Multi-geometry based hybrid state-aware point cloud registration method

Abstract

The application relates to the field of point cloud registration, in particular to a mixed state perception point cloud registration method based on multivariate geometry, which comprises the following steps executed in sequence: S1: acquiring a source point cloud and a reference point cloud; S2: inputting the source point cloud and the reference point cloud into a feature extraction network for feature extraction, acquiring hyperpoints and corresponding hyperpoint rotation equivariant features and hyperpoint rotation invariant features; S3: inputting each hyperpoint rotation invariant feature into a state space context aggregation module for feature interaction, obtaining corresponding mixed features, calculating two mixed features, and obtaining a hyperpoint matching score matrix; S4: performing spatial diversity sampling on the hyperpoint matching score matrix to obtain corresponding dense point matching score matrices; S5: obtaining a candidate point pair set from each dense point matching score matrix; S6: performing length consistency check to filter out false matches; S7: acquiring a candidate transformation hypothesis of each matching point pair in the candidate point pair set; S8: outputting a final transformation matrix; and the quality of point cloud registration is improved.

Description

Technical Field

[0001] This invention relates to the field of point cloud registration, and more specifically to a hybrid state-aware point cloud registration method based on multi-geometry. Background Technology

[0002] In complex indoor scenarios, the acquisition space differs from a single, isolated object structure. It commonly exhibits areas of confusion, such as white walls, symmetrical furniture, and similar point cloud distributions, often involving single geometric features. Furthermore, the inevitable drastic viewpoint shifts during mobile robot inspections or human scanning operations lead to low overlap and large-scale pose variations in point clouds between adjacent frames. Achieving stable and high-precision 3D point cloud registration under these complex conditions is a key challenge for high-quality 3D reconstruction. Traditional point cloud registration algorithms (such as ICP) are essentially local optimization strategies, typically requiring a good initial pose of the input point cloud and failing to effectively handle large rotations between two frames. To overcome the dependence of traditional algorithms on initial values, feature matching methods based on deep learning have gradually become the mainstream solution. However, existing deep learning networks learn local structures only through coordinate information. This single feature extraction mechanism is susceptible to interference from spatial rotation and pose, and struggles to distinguish geometrically similar regions. Its discriminative ability is insufficient, easily leading to mismatches in confusing areas such as flat walls or repetitive symmetrical spaces, resulting in registration failure. Summary of the Invention

[0003] The purpose of this invention is to provide a hybrid state-aware point cloud registration method based on multi-geometry suitable for complex indoor scenes.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: The hybrid state-aware point cloud registration method based on multivariate geometry includes the following steps performed sequentially: S1: Use a 3D acquisition device to scan the scene or object, and obtain two partially overlapping point clouds for any scene or object, one of which is the source point cloud and the other is the reference point cloud. S2: Input the source point cloud and the reference point cloud into the feature extraction network for feature extraction, and obtain the superpoints and corresponding rotational equivariant features of the source point cloud and the reference point cloud respectively. Two branches are used to process each superpoint and the corresponding rotational equivariant features. One branch constructs a local orthogonal coordinate system for each superpoint rotational equivariant feature through the Gram-Schmidt orthogonalization algorithm, and projects it to obtain the rotational invariant features of the superpoints corresponding to the source point cloud and the reference point cloud respectively. The other branch uses nearest neighbor upsampling and skip connections to distribute each superpoint rotational equivariant feature to high-resolution dense points and perform linear mapping, thereby obtaining the dense points and rotational equivariant features of the dense points corresponding to the source point cloud and the reference point cloud respectively. The rotational equivariant features of the dense points are converted into rotational invariant features of the dense points through the Gram-Schmidt orthogonalization algorithm. S3: Input each superpoint and its corresponding rotation-invariant feature into the state space context aggregation module for feature interaction, obtain the hybrid features corresponding to the source point cloud and the reference point cloud respectively, calculate the Gaussian correlation matrix of the two hybrid features and perform double normalization to obtain the superpoint matching score matrix. S4: Perform spatial diversity sampling on the superpoint matching score matrix: Add random noise perturbation to the superpoint matching score matrix to obtain the superpoint score matrix. Select a first preset number of matching superpoint pairs with the highest superpoint scores in the superpoint score matrix. Using the matching superpoint pairs as the center, use the K-nearest neighbor algorithm to extract a second preset number of adjacent dense points from the dense points obtained in the second branch of step S2 and obtain the corresponding dense point coordinates. Construct a superpoint local segment of the source point cloud and a superpoint local segment of the reference point cloud. Calculate the feature association score matrix between the corresponding dense points in the two superpoint local segments. Normalize each feature association score matrix through bidirectional Softmax and combine the saliency scores at both ends to obtain the corresponding dense point matching score matrix. S5: Construct a candidate point pair set for generating candidate transformation hypotheses and a verification point pair set for verifying the generated hypotheses using each dense point matching score matrix. Flatten each dense point matching score matrix to the global space. Use the global Top-k algorithm to select the top-ranking dense point pairs in the flattened dense point matching score matrix to obtain the candidate point pair set. Use the local bidirectional Top-k algorithm to filter in each dense point matching score matrix. At the same time, set a confidence threshold and extract all matching point pairs whose matching scores are greater than the confidence threshold and whose matching scores rank in the top three in both the row and column directions of the dense point matching score matrix to obtain the verification point pair set. S6: Using the dense point rotation isomorphic features, perform a modulus consistency check on the dense points in the candidate point pair set to filter out incorrect matches. Calculate the L2 norm of the dense point rotation isomorphic features of the source point cloud and the reference point cloud using the following formula, and calculate their relative difference ratio. : ; in, and These represent the source point cloud and the reference point cloud, respectively. This represents the rotational variation of the source point cloud dense points in the h-th matching point pair in the candidate point pair set. This represents the rotational variation feature of the reference point cloud dense points in the h-th matching point pair in the candidate point pair set; If the relative difference ratio If the threshold is exceeded, the match is determined to violate the modulus invariance constraint of rigid transformation and is removed from the candidate point pair set. S7: Obtain candidate transformation hypotheses for each matching point pair in the candidate point pair set after modulus consistency check through singular value decomposition: ; in, This represents the candidate transformation hypothesis calculated for the h-th matching point pair in the candidate point pair set. This hypothesis is represented as a candidate transformation matrix in the specific spatial calculation. Rotation is calculated based on rotational isomorphism. , This represents the candidate space rotation matrix calculated for the h-th matching point pair in the candidate point pair set, and the translation calculated based on the coordinates. , This represents the candidate spatial translation vector calculated for the h-th matching point pair in the candidate point pair set. The coordinates of the dense points on the reference point cloud side in the current matched point pair. These are the coordinates of the dense points on the source point cloud side in the current matched point pair. The Frobenius norm of a matrix is ​​used to measure the overall spatial error between characteristic matrices, thereby obtaining the candidate transformation hypothesis pool. , The number of hypotheses; S8: Utilize the candidate transformation hypothesis pool For each candidate transformation hypothesis, a candidate transformation matrix is ​​used to perform a spatial transformation on the source point cloud in the verification point pair set. The spatial residual between the transformed source point cloud and the reference point cloud is calculated, and the proportion of matching points whose spatial residual is less than a preset distance threshold is counted as the inlier rate of the candidate transformation matrix. The candidate transformation matrix with the highest inlier rate is selected as the optimal initial transformation matrix. With this optimal initial transformation matrix Starting from the set of verification points, a weighted Procrustes iterative refinement is performed a predetermined number of times; let the candidate transformation matrix of the u-th iteration be... The spatial residuals of each matching point pair are recalculated based on this matrix, and an annealing smoothing parameter that decays linearly with the number of iterations is introduced. Combining spatial residuals and annealing smoothing parameters, a Gaussian kernel function is used. A Gaussian soft weight is assigned to each matching point pair. The Gaussian soft weight is then multiplied by the corresponding element in the dense point matching score matrix to construct a joint weight. Combined with the interior point mask generated by the preset distance threshold, the joint weight is used to perform weighted singular value decomposition on the verification point pair set to solve the following objective function to update the current transformation matrix:

[0005] in, This indicates the number of point pairs in the verification point pair set. This represents the dense point matching score of the v-th matching point pair in the verification point pair set. This represents the Gaussian soft weight of the current matching point pair in the u-th iteration. This represents the coordinates of the dense points on the source point cloud side of the currently matched point pair. This represents the coordinates of the dense points on the reference point cloud side of the currently matched point pair. This represents the preset distance threshold for determining interior points. The indicator function, combined with a preset distance threshold, represents the interior point mask; Repeat the weighted Procrustes iterative refinement until the preset number of iterations is reached, and output the final transformation matrix. .

[0006] Preferably, the feature extraction network in step S2 uses a rotationally equivariant convolution module as the feature extraction unit. The rotationally equivariant convolution module includes an explicit geometric feature extraction module, a geometric scalar encoding module, a geometric enhancement correlation module, and a geometrically guided dynamic convolution kernel module connected in sequence. The explicit geometric feature extraction module extracts the center points of the input point cloud. and its neighboring points in the neighborhood point set Calculate the covariance matrix of the neighborhood point set after decentralization. : ; in, Indicates the center point The number of neighboring points in the neighborhood point set. Represents the centroid of the neighborhood point set; For covariance matrix Singular Value Decomposition (SVD) is performed to explicitly obtain the geometric prior, and the right singular vector corresponding to the minimum singular value is extracted as the normal vector of the neighborhood point set. This is used to model the normal of the local tangent plane of the neighborhood point set, and the minimum singular value is directly used as the curvature intensity. ; This geometric scalar encoding module is used to encode the normal vector. Perform normalization processing, and calculate the normalized normal vector and the centroid direction vector of the neighborhood point set. The spatial dot product is used to obtain the projection scalar of the neighborhood point set along the normal vector direction. This projection scalar is then multiplied by the curvature intensity. Stitching along the channel dimension This transforms the abstract spatial distribution into an explicit geometric scalar descriptor with rotation invariance. This provides a strong geometric prior for the generation of subsequent convolutional kernel weights, using explicit geometric scalar descriptors. It is expressed by the following formula: ; in, Indicates channel-level splicing; This geometry-enhanced correlation module employs a correlation mapping network based on explicit geometric scalar descriptors. Perform dynamic weight calculation of the convolution kernel based on the center points of the input point cloud. and its neighboring points in the neighborhood point set Calculate the distance of each neighboring point relative to the center point of the point cloud. relative coordinates Calculate the relative coordinates with the centroid direction vector cross product vector The extended channel will use the relative coordinates centroid direction vector and the cross product vector Perform splicing to obtain rotationally variable spatial features. Vector neurons are used to extract the rotational isotropic spatial features. The implicit isovariant features are converted into rotation-invariant scalar features through a 2-norm modulo operation. These scalar features are then compared with the explicit geometric scalar descriptor. Channel-level concatenation is performed to obtain a rotation-invariant hybrid descriptor, which is then input into a lightweight relevance mapping network. The relevant weights are obtained through processing. The correlation weight It is expressed by the following formula: ; in, Represents a correlation mapping network. Represents a vector neuron. This represents the modulo operation of the 2-norm; Current center point Rotational equivariance features of all neighboring points within the neighborhood point set Input this geometry-guided dynamic convolution kernel module and use this relevance weight. For an internally initialized set of learnable weight shadow kernel points Perform dynamic assembly. This represents the m-th learnable weight shadow kernel point in the set of learnable weight shadow kernel points, thereby generating a dynamic convolution kernel. Using this dynamic convolution kernel Rotate the equivariant features of all neighboring points of the input. Perform weighted aggregation guided by geometric weights, ultimately at the center point. Output the updated rotational isomorphic features Rotational isomorphic features The formula is as follows: ; Updated rotational isomorphic features The features are used as input for subsequent rotationally equivariant convolutional modules; combined with point cloud downsampling and cascaded rotationally equivariant convolutional modules, the superpoint is finally output at the deepest layer of the feature extraction network. And the corresponding superpoint rotation equivariant features; The Gram-Schmidt orthogonalization algorithm is used to construct a local orthogonal coordinate system, and the corresponding rotation-invariant features of the hyperpoints are obtained by projecting the rotationally equivariant features onto them. .

[0007] Preferably, the state space context aggregation module includes a local geometric self-attention module, a context aggregation module, and a feature interaction cross-attention module; This local geometric self-attention module is used to exceed the input point for each input. Centered on the network, the KNN algorithm is used as the superpoint. The search build size is super-neighborhood point set For the j-th neighboring superpoint within this neighborhood... ,from Filter out except outside distance For the three nearest super-points, construct the corresponding subset of super-point neighborhoods. The Euclidean distance embedding between superpoints and the angular embedding between triples are calculated for aggregation projection. The geometric embedding of the source point cloud is expressed by the following formula. : ; in, and These represent multilayer perceptrons used to process relative distance and angular features, respectively, providing nonlinear representations. This represents the max pooling operation performed within a subset of points in the superpoint's neighborhood. Represents the sine position code. Representative Center Exceeds Points and the j-th neighborhood super point The distance between them Representative Center Exceeds Points Pointing to the x-th neighboring superpoint in the subset of superpoint neighborhoods The vector and the direction point to the j-th neighboring superpoint in the neighborhood set of the superpoint. The spatial angle formed by the vectors; Embed the geometry The first fusion feature of the source point cloud, injected as a relative position encoding into the self-attention mechanism, is represented by the following formula: ; in, Describe the feature fusion function operation of the local geometric self-attention module; Based on the self-attention structure, the network utilizes independent, learnable linear transformation matrices to transform the input superpoint rotation-invariant features. Mapped to content query matrix respectively Geometric query matrix The rotation-invariant features of all neighborhood superpoints in the neighborhood set corresponding to each input superpoint are linearly mapped and combined into a key matrix. and value matrix The geometry is embedded using another linear transformation matrix. Mapped to projected position vector All the above feature matrices are uniformly divided into h independent attention heads, each with a feature dimension of d. For each input superpoint, the feature and geometric attention scores between superpoints are calculated using the neighboring superpoints in its neighborhood set. The two scores are then added together and divided by a scaling factor. After normalization, the final attention weights are obtained. These attention weights are then used to perform a weighted summation of the value vectors of all neighboring superpoints, thereby obtaining the first fusion feature of the source point cloud. ; This context aggregation module uses state-space based Mamba with linear computational complexity to process a large number of input features, so as to achieve global awareness while avoiding the quadratic cost of Transformer. The context aggregation module includes two branches. One branch is used to sequentially apply layer normalization, linear layers, deep convolutional layers, and activation functions to the first fused feature. Processing is performed to obtain global state features with rich local contextual information. ; Another branch is used to obtain gated features through layer normalization, linear layers, and activation functions, employing selective state space modules and layer normalization sequentially to process the global state features. The process is performed to obtain intermediate state features. These intermediate state features are then multiplied by the gated features, linearly projected, and then fused with the first fused feature. Perform residual connections to obtain the second fused feature of the source point cloud. This process is represented by the following formula: ; ; in, Represents the SiLu activation function. Represents a one-dimensional depthwise convolution operation. This represents a linear projection transformation operation. Representative layer normalization operation, Represents a discretized selective state-space model; This feature interaction cross-attention module is used to integrate the second fused feature of the source point cloud. Second fusion feature with reference point cloud In the standard cross-attention mechanism, the feature similarity matrix across the point clouds is calculated to guide the feature interaction between two frames of point clouds, ultimately obtaining the hybrid features after the two frames of point clouds are fused together. and It is expressed by the following formula: ; ; Specifically, the second fusion feature of the source point cloud is obtained by using an independent, learnable linear transformation matrix. Mapped to content query matrix respectively Key matrix and value matrix The second fusion feature of the reference point cloud Mapped to content query matrix respectively Key matrix and value matrix ; The function operations representing the feature interaction cross-attention module; This hybrid feature and Calculate the Gaussian correlation matrix and perform double normalization optimization to obtain the superpoint matching score matrix. : ; ; in, Represents the i-th mixed feature in the source point cloud. Represents the j-th blending feature in the reference point cloud. These represent the number of superpoints contained in the source point cloud and the reference point cloud, respectively.

[0008] A point cloud registration system includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the hybrid state-aware point cloud registration method based on multi-geometry as described in any of the preceding claims.

[0009] By adopting the aforementioned design scheme, the beneficial effects of the present invention are as follows: This application extracts features through a rotationally equivariant convolution module, and implicit vector neurons capture spatial information in local areas. Real-time singular value decomposition is used to comprehensively characterize local surface details, effectively dealing with confusing regions with single or similar features in complex scenes. Without the need for an initial pose, it can still accurately capture identifiable local topological information, greatly reducing the probability of confusing matching. The state space context aggregation module designed in this application adopts a cascaded strategy of local geometric attention anchoring plus global diffusion of selective state space model, and finally performs cross-point cloud interactive matching to obtain hybrid features. This strategy preserves rotation-invariant geometric features while giving the network a low-cost global receptive field. This application generates high-quality pose assumptions by introducing spatial diversity sampling and modulus consistency checks, and iteratively refines the best assumptions by combining a Gaussian soft weighting strategy, thereby improving the robustness of pose estimation and helping to improve the quality of point cloud registration. Attached Figure Description

[0010] Figure 1 This is a flowchart of the point cloud registration method of the present invention; Figure 2 This is a flowchart of the rotational isovariant convolution module of the present invention. Figure 3 This is an architecture diagram of the state space context aggregation module of the present invention; Figure 4 This is a flowchart for generating the robust assumptions of the present invention; Figure 5 This is a diagram showing the corresponding points and relationships in the superpoint level prediction of the present invention (green indicates correct prediction, and red indicates incorrect prediction). Figure 6Visualization of the registration effect in complex indoor scenes of the present invention (blue: source point cloud; yellow: reference point cloud). Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0012] The terms "first," "second," "third," etc., used in the specification, claims, and accompanying drawings of this invention are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0013] A hybrid state-aware point cloud registration method based on multi-geometry, such as Figure 1 As shown, the steps are executed sequentially as follows: S1: Use a 3D acquisition device to scan the scene or object, and obtain two partially overlapping point clouds for any scene or object, one of which is the source point cloud and the other is the reference point cloud. S2: Input the source point cloud and the reference point cloud into the feature extraction network for feature extraction, and obtain the superpoints and corresponding rotational isomorphic features of the source point cloud and the reference point cloud respectively. Two branches are used to process each superpoint and its corresponding rotational isomorphic feature. One branch constructs a local orthogonal coordinate system for each superpoint rotational isomorphic feature using the Gram-Schmidt orthogonalization algorithm, and projects it to obtain the superpoint rotational invariant features corresponding to the source point cloud and the reference point cloud respectively. The other branch uses nearest neighbor upsampling and skip connections to distribute each superpoint rotational isomorphic feature to high-resolution dense points and perform linear mapping, thereby obtaining the dense points and their rotational isomorphic features corresponding to the source point cloud and the reference point cloud respectively. The Gram-Schmidt orthogonalization algorithm is used to convert the rotational isomorphic features of the dense points into rotational invariant features of the dense points. Then, the superpoints and the rotational invariant features of the superpoints obtained by the first branch are output to step S3. The dense points and their corresponding rotational invariant features obtained by the second branch are output to step S4, and the rotational isomorphic features of the dense points obtained by the second branch are output to step S6. In this embodiment, the feature extraction network uses rotationally equivariant convolutional modules (MG-Conv) as feature extraction units, and combines voxel grid downsampling algorithm and K-nearest neighbor algorithm (KNN) between adjacent layers to construct a multi-scale feature pyramid architecture.

[0014] This voxel grid downsampling algorithm divides the input point cloud into a voxel grid, extracts the centroids of the point cloud within the non-empty voxel grid of the current layer to construct the point cloud for the next layer. As the number of layers increases, the voxel grid gradually increases in size, while the number of point clouds gradually decreases, thus obtaining a multi-layered point cloud set. The sparse point cloud output from the deepest layer of the feature extraction network is the superpoint. .

[0015] Assume the 0th layer point cloud of the input source point cloud is As downsampling proceeds, the point cloud of layer L becomes... , Let L be the number of points in the L-th layer of the point cloud; the KNN algorithm is used to construct neighborhood point sets of the source point cloud at different scales. The rotational equivariant convolution module is used to alternately perform cross-level feature aggregation and same-level feature update. The feature output by the deepest layer of the network is the superpoint rotational equivariant feature.

[0016] For cross-level feature aggregation, the rotation-equivariant convolution module uses the current L-th layer point cloud center point as the reference point. For query points, in the relatively dense point cloud of the upper layer. Search for the nearest location to the query point Obtain a cross-level neighborhood point set from a set of neighboring points. By using the neighborhood set of the center point as a cross-scale neighborhood query, the feature extraction network can transfer local geometric details from high resolution to coarser layers through rotational equivariant convolution modules.

[0017] For feature updates at the same level, the rotationally equivariant convolutional module uses the center point of the current Lth layer as the reference point. For query points, in the same level of point cloud Get from Construct a set of neighboring points at the same level using 1 neighboring point. The neighborhood point set of the center point is used to deepen the local geometric representation at the current scale.

[0018] In this embodiment, the center point of the point cloud at a certain generalization level of the source point cloud is denoted as... This rotationally equivariant convolution module is explained.

[0019] like Figure 2 As shown, the rotationally equivariant convolution module includes an explicit geometric feature extraction module, a geometric scalar encoding module, a geometric enhancement correlation module, and a geometrically guided dynamic convolution kernel module connected in sequence. This explicit geometric feature extraction module targets the sampling center points of the input point cloud. and its neighboring points in the neighborhood point set Calculate the covariance matrix of the neighborhood point set after decentralization. : ; in, Indicates the center point The number of neighboring points in the neighborhood point set. Represents the centroid of the neighborhood point set; For covariance matrix Singular Value Decomposition (SVD) is performed to explicitly obtain the geometric prior, and the right singular vector corresponding to the minimum singular value is extracted as the normal vector of the neighborhood point set. This is used to model the normal of the local tangent plane of the neighborhood point set, and the minimum singular value is directly used as the curvature intensity. This reflects the surface undulations of the neighborhood point set, thus overcoming the geometric perception limitation of the original network, which relies solely on relative coordinates for implicit feature learning.

[0020] This geometric scalar encoding module is used to encode the normal vector. Perform normalization processing, and calculate the normalized normal vector and the centroid direction vector of the neighborhood point set. The spatial dot product is used to obtain the projection scalar of the neighborhood point set along the normal vector direction. This projection scalar is then multiplied by the curvature intensity. Stitching along the channel dimension This transforms the abstract spatial distribution into an explicit geometric scalar descriptor with rotation invariance. This provides a strong geometric prior for the generation of subsequent convolutional kernel weights, using explicit geometric scalar descriptors. It is expressed by the following formula: ; in, This indicates channel-level splicing.

[0021] This geometric scalar encoding module is designed to guarantee the rotational invariance of explicit geometric features.

[0022] This geometry-enhanced correlation module employs a correlation mapping network based on explicit geometric scalar descriptors. Perform dynamic weight calculation for the convolution kernel. To obtain the local spatial location features of this neighborhood point set, calculate the weights based on the center point of the input point cloud. and its neighboring points in the neighborhood point set Calculate the distance of each neighboring point relative to the center point of the point cloud. relative coordinates Calculate the relative coordinates with the centroid direction vector cross product vector The extended channel will use the relative coordinates centroid direction vector and the cross product vector Perform splicing to obtain rotationally variable spatial features. Vector neurons (VNs) are used to extract the rotationally equivariant spatial features. To strictly maintain rotational invariance, the implicit equivariant feature is converted into a rotationally invariant scalar feature through a 2-norm modulo operation. This scalar feature is then compared with the aforementioned explicit geometric scalar descriptor. Channel-level concatenation is performed to obtain a rotation-invariant blend descriptor that incorporates position, orientation, and undulation. This blend descriptor is then input into a lightweight relevance mapping network. In the process of learning, it is not only dependent on the location distribution, but also influenced by the correlation weights guided by the local surface roughness and orientation. To dynamically generate convolution kernels and correlation weights It is expressed by the following formula: ; in, Represents a correlation mapping network. Represents a vector neuron. This represents the modulo operation of the 2-norm. This indicates channel-level splicing; in this embodiment, the network It consists of a multilayer perceptron (MLP) and a softmax regularization layer.

[0023] Current center point Rotational equivariance features of all neighboring points within the neighborhood point set Input this geometry-guided dynamic convolution kernel module and use this relevance weight. For an internally initialized set of learnable weight shadow kernel points Perform dynamic assembly. This represents the m-th learnable weight shadow kernel point in the set of learnable weight shadow kernel points, thereby generating a dynamic convolution kernel. Using this dynamic convolution kernel Rotate the equivariant features of all neighboring points of the input. Perform weighted aggregation guided by geometric weights, ultimately at the center point. Output the updated rotational isomorphic features Rotational isomorphic features The formula is as follows: ; in, Indicates the center point The number of neighboring points in the neighborhood point set.

[0024] Updated rotational isomorphic features This serves as the input feature for the subsequent MG-Conv rotationally equivariant convolutional module. Furthermore, due to the relevance weights we construct... It is a strictly rotation-invariant scalar, and its weighted operations are... This will not violate the rotational isovariability of the network as a whole, i.e., for the MG-Conv function. If the input point cloud features After rotation The output still satisfies This preserves the rotational isovariability of features during the extraction process.

[0025] The MG-Conv captures spatial information within a local region through implicit vector neurons and uses real-time singular value decomposition to comprehensively characterize local surface details. It effectively addresses confusing regions with single or similar features in complex scenes. Without requiring an initial pose, it can still accurately capture distinctive local topological information, significantly reducing the probability of confusing matches.

[0026] As mentioned earlier, the feature extraction network constructs a multi-level point cloud set and corresponding multi-level features through rotationally equivariant convolution modules and voxel grid downsampling algorithms. In this embodiment, the sparse point cloud output by the deepest layer (i.e., the Lth layer) of the feature extraction network and its corresponding features are the superpoints. The superpoint rotation isovariant features are distributed to the dense points in the shallower dense point layer (e.g., the first layer of point cloud) through nearest neighbor upsampling and skip connections, and linear mapping is performed. The resulting features are the corresponding dense point rotation isovariant features.

[0027] For the source point cloud and the reference point cloud, the Gram-Schmidt orthogonalization algorithm is used to construct local orthogonal coordinate systems, and the rotation-invariant features of each hyperpoint are projected onto the source point cloud to obtain the corresponding rotation-invariant features. and By projecting the rotationally invariant features of each dense point onto the corresponding dense point rotation-invariant features, the rotation-invariant features of the dense points can be obtained. and .

[0028] S3: Input each superpoint and its corresponding rotation-invariant feature into the state space context aggregation module (HGSM) for feature interaction, obtain the hybrid features corresponding to the source point cloud and the reference point cloud respectively, calculate the Gaussian correlation matrix of the two hybrid features and perform double normalization to obtain the superpoint matching score matrix. In this embodiment, as Figure 3As shown, the state space context aggregation module includes a local geometric self-attention module ( ), context aggregation module and feature interaction cross-attention module ( ); This local geometric self-attention module is used to exceed the input point for each input. Centered on the network, the KNN algorithm is used as the superpoint. The search build size is super-neighborhood point set For the j-th neighboring superpoint within this neighborhood... ,from Filter out except outside distance For the three nearest super-points, construct the corresponding subset of super-point neighborhoods. The Euclidean distance embedding between superpoints and the angular embedding between triples are calculated for aggregation projection. The geometric embedding of the source point cloud is expressed by the following formula. : ; in, and These represent multilayer perceptrons used to process relative distance and angular features, respectively, providing nonlinear representations. This represents the max pooling operation performed within a subset of points in the superpoint's neighborhood. Represents the sine position code. Representative Center Exceeds Points and the j-th neighborhood super point The distance between them Representative Center Exceeds Points Pointing to the x-th neighboring superpoint in the subset of superpoint neighborhoods The vector and the direction point to the j-th neighboring superpoint in the neighborhood set of the superpoint. The spatial angle formed by the vectors; Embed the geometry As a relative position encoding, it is injected into the self-attention mechanism to guide the geometric fusion of features. The first fused feature of the source point cloud is represented by the following formula: ; in, Describe the feature fusion function operation of the local geometric self-attention module; In this embodiment, based on the self-attention structure, the network utilizes independent learnable linear transformation matrices to transform the input superpoint rotation-invariant features. Mapped to content query matrix respectively and geometric query matrix The rotation-invariant features of all neighborhood superpoints in the neighborhood set corresponding to each input superpoint are linearly mapped and combined into a key matrix. and value matrix The geometry is embedded using another linear transformation matrix. Mapped to projected position vector All the above feature matrices are uniformly divided into h independent attention heads, each with a feature dimension of d. For each input superpoint, the feature and geometric attention scores between superpoints are calculated using the neighboring superpoints in its neighborhood set. The two scores are then added together and divided by a scaling factor. After normalization, the final attention weights are obtained. These attention weights are then used to perform a weighted summation of the value vectors of all neighboring superpoints, thereby obtaining the first fusion feature of the source point cloud. ; Then, the first fusion feature of the reference point cloud can be obtained using the same method. .

[0029] This module reduces computational complexity from the original Reduced to At the same time, it also ensures that the rigid transformation of the point cloud during the feature interaction process has inherent invariance, providing a precise local geometric reference for subsequent processing.

[0030] This context aggregation module uses state-space based Mamba with linear computational complexity to process a large number of input features, achieving global awareness while avoiding the quadratic cost of Transformer.

[0031] The context aggregation module includes two branches. One branch is used to sequentially apply Layer Normalization (LN), Linear layers, Depthwise Convolution (DWConv), and the SiLu activation function to the first fused feature. Processing is performed to obtain global state features with rich local contextual information. ; Another branch is used to obtain gated features through layer normalization, linear layers, and the SiLu activation function. It employs a Selective State Space Model (Selective SSM) and layer normalization sequentially to process the global state features. The process is performed to obtain intermediate state features. These intermediate state features are then multiplied by the gated features, linearly projected, and then fused with the first fused feature. Perform residual connections to obtain the second fused feature of the source point cloud. This process is represented by the following formula: ; ; in, Represents the SiLu activation function. Represents a one-dimensional depthwise convolution operation. This represents a linear projection transformation operation. Representative layer normalization operation, This represents a discretized selective state-space model. Controlled by the following discretized selective SSM equations:

[0032] in and Representing the discretized parameters, the function of the continuous state-space model is obtained by applying the zero-order preservation rule combined with the dynamic time scale. The derivation is as follows: and In the formula, A represents the continuous evolution state matrix and B represents the continuous projection matrix; Representing intermediate variables Features of the t-th point and Let represent the hidden states at step t and step t-1, respectively. Represents the output projection matrix. This represents the intermediate state output of the module at step t.

[0033] Similarly, the second fusion feature of the reference point cloud can be obtained. ; The feature interaction cross-attention module is located at the end of the context aggregation module and is designed to achieve information exchange between the source point cloud and the reference point cloud through cross-attention.

[0034] This feature interaction cross-attention module is used to integrate the second fused feature of the source point cloud. Second fusion feature with reference point cloud In the standard cross-attention mechanism, the feature similarity matrix across the point clouds is calculated to guide the feature interaction between two frames of point clouds, ultimately obtaining the hybrid features after the two frames of point clouds are fused together. and It is expressed by the following formula: ; ; Specifically, the second fusion feature of the source point cloud is obtained by using an independent, learnable linear transformation matrix. Mapped to content query matrix respectively Key matrix and value matrix The second fusion feature of the reference point cloud Mapped to content query matrix respectively Key matrix and value matrix ; The function operations representing the feature interaction cross-attention module; This hybrid feature and Calculate the Gaussian correlation matrix and perform double normalization optimization to obtain the superpoint matching score matrix. : ; .

[0035] in, Represents the i-th mixed feature in the source point cloud. Represents the j-th blending feature in the reference point cloud. These represent the number of superpoints contained in the source point cloud and the reference point cloud, respectively; S4: As Figure 4 As shown, spatial diversity sampling is performed on the superpoint matching score matrix: to prevent high-confidence matching points from being overly concentrated in a local region of the point cloud, which would lead to a lack of global representativeness in the generated transformation hypothesis, Add random noise to the superpoint matching score matrix Perturbation to obtain the superpoint score matrix : ; In the superpoint score matrix In this embodiment, a first preset number of matching superpoint pairs with the highest superpoint scores are selected. In this embodiment, the first preset number is 256.

[0036] Since the resolution of superpoint hierarchical matching is low, it cannot be directly used to calculate high-precision rigid transformation matrices. Using the matched superpoint pair as the center, the KNN algorithm is employed to extract a second preset number of adjacent dense points in the dense point layer and obtain the corresponding dense point coordinates and rotation-invariant features. In this embodiment, the second preset number is 64, and the dense point layer is the first layer of the point cloud. Local segments of the source point cloud and the reference point cloud corresponding to the matched superpoint pair are constructed, and the feature association score matrix between corresponding dense points within the two superpoint local segments is calculated. : ; in, This represents the rotation-invariant feature of the m-th dense point within the local segment of the source point cloud corresponding to the currently matched superpoint pair. This represents the rotation-invariant feature of the nth dense point within the local segment of the reference point cloud corresponding to the currently matched superpoint pair. Represents a linear transformation. Represents the feature dimension.

[0037] Each feature association score matrix is ​​normalized bidirectionally using Softmax, and the corresponding dense point matching score matrix is ​​obtained by combining the saliency scores at both ends: ; in, , This represents the significance score of the rotation-invariant feature of the m-th dense point within the local segment of the source point cloud corresponding to the currently matched superpoint pair, after linear transformation and Sigmoid. It represents the significance score of the rotation-invariant feature of the nth dense point within the local segment of the reference point cloud corresponding to the current matching superpoint pair after linear transformation and Sigmoid.

[0038] S5: Construct a candidate point pair set for generating candidate transformation hypotheses and a verification point pair set for verifying the generated hypotheses using each dense point matching score matrix. Flatten each dense point matching score matrix to the global space. Use the global Top-k algorithm to select the top-ranking dense point pairs with a third preset number of dense point matching scores from the flattened dense point matching score matrix to obtain the candidate point pair set. In this embodiment, the third preset number is 1000. Use the local bidirectional Top-k algorithm to select from each dense point matching score matrix. At the same time, set a confidence threshold and extract all matching point pairs with matching scores greater than the confidence threshold and ranking in the top three in both the row and column directions of the dense point matching score matrix to obtain the verification point pair set. S6: Using the dense point rotation isomorphic features, perform a modulus consistency check on the dense points in the candidate point pair set to filter out incorrect matches. Calculate the L2 norm of the dense point rotation isomorphic features of the source point cloud and the reference point cloud using the following formula, and calculate their relative difference ratio. : ; in, and These represent the source point cloud and the reference point cloud, respectively. This represents the rotational variation of the source point cloud dense points in the h-th matching point pair in the candidate point pair set. This represents the rotational variation feature of the reference point cloud dense points in the h-th matching point pair in the candidate point pair set.

[0039] If the relative difference ratio If the threshold is exceeded, the match is determined to violate the modulus invariance constraint of rigid transformation and is removed from the candidate point pair set. S7: Obtain candidate transformation hypotheses for each matching point pair in the candidate point pair set after modulus consistency check through singular value decomposition: ; in, This represents the candidate transformation hypothesis calculated for the h-th matching point pair in the candidate point pair set. This hypothesis is represented as a candidate transformation matrix in the specific spatial calculation. Rotation is calculated based on rotational isomorphism. , This represents the candidate space rotation matrix calculated for the h-th matching point pair in the candidate point pair set, and the translation calculated based on the coordinates. , This represents the candidate spatial translation vector calculated for the h-th matching point pair in the candidate point pair set. The coordinates of the dense points on the reference point cloud side in the current matched point pair. These are the coordinates of the dense points on the source point cloud side in the current matched point pair. The Frobenius norm of a matrix is ​​used to measure the overall spatial error between characteristic matrices, thereby obtaining the candidate transformation hypothesis pool. , The number of hypotheses; S8: Utilize the candidate transformation hypothesis pool For each candidate transformation hypothesis, a candidate transformation matrix is ​​used to perform a spatial transformation on the source point cloud in the verification point pair set. The spatial residual between the transformed source point cloud and the reference point cloud is calculated, and the proportion of matching points whose spatial residual is less than a preset distance threshold is counted as the inlier rate of the candidate transformation matrix. The candidate transformation matrix with the highest inlier rate is selected as the optimal initial transformation matrix. With this optimal initial transformation matrix Starting with the set of validation points, a weighted Procrustes iteration refinement is performed a predetermined number of times. Let the candidate transformation matrix of the u-th iteration be... The spatial residuals of each matching point pair are recalculated based on this matrix, and an annealing smoothing parameter that decays linearly with the number of iterations is introduced. Combining spatial residuals and annealing smoothing parameters, a Gaussian kernel function is used. A Gaussian soft weight is assigned to each matching point pair. The Gaussian soft weight is then multiplied by the corresponding element in the dense point matching score matrix to construct a joint weight. Combined with the interior point mask generated by the preset distance threshold, the joint weight is used to perform weighted singular value decomposition on the verification point pair set to solve the following objective function to update the current transformation matrix:

[0040] in, This indicates the number of point pairs in the verification point pair set. This represents the dense point matching score of the v-th matching point pair in the verification point pair set. This represents the Gaussian soft weight of the current matching point pair in the u-th iteration. This represents the coordinates of the dense points on the source point cloud side of the currently matched point pair. This represents the coordinates of the dense points on the reference point cloud side of the currently matched point pair. This represents the preset distance threshold for determining interior points. This is an indicator function that combines a preset distance threshold to represent an interior point mask.

[0041] Repeat the weighted Procrustes iterative refinement until the preset number of iterations is reached, and output the final transformation matrix. .

[0042] In this embodiment, a system for implementing the above method is also provided.

[0043] A point cloud registration system includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the hybrid state-aware point cloud registration method based on multi-geometry as described in any of the preceding claims.

[0044] To verify the effectiveness and significant advancements of the proposed method, detailed comparative and ablation experiments were conducted on the 3DMatch 3D point cloud dataset. This dataset contains a wealth of realistic indoor scenes, including bedrooms, offices, and hotels, fully preserving the large areas of smooth walls and floors commonly found in real-world scenes. It also features highly symmetrical and repetitive furniture structures such as sofas and chairs, making it ideal for testing the performance of point cloud registration algorithms in terms of overlapping areas of interest and their robustness in distinguishing confused features. As shown in Table 1, the method in this application was comprehensively evaluated against current mainstream advanced point cloud registration algorithms. Regarding transformation matrix calculation, FCGF and RoReg employ a 50k iteration random sampling consensus algorithm (RANSAC-50k), Predator and GeoTransformer use a global singular value decomposition hypothesis generator (LGR) to extract superpoint local fragments, and PARENet uses a point-pair feature hypothesis generator (FHP). Experimental data show that this application achieves a registration recall rate (RR) of 96.3% on the 3DMatch dataset, demonstrating that this application can achieve successful registration in multiple point cloud scenes. Meanwhile, in terms of the two core indicators reflecting point cloud registration accuracy, the relative rotation error (RRE) and relative translation error (RTE), this method achieves low error levels of 1.705° and 0.062m, respectively. Furthermore, the model parameter size of this application is only 5.40MB, far lower than GeoTransformer's 9.83MB and slightly higher than PARENet's 3.84MB. This demonstrates that this application achieves a dual breakthrough in registration accuracy and robustness while maintaining a lightweight design, verifying the effectiveness and advancement of this method.

[0045] Table 1. Comparison experiment between the method in this application and existing methods (3DMatch dataset):

[0046] To further verify the effectiveness of the improved modules in this invention, a comprehensive ablation study was conducted on the 3DMatch dataset. As shown in Table 2, the performance metrics were observed by progressively using MG-Conv for feature extraction, HGSM in the feature interaction module, and PCRH-Proposer for transformation matrix calculation. Specifically, compared to the base model A which uses vector neurons for implicit learning based on coordinate information to extract features and uses a fully connected geometric embedding self-attention mechanism for feature interaction, introducing MG-Conv or HGSM alone can bring steady improvements to various metrics, which confirms the powerful ability of these modules to extract discriminative features and find overlapping regions. When the above modules are used together and supplemented by PCRH-Proposer to calculate the transformation matrix to form the complete architecture of this invention, the various metrics reach their optimal levels, effectively solving the feature ambiguity problem caused by repetitive structures and jointly overcoming the technical challenge of partially overlapping point cloud registration.

[0047] Table 2 Ablation experiments of the method in this application (3DMatch dataset):

[0048] To reveal and explore the role and effect of point cloud registration at the level of micro-feature matching, Figure 5 The results of this application in predicting corresponding points and correspondences at the superpoint level are visualized. It can be seen that in the comparative scheme lacking the HGSM interaction module, due to the inability to effectively shield the interference of non-overlapping region features, the network incorrectly predicts a large number of corresponding superpoints in non-overlapping regions, leading to the algorithm forcibly establishing dense false matches (red lines), with an inlier rate of only 26.6%. Conversely, after introducing the HGSM interaction module of this invention, the network exhibits efficient overlapping region focus capabilities, significantly reducing the number of invalid points in non-overlapping regions, significantly increasing the number of effective predicted points falling into the real overlapping regions, significantly increasing the number of correctly matched associations (green lines), and raising the inlier rate to 63.7%. This verifies that the decoupling structure of this invention effectively alleviates the generation of false correspondences in low-overlap, high-similarity scenarios, providing a higher-quality correspondence set for subsequent transformation matrix calculations.

[0049] Furthermore, in order to verify the effectiveness of this invention in real and challenging scenarios, Figure 6The visualization of the model's macroscopic registration results in complex indoor scenes is presented. It can be seen that, limited by the single geometric feature extraction mechanism based on point cloud position information and non-overlapping interference, the baseline network is highly susceptible to interference from low overlap rates or similar spatial distributions when facing indoor scenes such as symmetrical sofas and large areas of similar flat structures. This causes the registration results between the source and reference point clouds to get stuck in local optima, resulting in significant spatial misalignment and large rotation errors, failing to correctly align the two frames of point clouds. In contrast, thanks to the multi-dimensional geometric cue injection of feature extraction convolution, the model's perception of subtle geometry is effectively enhanced. Combined with HGSM to establish the connection between geometric dependencies and the global context, the proposed method (MGS-Net) can still obtain the correct overlapping region and correspondence between two frames of point clouds even in equally challenging scenes. By guiding the source and reference point clouds to achieve registration alignment through robust pose assumptions, it demonstrates strong registration performance.

[0050] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A hybrid state-aware point cloud registration method based on multivariate geometry, characterized in that: The steps are as follows, performed sequentially: S1: Use a 3D acquisition device to scan the scene or object, and obtain two partially overlapping point clouds for any scene or object, one of which is the source point cloud and the other is the reference point cloud. S2: Input the source point cloud and the reference point cloud into the feature extraction network for feature extraction, and obtain the superpoints and corresponding rotational isomorphic features of the source point cloud and the reference point cloud respectively. Two branches are used to process each superpoint and the corresponding rotational isomorphic features. One branch constructs a local orthogonal coordinate system for each superpoint rotational isomorphic feature using the Gram-Schmidt orthogonalization algorithm, and projects it to obtain the superpoint rotational invariant features of the source point cloud and the reference point cloud respectively. The other branch uses nearest neighbor upsampling and skip connections to assign each superpoint rotational isomorphic feature to high-resolution dense points and perform linear mapping, and obtains the corresponding dense points and dense point rotational isomorphic features of the source point cloud and the reference point cloud respectively. The Gram-Schmidt orthogonalization algorithm is used to convert the dense point rotational isomorphic features into dense point rotational invariant features. Output the superpoints and the superpoint rotational invariant features obtained by the first branch to step S3. Output the dense points and the corresponding dense point rotational invariant features obtained by the second branch to step S4, and output the dense point rotational isomorphic features obtained by the second branch to step S6. S3: Input each superpoint and its corresponding rotation-invariant feature into the state space context aggregation module for feature interaction, obtain the hybrid features corresponding to the source point cloud and the reference point cloud respectively, calculate the Gaussian correlation matrix of the two hybrid features and perform double normalization to obtain the superpoint matching score matrix. S4: Perform spatial diversity sampling on the superpoint matching score matrix: Add random noise perturbation to the superpoint matching score matrix to obtain the superpoint score matrix. Select a first preset number of matching superpoint pairs with the highest superpoint scores in the superpoint score matrix. Using the matching superpoint pairs as the center, use the K-nearest neighbor algorithm to extract a second preset number of adjacent dense points and obtain the corresponding dense point coordinates. Construct a superpoint local segment of the source point cloud and a superpoint local segment of the reference point cloud. Calculate the feature association score matrix between the corresponding dense points in the two superpoint local segments. Normalize each feature association score matrix through bidirectional Softmax and combine the saliency scores at both ends to obtain the corresponding dense point matching score matrix. S5: Construct a candidate point pair set for generating candidate transformation hypotheses and a verification point pair set for verifying the generated hypotheses using each dense point matching score matrix. Flatten each dense point matching score matrix to the global space. Use the global Top-k algorithm to select the top-ranking dense point pairs in the flattened dense point matching score matrix to obtain the candidate point pair set. Use the local bidirectional Top-k algorithm to filter in each dense point matching score matrix. At the same time, set a confidence threshold and extract all matching point pairs whose matching scores are greater than the confidence threshold and whose matching scores rank in the top three in both the row and column directions of the dense point matching score matrix to obtain the verification point pair set. S6: Using the dense point rotation isomorphic features, perform a modulus consistency check on the dense points in the candidate point pair set to filter out incorrect matches. Calculate the L2 norm of the dense point rotation isomorphic features of the source point cloud and the reference point cloud using the following formula, and calculate their relative difference ratio. : ； in, and These represent the source point cloud and the reference point cloud, respectively. This represents the rotational variation of the source point cloud dense points in the h-th matching point pair in the candidate point pair set. This represents the rotational variation feature of the reference point cloud dense points in the h-th matching point pair in the candidate point pair set; If the relative difference ratio If the threshold is exceeded, the match is determined to violate the modulus invariance constraint of rigid transformation and is removed from the candidate point pair set. S7: Obtain candidate transformation hypotheses for each matching point pair in the candidate point pair set after modulus consistency check through singular value decomposition: ； in, This represents the candidate transformation hypothesis calculated for the h-th matching point pair in the candidate point pair set. This hypothesis is represented as a candidate transformation matrix in the specific spatial calculation. Rotation is calculated based on rotational isomorphism. , This represents the candidate space rotation matrix calculated for the h-th matching point pair in the candidate point pair set, and the translation calculated based on the coordinates. , This represents the candidate spatial translation vector calculated for the h-th matching point pair in the candidate point pair set. The coordinates of the dense points on the reference point cloud side in the current matched point pair. These are the coordinates of the dense points on the source point cloud side in the current matched point pair. The Frobenius norm of a matrix is ​​used to measure the overall spatial error between characteristic matrices, thereby obtaining the candidate transformation hypothesis pool. , The number of hypotheses; S8: Utilize the candidate transformation hypothesis pool For each candidate transformation hypothesis, a candidate transformation matrix is ​​used to perform a spatial transformation on the source point cloud in the verification point pair set. The spatial residual between the transformed source point cloud and the reference point cloud is calculated, and the proportion of matching points whose spatial residual is less than a preset distance threshold is counted as the inlier rate of the candidate transformation matrix. The candidate transformation matrix with the highest inlier rate is selected as the optimal initial transformation matrix. With this optimal initial transformation matrix Starting from the set of verification points, a weighted Procrustes iterative refinement is performed a predetermined number of times; let the candidate transformation matrix of the u-th iteration be... The spatial residuals of each matching point pair are recalculated based on this matrix, and an annealing smoothing parameter that decays linearly with the number of iterations is introduced. Combining spatial residuals and annealing smoothing parameters, a Gaussian kernel function is used. A Gaussian soft weight is assigned to each matching point pair. The Gaussian soft weight is then multiplied by the corresponding element in the dense point matching score matrix to construct a joint weight. Combined with the interior point mask generated by the preset distance threshold, the joint weight is used to perform weighted singular value decomposition on the verification point pair set to solve the following objective function to update the current transformation matrix: in, This indicates the number of point pairs in the verification point pair set. This represents the dense point matching score of the v-th matching point pair in the verification point pair set. This represents the Gaussian soft weight of the current matching point pair in the u-th iteration. This represents the coordinates of the dense points on the source point cloud side of the currently matched point pair. This represents the coordinates of the dense points on the reference point cloud side of the currently matched point pair. This represents the preset distance threshold for determining interior points. The indicator function, combined with a preset distance threshold, represents the interior point mask; Repeat the weighted Procrustes iterative refinement until the preset number of iterations is reached, and output the final transformation matrix. .

2. The hybrid state-aware point cloud registration method based on multi-geometry as described in claim 1, characterized in that: The feature extraction network in step S2 uses a rotationally equivariant convolution module as the feature extraction unit. The rotationally equivariant convolution module includes an explicit geometric feature extraction module, a geometric scalar encoding module, a geometric enhancement correlation module, and a geometrically guided dynamic convolution kernel module connected in sequence. The explicit geometric feature extraction module extracts the center points of the input point cloud. and its neighboring points in the neighborhood point set Calculate the covariance matrix of the neighborhood point set after decentralization. : ； in, Indicates the center point The number of neighboring points in the neighborhood point set. Represents the centroid of the neighborhood point set; For covariance matrix Singular Value Decomposition (SVD) is performed to explicitly obtain the geometric prior, and the right singular vector corresponding to the minimum singular value is extracted as the normal vector of the neighborhood point set. This is used to model the normal of the local tangent plane of the neighborhood point set, and the minimum singular value is directly used as the curvature intensity. ; This geometric scalar encoding module is used to encode the normal vector. Perform normalization processing, and calculate the normalized normal vector and the centroid direction vector of the neighborhood point set. The spatial dot product is used to obtain the projection scalar of the neighborhood point set along the normal vector direction. This projection scalar is then multiplied by the curvature intensity. Stitching along the channel dimension This transforms the abstract spatial distribution into an explicit geometric scalar descriptor with rotation invariance. This provides a strong geometric prior for the generation of subsequent convolutional kernel weights, using explicit geometric scalar descriptors. It is expressed by the following formula: ； in, Indicates channel-level splicing; This geometry-enhanced correlation module employs a correlation mapping network based on explicit geometric scalar descriptors. Perform dynamic weight calculation of the convolution kernel based on the center points of the input point cloud. and its neighboring points in the neighborhood point set Calculate the distance of each neighboring point relative to the center point of the point cloud. relative coordinates Calculate the relative coordinates with the centroid direction vector cross product vector The extended channel will use the relative coordinates centroid direction vector and the cross product vector Perform splicing to obtain rotationally variable spatial features. Vector neurons are used to extract the rotational isotropic spatial features. The implicit isovariant features are converted into rotation-invariant scalar features through a 2-norm modulo operation. These scalar features are then compared with the explicit geometric scalar descriptor. Channel-level concatenation is performed to obtain a rotation-invariant hybrid descriptor, which is then input into a lightweight relevance mapping network. The relevant weights are obtained through processing. The correlation weight It is expressed by the following formula: ； in, Represents a correlation mapping network. Represents a vector neuron. This represents the modulo operation of the 2-norm; Current center point Rotational equivariance features of all neighboring points within the neighborhood point set Input this geometry-guided dynamic convolution kernel module and use this relevance weight. For an internally initialized set of learnable weight shadow kernel points Perform dynamic assembly. This represents the m-th learnable weight shadow kernel point in the set of learnable weight shadow kernel points, thereby generating a dynamic convolution kernel. Using this dynamic convolution kernel Rotate the equivariant features of all neighboring points of the input. Perform weighted aggregation guided by geometric weights, ultimately at the center point. Output the updated rotational isomorphic features Rotational isomorphic features The formula is as follows: ； Updated rotational isomorphic features The features are used as input for subsequent rotationally equivariant convolutional modules; combined with point cloud downsampling and cascaded rotationally equivariant convolutional modules, the superpoint is finally output at the deepest layer of the feature extraction network. And the corresponding superpoint rotation equivariant features; The Gram-Schmidt orthogonalization algorithm is used to construct a local orthogonal coordinate system, and the corresponding rotation-invariant features of the hyperpoints are obtained by projecting the rotationally equivariant features onto them. .

3. The hybrid state-aware point cloud registration method based on multi-geometry as described in claim 2, characterized in that: The state-space context aggregation module includes a local geometric self-attention module, a context aggregation module, and a feature interaction cross-attention module; This local geometric self-attention module is used to exceed the input point for each input. Centered on the network, the KNN algorithm is used as the superpoint. The search build size is super-neighborhood point set For the j-th neighboring superpoint within this neighborhood... ,from Filter out except outside distance For the three nearest super-points, construct the corresponding subset of super-point neighborhoods. The Euclidean distance embedding between superpoints and the angular embedding between triples are calculated for aggregation projection. The geometric embedding of the source point cloud is expressed by the following formula. : ； in, and These represent multilayer perceptrons used to process relative distance and angular features, respectively, providing nonlinear representations. This represents the max pooling operation performed within a subset of points in the superpoint's neighborhood. Represents the sine position code. Representative Center Exceeds Points and the j-th neighborhood super point The distance between them Representative Center Exceeds Points Pointing to the x-th neighboring superpoint in the subset of superpoint neighborhoods The vector and the direction point to the j-th neighboring superpoint in the neighborhood set of the superpoint. The spatial angle formed by the vectors; Embed the geometry The first fusion feature of the source point cloud, injected as a relative position encoding into the self-attention mechanism, is represented by the following formula: ； in, Describe the feature fusion function operation of the local geometric self-attention module; Based on the self-attention structure, the network utilizes independent, learnable linear transformation matrices to transform the input superpoint rotation-invariant features. Mapped to content query matrix respectively Geometric query matrix The rotation-invariant features of all neighborhood superpoints in the neighborhood set corresponding to each input superpoint are linearly mapped and combined into a key matrix. and value matrix The geometry is embedded using another linear transformation matrix. Mapped to projected position vector All the above feature matrices are uniformly divided into h independent attention heads, each with a feature dimension of d. For each input superpoint, the feature and geometric attention scores between superpoints are calculated using the neighboring superpoints in its neighborhood set. The two scores are then added together and divided by a scaling factor. After normalization, the final attention weights are obtained. These attention weights are then used to perform a weighted summation of the value vectors of all neighboring superpoints, thereby obtaining the first fusion feature of the source point cloud. ; This context aggregation module uses state-space based Mamba with linear computational complexity to process a large number of input features, so as to achieve global awareness while avoiding the quadratic cost of Transformer. The context aggregation module includes two branches. One branch is used to sequentially apply layer normalization, linear layers, deep convolutional layers, and activation functions to the first fused feature. Processing is performed to obtain global state features with rich local contextual information. ; Another branch is used to obtain gated features through layer normalization, linear layers, and activation functions, employing selective state space modules and layer normalization sequentially to process the global state features. The process is performed to obtain intermediate state features. These intermediate state features are then multiplied by the gated features, linearly projected, and then fused with the first fused feature. Perform residual connections to obtain the second fused feature of the source point cloud. The process is represented by the following formula: ； ； in, Represents the SiLu activation function. Represents a one-dimensional depthwise convolution operation. This represents a linear projection transformation operation. Representative layer normalization operation, Represents a discretized selective state-space model; This feature interaction cross-attention module is used to integrate the second fused feature of the source point cloud. Second fusion feature with reference point cloud In the standard cross-attention mechanism, the feature similarity matrix across the point clouds is calculated to guide the feature interaction between two frames of point clouds, ultimately obtaining the hybrid features after the two frames of point clouds are fused together. and It is expressed by the following formula: ； ； Specifically, the second fusion feature of the source point cloud is obtained by using an independent, learnable linear transformation matrix. Mapped to content query matrix respectively Key matrix and value matrix The second fusion feature of the reference point cloud Mapped to content query matrix respectively Key matrix and value matrix ; The function operations representing the feature interaction cross-attention module; This hybrid feature and Calculate the Gaussian correlation matrix and perform double normalization optimization to obtain the superpoint matching score matrix. : ； ； in, Represents the i-th mixed feature in the source point cloud. Represents the j-th blending feature in the reference point cloud. These represent the number of superpoints contained in the source point cloud and the reference point cloud, respectively.

4. A point cloud registration system, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When executing the computer program, the processor implements the hybrid state-aware point cloud registration method based on multi-geometry as described in any one of claims 1-3 above.

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