Low-overlapping curved surface point cloud registration method based on improved GeoTransform

Abstract

The invention belongs to the technical field of point cloud registration, and particularly relates to a low-overlapping curved surface point cloud registration method based on an improved GeoTransform. The method comprises the following steps: firstly, collecting point cloud data, and generating a source point cloud and a target point cloud according to the collected point cloud data; then, a point cloud registration model is constructed based on GeoTransform, and the point cloud registration model comprises a feature extraction module, a high-richness geometric feature embedding layer, an over-point matching module, a point matching module and a node-oriented maximum clique search registration module; the high-richness geometric feature embedding layer is used for embedding distance, angle and normal information of the point pairs to obtain a distance embedding vector, an angle embedding vector and a normal embedding vector; carrying out weighted fusion on the distance embedding vector, the angle embedding vector and the normal embedding vector to obtain a position embedding vector of the point pair; the position embedding vectors of all the point pairs form position embedding features, and then the position embedding features of the lowest-resolution source point cloud and the target point cloud are extracted; the node-oriented maximum clique search registration module models the point correspondence into a compatibility graph. According to the method, the fine geometric structure of the object is extracted, mismatching is reduced, and the registration precision of the low-overlapping point cloud is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of point cloud registration, and in particular relates to a low-overlap surface point cloud registration method based on an improved GeoTransformer. Background Art

[0002] Aircraft are used in a complex environment, and the coating is easily damaged, which causes its performance in absorbing radar signals to deteriorate. Therefore, the coating needs to be inspected regularly. Coating inspection based on optical imaging technology requires the acquisition of point cloud data. Since the sensor can only capture scanned point clouds within a limited field of view, it is necessary to generate point cloud data for large 3D scenes through registration. Point cloud registration is actually estimating the transformation matrix between the source point cloud and the target point cloud. The transformation matrix can be used to merge partial point clouds of the same 3D scene or object into a complete 3D point cloud. For aircraft surface point clouds, capturing geometric features including shape, volume, and position not only helps to further analyze coating quality and detect the location and size of defects, but also can use the reconstructed model for additive repair and path planning for terahertz detection.

[0003] With the development of deep learning technology, neural networks are used to extract point correspondences between two point clouds, and robust estimators (such as RANSAC) are used based on point correspondences to calculate the alignment transformation matrix. Most registration methods based on point correspondences rely on key point detection. However, it is challenging to detect repeatable key points across two point clouds, especially when the overlapping area of ​​the two point clouds is small. Key point detection methods assume that key points are invariant under arbitrary rigid transformations. Artificially designed key point detectors such as ISS, Harris3D, and SIFT3D can usually detect edge points and corner points, and perform well on small-scale and high-quality datasets, but cannot perform poorly on high-noise and large-scale real datasets. The key point detector based on deep learning does not learn feature descriptors at key points. Although it can extract points in salient areas, the quality of feature matching cannot be guaranteed. In the early days, there were many manual local feature descriptors used to describe features at key points, such as PFH, FPFH, SHOT, RoPS, etc. These methods performed well on small-scale datasets, all due to artificially designed low-level features, so they have poor robustness and insufficient feature description capabilities. Based on the availability of large-scale labeled 3D point cloud datasets, methods such as 3DMatch, CGF, PerfectMatch, FCGF, and DIP have achieved outstanding results in learning better local features.

[0004] GeoTransformer is a Transformer-based point cloud registration network that uses kernel-based point convolution to extract point features, resulting in the learned features not being rotationally invariant. Position encoding based on relative distance and relative angle helps the network obtain global structural information of the point cloud, significantly improving the registration accuracy. However, since the area of ​​the surface is relatively large relative to the field of view of the sensor, smooth and flat surfaces with small texture and curvature or no curvature may be encountered during the point cloud acquisition process. The acquired point cloud data lacks obvious geometric and texture features, and most of them are repeated geometric structures, making it difficult to distinguish different parts, which is very likely to cause registration failure. At the same time, since the two frames of point cloud data collected by the sensor are obtained from different positions and angles, the two frames of point cloud data have low overlap and different relative density features, which leads to the problem of difficult feature matching. GeoTransformer still has the problem of difficult feature matching for point clouds with low overlap and different relative density, so multi-view point cloud registration for large 3D scenes is still a challenging task. Summary of the invention

[0005] In view of the deficiencies in the prior art, the technical problem that the present invention intends to solve is to provide a low-overlap surface point cloud registration method based on an improved GeoTransformer.

[0006] The present invention solves the technical problem by adopting the following technical solution:

[0007] A low-overlap surface point cloud registration method based on improved GeoTransformer includes the following steps:

[0008] Step 1: Collect point cloud data, and generate source point cloud and target point cloud from the collected point cloud data;

[0009] Step 2: Build a point cloud registration model based on GeoTransformer. The point cloud registration model includes feature extraction module, high-richness geometric feature embedding layer, superpoint matching module, point matching module and node-guided maximum clique search registration module; the feature extraction module extracts features from the source point cloud and the target point cloud, and the intermediate layer of the feature extraction module outputs the lowest resolution source point cloud. and target point cloud The high-richness geometric feature embedding layer is used to extract the position embedding features of the lowest resolution source point cloud and the position embedding features of the lowest resolution target point cloud Given the lowest resolution source point cloud Any pair of points in and point and The distance between Calculate the point pair by formula (1) and The distance embedding vector

[0010]

[0011] In the formula, Point pair and The distance embedding vector The odd and even columns of d is a hyperparameter;

[0012] Pick Point Neighbors of Calculation Point and Line and point and The angle between the straight lines ∠(Δ x，i , Δ j，i ), Calculate the point pair by formula (2) and The angle embedding vector

[0013]

[0014] In the formula, Point pair and The angle embedding vector The odd and even columns of a is a hyperparameter;

[0015] Assume n i 、n j They are points and The normal vector of the point pair and The local coordinate system uvw is:

[0016]

[0017] According to formula (4), the point pair is calculated and The normal feature β i，j ,φ i，j and θ i,j :

[0018]

[0019] The point pair is calculated by the following formula and The three normal embedding vectors

[0020]

[0021]

[0022] In the formula, They are the normal embedding vectors The odd and even columns of They are the normal embedding vectors The odd and even columns of They are the normal embedding vectors The odd and even columns of l , σ m , σ n These are all hyperparameters;

[0023] According to formula (8), the distance embedding vector, angle embedding vector and normal embedding vector are weighted fused to obtain the point pair and The position embedding vector r i，j ;

[0024]

[0025] Where W L , W M , W N , W D , W A are all learnable weight matrices, Yes The set of neighboring points of ;

[0026] The position embedding vectors of all point pairs in the lowest resolution source point cloud constitute the position embedding features of the lowest resolution source point cloud Similarly, the position embedding feature of the lowest resolution target point cloud is obtained

[0027] Step 3: Train the point cloud registration model and use the trained point cloud registration model for the registration of low-overlap surface point clouds.

[0028] Furthermore, the node-guided maximal clique search and registration module models the global dense point correspondence obtained by the point matching module as a compatibility graph. The compatibility graph consists of nodes and edges connecting nodes, and nodes represent point pairs. Definition: A clique is a subset of the compatibility graph, and there is an edge between any two nodes. A clique that cannot be expanded by adding any more nodes is called a maximal clique. The Bron-Kerbosch algorithm is used to find all maximal cliques in the compatibility graph, and the weight of each maximal clique is calculated according to formula (12):

[0029]

[0030] In the formula, It is a maximal group C g The weight of Represents the maximum clique C g In the edge set of f The weight of

[0031] The maximum clusters are screened according to their weights. If a node is included in multiple maximum clusters, only the maximum cluster with the largest weight is retained, and the duplicate maximum clusters are deleted to obtain the retained maximum clusters. The top K maximum clusters with large weights are selected from the retained maximum clusters, and the optimal rigid transformation matrix is ​​estimated using the SVD algorithm.

[0032] Furthermore, the modeling process of the compatibility graph is:

[0033] According to formula (9), calculate the point pair c i With c j The rigid distance between:

[0034]

[0035] In the formula, S dist (c i , c j ) is a point to c i With c j The rigid distance between is a point of the source point cloud, is a point of the target point cloud;

[0036] The compatibility score of the point pair group is calculated according to formula (10):

[0037]

[0038] In the formula, S cmp (c i , c j ) is a point pair group (c i , c j ) compatibility score, d cmp is the distance parameter;

[0039] If the point pair group (c i , c j ) has a compatibility score greater than the threshold t cmp , then point c i With c j The edge e ij , S cmp (c i , c j ) is the edge e ij The weight of each point pair group constitutes the weight matrix W of the first-order graph FOG ; Construct a second-order graph from the first-order graph, and the weight matrix W of the second-order graph SOG It is expressed as:

[0040] W SOG =W FOG ⊙(W FOG ×W FOG ) (11)

[0041] Where ⊙ represents element-by-element multiplication of matrices and × represents matrix multiplication.

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

[0043] (1) High-richness geometric feature embedding layer Based on the distance information and angle information of the original GeoTransformer embedded point pair, normal information is added, and normal information is fully utilized for feature encoding to enhance the geometric feature expression. Normal information describes the local orientation of the point cloud surface, which helps to accurately express the fine geometric structure of the object. Normal information can reflect whether the point cloud surface is smooth or has mutations. When the normal directions of adjacent points are very different, it usually indicates the edge of the surface or an uneven area. Therefore, adding normal information can better detect changes in the point cloud surface and capture important features such as edges. The high-richness geometric feature embedding layer can not only encode the high-level features of the point cloud, but also explicitly capture the internal geometric structure of the point cloud, the changes in the point cloud surface, and the geometric consistency between point clouds, thereby improving the registration accuracy in the absence of obvious geometric features.

[0044] (2) When the two adjacent frames of surface point clouds collected by the sensor are low-overlap point clouds, feature mismatching problems are prone to occur. Specifically, in the process of calculating the point correspondence, the non-overlapping parts produce correspondences, resulting in mismatches. The node-guided maximum clique search and registration uses the graph space to more accurately describe the correspondence between point pairs. In the process of maximum clique search and filtering, mismatched point pairs can be effectively eliminated, effectively improving the registration accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is the structural diagram of the point cloud registration model;

[0046] Figure 2 Schematic diagram of the high-richness geometric feature embedding layer;

[0047] Figure 3 This is the structural diagram of the super-point matching module;

[0048] Figure 4 This is the structural diagram of the point matching module;

[0049] Figure 5 Schematic diagram of the node-guided maximal clique search registration module;

[0050] Figure 6 Comparison of the registration results of different methods. DETAILED DESCRIPTION

[0051] Specific embodiments are given below in conjunction with the accompanying drawings. The specific embodiments are only used to illustrate the technical solutions of the present invention in detail and are not intended to limit the protection scope of the present application.

[0052] The present invention provides a low-overlap surface point cloud registration method based on an improved GeoTransformer (hereinafter referred to as the method, see Figures 1 to 6 ), including the following steps:

[0053] Step 1: Collect point cloud data, randomly rotate and translate the point cloud data; randomly generate a normal vector of a plane in the point cloud space, the plane passes through the origin of the spatial coordinate system and has a random direction, use the generated plane to crop the point cloud data to generate a source point cloud; similarly, generate a target point cloud.

[0054] Step 2: Build a point cloud registration model based on GeoTransformer;

[0055] like Figure 1 As shown in the figure, the point cloud registration model includes a feature extraction module, a highly detailed geometric embedding layer (HDGE), a superpoint matching module (Superpoint Matching Module), a point matching module (Point Matching Module) and a node-guided maximal cliques registration module (NMCRM).

[0056] The source point cloud and the target point cloud are input into the feature extraction module for feature extraction. The feature extraction module includes an encoder, a decoder, and an intermediate layer connecting the encoder and the decoder. Multiple kernel point convolution layers (KPCon v) to perform multi-level feature extraction, and obtain the final resolution source point cloud through the feature extraction module and target point cloud Its characteristics are expressed as and Represents the final resolution source point cloud The number of points, Represents the final resolution target point cloud The number of points, Represents the dimensions of the final resolution point cloud; the intermediate layer connecting the encoder and decoder outputs the lowest resolution source point cloud and target point cloud is regarded as a super point, and its characteristics are expressed as and Represents the lowest resolution source point cloud The number of points, Represents the lowest resolution target point cloud The number of points, Represents the dimensions of the lowest resolution point cloud.

[0057] like Figure 2 As shown in the figure, the high-richness geometric feature embedding layer designs a new geometric structure embedding to encode the rigid body invariant geometric structure of the super point, which is used to extract the position embedding features of the lowest resolution source point cloud. and the position embedding features of the lowest resolution target point cloud First, distance embedding is performed on point pairs, given the lowest resolution source point cloud Any pair of points in and point and The distance between According to i,j / σ d , calculate the point pair by formula (1) and The distance embedding vector

[0058]

[0059] In the formula, Point pair and The distance embedding vector The odd and even columns of , dt is the feature dimension; σ d is a hyperparameter that controls the sensitivity of distance changes;

[0060] Next, perform angle embedding on the point pairs; select the point Neighbors of Calculation Point and Line and point and The angle between the straight lines in according to Calculate the point pair by formula (2) and The angle embedding vector

[0061]

[0062] In the formula, Point pair and The angle embedding vector The odd and even columns of ; σa is a hyperparameter used to control the sensitivity of angle changes;

[0063] Then, the normal information of the point pairs is embedded; assuming n i 、n j They are points and The normal vector of the point pair and The local coordinate system uvw is:

[0064]

[0065] According to formula (4), the point pair is calculated and The normal feature β i，j ,φ i，j and θ i,j :

[0066]

[0067] According to β i，j / σ l ,φ i，j / σ m ,θ i,j / σ n , calculate the point pair through equations (5), (6) and (7) and The three normal embedding vectors

[0068]

[0069] In the formula, They are the normal embedding vectors The odd and even columns of They are the normal embedding vectors The odd and even columns of They are the normal embedding vectors The odd and even columns of σ l , σ m , σ n These are all hyperparameters used to control the sensitivity of normal feature changes;

[0070] Finally, the distance embedding vector, angle embedding vector and normal embedding vector are weighted fused to obtain the point pair and The position embedding vector r i，j , the calculation formula is as follows:

[0071]

[0072] Where W L , W M , W N , W D , are all learnable weight matrices, Yes The set of neighboring points of ;

[0073] Similarly, repeat the above process to obtain the position embedding vectors of the remaining point pairs in the lowest resolution source point cloud; the position embedding vectors of all point pairs in the lowest resolution source point cloud constitute the position embedding features of the lowest resolution source point cloud Similarly, the position embedding feature of the lowest resolution target point cloud is obtained

[0074] The high-richness geometric feature embedding layer explicitly encodes geometric information, making the point cloud matching with low overlap more robust. Therefore, post-processing does not rely on the RANSAC algorithm, thereby improving the registration rate.

[0075] like Figure 3 As shown in Figure 1, the super-point matching module includes a geometric self-attention block and a cross-attention block. The geometric self-attention block is used to learn the internal features of the point cloud, and the cross-attention block is used to learn the consistency of the internal features of different point clouds. The features of the lowest resolution source point cloud are Embedding features with position Addition, and the features of the lowest resolution target point cloud and position embedding features After addition, it is input into the super point matching module, and after the geometric self-attention block and the cross-attention block, the attention features of the lowest resolution source point cloud and target point cloud are obtained. and Attention Characteristics and After normalization, the Gaussian correlation coefficient matrix is ​​calculated In order to further suppress fuzzy matching, the Gaussian correlation coefficient matrix S is double normalized by equation (9) to obtain the normalized Gaussian correlation coefficient matrix According to the normalized Gaussian correlation coefficient matrix Select the first N point pairs with the largest Gaussian correlation coefficient as the matching results to obtain the super-point correspondence

[0076] like Figure 4 As shown, the super point correspondence relationship Input into the point matching module for point matching, extract point correspondence, and obtain global dense point correspondence

[0077] like Figure 5 As shown in Figure 2, compared with Euclidean space, graph space can more accurately describe point correspondence. The node-guided maximal clique search registration module converts the global dense point correspondence into Modeled as a compatibility graph, the point correspondence is represented by geometrically compatible point pairs and edges connecting the point pairs; specifically, according to the point pair c i With c j The rigid distance constraint between points is used to construct a first-order graph (FOG). The rigid distance between point pairs is calculated as follows:

[0078]

[0079] In the formula, S dist (c i , c j ) is a point to c i With c j The rigid distance between is a point of the source point cloud, is a point of the target point cloud;

[0080] The compatibility score of a point pair group is calculated based on the rigid distance between the point pairs:

[0081]

[0082] In the formula, S cmp (c i , c j ) is a point pair group (c i , c j ) compatibility score, d cmp is the distance parameter;

[0083] If the compatibility score of the point pair is greater than the threshold t cmp , then point c i With c j There is an edge e between ij , S cmp (c i , c j ) is the edge e ij The compatibility scores of each point pair group constitute the weight matrix W of the first-order graph FOG , since the compatibility graph is undirected, the weight matrix W of the first-order graph is FOG is symmetrical.

[0084] The second-order graph (SOG) is constructed from the first-order graph. The second-order graph is sparser and more conducive to searching for groups. The weight matrix W of the second-order graph is SOG The calculation formula is:

[0085] W SOG =W FOG ⊙(W FOG ×W FOG ) (11)

[0086] Among them, ⊙ represents element-by-element multiplication of matrices, and × represents matrix multiplication.

[0087] The compatibility graph is represented by G = (V, E), and the group is defined as: Clique C is a subset of the compatibility graph, and there is an edge between any two nodes. A clique that cannot be expanded by adding any more nodes is called a maximal clique. Usually, a maximal clique is a very strict constraint, which only focuses on the global consensus information in the graph. The maximal clique in this application relaxes the constraint and uses the maximal clique to mine more local graph information. First, the Bron-Kerbosch algorithm is used to find all maximal cliques in the compatibility graph to obtain the maximal clique set MC (maximal clique); then, the weights of each maximal clique in the maximal clique set are calculated. Given a maximal clique C g =(V g , E g ), C g ∈C,V g 、E g The maximal cluster C g The node set and edge set of the maximal clique C g Weight Calculated by the following formula:

[0088]

[0089] In the formula, Represents the maximum clique C g In the edge set off The weight of

[0090] Finally, the maximum clusters are screened according to the weights. A node may be included in multiple maximum clusters. Only the maximum cluster with the largest weight is retained, and then the repeated maximum clusters are deleted to obtain the retained maximum clusters. The number of retained maximum clusters is still very large. The first K maximum clusters with large weights are selected. The transformation estimation of the corresponding relationship is realized by the SVD algorithm. Its goal is to realize the rigid transformation matrix, maximize the objective function of formula (13), obtain the optimal rigid transformation matrix, and complete the point cloud registration. The objective function is as follows:

[0091]

[0092] Where R and t are the rotation matrix and translation vector between the source point cloud and the target point cloud, respectively; R* and t* are the estimated values ​​of the rotation matrix and translation vector; s(c i ) is the point pair c in the transformation estimation process i The score, c i ∈C, C is the set of point pairs, and U is the number of point pairs.

[0093] Step 3: Train the point cloud registration model and use the trained point cloud registration model for the registration of low-overlap surface point clouds.

[0094] Example

[0095] Parameter settings for the high-richness geometric feature embedding layer: σ d =0.02,σa=15°,σ l =0.35,σ m =0.27,σ n =0.3, initialize the point cloud registration model. Use PCL's NormalEstmation class to calculate the normal vector, using 20 nearest neighbor points. When searching for the maximum cluster, the lower limit of the cluster size is set to 3, and no upper limit is defined. The k=2500 in the mutual top-k selection of the point matching module controls the number of point correspondences; the maximum number of iterations (epoch) is 300, the learning rate is set to 0.001, and the weight decay of the regularization term is 10 -6 .

[0096] Following traditional training experience, an evaluation criterion is used, which regards the inlier ratio (IR) as the proportion of inlier matches in all assumed point matches, and the distance between two points less than 5cm is considered as inliers. The training set is input into the point cloud registration model for training, and the trained point cloud registration model is verified by the validation set, and the model parameters are optimized by back propagation. After the source point cloud and the target point cloud to be registered are normalized, they are input into the trained point cloud registration model for registration, and the registration results are evaluated by three indicators: mean square error (MSE), mean absolute error (MSE) and root mean square error (RMSE).

[0097] In order to verify the effectiveness of the method of the present invention, the method of the present invention is compared with the common point cloud registration method. The test results are shown in Figure 6 and Table 1.

[0098] Table 1 Comparison of registration results of different methods

[0099] method MSE(R) RMSE(R) MAE(R) MSE(t) RMSE(t) MAE(t) <![CDATA[3DSN [1] ]]> 15.421329 3.927 2.2647 0.001193 0.034539 0.023865 <![CDATA[FCGF [2] ]]> 12.556639 3.5435 1.805842 0.001072 0.032741 0.002132 <![CDATA[D3Feat [3] ]]> 9.894479 3.144549 1.505842 0.000017 0.004087 0.002195 <![CDATA[Predator [4] ]]> 7.1486716 2.6737 1.355647 0.0334 0.18275 0.0145 <![CDATA[CoFiNet [5] ]]> 5.619744 2.3706 0.8006 0.00032041 0.0179 0.0035 <![CDATA[GeoTransformer [6] ]]> 1.51757 1.2319 0.7973 0.02552 0.1563 0.0135 Ours 0.95179 0.97565 0.4763 0.000084 0.009175 0.005842

[0100] It can be seen from the table that the method of the present invention is superior to other common point cloud registration methods for aviation coating surface point cloud registration, which verifies the effectiveness of the method of the present invention.

[0101] Aiming at the features of low-overlap point clouds, the method of the present invention proposes a high-richness geometric feature embedding layer based on GeoTransformer, which makes full use of normal information for feature encoding and enhances the expression of geometric features. Normal information describes the local orientation of the point cloud surface, which helps to accurately express the fine geometric structure of the object. Therefore, the high-richness geometric feature embedding layer can not only encode the high-level features of the point cloud, but also explicitly capture the internal geometric structure of the point cloud, the surface changes of the point cloud, and the geometric consistency between the point clouds, thereby improving the registration accuracy in the absence of obvious geometric features. In addition, the node-guided maximum clique search registration can more accurately depict the correspondence between point pairs using graph space, and can effectively eliminate mismatched point pairs during the maximum clique search and filtering process, effectively improving the registration accuracy and efficiency.

[0102] The sources of the above common point cloud registration methods are as follows:

[0103] [1].Gojcic Z,Zhou C,Wegner J D,et al.The perfect match:3d point cloudmatching with smoothed densities[C] / / Proceedings of the IEEE / CVF conferenceon computer vision and pattern recognition.2019:5545-5554.

[0104] [2].Choy C,Park J,Koltun V.Fully convolutional geometric features[C] / / Proceedings of the IEEE / CVF international conference on computervision.2019:8958-8966.

[0105] [3].Bai X,Luo Z,Zhou L,et al.D3feat:Joint learning of dense detectionand description of 3d local features[C] / / Proceedings of the IEEE / CVFconference on computer vision and pattern recognition.2020:6359-6367.

[0106] [4].Huang S,Gojcic Z,Usvyatsov M,et al.Registration of 3D PointClouds with Low Overlap[C] / / Proceedings Computer Vision and PatternRecognition.2021:1-60.

[0107] [5].Yu H,Li F,Saleh M,et al.Cofinet:Reliable coarse-to-finecorrespondences for robust pointcloud registration[J].Advances in NeuralInformation Processing Systems,2021,34:23872-23884.

[0108] [6]. Qin Z, Yu H, Wang C, et al. Geotransformer: Fast and robust pointcloud registration with geometric transformer [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2023, 45(8): 9806-9821.

[0109] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A low-overlap surface point cloud registration method based on improved GeoTransformer, characterized in that: The method comprises the following steps: Step 1: Collect point cloud data, and generate source point cloud and target point cloud from the collected point cloud data; Step 2: Build a point cloud registration model based on GeoTransformer. The point cloud registration model includes feature extraction module, high-richness geometric feature embedding layer, superpoint matching module, point matching module and node-guided maximum clique search registration module; the feature extraction module extracts features from the source point cloud and the target point cloud, and the intermediate layer of the feature extraction module outputs the lowest resolution source point cloud. and target point cloud The high-richness geometric feature embedding layer is used to obtain the position embedding features of the lowest resolution source point cloud and the position embedding features of the lowest resolution target point cloud Given the lowest resolution source point cloud Any pair of points in and point and The distance between Calculate the point pair by formula (1) and The distance embedding vector In the formula, Point pair and The distance embedding vector The odd and even columns of d t is the feature dimension, σ d is a hyperparameter; Pick Point Neighbors of Calculation Point and Line and point and The angle between the straight lines Calculate the point pair by formula (2) and The angle embedding vector In the formula, Point pair and The angle embedding vector The odd and even columns of a is a hyperparameter; Assume n i 、n j They are points and The normal vector of the point pair and The local coordinate system uvw is: According to formula (4), the point pair is calculated and The normal feature β i,j ,φ i,j and θ i,j : The point pair is calculated by the following formula and The three normal embedding vectors In the formula, They are the normal embedding vectors The odd and even columns of They are the normal embedding vectors The odd and even columns of They are the normal embedding vectors The odd and even columns of l , σ m , σ n These are all hyperparameters; According to formula (8), the distance embedding vector, angle embedding vector and normal embedding vector are weighted fused to obtain the point pair and The position embedding vector r i,j ; Where W L , W M , W N , W D , W A are all learnable weight matrices, Yes The set of neighboring points of ; The position embedding vectors of all point pairs in the lowest resolution source point cloud constitute the position embedding features of the lowest resolution source point cloud Similarly, the position embedding feature of the lowest resolution target point cloud is obtained Step 3: Train the point cloud registration model and use the trained point cloud registration model for the registration of low-overlap surface point clouds.

2. The low-overlap surface point cloud registration method based on improved GeoTransformer according to claim 1, characterized in that: The node-guided maximal clique search registration module models the global dense point correspondence obtained by the point matching module as a compatibility graph. The compatibility graph consists of nodes and edges connecting nodes, and nodes represent point pairs. Definition: A clique is a subset of the compatibility graph, and there is an edge between any two nodes. A clique that cannot be expanded by adding any more nodes is called a maximal clique. Use the Bron-Kerbosch algorithm to find all maximal cliques in the compatibility graph, and calculate the weight of each maximal clique according to formula (12): In the formula, It is a maximal group C g The weight of Represents the maximum clique C g In the edge set of f The weight of The maximum clusters are screened according to their weights. If a node is included in multiple maximum clusters, only the maximum cluster with the largest weight is retained, and the duplicate maximum clusters are deleted to obtain the retained maximum clusters. The top K maximum clusters with large weights are selected from the retained maximum clusters, and the optimal rigid transformation matrix is ​​estimated using the SVD algorithm.

3. The low-overlap surface point cloud registration method based on improved GeoTransformer according to claim 2, characterized in that: The modeling process of the compatibility graph is: According to formula (9), calculate the point pair c i With c j The rigid distance between: In the formula, S dist (c i ,c j ) is a point to c i With c j The rigid distance between is a point of the source point cloud, is a point of the target point cloud; The compatibility score of the point pair group is calculated according to formula (10): In the formula, S cmp (c i ,c j ) is a point pair group (c i ,c j ) compatibility score, d cmp is the distance parameter; If the point pair group (c i ,c j ) has a compatibility score greater than the threshold t cmp , then point c i With c j The edge e ij , S cmp (c i ,c j ) is the edge e ij The weight of each point pair group constitutes the weight matrix W of the first-order graph FOG ; Construct a second-order graph from the first-order graph, and the weight matrix W of the second-order graph SOG It is expressed as: IN SOG =In FOG ⊙(In FOG ×W FOG ) (11) Where ⊙ represents element-by-element multiplication of matrices and × represents matrix multiplication.

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