CN-121810751-B - Low-overlap-ratio point cloud registration method based on topology-metric decoupling

CN121810751BCN 121810751 BCN121810751 BCN 121810751BCN-121810751-B

Abstract

The invention discloses a low-overlapping-rate point cloud registration method based on topology-metric decoupling, which belongs to the technical field of computer vision and three-dimensional reconstruction, and comprises the steps of scanning objects by a three-dimensional laser scanning acquisition terminal, acquiring two point clouds with different angles as a source point cloud and a target point cloud, realizing high-robustness registration under a difficult scene with extremely low overlapping rate, solving a zero solution problem under the low overlapping rate through a one-way matching union by an asymmetric correlation strategy, remarkably improving the recall rate, and simultaneously, eliminating quantization errors by utilizing anisotropic covariance and Lipozzolanic optimization mechanisms through DGTG geometric pruning and probability manifold optimization mechanisms, greatly reducing translation errors and rotation errors, and effectively breaking through precision bottlenecks caused by voxelization. The invention not only can ensure the existence of the solution under the condition of extremely low overlapping rate, but also can eliminate voxel quantization error through manifold optimization based on covariance, thereby realizing high-precision and high-efficiency registration of the point cloud with low overlapping rate.

Inventors

SUN YUYU
Shang Zongkai
YANG MINGXIAO
Yan Heqi
Mou Mengxuan
MENG FANDI

Assignees

长春大学

Dates

Publication Date: 20260508
Application Date: 20260306

Claims (7)

1. The low overlap rate point cloud registration method based on topology-metric decoupling is characterized by comprising the following steps of: Step one, scanning and acquiring point cloud data of a scanned object in two selected different directions through a three-dimensional laser scanning acquisition terminal, and respectively marking the point cloud data as a source point cloud and a target point cloud; Step two, carrying out coordinate mapping and matrixing on the source point cloud and the target point cloud to respectively obtain a source matrix and a target matrix; Respectively carrying out grid noise reduction on the source matrix and the target matrix to obtain two groups of sparse skeleton node matrixes, namely a source skeleton coordinate matrix and a target skeleton coordinate matrix, and generating KD-Tree indexes; performing geometric coding on each skeleton node, and correspondingly generating two groups of regional convolution fusion FPFH feature matrixes, namely a source feature matrix and a target feature matrix; Step three, searching the best matching row of the target feature matrix by traversing each row of the source feature matrix in a unidirectional way to form a matching pair, further generating an initial rough corresponding set for representing the index corresponding relation, and establishing preliminary logic connection between a source point cloud and a target point cloud; Step four, taking two random matching pairs in the initial rough corresponding set, removing outliers by utilizing a rigid constraint and DGTG dynamic geometric topology gating maximum cluster consistency principle to obtain a corresponding set with consistent geometric structures, namely a maximum cluster structure, and screening and outputting a fine corresponding set again; Step five, performing global attraction domain anchoring operation on the fine corresponding set to obtain an anchoring transformation matrix as an initial value of probability plane sliding of the next step; And step six, constructing a virtual sliding plane for the maximum group target skeleton node in the fine corresponding set, and driving the maximum group source node to slide to the superposition position of the target node along the tangential plane by minimizing the probability sliding loss function so as to realize the registration of the source point cloud and the target point cloud.
2. The method for registering the point cloud with low overlapping rate based on topology-metric decoupling as claimed in claim 1, wherein the mesh noise reduction in the second step adopts a voxel filtering technology, and the specific method is as follows: 1) Setting voxel side length For source point cloud floating point type coordinate matrix And target point cloud floating point type coordinate matrix Spatial downsampling is performed, respectively, with uniform data density, wherein, The dimension is , The dimension is , As the total number of points of the source point cloud, The total number of points for the target point cloud; setting any point in a coordinate matrix Its spatial components in three-dimensional coordinates are Calculating three-dimensional index vector of voxels thereof : ; 2) Center of gravity aggregation, search falls into the same index A kind of electronic device Calculating the geometric gravity center of each point as a unique skeleton node : ; In the formula, Representing the first of a source or target point cloud to fall within the current voxel grid A point of the light-emitting diode is located, ; 3) Respectively obtaining source skeleton coordinate matrixes after dimension reduction Dimension (dimension) And a target skeleton coordinate matrix Dimension (dimension) , wherein, The number of skeleton nodes of the source point cloud and the target point cloud after dimension reduction is respectively.
3. The method for registering point cloud with low overlapping rate based on topology-metric decoupling of claim 1, wherein the generating method of the regional convolution fusion FPFH feature matrix in the second step is as follows: The first step, obtaining a normal vector; 1) Searching for the first of the skeleton coordinate matrix using KD-Tree Personal node A kind of electronic device Calculating local centroid by neighboring nodes And constructing covariance matrix : ; In the formula, Representing nodes Is the first of (2) The number of neighboring nodes is chosen to be equal, ; Indicating this Geometric centroids of the neighboring nodes; 2) And (3) performing eigenvalue decomposition: for covariance matrix Performing orthogonal decomposition and solving equations Three characteristic values are obtained Feature vectors corresponding to the feature vectors A kind of electronic device ; Wherein, the Representing the principal direction of greatest variance of data distribution Representing the direction of least variance of the data distribution, the direction perpendicular to the local plane geometrically having the least variation of the data, therefore, will Defined as nodes Normal vector of (2) ; The second step is to perform relative angle coding SPFH; in order to eliminate the influence of the rotation of the coordinate system, the node is provided with Up-construction Dabuframe local orthogonal coordinate system , wherein, Representing the normal vector as A shaft; Determination by cross-product of line and normal A shaft; by right-hand rule A shaft; the function of the arrival frame is to construct a follow-up local reference, ensure the rotation invariance of the angle characteristic, calculate the angle deviation of the neighbor normal vector under the coordinate system Generating 33-dimensional histogram relative angle codes ; Calculating the angular deviation of neighbor normal vector under the coordinate system The specific calculation formula is as follows: ; ; ; in the formula, Representing neighbor node normal vectors And (3) with A projection angle deviation between the axes; Representing a central node normal vector And (3) with 、 The inclination angle deviation between the two point connecting line vectors; representing neighbor node normal vectors At the position of Azimuth rotation angle deviation on a plane; respectively dividing the value ranges of the three angle deviations into 11 equal-width intervals for projection counting; thirdly, performing regional convolution fusion FPFH, and splicing the generated three 11-dimensional sub-histograms end to end so as to construct a final 33-dimensional SPFH feature vector; Performing a distance weighted convolution to convolve the nodes Is to be used for relative angle coding SPFH and its neighboring nodes Is fused by the relative angle codes SPFH of the following formula: ; in the formula, Representing fused nodes Is defined as the final 33-dimensional feature vector of (a); Is a node Is a relative angular code of (2); Is a node With neighbor nodes Is a distance between the pairs of points of (a), Is a node Is a relative angular code of (2); fourth, constructing a feature matrix and a logic expression of the feature matrix: For source skeleton coordinate matrix All nodes in (i.e.) Traversing the first step to the third step one by each node to respectively obtain corresponding 33-dimensional FPFH feature vectors; This is put into effect The vectors are stacked in rows in the memory according to the index sequence of the points, thereby constructing a source characteristic matrix ; Similarly, for the target skeleton coordinate matrix Traversing and stacking to construct a target feature matrix ; Wherein, the ; Each row in the matrix structure represents the geometric fingerprint of the corresponding node: The dimension 1 to 11 is that whether the local surface is close to a plane structure is represented, and the higher the numerical value of the interval is, the smaller the deviation of the normal direction in the adjacent area is indicated; The dimensions 12 to 22 show whether the local area presents a cylindrical or rod structure, and the higher the numerical value of the interval is, the more obvious the curvature change of the point-to-line direction is; the dimensions 23 to 33 are that whether the local area contains a right angle or an obvious prismatic line structure is represented, and the higher the numerical value of the interval is, the closer the included angle of the neighborhood normal is to the orthonormal state; So far, two groups of source point cloud and target point cloud with coordinates only are converted into two groups of enhanced data structures with skeleton coordinates and geometric characteristics.
4. The method for registering point clouds with low overlapping rate based on topology-metric decoupling as set forth in claim 3, wherein the specific method for establishing the preliminary logical connection between the source point clouds and the target point clouds in the third step is as follows: 1) The source characteristic matrix Dimension (dimension) Target feature matrix Dimension (dimension) Using a source skeleton coordinate matrix Coordinate matrix with target skeleton As an auxiliary index, the characteristic index is restored to a physical coordinate index subsequently; 2) High-dimensional index construction: To solve at The problem of low linear searching efficiency in the 33-dimensional vectors is solved, and a high-dimensional index is constructed as follows: Matrix the target characteristic Is regarded as one having High-dimensional dataset of data points, and constructing index structure of 33-dimensional feature space by adopting FLANN rapid nearest neighbor search package algorithm or high-dimensional KD-Tree The method is used for dividing the 33-dimensional feature space into a plurality of hyperplane regions so that similar geometric fingerprints are mutually adjacent on a memory address, thereby accelerating retrieval; 3) Asymmetric nearest neighbor search Traversing source feature matrices Each line of feature vectors in the database is used as a query vector to execute a unidirectional matching strategy, and the query vector is used as a query vector Searching a target feature vector closest to the target feature vector, preliminarily recognizing that the feature vectors of the target feature vector and the target feature vector are consistent, namely the same node is also called a homologous point, and measuring the distance is adopted Norms, obtaining the searched best matching target index Establishing a preliminary logic connection between a source point cloud and a target point cloud; ; in the formula, Is the source characteristic matrix The feature vector of the row, ; For the sum in the target feature matrix Nearest to the first The line feature vector is used to determine the line feature vector, ; 4) Result mapping and set generation: source index for each traversal Record the best target index searched by it Forms an index corresponding relation binary group abbreviated as index pair ; And then all Gathering the two binary groups to form an initial rough corresponding set : ; At this time, the Is one Each row represents a pair of estimated homologous points, and the total number of rows in the set is , 。
5. The method for point cloud registration with low overlapping rate based on topology-metric decoupling as recited in claim 4, wherein the specific operation steps of the fourth step are as follows: 1) Geometric pruning: by initial coarse correspondence set Any two points in (a) And As a matching pair, a source skeleton coordinate matrix is obtained by indexing Medium reading source node And From the target skeleton coordinate matrix Medium reading target node And Coordinates of (2) to calculate and obtain source node And Distance of (2) Calculating to obtain target node And Distance of (2) ; Calculating the absolute value of the difference between the two lengths by a geometric residual calculation formula : ; Setting tolerance thresholds for geometric consistency decisions , Then judge And The two matching pairs are compatible geometrically, and the logical connection relation is reserved; If the result is determined to be an incorrect match, the device is cut off And The logical connection relation of the two matched pairs is used for completing geometric pruning; 2) Constructing a compatibility matrix: Initial coarse correspondence set All possible matching pair combinations, co- Grouping, constructing a dimension as Is of the correlation matrix of (a) Traversing all matching pair combinations, and filling matrix elements according to the result of the geometric pruning : ; 3) Further screening to generate fine corresponding set : Pair matrix Performing eigenvalue decomposition or power iteration to obtain main eigenvector corresponding to maximum eigenvalue , Is of the dimension of ; Vector quantity Elements of (a) Is the first Scalar values of rows also represent the th Geometric consistency scores of the matching pairs are sorted from high to low and kept before Generating fine corresponding sets by matching pairs Fine correspondence set The largest cluster in the geometry theory is constituted, i.e. all the remaining pairs of points are spatially uniform.
6. The method for point cloud registration with low overlapping rate based on topology-metric decoupling as recited in claim 5, wherein the specific operation steps of the fifth step are as follows: 1) Traversing fine correspondence sets Is provided with an index pair corresponding to each of the index pairs, Original physical coordinates of the source node and the target node in the c-th pair of matching pairs respectively, and are The column vector is used to determine the position of the column, From a source skeleton coordinate matrix Is obtained by the reading of the data, From a target skeleton coordinate matrix Is obtained by reading; 2) Calculating geometric centroid, namely carrying out mean statistics on all extracted node coordinate vectors to respectively obtain physical space geometric centroid of the maximum group source framework and the target framework: ; in the formula, The physical space geometric centroid of the largest cluster source skeleton; is the physical space geometric centroid of the maximum clique target skeleton, The total number of matching pairs in the largest cluster; For the iterative index of the summation operation, ; 3) De-centering mapping, namely performing explicit vector subtraction operation, translating all points into a local coordinate system with the centroid as an origin, and generating relative coordinate vectors: ; in the formula, The c-th pair after the decentralization of the maximum group source framework is matched with the relative coordinate vector of the source node in the pair, The c-th pair after the decentralization of the maximum group target skeleton is matched with the relative coordinate vector of the target node in the pair; 4) Packaging the relative coordinate set, namely stacking all obtained relative coordinate vectors according to columns to construct a relative coordinate set matrix And : ; In the formula, Is the matrix of the relative coordinate set of the maximum group source framework and the dimension ; Relative coordinate set matrix for maximum group target skeleton, dimension ; 5) For relative coordinate set matrix And (3) with Performing global attraction domain anchoring rotation analysis: Covariance matrix construction, namely calculating and reflecting geometrical relevance between the maximum group source skeleton point cloud and the maximum group target skeleton point cloud by utilizing a relative coordinate set Attraction domain cross covariance matrix : ; Wherein, the Representing a matrix transposition operation; For a pair of Singular Value Decomposition (SVD) is performed, and the SVD is disassembled into three orthogonal components: ; in the formula, Respectively representing a left singular vector matrix, a singular value diagonal matrix and a right singular vector matrix transpose obtained by SVD decomposition; Closed anchoring of rotation matrix, namely directly resolving an optimal rotation matrix according to the principle of orthogonal Prak analysis : ; To introduce determinant terms for forced correction of SVD generated reflection matrices, ensure The rigid body rotation constraint under the right-hand coordinate system is satisfied; 6) To the rotation matrix Physical space geometric centroid with maximum group source framework and target framework Performing translation calculation and matrix assembly: Retrospective translation by means of transformations And (3) with Coincident constraint condition, solving global anchor translation vector : ; Final matrix assembly, namely merging the rotation matrix and the translation vector into a standard homogeneous transformation matrix as an anchoring transformation matrix : ; Will be As an initial rigid transformation instruction.
7. The method for point cloud registration with low overlap ratio based on topology-metric decoupling as recited in claim 6, wherein the specific operation steps of the sixth step are as follows: 1) Constructing a virtual sliding plane; Fine correspondence set Middle (f) For the original physical coordinates of the source node and the target node in the matching pair respectively Representing the corresponding node by the coordinates, and for the target node Feature vectors are extracted from a neighborhood point set to construct a local orthogonal basis , wherein, For the target node A surface normal vector at; Respectively, are target nodes Two orthogonal tangential vectors on a tangential plane; constructing an anisotropic covariance matrix using spectral decomposition theorem Performing plane construction, and artificially setting the maximum tangential uncertainty and the minimum normal uncertainty: ; in the formula, For the uncertainty variance in the normal direction and tangential direction, respectively, the settings are set ; 2) Probability sliding optimization is performed by lie algebra solution: constructing a sliding loss function , The sum of the mahalanobis distances of the matched pairs in all fine corresponding sets is targeted at minimizing the loss; ; Wherein, the The total number of matching pairs in the largest cluster; as a vector of the position residuals, ; Due to Variance in tangential direction Extremely large, its inverse matrix The weight of the tangential eigenvalue approaches 0, so that tangential residual errors are eliminated in a position residual error vector formula, and only normal residual error terms are reserved; 3) Dynamic evolution through Gaussian-Newton iteration and solving optimal perturbation vector with minimum loss in lie algebra space ; For each matched pair, the partial derivative of the position residual with respect to the perturbation vector, i.e. the jacobian matrix, is calculated : ; Wherein, the Represent the first Of matched pairs A jacobian matrix; The 6-dimensional perturbation vector on the lie algebra space is represented, is taken as an independent variable to participate in derivation, and is also a pose update increment to be solved in the iteration of the round; Representation of A unit matrix; representing skeleton node coordinates in a source point cloud; representing an antisymmetric operator, here used to vector 3-dimensions Mapping to An antisymmetric matrix; Representing the application of a current rigid transformation matrix to source point cloud skeleton nodes The resulting transformed coordinate vector is then used to generate a transformed coordinate vector, ; The method comprises the steps of representing a rotation matrix to be solved, and describing the attitude change of a source point cloud; Representing a translation vector to be solved for describing the spatial displacement of the source point cloud; Constructing and solving linear delta equations to obtain optimal lie algebra update amount : ; Wherein, the The inverse matrix of the anisotropic covariance matrix constructed by the corresponding target skeleton node is represented and used for weighting errors in different directions in optimization; 4) Pose manifold update: update amount to be obtained by using index map Restoring to rigid body transformation matrix and correcting current pose Updating to obtain new pose : ; Wherein, the Respectively representing an updated target pose matrix and a current pose matrix before updating; Representing a matrix exponential function for mapping lie algebra delta in cut space back to lie group manifold.

Description

Low-overlap-ratio point cloud registration method based on topology-metric decoupling Technical Field The invention belongs to the technical field of computer vision and three-dimensional reconstruction, and particularly relates to a low-overlapping-rate point cloud registration method based on topology-metric decoupling. Background Currently, the known three-dimensional point cloud registration technology mainly adopts random sampling consistency (RANSAC) and a variant algorithm thereof, or a feature matching method based on deep learning. Conventional geometric methods typically employ a "reciprocal consistency check" strategy to screen the correspondence, i.e., requiring that points in the source point cloud and points in the target point cloud must be nearest neighbors of each other to be considered valid. However, in a scene with an overlap ratio lower than 30%, more than 95% of real corresponding points only satisfy the unidirectional nearest neighbor relationship due to the physical truncation of the sensor field of view, and the reciprocity check may falsely reject these unidirectional valid geometric cues, resulting in the algorithm being trapped in "zero-solution" dilemma in the low overlap region because enough corresponding points cannot be found. In addition, in order to balance the calculation efficiency, the prior art generally performs voxel downsampling on point cloud, and the coordinate discretization inevitably introduces centimeter-level quantization errors, so that the final registration precision is locked at a voxel resolution level, and the precision flat-top effect is presented, so that the high-precision alignment requirement of sub-voxel level cannot be met. While the deep learning-based method is improved in feature extraction, the reasoning process of the deep learning-based method is seriously dependent on a high-performance GPU and a large amount of training data, so that the deep learning-based method is high in power consumption and poor in scene generalization capability, and is difficult to apply to edge computing equipment with only low-power consumption CPU. There is a need in the art for a new solution to this problem. Disclosure of Invention A low overlap rate point cloud registration method based on topology-metric decoupling, comprising the following steps, and the following steps are performed in sequence: Step one, scanning and acquiring point cloud data of a scanned object in two selected different directions through a three-dimensional laser scanning acquisition terminal, and respectively marking the point cloud data as a source point cloud and a target point cloud; Step two, carrying out coordinate mapping and matrixing on the source point cloud and the target point cloud to respectively obtain a source matrix and a target matrix; Respectively carrying out grid noise reduction on the source matrix and the target matrix to obtain two groups of sparse skeleton node matrixes, namely a source skeleton coordinate matrix and a target skeleton coordinate matrix, and generating KD-Tree indexes; performing geometric coding on each skeleton node, and correspondingly generating two groups of regional convolution fusion FPFH feature matrixes, namely a source feature matrix and a target feature matrix; Step three, searching the best matching row of the target feature matrix by traversing each row of the source feature matrix in a unidirectional way to form a matching pair, further generating an initial rough corresponding set for representing the index corresponding relation, and establishing preliminary logic connection between a source point cloud and a target point cloud; Step four, taking two random matching pairs in the initial rough corresponding set, removing outliers by utilizing a rigid constraint and DGTG dynamic geometric topology gating maximum cluster consistency principle to obtain a corresponding set with consistent geometric structures, namely a maximum cluster structure, and screening and outputting a fine corresponding set again; Step five, performing global attraction domain anchoring operation on the fine corresponding set to obtain an anchoring transformation matrix as an initial value of probability plane sliding of the next step; And step six, constructing a virtual sliding plane for the maximum group target skeleton node in the fine corresponding set, and driving the maximum group source node to slide to the superposition position of the target node along the tangential plane by minimizing the probability sliding loss function so as to realize the registration of the source point cloud and the target point cloud. In the second step, the grid noise reduction adopts a voxel filtering technology, and the concrete method comprises the following steps: 1) Setting voxel side length For source point cloud floating point type coordinate matrixAnd target point cloud floating point type coordinate matrixSpatial downsampling is performed, respectively, with unif