Point cloud registration method for constructing random model based on synthetic variance covariance matrix

Abstract

The invention relates to a point cloud registration method for constructing a random model based on a synthetic variance and covariance matrix. The method comprises the following steps: S1, obtaining a coarse registration transformation matrix and a corresponding coarse registration transformation point cloud; s2, calculating distances between a query point and all points in the KD-Tree index structure, and determining the number of nearest neighbor points corresponding to the query point based on the distances; s3, screening a new corresponding point pair set; s4, solving a cofactor matrix; s5, calculating an estimated value of a fine distribution conversion parameter and an estimated value of a random error; s6, calculating source point cloud coordinates in a new state, and if the source point cloud coordinates are smaller than a set threshold value, integrating the fine registration transformation parameters after iteration and the coarse registration transformation matrix to obtain a final transformation parameter matrix; and otherwise, taking the source point cloud coordinates in the new state as the current point cloud data, taking the conversion parameter estimation value as the current fine registration parameter, and returning to S1. Compared with the prior art, the method has the advantages of realizing higher-precision parameter estimation and the like.

Description

Technical Field

[0001] The invention relates to the technical field of three-dimensional laser scanning, and in particular to a point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix. Background Art

[0002] As an emerging measurement method, 3D laser scanning technology scans the surface of an object by emitting a high-brightness, high-directional, and high-coherence laser beam to perform non-contact measurement of the target, thereby directly collecting the target's geometric information (3D coordinates) and physical property information (color, laser intensity, etc.). Compared with traditional measurement methods, 3D laser scanning technology is considered to be a revolutionary advancement, achieving a breakthrough from single-point measurement to surface measurement. With the advancement and development of science and technology, 3D laser scanning technology has become more mature and has been widely used in many fields such as autonomous driving, deformation monitoring, industrial inspection, and 3D reconstruction.

[0003] In many practical applications of 3D lasers, due to occlusion and the inability of a single station to fully cover the target, it is usually necessary to set up instruments at different angles or positions to scan the target. The essence of point cloud registration is to convert point cloud data in multiple independent coordinate systems into a unified coordinate system, after which a complete data set of the target object can be obtained. As an important part of the preprocessing step, point cloud registration is the key to the application of point cloud data, and the quality of registration directly affects the quality of subsequent analysis and ultimately determines the accuracy of the model. In view of the existence of various errors in the observations, the acquired point cloud data is not the true value, so the point cloud data itself is often uncertain. With the continuous improvement of data quality requirements and the growing demand for point cloud data applications, the existence of uncertainty may affect the application effect of point cloud data, which is one of the main challenges in achieving high-precision registration.

[0004] With the development of 3D scanning technology, it is easier to acquire and store large-scale point cloud data. Efficient and accurate algorithms are needed to process these data. To this end, multiple influencing factors can be set as parameters to be estimated and substituted into the function model. The parameter values ​​can be estimated using the least squares criterion to correct the original observations; or they can be included in the random model and weighted by the uncertainty of the observations to derive better parameter estimation results. The former method is usually used for specific tasks, such as system error calibration, but it is difficult to combine calibration and point cloud registration because the function models are inconsistent. In addition, the value of the system error may change depending on the data acquisition method or scanning configuration, that is, it is no longer a constant value. Other reasons, such as laser beam refraction caused by the external environment (air pressure, humidity, water vapor bias), also follow similar rules. Therefore, the second method, that is, to build a complete random model to better describe each observation involved in the operation, is more reasonable. The core idea is to determine its contribution to the registration parameter estimation process by assigning different weights to the observations.

[0005] The noise caused by angle measurement, distance measurement and target objects causes the accuracy of each point in the point cloud to be not a fixed value. In this case, a good registration result can be guaranteed by introducing a random model to reflect the different contributions of each point. In fact, most methods ignore the randomness of point cloud data. Therefore, each point in the point cloud is considered to be independent and has the same accuracy. For descriptor-based registration methods, they are more interested in key point detection and descriptor construction, with the goal of minimizing the Euclidean distance between corresponding points. The registration results will then be further optimized using the Iterative Closest Points (ICP) algorithm or its variants. ICP usually estimates the transformation result through singular value decomposition (SVD) and regards each point pair as a calculated value with a weight of 1, or simply uses the inverse of the absolute value of the distance between the point pairs as the weight. However, due to the existence of errors, the relative relationship between the obtained point pairs is not consistent, so the results obtained in this way have the potential to be further optimized on the random model.

[0006] Based on the angle measurement and distance measurement accuracy provided by the manufacturer or obtained by self-calibration, the error propagation law is used to obtain the block diagonal form of the variance covariance matrix (or cofactor matrix), which can be converted into a weight matrix through the prior unit weight error. In contrast, the points in the point cloud here are independent and have different accuracies, that is, there is only intra-point correlation (the x, y, and z components of each point are correlated) and no inter-point correlation (points are uncorrelated). Compared with the first method, it can effectively consider the influence of random errors in angle and distance observations, thereby improving the accuracy of estimated parameters. In addition to geometric information, physical information can also be used to construct a weight matrix, such as incident angle, intensity, etc.

[0007] In summary, in the theory and methods of massive point cloud data processing, for the purposes of computational efficiency and model accuracy, the construction of random models usually has the following methods:

[0008] (1) Treating point cloud data as equal precision

[0009] The most commonly used registration methods such as ICP and its variants assume that the coordinates of the point clouds involved in the calculation are independent and of equal precision. In this case, the random model is represented as a unit matrix, that is, each observation contributes the same to the parameter estimation. This method obviously cannot effectively take into account the errors in the observations, and is easily affected by noise points and discrete points, and cannot obtain the optimal parameter estimation results.

[0010] (2) Weighting based on the angle and distance measurement calibration accuracy (nominal accuracy) provided by the manufacturer

[0011] Weighting according to the angle and distance measurement accuracy provided by the manufacturer can effectively take into account the random errors in the distance and angle observations, and parameter estimation can be performed based on the least squares criterion. This type of weighting method has also been widely used. For example, Fitzgibbon treated point cloud registration as a general nonlinear optimization problem, used the Levenberg-Marquardt algorithm to directly minimize the registration error, and introduced the Huber function to expand it, and derived more robust registration parameter estimates; Gruen and Akca, Akca proposed an LS3D transformation parameter estimation method based on the generalized Gauss-Markov (GM) model, which assumes that the measurement error has a simple unbiased random characteristic, and ignores the error of the source point cloud in the mathematical model, and only considers the random error of the target point cloud observation value; Ge and Wunderlich expanded the LS3D method through the Gauss-Helmert (GH) model, and realized the registration of arbitrary point clouds based on the iterative solution of the linearized GH model; Zou Min proposed the Delaunay-TLS algorithm for multi-view point cloud registration based on the overall least squares principle, which overcomes the deficiency that rigid body transformation is only suitable for small rotation angles, and has higher registration accuracy than the traditional LS algorithm. However, the nominal accuracy is often obtained in a standard calibration field, which is not suitable for all field environments. In addition, this method cannot take into account the systematic errors in the observations and the influence of the external environment, so the parameter estimates are not optimal. In addition, this weighting method cannot take into account the correlation between points. It is worth noting that some manufacturers' manuals lack the angular measurement accuracy and only provide angular measurement resolution parameters, such as the Leica HDS series. Therefore, this random model construction method still has defects.

[0012] (3) Weighting based on physical attributes

[0013] Cang Guihua, Jiang Ronghua, Soudarissanane, Wujanz, etc. used numerical inversions such as incident angle and intensity to invert weight information. Among them, a smaller incident angle means that the light is closer to vertically irradiating the surface. Such observations often have larger weights, and as the incident angle increases, the weight gradually decreases; the intensity information reflects the energy change of light during propagation and reflection, and is usually associated with the noise of distance measurement to derive a random model. However, the factors affecting intensity data come from multiple aspects, such as instruments and equipment, external environmental conditions, surface characteristics of objects, and scanning geometry. Existing modeling methods cannot effectively incorporate multiple influencing factors, and smoother targets must be used to avoid additional ranging noise caused by surface roughness. This is difficult to achieve in many practical scenarios, limiting its scope of application.

[0014] (4) Directly ignore the random features of the point cloud

[0015] Registration methods such as those based on deep learning do not take into account the random characteristics of point cloud data, so there is no involvement of random models in the solution process.

[0016] Considering that point cloud data is affected by multiple errors at the same time, the above random model construction method is not rigorous, and there is some random information that has not been utilized and quantified. Regarding the fact that point clouds are affected by multiple errors at the same time, from uncompensated instrument bias to atmospheric effects, all of which are known to hinder the accuracy of target point coordinates, they should be considered and modeled in theory; on the other hand, the original points are usually assumed to be independent in processing, and the random properties (i.e., correlation) between coordinates have not been deeply analyzed and verified. Incomplete error modeling or ignoring the correlation between points during the adjustment process may lead to overly optimistic estimation results.

[0017] In summary, the random model constructed by the existing point cloud registration method ignores the various influencing factors in the data acquisition process, and the original points are set as independent points. There is a lack of correlation analysis between the coordinates, which makes it impossible to achieve higher-precision parameter estimation. Summary of the invention

[0018] The purpose of the present invention is to provide a point cloud registration method based on a synthetic variance covariance matrix to construct a random model in order to achieve higher precision parameter estimation. The elementary error model (EEM) model and the error propagation law are used to establish a synthetic variance covariance matrix (SVCM) to comprehensively consider various influencing factors in the data acquisition process, and further derive the random model of point cloud registration through the prior unit weighted mean error to achieve higher precision parameter estimation.

[0019] The purpose of the present invention can be achieved by the following technical solutions:

[0020] A point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix, the method comprising the following steps:

[0021] S1. Obtain the current point cloud data and perform preprocessing. The preprocessed current point cloud data is coarsely registered with the target point cloud to obtain a coarse registration transformation matrix and a corresponding coarse registration transformation point cloud. Then, a KD-Tree is created for the coarse registration transformation point cloud.

[0022] S2. Obtain the current fine registration parameters, select each point in the coarse registration transformation point cloud as a query point in turn, calculate the distance between the query point and all points in the KD-Tree index structure, and determine the number of nearest neighbor points corresponding to the query point based on the distance;

[0023] S3, using KNN search to calculate the distance between each pair of corresponding points, where the pair of corresponding points is a query point and a corresponding nearest neighbor point, calculating the RMSE value based on the distance between the corresponding points, using the RMSE value as a threshold to eliminate the corresponding points, and obtaining a new set of corresponding point pairs;

[0024] S4. For each point in the new set of corresponding point pairs, the distance and angle of each point are calculated by the polar coordinate formula as the distance and angle observation values ​​of the coordinate point, and the standard deviation is introduced. Based on the observation values, the influence matrices corresponding to the three types of element errors of the point cloud, namely, non-correlated error NCE, function-correlated error FCE and random-correlated error SCE, are constructed. Based on the influence matrix, the synthetic variance covariance matrix is ​​obtained, and based on the synthetic variance covariance matrix, the cofactor matrix is ​​obtained;

[0025] S5, constructing the method equation according to the indirect adjustment principle, and calculating the estimated values ​​of the precise conversion parameters and the predicted values ​​of the random errors based on the cofactor matrix;

[0026] S6. Based on the estimated values ​​of the fine matching conversion parameters and the current fine matching parameters, the fine matching conversion parameters after this iteration are obtained. Based on the fine matching conversion parameters after this iteration, the coarse matching transformation point cloud is rotated and translated to obtain the source point cloud coordinates in the new state. If the absolute value of the difference between the conversion parameters after this iteration and the current fine matching parameters is less than the set threshold, the fine matching conversion parameters after this iteration and the coarse matching transformation matrix are integrated to obtain the final conversion parameter matrix. Otherwise, the source point cloud coordinates in the new state are used as the current point cloud data, the estimated values ​​of the conversion parameters are used as the current fine matching parameters, and the predicted values ​​of the random errors are used to update the point cloud observations, and then return to S1.

[0027] Furthermore, the influence matrices corresponding to the three types of element errors of the non-correlated error NCE, the function-correlated error FCE and the random-correlated error SCE are specifically:

[0028]

[0029] Among them, D k With G h are the influence matrices corresponding to NCE and SCE respectively, both are diagonal matrices, F is the influence matrix corresponding to FCE, and is a fully filled matrix, l1, l2, …, l n represents the observed value of the coordinate point, δ k , η and γ h There are three types of element errors: non-correlated error NCE, function-correlated error FCE and random correlation error SCE.

[0030] Furthermore, the composite variance-covariance matrix is:

[0031]

[0032] Among them, each element of the synthetic variance-covariance matrix is ​​obtained based on the error propagation law, and x, y, and z represent three coordinate components.

[0033] Furthermore, the step of obtaining the co-factor matrix based on the composite variance-covariance matrix is ​​specifically: dividing the composite variance-covariance matrix by the square of the error in the set priori unit weights to obtain the co-factor matrix.

[0034] Furthermore, the specific process of calculating the estimated value of the precise conversion parameter and the predicted value of the random error based on the cofactor matrix is ​​as follows:

[0035] Get the point cloud observation values ​​in the overlapping area between the current point cloud data and the target point cloud:

[0036] f(x,y,z)+e f (x,y,z)=g{(x,y,z)+e g (x,y,z)}

[0037] Among them, e f and e g are the random errors of the current point cloud data and the target point cloud respectively;

[0038] Linearization is performed through Taylor series expansion, and the linearized equation system is:

[0039] Φ(e,ξ)=g{(x,y,z)+e g (x,y,z)}-f(x,y,z)-e f (x,y,z)

[0040] =B(ee 0 )+A(ξ-ξ 0 )+Φ 0 (e,ξ)=0

[0041] The solution of the equation system after the point cloud observation value is linearized is:

[0042]

[0043] in,

[0044]

[0045] f(x, y, z) and g(x, y, z) represent the point cloud observation values ​​in the corresponding coordinate system in the overlapping area of ​​the current point cloud data and the target point cloud, respectively. A and B are the parameters of the three-dimensional Cartesian coordinate filling method equation of the corresponding point pair set, w is the error vector, ^ represents the estimated value; K is the Lagrange multiplier, dξ is the estimated value of the precise transformation parameter, Q g , Qf are the cofactor matrices of the current point cloud data and the target point cloud respectively; R is the rotation parameter matrix obtained in the previous iteration; g x , g y and g z are the first-order partial derivatives of the function g(x,y,z) with respect to the x, y, and z coordinate components, respectively, and e 0 ,ξ 0 is the approximate value of the random error and parameter, a ij represents the rotation parameter, e=[e g ,e f ] is the residual of the overall current point cloud data and the target point cloud obtained in the previous iteration, Φ represents the Lagrangian objective function;

[0046] Based on the solution of the personalized equation group, the predicted values ​​of the precise transformation parameters and random errors after this iteration are obtained.

[0047] Furthermore, the precise matching conversion parameter after this iteration is: the sum of the current precise matching parameter ξ obtained in the previous iteration and the precise matching conversion parameter estimation value dξ.

[0048] Furthermore, the predicted value of the random error is:

[0049]

[0050] in, and are the predicted values ​​of random errors of the current point cloud data and the target point cloud, represents the Lagrange multiplier estimate.

[0051] Furthermore, the error vector is:

[0052] w=-Be 0 +Φ 0 (e 0 ,ξ 0 )

[0053] Among them, e 0 ,ξ 0 are random errors and approximate values ​​of parameters.

[0054] Furthermore, the specific steps of creating the KD-Tree are:

[0055] Select a dimension as the segmentation axis and find the segmentation point on this dimension. Based on the segmentation point, divide the coarse registration transformation point cloud into two parts, and then recursively perform the same segmentation operation on the two parts of the data. In the above process, each segmentation operation will create a new KD-Tree node and store the segmentation point information, segmentation dimension, and pointers to the left and right subtrees, and finally obtain the KD-Tree.

[0056] Furthermore, the distance between the query point and all the points in the KD-Tree index structure is specifically the Euclidean distance between the query point and all the points in the KD-Tree index structure.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] The present invention uses the meta-error model and the error propagation law to establish a synthetic variance-covariance matrix to comprehensively consider various influencing factors in the data acquisition process. The method further derives a random model of point cloud registration through a priori unit weighted mean error to achieve higher precision parameter estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a flow chart of the present invention;

[0060] Figure 2 is the plane fitting parameter residual and RMSE, where Figure 2 (a) is RMSE. Figure 2 (b) is the deviation of parameter a, Figure 2 (c) is the parameter b deviation, Figure 2 (d) is the parameter c deviation;

[0061] Figure 3 is the unit weighted mean error after plane fitting test;

[0062] Figure 4 is the deviation between the estimated value and the true value of the registration parameter, where Figure 4 (a) is the Δx deviation, Figure 4 (b) is the Δy deviation, Figure 4 (c) is the Δz deviation, Figure 4 (d) is deviation, Figure 4 (e) is the Δω deviation, Figure 4 (f) is the Δκ deviation;

[0063] Figure 5 is the registration parameter RMSE;

[0064] Figure 6 are the preprocessed source point cloud and target point cloud, where Figure 6 (a) is the source point cloud, Figure 6 (b) is the target point cloud;

[0065] Figure 7 Comparison of RMSE of different schemes;

[0066] Figure 8 is the Euclidean distance residual between point pairs after registration, where Figure 8 (a) is the Euclidean distance residual of ICP, Figure 8 (b) is the Euclidean distance residual of GH-LS3D-E, Figure 8 (c) is the Euclidean distance residual of GH-LS3D-N, Figure 8 (d) is the Euclidean distance residual of GH-LS3D-S;

[0067] Fig. 9 is the plane Euclidean distance after registration, where Fig. 9 (a) is the ICP plane Euclidean distance, where Fig. 9 (b) is the Euclidean distance of the GH-LS3D-E plane, Fig. 9 (c) is the Euclidean distance of the GH-LS3D-N plane, Fig. 9 (d) is the Euclidean distance in the GH-LS3D-S plane;

[0068] Fig.10 This is the right view of the standard plane registration result. DETAILED DESCRIPTION

[0069] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0070] The present invention proposes a point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix. The flowchart of the method is as follows: Figure 1 shown.

[0071] The present invention uses the Elementary Error Model (EEM) model and the error propagation law to establish a synthetic variance covariance matrix (SVCM) to fully consider the various influencing factors in the data acquisition process. The method further derives a random model for point cloud registration through a priori unit weighted mean error to achieve higher precision parameter estimation. The specific implementation is based on the Gauss-Helmert mathematical model, which provides an effective solution for high-precision data processing. The specific steps are as follows:

[0072] S1. Obtain the current point cloud data and perform preprocessing. The preprocessed current point cloud data is coarsely registered with the target point cloud to obtain a coarse registration transformation matrix and a corresponding coarse registration transformation point cloud. Then, a KD-Tree is created for the coarse registration transformation point cloud.

[0073] S2. Obtain the current fine registration parameters, select each point in the coarse registration transformation point cloud as a query point in turn, calculate the distance between the query point and all points in the KD-Tree index structure, and determine the number of nearest neighbor points corresponding to the query point based on the distance;

[0074] S3, using KNN search to calculate the distance between each pair of corresponding points, where the pair of corresponding points is a query point and a corresponding nearest neighbor point, calculating the RMSE value based on the distance between the corresponding points, using the RMSE value as a threshold to eliminate the corresponding points, and obtaining a new set of corresponding point pairs;

[0075] S4. For each point in the new corresponding point pair set, the distance and angle of each point are calculated by the polar coordinate formula as the distance and angle observation values ​​of the coordinate point, and the standard deviation is introduced. Based on the observation values, the influence matrices corresponding to the three types of element errors of the point cloud, namely, non-correlated error NCE, function-correlated error FCE and random-correlated error SCE, are constructed. Based on the influence matrix, the synthetic variance-covariance matrix is ​​obtained, and the co-factor matrix is ​​solved based on the set prior unit weighted mean error;

[0076] S5, constructing the method equation according to the indirect adjustment principle, and calculating the estimated values ​​of the precise conversion parameters and the random error based on the cofactor matrix;

[0077] S6. Based on the estimated values ​​of the fine matching conversion parameters and the current fine matching parameters, the fine matching conversion parameters after this iteration are obtained. Based on the fine matching conversion parameters after this iteration, the coarse matching transformation point cloud is rotated and translated to obtain the source point cloud coordinates in the new state. If the absolute value of the difference between the conversion parameters after this iteration and the current fine matching parameters is less than the set threshold, the fine matching conversion parameters after this iteration and the coarse matching transformation matrix are integrated to obtain the final conversion parameter matrix; otherwise, the source point cloud coordinates in the new state are used as the current point cloud data, and the estimated values ​​of the conversion parameters are used as the current fine matching parameters, and return to S1.

[0078] Figure 1 In the above process, according to the different calculation purposes, it can be divided into four steps: preprocessing process (P-step, that is, S1); feature point matching process (M-step, S2 and S3); registration parameter calculation process (C-step,); and finally the accuracy estimation process (E-step). The SVCM derived in the C-step is dynamic, that is, since the selection of the nearest point in each iteration may be different, after obtaining the matching point pair, the SVCM will be dynamically adjusted with the iteration to estimate the parameters more accurately. It is worth mentioning that the SVCM calculation process requires a lot of computing memory and computing power. Using Matlab R2022a as the computing platform, 8G memory can process matrix calculations of size 21000×21000; if the computer memory is 16G, it can only process data of about 10,000 points at most. Therefore, in order to prevent the calculation failure due to memory overflow during the calculation process, it is necessary to perform preprocessing operations such as downsampling on the point cloud data during the data preprocessing process.

[0079] The specific steps are as follows:

[0080] 1) Pretreatment process

[0081] (1) Point cloud denoising and sampling

[0082] The present invention calculates the distance between each point and other points in its neighborhood based on statistical filtering. If the distance statistics of a point deviates from the set threshold range, the point is considered to be a noise point and is removed. The parameters involved in this process include neighborhood radius, standard deviation multiple, etc. The intensity and effect of denoising can be controlled by adjusting these parameters. After the operation, the point cloud data with noise points removed is purer, providing a better basis for subsequent processing.

[0083] The present invention uses voxel grid sampling, which first divides the point cloud space into a number of small cubes (voxels) of equal size, and then selects a representative point in each voxel (such as the center point or the average value of all points in the voxel) as a sampling point, and finally obtains the sampled point cloud. The parameters involved in this process include the size of the voxel, which determines the sparsity of the sampling. By adjusting the voxel size, the number and density of the sampled point cloud can be controlled. After the operation, the obtained sampled point cloud retains the main shape features of the original point cloud while greatly reducing the number of points, thereby improving the efficiency of subsequent processing.

[0084] (2) Rough registration of point cloud data

[0085] The main purpose of point cloud coarse registration is to roughly align the source point cloud and the target point cloud when the transformation parameters are completely unknown, so that the relative pose relationship between the two can be preliminarily determined, providing good initial conditions for subsequent point cloud fine registration.

[0086] The present invention first uses the point cloud processing software CloudCompare to select at least three or more pairs of corresponding points in the source point cloud and the target point cloud respectively. Based on the selected corresponding points, the transformation matrix from the source point cloud to the target point cloud is calculated through the "Align" function in CloudCompare. The point cloud rough alignment will eventually obtain a transformation matrix as output. This transformation matrix contains two key parameters: the rotation matrix and the translation vector, which together describe the transformation operations required to rotate and translate the source point cloud to roughly align with the target point cloud.

[0087] (3) Create KD-Tree

[0088] The existing methods are used to create a KD-Tree for the processed point cloud data. The main purpose of KD-Tree is to improve the efficiency of spatial search during point cloud registration. KD-Tree recursively divides the point cloud data into multiple regions in multidimensional space and creates an index node for each region, allowing faster positioning of point cloud data near any query point. It usually involves the following steps: first, select a dimension as the split axis and find a split point (such as the median) on the dimension to divide the point cloud data into two parts; then, recursively perform the same split operation on the two parts of the data until a certain termination condition is met. In this process, each split operation creates a new KD-Tree node and stores the split point information, split dimension, and pointers to the left and right subtrees. The parameters used are the minimum number of points in the subset or the depth of the tree. After constructing the KD-Tree, the main parameter or data structure obtained is the complete KD-Tree itself. This KD-Tree is an efficient spatial index structure that contains the spatial partition information of all point cloud data and allows fast access to data in any area through links between nodes.

[0089] 2) Feature matching process

[0090] (1) KNN search for the closest point pair

[0091] Fine registration is an iterative optimization process. The parameter estimates approach the optimum during the adjustment process. Since the coarse registration has provided a good initial state of the point cloud, the initial values ​​of the fine registration parameters can be set to 0.

[0092] The purpose of KNN search in point cloud registration is to find the K nearest neighbor points in space for each point. After selecting a query point, KNN will calculate the distance between the point and all points in the KD-Tree index structure, sort them according to the distance, and finally select the K points with the smallest distance as the nearest neighbor points of the query point. In the KNN search process, the main parameters used include the K value, that is, the number of nearest neighbor points to be searched. In the present invention, K is set to 1; the distance measurement method, which is a specific way to calculate the distance between points. The present invention uses the Euclidean distance. The parameters finally obtained by the KNN search are the K nearest neighbor points of each query point and their corresponding distance information.

[0093] (2) Calculate the distance between point pairs and the root mean square error (RMSE)

[0094] Calculating the point pair distance and RMSE is a crucial step, which is directly related to the evaluation of the registration effect. When executing this step, the corresponding points are obtained by the "KNN search for the nearest point pair" step. Next, the Euclidean distance between each pair of corresponding points is calculated, that is, their straight-line distance in three-dimensional space. Subsequently, these point pair distances are used to calculate the RMSE value. The specific method is to first add up the squares of all point pair distances, then divide by the total number of corresponding points (that is, the number of point pairs), and finally take the square root of the average to obtain the RMSE. The key parameters used in this step include the corresponding point set, the distance measurement method (usually the Euclidean distance), and the total number of point pairs. By performing the above operations, the key parameter of the RMSE value is finally obtained.

[0095] (3) Point pair elimination

[0096] Point pair elimination is a commonly used data cleaning and optimization method to improve the accuracy and efficiency of registration. The mean error is calculated based on the distance between all corresponding point pairs; 2 times the mean error is used as the threshold to determine which point pairs have deviations beyond the acceptable range and should be eliminated. After the above operation, a corresponding point pair set with large deviations eliminated can be obtained. This new corresponding point pair set reduces the interference of noise and errors, and is purer and more reliable.

[0097] 3) Parameter calculation process

[0098] (1) Back-calculating distance and angle observations

[0099] Based on the retained point pairs, the distance and angle (vertical angle and horizontal angle) observation values ​​of each point are calculated by reverse calculation using the polar coordinate formula.

[0100] (2) Calculate the influence matrix

[0101] The influence matrix is ​​used to quantify the contribution or influence of different factors or variables on the overall variance-covariance matrix, which can be determined by the partial derivative of the observed value to the error. For non-correlated errors, the partial derivative of the ranging and angle measurement errors is calculated using the polar coordinate formula; for function-related errors, the partial derivatives of each system error term are calculated using the system error self-calibration model; for random related errors, the partial derivatives of air pressure, water vapor bias pressure and temperature should be calculated using the atmospheric refraction formula. Finally, through the above operations, the key parameter of the influence matrix is ​​obtained. For the specific calculation process, see the "5) Construction of random model based on SVCM" section.

[0102] (3) Derivation of SVCM

[0103] The purpose of SVCM is to simulate or construct a matrix that reflects the variance and covariance relationship between multiple variables. In order to achieve this goal, the use of multiple parameters is involved in the process of constructing SVCM. First, it is necessary to clarify the variables involved and their basic properties, such as the type of variables. The present invention uses 3 types, namely non-correlated errors, function-related errors, and random-related errors. In addition, it is necessary to set the variance value of each variable. The variance of non-correlated errors uses the angle-measuring accuracy given by the instrument manufacturer, the variance of function-related errors is obtained by the instrument self-calibration, and the variance of random-related errors is measured in the laboratory. Based on the above parameters and the influence matrix, the derivation of SVCM can be realized using the law of error propagation. The specific calculation process is shown in the section "5) Construction of a random model based on SVCM".

[0104] (4) Filling method equation

[0105] Based on formula (13), according to the coefficient matrix A, B and error vector w in the three-dimensional Cartesian coordinate filling method equation of the retained point pair, the cofactor matrix Q is derived by the constructed SVCM and the set prior unit weight error g , Q f .

[0106] (5) Calculation of conversion parameters and random errors

[0107] According to the normal equation and the principle of indirect adjustment, the estimated values ​​of transformation parameters and random errors are calculated.

[0108] (6) Update the precise registration transformation parameters

[0109] The calculated conversion parameter estimates and the set conversion parameter initial values ​​are used to update the conversion parameters. The conversion parameters after the current iteration are obtained and brought into the next iteration to continue the calculation.

[0110] 4) Accuracy estimation process

[0111] (1) Calculate the RMSE under the new state

[0112] According to the estimated fine registration transformation parameters, the source point cloud data after coarse registration is rotated and translated to obtain the source point cloud coordinates in the new state. After that, KNN is used again to search for the nearest point to construct the corresponding point pair and calculate the RMSE in the new state.

[0113] (2) Convergence judgment

[0114] Compare the estimated values ​​of the conversion parameters obtained in this iteration with those obtained in the previous iteration. If the absolute value of the difference between the rotation parameters and the absolute value of the difference between the translation parameters is less than the set threshold, exit the loop. Otherwise, return to step 2) to continue the calculation.

[0115] (3) Parameter update

[0116] The calculated rough registration parameter estimate and fine registration parameter estimate are used to update the transformation parameters to obtain the final transformation parameter matrix, including rotation parameters and translation parameters.

[0117] In order to explain the core content of the present invention more clearly and in detail, the following will present a detailed algorithm derivation and calculation process so that readers can deeply understand and grasp the technical details and logical context of the present invention:

[0118] 5) Stochastic model construction based on SVCM

[0119] In order to describe the random characteristics of point cloud data, it is necessary to model the variance covariance matrix (VCM) of the point cloud. The traditional construction method is to estimate the variance of each point based on the nominal accuracy using the error propagation law. In this case, the VCM can be expressed as a block diagonal matrix (see formula (1)). Each element on the diagonal represents the variance of a single scan point in three components, and the point accuracy can be derived from their square sum. At this time, for a single point, its components are correlated (intra-point correlation).

[0120]

[0121] Where D represents variance covariance; x, y, z represent three coordinate components; n is the total number of coordinate points; i is the index of the coordinate point.

[0122] According to Hagen and Bessel's assumption that the error is the result of the combined effect of many small, independent factors, the influence of these factors can be regarded as independent "meta-errors". Here we express the deviation between the observed value and the true value as a combination of several meta-errors, including non-correlating errors (NCE), functional correlation errors (FCE) and stochastic correlation errors (SCE). Among them, NCE represents random errors, FCE represents systematic errors caused by instrument assembly and other reasons, and SCE represents external environmental errors and errors related to the target object. The above construction method (Formula (1)) obviously only considers the influence of non-correlated errors on the observed value, which is not strict in theory.

[0123] Based on the EEM theory proposed and extended by Pelzer and Schwieger, an SVCM that takes into account multiple error sources can be constructed. This theory has been applied in electronic laser ranging, deformation monitoring, and 3D laser scanner error analysis. Modeling the random characteristics of point clouds using element errors requires the simultaneous participation of error vectors and influence matrices, where the influence matrix can be determined by the partial derivatives of the observed values ​​with respect to the error. Let NCE, FCE, and SCE be δ k , η and γ h , and their corresponding influence matrices are D k , F and G h . Therefore, the error in an observation is the algebraic sum of all the element errors:

[0124]

[0125] Where p, q are the number of observations containing NCE and SCE; k, h are the indices of the corresponding observations in the point cloud data.

[0126] Let Σ δδ,k ,Σ ηη ,Σ γγ,h They represent the VCM of the three types of element errors, NCE, FCE and SCE. According to the relationship between element errors, Σ δδ,k ,Σ ηη is a diagonal matrix; since the atmospheric environment is mutually influential, Σ γγ,h is a fully filled form. The covariance matrix definition and structure of the element error can be expressed as:

[0127]

[0128] Since different types of element errors affect the observed values ​​in different ways, for example, the ranging accuracy only affects the distance observed values ​​but not the angle observed values, the impact matrix has different forms. k With G h is a diagonal matrix, because the non-correlated and randomly correlated element errors only affect one observation in the function; on the contrary, the matrix F is fully filled, because a function-related error may affect several observations at the same time. According to the functional relationship between the observation value and the element error, the influence matrix can be expressed as:

[0129]

[0130] Where l1, l2, …, l n Represents the coordinate point observation value.

[0131] At this time, combining equations (2) to (4), based on the error propagation law, the SVCM can be derived as:

[0132]

[0133] According to formula (5), in order to obtain SVCM, the variance and covariance of all element errors must be quantified first. They can be specified by using information provided by the manufacturer, empirical values, etc.; in addition, Pelzer pointed out that under the premise that the probability distribution is known, the standard deviation of the element error can also be estimated based on the maximum error. Due to the simultaneous participation of multiple errors, the final SVCM is no longer a sparse matrix, but a fully filled form, as shown in formula (6).

[0134]

[0135] Comparing equation (1) and equation (6), it can be seen that SVCM can estimate multiple error factors to model the random characteristics of point clouds, and can also take into account the correlation of point cloud data compared to traditional methods. In random models, the basic idea of ​​using the variance-covariance matrix to determine weights is to determine weights based on the size of the variance. Generally, the smaller the variance, the more stable and reliable the observed value of the variable, and the greater the weight assigned; conversely, the larger the variance, the smaller the weight. In addition to the weight matrix, the cofactor matrix can also be used. The relationship between the variance-covariance matrix D, the weight matrix P, and the cofactor matrix Q is:

[0136]

[0137] In the formula, is the square of the error in the prior unit weights.

[0138] 6) Point cloud registration function model based on Gauss-Helmert model

[0139] Assume that f(x, y, z) and g(x, y, z) represent the point cloud observation values ​​in the target coordinate system and source coordinate system in the overlapping area of ​​the point cloud, respectively, then the observation equation can be expressed as:

[0140] f(x,y,z)+e f (x,y,z)=g{(x,y,z)+e g (x,y,z)} (8)

[0141] Assume the approximate values ​​of random errors and parameters to be e 0 ,ξ 0 , linearized by Taylor series expansion:

[0142]

[0143] In the formula, e=[e g ,e f ] is the residual of the two point clouds, and

[0144]

[0145]

[0146] Where R is the rotation parameter matrix; g x , g y and g z They are the first-order partial derivatives of the function g(x,y,z) with respect to the x, y, and z coordinate components:

[0147]

[0148] The estimated values ​​of the unknown parameters are the solutions to the above linearized equations:

[0149]

[0150] Where, ^ represents the estimated value; K is the Lagrange multiplier; dξ is the correction number of the registration parameter, which needs to be continuously updated during the iterative calculation process; Q g , Q f are the cofactor matrices of the two point clouds respectively; w = -Be 0 +Φ 0 (e 0 ,ξ 0 ).

[0151] At this time, the estimated value of the residual vector, that is, the predicted value of the random error is:

[0152]

[0153] The above solution process needs to be iterated. If the unknown parameter increment If it is lower than the predetermined threshold, the iteration is stopped. In each iteration, the estimation of the residual vector is used to correct the observed value, which in turn affects the update of matrices A and B.

[0154] Based on EEM, the present invention models various error factors in the scanning process, including angle measurement and distance measurement errors, instrument system deviations and environmental uncertainties, and uses the Gauss-Helmert mathematical model to establish a registration function model to achieve more accurate parameter estimation. The main contributions are as follows:

[0155] (1) Introducing a meta-error model to comprehensively model the errors in point cloud data can deepen our understanding of the nature, sources, and characteristics of errors in the data, such as revealing the causes of errors in measurement and prediction work.

[0156] At the same time, it provides a more accurate and comprehensive means for evaluating data quality, which can determine the size and distribution of errors and judge the reliability and applicability of data;

[0157] (2) Compared with the traditional random model, a more complete SVCM is constructed based on the error propagation law, which can fully reflect the random characteristics of point cloud data, especially the correlation between points;

[0158] (3) The SVCM is used to establish a random model for point cloud registration, and the Gauss-Helmert function model is used to realize point cloud registration. This is more rigorous than the traditional weight determination method, which has not been considered in previous studies.

[0159] Simulation experiments and measured data experiments were designed to verify this method, and the optimal parameter estimation results were obtained, which showed the shortcomings of traditional weight determination methods and the superiority of this method.

[0160] In order to verify the application effect of the random model constructed by SVCM in point cloud registration, experiments were carried out based on simulation data and measured data.

[0161] The simulation experiment first verifies the advantages of SVCM over the unit matrix and nominal accuracy weighting methods by plane fitting. The plane point cloud data is generated according to the TLS real field of view. A plane is set to include 200 coordinate points, and the true values ​​of the x and y components are generated in the range of [-0.5, 0.5] by a random function. The true values ​​(TV) of the plane parameters are set to ξ TV =[abc]=

[231] . At this time, the plane equation is:

[0162] z=2x+3y+1 (15)

[0163] The random model is constructed by using three methods: unit matrix (Equal), nominal precision weight (Nominal), and synthetic variance covariance matrix (SVCM) to fit the plane point cloud data. The prior unit weight error σ0 = 1 × 10 -4 SVCM still uses three types of element errors: NCE, FCE and SCE. Among them, the standard deviation of FCE is taken from the calibration results of Leica HDS 7000 by Raschhofer et al. The standard deviation values ​​of element errors are shown in Table 1:

[0164] Table 1 Prior information of element error

[0165]

[0166] The SVCM of the Cartesian coordinates of the point cloud is derived according to the error propagation law. Under the standard null hypothesis, random errors are generated and added to the true value of the Cartesian coordinates to obtain simulated point cloud data, which is repeated 1000 times. After the adjustment is completed, the parameter estimation deviation (dξ), the RMSE of the parameter and the post-test unit weighted mean error are used to calculate the error. as an evaluation indicator.

[0167]

[0168] Where n is the number of observations; t is the necessary number of observations; V and P represent the residual and observation weight matrices, respectively.

[0169] according to Figure 2-3 , all three weight determination methods can achieve plane fitting, but there are certain differences in the fitting results. The random model constructed based on SVCM can obtain the optimal parameter RMSE. Compared with equal weight and nominal accuracy weight determination, the parameters a, b, and c are improved by nearly 70%, 70%, and 55% respectively; in addition, its parameter residual sequence is closer to 0 than the other two schemes and is more stable in 1000 simulation experiments. In terms of the post-test unit weight error ( Figure 3 ), SVCM can obtain a posteriori accuracy that is closer to the prior unit weight error, while both the equal weight and nominal accuracy weighting schemes are greater than 10 -4 (priori unit weighted mean error), indicating that ignoring the correlation between observations can easily lead to overly optimistic parameter estimates. On the other hand, the RMSE performance of equal-weighted and nominal-precision weighted parameters is almost the same, but nominal-precision weighted parameters can obtain better fitting results than equal-weighted parameters ( Figure 3 (a) This is because although the former has poor RMSE performance in parameters a and b, it is better than the former in parameter c; another reason is that the weight matrix participates in the evaluation of the posterior accuracy, which leads to the difference between the two. There is a big difference.

[0170] 2) Point cloud registration based on simulation data

[0171] Through the plane fitting experiment, it can be found that if there is no complete random model involved in the adjustment process, the estimation accuracy of the parameters will be directly affected. Point cloud registration is a key process in point cloud data processing, and the quality of registration is of vital importance to point cloud data processing. This section takes point cloud registration as an example to study the impact of different random models on the registration quality.

[0172] Assume that there are 300 coordinate points randomly distributed in space to simulate the coordinates of the feature points of the target object. The range of the coordinate components in the source point cloud is specified as x∈[-2 2]m, y∈[-2 2]m, z∈[-0.5 1]m; the true value of the external orientation parameters (EOPs) is set to the translation parameter [ΔxΔyΔz]=[1 1.5 0.5]m, and the rotation parameter The true coordinate value (X, Y, Z) of the target point cloud is calculated according to the coordinate transformation equation:

[0173]

[0174] Afterwards, the SVCM is constructed using the prior information of the meta-errors given in Table 1. The Monte Carlo method is used to simulate the random errors with correlation and append them to the true values ​​of the source and target coordinates to obtain the point cloud data observations. The simulation process is repeated 1000 times.

[0175] According to different combinations of functional models and random models, the experimental scheme is designed as follows:

[0176] Solution 1: LS3D point cloud registration based on equal weights (LS3D-E);

[0177] Solution 2: LS3D point cloud registration based on nominal accuracy weighting (LS3D-N);

[0178] Scheme 3: LS3D point cloud registration based on SVCM weighting (LS3D-S);

[0179] Scheme 4: GH-LS3D point cloud registration based on nominal accuracy weighting (GH-LS3D-N);

[0180] Scheme 5: GH-LS3D point cloud registration based on SVCM weighting (GH-LS3D-S).

[0181] Since the least squares solution of the GM model under equal weight conditions is consistent with the overall least squares solution of the GH model, and the number of unknown parameters of GH-LS3D is greater, the above scheme does not include the GH-LS3D point cloud registration algorithm based on equal weights in consideration of calculation speed.

[0182] After the registration is completed, the deviation between the parameter estimate and the true value and the parameter RMSE are used to evaluate the registration quality of each scheme. The results are statistically shown as follows: Figure 4-5As shown. Under different combinations of random models and function models, there are certain differences in the registration results. In 1000 simulation experiments, compared with the other four registration algorithms, since Scheme 5 uses a complete random model and the function model can take into account the error terms of the source point cloud and target point cloud coordinate point observations at the same time, the deviation between its parameter estimation and the true value and the RMSE are the smallest, so the calculation result of Scheme 5 is the best. Although Scheme 3 also uses SVCM to construct a random model, its results are slightly worse than those of Scheme 5, which is mainly due to the difference in mathematical models. Schemes 1, 2 and 4 use equal weights and nominal accuracy weights to construct random models, respectively, and the RMSE of parameter estimation is at a disadvantage. In theory, the Gauss-Helmert model is more reasonable than the Gauss-Markov model, and its estimation results should be better, as shown in the parameter RMSE of Schemes 3 and 5, but the results of Schemes 2 and 4 are the opposite, indicating that in order to obtain high-precision parameter estimation, in addition to a rigorous function model, a complete random model should also be involved. For Schemes 1, 2 and 3 based on the GM model, Scheme 3 is generally better than Scheme 2 and Scheme 1, which reflects the advantages of the random model. However, these three schemes cannot effectively take into account the random errors of the target point cloud in both the function model and the random model, and the calculation results are not ideal. The RMSE of the parameter ω in Scheme 3 is slightly larger than that in Scheme 2, which may be related to the error of the coordinate points. It should be noted that the common RMSE calculated based on the Euclidean distance of corresponding points is not included in the registration quality evaluation index. The main reason is that it is affected by the error term of the point cloud coordinates. Even if the source point cloud is converted to the target point cloud coordinate system using high-precision parameter estimates, its RMSE index may not be optimal.

[0183] 3) Point cloud registration based on measured data

[0184] A certain indoor environment was selected as the scanning object, and the Leica HDS 7000 laser scanner was used to perform two scans at different locations (the horizontal distance between the two stations was about 6.5m) to obtain the measured point cloud data. Before registration, the cloud data of the two stations were first preprocessed to remove noise and outliers, and the area was cropped through manual interaction to ensure that the two point clouds had a high degree of overlap. The processed point cloud data was used as experimental data, such as Figure 6 shown.

[0185] At this point, the source point cloud and the target point cloud contain 370818 and 734279 data points, respectively. In the P-step, the point cloud data is first downsampled using a voxel grid with a grid size of 3 cm; then the ISS feature points of the point cloud are extracted as the registration object to reduce the matrix dimension and improve the computational efficiency. The main characteristics of ISS feature points are rotation invariance and scale invariance, that is, they can remain consistent under different postures and scales. The ISS algorithm first calculates the curvature and normal vector information of each point in the point cloud, and then uses this information to calculate the intrinsic shape signature of each point. Finally, the ISS algorithm detects key points based on these features. The number of ISS feature points of the source point cloud and the target point cloud is 1185 and 1674, respectively; the initial value of the conversion parameter is obtained by manually selecting four groups of point pairs in the open source software CloudCompare for coarse registration calculation, and the source point cloud is converted to the target point cloud coordinate system. In the M-step, in order to ensure the accuracy and robustness of the registration, the matching point pairs need to be screened. Based on the concept of Picky ICP algorithm, the median of the Euclidean distance of a point pair and the sum of two times the standard deviation are used as constraints, and only point pairs with a distance less than this standard are retained for calculation.

[0186] Since GH-LS3D is more rigorous in terms of model and can obtain more accurate parameter estimation than LS3D, only GH-LS3D is used as the registration model to study and analyze the registration results under different random models. The experimental plan is designed as follows:

[0187] Solution 1: Point cloud registration based on ICP algorithm (ICP);

[0188] Solution 2: GH-LS3D point cloud registration based on equal weights (GH-LS3D-E);

[0189] Scheme 3: GH-LS3D point cloud registration based on nominal accuracy weighting (GH-LS3D-N);

[0190] Scheme 4: GH-LS3D point cloud registration based on SVCM weighting (GH-LS3D-S).

[0191] The minimum and maximum number of iterations for all schemes are set to 5 and 20. Two criteria are used to determine whether convergence has been achieved during the iterative calculation process: (1) the changes in the registration parameters (i.e., translation parameters and rotation parameters) within a single iteration are less than 10 -4 m and 10 -5 rad; (2) Whether the RMSE change of ISS feature points between adjacent iterations is less than 10 -4m. If convergence is not achieved after 20 iterations, the registration process is terminated and the calculation results are output. After the iteration converges successfully, the source point cloud coordinates are converted to the target point cloud coordinate system using the final parameter estimation value. The RMSE of the overall point cloud, the Euclidean distance of the corresponding points, the number of point pairs and the angle of the plane normal vector are used as indicators to evaluate the registration accuracy. Among them, the number of point pairs is calculated using the overall point cloud instead of the ISS feature points; the plane normal vector is calculated using the standard plane set in the scanning area ( Figure 6 The results are shown in Table 3. In addition, the 3D Compare module of Geomagic Studio 2012 software is used to compare the overlapping areas between the two point clouds, as shown in Fig. 9 shown.

[0192] Table 3 Computation time and registration quality of different schemes

[0193] plan ICP GH-LS3D-E GH-LS3D-N GH-LS3D-S Overall RMSE(m) 0.0498 0.0167 0.0265 0.0159 The total number of point pairs 65200 71898 70011 73509 Angle between plane normal vectors (rad) 0.0260 0.0070 0.0125 0.0059

[0194] according to Figure 7 It can be seen that by using ISS feature points for registration, Schemes 1 to 4 converge after the 6th, 8th, 5th and 5th iterations, respectively, with RMSEs of 0.1261m, 0.1031m, 0.1041m and 0.1016m, respectively. After registration, the median of the Euclidean distance of the point pair and the sum of 2 times the standard deviation are also used as constraints. The number of point pairs in the overall point cloud is 65200, 71898, 70011 and 73509, respectively. Based on this, the RMSE of the overall point cloud can be calculated to be 0.0498m, 0.0167m, 0.0265m and 0.0159m (see Table 3). Therefore, Scheme 4 (GH-LS3D-S) is superior to the other three methods in terms of registration accuracy; in terms of convergence speed, taking the number of iterations as a reference, it is equivalent to Scheme 3, but better than Scheme 1 and Scheme 2. However, it is interesting to note that although Scheme 3 uses the nominal information provided by the instrument manufacturer, i.e., the distance and angle measurement accuracy, to weight the observations, it should obtain a better calculation result than the equal weighting, but this is not the case in reality. This may be directly related to the distribution and number of point pairs, because a large part of the data in the source point cloud is missing in the ground area due to line of sight occlusion (see Figure 6 ); or considering the time the instrument has been used, the nominal accuracy cannot accurately describe the prior information of the instrument at that time. This shows that in some cases, the weighting of nominal accuracy does not always improve the estimation accuracy of parameters. Compared with the other three algorithms, the RMSE of the ICP algorithm is the largest and has almost no change during the iteration process, which may be determined by the function model. In addition, the GH-LS3D method can simultaneously consider the random errors of the two point clouds, and realize the estimation of random errors and the correction of observations during the iteration process, which is more rigorous in theory.

[0195] According to the distance statistics between the point pairs after registration, GH-LS3D-E and GH-LS3D-S are closer to normal distribution, and GH-LS3D-E~N(0.0147,0.0079 2 ), GH-LS3D-S□N(0.0138,0.0079 2 ),like Figure 8 As shown. At the same variance level, the mean of GH-LS3D-S is smaller. The distance residual distribution of ICP and GH-LS3D-N is irregular. If the highest point of each histogram and the standard deviation of GH-LS3D-S (GH-LS3D-E has the same standard deviation as GH-LS3D-S) are regarded as the mean and 1 times the mean error. 48.02% of the point pair distances of ICP exceed this indicator, while that of GH-LS3D-N is 38.87%. Referring to the sigma principle of normal distribution (31.74%), it is obvious that the results of these two methods are not credible, which is mainly caused by inaccurate parameter estimation. In addition, the mean of the distance between the corresponding points of the four schemes is not 0, which is mainly due to the missing source point cloud data, resulting in a larger distance between the nearest point pairs. Because the number of ISS feature points is small and cannot reflect the statistical law of the overall point cloud, the distance between point pairs is used here as the evaluation indicator instead of the residual of the observation value after adjustment.

[0196] Cut the standard plane after registration ( Figure 6 The point cloud data (black box in the figure) can be used to obtain the chromatographic analysis results of the distance distribution using Geomagic Studio 2012 software (such as Fig. 9 ), where the color bar is in meters. Compared with the other three methods, GH-LS3D-S can obviously obtain better comparison results, and its parameter estimation value can make the Euclidean distance between the two point clouds smaller. Without considering the edge area, the difference in the overlapping area between the source point cloud and the target point cloud is about 1mm; GH-LS3D-N is about 20mm; while the difference between GH-LS3D-E and ICP is mostly between 1mm and 20mm, and the middle part of ICP and the lower end of GH-LS3D-E are worse. This is because after the source point cloud is converted using the registration parameters, ICP causes the source point cloud to move downward, GH-LS3D-E causes the source point cloud to tilt, and GH-LS3D-N causes the point cloud to translate in the horizontal direction, see Fig.10 .

[0197] To save space, the cross-sectional view is changed from a vertical state to a horizontal state, that is, the left end is the upper part and the right end is the lower part. Fig. 9The large deviation in the edge area is caused by the lack of point cloud data due to different scanning angles; another possible reason is that the point cloud noise is not completely eliminated. By fitting the registered plane point cloud data, it can be found from Table 3 that the normal vector angle between GH-LS3D-S and the original target point cloud is the smallest, followed by GH-LS3D-E, and GH-LS3D-N and ICP are the worst, indicating the superiority of GH-LS3D-S.

[0198] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A point cloud registration method based on a synthetic variance-covariance matrix to construct a random model, characterized in that: The method comprises the following steps: S1. Obtain the current point cloud data and perform preprocessing. The preprocessed current point cloud data is coarsely registered with the target point cloud to obtain a coarse registration transformation matrix and a corresponding coarse registration transformation point cloud. Then, a KD-Tree is created for the coarse registration transformation point cloud. S2. Obtain the current fine registration parameters, select each point in the coarse registration transformation point cloud as a query point in turn, calculate the distance between the query point and all points in the KD-Tree index structure, and determine the number of nearest neighbor points corresponding to the query point based on the distance; S3, using KNN search to calculate the distance between each pair of corresponding points, where the pair of corresponding points is a query point and a corresponding nearest neighbor point, calculating the RMSE value based on the distance between the corresponding points, using the RMSE value as a threshold to eliminate the corresponding points, and obtaining a new set of corresponding point pairs; S4. For each point in the new set of corresponding point pairs, the distance and angle of each point are calculated by the polar coordinate formula as the distance and angle observation values ​​of the coordinate point, and the standard deviation is introduced. Based on the observation values, the influence matrices corresponding to the three types of element errors of the point cloud, namely, non-correlated error NCE, function-correlated error FCE and random-correlated error SCE, are constructed. Based on the influence matrix, the synthetic variance covariance matrix is ​​obtained, and based on the synthetic variance covariance matrix, the cofactor matrix is ​​obtained; S5, constructing the method equation according to the indirect adjustment principle, and calculating the estimated values ​​of the precise conversion parameters and the predicted values ​​of the random errors based on the cofactor matrix; S6. Based on the estimated values ​​of the fine matching conversion parameters and the current fine matching parameters, the fine matching conversion parameters after this iteration are obtained. Based on the fine matching conversion parameters after this iteration, the coarse matching transformation point cloud is rotated and translated to obtain the source point cloud coordinates in the new state. If the absolute value of the difference between the conversion parameters after this iteration and the current fine matching parameters is less than the set threshold, the fine matching conversion parameters after this iteration and the coarse matching transformation matrix are integrated to obtain the final conversion parameter matrix. Otherwise, the source point cloud coordinates in the new state are used as the current point cloud data, the estimated values ​​of the conversion parameters are used as the current fine matching parameters, and the predicted values ​​of the random errors are used to update the point cloud observations, and then return to S1.

2. A point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 1, characterized in that: The influence matrices corresponding to the three types of element errors of the non-correlated error NCE, the function-correlated error FCE and the random-correlated error SCE are specifically: Among them, D k With G h are the influence matrices corresponding to NCE and SCE respectively, both are diagonal matrices, F is the influence matrix corresponding to FCE, and is a fully filled matrix, l1, l2, …, l n represents the observed value of the coordinate point, δ k , η and γ h There are three types of element errors: non-correlated error NCE, function-correlated error FCE and random correlation error SCE.

3. A point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 2, characterized in that: The composite variance-covariance matrix is: Among them, each element of the synthetic variance-covariance matrix is ​​obtained based on the error propagation law, and x, y, and z represent three coordinate components.

4. A point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 3, characterized in that: The method of obtaining the cofactor matrix based on the composite variance-covariance matrix is ​​specifically: dividing the composite variance-covariance matrix by the square of the error in the set priori unit weights to obtain the cofactor matrix.

5. A point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 4, characterized in that: The specific process of calculating the estimated values ​​of the precise conversion parameters and the predicted values ​​of the random errors based on the cofactor matrix is ​​as follows: Get the point cloud observation values ​​in the overlapping area between the current point cloud data and the target point cloud: f(x,y,z)+e f (x,y,z)=g{(x,y,z)+e g (x,y,z)} Among them, e f and e g are the random errors of the current point cloud data and the target point cloud respectively; Linearization is performed through Taylor series expansion, and the linearized equation system is: Φ(e,ξ)=g{(x,y,z)+e g (x,y,z)}-f(x,y,z)-e f (x,y,z) =B(ee 0 )+A(ξ-ξ 0 )+Φ 0 (e,ξ)=0 The solution of the equation system after the point cloud observation value is linearized is: in, f(x, y, z) and g(x, y, z) represent the point cloud observation values ​​in the corresponding coordinate system in the overlapping area of ​​the current point cloud data and the target point cloud, respectively. A and B are the parameters of the three-dimensional Cartesian coordinate filling method equation of the corresponding point pair set, w is the error vector, ^ represents the estimated value; K is the Lagrange multiplier, dξ is the estimated value of the precise transformation parameter, Q g , Q f are the cofactor matrices of the current point cloud data and the target point cloud respectively; R is the rotation parameter matrix obtained in the previous iteration; g x , g y and g z are the first-order partial derivatives of the function g(x,y,z) with respect to the x, y, and z coordinate components, respectively, and e 0 ,ξ 0 is the random error and the approximate value of the parameter, a ij represents the rotation parameter, e=[e g ,e f ] is the residual of the overall current point cloud data and the target point cloud obtained in the previous iteration, Φ represents the Lagrangian objective function; Based on the solution of the personalized equation group, the predicted values ​​of the precise transformation parameters and random errors after this iteration are obtained.

6. A point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 5, characterized in that: The precise matching conversion parameter after this iteration is: the sum of the current precise matching parameter ξ obtained in the previous iteration and the precise matching conversion parameter estimation value dξ.

7. The point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 5, characterized in that: The predicted value of the random error is: in, and are the predicted values ​​of random errors of the current point cloud data and the target point cloud, represents the Lagrange multiplier estimate.

8. The point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 5, characterized in that: The error vector is: w=-Be 0 +F 0 (e 0 ,x 0 ) Among them, e 0 ,ξ 0 are random errors and approximate values ​​of parameters.

9. The point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 1, characterized in that: The specific steps of creating a KD-Tree are: Select a dimension as the segmentation axis and find the segmentation point on this dimension. Based on the segmentation point, divide the coarse registration transformation point cloud into two parts, and then recursively perform the same segmentation operation on the two parts of the data. In the above process, each segmentation operation will create a new KD-Tree node and store the segmentation point information, segmentation dimension, and pointers to the left and right subtrees, and finally obtain the KD-Tree.

10. The point cloud registration method based on constructing a random model based on a synthetic variance-covariance matrix according to claim 1, characterized in that: The distance between the query point and all the points in the KD-Tree index structure is specifically the Euclidean distance between the query point and all the points in the KD-Tree index structure.

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