Point cloud registration method based on registration error zero norm minimization

Abstract

The invention 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, which comprises the following steps of: respectively solving an optimization model of rotation fitting error minimization and an optimization model of translation fitting error minimization based on three-dimensional space coordinate data of two-point clouds; correspondingly obtaining a rotation fitting error # imgabs0 # and a translation fitting error O *; an integral fitting error of fitting errors in three spatial dimensions corresponding to each relative point pair in # imgabs1 # is quantified by using an l2 norm, and a rotation matrix R * is fitted according to matching point pairs corresponding to the minimum Kr integral fitting errors; and an integral fitting error of fitting errors in three spatial dimensions corresponding to each matching point pair in the O * is quantified by using an l2 norm, and point cloud registration is realized according to the matching point pairs corresponding to the minimum Kt integral fitting errors in combination with the rotation matrix R * and the fitting translation vector t *. According to the method, efficient point cloud registration can be realized in the presence of a large number of abnormal values.

Description

Technical Field

[0001] The present invention belongs to the field of three-dimensional 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 Art

[0002] Point cloud registration is a fundamental task in vision and robotics, and plays an important 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 include extracting features through feature descriptors, establishing assumed correspondences 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 correspondences are prone to outliers (incorrect correspondences), resulting in inaccurate alignment.

[0003] The problem of handling outlier registration has been studied for decades. They are generally divided into traditional and learning-based methods. For traditional methods, although FGR and RANSAC are simple and efficient, they tend to fail when the outlier ratio is high. Some methods rely on branch-and-bound (BnB) algorithms for global registration, but they have high computational complexity and may run in exponential time in the worst case. MAC uses a graph-theoretic framework and hypothesis evaluation to estimate the transformation. However, it cannot provide global optimality guarantees and may return estimates that are far from the true transformation. Learning-based methods use a network to filter correspondences to obtain more accurate transformation estimates. They require a large amount of data for training and usually lack the ability to generalize across different datasets. Therefore, providing guaranteed, accurate, and efficient registration in the presence of a large number of outliers, noise, and across various datasets remains a huge challenge. Summary of the invention

[0004] In view of the defects and improvement needs of the prior art, the present invention provides a point cloud registration method based on minimizing the zero norm of the registration error, which aims to achieve efficient registration of the source point cloud and the target point cloud even in the presence of a large number of outliers.

[0005] To achieve the above object, 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 point cloud and the target point cloud in the current point cloud registration task, the optimization model for minimizing the rotation fitting error and the optimization model for minimizing the translation fitting error are solved respectively, and the rotation fitting error under the current point cloud registration task is obtained accordingly. and translation fitting error O * ;

[0007] Quantization using l2 norm The overall fitting error of the fitting errors in the three spatial dimensions corresponding to each relative point pair in the error matrix E is obtained. r , according to the error matrix E r Minimum K in r K corresponding to the overall fitting error r Matching point pairs, fitting to get the rotation matrix R * ; Use l2 norm to quantify O * The overall fitting error of the fitting errors on the three spatial dimensions corresponding to each matching point pair in , and the error matrix E is obtained t , according to the error matrix E t Minimum K in t K corresponding to the overall fitting error t Matching point pairs, combined with the rotation matrix R * , fitting to obtain the translation vector t * ; Rotation matrix R based on each point cloud registration task * and the translation vector t * Realize global point cloud registration between source point cloud and target point cloud;

[0008] Among them, the two optimization models are constructed in the following way: by subtracting the point pair registration fitting error formulas of any two matching point pairs, the relative point pair registration fitting error formula is obtained to eliminate the translation-related terms, and the zero space matrix is ​​used to multiply the terms in the relative point pair registration fitting error formula to eliminate the rotation-related terms, and the obtained error formula is minimized by zero norm to obtain the optimization model with minimized rotation fitting error; the rotation matrix in the point pair registration fitting error formula is used as a known quantity, and the matrix is ​​transposed on the terms in the point pair registration fitting error formula and the transposed terms are multiplied by the zero space matrix to eliminate the translation-related terms, and the obtained error formula is minimized by zero norm to obtain the optimization model with minimized translation fitting error.

[0009] Furthermore, the point pair registration fitting error formula contains a noise term, and the point pair registration fitting error model used to represent the point pair registration fitting error formula of all matching point pairs is expressed as:

[0010]

[0011] Where 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 full 1 column vector; 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 for minimizing the rotation fitting error is expressed as:

[0013]

[0014] satisfy:

[0015] In the formula, represents the rotation fitting error, represents the zero norm, Express satisfaction The null space matrix of Represents the matrix composed of the three-dimensional space coordinate differences between two points in the source point cloud under the current point cloud registration task. Represents the matrix composed of the three-dimensional space coordinate differences between two points in the target point cloud under the current point cloud registration task. represents Gaussian noise.

[0016] Furthermore, the optimization model for minimizing the translation fitting error is expressed as:

[0017]

[0018] satisfy:

[0019] Where O represents the translation fitting error, represents the zero norm, and Θ represents the null space matrix satisfying Θ1=0.

[0020] Furthermore, the maximum likelihood estimation and Bayesian optimization theory are used to solve the optimization model for minimizing the rotation fitting error and the optimization model for minimizing the translation fitting error, respectively.

[0021] Furthermore, the optimization model for minimizing the rotation fitting error is implemented as follows:

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

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

[0024] In the formula, To satisfy The null space matrix of Represents the matrix composed of the three-dimensional space coordinate differences between two points in the target point cloud under the current point cloud registration task. λ R is a hyperparameter, is the Frobenius norm, represents the rotation fitting error, and I represents the identity matrix.

[0025] Furthermore, the optimization model for minimizing the translation fitting error is implemented as follows:

[0026] Using maximum likelihood estimation and Bayesian optimization theory, the optimization model for minimizing the translational fitting error is expressed in an unconstrained form:

[0027] By minimizing the gradient of the optimization model and setting it to zero, the explicit solution to the optimization problem of minimizing the translational fitting error is expressed as: * =(2λ t I+Θ T Π -1 Θ) -1 Θ T Π -1 X; Based on this formula, combined with 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] Where X = Θ(Q T -(PR * ) T ), Π=ΘΘ T , Θ is the null space matrix satisfying Θ1=0, Q and P represent the three-dimensional space coordinate data of the target point cloud and the source point cloud respectively, O represents the translation fitting error, λ t is a hyperparameter, is the Frobenius norm.

[0029] The present invention also provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

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

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

[0032] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0033] (1) The present invention proposes a point cloud registration method based on minimizing the zero norm of the registration error. The registration method uses an optimization model for minimizing the rotation fitting error and an optimization model for minimizing the translation fitting error. Regarding these two optimization models, the present invention uses the L0 norm to reformulate the registration problem as an optimization problem for minimizing the registration error. This is based on the principle that only the inliers can be fitted by the same transformation, so the optimal transformation should be the transformation that fits the largest number of inliers. By introducing the L0 norm, compared with other norms, the focus is on reducing the number of non-zero vectors rather than the size, so the method of the present invention better reduces the impact of outliers. In addition, by performing different decoupling methods on the optimization problem of minimizing the registration error, the optimization problem of minimizing the registration error is decoupled into optimization problems of minimizing the rotation fitting error and minimizing the translation fitting error. The decoupling methods include calculating the point-to-point relative position and introducing the null space. The rotation fitting error and the translation fitting error are solved based on the two optimization problems. By decoupling the rotation and translation solutions, the method of the present invention improves the computational efficiency, and by introducing the null space, the robustness to noise is improved. Therefore, the present invention can achieve efficient registration of the source point cloud and the target point cloud even in the presence of a large number of outliers.

[0034] (2) The present invention takes the influence of noise into consideration when optimizing the solution, thereby further improving the robustness against noise.

[0035] (3) The present invention adopts Bayesian optimization theory and maximum likelihood estimation method to solve the two decoupled optimization problems respectively, thereby ensuring the estimation accuracy of the rotation matrix and the translation vector. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0037] Figure 2 A robustness comparison diagram of outlier ratios provided by an embodiment of the present invention;

[0038] Figure 3 A comparison chart of the efficiency and effectiveness of the embodiments of the present invention with other optimization-based methods;

[0039] Figure 4 A robustness comparison diagram of Gaussian noise variance provided by an embodiment of the present invention;

[0040] Figure 5 A diagram showing the effect of Gaussian noise variation on a scanning model provided by an embodiment of the present invention;

[0041] Figure 6 A comparison diagram of the BTE algorithm provided in an embodiment of the present invention and other optimization-based methods. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0043] Embodiment 1

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

[0045] Based on the 3D spatial coordinate data of the source point cloud and the target point cloud in the current point cloud registration task, the optimization model for minimizing the rotation fitting error and the optimization model for minimizing the translation fitting error are solved respectively, and the rotation fitting error under the current point cloud registration task is obtained accordingly. and translation fitting error O * ;

[0046] Quantization using l2 norm The overall fitting error of the fitting errors in the three spatial dimensions corresponding to each relative point pair in the error matrix E is obtained. r , according to the error matrix E r Minimum K in r K corresponding to the overall fitting error r Matching point pairs, fitting to get the rotation matrix R * ;

[0047] Quantify O using the l2 norm * The overall fitting error of the fitting errors on the three spatial dimensions corresponding to each matching point pair in , and the error matrix E is obtained t , according to the error matrix E t Minimum K in t K corresponding to the overall fitting error t Matching point pairs, combined with the rotation matrix R * , fitting to obtain the translation vector t * , complete point cloud registration;

[0048] The rotation matrix R based on each point cloud registration task * and the translation vector t * Realize global point cloud registration between source point cloud and target point cloud;

[0049] Among them, the two optimization models are constructed in the following way: by subtracting the point pair registration fitting error formulas of any two matching point pairs, the relative point pair registration fitting error formula is obtained to eliminate the translation-related terms, and the zero space matrix is ​​used to multiply the terms in the relative point pair registration fitting error formula to eliminate the rotation-related terms, and the obtained error formula is minimized by zero norm to obtain the optimization model with minimized rotation fitting error; the rotation matrix in the point pair registration fitting error formula is used as a known quantity, and the matrix is ​​transposed on the terms in the point pair registration fitting error formula and the transposed terms are multiplied by the zero space matrix to eliminate the translation-related terms, and the obtained error formula is minimized by zero norm to obtain the optimization model with minimized translation fitting error.

[0050] When actually performing point cloud registration, it is necessary to first construct multiple consistent local sets for the two point clouds, and execute the above method for each consistent local set. That is, the current point cloud registration task mentioned above is the registration task performed for a consistent local set. Finally, the rotation matrices and translation vectors 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 target point cloud Q={q i ∈R 3 |i=1,…,M}, the goal of the method in 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 represents the translation vector, and the formula is as follows: In order to explain this embodiment more clearly, the embodiment is now explained according to the following steps:

[0052] S1. Construct a global compatibility graph, represent point pairs as nodes of 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 converted into an optimization problem of minimizing the registration fitting error;

[0054] S3, decomposing the registration error optimization problem into rotation error optimization and translation error optimization problems; using maximum likelihood estimation and Bayesian theory to solve the rotation fitting error and translation fitting error respectively, screening matching points according to the errors, and estimating the rotation matrix and translation vector respectively;

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

[0056] The construction of the global compatibility graph described in S1 includes: obtaining the initial matching points of two point cloud data sets; defining the geometric compatibility between point pairs by calculating the Euclidean distance between the two points; calculating the 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 input hypothetical corresponding points, we first construct a global compatibility graph, where the corresponding points are represented as nodes and geometrically compatible nodes are connected by edges. Specifically, we calculate the corresponding point pairs (c i ,c j ), as follows:

[0058]

[0059] Among them, p i and p j represents a point in the source point cloud, q i and q k are corresponding points in the target point cloud. i ,c j ) is calculated based on the Euclidean distance using the following formula:

[0060]

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

[0062]

[0063] However, the first-order compatibility metric is susceptible to outliers due to its locality and fuzziness. To this end, the second-order compatibility metric is used as the edge in the graph to reduce the impact of false correspondence. Considering global compatibility, the second-order compatibility score is calculated by the hard compatibility matrix, as follows:

[0064]

[0065] Among them, N c Indicates the number of corresponding points of the input.

[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 first 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 first 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 thus 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 will be 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, i.e., Rp i + t - q i = 0. However, considering the presence 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] where, 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 i, the above-mentioned internal point set maximization problem is reformulated as the optimization problem of registration error, thus o i It can also be regarded as a given correspondence (p i ,q i ) is an indicator of whether it is an interior point. i ,q i ) is an interior point, o i is 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 ∣i=1,…,K2}, represents the registration fitting error of all correspondences in the kth 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 ones, ensuring that the translation vector t is applied to every point in P.

[0078] In order to improve the accuracy of registration, by focusing on O norm, a robust method is proposed to minimize the overall error. This norm quantifies the sparsity of the registration error and effectively screens out accurate corresponding points. 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 correspond to the indices of the inliers, 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 inliers, thereby enhancing the overall robustness of the registration process.

[0082] Regarding S3, it is divided into two steps: (1) Calculate the relative position of the matching point pair to eliminate the translation-related terms, and further introduce the null space matrix to eliminate the rotation-related terms. After two decouplings, the optimization problem of minimizing the rotation fitting error is obtained. In addition, after estimating the rotation matrix, bring the estimated rotation matrix into the optimization problem of minimizing the registration fitting error, which is equivalent to realizing the decoupling of one rotation and translation. Then, in the optimization problem after being brought in, introduce the null space matrix to eliminate the translation-related terms, and realize the decoupling of the translation-related terms and the registration fitting error. After two decouplings, the optimization problem of minimizing the translation fitting error is obtained. Therefore, 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 the translation vector. (2) Solve the rotation fitting error separately. and translation fitting error O * , matching point pairs are screened according to the error, and the rotation hypothesis (i.e., rotation matrix) and translation hypothesis (i.e., translation vector) are estimated respectively. As a preferred method, maximum likelihood estimation and Bayesian theory are used for solution.

[0083] The following describes in detail the operation process of step (1) of S3 in the embodiment of the present invention.

[0084] (1) Optimizing both the rotation matrix and the translation vector simultaneously can be complex because they are in different mathematical spaces. In particular, translation transformations are invariant to relative positions, so the effects of rotation and translation can be decoupled by computing the relative position between any two correspondences. Mathematically, for a given pair of points p i and q j , and its relative position can be expressed as:

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

[0086] The translation vector is eliminated in the subtraction. The relative position is recorded as and So the equation can be expressed as:

[0087]

[0088] in, represents the registration error caused by rotation fitting (when the i-th and j-th correspondences are both inliers is zero), and represents Gaussian noise. The rotation fitting error model is:

[0089]

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

[0091]

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

[0093]

[0094] satisfy:

[0095] For rotation estimation, in order to more accurately screen the correspondence, the rotation fitting error is further The optimization of is decoupled from the estimation of the rotation matrix R. The key step is to define a null space matrix This matrix is ​​composed of The left null space of is constructed by By multiplying each term of the equation on the left, we eliminate the component 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 the above rotation estimation. The translation fitting error model is:

[0101]

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

[0103]

[0104] satisfy:

[0105]

[0106] Similar to rotation estimation, a null space matrix θ of 1 is introduced, which satisfies θ1 = 0, to eliminate the translation-related components. The optimization problem of minimizing the translation fitting error is transformed into:

[0107]

[0108] satisfy:

[0109] It should be noted that in the actual point cloud registration task, the optimization problem of minimizing the rotation fitting error and the optimization problem of minimizing the translation fitting error obtained by the above decomposition can be directly applied as model tools, and the specific formula form can be used as an optimal implementation method without the need to perform the above derivation process.

[0110] The following is a detailed description of the operation process of step (2) of S3 in the embodiment of the present invention, as follows:

[0111] (a) For rotation estimation, since is Gaussian noise, and multiplied by is a linear operation, the noise after transformation It still obeys the Gaussian distribution with a mean of zero, and its covariance matrix is ​​transformed into Recorded as According to the properties of Gaussian distribution, given back, The likelihood function is:

[0112]

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

[0114]

[0115] because The optimization complexity caused by the non-convexity of the norm is usually used The norm is convexly relaxed. However, The norm cannot be explicitly solved, which significantly increases the computational complexity of the algorithm. Therefore, this embodiment introduces the Bayesian optimization theory and converts The norm is replaced by 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 replacement is:

[0116]

[0117] Among them, λ R is a hyperparameter that is used to trade off between error and model complexity. By minimizing the gradient of the objective function and setting it to zero, the gradient of the optimization problem for minimizing the error of the replaced rotation fitting 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, the optimization problem of minimizing the translation fitting error is solved in the same way as the above-mentioned optimization problem of minimizing the rotation fitting error. Based on Bayesian optimization theory and maximum likelihood estimation, the optimization problem of minimizing the 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 the translation fitting error is:

[0122]

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

[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 hypothesis and translation hypothesis separately and select the optimal hypothesis.

[0128] Specifically, estimating the rotation hypothesis and the translation hypothesis and selecting the optimal hypothesis includes:

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

[0130] The process of estimating rotation and translation hypotheses and selecting the optimal hypothesis according to an embodiment of the present invention is described in detail below.

[0131] (c1) Based on The relative correspondence with the smallest rotation fitting error is selected to estimate the rotation matrix. Norm to quantify The overall fitting error of the fitting error of each relative correspondence in the three spatial dimensions can be obtained by the error matrix E r , the formula is: Select K with the smallest overall fitting error r corresponding relationship, and its index set is denoted as I R Then solve the rotation matrix, as an example, based on the K r Correspondence relationship matrix The matrix is ​​subjected to singular value decomposition (SVD) to obtain the corresponding orthogonal matrices U and V. According to R * =Udiag(1,1,det(UV T ))V, the estimated rotation matrix R * .

[0132] (c2) Based on O * , the correspondence with the smallest translation fitting error is selected to estimate the translation vector. By using the l2 norm to quantize O * The overall fitting error of the fitting error of each corresponding relationship in the three spatial dimensions is calculated, and the error matrix E is calculated. t , the formula is: Select the top K with the smallest overall fitting error t The corresponding relations are used for translation estimation, and their index set is recorded as I t Then solve for the translation vector. For example, the translation vector t * The least square 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 the rigid transformations generated by all consistent local sets. This embodiment uses the same criterion as RANSAC, i.e., the inlier count, to select the final estimate. Specifically, for the estimate R of the kth consistent local set, k and t k , this embodiment calculates the number of point pairs successfully aligned with the transformation through a predefined error threshold τ:

[0134]

[0135] The symbol [·] represents the Iverson bracket, N c Represents the number of input point pairs.

[0136] Finally, the transformation R with the highest inlier count is selected k and t k as the final rigid transformation estimate.

[0137] The point cloud registration method provided by the present invention is experimentally described below, so as to further confirm that the point cloud registration method provided by the present invention can achieve good robustness and efficiency when facing high noise and high outlier ratio.

[0138] The accuracy, robustness, and efficiency of the algorithm are tested using the Bunny point cloud from the Stanford 3D Scan Repository. The Bunny is downsampled to N c , and resize to fit [0,1] 3 cube to create the source point cloud P. To generate the target point cloud Q, a random transformation (R, t) is applied and then Gaussian noise ∈ i ~N(0,σ 2 I3) is added to P. The correspondence between the original point and the moved point is defined as the inlier match. We contaminate the inlier match by outliers generated by random transformations.

[0139] For evaluation on outdoor scenes, experiments were conducted on the KITTI dataset. 555 pairs of point clouds were obtained from scenes 8 to 10 for testing. Then, a 30 cm voxel grid was constructed to downsample the point clouds and form correspondences using handcrafted FPFH and learned FCGF descriptors, respectively.

[0140] Experiments are conducted on the 3DMatch dataset to evaluate the performance on indoor scenes. Next, 8 RGB-D scans of real indoor scenes are used for testing. The point cloud in each scan is downsampled using a 5 cm voxel grid. Feature extraction is performed using a hand-crafted descriptor FPFH and two learned descriptors FCGF and 3DSmoothNet, and then inferred correspondences are formed based on feature matching. We further conduct experiments on the 3DLoMatch dataset to evaluate our method in more challenging scenes (with an overlap rate of <30% between scenes). Next, Predator is used as a feature descriptor in this dataset.

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

[0142] The method of the present invention is implemented using PyTorch. For fair comparison, all experiments are performed on a machine equipped with an INTEL XeonGold 6134CPU and an NVIDIA GTX3090 graphics card.

[0143] First, we increase the outlier ratio from 10% to 90% and increase the N c The error is fixed to 500 for robustness comparison. Gaussian noise with a mean of zero and a standard deviation of 0.01 is added. At each outlier ratio, 50 independent experiments are performed and the average rotation error (RE) and translation error (TE) are reported. The proposed method is compared with the most advanced traditional method. Figure 2 As shown in the first row, the error of FGR increases dramatically with the increase of outlier ratio. RANSAC and GORE start to fail at 70% outlier ratio. The proposed method is still robust up to 90% outlier ratio and produces more accurate estimation results than all other methods. The performance of different methods is further compared under extreme outlier ratio, that is, when the outlier ratio increases from 91% to 99%. Figure 2 The second row shows that our method performs well up to 99% outlier ratio and consistently produces lower estimation errors than other methods.

[0144] The robustness to different Gaussian noise variances is further evaluated. Figure 5As shown in Figure 1, when the noise standard deviation is σ = 0.01, the geometric structure of the model is still clear. When the noise standard deviation increases to σ = 0.1, the geometric structure of the data is completely destroyed. In order to show the robustness of the algorithm to noise, we conducted experiments when the noise standard deviation increased from 0.01 to 0.09. Figure 4 As shown in the figure, 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 have large rotation errors. Even when the noise increases to 0.09, the method of the present invention still maintains the lowest rotation and translation errors, demonstrating its robustness to noise.

[0145] To compare efficiency and accuracy, we set N c The number of outliers was increased from 250 to 5000, and the experiment was conducted with σ = 0.01 and the outlier ratio fixed at 50%. Figure 3 As shown in (a) in the figure, the running time of GORE and TEASER increases significantly with the increase of 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. c When the number of ions increases to 2500, the running time of TEASER and GORE is about 10 times that of the method of the present invention. 4 The method of the present invention achieves high efficiency while maintaining competitive accuracy.

[0146] The effectiveness of our proposed algorithm is evaluated by applying the Bayesian transformation estimation (BTE) algorithm to the Bunny dataset. Specifically, the Bunny model is downsampled to N c = 100 points, and set the noise to 0.01. Figure 6 As shown in , a comparison of the estimation errors is provided when 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 a 90% outlier ratio. The BTE algorithm of the present invention demonstrates excellent outlier filtering capabilities and achieves the highest registration accuracy, proving its effectiveness.

[0147] In order to evaluate in real outdoor scenes, experiments were conducted on the KITTI dataset. The comparison results are shown in Table 1. The most advanced traditional methods and deep learning methods were selected for comparison, including FGR, RANSAC, TEASER++, SC2-PCR, MAC, TR-DE, TEAR, DGR, PointDSC and VBReg. The FPFH descriptor is first used to generate hypothetical corresponding point relationships. As shown in the left column of Table 2, the method of the present invention outperforms traditional methods and learning-based methods in all indicators. For the most important indicator, the registration recall rate (RR), the method of the present invention improves by about 2% over the nearest competitor MAC when combined with the FPFH descriptor. Since failed registrations will produce large translation and rotation errors, only the average rotation error (RE) and translation error (TE) of the successfully registered point cloud pairs of each method are calculated to avoid unreliable indicators. This measurement strategy makes methods with high registration recall rates more likely to have larger average errors when calculating the average error because they contain more difficult data. Despite this, the method of the present invention still achieves the best results in RE and TE. The performance is further verified using the FCGF descriptor, and the results are shown in the right column of Table 2. Compared with all methods, our method still achieves the highest registration recall and the lowest rotation error. The excellent performance demonstrates the ability of our method to align sparse and unevenly distributed low-overlap data.

[0148] Further experiments are conducted on the 3DMatch dataset to compare the performance in real indoor scenes. The results are shown in Tables 2 and 3. Among the methods considered, DGR, PointDSC, and VBReg are deep learning-based methods, while the rest are non-learning methods. Since TR-DE and TEAR do not provide public codes or results of FPFH and FCGF, their results are not included in Table 2.

[0149] Combining FPFH, FCGF and 3DSmoothNet. The left column of Table 2 reports the estimation error using the FPFH descriptor. Compared with traditional methods and learning-based methods, the proposed method achieves the highest registration recall. Although it is slightly inferior to MAC in rotation error (RE) and slightly inferior to PointDSC in translation error (TE), it is still better than other methods. Under the FCGF setting, as shown in the middle column of Table 2, the proposed method is lower than other methods in RE and TE. It is worth noting that compared with SC2-PCR, the improvement of registration recall (RR), rotation error (RE) and translation error (TE) is very significant (by 0.13%, 0.97%, and 0.77%, respectively), thanks to the effectiveness of Bayesian-based inlier search. The learned 3DSmoothNet is also used as a feature descriptor for the 3DMatch dataset. The results using the 3DSmoothNet descriptor are shown in the right column of Table 2. The proposed method still significantly outperforms all other methods in all indicators, and the registration recall is improved by 0.26% over SC2-PCR.

[0150] In addition, this example also reports the results on the more challenging dataset 3DLoMatch (overlap rate <30%). The correspondence is generated using the Predator descriptor. The registration recall rates under different numbers of corresponding points are compared. As shown in Table 3, the proposed method improves the average registration recall rate by about 7% compared with TR-DE, proving the effectiveness of the proposed method in dealing with low overlap scenes.

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

[0152]

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

[0154]

[0155]

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

[0157]

[0158] Embodiment 2

[0159] The present application also relates to an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0160] The electronic device may be a computing device such as a desktop computer, a notebook, a PDA, a cloud server, etc. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. The memory may be used to store computer programs and / or modules, and the processor may perform various functions of the electronic device by running or executing computer programs and / or modules stored in the memory, and calling data stored in the memory.

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

[0162] Embodiment 3

[0163] The present application also relates to a computer-readable storage medium having a computer program stored thereon, and the steps of the above method are implemented when the computer program is executed by a processor.

[0164] Specifically, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, an internal memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

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

[0166] Embodiment 4

[0167] The embodiment of the present application provides a computer program product or a computer program, which includes computer instructions stored in a computer-readable storage medium. The processor of a computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device performs the steps of the method of the above embodiment of the present application.

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

[0169] It will be easily understood by those skilled in the art that the above description is only 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 in the protection scope 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 point cloud and the target point cloud in the current point cloud registration task, the optimization model for minimizing the rotation fitting error and the optimization model for minimizing the translation fitting error are solved respectively, and the rotation fitting error under the current point cloud registration task is obtained accordingly. and translation fitting error O * ; Quantization using l2 norm The overall fitting error of the fitting errors in the three spatial dimensions corresponding to each relative point pair in the error matrix E is obtained. r , according to the error matrix E r Minimum K in r K corresponding to the overall fitting error r Matching point pairs, fitting to get the rotation matrix R * ; Use l2 norm to quantify O * The overall fitting error of the fitting errors on the three spatial dimensions corresponding to each matching point pair in , and the error matrix E is obtained t , according to the error matrix E t Minimum K in t K corresponding to the overall fitting error t Matching point pairs, combined with the rotation matrix R * , fitting to obtain the translation vector t * ; Rotation matrix R based on each point cloud registration task * and the translation vector t * Realize global point cloud registration between source point cloud and target point cloud; Among them, the two optimization models are constructed in the following way: by subtracting the point pair registration fitting error formulas of any two matching point pairs, the relative point pair registration fitting error formula is obtained to eliminate the translation-related terms, and the zero space matrix is ​​used to multiply the terms in the relative point pair registration fitting error formula to eliminate the rotation-related terms, and the obtained error formula is minimized by zero norm to obtain the optimization model with minimized rotation fitting error; the rotation matrix in the point pair registration fitting error formula is used as a known quantity, and the matrix is ​​transposed on the terms in the point pair registration fitting error formula and the transposed terms are multiplied by the zero space matrix to eliminate the translation-related terms, and the obtained error formula is minimized by zero norm to obtain the optimization model with minimized 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, so the point pair registration fitting error model used to represent the point pair registration fitting error formula of all matching point pairs is expressed as: O=Q-(PR+t1 T )-Ξ Where 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 the all-one column vector; 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 for minimizing the rotation fitting error is expressed as: satisfy: In the formula, represents the rotation fitting error, represents the zero norm, Express satisfaction The null space matrix of Represents the matrix composed of the three-dimensional space coordinate differences between two points in the source point cloud under the current point cloud registration task. Represents the matrix composed of the three-dimensional space coordinate differences between two points in the target point cloud under the current point cloud registration task. represents Gaussian noise.

4. The point cloud registration method according to claim 2, characterized in that: The optimization model for minimizing the translation fitting error is expressed as: Satisfy: Θ(Q T -(PR * ) T )=ΘO T +ΘΞ T Where O represents the translation fitting error, represents the zero norm, and Θ represents 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, the optimization model for minimizing the rotation fitting error and the optimization model for minimizing the translation fitting error are solved respectively.

6. The point cloud registration method according to claim 5, characterized in that: The optimization model for minimizing the rotation fitting error is implemented as follows: Using maximum likelihood estimation and Bayesian optimization theory, the optimization model for minimizing the rotation fitting error is expressed in an unconstrained form: By minimizing the gradient of the optimization model and setting it to zero, the explicit solution to the optimization problem of minimizing the rotational fit error is expressed as: Based on this formula, the rotation fitting error under the current point cloud registration task is calculated by combining the three-dimensional spatial coordinate data of the source point cloud and the target point cloud. In the formula, To satisfy The null space matrix of Represents the matrix composed of the three-dimensional space coordinate differences between two points in the target point cloud under the current point cloud registration task. λ R is a hyperparameter, is the Frobenius norm, represents the rotation fitting error, and I represents the identity matrix.

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

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to perform the steps of any one of the methods according to claims 1 to 7.

10. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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