[0081]

[0082] p' si =C T +(p si +Trans init -C T )×Scale init (10)

[0083] Among them, p' si Represents the point cloud S s ' is a three-dimensional point coordinate.

[0084] In detail, the specific process of performing point cloud coarse registration in S3 includes:

[0085] S31: Use Harris3D to extract point cloud key points and remove invalid key points;

[0086] S32: Then use the SHOT descriptor to describe the local geometric features around the key points and calculate the source point cloud S s 'With the target point cloud T s Feature similarity, and obtain the corresponding matching point set.

[0087] S33: Take the topK ranked corresponding point sets and use a guided three-point sampling method to represent the matching point pairs and corresponding relationships in the form of a graph, that is, a node of the graph represents a set of matching points, and the corresponding relationship is represented by the distance approximation between the matching point pairs. Then, the compatible triangles formed are sorted according to the degree of the nodes.

[0088] S34: Perform three-point sampling on the top-ranked compatible triangles to calculate the optimal rotation transformation Translation Transformation For the source point cloud S s 'Transform to obtain the rough registration result S s ”:

[0089] p' s ' i =R 0 p' si +Trans 0 (11)

[0090]

[0091] Among them, p' s ' i Represents the point cloud S after rough registration s " is a three-dimensional point coordinate in .

[0092] In detail, the specific process of performing point cloud precise registration in S4 includes:

[0093] S41: source point cloud S after rough registration s "Search target point cloud T s Middle distance p' s ' i The nearest point sj , forming N S Matching point pairs, the rotation matrix is ​​obtained by singular value decomposition For the source point cloud S s "Perform rotation transformation;

[0094]

[0095]

[0096] Where n represents the number of iterations, R k , Respectively represent the rotation matrix and the transformed point cloud obtained at the kth iteration, express The coordinates of a three-dimensional point in Represents the point cloud after the k-1th iterative transformation;

[0097] S42: Source point cloud after rotation transformation Jointly optimize the translation vector and the scaling factor by minimizing the error E(Scale k ,Trans k ), get the scaling factor Scale k , translation vector

[0098]

[0099] Among them, Scale k 、Trans k They represent the scaling factor and translation vector obtained at the kth iteration, respectively. Indicates the matching points of the target point cloud corresponding to the source point cloud in the kth iteration;

[0100] S43: Use the scaling factor Scale calculated in step 4-2 k , translation vector Trans k Source point cloud Perform the transformation, and then calculate the mean square error RMSE between the two point clouds after the transformation;

[0101]

[0102] Among them, RMSE k represents the root mean square error obtained at the kth iteration;

[0103] S44: When the mean square error of two iterations is less than the threshold or reaches the set number of iterations n, the iteration is stopped, otherwise S41 to S43 are repeated.

[0104] Example:

[0105] The embodiment of the technical solution of the present invention provides a coarse-to-fine cross-scale three-dimensional point cloud registration method, the process of which is as follows: Figure 1 The following is a detailed explanation with examples:

[0106] (1) Point cloud downsampling: Input dense source point cloud and target point cloud, such as Figure 2 As shown in , the global voxel structure and local farthest point sampling are combined to simplify the point cloud. First, the point cloud is divided into voxel blocks, and then the farthest point sampling is used in each voxel block to simplify the point cloud, where the number of sampling points in each voxel block is determined by the sampling rate k. Finally, the sampling results in different voxel blocks are combined to obtain a point cloud with uniform density after sampling, as shown in Figure 3 shown.

[0107] (2) Initial scale restoration and transformation of the source point cloud: Calculate the centroids of the simplified source point cloud and target point cloud respectively, use the ratio of the average distances of the target point cloud and the source point cloud to the corresponding centroids as the initial scale factor, and use the distance between the centroids as the initial translation matrix to perform initial translation transformation and scale correction on the source point cloud, such as Figure 4 shown.

[0108] (3) Point cloud coarse registration: Harris3D is first used to detect the key points of the target point cloud, the initial translation transformation and the scale-corrected source point cloud. Then, the SHOT descriptor is used to describe the local geometric features around the key points. The feature similarity between the source point cloud and the target point cloud is calculated to obtain the matching point set. Then, the topK ranked corresponding point sets are taken, and the matching point pairs and corresponding relationships are represented in the form of a graph. Finally, the compatible triangles formed are sorted and three-point sampled according to the degree of the nodes to obtain the optimal rotation and translation matrix to transform the source point cloud, as shown in Fig. Figure 5 shown.

[0109] (4) Point cloud fine registration: Based on the coarse registration, a scale-adaptive closest point iterative algorithm is used. First, the corresponding point closest to each point in the source point cloud is searched in the target point cloud, and the rotation matrix is ​​obtained through singular value decomposition (SVD). The source point cloud is rotated and transformed, and then the error E (Scale k ,Trans k ) Jointly optimize the translation vector and the scaling factor until the mean square error of two iterations is less than the threshold or the set number of iterations is reached, and the iteration is stopped, such as Figure 6 shown.

[0110] (5) Apply the above-obtained scale, rotation, and translation transformations to the unsampled source point cloud in turn to obtain the final registration result of the source point cloud and the target point cloud, as shown in Figure 7 shown.

[0111] The algorithm of the present invention is applied to actual 3D point cloud registration. Figure 7 As shown, it can be seen that the present invention can realize the registration of partially overlapping point clouds with differences in resolution and scale.

Claims

1. A coarse-to-fine cross-scale 3D point cloud registration method, characterized in that: The steps include: Step 1: Input the source point cloud and the target point cloud, and perform point cloud downsampling by combining the global voxel structure and the local farthest point sampling; Step 2: Calculate the centroids of the sampled source point cloud and target point cloud to obtain the initial value of the translation matrix, and calculate the initial scale factor to perform translation transformation and scale correction on the sampled source point cloud; Step 3: Extract and match the features of the downsampled target point cloud and the source point cloud after scale correction and translation transformation, use guided three-point sampling to obtain the optimal rotation and translation matrix, and complete the rough registration of the point cloud; Step 4: Based on the coarse registration, the scale-adaptive closest point iteration algorithm is iterated to jointly optimize the translation and scaling factors based on the obtained rotation transformation to perform fine registration; Step 5: Apply the scale ratio, rotation transformation, and translation transformation of steps 2 to 4 to the unsampled source point cloud in sequence to obtain the final registration result.

2. The method for cross-scale three-dimensional point cloud registration from coarse to fine according to claim 1, characterized in that: The process of downsampling the point cloud in step 1 includes: Step 1-1: Set the source point cloud Target point cloud Segment the input point cloud into a voxel structure consisting of voxel blocks of the same proportion; where p i ,q j Represents the three-dimensional point coordinates of the source point cloud and the target point cloud respectively, N and M represent the number of source point clouds and target point clouds respectively, and V S 、V T Respectively represent the voxel size of the source point cloud S and the target point cloud T, L S , L T The longest sides of the bounding boxes of the source point cloud S and the target point cloud T respectively; Step 1-2: Use local farthest point sampling to sample the point clouds in different voxel blocks in parallel; finally, combine the sampling results in different voxel blocks to obtain the final downsampled source point cloud S s , target point cloud T s : Where N V 、M V The number of point clouds per voxel block of the source point cloud S and the target point cloud T, N' V , M' V It represents the number of point clouds in each voxel block of the source point cloud S and the target point cloud T after sampling. k is the sampling rate, which controls the number of point clouds after final downsampling.

3. The method for cross-scale three-dimensional point cloud registration from coarse to fine according to claim 2, characterized in that: The process of performing translation transformation and scale correction on the sampled source point cloud in step 2 includes: Step 2-1: Calculate the sampled source point cloud S respectively s , target point cloud T s The average position of all points gives the centroid And according to the centroid C S , C T Calculate the source point cloud S s To the target point cloud T s The initial value of the translation matrix Trans init =C T -C S (5) Among them, p si ,q sj Respectively represent the three-dimensional point coordinates of the source point cloud and the target point cloud after sampling, N S 、M T Respectively represent the source point cloud S after sampling s , target point cloud T s The number of point clouds; Step 2-2: Transform the target point cloud T s To the centroid C T The average distance With the source point cloud S s To the centroid C S The average distance The ratio of is used as the initial scale factor Scale init : Step 2-3: Source point cloud S s Perform translation transformation and scale correction to get S s ': p' si =C T +(p si +Trans init -C T )×Scale init (10) Among them, p' si Represents the point cloud S after translation transformation and scale correction s ' is a three-dimensional point coordinate.

4. The method for cross-scale 3D point cloud registration from coarse to fine according to claim 3, characterized in that: The specific process of performing point cloud coarse registration in step 3 includes: Step 3-1: Use Harris3D to extract point cloud key points and remove invalid key points; Step 3-2: Then use the SHOT descriptor to describe the local geometric features around the key points and calculate the source point cloud S s 'With the target point cloud T s Feature similarity, get the corresponding matching point set; Step 3-3: Take the corresponding point set ranked TopK, and use the guided three-point sampling method to represent the matching point pairs and the corresponding relationship in the form of a graph, that is, a node in the graph represents a set of matching points, and the corresponding relationship is represented by the distance approximation between the matching point pairs. Then, the compatible triangles formed are sorted according to the degree of the node; Step 3-4: Sample three points of the top-ranked compatible triangles and calculate the optimal rotation transformation Translation Transformation For the source point cloud S s 'Transform to obtain the rough registration result S s ”: p' s ' i =R 0 p' si +Trans 0 (11) Among them, p' s ' i Represents the point cloud S after rough registration s " is a three-dimensional point coordinate in .

5. The method for cross-scale three-dimensional point cloud registration from coarse to fine according to claim 4, characterized in that: The specific process of performing point cloud precise registration in step 4 includes: Step 4-1: Roughly register the source point cloud S s "Search target point cloud T s Middle distance p' s ' i The nearest point sj , forming N S Matching point pairs, the rotation matrix is ​​obtained by singular value decomposition For the source point cloud S s "Perform rotation transformation; Where n represents the number of iterations, R k , Respectively represent the rotation matrix and the transformed point cloud obtained at the kth iteration, express The coordinates of a three-dimensional point in Represents the point cloud after the k-1th iterative transformation; Step 4-2: Rotate the source point cloud Jointly optimize the translation vector and the scaling factor by minimizing the error E(Scale k ,Trans k ), get the scaling factor Scale k , translation vector Among them, Scale k 、Trans k They represent the scaling factor and translation vector obtained at the kth iteration, respectively. Indicates the matching points of the target point cloud corresponding to the source point cloud in the kth iteration; Step 4-3: Use the scaling factor Scale calculated in step 4-2 k , translation vector Trans k Source point cloud Perform the transformation, and then calculate the mean square error RMSE between the two point clouds after the transformation; Among them, RMSE k represents the root mean square error obtained at the kth iteration; Step 4-4: When the mean square error of two consecutive iterations is less than the threshold or reaches the set number of iterations n, stop the iteration, otherwise repeat steps 4-1 to 4-3.

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