Two-stage point cloud registration method based on angle consistency constraint

Abstract

The invention discloses a two-stage point cloud registration method based on angle consistency constraint, and belongs to the technical field of three-dimensional computer vision. The method comprises the following steps: firstly, extracting multi-level features of a point cloud and performing rough matching; then, constructing a first-order similarity matrix and a second-order similarity matrix by utilizing rotation invariance of a vector included angle, and accurately distinguishing an inner point and an outer point through global geometric compatibility; then, the optimal pose is solved by adopting seed selection, local spectrum matching and weighted singular value decomposition, and error overpoint pairs are eliminated; and finally, guiding fine registration by using the reserved high-quality overpoint pair. According to the method, the registration precision and robustness in low-overlap, weak-texture and repeated-structure scenes can be remarkably improved, and the registration problem in complex scenes is effectively solved.

Description

Technical Field

[0001] This invention relates to improvements in point cloud registration technology, specifically to a method for removing erroneous matching pairs by utilizing angular consistency geometric constraints, thereby improving the accuracy of two-stage point cloud registration, belonging to the field of 3D computer vision technology. Background Technology

[0002] Point cloud registration is a fundamental technology for 3D reconstruction, autonomous driving localization, and robot navigation. Current mainstream registration methods mostly employ a two-stage "coarse-to-fine" strategy: first, coarse matching of block-level superpoints, followed by fine matching of dense point-level points within the superpoint neighborhood. This strategy effectively alleviates the sensitivity of traditional methods to initial pose. However, when dealing with complex scenes with low overlap, weak texture, or repetitive geometry, the coarse matching stage often generates a large number of erroneous superpoint matching pairs (i.e., outliers). If these outliers cannot be effectively removed, they will mislead the subsequent fine matching process, leading to registration failure. Existing outlier removal methods are mainly divided into learning-based methods and geometric consistency-based methods. Among them, spatial consistency based on Euclidean distance is a commonly used geometric constraint method, such as SC²-PCR (ASecond Order Spatial Compatibility for Efficient and Robust Point Cloud Registration). This method assumes that the distance between two points remains unchanged before and after rigid body transformation. However, research has found that distance consistency has discriminative ambiguity: in some cases, the distance between two incorrect matching point pairs may be equal by chance (e.g., incorrect matching in symmetric structures), thus passing the consistency check. Summary of the Invention

[0003] To address the problems of existing two-stage registration methods that easily generate a large number of erroneous matches in the coarse matching stage, and the ambiguity in the discrimination of outliers removed based on distance consistency affecting the accuracy of point cloud registration, the present invention aims to propose a two-stage point cloud registration method based on angle consistency constraints. The present invention utilizes angle features to construct high-order geometric constraints, which can accurately identify and eliminate erroneous outlier pairs in the coarse matching stage, thereby significantly improving the accuracy and success rate of point cloud registration.

[0004] The technical solution of this invention is implemented as follows:

[0005] The two-stage point cloud registration method based on angle consistency constraints includes the following steps:

[0006] 1) Coarse matching: Input the source point cloud and target point cloud to be registered into the neural network for downsampling and feature extraction, calculate the feature correlation between superpoints of the source point cloud and target point cloud, and select the top several superpoint pairs with the highest correlation to form the initial superpoint matching pair set;

[0007] 2) Constructing a first-order angular similarity matrix: In the initial set of superpoint matching pairs, for any two pairs of matching points, a third reference matching point is introduced, and triangles are constructed in the source point cloud and the target point cloud based on the three points respectively; using the rotation invariance of the vector angle under rigid body transformation, the difference of the angle between the corresponding edge vectors is calculated, and the difference of the angle is converted into a similarity score to construct a first-order angular similarity matrix that reflects the degree of geometric compatibility between matching pairs;

[0008] 3) Construct a second-order similarity matrix: Binarize the first-order angular similarity matrix, count the number of adjacent matching pairs that are compatible in the global scope for each pair of matching pairs, and transform the local first-order angular consistency into a second-order similarity matrix that reflects the global geometric distribution consistency.

[0009] 4) Seed selection and consensus set construction: Spectral decomposition is performed on the binarized first-order angular similarity matrix to obtain the initial confidence level, and high-confidence seed matching pairs with uniform spatial distribution are selected; for each seed matching pair, its nearest neighbor matching pair is searched in the second-order similarity matrix to construct a local consensus set.

[0010] 5) Local Spectral Matching and Transformation Estimation: The weights of each point in the local consensus set are calculated using the spectral matching method, and weighted singular value decomposition is performed based on these weights to solve for multiple candidate rigid body transformation matrices;

[0011] 6) Optimal transformation screening and exterior point elimination: The candidate rigid body transformation matrix is ​​used to perform residual verification on the initial superpoint matching pair set, and the candidate rigid body transformation matrix with the most interior points is selected as the optimal transformation. Based on this, all incorrect superpoint matching pairs that do not conform to the transformation are eliminated from the initial superpoint matching pair set, and the correct superpoint matching pairs are retained.

[0012] 7) Fine matching: The retained correct superpoint matching pairs are expanded into neighborhood blocks. Local dense point matching is performed within the neighborhood blocks. Finally, a local to global weighted singular value decomposition iterative strategy is adopted to calculate the final high-precision rigid body transformation matrix and obtain the final point cloud registration result.

[0013] Furthermore, the specific implementation steps of step 1) are as follows:

[0014] 1.1) Downsampling and feature extraction: Perform multi-level downsampling on the source point cloud and the target point cloud to obtain the dense point set and superpoint set of the source point cloud and the target point cloud respectively, and extract the corresponding dense point features and superpoint features.

[0015] 1.2) Geometric structure embedding construction: superpoints in the superpoint sets of the source point cloud and the target point cloud. Select k nearest neighbor superpoints to form a set For sets Two superpoints in and ,calculate and The Euclidean distance between them, and and Its neighboring super point The three angles formed Among them, the nearest super point The distance and angle are mapped to high-dimensional features using sine and cosine functions, and the distance embedding is calculated using the following formula. and angle embedding :

[0016]

[0017] In the formula and It is a sensitivity parameter for controlling changes in distance and angle;

[0018] Geometric embeddings are computed by aggregating pairwise distance embeddings and angle embeddings. :

[0019]

[0020] in and These are for distance embedding. and angle embedding The projection matrix;

[0021] 1.3) Attention Mechanism Feature Interaction: Construct a geometric self-attention module, use the embedded features of the geometric structure to correct the attention weights, and learn the global correlation between features inside a single point cloud and the geometric space; construct a feature-based cross-attention module to perform bidirectional feature interaction between the source point cloud and the target point cloud; alternately stack the geometric self-attention module and the cross-attention module to output hybrid features;

[0022] 1.4) Superpoint matching: Calculate the Gaussian correlation matrix of the mixed features of the source point cloud and the target point cloud, and select the top few matching pairs with the highest correlation scores to form the initial set of superpoint matching pairs.

[0023] Furthermore, the method for constructing the first-order angular similarity matrix in step 2) is as follows:

[0024] 2.1) First, randomly select several matching pairs from the initial superpoint matching pair set to construct the baseline matching pair set M;

[0025] 2.2) For any two matching pairs i and j in the initial superpoint matching pair set whose similarity is to be calculated, randomly select a matching pair from the benchmark matching pair set M as the benchmark matching pair m for this calculation; extract the source points corresponding to matching pairs i, j, and m in the source point cloud, and the target points corresponding to m in the target point cloud; in the source point cloud, connect the source points of the benchmark matching pair m and the source points of the matching pair j using the source points of matching pair i, respectively, to construct two source vectors. and In the target point cloud, two target vectors are constructed by connecting the target points of the baseline matching pair m and the target points of the matching pair j with the target points of the matching pair i. and ; Calculate the two vectors constructed in the source point cloud and The included angle and the corresponding vector in the target point cloud. and The included angle ; Calculate the absolute value of the difference between the angles between two sets of vectors. :

[0026]

[0027] The first-order similarity values ​​of matching pair i and matching pair j are calculated using a monotonically decreasing function. :

[0028]

[0029] in, It is a linear rectified function;

[0030] 2.3) Keeping the matching pair i unchanged, repeat step 2.2), traverse all matching pairs in the initial superpoint matching pair set, and obtain the first-order similarity value of matching pair i and all matching pairs including itself;

[0031] 2.4) Repeat steps 2.2)-2.3), traverse the initial superpoint matching pair set, calculate the first-order similarity value of each matching pair and all matching pairs including itself, thereby obtaining the first-order similarity values ​​of all matching pairs in the initial superpoint matching pair set and constructing the first-order angular similarity matrix. .

[0032] Further, step 3) involves constructing the second-order similarity matrix by setting an angle threshold. ;like Then determine that matching pair i and matching pair j are geometrically compatible, let Otherwise, determine that matching pair i and matching pair j are incompatible, and let In step 3), construct a second-order similarity matrix. The specific formula is:

[0033]

[0034] in, The total number of matching pairs in the initial superpoint matching pair set; this formula means that the number of third matching pairs k that are mutually compatible are counted as the second-order similarity value only if matching pair i and matching pair j are compatible with themselves.

[0035] Further, the seed selection method in step 4) is as follows: perform power iteration on the binarized first-order angular similarity matrix to solve for the principal feature vector, and use the element values ​​of the principal feature vector as the initial inlier probability of each matching pair; perform non-maximum suppression within the preset spatial radius R, retain the matching pair with the highest local inlier probability as the seed, and suppress the matching pair with the lower probability in the neighborhood, thereby selecting a set of seed matching pairs with uniform spatial distribution and high confidence.

[0036] Further, step 5) specifically involves:

[0037] 5.1) Constructing a local graph: Treat the matching pairs in the local consensus set as nodes, and the second-order similarity values ​​between matching pairs as edge weights, thereby constructing a local graph based on the local consensus set;

[0038] 5.2) Spectral decomposition: Perform eigenvalue decomposition on the adjacency matrix of the local graph, and take the principal eigenvector as the inlier probability weight of each matching pair in the local consensus set.

[0039] 5.3) Weighted Singular Value Decomposition: The coordinates of point pairs in the local consensus set are weighted using the aforementioned interior point probability weights, and the candidate rotation matrix is ​​solved through singular value decomposition. Translation vector This yields multiple candidate rigid body transformation matrices.

[0040] Further, the specific implementation method of step 6) is as follows: traverse all candidate rigid body transformation matrices, calculate the residuals of all matching pairs in the initial superpoint matching pair set under the transformation, count the number of interior points with residuals less than the distance threshold, and select the transformation with the most interior points as the best transformation; retain the matching pairs in the initial superpoint matching pair set whose residuals are less than the threshold under the best transformation as the correct superpoint matching pairs, and remove the remaining matching pairs.

[0041] Further, step 7 is specifically implemented as follows: the correct superpoint matching pairs retained in step 6) are expanded into local neighborhood block matching pairs centered on the superpoints; the features and coordinates of dense points within the neighborhood blocks are extracted and input into the dense point matching module for dense point matching; the correspondence of dense points within the neighborhood blocks is calculated using weighted singular value decomposition; based on the correspondence of all dense points, weighted singular value decomposition is performed again to obtain the final rigid body transformation matrix.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] This invention utilizes the rotation invariance of the angle between vectors as a constraint. Compared to Euclidean distance constraints, the angular features between vectors are more sensitive to rotation transformations and possess stronger uniqueness, providing a more rigorous and reliable criterion for interior point discrimination. This effectively eliminates misclassifications caused by symmetrical structures or accidental equal distances, resolving the ambiguity problem of distance consistency. By constructing a second-order similarity matrix, not only are the local relationships between two point pairs considered, but global common neighbor information is also introduced, significantly enhancing robustness to high proportions of outliers. This invention significantly improves registration accuracy and robustness in low-overlap, weak-texture, and repetitive structure scenes, effectively solving the registration challenge in complex scenes. Experiments show that the proposed method achieves a registration recall rate (RR) of 92.6% on the 3DMatch benchmark dataset, a significant improvement over existing techniques; and reduces the translation error by 0.6 cm on the KITTI outdoor dataset, demonstrating good generalization ability. Attached Figure Description

[0044] Figure 1 - Schematic diagram of the two-stage point cloud registration framework for angle consistency constraints of this invention.

[0045] Figure 2 - Working principle diagram of the super-point matching module of this invention.

[0046] Figure 3 - Overall flowchart of external point removal in this invention.

[0047] Figure 4 - A comparison of the visualization experimental results of the point cloud registration method proposed in this invention and some existing methods in a certain embodiment.

[0048] Figure 5 This is an example diagram of the similarity matrix in a certain embodiment of the present invention; where (a) is a first-order angular similarity matrix; (b) is a first-order angular similarity matrix after binarization; and (c) is a second-order similarity matrix. Detailed Implementation

[0049] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0050] See Figure 1 The present invention provides a two-stage point cloud registration method based on angle consistency constraints, comprising the following steps:

[0051] 1) Data preprocessing and coarse matching: The source and target point clouds to be registered are input into a neural network for downsampling and feature extraction. The feature correlation between superpoints in the source and target point clouds is calculated, and the top few superpoint pairs with the highest correlation are selected to form the initial superpoint matching pair set. Specific implementation steps are as follows, and see also... Figure 2 :

[0052] 1.1) Downsampling and Feature Extraction: This involves downsampling the input source point cloud... and target point cloud Voxel downsampling is performed separately, and the first-level downsampling yields the set of dense points in the source point cloud. and the set of dense points in the target point cloud The final downsampling stage yields the source point cloud superpoint set. and target point cloud super set For each dense point, a corresponding superpoint is assigned using nearest neighbor search, forming a local neighborhood block centered on the superpoint. .

[0053] The KPConv-FPN (Kernel Point Convolution - Feature Pyramid Network) network is used to extract the features corresponding to each scale of the source point cloud, thus obtaining super-point features. and dense point features ,in Defined as a set of superpoints The number of midpoints Defined as a set of dense points The number of midpoints , These represent the dimensions of the superpoint feature and the dense point feature, respectively. The feature matrix associated with points in the matrix is ​​represented as follows: Target point cloud The relevant attributes are also represented in the same form.

[0054] 1.2) Geometric Structure Embedding Construction: The superpoint matching module works by using a self-attention module to learn the features between each superpoint and the global correlation in the geometric space. A subsequent cross-attention module is used for bidirectional feature interaction between the two input point clouds. The superpoint matching module incorporates geometric structure embedding to learn the geometric features of the superpoints. Taking the source point cloud as an example (the target point cloud is similar), given two superpoints... and Their geometry consists of opposing distances and angles. For superpoints in the set of superpoints... Select k nearest neighbor superpoints to form a set For sets Two superpoints in and ,calculate and The Euclidean distance between them, and and Its neighboring super point The three angles formed Among them, the nearest super point The distance embedding is calculated using equation (1). and angle embedding :

[0055] (1)

[0056] In formula (1) and These are parameters controlling the sensitivity to changes in distance and angle, respectively. Distance and angle are decomposed into sin and cosine components to accommodate high-dimensional similarity calculations for geometric self-attention. Finally, geometric embeddings are calculated by aggregating pairwise distance embeddings and ternary angle embeddings. As shown in equation (2):

[0057] (2)

[0058] in and These are for distance embedding. and angle embedding The projection matrix.

[0059] 1.3) Attention mechanism feature interaction: Obtain the geometric embeddings of all superpoints. Then, compare it with the initial features. These are used as inputs to the geometric self-attention module. This geometric self-attention is used to learn features between superpoints and global correlations in the geometric space. First, attention scores are calculated. :

[0060] (3)

[0061] Weight coefficient matrix From attention score line by line Calculate the final output feature matrix. The weighted sum of all projected input features is expressed as:

[0062] (4)

[0063] in These are weight parameters obtained through network learning. Since geometric embedding introduces significant computational overhead, to reduce computation, all geometric self-attention modules share these parameters. parameter.

[0064] The cross-attention module, as the core component of the point cloud registration task, realizes information fusion between input point clouds through a two-way feature interaction mechanism. As and (at this time and The feature correlations of the output features of the self-attention module are shown in Equation (5).

[0065] (5)

[0066] Line by line, the attention score is calculated. Obtain the weight coefficient matrix ,use Feature calculation Cross-attention feature matrix Represented as equation (6):

[0067] (6)

[0068] The cross-attention features were calculated in the same way.

[0069] 1.4) Superpoint Matching: The geometric self-attention module focuses on modeling the spatially consistent geometric structure within a single point cloud, while the feature-based cross-attention module establishes geometrically consistent associations through cross-point cloud feature interactions. By alternately stacking these two complementary attention modules, hybrid features are obtained. and The mixed features are normalized and the Gaussian correlation matrix is ​​calculated. ,in Finally, select the top ones with the highest relevance. Each pair of points is used as the superpoint matching result:

[0070] (7)

[0071] 2) Constructing a first-order angular similarity matrix: In the initial set of superpoint matching pairs, for any two pairs of matching points, a third reference matching point is introduced. Triangles are constructed in the source and target point clouds based on these three points. Utilizing the rotation invariance of vector angles under rigid body transformation, the difference in angles between corresponding edge vectors is calculated. This difference in angles is then converted into a similarity score, constructing a first-order angular similarity matrix that reflects the geometric compatibility between matching pairs. The specific implementation is as follows.

[0072] To avoid potential errors from a single reference point, multiple reference points are randomly selected (e.g.) (Number) benchmarks correspond to This constitutes the benchmark matching pair set M. For the set... Any two matching pairs in and Vectors are constructed in the source point cloud and the target point cloud, respectively. For any two matching pairs i and j in the initial superpoint matching pair set whose similarity is to be calculated, a matching pair is randomly selected from the benchmark matching pair set M as the benchmark matching pair m for this calculation; the source points corresponding to matching pairs i, j, and benchmark matching pair m in the source point cloud and the target points corresponding to them in the target point cloud are extracted respectively; in the source point cloud, the source points of benchmark matching pair m and matching pair j are connected using the source points of matching pair i to construct two source vectors. and In the target point cloud, two target vectors are constructed by connecting the target points of the baseline matching pair m and the target points of the matching pair j with the target points of the matching pair i. and Calculate the angle between the source point cloud vectors:

[0073] (8)

[0074] Similarly, calculate the angle between the target point cloud vectors. Then, the angle difference between the source point cloud and the target point cloud vectors is calculated. The first-order similarity values ​​of matching pair i and matching pair j are calculated using a monotonically decreasing function:

[0075] (9)

[0076] in, The function is a linear rectified function; the smaller the angle difference, the higher the similarity. The first-order similarity value of all matching pairs is calculated by traversing the initial set of superpoint matching pairs. This yields the first-order similarity value of all matching pairs in the initial set of superpoint matching pairs, and a first-order angle similarity matrix is ​​constructed. .

[0077] 3) Constructing a second-order similarity matrix: The first-order angular similarity matrix is ​​binarized, and the number of globally compatible adjacent matching pairs for each pair is counted, transforming the local first-order angular consistency into a second-order similarity matrix reflecting the global geometric distribution consistency. Since inliers exhibit high global consistency, while outliers are typically randomly distributed, the second-order similarity value of inliers is significantly higher than that of outliers. The specific implementation is as follows...

[0078] Under the constraint of rigid transformation angle consistency, the relative angles between correct matches should remain strictly consistent, i.e., the angle difference should be equal to 0. However, due to noise introduced by data acquisition and point cloud downsampling, the actual angle difference of real superpoint matching pairs is not completely 0, but is less than a certain threshold. Therefore, two matching pairs with angle differences within the threshold range are considered compatible. This is achieved by setting an angle threshold. (In this embodiment) (Set to 0.3 rad). Construct a binarized matrix. ,like Then determine the matching pair and matching pairs Geometric compatibility, making Otherwise, determine a matching pair. and matching pairs Incompatible, making Construct a second-order similarity matrix based on the binary matrix. :

[0079] (10)

[0080] in, This represents the total number of matching pairs in the initial set of superpoint matching pairs. The physical meaning of this formula is: only when point pairs... and They satisfy angular consistency and have a large number of common geometrically compatible neighbors. Only when these conditions are met do their second-order similarity scores become high. This greatly suppresses accidental geometric similarities.

[0081] Figure 5 Here is a similarity matrix calculated using 6 matching pairs as examples in a certain embodiment of the present invention, where (a) is a first-order angular similarity matrix; (b) is a first-order angular similarity matrix after binarization; and (c) is a second-order similarity matrix.

[0082] 4) Seed selection and consensus set construction: Constructing a second-order similarity matrix. Next, the optimal pair needs to be calculated as the seed. The steps for selecting the seed pair are as follows: [The text then abruptly shifts to a different topic:] ...the binarized first-order angular similarity matrix... The principal eigenvector is calculated through exponential iteration. The elements of this principal eigenvector are used as the initial inlier probabilities for each matching pair, thus obtaining the initial confidence level for each pair. To avoid over-concentration of seed points, a preset spatial radius is used... Non-Maximum Suppression (NMS) is performed within the neighborhood of the target, retaining the matching pair with the highest local probability as the seed and suppressing matching pairs with lower probability in the neighborhood, thereby selecting spatially evenly distributed and high-confidence targets. One (e.g.) The matching pair is used as the seed.

[0083] 5) Local Spectral Matching and Transformation Estimation: After selecting the optimal seed pair, local spectral matching and pose calculation are performed. The weights of each point within the local consensus set are calculated using the spectral matching method, and weighted singular value decomposition is performed based on these weights to solve for multiple candidate rigid body transformation matrices. Details are as follows...

[0084] 5.1) Constructing a local graph: For each seed, in Selecting from the matrix One (e.g.) The nearest neighbors form a local consensus set. Matching pairs in the local consensus set are considered nodes, and the second-order similarity values ​​between matching pairs are considered edge weights, thus constructing a local graph based on the local consensus set.

[0085] 5.2) Spectral decomposition: Perform eigenvalue decomposition on the adjacency matrix of the local graph, and take the principal eigenvector as the inlier probability weight of each matching pair in the local consensus set.

[0086] 5.3) Weighted Singular Value Decomposition: The coordinates of point pairs in the local consensus set are weighted using the aforementioned interior point probability weights, and then the candidate rotation matrix is ​​solved using weighted SVD (Singular Value Decomposition). Translation vector This yields multiple candidate rigid body transformation matrices.

[0087] 6) Optimal Transform Selection and Outlier Removal: In order to select the optimal transformation, for each calculated transformation... Calculate the residuals of all initial matching pairs. Statistically, residuals less than a threshold are considered valid. (For example Number of interior points :

[0088] (11)

[0089] in It represents the number of super-matching pairs obtained from coarse matching. It is one of the sets of superpoint correspondences. This is the interior point threshold. The transformation with the largest number of interior points is selected as the optimal transformation, and all interior points under this transformation are retained as correct superpoint pairs, while all incorrect superpoint matching pairs that do not conform to this transformation are discarded. All interior points under this transformation will be propagated to the dense point matching stage as correct superpoint correspondences.

[0090] Steps 2) through 6) involve outlier removal based on angle consistency, and the overall process is as follows: Figure 3 As shown.

[0091] 7) Fine Matching: The retained correct superpoint matching pairs are expanded into neighborhood blocks. Local dense point matching is performed within these neighborhood blocks. Finally, a weighted singular value decomposition iterative strategy from local to global is used to calculate the final high-precision rigid body transformation matrix, obtaining the final point cloud registration result. Details are as follows:

[0092] After obtaining reliable superpoint matching pairs, the fine matching stage uses the dense point features learned by the KPConv-FPN network during the superpoint matching process. and The correspondences of dense points are obtained. Specifically, for each superpoint correspondence... Extract using the optimal transport layer Blocks and The correspondence between locally dense points between blocks. In this process, the cost matrix is ​​first calculated. ,in , ,and , Indicates to respectively and , The feature matrix associated with dense points in the block. First, a relaxation row and column are filled into the cost matrix. Then, the Sinkhorn algorithm is used to calculate the confidence matrix of dense point matching on the cost matrix. And obtain the correspondence of dense points based on bidirectional top-k selection:

[0093] (12)

[0094] Then, the dense point correspondences calculated from all superpoint matching pairs are collected together to form the final global dense point correspondences. After obtaining the correspondences of dense points, this invention adopts a local-to-global pose estimation scheme. In the local stage, based on the dense point correspondences of each superpoint's neighborhood block, the transformation is solved for each superpoint's neighborhood block using the weighted singular value decomposition (SVD) method. The weights used in weighted SVD are... Each corresponding confidence score is calculated. Thanks to the high-quality correspondence, the transformation obtained at this stage is already very accurate. In the global stage, the transformation that maximizes the rate of interior points corresponding to dense points is selected as the current optimal transformation matrix, expressed as equation (13):

[0095] (13)

[0096] Then, the interior points under the optimal transformation are retained and used again to solve the local pose, resulting in a new round of local transformation matrices. The global optimal transformation is obtained in the same way. This process is iteratively calculated until the set number of iterations is reached, yielding the final rigid body transformation matrix.

[0097] The following is a verification example to demonstrate the feasibility of this method.

[0098] Dataset selection:

[0099] To comprehensively test the registration performance of the proposed method, the following three representative point cloud registration benchmark datasets were selected: ModelNet40: Contains point clouds of CAD model objects across 40 categories, used to verify object-level registration performance. 3DMatch / 3DLoMatch: Composed of 62 real-world indoor scenes. 3DMatch contains point cloud pairs with an overlap rate >30%, while 3DLoMatch contains low-overlap point cloud pairs with an overlap rate between 10% and 30%, used to verify performance in complex indoor scenes. KITTI: Contains large-scale outdoor autonomous driving scene point clouds acquired via LiDAR, used to verify the algorithm's generalization ability in outdoor scenes.

[0100] Data processing and experimental setup:

[0101] In the experiment, data preprocessing and network baseline parameters followed the baseline method (GeoTransformer). For the outlier removal module, an angle threshold was used when calculating the second-order similarity matrix. The threshold was set to 0.3 rad. Experiments showed that this threshold effectively balanced inlier retention and outlier removal. The seed number was set to the total number of initial matching pairs. 20% (e.g. in 3DMatch) (The number of seeds is approximately 50). The number of nearest neighbors selected for each seed is... Set to 20 to build a local consensus set.

[0102] Specific experiments and analysis:

[0103] The experiments for the examples of this invention mainly test the performance of the baseline network (GeoTransformer) and the network improved by the angle consistency error outlier pair removal method proposed in this invention (denoted as Outlier Removal_Patch-to-Point, OR_P2P) on the above dataset.

[0104] The OR_P2P network using the proposed method was compared with existing state-of-the-art registration methods (including FCGF, D3Feat, Predator, CoFiNet, GeoTransformer, RIGA, etc.). Indoor scene comparisons on 3DMatch and 3DLoMatch: As shown in Table 1, on the 3DMatch dataset, compared to the baseline GeoTransformer, the proposed method improved the registration recall (RR) from 91.8% to 92.6% and the inlier rate (IR) from 70.8% to 76.3%. The significant improvement in the inlier rate indicates that the proposed method effectively eliminated false matches. On the low-overlap 3DLoMatch dataset, OR_P2P achieved a registration recall of 74.9%, outperforming GeoTransformer (74.0%) and RIGA (65.1%), demonstrating the robustness of the method in low-overlap scenes.

[0105] Table 1. Comparison of registration results of the method of the present invention in 3DMatch, 3DLoMatch, and KITTI.

[0106]

[0107] Table 2 Comparison of registration results of the method of the present invention on ModelNet40 and ModelLoNet

[0108]

[0109] On the KITTI dataset, OR_P2P achieves a relative translation error (RTE) of 6.2 cm, which is lower than GeoTransformer's 6.8 cm and RIGA's 13.5 cm. This demonstrates that the angle consistency constraint is also effective in sparse, large-scale outdoor scenes, providing more accurate pose estimation. Table 2 shows a comparison of this invention with other methods on the ModelNet40 dataset: On the ModelNet40 dataset, OR_P2P achieves lower relative rotation error (RRE) and translation error (RTE), at 0.019° and 1.653 cm, respectively, which are superior to GeoTransformer's 0.024° and 2.160 cm.

[0110] As can be seen from Tables 1 and 2, the registration method proposed in this invention outperforms other methods in all aspects of the registration results on the datasets involved in the experiment.

[0111] Visualization Experiment:

[0112] To visually demonstrate the effectiveness of the method of this invention, multiple sets of visualization experiments were conducted. The registration details were visualized in a 3DMatch scene, such as... Figure 4As shown, in the indoor Lab and Kitchen scenes, GeoTransformer exhibits slight misalignment in some weakly textured areas (such as flat tabletops or walls). OR_P2P, with its outlier removal module, successfully eliminates these mismatches, resulting in a final registration result that is closer to the true value in detail.

[0113] Experimental results show that on the standard 3DMatch dataset, compared to the baseline method (GeoTransformer), the proposed method improves the registration recall (RR) from 91.8% to 92.6% and the inlier rate (IR) from 70.8% to 76.3%. On the KITTI dataset, the relative translation error (RTE) is reduced from 6.8 cm to 6.2 cm. This invention effectively improves registration accuracy while maintaining computational efficiency, verifying the superiority of angle consistency constraints.

[0114] Finally, it should be noted that the above examples of the present invention are merely illustrative and not intended to limit the implementation of the invention. Although the applicant has described the present invention in detail with reference to preferred embodiments, those skilled in the art can make other variations and modifications based on the above description. It is impossible to exhaustively list all possible implementations here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A two-stage point cloud registration method based on angle consistency constraints, characterized in that: Includes the following steps: 1) Coarse matching: Input the source point cloud and target point cloud to be registered into the neural network for downsampling and feature extraction, calculate the feature correlation between superpoints of the source point cloud and target point cloud, and select the top several superpoint pairs with the highest correlation to form the initial superpoint matching pair set; 2) Constructing a first-order angular similarity matrix: In the initial set of superpoint matching pairs, for any two pairs of matching points, a third reference matching point is introduced, and triangles are constructed in the source point cloud and the target point cloud based on the three points respectively; using the rotation invariance of the vector angle under rigid body transformation, the difference of the angle between the corresponding edge vectors is calculated, and the difference of the angle is converted into a similarity score to construct a first-order angular similarity matrix that reflects the degree of geometric compatibility between matching pairs; 3) Construct a second-order similarity matrix: Binarize the first-order angular similarity matrix, count the number of adjacent matching pairs that are compatible in the global scope for each pair of matching pairs, and transform the local first-order angular consistency into a second-order similarity matrix that reflects the global geometric distribution consistency. 4) Seed selection and consensus set construction: Spectral decomposition is performed on the binarized first-order angular similarity matrix to obtain the initial confidence level, and high-confidence seed matching pairs with uniform spatial distribution are selected. For each seed matching pair, search for its nearest neighbor matching pair in the second-order similarity matrix to construct a local consensus set; 5) Local Spectral Matching and Transformation Estimation: The weights of each point in the local consensus set are calculated using the spectral matching method, and weighted singular value decomposition is performed based on these weights to solve for multiple candidate rigid body transformation matrices; 6) Optimal transformation screening and exterior point elimination: The candidate rigid body transformation matrix is ​​used to perform residual verification on the initial superpoint matching pair set, and the candidate rigid body transformation matrix with the most interior points is selected as the optimal transformation. Based on this, all incorrect superpoint matching pairs that do not conform to the transformation are eliminated from the initial superpoint matching pair set, and the correct superpoint matching pairs are retained. 7) Fine matching: The retained correct superpoint matching pairs are expanded into neighborhood blocks. Local dense point matching is performed within the neighborhood blocks. Finally, a local to global weighted singular value decomposition iterative strategy is adopted to calculate the final high-precision rigid body transformation matrix and obtain the final point cloud registration result.

2. The two-stage point cloud registration method based on angle consistency constraints according to claim 1, characterized in that, Step 1) The specific implementation steps are as follows: 1.1) Downsampling and feature extraction: Perform multi-level downsampling on the source point cloud and the target point cloud to obtain the dense point set and superpoint set of the source point cloud and the target point cloud respectively, and extract the corresponding dense point features and superpoint features. 1.2) Geometric structure embedding construction: superpoints in the superpoint sets of the source point cloud and the target point cloud. Select k nearest neighbor superpoints to form a set For sets Two superpoints in and ,calculate and The Euclidean distance between them, and and Its neighboring super point The three angles formed Among them, the nearest super point The distance and angle are mapped to high-dimensional features using sine and cosine functions, and the distance embedding is calculated using the following formula. and angle embedding : In the formula and It is a sensitivity parameter for controlling changes in distance and angle; Geometric embeddings are computed by aggregating pairwise distance embeddings and angle embeddings. : in and These are for distance embedding. and angle embedding The projection matrix; 1.3) Attention Mechanism Feature Interaction: Construct a geometric self-attention module, use the embedded features of the geometric structure to correct the attention weights, and learn the global correlation between features inside a single point cloud and the geometric space; construct a feature-based cross-attention module to perform bidirectional feature interaction between the source point cloud and the target point cloud; alternately stack the geometric self-attention module and the cross-attention module to output hybrid features; 1.4) Superpoint matching: Calculate the Gaussian correlation matrix of the mixed features of the source point cloud and the target point cloud, and select the top few matching pairs with the highest correlation scores to form the initial set of superpoint matching pairs.

3. The two-stage point cloud registration method based on angle consistency constraints according to claim 1, characterized in that, The method for constructing the first-order angular similarity matrix in step 2) is as follows: 2.1) First, randomly select several matching pairs from the initial superpoint matching pair set to construct the baseline matching pair set M; 2.2) For any two matching pairs i and j whose similarity is to be calculated in the initial superpoint matching pair set, randomly select a matching pair from the benchmark matching pair set M as the benchmark matching pair m for this calculation; Extract the source points corresponding to matching pair i, matching pair j, and benchmark matching pair m in the source point cloud, and the target points corresponding to them in the target point cloud, respectively; In the source point cloud, the source points of matching pair i are connected to the source points of the reference matching pair m and the source points of matching pair j to construct two source vectors. and ; In the target point cloud, two target vectors are constructed by connecting the target points of the baseline matching pair m and the target points of the matching pair j with the target points of the matching pair i. and ; Calculate the two vectors constructed in the source point cloud and The included angle and the corresponding vector in the target point cloud. and The included angle ; Calculate the absolute value of the difference between the angles between two sets of vectors. : ； The first-order similarity values ​​of matching pair i and matching pair j are calculated using a monotonically decreasing function. : ； in, It is a linear rectified function; 2.3) Keeping the matching pair i unchanged, repeat step 2.2), traverse all matching pairs in the initial superpoint matching pair set, and obtain the first-order similarity value of matching pair i and all matching pairs including itself; 2.4) Repeat steps 2.2)-2.3), traverse the initial superpoint matching pair set, calculate the first-order similarity value of each matching pair and all matching pairs including itself, thereby obtaining the first-order similarity values ​​of all matching pairs in the initial superpoint matching pair set and constructing the first-order angular similarity matrix. .

4. The two-stage point cloud registration method based on angle consistency constraints according to claim 3, characterized in that, Step 3) The method for constructing the second-order similarity matrix is ​​as follows: set an angle threshold. ;like Then determine that matching pair i and matching pair j are geometrically compatible, let ; Otherwise, determine that matching pair i and matching pair j are incompatible, and let In step 3), construct a second-order similarity matrix. The specific formula is: ； in, The total number of matching pairs in the initial superpoint matching pair set; this formula means that the number of third matching pairs k that are mutually compatible are counted as the second-order similarity value only if matching pair i and matching pair j are compatible with themselves.

5. The two-stage point cloud registration method based on angle consistency constraints according to claim 1, characterized in that, The seed selection method described in step 4) is as follows: perform exponential iteration on the binarized first-order angular similarity matrix to solve for the principal eigenvector, and use the element values ​​of the principal eigenvector as the initial inlier probability of each matching pair; perform non-maximum suppression within a preset spatial radius R, retain the matching pair with the highest local inlier probability as the seed, and suppress the matching pair with lower probability in the neighborhood, thereby selecting a set of seed matching pairs with uniform spatial distribution and high confidence.

6. The two-stage point cloud registration method based on angle consistency constraints according to claim 1, characterized in that, Step 5) specifically involves: 5.1) Constructing a local graph: Treat the matching pairs in the local consensus set as nodes, and the second-order similarity values ​​between matching pairs as edge weights, thereby constructing a local graph based on the local consensus set; 5.2) Spectral decomposition: Perform eigenvalue decomposition on the adjacency matrix of the local graph, and take the principal eigenvector as the inlier probability weight of each matching pair in the local consensus set. 5.3) Weighted Singular Value Decomposition: The coordinates of point pairs in the local consensus set are weighted using the aforementioned interior point probability weights, and the candidate rotation matrix is ​​solved through singular value decomposition. Translation vector This yields multiple candidate rigid body transformation matrices.

7. The two-stage point cloud registration method based on angle consistency constraints according to claim 1, characterized in that, The specific implementation method of step 6) is as follows: traverse all candidate rigid body transformation matrices, calculate the residuals of all matching pairs in the initial set of superpoint matching pairs under the transformation, count the number of inliers with residuals less than the distance threshold, and select the transformation with the most inliers as the best transformation. Retain the matching pairs in the initial set of superpoint matching pairs whose residuals are less than the threshold under the optimal transformation as correct superpoint matching pairs, and discard the rest of the matching pairs.

8. The two-stage point cloud registration method based on angle consistency constraints according to claim 1, characterized in that, The specific implementation method of step 7 is as follows: expand the correct superpoint matching pairs retained in step 6) into local neighborhood block matching pairs centered on the superpoints; extract the features and coordinates of dense points within the neighborhood blocks and input them into the dense point matching module for dense point matching; use weighted singular value decomposition to calculate the correspondence of dense points within the neighborhood blocks; based on the correspondence of all dense points, perform weighted singular value decomposition again to obtain the final rigid body transformation matrix.

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