A point cloud registration method based on registration error zero norm minimization

Abstract

The application belongs to the field of computer vision three-dimensional point cloud registration, and particularly relates to a point cloud registration method based on registration error zero norm minimization. * ; using l2 norm to quantify the overall fitting error of the fitting error of each relative point pair in three spatial dimensions, and according to the matching point pair corresponding to the minimum K r ; using l2 norm to quantify the overall fitting error of the fitting error of each relative point pair in three spatial dimensions, and according to the matching point pair corresponding to the minimum K * ; using l2 norm to quantify the overall fitting error of the fitting error of each relative point pair in three spatial dimensions, and according to the matching point pair corresponding to the minimum K * ; using l2 norm to quantify the overall fitting error of the fitting error of each relative point pair in three spatial dimensions, and according to the matching point pair corresponding to the minimum K t ; using l2 norm to quantify the overall fitting error of the fitting error of each relative point pair in three spatial dimensions, and according to the matching point pair corresponding to the minimum K * ; using l2 norm to quantify the overall fitting error of the fitting error of each relative * point pair in three spatial dimensions, and according to the matching point pair corresponding to the minimum K The application can realize efficient point cloud registration in the presence of a large number of outliers.

Description

Technical Field

[0001] This invention belongs to the field of 3D point cloud registration in computer vision, and more specifically, relates to a point cloud registration method based on minimizing the zero-norm of registration error. Background Technology

[0002] Point cloud registration is a fundamental task in vision and robotics, playing a crucial role in many applications such as 3D scene reconstruction, Simultaneous Localization and Mapping (SLAM), and autonomous driving. It aims to align two partially overlapping point clouds by estimating the rigid transformation between them. Common solutions for point cloud registration involve extracting features using feature descriptors, establishing a hypothetical correspondence through feature matching, and estimating the rigid transformation. However, due to the limitations of 3D feature descriptors, low overlap between point clouds, and data noise, the established correspondence is prone to outliers (incorrect correspondences), leading to inaccurate alignment.

[0003] The problem of outlier registration has been studied for decades. These methods are generally categorized into traditional and learning-based approaches. For traditional methods, while FGR and RANSAC are simple and efficient, they often fail when the outlier ratio is high. Some methods rely on branch-and-bound (BnB) algorithms for global registration, but these are computationally complex and can run in exponential time in the worst case. MAC uses a graph-theoretic framework and hypothesis evaluation to estimate the transformation. However, it does not provide a guarantee of global optimality and may return estimates far removed from the true transformation. Learning-based methods use networks to filter correspondences to obtain more accurate transformation estimates. They require large amounts of data for training and often lack generalization ability across different datasets. Therefore, providing guaranteed, accurate, and efficient registration with a large number of outliers, noise, and across diverse datasets remains a significant challenge. Summary of the Invention

[0004] To address the shortcomings and improvement needs of existing technologies, this invention provides a point cloud registration method based on minimizing the zero norm of registration error, aiming to achieve efficient registration between source and target point clouds even when a large number of outliers exist.

[0005] To achieve the above objectives, according to one aspect of the present invention, a point cloud registration method based on minimizing the zero-norm of registration error is provided, comprising:

[0006] Based on the 3D spatial coordinate data of the source and target point clouds in the current point cloud registration task, optimization models that minimize rotation fitting error and translation fitting error are solved respectively, yielding the corresponding rotation fitting error for the current point cloud registration task. Translational fitting error O * ;

[0007] Using L2 norm quantization The overall fitting error of each relative point in the three spatial dimensions is obtained by calculating the overall fitting error, which gives the error matrix E. r According to the error matrix E r Minimum K in r K corresponding to the overall fitting error r A set of matching point pairs are fitted to obtain the rotation matrix R. * ; Use l2 norm to quantize O * The overall fitting error of each matching point in the three spatial dimensions is used to obtain the error matrix E. t According to the error matrix E t Minimum K in t K corresponding to the overall fitting error t A pair of matching points, combined with the rotation matrix R * The translation vector t is obtained by fitting. * Based on the rotation matrix R of each point cloud registration task * Translation vector t * Achieve global point cloud registration between the source point cloud and the target point cloud;

[0008] The two optimization models are constructed as follows: First, by subtracting the point-pair registration fitting error formulas for any two matched point pairs, a relative point-pair registration fitting error formula is obtained to eliminate translation-related terms. Then, the terms in the relative point-pair registration fitting error formula are multiplied by the null space matrix to eliminate rotation-related terms. Finally, the zero-norm of the obtained error formula is minimized to obtain an optimization model that minimizes the rotation fitting error. Second, using the rotation matrix in the point-pair registration fitting error formula as a known quantity, the terms in the point-pair registration fitting error formula are matrix transposed, and the transposed terms are multiplied by the null space matrix to eliminate translation-related terms. Finally, the zero-norm of the obtained error formula is minimized to obtain an optimization model that minimizes the translation fitting error.

[0009] Furthermore, since the point pair registration fitting error formula contains a noise term, the point pair registration fitting error model used to represent the point pair registration fitting error formula for all matched point pairs is expressed as follows:

[0010]

[0011] In the formula, O represents the point pair registration fitting error; Q and P represent the three-dimensional spatial coordinate data of the target point cloud and the source point cloud, respectively; R and t represent the rotation matrix and translation vector in point cloud registration, respectively; 1 represents a column vector of all 1s. K2 represents the noise associated with each matching point pair, and K2 is the number of matching point pairs in the current point cloud registration task.

[0012] Furthermore, the optimization model that minimizes the rotation fitting error is expressed as:

[0013]

[0014] satisfy:

[0015] In the formula, This represents the rotation fitting error. Represents the zero norm, Indicates satisfaction The null space matrix, This represents a matrix composed of the differences in the three-dimensional spatial coordinates of every pair of points in the source point cloud under the current point cloud registration task. This represents a matrix composed of the differences in the three-dimensional spatial coordinates of every pair of points in the target point cloud under the current point cloud registration task. This represents Gaussian noise.

[0016] Furthermore, the optimization model that minimizes the translation fitting error is expressed as:

[0017]

[0018] satisfy:

[0019] In the formula, O represents the translation fitting error. Let θ denote the zero norm, and let Θ denote the null space matrix satisfying Θ1 = 0.

[0020] Furthermore, using maximum likelihood estimation and Bayesian optimization theory, we solve the optimization models that minimize the rotation fitting error and the translation fitting error, respectively.

[0021] Furthermore, the implementation method for solving the optimization model that minimizes the rotation fitting error is as follows:

[0022] Using maximum likelihood estimation and Bayesian optimization theory, the optimization model that minimizes the rotation fitting error is expressed in an unconstrained form:

[0023] By minimizing the gradient of this optimization model and setting it to zero, the explicit solution to the optimization problem that minimizes the rotation fitting error is expressed as: Based on this formula, and combining the three-dimensional spatial coordinate data of the source and target point clouds, the rotation fitting error under the current point cloud registration task is calculated.

[0024] In the formula, To meet The null space matrix, This represents a matrix composed of the differences in the three-dimensional spatial coordinates of every pair of points in the target point cloud under the current point cloud registration task. λ R For hyperparameters, It is the Frobenius norm. Let I represent the rotation fitting error, and let I represent the identity matrix.

[0025] Furthermore, the implementation method for solving the optimization model that minimizes the translation fitting error is as follows:

[0026] Using maximum likelihood estimation and Bayesian optimization theory, the optimization model that minimizes the translation fitting error is expressed in an unconstrained form:

[0027] By minimizing the gradient of this optimization model and setting it to zero, the explicit solution to the optimization problem of minimizing the translation fitting error is expressed as: O * =(2λ) t I+Θ T Π -1 Θ) -1 Θ T Π -1 X; Based on this formula, and combining the three-dimensional spatial coordinate data of the source point cloud and the target point cloud, the translation fitting error O under the current point cloud registration task is calculated. * ;

[0028] In the formula, X = Θ(Q) T -(PR * ) T ), Π=ΘΘ T Θ is the null space matrix satisfying Θ1=0, Q and P represent the 3D spatial coordinate data of the target point cloud and the source point cloud, respectively, O represents the translation fitting error, and λ t For hyperparameters, It is the Frobenius norm.

[0029] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described above.

[0030] The present invention also provides a computer-readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls the device on which the storage medium is located to perform the steps of the method described above.

[0031] The present invention also provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the steps of the method described above.

[0032] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0033] (1) This invention proposes a point cloud registration method based on minimizing the zero-norm of registration error. The registration method uses optimization models that minimize rotation fitting error and translation fitting error. Regarding these two optimization models, this invention reformulates the registration problem using the L0 norm as an optimization problem concerning minimizing registration error. This is based on the principle that only inliers can be fitted by the same transformation; therefore, the optimal transformation should be the one that fits the largest number of inliers. By introducing the L0 norm, compared to other norms, the focus is on reducing the number of non-zero vectors rather than their size. Therefore, the method of this invention better reduces the influence of outliers. Furthermore, by applying different decoupling methods to the optimization problem of minimizing registration error, the optimization problem of minimizing registration error is decoupled into optimization problems of minimizing rotation fitting error and translation fitting error. The decoupling methods include calculating the relative positions of points to points and introducing null space. Based on the two optimization problems, the rotation fitting error and translation fitting error are solved. By decoupling the solutions for rotation and translation, the method of the present invention improves the computational efficiency. By introducing null space, the robustness to noise is improved. Therefore, the present invention can achieve efficient registration of source point cloud and target point cloud even when a large number of outliers exist.

[0034] (2) The present invention takes into account the influence of noise when optimizing the solution, which further improves the robustness to noise.

[0035] (3) The present invention uses Bayesian optimization theory and maximum likelihood estimation to solve the two decoupled optimization problems respectively, which ensures the estimation accuracy of the rotation matrix and translation vector. Attached Figure Description

[0036] Figure 1 A flowchart of a point cloud registration method based on minimizing the zero norm of registration error is provided in an embodiment of the present invention;

[0037] Figure 2 A robustness comparison chart regarding the proportion of outliers provided in an embodiment of the present invention;

[0038] Figure 3 A comparison chart of efficiency and effectiveness with other optimization-based methods provided in this embodiment of the invention;

[0039] Figure 4 A robustness comparison chart regarding Gaussian noise variance provided for embodiments of the present invention;

[0040] Figure 5 This is a diagram illustrating the effect of Gaussian noise variation on the scanning model, provided in an embodiment of the present invention.

[0041] Figure 6 The graph shows the comparison results between the BTE algorithm provided in this embodiment of the invention and other optimization-based methods. Detailed Implementation

[0042] 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 and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0043] Example 1

[0044] A point cloud registration method based on minimizing the zero-norm of registration error, such as... Figure 1 As shown, it includes:

[0045] Based on the 3D spatial coordinate data of the source and target point clouds in the current point cloud registration task, optimization models that minimize rotation fitting error and translation fitting error are solved respectively, yielding the corresponding rotation fitting error for the current point cloud registration task. Translational fitting error O * ;

[0046] Using L2 norm quantization The overall fitting error of each relative point in the three spatial dimensions is obtained by calculating the overall fitting error, which gives the error matrix E. r According to the error matrix E r Minimum K in r K corresponding to the overall fitting error r A set of matching point pairs are fitted to obtain the rotation matrix R. * ;

[0047] Using l2 norm to quantize O * The overall fitting error of each matching point in the three spatial dimensions is used to obtain the error matrix E. t According to the error matrix E t Minimum K in t K corresponding to the overall fitting error t A pair of matching points, combined with the rotation matrix R * The translation vector t is obtained by fitting. * Complete point cloud registration;

[0048] Based on the rotation matrix R of each point cloud registration task * Translation vector t * Achieve global point cloud registration between the source point cloud and the target point cloud;

[0049] The two optimization models are constructed as follows: First, by subtracting the point-pair registration fitting error formulas for any two matched point pairs, a relative point-pair registration fitting error formula is obtained to eliminate translation-related terms. Then, the terms in the relative point-pair registration fitting error formula are multiplied by the null space matrix to eliminate rotation-related terms. Finally, the zero-norm of the obtained error formula is minimized to obtain an optimization model that minimizes the rotation fitting error. Second, using the rotation matrix in the point-pair registration fitting error formula as a known quantity, the terms in the point-pair registration fitting error formula are matrix transposed, and the transposed terms are multiplied by the null space matrix to eliminate translation-related terms. Finally, the zero-norm of the obtained error formula is minimized to obtain an optimization model that minimizes the translation fitting error.

[0050] In actual point cloud registration, it is necessary to first construct multiple consistent local sets for two point clouds, and then execute the above method for each consistent local set. That is, the current point cloud registration task is a registration task performed on a consistent local set. Finally, the rotation matrix and translation vector corresponding to all consistent local sets are combined to achieve global registration.

[0051] Given two point clouds: source point cloud P = {p i ∈R 3 |i=1,…,N} and the target point cloud Q={q i ∈R 3 The goal of this embodiment is to align the two point clouds by estimating the rigid transformation T = {R, t}, where R ∈ SO(3) represents the rotation matrix and t ∈ R 3 The translation vector is represented by the following formula: To more clearly illustrate the solution of this embodiment, the solution of this embodiment will now be explained and described according to the following steps:

[0052] S1. Construct a global compatibility graph, representing point pairs as nodes in the graph, and select reliable seed matching points based on geometric compatibility to form a consistent local set;

[0053] S2. In each consistent local set, the transformation estimation problem is transformed into an optimization problem that minimizes the registration fitting error;

[0054] S3. Decompose the registration error optimization problem into rotation error optimization and translation error optimization problems; use maximum likelihood estimation and Bayesian theory to solve the rotation fitting error and translation fitting error respectively; select matching points according to the error, and estimate the rotation matrix and translation vector respectively.

[0055] S4. Select the optimal estimate and perform global point cloud registration.

[0056] The construction of the global compatibility graph described in S1 includes: obtaining initial matching points from two point cloud datasets; defining the geometric compatibility between point pairs by calculating the Euclidean distance between the two points; calculating a first-order compatibility score based on the geometric characteristics and distance of the point pairs, and selecting high-compatibility point pairs as initial seeds; and connecting geometrically compatible point pairs using the second-order compatibility score to establish a complete global compatibility graph. Specifically:

[0057] For the hypothetical corresponding points in the input, a global compatibility graph is first constructed, where corresponding points are represented as nodes, and geometrically compatible nodes are connected by edges. Specifically, the corresponding point pairs (c) are computed. i ,c j The Euclidean distance between them is shown below:

[0058]

[0059] Where, p i and p j q represents a point in the source point cloud. i and q k These are the corresponding points in the target point cloud. Each pair (c i ,c j The first-order compatibility score is calculated based on Euclidean distance, using the following formula:

[0060]

[0061] Where d t It is a distance threshold. When the distance difference between two corresponding points is less than d... t In this case, they are considered compatible because rigid transformations have length consistency. The hard compatibility matrix can be represented as:

[0062]

[0063] However, first-order compatibility metrics are susceptible to outliers due to their locality and ambiguity. Therefore, second-order compatibility metrics are used as edges in the graph to reduce the impact of errors. Considering global compatibility, the second-order compatibility score is calculated using a hard compatibility matrix, as shown in the following formula:

[0064]

[0065] Where, N c This indicates the number of corresponding input points.

[0066] To improve the computational efficiency and reduce the influence of outliers, some reliable corresponding points are selected as seeds, and a consistent local set is constructed for each seed. Specifically, using the first-order compatibility matrix, the eigenvector is calculated by the power iteration algorithm. The principal eigenvector is used as the confidence measure for each pair of corresponding points to select reliable seeds. For each seed, the top K1 neighbors are selected in the second-order compatibility metric space, and the second-order compatibility score is recalculated in each neighbor set, and the top K2 (K2 < K1) corresponding points are selected as the consistent local set of the seed.

[0067] Regarding S2, considering that outliers generally correspond to different rigid transformations, and the points that can be fitted by the same set of rigid transformations must be inliers, the rigid transformation estimation problem to be estimated can be converted into a problem of maximizing the number of inliers. Further, maximizing the number of inliers corresponds to minimizing the registration fitting error. Therefore, in this embodiment, the rigid transformation estimation problem of point cloud registration is converted into a problem of minimizing the registration fitting error.

[0068] The process of converting the rigid transformation estimation problem into an optimization problem of minimizing the registration fitting error in the embodiment of the present invention is described in detail below, specifically as follows:

[0069] (1) According to the construction process of the consistent local set, each consistent local set contains K2 possible 3D-3D point correspondences, which may be contaminated by outliers. Ideally, in a noise-free scenario, the inlier correspondence (p i , q i ) perfectly matches the transformation equation, that is, Rp i + t - q i = 0. However, considering the existence of noise, this constraint is relaxed to Rp i + t - q i ≤ ξ i , where ξ i is used as the inlier threshold to accommodate the changes introduced by noise. The goal of maximizing the inlier set is to maximize the number of inliers by fitting the transformation to the largest set of corresponding points:

[0070]

[0071] Subject to:

[0072] Among them, represents the index set of inliers, represents the cardinality of the set ξ i is an isotropic Gaussian noise with zero mean and covariance , and is used as the inlier threshold.

[0073] (2) By introducing a registration error o for each correspondence iThe problem of maximizing the interior point set described above can be reformulated as an optimization problem of registration error. i It can also be viewed as a given correspondence (p) i ,q i Whether ) is an indicator of an interior point. When the correspondence (p) i ,q i When ) is an interior point, o i Equal to the zero vector; otherwise o i It can be any vector. The registration error formula for the i-th correspondence is as follows:

[0074] o i =q i -Rp i -t-ξ i

[0075] Let O={o i ∈R 3 Let |i=1,…,K2} represent the registration fitting error of all correspondences in the k-th consistent local set, and O is defined as:

[0076]

[0077] in, represents the noise associated with each correspondence; 1 is a column vector of all 1s that ensures that the translation vector t is applied to each point in P.

[0078] To improve registration accuracy, focus on O The norm is proposed as a robust method to minimize the overall error. It quantifies the sparsity of the registration error, effectively filtering out accurate correspondences. The optimization problem of minimizing the registration fitting error is formalized as:

[0079]

[0080] satisfy:

[0081] Among them, O * The indices of the zero vector in the error vector o correspond to the indices of the interior points, indicating that these corresponding points can be perfectly aligned under the same transformation. By minimizing the number of non-zero elements in the error vector o, the proposed optimization method maximizes the number of interior points, thereby enhancing the overall robustness of the registration process.

[0082] Regarding S3, it is divided into two steps: (1) Calculate the relative positions of the matching point pairs to eliminate translation-related terms, and further introduce the null space matrix to eliminate rotation-related terms. After two decouplings, the optimization problem of minimizing the rotation fitting error is obtained. In addition, after estimating the rotation matrix, the estimated rotation matrix is ​​substituted into the optimization problem of minimizing the registration fitting error, which is equivalent to achieving one decoupling of rotation and translation. Then, in the optimization problem after substitution, the null space matrix is ​​introduced to eliminate translation-related terms, realizing the decoupling of translation-related terms and registration fitting error. Similarly, after two decouplings, the optimization problem of minimizing the translation fitting error is obtained. Thus, this step decomposes the optimization problem of minimizing the registration fitting error into the optimization problem of minimizing the rotation fitting error and the optimization problem of minimizing the translation fitting error, thereby improving the estimation efficiency of the rotation matrix and translation vector; (2) Solve the rotation fitting error respectively. Translational fitting error O * Based on the error, the matching point pairs are screened, and the rotation hypothesis (i.e., rotation matrix) and translation hypothesis (i.e. translation vector) are estimated respectively. The preferred ones are solved using maximum likelihood estimation and Bayesian theory.

[0083] The process of step (1) of S3 in the present invention will be described in detail below.

[0084] (1) Simultaneously optimizing the rotation matrix and translation vector can be complex because they reside in different mathematical spaces. In particular, translation transformations are invariant to relative positions, so the effects of rotation and translation can be decoupled by calculating the relative positions between any two correspondences. Mathematically, for a given two points p... i and q j Their relative positions can be represented as:

[0085] q j -q i =R(p j -p i )+(o j -o i )+(ξ j -ξ i )

[0086] In this process, the translation vector is eliminated during subtraction. The relative position is denoted as... and Therefore, the equation can be expressed as:

[0087]

[0088] in, This represents the registration error caused by rotation fitting (when the correspondence between the i-th and j-th points is an interior point). (for zero), and This represents Gaussian noise. The rotation fitting error model is:

[0089]

[0090] For each pair of relative positions of the source and target points in the consistent local concentration, the following rotation fitting error model is generated by subtraction.

[0091]

[0092] in, and It contains all relative positions in the target point cloud and the source point cloud. This indicates the number of relative correspondences. It is Gaussian noise, following the distribution N(0,λ) R I) represents the variance. The optimization problem for the rotation fitting error is:

[0093]

[0094] satisfy:

[0095] For rotation estimation, in order to more accurately filter correspondences, the rotation fitting error is further reduced. The optimization is decoupled from the estimation of the rotation matrix R. The key step is to define a null space matrix. The matrix is ​​composed of The left null space is constructed by... Multiplying each term of the equation on the left eliminates the components related to the rotation matrix R in the optimization problem of minimizing the rotation fitting error:

[0096]

[0097] The optimization problem of rotation fitting error is transformed into:

[0098]

[0099] satisfy:

[0100] For translation estimation, the process is similar to that of rotation estimation described above. The translation fitting error model is as follows:

[0101]

[0102] in, This represents uncorrelated Gaussian noise that follows the order N(0,λ). t I) Distribution, λ t Let represent the variance. The optimization problem of the translation fitting error is defined as:

[0103]

[0104] satisfy:

[0105]

[0106] Similar to rotation estimation, a null space matrix Θ of 1 is introduced, satisfying Θ1 = 0, to eliminate translation-dependent components. The optimization problem of minimizing the translation fitting error is then transformed into:

[0107]

[0108] satisfy:

[0109] It should be noted that in actual point cloud registration tasks, the optimization problems of minimizing rotation fitting error and minimizing translation fitting error obtained from the above decomposition can be directly applied as model tools, and the specific formula form can be used as the preferred implementation method without performing the above derivation process.

[0110] The process of step (2) of S3 in the embodiment of the present invention is described in detail below:

[0111] (a) For rotation estimation, since It is Gaussian noise, and multiplied by the left. It is a linear operation, and the noise after transformation It still follows a Gaussian distribution with a mean of zero, and its covariance matrix is ​​transformed as follows: Record Based on the properties of the Gaussian distribution, given back, The likelihood function is:

[0112]

[0113] in, Next, based on Bayesian optimization theory and maximum likelihood estimation, the optimization problem of minimizing rotation fitting error is expressed in an unconstrained form:

[0114]

[0115] because The optimization complexity introduced by the nonconvexity of the norm is usually addressed by using... The norm is used for convex relaxation. However, The norm cannot be explicitly solved, which significantly increases the computational complexity of the algorithm. Therefore, this embodiment introduces Bayesian optimization theory to... The norm is replaced with the Frobenius norm. The optimization objective aims to maximize the marginal likelihood and minimize the combination of error and regularization terms, thereby achieving a balance between computational efficiency and model accuracy. The unconstrained form after the replacement is:

[0116]

[0117] Where, λ R `<parameter>` is a hyperparameter used to weigh the tradeoff between error and model complexity. By minimizing the gradient of the objective function and setting it to zero, the gradient of the optimization problem minimizing the rotation fitting error after replacement can be expressed as:

[0118] Explicit solution It can be calculated directly:

[0119]

[0120] This is the solution to the optimization problem of minimizing the rotation fitting error.

[0121] (b) For translation estimation, similar to solving the optimization problem of minimizing rotation fitting error mentioned above, based on Bayesian optimization theory and maximum likelihood estimation, the optimization problem of minimizing translation fitting error is rewritten as an unconstrained minimization problem, and a regularization term is added to control the sparsity of O. That is, the unconstrained form of the optimization problem of minimizing translation fitting error is:

[0122]

[0123] Where X = Θ(Q) T -(PR * ) T ), Π=ΘΘ T , λ t It is a hyperparameter. Ultimately, O can be calculated by differentiation. * :

[0124] O * =(2λ) t I+Θ T Π -1 Θ) -1 Θ T Π -1 X

[0125] Where I represents the identity matrix.

[0126] O * This is the solution to the optimization problem of minimizing the translation fitting error.

[0127] (c) Estimate the rotation and translation assumptions respectively, and select the optimal assumption.

[0128] Specifically, the estimation of rotation and translation assumptions and the selection of the optimal assumption includes:

[0129] The rotation and translation assumptions for each consistent local set are estimated, and the rationality of the assumptions is further evaluated using the correspondence in the global scope. The rotation and translation assumption with the smallest fitting error is selected as the final transformation for global point cloud registration.

[0130] The process of estimating rotation and translation assumptions and selecting the optimal assumptions in the embodiments of the present invention is described in detail below.

[0131] (c1) based on The relative correspondence with the smallest rotation fitting error is selected for estimating the rotation matrix. This is achieved by using... Norm for quantification The overall fitting error of each relative correspondence in the three spatial dimensions can be obtained by taking the fitting error of the error matrix E as the total fitting error of the three spatial dimensions. r The formula is: Choose K that minimizes the overall fitting error. r There are 1 correspondence, and its index set is denoted as I. R Then solve for the rotation matrix, which can be used as an example based on K. r A matrix is ​​constructed from the correspondences. Singular value decomposition (SVD) of this matrix yields the corresponding orthogonal matrices U and V, according to R... * =Udiag(1,1,det(UV) T The rotation matrix R is estimated from V. * .

[0132] (c2) Based on O * The correspondence with the smallest translation fitting error is selected for estimating the translation vector. O is quantized using the l2 norm. * The overall fitting error of each correspondence in the three spatial dimensions is calculated using the error matrix E. t Its formula is: Select the K elements with the smallest overall fitting error. t A set of correspondences is used for translation estimation, and its index set is denoted as I. t Then solve for the translation vector. For example, the translation vector t... * The least squares method is used to optimize the selected correspondence, and the formula is as follows: Where |I t | indicates the number of selected correspondences.

[0133] (c3) Select the best estimate from all rigid transformations generated from consistent local sets. This embodiment uses the same criterion as RANSAC, namely interior point counting, to select the final estimate. Specifically, for the estimate R of the k-th consistent local set... k and t k In this embodiment, the number of point pairs successfully registered with the transformation is calculated using a predefined error threshold τ.

[0134]

[0135] Wherein, the symbol [·] represents Iverson brackets, N c This indicates the number of input point pairs.

[0136] Finally, the transformation R with the highest interior point count is selected. k and t k As the final stiff transformation estimate.

[0137] The point cloud registration method provided by this invention will be experimentally demonstrated below, which will further confirm that the point cloud registration method provided by this invention can achieve good robustness and efficiency when facing high noise and high outlier ratio.

[0138] The accuracy, robustness, and efficiency of the algorithm were tested using Bunny point clouds from the Stanford 3D Scan repository. Bunny was downsampled to N. c And adjust the size to fit [0,1]. 3 A cube is used to create the source point cloud P. To generate the target point cloud Q, a random transformation (R,t) is applied, followed by Gaussian noise ∈ i ~N(0,σ 2 I3) is added to P. The correspondence between the original point and the moving point is defined as an interior point match. We pollute the interior point match with outliers generated by random transformations.

[0139] For outdoor scene evaluation, experiments were conducted on the KITTI dataset. 555 point cloud pairs were obtained from scenes 8 to 10 for testing. A 30 cm voxel mesh was then constructed, and the point clouds were downsampled and mapped using both handcrafted FPFH and learned FCGF descriptors.

[0140] Experiments were conducted on the 3DMatch dataset to evaluate performance on indoor scenes. Next, tests were performed using RGB-D scans of eight real-world indoor scenes. Point clouds in each scan were downsampled using a 5 cm voxel grid. Feature extraction was performed using the handcrafted descriptor FPFH and two learned descriptors, FCGF and 3DSmoothNet, and then inferred correspondences were formed based on feature matching. We further experimented on the 3DLoMatch dataset to evaluate our method in more challenging scenes (overlap between scenes <30%). Predator was then used as the feature descriptor for this dataset.

[0141] Next, rotation error (RE), translation error (TE), and registration recall (RR) were used as evaluation metrics. Registration was considered successful when RE ≤ 15 and TE ≤ 30 cm for the 3DMatch and 3DLoMatch datasets, and when RE ≤ 5 and TE ≤ 60 cm for the KITTI dataset. Average RE and TE were calculated only for successfully registered point pairs.

[0142] The method of this invention is implemented using PyTorch. For fair comparison, all experiments were conducted on a machine equipped with an Intel Xeon Gold 6134 CPU and an NVIDIA GTX 3090 graphics card.

[0143] First, by increasing the outlier ratio from 10% to 90%, and then on the Bunny dataset, N... c A robustness comparison was performed using a fixed value of 500. Gaussian noise with a mean of zero and a standard deviation of 0.01 was added. Fifty independent experiments were conducted at each outlier proportion, and the mean rotation error (RE) and translation error (TE) were reported. The method of this invention was compared with state-of-the-art conventional methods. Figure 2 As shown in the first row, the error of FGR increases sharply with the increase of the outlier ratio. RANSAC and GORE begin to fail at an outlier ratio of 70%. The method of this invention remains robust at outlier ratios up to 90% and produces more accurate estimates than all other methods. The performance of different methods is further compared at extreme outlier ratios, i.e., when the outlier ratio increases from 91% to 99%. Figure 2 The second line indicates that the method of the present invention performs well with an outlier rate of up to 99% and consistently produces a lower estimation error than other methods.

[0144] Robustness to different Gaussian noise variances was further evaluated. Figure 5As shown, when the noise standard deviation is σ = 0.01, the model's geometry remains clear. When the noise standard deviation increases to σ = 0.1, the data's geometry is completely destroyed. To demonstrate the algorithm's robustness to noise, we conducted experiments when the noise standard deviation increased from 0.01 to 0.09. Figure 4 As shown, when the noise increases to 0.03, the translation error of the geometric method MAC increases sharply. When the noise increases to 0.05, both FGR and RANSAC exhibit large rotation errors. The method of this invention maintains the lowest rotation and translation errors even when the noise increases to 0.09, demonstrating its robustness to noise.

[0145] To compare efficiency and accuracy, by using N c The number was increased from 250 to 5000, and the experiment was conducted with σ = 0.01 and the outlier ratio fixed at 50%. The results are as follows... Figure 3 As shown in (a) of the diagram, the runtime of GORE and TEASER increases significantly with the increase in the number of corresponding points. In contrast, the efficiency of the method of the present invention is less affected by the number of corresponding points. Especially when N c When the number is increased to 2500, the runtime of TEASER and GORE is approximately 10 times that of the method of this invention. 4 The method of this invention achieves high efficiency while maintaining competitive accuracy.

[0146] The effectiveness of our proposed algorithm is evaluated by applying the Bayesian Transform Estimation (BTE) algorithm to the Bunny dataset. Specifically, the Bunny model is downsampled to N... c =100 points, and set the noise level to 0.01. For example... Figure 6 As shown, a comparison of estimation errors is provided as the proportion of outliers increases from 0% to 90%. Figure 3 As shown in (b), the BTE algorithm is compared with other optimization-based methods at an outlier ratio of 90%. The BTE algorithm of this invention demonstrates superior outlier filtering capability and achieves the highest registration accuracy, proving its effectiveness.

[0147] To evaluate the method in real-world outdoor scenarios, experiments were conducted on the KITTI dataset. The comparison results are shown in Table 1. State-of-the-art traditional and deep learning methods were selected for comparison, including FGR, RANSAC, TEASER++, SC2-PCR, MAC, TR-DE, TEAR, DGR, PointDSC, and VBReg. First, the hypothetical correspondences were generated using the FPFH descriptor. As shown in the left column of Table 2, the method of this invention outperforms both traditional and learning-based methods on all metrics. For the most important metric, registration recall (RR), the method of this invention, when combined with the FPFH descriptor, improves by approximately 2% compared to the recent competitor MAC. Since failed registrations produce large translation and rotation errors, only the average rotation error (RE) and translation error (TE) of successfully registered point cloud pairs for each method were calculated to avoid unreliable metrics. This measurement strategy makes methods with high registration recall more likely to have larger average errors when calculating the average error, as they contain more challenging data. Nevertheless, the method of this invention still achieves the best results in RE and TE. The performance was further validated using the FCGF descriptor, and the results are shown in the right column of Table 2. Compared with all other methods, the method of this invention still achieves the highest registration recall and the lowest rotation error. The superior performance demonstrates the ability of the method of this invention to align sparse and non-uniformly distributed low-overlap data.

[0148] Further experiments were conducted on the 3DMatch dataset to compare performance in real-world indoor scenes. The results are shown in Tables 2 and 3. Of the methods considered, DGR, PointDSC, and VBReg are deep learning-based, while the rest are non-learning methods. Since TR-DE and TEAR did not provide publicly available code or results for FPFH and FCGF, their results are not included in Table 2.

[0149] The proposed method combines FPFH, FCGF, and 3DSmoothNet. The left column of Table 2 reports the estimation errors using the FPFH descriptor. Compared to traditional and learning-based methods, the proposed method achieves the highest registration recall. Although slightly inferior to MAC in rotation error (RE) and PointDSC in translation error (TE), it still outperforms other methods. In the FCGF setting, as shown in the middle column of Table 2, the proposed method has lower RE and TE than other methods. Notably, the improvements in registration recall (RR), rotation error (RE), and translation error (TE) compared to SC2-PCR are very significant (0.13%, 0.97%, and 0.77%, respectively), thanks to the effectiveness of the Bayesian-based interior point search. The learned 3DSmoothNet was also used as the feature descriptor for the 3DMatch dataset. Results using the 3DSmoothNet descriptor are shown in the right column of Table 2. The proposed method still significantly outperforms all other methods across all metrics, with a 0.26% improvement in registration recall compared to SC2-PCR.

[0150] Furthermore, this example also reports results on the more challenging 3DLoMatch dataset (overlap rate <30%). Correspondences are generated using Predator descriptors. Registration recall is compared with different numbers of correspondences. As shown in Table 3, the proposed method improves the average registration recall by approximately 7% compared to TR-DE, demonstrating the effectiveness of the method in handling low-overlap scenarios.

[0151] Table 1 compares the results of using hand-designed FPFH and learned FCGF descriptors on the KITTI dataset.

[0152]

[0153] Table 2 shows the registration results using FPFH, FCGF, and 3DSmoothNet descriptors on the indoor 3DMatch dataset.

[0154]

[0155]

[0156] Table 3 shows the registration rates on the 3DLoMatch dataset using different numbers of corresponding points.

[0157]

[0158] Example 2

[0159] This application also relates to an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described above.

[0160] The electronic device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The memory can be used to store computer programs and / or modules. The processor performs various functions of the electronic device by running or executing the computer programs and / or modules stored in the memory, and by accessing data stored in the memory.

[0161] The relevant technical solutions are the same as above, and will not be repeated here.

[0162] Example 3

[0163] This application also relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0164] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital cards (SD), flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0165] The relevant technical solutions are the same as above, and will not be repeated here.

[0166] Example 4

[0167] This application provides a computer program product or computer program that includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps of the method described in the above embodiments of this application.

[0168] The relevant technical solutions are the same as above, and will not be repeated here.

[0169] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 point cloud registration method based on minimizing the zero-norm of registration error, characterized in that, include: Based on the 3D spatial coordinate data of the source and target point clouds in the current point cloud registration task, optimization models that minimize rotation fitting error and translation fitting error are solved respectively, yielding the corresponding rotation fitting error for the current point cloud registration task. Translational fitting error O * ; Using L2 norm quantization The overall fitting error of each relative point in the three spatial dimensions is obtained by calculating the overall fitting error, which gives the error matrix E. r According to the error matrix E r Minimum K in r K corresponding to the overall fitting error r A set of matching point pairs are fitted to obtain the rotation matrix R. * ; Use l2 norm to quantize O * The overall fitting error of each matching point in the three spatial dimensions is used to obtain the error matrix E. t According to the error matrix E t Minimum K in t K corresponding to the overall fitting error t A pair of matching points, combined with the rotation matrix R * The translation vector t is obtained by fitting. * Based on the rotation matrix R of each point cloud registration task * Translation vector t * Achieve global point cloud registration between the source point cloud and the target point cloud; The two optimization models are constructed as follows: First, by subtracting the point-pair registration fitting error formulas for any two matched point pairs, a relative point-pair registration fitting error formula is obtained to eliminate translation-related terms. Then, the terms in the relative point-pair registration fitting error formula are multiplied by the null space matrix to eliminate rotation-related terms. Finally, the zero-norm of the obtained error formula is minimized to obtain an optimization model that minimizes the rotation fitting error. Second, using the rotation matrix in the point-pair registration fitting error formula as a known quantity, the terms in the point-pair registration fitting error formula are matrix transposed, and the transposed terms are multiplied by the null space matrix to eliminate translation-related terms. Finally, the zero-norm of the obtained error formula is minimized to obtain an optimization model that minimizes the translation fitting error.

2. The point cloud registration method according to claim 1, characterized in that, The point pair registration fitting error formula contains a noise term. Therefore, the point pair registration fitting error model used to represent the point pair registration fitting error formula for all matched point pairs is expressed as follows: O=Q-(PR+t1 T )-Ξ In the formula, O represents the point pair registration fitting error; Q and P represent the three-dimensional spatial coordinate data of the target point cloud and the source point cloud, respectively; R and t represent the rotation matrix and translation vector in point cloud registration, respectively; 1 represents a column vector of all 1s; Ξ={ξ i ∈R 3 ∣i=1,…,K2} represents the noise associated with each matching point pair, and K2 is the number of matching point pairs in the current point cloud registration task.

3. The point cloud registration method according to claim 2, characterized in that, The optimization model that minimizes the rotation fitting error is expressed as: satisfy: In the formula, This represents the rotation fitting error. Represents the zero norm, Indicates satisfaction The null space matrix, This represents a matrix composed of the differences in the three-dimensional spatial coordinates of every pair of points in the source point cloud under the current point cloud registration task. This represents a matrix composed of the differences in the three-dimensional spatial coordinates of every pair of points in the target point cloud under the current point cloud registration task. This represents Gaussian noise.

4. The point cloud registration method according to claim 2, characterized in that, The optimization model that minimizes the translation fitting error is expressed as: Satisfy: Θ(Q T -(PR * ) T )=ΘO T +ΘΞ T In the formula, O represents the translation fitting error. Let θ denote the zero norm, and let Θ denote the null space matrix satisfying Θ1 = 0.

5. The point cloud registration method according to claim 1, characterized in that, Using maximum likelihood estimation and Bayesian optimization theory, we solve the optimization models that minimize rotation fitting error and translation fitting error, respectively.

6. The point cloud registration method according to claim 5, characterized in that, The implementation method for solving the optimization model that minimizes the rotation fitting error is as follows: Using maximum likelihood estimation and Bayesian optimization theory, the optimization model that minimizes the rotation fitting error is expressed in an unconstrained form: By minimizing the gradient of this optimization model and setting it to zero, the explicit solution to the optimization problem that minimizes the rotation fitting error is expressed as: Based on this formula, and combining the three-dimensional spatial coordinate data of the source and target point clouds, the rotation fitting error under the current point cloud registration task is calculated. In the formula, To meet The null space matrix, This represents a matrix composed of the differences in the three-dimensional spatial coordinates of every pair of points in the target point cloud under the current point cloud registration task. λ R For hyperparameters, It is the Frobenius norm. Let I represent the rotation fitting error, and let I represent the identity matrix.

7. The point cloud registration method according to claim 5, characterized in that, The implementation method for solving the optimization model that minimizes the translation fitting error is as follows: Using maximum likelihood estimation and Bayesian optimization theory, the optimization model that minimizes the translation fitting error is expressed in an unconstrained form: By minimizing the gradient of this optimization model and setting it to zero, the explicit solution to the optimization problem of minimizing the translation fitting error is expressed as: O * =(2λ) t I+Θ T Π -1 Θ) -1 Θ T ∏ -1 X; Based on this formula, and combining the three-dimensional spatial coordinate data of the source point cloud and the target point cloud, the translation fitting error O under the current point cloud registration task is calculated. * ; In the formula, X = Θ(Q) T -(PR * ) T ), Π=ΘΘ T Θ is the null space matrix satisfying Θ1=0, Q and P represent the 3D spatial coordinate data of the target point cloud and the source point cloud, respectively, O represents the translation fitting error, and λ t For hyperparameters, It is the Frobenius norm.

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein the computer program, when executed by a processor, controls the device on which the storage medium is located to perform the steps of the method as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method as described in any one of claims 1 to 7.

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