Global optimization method for 3D coordinate transformation parameters of multi-source data in trusted space evaluation

Abstract

The application discloses a method for globally optimizing 3D coordinate conversion parameters of multi-source three-dimensional data in a trusted space, acquires two groups of source point cloud data to be converted, target reference point cloud data, conversion quality constraint data and conversion parameter constraint interval, and performs standardization; constructs a trusted space unit according to the number of points, point cloud density and covariance eigenvalue of the space grid unit, and divides search trusted space units and verification trusted space units; in a joint conversion parameter search domain, a distance error lower bound and an overlap rate upper bound pruning parameter box are used, a processing order is determined according to the trusted space characteristics, and the parameter box is subdivided, so that candidate joint conversion parameters are obtained; verification error, overlap rate and parameter distinguishability are used to determine the joint conversion parameters to be output, coordinate conversion, quantization and post-quantization rechecking are performed, original coordinate conversion matrix and converted point cloud data are output, and the risk of mispairing of heterogeneous point clouds is reduced.

Description

Technical Field

[0001] This invention relates to the field of low-altitude mapping 3D data processing technology, and in particular to a global optimization method for 3D coordinate transformation parameters of multi-source 3D data for reliable spatial assessment. Background Technology

[0002] Photogrammetric point cloud data, UAV laser point cloud data, and ground laser point cloud data generated by low-altitude UAV mapping may differ in coordinate units, coordinate axis directions, coordinate origins, scaling ratios, point cloud density, and point position uncertainty due to differences in acquisition equipment and processing procedures. When performing 3D fusion of these data, it is necessary to establish a target coordinate reference and determine the translation, rotation, and scaling parameters for each source point cloud data to be converted.

[0003] Existing technologies typically obtain initial parameters based on flight positioning data, attitude data, or corresponding control points, and then perform registration using nearest-neighbor iteration, local feature matching, or bounded parameter search. When the initial parameters have large deviations, or when there are large rotation angles, scaling biases, density differences, or repetitive structures between point clouds, the parameter solution may concentrate on parameter regions with small local errors but incorrect overall geometric relationships. If two sets of source point cloud data to be converted are registered with target reference point cloud data respectively, the lack of joint geometric constraints between the source point clouds may lead to misalignment of the conversion results.

[0004] Furthermore, when using all points directly for evaluation, dense regions may dominate the search, and regions that are approximately collinear or have locally degraded projections can reduce the stability of correspondences. Using the same spatial region for search and verification may lead to mismatches affecting the result judgment. The lack of conservative lower bounds for distance error and upper bounds for overlap rate during parameter frame pruning, or when the termination accuracy deviates from the coordinate recording capability, may also cause erroneous deletion or invalid subdivision of parameter regions. Coordinate quantization may also alter point position errors and grid occupancy relationships. Therefore, a method is needed to implement joint bounded search under credible spatial constraints and to verify candidate parameters using spatial units not involved in the search. Summary of the Invention

[0005] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0006] Therefore, to solve the above-mentioned technical problems, the present invention provides the following technical solution: a global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment, comprising the following steps: Two sets of source point cloud data to be transformed, target reference point cloud data, transformation quality constraint data, and transformation parameter constraint intervals are acquired to determine the coordinate output resolution. The three sets of point cloud data are then divided into a spatial grid, and reliable spatial units are determined based on the number of points, point cloud density, and covariance eigenvalues. This grid is further divided into search reliable spatial units and verification reliable spatial units. A joint transformation parameter search domain and parameter box are formed using the transformation parameter constraint intervals. The search reliable spatial units are used to determine the lower bound of the distance error and the upper bound of the overlap rate between each pair of the three sets of point cloud data. The grid is pruned according to the transformation quality constraint data, and the parameter boxes are sorted and subdivided according to point cloud density and the local 3D discreteness determined by the covariance eigenvalues ​​until the change in source point coordinates is no greater than the coordinate output resolution, thus obtaining candidate joint transformation parameters. The verification reliable spatial units are used to verify the error, overlap rate, and parameter identifiability of the candidate joint transformation parameters to determine the joint transformation parameters to be output. The two sets of source point cloud data to be transformed are then transformed using the joint transformation parameters to be output, resulting in the original coordinate transformation matrix and the transformed point cloud data.

[0007] As a preferred embodiment of the global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment described in this invention, the following steps are taken: the two sets of source point cloud data to be transformed are photogrammetric point cloud data and UAV laser point cloud data, respectively; local ground laser point cloud data is acquired, the above three sets of point cloud data are cleaned, and the correspondence between the original valid point records and the original point record numbers is saved; a coordinate standardization matrix is ​​established according to the coordinate units, coordinate component arrangement order, and positive coordinate axis direction of each of the two sets of source point cloud data to be transformed, to obtain the first standardized source point cloud data and the second standardized source point cloud data, and the corresponding source point cloud center is subtracted from each of them to obtain the first standardized centered source point cloud data and the second standardized centered source point cloud data; the maximum value among the minimum coordinate recording interval required by the project and the point position uncertainty of the above three sets of point cloud data is determined as the coordinate output resolution; the minimum number of valid points of each spatial grid unit of the above three sets of point cloud data read from the point cloud acquisition technology design data is determined by the maximum value in step 3 as the minimum number of points of the reliable spatial unit.

[0008] As a preferred embodiment of the global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment described in this invention, the method includes: acquiring coordinate data of corresponding control points, definition data of the target coordinate reference system, and boundary data of the target evaluation space; establishing a target calculation coordinate reference system with meters as the unit of length based on the definition data of the target coordinate reference system; synchronously standardizing local ground laser point cloud data and coordinates of local ground laser control points; pairing local ground laser control point coordinates and target control point coordinates according to control point identifiers; performing singular value decomposition and reflection correction on the cross-covariance matrix of the paired control points to determine the control point orientation rotation matrix and the control point orientation translation vector; when the root mean square error of control point orientation is not greater than the allowable root mean square error of control point orientation, orienting the local ground laser point cloud data and clipping it according to the boundary data of the target evaluation space to obtain the target reference point cloud data and the origin of the target space; using the sum of the uncertainty of the local ground laser point cloud position and the root mean square error of the control point orientation as the conservative uncertainty of the target reference point cloud position.

[0009] As a preferred embodiment of the global optimization method for 3D coordinate transformation parameters of multi-source 3D data for reliable spatial assessment described in this invention, the method includes: calculating and sorting the three eigenvalues ​​of the point coordinate covariance of each spatial grid cell in descending order, and projecting the points onto the local principal plane formed by the first two eigenvectors; when the convex hull area of ​​the projected points is greater than 0, the point cloud density is obtained by dividing the number of points by the convex hull area of ​​the projected points; when the sum of the three covariance eigenvalues ​​is greater than 0, the local 3D dispersion is obtained by dividing three times the third covariance eigenvalue by the sum of the eigenvalues; a spatial grid cell with an actual number of points not less than the minimum number of points in the reliable spatial cell, a point cloud density not less than the corresponding minimum point cloud density, a square root of the second covariance eigenvalue greater than the larger of the coordinate output resolution and the corresponding point cloud position uncertainty, and a sum of eigenvalues ​​greater than 0 is determined as a reliable spatial cell; the target reference point cloud data adopts the conservative point position uncertainty of the target reference point cloud; and searching for reliable spatial cells and verifying reliable spatial cells are divided according to the parity of the grid index sum.

[0010] As a preferred embodiment of the global optimization method for 3D coordinate transformation parameters of multi-source 3D data for reliable spatial evaluation described in this invention, the transformation parameter constraint interval includes the original coordinate origin translation constraint interval, the rotation vector component constraint interval, and the scaling ratio constraint interval for each set of source point cloud data to be transformed; substituting the rotation vector component constraint interval into the transformation relationship between the rotation vector and the rotation matrix, and using outward rounding interval operation to enclose the sine, cosine, and matrix operation results, the rotation matrix element interval used to generate the source point coordinate interval box is obtained; candidate scaling and candidate rotation are performed on the center of the source point cloud, added to the original coordinate origin translation constraint interval, and the target space origin is subtracted to obtain the center translation parameter interval; the center translation parameter interval, rotation vector component constraint interval, and scaling ratio constraint interval of the two sets of source point cloud data to be transformed are combined in a Cartesian manner to obtain the joint transformation parameter search domain; the maximum center radius of the source point cloud is the maximum Euclidean distance from the standardized source point to the corresponding source point cloud center.

[0011] As a preferred embodiment of the global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment described in this invention, the method comprises: taking the midpoint of each parameter interval in the parameter box to form representative transformation parameters, determining three search distance errors, three actual search overlap rates, and the search target value; recording the representative transformation parameters that satisfy the transformation quality constraints as searchable transformation parameters and recording the parameter box identifier, taking the smallest search target value as the current feasible upper bound parameter, and taking its search target value as the current feasible upper bound; when there are no searchable transformation parameters, the current feasible upper bound is positive infinity; rounding out the possible transformation coordinates of the source point in the parameter box to form the source point coordinate interval box, determining the lower bounds of the three search distance errors and the upper bounds of the two source-target search overlap rates, and setting the upper bound of the inter-source search overlap rate to 1, and determining the lower bound of the parameter box search target value; deleting the parameter box when any search distance error lower bound is greater than the corresponding allowable root mean square error, any source-target search overlap rate upper bound is less than the corresponding minimum overlap rate, or the lower bound of the parameter box search target value is greater than the current feasible upper bound.

[0012] As a preferred embodiment of the global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial evaluation described in this invention, the following steps are taken: the coordinate output resolution is divided by the sum of the ratios obtained by dividing the three allowable root mean square errors by 6 to obtain the search target value comparison tolerance; the processing order is determined in ascending order according to the lower bound of the search target value of the parameter box; when the lower bound difference is not greater than the search target value comparison tolerance, the processing order is determined in descending order according to the number of corresponding point pairs whose distance is not greater than the corresponding allowable root mean square error, the median of the smaller local three-dimensional dispersion at both ends of the point pair, and the median of the smaller ratio of the point cloud density to the lowest point cloud density; the equivalent displacement width of each parameter component is determined according to the width of each parameter interval and the maximum center radius of the source point cloud, and the parameter interval corresponding to the largest one is bisected; the terminating parameter box is assigned to the parameter connected region according to the intersection or connection relationship, and the current feasible upper bound parameter is assigned to the corresponding parameter connected region according to the parameter box identifier and subdivision relationship; the parameter vector with the smallest search target value and satisfying the transformation quality constraint data is selected from each region as the candidate joint transformation parameter.

[0013] As a preferred embodiment of the global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment described in this invention, the following steps are taken: The candidate joint transformation parameters are used to transform the points within the verification reliable spatial units of two sets of standardized centralized source point cloud data. Three actual verification overlap rates and three verification root mean square errors are calculated. Those meeting the corresponding minimum overlap rate and allowable root mean square error pass the basic verification. The smaller of the allowable root mean square error between the source and target and the allowable root mean square error of geometric consistency between sources, and the larger of the coordinate output resolution, is used as the target verification displacement. The remaining parameter components are fixed, and trial parameters are generated along the decreasing and increasing directions of the parameters being verified. The maximum Euclidean distance between the transformed coordinates of the same verification point and the original candidate joint transformation parameters is recorded. This distance is bisected until the maximum value reaches the target verification displacement, thus obtaining the direction verification parameter. The larger of the absolute changes in the source-target verification root mean square error and the root mean square error of geometric consistency between sources relative to the original candidate joint transformation parameters is used as the direction error change.

[0014] As a preferred embodiment of the global optimization method for multi-source 3D coordinate transformation parameters of credible spatial assessment described in this invention, the following steps are taken: the maximum value among the coordinate output resolution, the sum of the uncertainty of the corresponding source point cloud and the conservative uncertainty of the target reference point cloud, and the sum of the uncertainties of the two sets of source point clouds is taken as the parameter identifiable change threshold; when the root mean square error of the three verifications of any direction verification parameter is not greater than the corresponding allowable root mean square error, the overlap rate of the three actual verifications is not lower than the corresponding minimum overlap rate, and the change in direction error is not greater than the parameter identifiable change threshold, the original candidate joint transformation parameter is excluded; processing stops when all candidate joint transformation parameters are excluded; the average value of the root mean square error of the three verifications of those not excluded is taken as the comprehensive verification error; when there are two or more candidate joint transformation parameters that have not been excluded, and the error difference between the two candidate joint transformation parameters with the smallest comprehensive verification error is not greater than the coordinate output resolution, the output shows a state of multiple indistinguishable parameter regions; otherwise, the one with the smallest comprehensive verification error is determined as the joint transformation parameter to be output.

[0015] As a preferred embodiment of the global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for trusted spatial assessment described in this invention, the following steps are taken: Point coordinates are represented by homogeneous column vectors. For each set of source point cloud data to be transformed, the origin recovery matrix, center translation matrix, scaling and rotation matrix, source point cloud center subtraction matrix, and coordinate standardization matrix of the target space are multiplied sequentially to obtain the original coordinate transformation matrix from the original source point coordinates to the target computational coordinate reference system. The original valid point records are then processed using the original coordinate transformation matrix. The transformed point coordinates are quantized according to the coordinate output resolution. Based on the correspondence of the original point record numbers, the quantized target point coordinates corresponding to the points within the trusted spatial unit are extracted and verified. The root mean square error of the three quantized verification items and the actual verification overlap rate of the three quantized items are redefined. When the quantized verification results meet the transformation quality constraints, two sets of original coordinate transformation matrices, two sets of quantized transformed point cloud data, and the definition data of the target computational coordinate reference system are output; otherwise, processing is stopped.

[0016] The beneficial effects of this invention are: 1. This invention cleans up the original point records, establishes a coordinate standardization relationship according to the coordinate unit, coordinate component arrangement order and positive direction of the coordinate axis, and uses corresponding control points to orient the local laser point cloud data of the ground to the target calculation coordinate reference system with the length unit as meters. This provides a unified coordinate basis for evaluating the distance, density, overlap rate and geometric consistency among the three sets of point cloud data, and reduces the impact of coordinate expression differences on the solution of transformation parameters.

[0017] 2. This invention determines reliable spatial cells based on the actual number of points in the spatial grid cell, the local principal plane point cloud density, and the covariance eigenvalue, and excludes spatial grid cells with insufficient point count, local projection degradation, or sampling density that do not meet the requirements from the reliable space; furthermore, the point cloud density and local three-dimensional dispersion are used for the parameter frame processing order, which helps to reduce the unbalanced influence of local high-density regions or degraded spatial distribution on the search direction.

[0018] 3. This invention incorporates the translation, rotation, and scaling parameters of the two sets of source point cloud data to be converted into the same joint conversion parameter search domain, and simultaneously evaluates the distance error and overlap rate between the two sets of source point cloud data to be converted and the target reference point cloud data, as well as between the two sets of source point cloud data to be converted. This ensures that the two sets of conversion parameters are jointly constrained by the source-target relationship and the geometric consistency between the sources during the same search process, which can reduce the spatial misalignment between source point clouds caused by separate registration.

[0019] 4. This invention utilizes the lower bound of distance error and the upper bound of overlap rate obtained through outward rounding to prune the parameter box. It combines the current feasible upper bound, reliable spatial features, and equivalent displacement width to determine the processing and subdivision order of the parameter box, and constrains the search termination accuracy with coordinate output resolution. Under the condition that the joint transformation parameter search domain is bounded and the upper and lower bounds of the interval remain conservative, it can reduce the dependence on a single initial transformation parameter, lowering the risk of the parameter search prematurely concentrating in the erroneous parameter region and the search accuracy significantly exceeding the coordinate recording capability.

[0020] 5. This invention divides the credible spatial unit into a search credible spatial unit and a verification credible spatial unit that does not participate in the parameter search. It uses the root mean square error of verification, the actual verification overlap rate, the bidirectional parameter perturbation, and the maximum coordinate displacement to verify the identifiability of the candidate joint transformation parameters. By combining the parameter connectivity region and the comprehensive verification error, the candidate joint transformation parameters are selected, which can identify parameter results that are difficult to distinguish under the current point uncertainty and coordinate output resolution, and reduce the risk of directly outputting ambiguous transformation results.

[0021] 6. This invention establishes a one-time original coordinate transformation matrix based on coordinate standardization, source point cloud center deduction, scaling and rotation, center translation, and target space origin restoration relationship, avoiding repeated unit conversion or coordinate axis adjustment for the same original valid point record; the quantized verification points are extracted through the correspondence of the original point record numbers, and the root mean square error of the quantized verification and the actual verification overlap rate after quantization are recalculated, so that the quantized transformed point cloud data is still checked according to the transformation quality constraint data before output, and the output coordinates are kept in correspondence with the target calculation coordinate reference system definition. Attached Figure Description

[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart illustrating the overall workflow of the present invention.

[0023] Figure 2 A sub-flowchart is established for the target reference point cloud data of this invention.

[0024] Figure 3 This is a flowchart of the construction and partitioning of the trusted spatial unit according to the present invention.

[0025] Figure 4 This is a flowchart of the parameter frame search and pruning process of the present invention.

[0026] Figure 5 This is a flowchart of the candidate joint conversion parameter verification and output sub-process of the present invention. Detailed Implementation

[0027] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0028] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0029] Secondly, an embodiment or embodiment referred to herein means a specific feature, structure or characteristic that may be included in at least one implementation of the present invention; an embodiment appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0030] Reference Figures 1-5 This embodiment provides a global optimization method for 3D coordinate transformation parameters of multi-source 3D data for reliable spatial assessment. The method is executed by a coordinate transformation processor and is used to transform a first source point cloud data and a second source point cloud data to be transformed to a target coordinate reference system. The first source point cloud data and the second source point cloud data are collectively referred to as the source point cloud data to be transformed.

[0031] The first source point cloud data to be converted is photogrammetric point cloud data obtained through aerial triangulation and dense matching based on UAV imagery, UAV flight positioning data, and camera calibration data. The second source point cloud data to be converted is UAV laser point cloud data generated by the UAV laser scanning equipment based on laser ranging data, satellite navigation positioning data, inertial measurement data, and equipment installation angle calibration data. The target reference point cloud data is established from ground laser local point cloud data and coordinate data of corresponding control points associated with the ground laser local point cloud data.

[0032] In this embodiment, a reliable spatial cell refers to a spatial grid cell whose number of points, point cloud density, and spatial distribution state all satisfy the reliability conditions described later; local three-dimensional dispersion refers to the geometric distribution characteristic quantity determined based on the covariance characteristic value of the point coordinates within the spatial grid cell; and the parameter frame refers to the multidimensional transformation parameter range formed by using the translation parameter range, rotation parameter range, and scaling ratio range as coordinate ranges, respectively.

[0033] Step S1: Read point cloud data, spatial reference data, and transformation constraint data; The coordinate transformation processor reads the first source point cloud data to be transformed, the second source point cloud data to be transformed, the local point cloud data of ground laser, the coordinate data of the corresponding control points, the target coordinate reference system definition data, the target evaluation space boundary data, and the transformation quality constraint data.

[0034] The first source point cloud data to be converted is output by the UAV photogrammetric processing equipment, and each point record includes at least a point record number and three-dimensional coordinates in the photogrammetric source coordinate system. The second source point cloud data to be converted is output by the UAV laser scanning processing equipment, and each point record includes at least a point record number and three-dimensional coordinates in the UAV laser source coordinate system. The ground laser local point cloud data is output by the ground laser scanning equipment, and each point record includes at least a point record number and three-dimensional coordinates in the ground laser local coordinate system.

[0035] The coordinate data for control points with the same name includes the control point identifier, the three-dimensional coordinates of the control point in the local ground laser coordinate system, and the three-dimensional coordinates of the same control point in the target coordinate reference system. The coordinates of the control point in the target coordinate reference system are obtained in the field by control surveying equipment. The control point identifier is used to establish a one-to-one correspondence between the two sets of control point coordinates.

[0036] The target coordinate reference system definition data includes at least the coordinate reference system identifier, coordinate datum, horizontal coordinate expression method, elevation datum, length unit, coordinate component arrangement order, and positive coordinate axis direction. The target control point coordinates and target evaluation space boundary data are interpreted according to the target coordinate reference system definition data. When the target control point coordinates are expressed in longitude and latitude, the target control point coordinates and target evaluation space boundary data are converted to the target calculation coordinate reference system with meters as the length unit, according to the coordinate datum, projection method, and projection parameters recorded in the target coordinate reference system definition data. Subsequent covariance, Euclidean distance, root mean square error, spatial grid, and coordinate quantization are all performed under the target calculation coordinate reference system. When outputting converted point cloud data, the target calculation coordinate reference system's coordinate datum, projection method, projection parameters, elevation datum, length unit, coordinate component arrangement order, and positive coordinate axis direction are simultaneously associated, not only with the original longitude and latitude coordinate reference system identifier. When the target control point coordinates are expressed in projected coordinates but the length unit is not meters, the target control point coordinates and the target evaluation space boundary data are converted to the target calculation coordinate reference system with meters as the length unit, according to the length unit conversion relationship recorded in the target coordinate reference system definition data.

[0037] The target evaluation spatial boundary data includes the coordinates of the horizontal boundary polygon, the lowest elevation, and the highest elevation in the target coordinate reference system. The coordinates of the horizontal boundary polygon, the lowest elevation, and the highest elevation are read from the control survey data of the survey area and the project spatial range data. They are subsequently used to trim the initial target reference point cloud data and to determine the target grid origin and the target spatial origin.

[0038] The conversion quality constraint data includes the minimum point cloud density of the first source point cloud to be converted, the minimum point cloud density of the second source point cloud to be converted, and the minimum point cloud density of the ground laser local point cloud; the position uncertainty of the first source point cloud to be converted, the position uncertainty of the second source point cloud to be converted, the position uncertainty of the ground laser local point cloud, the position uncertainty of the ground laser local control point, and the position uncertainty of the target control point; the allowable root mean square error between the first source point cloud to be converted and the target reference point cloud, the allowable root mean square error between the second source point cloud to be converted and the target reference point cloud, and the allowable root mean square error of geometric consistency between the two sets of source point clouds to be converted; the minimum overlap rate between the first source point cloud to be converted and the target reference point cloud, the minimum overlap rate between the second source point cloud to be converted and the target reference point cloud, and the minimum overlap rate between the two sets of source point clouds to be converted; the conversion quality constraint data also includes the allowable root mean square error of control point orientation, the minimum coordinate recording interval required by the project, the minimum scale of retained geometric features in the survey area, and the minimum number of effective points in the spatial grid cells of the first source point cloud data, the second source point cloud data to be converted, and the ground laser local point cloud data. The minimum point cloud density of the first source point cloud to be converted, the minimum point cloud density of the second source point cloud to be converted, and the minimum point cloud density of the local point cloud from the ground laser are read from the corresponding point cloud data acquisition technology design data, and the unit is points per square meter. The three minimum point cloud densities are calculated using the same caliber as the spatial grid cell point cloud density obtained in step S4 by dividing the number of points by the convex hull area of ​​the projected points.

[0039] The positional uncertainty of the local control point on the ground laser is determined based on the repeated extraction results of the same control point in the local point cloud data of the ground laser; the positional uncertainty of the target control point is determined based on the adjustment results of the target control point measurement data. Both control point positional uncertainties are converted to meters and used in step S3 to determine whether the corresponding control points are substantially collinear.

[0040] The minimum coordinate recording interval required by the project is read from the project coordinate results recording requirements, and the minimum scale of retained geometric features of the survey area is read from the project spatial object retention requirements. Both are converted to meters.

[0041] The coordinate transformation processor first verifies the transformation quality constraint data. The three minimum point cloud densities, the minimum coordinate recording interval required by the project, the minimum scale of retained geometric features in the survey area, the three allowable root mean square errors, and the allowable root mean square error for control point orientation should all be greater than 0; the positional uncertainty of each point should be greater than or equal to 0; the three minimum overlap rates should all be greater than 0 and not greater than 1; and the three minimum effective point requirements for spatial grid cells should all be positive integers. If any input data does not meet the corresponding value conditions, the processor outputs an invalid transformation quality constraint data status and stops the current coordinate transformation.

[0042] The positional uncertainties of the first and second source point clouds to be converted, as well as the positional uncertainties of the local ground laser point cloud, are determined based on the calibration data, repeated measurement data, and point cloud quality inspection data of the corresponding acquisition equipment, and are uniformly converted to meters. The nominal accuracy of the equipment is only used as the initial basis for equipment calibration and does not directly replace the positional uncertainty under the actual measurement area conditions.

[0043] The three allowable root mean square errors and the allowable root mean square error for control point orientation are read from the project coordinate connection accuracy requirements and control measurement accuracy requirements, respectively, in meters, and should all be greater than 0. The three minimum overlap rates are predetermined according to the minimum common coverage area specified in the project, using the same calculation caliber as the intersection-union ratio of the subsequently occupied grid, and the values ​​range from greater than 0 to no greater than 1.

[0044] The coordinate transformation processor reads the position uncertainty of the first source point cloud to be transformed, the position uncertainty of the second source point cloud to be transformed, and the position uncertainty of the local point cloud of ground laser, respectively, and takes the maximum value of the three position uncertainties; then compares the maximum value with the minimum coordinate recording interval required by the project, and determines the larger of the two as the coordinate output resolution, in meters.

[0045] The coordinate transformation processor reads the minimum effective point count requirements for spatial grid cells from the acquisition technology design data of the first source point cloud data to be transformed, the second source point cloud data to be transformed, and the local point cloud data of ground laser, respectively. It takes the maximum value among the three minimum effective point count requirements and value 3 as the minimum number of points for a reliable spatial cell. The minimum number of points for a reliable spatial cell is an integer. Value 3 only represents the minimum number of points required to form a non-collinear projection point set; whether the points within the spatial grid cell actually form a two-dimensional non-degenerate projection region is still determined by step S4 based on the convex hull area and the second covariance eigenvalue of the projection points.

[0046] The coordinate output resolution should be greater than 0, and the minimum number of points in the reliable spatial cell should be an integer not less than 3. If any calculation result does not meet the corresponding conditions, the output spatial evaluation parameters will be invalid, and the coordinate transformation will be stopped.

[0047] The side length of the spatial grid cell is determined according to the following rules: the coordinate output resolution is used as the basic increment, and the length is increased step by step starting from the coordinate output resolution; for each candidate side length, the square of the candidate side length is multiplied by the three lowest point cloud densities to obtain three estimated values ​​of the number of surface sampling points; when all three estimated values ​​of the number of surface sampling points are not less than the lowest number of points of the credible spatial cell, the first candidate side length that meets the condition is determined as the side length of the spatial grid cell.

[0048] It should be noted that the square of the candidate side length represents the reference surface area corresponding to the side length of the cubic grid. The estimated number of surface sampling points is only used to select the initial spatial evaluation scale and is not used as the actual number of points in the spatial grid cell. Since local surfaces may be tilted, only pass through part of the cubic grid, or be unevenly distributed in the elevation direction, step S4 still determines the actual number of points, actual projected area, and point cloud density of each spatial grid cell separately. Therefore, the estimated number of surface sampling points does not directly replace the actual reliability judgment of the spatial grid cell.

[0049] The side length of a spatial grid cell must not exceed the minimum retained geometric feature scale of the survey area. If there is no spatial grid cell side length that simultaneously satisfies the surface sampling point number condition and the minimum retained geometric feature scale condition, the output spatial evaluation scale is mismatched with the point cloud sampling capability, and the current coordinate transformation is stopped.

[0050] The coordinate transformation processor reads the coordinate units, coordinate component order, and positive direction of the coordinate axes of the first source point cloud data to be transformed, the second source point cloud data to be transformed, and the local point cloud data of ground laser, respectively; it also reads the original coordinate origin translation constraint interval, rotation vector component constraint interval, and scaling ratio constraint interval of the two sets of source point cloud data to be transformed, respectively.

[0051] The original coordinate origin translation constraint interval is determined based on the UAV's initial positioning data, exterior orientation data, and coarse control point positioning data; the rotation vector component constraint intervals are determined based on the UAV's flight attitude data, sensor installation orientation calibration data, and the uncertainty of the corresponding attitude data; the scaling ratio constraint interval is determined based on sensor scale calibration data, photogrammetric scale information, and coordinate unit conversion relationships. All constraint intervals are finite closed intervals, and the lower limit of the scaling ratio must be greater than 0.

[0052] Step S2: Clean up the original point records and establish coordinate standardization relationships; the coordinate transformation processor checks the three-dimensional coordinates in the first source point cloud data to be transformed, the second source point cloud data to be transformed, and the ground laser local point cloud data respectively. For any point record whose coordinate component is non-numerical or positive / negative infinity, the corresponding point record is marked as an invalid point record; for duplicate point records with completely identical three-dimensional coordinates in the same set of point cloud data, only the point record with the earlier point record number is retained, and a correspondence is established between the retained point records and the original point record numbers.

[0053] After deleting invalid and duplicate point records, the remaining point records are determined as the original valid point records. If the number of original valid point records in any set of point cloud data is less than the minimum number of points in a reliable spatial cell, an insufficient number of valid points is output, and the current coordinate transformation is stopped.

[0054] Based on the coordinate units, coordinate component order, and positive coordinate axis directions read in step S1, the first source point cloud coordinate normalization matrix, the second source point cloud coordinate normalization matrix, and the ground laser local point cloud coordinate normalization matrix are established respectively. Each coordinate normalization matrix is ​​a 4×4 homogeneous matrix, where the 3×3 part is used to complete the length unit conversion, coordinate component rearrangement, and coordinate axis positive direction adjustment, and the last row is used to maintain the homogeneous coordinate form. The coordinate normalization matrix does not perform translation.

[0055] The original valid point records were processed using the corresponding coordinate standardization matrix to obtain first-standardized source point cloud data, second-standardized source point cloud data, and standardized terrestrial laser local point cloud data, all in meters, arranged with the same coordinate components and conforming to the right-hand coordinate rule. The coordinates of control points with the same name in the terrestrial laser local coordinate system were standardized using the same terrestrial laser local point cloud coordinate standardization matrix.

[0056] Calculate the arithmetic mean coordinates of all points in the first and second normalized source point cloud data respectively, and determine the two arithmetic mean coordinates as the centers of the first and second source point clouds, respectively. Then, subtract the corresponding source point cloud center from each normalized source point coordinate to obtain the first normalized and centralized source point cloud data and the second normalized and centralized source point cloud data.

[0057] Step S2 outputs three sets of standardized point cloud data, two sets of standardized centered source point cloud data, two source point cloud centers, three coordinate standardization matrices, and original valid point records corresponding to each point in the standardized point cloud data. The original valid point records and the three coordinate standardization matrices are used in step S8 to establish a one-time coordinate transformation relationship, eliminating the need for repeated unit conversions or coordinate axis adjustments.

[0058] Step S3: Establish target reference point cloud data and target evaluation space; The coordinate transformation processor checks the coordinate data of control points with the same name according to the control point identifier. If one control point identifier corresponds to multiple different ground laser local coordinates or multiple different target coordinates, a control point identifier conflict is determined, the conflict status is output, and the current coordinate transformation is stopped. If there is no control point identifier conflict, a one-to-one correspondence between the ground laser local control points and the target control points is established according to the control point identifiers.

[0059] If the number of control points with the same name is less than 3, output a status indicating insufficient control points and stop processing. If the number of control points with the same name is not less than 3, calculate the coordinate covariance matrix of the ground laser local control points and the target control points respectively, and obtain their three covariance eigenvalues ​​in descending order.

[0060] When determining the local control points of the ground laser, the square root of its second covariance eigenvalue is compared with the larger of the coordinate output resolution and the position uncertainty of the local control point of the ground laser; when the square root of the second covariance eigenvalue is not greater than the larger one, the local control points of the ground laser are determined to be basically collinear.

[0061] When determining the target control point, the square root of its second covariance eigenvalue is compared with the larger of the coordinate output resolution and the positional uncertainty of the target control point; when the square root of the second covariance eigenvalue is not greater than the larger one, the target control point is determined to be basically collinear.

[0062] If any set of control points is determined to be basically collinear, the spatial distribution of the output control points does not meet the rigid orientation condition, and the coordinate transformation is stopped; if neither set of control points is determined to be basically collinear, the control point cross-covariance matrix is ​​established.

[0063] When the spatial distribution of control points meets the conditions, the coordinate centers of the local ground laser control points and the target control points are calculated separately, and the corresponding coordinate center is subtracted from the coordinates of each control point. The centered column vector of local ground laser control point coordinates is multiplied by the transpose of the corresponding column vector of target control point coordinates, and the products of all corresponding control points are summed to obtain the control point cross-covariance matrix.

[0064] Singular value decomposition is performed on the control point cross-covariance matrix to obtain the left singular vector matrix, the singular value diagonal matrix, and the right singular vector matrix. The right singular vector matrix, the reflection correction diagonal matrix, and the transpose of the left singular vector matrix are multiplied sequentially to obtain the control point orientation rotation matrix.

[0065] The first two diagonal elements of the reflection correction diagonal matrix are set to 1, and the third diagonal element is set to the sign of the determinant of the product of the right singular vector matrix and the transpose of the left singular vector matrix, so that the determinant of the control point orientation rotation matrix is ​​1, thus eliminating reflection results with a determinant of -1.

[0066] The control point orientation translation vector is obtained by subtracting the product of the control point orientation rotation matrix and the ground laser local control point coordinate center from the target control point coordinate center. The control point orientation rotation and translation are then performed on each ground laser local control point to obtain the transformed control point coordinates.

[0067] Calculate the Euclidean distance between the transformed coordinates of each control point and the corresponding target control point coordinates. Sum the squares of all Euclidean distances, divide by the number of control points of the same name, and then take the square root of the result to obtain the root mean square error of the control point orientation.

[0068] When the root mean square error of the control point orientation is greater than the allowable root mean square error of the control point orientation, the output state of "control point orientation accuracy does not meet the requirements" is displayed, and processing is stopped; when the root mean square error of the control point orientation is not greater than the allowable root mean square error of the control point orientation, the same control point orientation rotation and translation are performed on the standardized ground laser local point cloud data to obtain the initial target reference point cloud data in the target coordinate reference system.

[0069] Points located outside the target evaluation space boundary in the initial target reference point cloud data are deleted to obtain the target reference point cloud data. Boundary determination adopts the rule of including the boundary, that is, points located on the edge of the horizontal boundary polygon, or whose elevation is equal to the lowest or highest elevation, are retained in the target reference point cloud data.

[0070] The conservative position uncertainty of the target reference point cloud is obtained by adding the local point cloud position uncertainty of the ground laser to the root mean square error of the actual control point orientation. This addition process does not assume that the two errors are independent and is used for subsequent confidence space and identifiability assessments. The term "conservative" in the conservative position uncertainty of the target reference point cloud indicates that an arithmetic sum is used instead of a square root sum and square root method to avoid narrowing the evaluation scale without assuming the two errors are independent. The conservative position uncertainty of the target reference point cloud serves only as a scale for confidence space and parameter identifiability assessments in this method and does not represent the upper limit of certainty for the actual error of each target reference point.

[0071] The origin of the target space is determined based on the boundary data of the target evaluation space. Specifically, the average of the minimum and maximum abscissas of the horizontal boundary polygon is used as the abscissa of the origin of the target space, the average of the minimum and maximum ordinates is used as the ordinate of the origin of the target space, and the average of the minimum and maximum elevations is used as the elevation coordinate of the origin of the target space.

[0072] Step S4: Construct trusted spatial units and divide them into search trusted spatial units and verification trusted spatial units; The coordinate transformation processor reads the first standardized centralized source point cloud data, the second standardized centralized source point cloud data, the target reference point cloud data, and the side length of the spatial grid cell determined in step S1.

[0073] For the first and second standardized centralized source point cloud data, the minimum x-coordinate, minimum y-coordinate, and minimum elevation within their respective point cloud coordinate ranges are taken, and then rounded to the nearest integer multiple of the spatial grid cell side length, not exceeding the corresponding coordinate values, to obtain the origins of the first and second source point cloud grids. For the target reference point cloud data, the minimum x-coordinate, minimum y-coordinate, and minimum elevation of the target evaluation space boundary are determined as the target grid origin.

[0074] Starting from the corresponding grid origin, the three sets of point cloud data were divided into three-dimensional grids according to the side length of the spatial grid cells. The grid index of each point was obtained by subtracting the corresponding grid origin coordinates from its x-coordinate, y-coordinate, and elevation coordinates, then dividing by the side length of the spatial grid cell and rounding down. Each spatial grid cell adopted a left-closed, right-open boundary rule; the target reference point located on the maximum boundary of the target evaluation space was assigned to the last spatial grid cell in that direction.

[0075] For each spatial grid cell containing point records, the arithmetic mean coordinates of the points within the cell are calculated, and a 3×3 coordinate covariance matrix is ​​constructed using the difference between each point's coordinates and the arithmetic mean coordinates. Each element of the coordinate covariance matrix is ​​obtained by summing the products of the corresponding two coordinate difference components and dividing by the number of points within the cell, with units of square meters.

[0076] The first, second, and third covariance eigenvalues ​​are obtained in descending order. Each point within a cell is projected onto a local principal plane formed by the two eigenvectors corresponding to the first and second covariance eigenvalues. A convex hull of the projected points is then established within this local principal plane. The spatial grid cell point cloud density is obtained by dividing the number of points within the cell by the area of ​​the projected convex hull. If there are fewer than three projected points, the projected points are collinear, or the area of ​​the projected convex hull is zero, the spatial grid cell point cloud density is not calculated, and the corresponding spatial grid cell is marked as an unreliable spatial cell.

[0077] To quantify the degree to which the point cloud deviates from a single plane within a spatial grid cell, the local 3D discretization is calculated using the following formula: ;in, This is the index of the current spatial grid cell; The local three-dimensional discreteness of the spatial grid cell is dimensionless. The three eigenvalues ​​of the spatial grid cell coordinate covariance matrix, arranged from largest to smallest, are given in square meters and satisfy the following conditions: ; when When the denominator of the local three-dimensional discreteness calculation formula is 0, the corresponding spatial grid cell is marked as an unreliable spatial cell, and division is not performed.

[0078] when ,but When the local three-dimensional discreteness is 0, it means that the corresponding points are distributed in the local plane under the current calculation precision; at this time, it is not affected by... Instead of directly deleting the corresponding spatial grid cells, the algorithm continues to determine whether a cell belongs to a reliable spatial cell based on the actual number of points, the point cloud density of the spatial grid cell, and the second covariance eigenvalue. This process preserves planar geometric regions with two-dimensional non-degenerate distributions.

[0079] Since the numerator and denominator in the above formula have the same dimensions, the local three-dimensional dispersion is dimensionless, ranging from 0 to 1. A local three-dimensional dispersion close to 0 indicates that points are mainly distributed in the local plane; an increasing local three-dimensional dispersion indicates that points have more obvious spatial dispersion in the direction perpendicular to the principal plane. The local three-dimensional dispersion is used to characterize the degree of dispersion of the point cloud along the third principal direction within a spatial grid cell.

[0080] A spatial grid cell is defined as a reliable spatial cell when it simultaneously meets the following conditions: the number of actual points in the cell is not less than the minimum number of points in a reliable spatial cell; the point cloud density of the spatial grid cell is not less than the minimum point cloud density of the corresponding point cloud data; the square root of the second covariance eigenvalue is greater than the larger of the coordinate output resolution and the corresponding point cloud position uncertainty; and the sum of the three covariance eigenvalues ​​is greater than 0.

[0081] The first standardized centralized source point cloud data is judged using the uncertainty of the first source point cloud to be converted and the minimum point cloud density of the first source point cloud to be converted; the second standardized centralized source point cloud data is judged using the uncertainty of the second source point cloud to be converted and the minimum point cloud density of the second source point cloud to be converted; the target reference point cloud data is judged using the conservative uncertainty of the target reference point cloud and the minimum point cloud density of the ground laser local point cloud.

[0082] For each set of point cloud data, the sum of its three grid indices is calculated. When the sum of the three grid indices is even, the corresponding trusted spatial unit is assigned to the search trusted spatial unit; when the sum of the three grid indices is odd, the corresponding trusted spatial unit is assigned to the verification trusted spatial unit. This creates a spatially staggered distribution of search trusted spatial units and verification trusted spatial units within each set of point cloud data.

[0083] The verified trusted spatial units and the search trusted spatial units are derived from the same set of point cloud data. The points within the verified trusted spatial units do not participate in the calculation of the search target value, parameter box pruning, and candidate parameter selection in step S6. Their verification role is limited to reviewing the candidate joint transformation parameters output in step S6.

[0084] If any set of point cloud data does not have a searchable trusted spatial unit or a verification trusted spatial unit, output a state that the number of trusted spatial units is insufficient and stop the current coordinate transformation.

[0085] Step S5: Establish the joint transformation parameter search domain; The coordinate transformation processor reads the original coordinate origin translation constraint interval, rotation vector component constraint interval, and scaling ratio constraint interval of the first source point cloud data to be transformed and the second source point cloud data to be transformed, respectively.

[0086] Each set of source point cloud data to be transformed corresponds to 7 transformation parameters, including 3 center translation parameters, 3 rotation vector components, and 1 scaling factor. The two sets of source point cloud data to be transformed together form 14 joint transformation parameters.

[0087] For any set of source point cloud data to be converted, let m represent the point cloud sequence number, and ;set up Let represent the rotation vector of the m-th group of source point cloud data to be transformed, where all three components of the rotation vector are expressed in radians; Indicate the rotation angle, and let .

[0088] set up This represents a 3×3 antisymmetric matrix of the rotation vector. When the three components of the rotation vector are the x-coordinate, y-coordinate, and elevation coordinate components, the first row of the antisymmetric matrix is ​​0, the negative of the elevation coordinate component, and the y-coordinate component; the second row is the elevation coordinate component, 0, and the negative of the x-coordinate component; and the third row is the negative of the y-coordinate component, the x-coordinate component, and 0.

[0089] The rotation matrix of the m-th group of source point cloud data to be converted is determined using the following rotation vector-rotation matrix conversion formula: ; in, Let m be the 3×3 rotation matrix of the source point cloud data to be converted; It is a 3×3 identity matrix; The unit is radians; The value is pi; when the rotation angle is 0, a 3×3 identity matrix is ​​used, and operations with the rotation angle as the divisor are not performed.

[0090] To obtain the intervals of each element of the rotation matrix from the intervals of each component of the rotation vector, we obtain the component value closest to 0 and the endpoint value with the largest absolute value from each of the three rotation vector component intervals. The lower limit of the rotation angle interval is obtained by summing the squares of the three component values ​​closest to 0 and taking the square root; the upper limit of the rotation angle interval is obtained by summing the squares of the three endpoint values ​​with the largest absolute values ​​and taking the square root.

[0091] For the first rotation coefficient in the rotation vector-rotation matrix transformation formula Second rotation coefficient Each of these is treated as a global continuous function of the rotation angle, and the range of function values ​​within the rotation angle interval is calculated without directly dividing the sine function interval by the rotation angle interval. When the rotation angle interval includes 0, the continuous limit value 1 of the first rotation coefficient at 0 and the continuous limit value 1 / 2 of the second rotation coefficient at 0 are included in the corresponding function value ranges.

[0092] Subsequently, the intervals of each component of the rotation vector, the first rotation coefficient interval, and the second rotation coefficient interval are substituted into the rotation vector-rotation matrix transformation formula, and interval operations are performed on antisymmetric matrices, antisymmetric matrix squares, matrix scalar multiplication, and matrix addition. The lower limit of the interval for each rotation matrix element is rounded towards negative infinity, and the upper limit of the interval is rounded towards positive infinity, thus obtaining the interval of the rotation matrix elements.

[0093] The rotation angles corresponding to all corner points within the constraint interval of each set of rotation vectors should be less than [a certain value]. If this condition is not met, the output rotation constraint exceeds the unique expression range and processing stops. The rotation constraint, formed by the UAV flight attitude data and sensor installation orientation calibration data, is used to limit the range of rotation parameters that correspond to the actual acquired attitude.

[0094] For each set of source point cloud data to be transformed, the original coordinate origin translation constraint interval, the corresponding scaling ratio constraint interval, the rotation matrix interval, and the corresponding source point cloud center are substituted into the center translation relationship. Specifically, candidate scaling and candidate rotation are first performed on the source point cloud center, then added to the original coordinate origin translation constraint interval, and finally subtracted from the target space origin. All possible results are then enveloped using outward rounding interval operations to obtain the corresponding center translation parameter interval.

[0095] The original coordinate origin translation constraint interval represents the possible position of the standardized source coordinate origin in the target coordinate reference system; the center translation parameter interval represents the possible position of the source point cloud center relative to the target space origin. The two are not the same physical quantity.

[0096] The center translation parameter interval, rotation vector component constraint interval, and scaling ratio constraint interval of the two sets of source point cloud data to be transformed are combined using a Cartesian combination to obtain a 14-dimensional joint transformation parameter search domain. Step S5 outputs the joint transformation parameter search domain and its corresponding initial parameter box.

[0097] Step S6: Perform a parameter bounding box search based on distance, overlap rate, and reliable spatial features; The coordinate transformation processor reads the initial parameter box, three sets of search reliable spatial cells and their point records, spatial grid cell point cloud density, and local 3D dispersion. It then establishes a spatial index for the points within the search reliable spatial cells of the target reference point cloud data, which is used for subsequent nearest-point queries.

[0098] The transformation parameters are represented by the midpoints of the parameter intervals in each parameter box. Using two sets of representative transformation parameters, the points within the search reliable spatial units in the first and second standardized centralized source point cloud data are scaled, rotated, and translated to their centers, and the origin of the target space is restored, resulting in two sets of representative transformation points.

[0099] For each search trusted spatial unit in the first standardized centralized source point cloud data, query the nearest point distance from each representative conversion point within the search trusted spatial unit to a point within the same search trusted spatial unit of the target reference point cloud data. Take the square root of the average of the squares of all nearest point distances within the same search trusted spatial unit to obtain the root mean square distance of that search trusted spatial unit. Then, obtain the median of the root mean square distances of all search trusted spatial units in the first standardized centralized source point cloud data to obtain the search distance error between the first source point cloud to be converted and the target reference point cloud.

[0100] Using the same method, the search distance error between the second source point cloud to be converted and the target reference point cloud is obtained. For two sets of representative conversion points, the nearest point query from the first source point cloud to be converted to the second source point cloud and the nearest point query from the second source point cloud to the first source point cloud are performed respectively. The root mean square distances of the search reliable spatial cells obtained in the two directions are combined and the median is taken to obtain the search distance error between the two sets of source point clouds to be converted.

[0101] When the number of data points involved in the median calculation is odd, the middle value after sorting is taken; when the number of data points involved in the median calculation is even, the arithmetic mean of the two middle values ​​after sorting is taken.

[0102] The three search distance errors mentioned above are used to evaluate the representative transformation parameters of the parameter box, calculate the search target value, and determine whether the representative transformation parameter belongs to the search feasible transformation parameters. Subsequently, the lower bounds of the three search distance errors determined by the source point coordinate interval box within the parameter box are used to determine whether to delete the corresponding parameter box. The three search distance errors are all summarized using the median of the root mean square distance of the search reliable spatial units to reduce the impact of different numbers of points contained in different search reliable spatial units on the distance error evaluation results.

[0103] The allowed root mean square error is used in step S6 to perform dimensionless processing on the search distance error and serves as a distance constraint for judging feasible transformation parameters and pruning the parameter box. Feasible transformation parameters only indicate that the corresponding transformation parameters meet the constraints of the search phase and are not directly output as the final transformation result. Step S7 determines the joint transformation parameters to be output based on the verification root mean square error, the actual verification overlap rate, and parameter identifiability; step S8 controls the output of the final transformation result based on the quantized verification root mean square error and the quantized actual verification overlap rate.

[0104] The two sets of representative transformation points are converted into target grid indices according to the target grid origin and the side length of the spatial grid cells. Duplicate grid indices are then removed to obtain the first set of source point cloud search-occupied grids and the second set of source point cloud search-occupied grids. The target reference point cloud's search-credible spatial cell grid indices are then deduplicated to form the target search-occupied grid set.

[0105] The actual overlap rate between any two sets of occupied grids is equal to the number of grids in the intersection of the two sets divided by the number of grids in the union of the two sets. When the union is empty, the actual overlap rate is set to 0. Based on this rule, the actual search overlap rates of the first source point cloud to be converted and the target reference point cloud, the second source point cloud to be converted and the target reference point cloud, and the actual search overlap rate between the two sets of source point clouds to be converted are obtained respectively.

[0106] To enable comparison of distance error and overlap rate within the same search target, the following formula for calculating the target value of the candidate transformation parameters is used: ; in, The current parameter box represents a 14-dimensional joint transformation parameter composed of transformation parameters; The target value is dimensionless. , and The numbers represent, in order, the search distance errors between the first source point cloud to be converted and the target reference point cloud, the search distance errors between the second source point cloud to be converted and the target reference point cloud, and the search distance errors between the two sets of source point clouds to be converted, all in meters. , and The permissible root mean square error (RMSE) for the first source point cloud to be converted versus the target reference point cloud, the permissible RMSE for the second source point cloud to be converted versus the target reference point cloud, and the permissible RMSE for geometric consistency between the two sets of source point clouds to be converted are, in order. All units are meters and all are greater than 0. , and The values ​​are, in order, the actual search overlap rate of the first source point cloud to be converted to the target reference point cloud, the actual search overlap rate of the second source point cloud to be converted to the target reference point cloud, and the actual search overlap rate between the two sets of source point clouds to be converted. All of these values ​​are dimensionless and range from 0 to 1.

[0107] Since the distance error is divided by the allowable root mean square error with the same length dimension, the first three terms are dimensionless; the last three terms are dimensionless themselves, and the search target value meets the dimension consistency requirement.

[0108] When the three search distance errors corresponding to the transformation parameter represented by the parameter box are all no greater than the corresponding allowable root mean square error, and the three actual search overlap rates are all no less than the corresponding minimum overlap rate, the representative transformation parameter is determined as a feasible transformation parameter, and the search target value of the feasible transformation parameter and its corresponding parameter box identifier are recorded. Among all the recorded feasible transformation parameters, the one with the smallest search target value is determined as the current feasible upper bound parameter, and its search target value is determined as the current feasible upper bound. When no feasible transformation parameter has been obtained, the current feasible upper bound is initialized to positive infinity, and the pruning judgment between the lower bound of the parameter box search target value and the current feasible upper bound is not performed.

[0109] To determine the lower bound of the distance error achievable by any transformation parameter within the parameter box, outward rounding interval operations are performed on the translation parameter interval, rotation vector interval, and scaling ratio interval within the parameter box. For each source point, the rotation matrix interval generation method disclosed in step S5 is used to calculate its possible x-coordinate interval, y-coordinate interval, and elevation coordinate interval within the parameter box, thereby obtaining the corresponding source point coordinate interval box.

[0110] For a fixed target point and a source point coordinate range box The lower bound of the distance between two points is determined using the following formula for calculating the lower bound of the distance from a point to the coordinate interval box: ;in, This is the lower bound of the distance between the target point and the source point coordinate interval, in meters; , , , These represent the lower and upper limits of the source point coordinate interval box in the three coordinate directions, respectively, both in meters; , and These represent the minimum coordinate intervals in the three coordinate directions, in meters.

[0111] Taking the horizontal axis as an example, when hour, Pick ;when hour, Take 0; when hour, Pick The same judgment rules are used for the vertical coordinate direction and the elevation coordinate direction.

[0112] For a source point coordinate interval box, calculate the lower bound of the distance from the point to the coordinate interval box between the source point and all target search confidence space points, and take the minimum value to obtain the lower bound of the source-target nearest distance within the parameter box.

[0113] For two source point coordinate interval boxes belonging to two different sets of source point cloud data to be transformed, determine whether the two coordinate intervals overlap in each coordinate direction. When the two coordinate intervals overlap, the corresponding coordinate interval is set to 0; when the two coordinate intervals do not overlap, the difference between the endpoints of two adjacent intervals is taken as the corresponding coordinate interval. The square root of the sum of the squares of the three coordinate intervals is used to obtain the lower bound of the distance between the two source point coordinate interval boxes.

[0114] For each source point coordinate interval box, take the minimum value of the lower bound of the distance between it and all source point coordinate interval boxes of another set of source point cloud data to be transformed, and obtain the lower bound of the nearest distance between sources.

[0115] Based on the cell division method representing the search distance error of the transformation parameters, the lower bound of the nearest distance within each search credible space cell is squared, averaged, and square-rooted. Then, the median of all cell results is taken to obtain the lower bound of the search distance error between the first source point cloud to be transformed and the target reference point cloud, the lower bound of the search distance error between the second source point cloud to be transformed and the target reference point cloud, and the lower bound of the search distance error between the two sets of source point clouds to be transformed.

[0116] The lower bound of the distance to each point is no greater than the actual nearest point distance of that point under any specific transformation parameter in the parameter box. Squaring, summing, dividing by a fixed number of points, taking the square root, and taking the median of a fixed unit sequence are all monotonically non-decreasing. Therefore, the results obtained after the above summarization constitute the conservative lower bound of the corresponding search distance error.

[0117] Furthermore, to determine the upper bound of the source-target overlap rate, the coordinate interval of each source point is converted into a possible grid index range according to the origin of the target grid and the side length of the spatial grid cell. The possible grid indices for each coordinate direction start from the floor index corresponding to the lower limit of the interval and end at the floor index corresponding to the upper limit of the interval, including both endpoints. All combinations of the index ranges for the three directions are enumerated and duplicate indices are removed to obtain the set of possible source-occupied grids corresponding to the parameter frame.

[0118] When the upper limit of the source point coordinate interval is exactly located at the grid boundary, the grids adjacent to the boundary are included in the set of grids that may be occupied by the source, so as to maintain the outer envelope property of the set of grids that may be occupied by the source.

[0119] Divide the number of intersections between the possible source-occupied grid set and the target search-occupied grid set by the number of target search-occupied grid sets, and limit the result to no more than 1 to obtain the upper bound of the corresponding source-target search overlap rate.

[0120] The actual source-occupied grid set is a subset of the possible source-occupied grid set. Therefore, the actual intersection size is no greater than the intersection size of the possible source-occupied grid set and the target search-occupied grid set. Simultaneously, the actual union necessarily includes the target search-occupied grid set. Replacing the actual union size with the target search-occupied grid set size is equivalent to using a denominator no greater than the actual union size; the resulting ratio constitutes an upper bound on the actual source-target search overlap rate.

[0121] The upper bounds of the first and second search overlap rates of the source point cloud and target reference point cloud to be converted are obtained according to the above rules.

[0122] For the search overlap rate between two sets of source point clouds to be converted, the two sets of actual source-occupied grid sets are unknown subsets of their respective possible source-occupied grid sets. Based solely on the two possible source-occupied grid sets, the number of intersections and unions of the two actual source-occupied grid sets cannot be directly determined; directly using the intersection-union ratio of the two possible source-occupied grid sets as an upper bound may underestimate the inter-source overlap rate corresponding to certain combinations of actual subsets. Therefore, without an additional lower bound on the number of occupies, the upper bound on the search overlap rate between the two sets of source point clouds to be converted is set to 1. This value is a conservative upper bound, which reduces pruning caused by the inter-source overlap rate condition, but does not expand the deletion range of the parameter box accordingly.

[0123] In the formula for calculating the target value of the candidate transformation parameter search, the corresponding actual search distance error is replaced by the lower bound of the three search distance errors, and the corresponding actual search overlap rate is replaced by the upper bound of the three search overlap rates to obtain the lower bound of the target value of the parameter box search.

[0124] The parameter box is deleted if any of the following conditions are met: the lower bound of any search distance error is strictly greater than the corresponding allowable root mean square error; the upper bound of any source-target search overlap rate is strictly less than the corresponding minimum overlap rate; or a current feasible upper bound already exists, and the lower bound of the parameter box search target value is strictly greater than the current feasible upper bound.

[0125] When the comparison result equals the threshold, the corresponding parameter box is retained. The lower limit of the interval coordinates is rounded towards negative infinity, the upper limit of the interval coordinates is rounded towards positive infinity, the lower limit of the distance is rounded towards the decreasing direction of the value, and the upper limit of the overlap rate is rounded towards the increasing direction of the value.

[0126] Furthermore, for the active parameter boxes that have not been deleted, the subdivision order is determined according to the lower bound of the parameter box search target value and the characteristics of the credible space.

[0127] Furthermore, the coordinate output resolution is divided by each of the three allowable root mean square errors, and the sum of the three ratios is divided by 6 to obtain the dimensionless search target value comparison tolerance. The processing order of active parameter frames is determined according to the lower bound of the parameter frame search target value from smallest to largest. When the difference between the lower bounds of the parameter frame search target values ​​of two active parameter frames is not greater than the search target value comparison tolerance, they are determined to have the same target value priority. Within the same target value priority, active parameter frames with a larger number of corresponding point pairs in the effective reliable space, a larger median of the 3D discrete support values, and a larger median of density sufficiency are processed in that order; if they are still the same, they are processed according to the order in which the parameter frames were generated.

[0128] Based on the transformation parameters represented by the parameter box, three types of search corresponding point pairs are formed. The first type of search corresponding point pair consists of the transformation point within the first source point cloud search trusted spatial unit and its nearest point in the target reference point cloud; the second type of search corresponding point pair consists of the transformation point within the second source point cloud search trusted spatial unit and its nearest point in the target reference point cloud; the third type of search corresponding point pair includes the nearest point pair from the first source point cloud transformation point to the second source point cloud transformation point, and the nearest point pair from the second source point cloud transformation point to the first source point cloud transformation point.

[0129] For the first, second, and third types of search corresponding point pairs, the allowed root mean square error of the first source point cloud to be transformed versus the target reference point cloud, the allowed root mean square error of the second source point cloud to be transformed versus the target reference point cloud, and the allowed root mean square error of geometric consistency between the two sets of source point clouds to be transformed are respectively used as the upper limit of distance. When both points in a search corresponding point pair belong to the corresponding search reliable spatial unit, and the Euclidean distance between the two points is not greater than the corresponding upper limit of distance, the search corresponding point pair is determined as a valid reliable spatial corresponding point pair.

[0130] For each pair of points in the valid and reliable space, the smaller of the local three-dimensional discreteness of the spatial grid cells to which the two points belong is taken to obtain the three-dimensional discrete support value; the density sufficiency is obtained by dividing the point cloud density of the spatial grid cells to which the two points belong by their respective lowest point cloud density and taking the smaller of the two ratios.

[0131] For the selected parameter box, calculate the equivalent displacement width for each parameter component. The equivalent displacement width for translation parameters is the width of the corresponding translation interval; the equivalent displacement width for rotation vector components is the product of the width of the corresponding rotation interval, the maximum center radius of the corresponding source point cloud, and the upper limit of the scaling ratio; the equivalent displacement width for scaling ratios is the product of the width of the scaling ratio interval and the maximum center radius of the corresponding source point cloud. The maximum center radius of the source point cloud is the maximum Euclidean distance from the corresponding normalized source point to the center of the source point cloud, in meters.

[0132] Select the parameter component with the largest equivalent displacement width, and bisect the current parameter box at its midpoint to obtain two sub-parameter boxes. When the equivalent displacement widths are the same, select the subdivision parameters in a fixed order of center translation parameter, rotation vector component, and scaling ratio. Calculate the representative transformation parameter, search target value, lower bound of distance, and upper bound of overlap rate for each of the two sub-parameter boxes, and then perform the deletion judgment described above.

[0133] To determine whether the parameter bounding box meets the coordinate output resolution, two sets of standardized, centered source point cloud data with axis-aligned coordinate bounding boxes are established, and the eight corner points of each bounding box are obtained. For each corner point, the translation interval, rotation matrix interval, and scaling ratio interval corresponding to the current parameter bounding box are used for interval transformation to obtain the target coordinate interval box for that corner point; the spatial diagonal length of the target coordinate interval box is calculated, and the maximum value of the spatial diagonal length corresponding to the eight corner points is taken.

[0134] Under the translation, rotation, and uniform scaling transformations defined in this embodiment, for any given transformation parameter, the transformation coordinates are affine functions of the source point coordinates. When the source point coordinates change within the axis-aligned coordinate bounding box, the extreme values ​​in each coordinate direction can be enveloped by the corner points of the bounding box. By substituting the parameter range into the eight corner points using outward rounding, a conservative envelope can be provided for the coordinate range of each point within the source point cloud's coordinate bounding box caused by the change in the parameter box. This termination condition does not apply to nonlinear local deformations not defined in this embodiment.

[0135] When the maximum diagonal length of the corner coordinate interval box space corresponding to both sets of source point cloud data to be transformed is not greater than the coordinate output resolution, the parameter box is determined as the termination parameter box; otherwise, further subdivision is performed. For each sub-parameter box obtained from each subdivision, representative transformation parameter evaluation, parameter box pruning, and termination condition judgment are performed respectively. Sub-parameter boxes that are not deleted and do not meet the termination condition are added to the active parameter box set; sub-parameter boxes that meet the termination condition are added to the termination parameter box set. The above process is repeated until the active parameter box set is empty.

[0136] For each sub-parameter box obtained from the sub-segmentation, perform representative transformation parameter evaluation, parameter box pruning, and termination condition judgment. Sub-parameter boxes that are not deleted and do not meet the termination condition are added to the active parameter box set; sub-parameter boxes that meet the termination condition are added to the termination parameter box set. Repeat the above process until the active parameter box set is empty, completing the joint transformation parameter search.

[0137] After the search is completed, a connection relationship judgment is performed on all terminating parameter boxes in the set of terminating parameter boxes. When two terminating parameter boxes intersect or connect in all 14 parameter directions, the two terminating parameter boxes are grouped into the same parameter connected region; terminating parameter boxes with connection relationships are repeatedly merged until there are no more terminating parameter boxes that can be merged. For each parameter connected region, the candidate joint transformation parameter with the smallest search target value is selected from the search feasible transformation parameters whose identifier is located within the parameter connected region. If no candidate joint transformation parameter exists, the joint parameter search is output as a status indicating that no feasible parameter was found, and the current coordinate transformation is stopped.

[0138] Step S7: Verify candidate transformation parameters using the verification trust space that did not participate in the parameter search; The coordinate transformation processor reads the candidate joint transformation parameters output in step S6, the verifiable trusted spatial cell interior points of the first standardized centralized source point cloud data, the verifiable trusted spatial cell interior points of the second standardized centralized source point cloud data, and the verifiable trusted spatial cell interior points of the target reference point cloud data. Using the corresponding candidate joint transformation parameters, scaling, rotation, center translation, and target space origin restoration are performed on the verifiable trusted spatial cell interior points of the two sets of standardized centralized source point cloud data, respectively, to obtain two sets of transformed verification points. The verifiable trusted spatial cell interior points are not involved in the search target value calculation, parameter box pruning, and candidate parameter selection in step S6.

[0139] The two sets of transformed verification points and the target reference point cloud are used to verify the points within the trusted spatial unit. A set of verification occupied grids is generated according to the origin of the target grid and the side length of the spatial grid unit. According to the intersection-union ratio rule of the occupied grids specified in step S6, the actual verification overlap rate of the first source point cloud to be transformed and the target reference point cloud, the actual verification overlap rate of the second source point cloud to be transformed and the target reference point cloud, and the actual verification overlap rate between the two sets of source point clouds to be transformed are calculated.

[0140] For each pair of point clouds to be evaluated, first obtain the intersection of the verification grid sets occupied by both parties, and determine the points located within the intersection grid as common coverage verification points. Calculate the nearest point distance from the common coverage verification point in the first direction to the common coverage verification point in the second direction, and the nearest point distance from the common coverage verification point in the second direction to the common coverage verification point in the first direction. Sum the squares of all nearest point distances in both directions, divide by the total number of nearest point distances in both directions, and take the square root to obtain the root mean square error of the verification for the corresponding point cloud pair. If there are no common coverage verification points, the corresponding candidate joint transformation parameters are judged as failing the verification.

[0141] Thus, the root mean square error of the first source point cloud to be converted versus the target reference point cloud, the root mean square error of the second source point cloud to be converted versus the target reference point cloud, and the root mean square error of the geometric consistency verification between the two sets of source point clouds to be converted are obtained respectively.

[0142] Candidate joint transformation parameters are deemed to have passed basic validation if they simultaneously meet the following conditions: the root mean square error of all three validations is no greater than the corresponding allowable root mean square error, and the overlap rate of all three actual validations is no less than the corresponding minimum overlap rate. If any condition is not met, the corresponding candidate joint transformation parameter is excluded.

[0143] For the candidate joint transformation parameters that passed the basic validation, the identifiability of each of the 14 parameter components was examined one by one. First, the identifiability change threshold of the parameters for each set of source point cloud data to be transformed was determined.

[0144] For the first source point cloud data to be converted, the maximum value among the coordinate output resolution, the sum of the position uncertainty of the first source point cloud to be converted and the conservative position uncertainty of the target reference point cloud, and the sum of the position uncertainty of the first source point cloud to be converted and the position uncertainty of the second source point cloud to be converted is taken as the threshold for the identifiable change of the parameters of the first source point cloud to be converted.

[0145] For the second source point cloud data to be converted, the maximum value among the coordinate output resolution, the sum of the position uncertainty of the second source point cloud to be converted and the conservative position uncertainty of the target reference point cloud, and the sum of the position uncertainty of the first source point cloud to be converted and the position uncertainty of the second source point cloud to be converted is taken as the threshold for identifiable changes in the parameters of the second source point cloud to be converted.

[0146] For the parameter components belonging to the first source point cloud data to be converted, first obtain the smaller value between the allowable root mean square error of the first source point cloud to be converted and the target reference point cloud and the allowable root mean square error of geometric consistency between the two sets of source point clouds to be converted, and then take the larger value between the smaller value and the coordinate output resolution as the target verification displacement of the first source point cloud parameter to be converted.

[0147] For the parameter components belonging to the second source point cloud data to be converted, first obtain the smaller value among the allowable root mean square error of the second source point cloud to be converted and the allowable root mean square error of geometric consistency between the two sets of source point clouds to be converted, and then take the larger value between the smaller value and the coordinate output resolution as the target verification displacement of the second source point cloud parameters.

[0148] The target inspection displacement represents the accuracy scale of the item to be inspected; the parameter identifiable change threshold represents the scale at which the verification error can be distinguished by the current point uncertainty and the coordinate output resolution. Both are determined separately. When the parameter identifiable change threshold is greater than the target inspection displacement, the target inspection displacement is not increased; instead, the current verification data is compared to determine whether the transformation parameter can be distinguished at the target inspection displacement scale.

[0149] The initial check step size for translation parameters is taken as the coordinate output resolution; the initial check step size for rotation vector components is taken as the coordinate output resolution divided by the product of the maximum center radius of the corresponding source point cloud and the upper limit of the scaling ratio; the initial check step size for scaling ratio is taken as the coordinate output resolution divided by the maximum center radius of the corresponding source point cloud. When the maximum center radius of the corresponding source point cloud is 0, the source point cloud spatial range degradation state is output and processing stops.

[0150] For each parameter component, keeping the other 13 parameters unchanged, trial parameters are generated step-by-step along the parameter decreasing direction and the parameter increasing direction, according to the corresponding initial verification step size. After each trial parameter is generated, all verification points of the corresponding source point cloud are re-transformed using the trial parameter.

[0151] For the same verification point record, calculate the Euclidean distance between its transformed coordinates under the trial parameters and its transformed coordinates under the original candidate joint transformation parameters; perform this calculation on all verification points of the corresponding source point cloud, and take the maximum value among all Euclidean distances as the maximum coordinate displacement corresponding to the trial parameters. The maximum coordinate displacement is not the maximum absolute value of the coordinate component difference.

[0152] Trial parameters are generated step by step along a parameter direction until the boundary of the joint parameter search domain is reached or the maximum coordinate displacement reaches the target verification displacement. When the maximum coordinate displacement generated by two adjacent trial parameters is less than and not less than the target verification displacement, the two trial parameters are further divided into two equal parts.

[0153] After each bisection, a sub-interval is retained where one endpoint has not reached the target test displacement and the other endpoint has reached the target test displacement. This process utilizes the property that the coordinate displacement changes continuously with respect to a single parameter, without relying on the premise that it is strictly monotonic throughout the entire parameter constraint interval.

[0154] When the difference in maximum coordinate displacement between the two endpoints of a sub-interval is not greater than the coordinate output resolution, the bisection stops, and the endpoint parameters that have reached the target test displacement are determined as the corresponding direction test parameters. If a direction cannot reach the target test displacement before reaching the boundary of the joint parameter search domain, no test parameters are generated for that direction.

[0155] For each generated direction verification parameter, recalculate the root mean square error of the first source point cloud to be converted versus the target reference point cloud, the root mean square error of the second source point cloud to be converted versus the target reference point cloud, the root mean square error of the geometric consistency verification between the two sets of source point clouds to be converted, and the corresponding three actual verification overlap rates.

[0156] For the perturbed parameters belonging to the first source point cloud data to be transformed, calculate the absolute changes of the root mean square error of the verification between the first source point cloud and the target reference point cloud, and the root mean square error of the verification geometric consistency between the two sets of source point clouds to be transformed, relative to the original candidate joint transformation parameters. Take the larger of the two absolute changes as the error change in that direction. For the perturbed parameters belonging to the second source point cloud data to be transformed, calculate the absolute changes of the root mean square error of the verification between the second source point cloud and the target reference point cloud, and the root mean square error of the verification geometric consistency between the two sets of source point clouds to be transformed, relative to the original candidate joint transformation parameters. Take the larger of the two absolute changes as the error change in that direction.

[0157] When the root mean square error of the three verification parameters corresponding to the direction verification parameter is not greater than the corresponding allowable root mean square error, the overlap rate of the three actual verification parameters is not lower than the corresponding minimum overlap rate, and the change in the direction error is not greater than the corresponding parameter identifiable change threshold, the original candidate joint transformation parameter is marked as an unidentifiable candidate parameter and excluded.

[0158] The direction of parameter decrease and the direction of parameter increase are judged separately. If either direction meets the indistinguishable condition, the corresponding candidate joint transformation parameter is excluded. If a direction fails to generate a direction verification parameter because it reaches the boundary of the joint parameter search domain, the judgment is made only based on the verification parameter of the other direction. If neither direction can reach the target verification displacement within the joint parameter search domain, the candidate joint transformation parameter is not excluded based on that parameter component.

[0159] For candidate joint transformation parameters that have passed basic verification and have not been excluded due to parameter indistinguishability, the root mean square error of the verification between the first source point cloud and the target reference point cloud, the root mean square error of the verification between the second source point cloud and the target reference point cloud, and the root mean square error of the verification of geometric consistency between the two sets of source point clouds are added together and divided by 3 to obtain the comprehensive verification error of the corresponding candidate joint transformation parameter. These parameters are then arranged in ascending order of comprehensive verification error. Since step S6 has already selected one candidate joint transformation parameter from each parameter connectivity region, it is no longer necessary to repeatedly determine whether the candidate joint transformation parameters come from different parameter connectivity regions.

[0160] If no candidate joint transformation parameters are found that have not been excluded, output a status indicating that the candidate transformation parameter verification has failed, and stop the current coordinate transformation.

[0161] When there is only one candidate joint transformation parameter that has not been excluded, the candidate joint transformation parameter is determined as the joint transformation parameter to be output.

[0162] When there are two or more candidate joint transformation parameters that have not been excluded, the difference in comprehensive verification error between the two candidate joint transformation parameters with the smallest comprehensive verification error is calculated. When the difference in comprehensive verification error is not greater than the coordinate output resolution, the two candidate joint transformation parameters are determined to be indistinguishable under the conditions of point location uncertainty and coordinate output resolution within the current verification credible spatial unit. The state of the region with multiple indistinguishable parameters and the corresponding candidate joint transformation parameters are output, and the current coordinate transformation is stopped without generating a unique transformation result. When the difference in comprehensive verification error is greater than the coordinate output resolution, the candidate joint transformation parameter with the smallest comprehensive verification error is determined as the joint transformation parameter to be output.

[0163] Step S8: Perform a one-time coordinate transformation, coordinate quantization, and post-quantization verification; The coordinate transformation processor reads the original source point coordinates from the original valid point record saved in step S2, and reads the corresponding coordinate normalization matrix, the source point cloud center, the joint transformation parameters to be output obtained in step S7, and the origin of the target space.

[0164] For each set of source point cloud data to be converted, establish the source point cloud center subtraction matrix, scaling and rotation matrix, center translation matrix, and target space origin restoration matrix respectively.

[0165] The source point cloud center subtraction matrix is ​​a 4×4 homogeneous translation matrix, used to subtract the corresponding source point cloud center from the standardized source point coordinates; the scaling rotation matrix is ​​a 4×4 homogeneous matrix, with its upper left 3×3 part being the product of the scaling ratio and the rotation matrix obtained using the rotation vector-rotation matrix conversion formula; the center translation matrix is ​​used to add the corresponding center translation vector; and the target space origin restoration matrix is ​​used to add the target space origin coordinates.

[0166] In this embodiment, homogeneous column vectors are used to represent point coordinates. The i-th original valid source point in the m-th group of source point cloud data to be transformed is converted using the following homogeneous transformation formula from original coordinates to the target coordinate reference system: ;in, , represents the sequence number of the source point cloud data to be converted; i is the original valid point record sequence number in the corresponding point cloud data; It is a 4-dimensional homogeneous column vector composed of the original three-dimensional source point coordinates and the last constant 1; This is a 4-dimensional homogeneous column vector after transformation to the target coordinate reference frame. Let m be the coordinate normalization matrix of the source point cloud data to be transformed; Subtract the matrix from the center of the source point cloud; For scaling and rotation matrices; The center translation matrix; The matrix is ​​used to recover the origin of the target space; each matrix is ​​a 4×4 matrix.

[0167] The homogeneous transformation formula from the original coordinates to the target coordinate reference frame is executed from right to left. Specifically, it starts with... Perform length unit conversion, coordinate component rearrangement, and coordinate axis orientation adjustment on the original source point; then... Deduct the corresponding source point cloud center; then by Perform scaling and rotation by The execution center was moved, and finally... Restore the origin of the target space.

[0168] Matrix multiplication The original coordinate transformation matrix of the m-th group of source point cloud data to be transformed is determined. The coordinate normalization matrix appears only once in the product of this matrix. Therefore, step S8 directly processes the original valid point records saved in step S2, and does not repeatedly perform unit conversion, coordinate component rearrangement, or coordinate axis direction adjustment on the normalized point cloud data obtained in step S2.

[0169] For each target point after transformation, divide its x-coordinate, y-coordinate, and elevation coordinates by the coordinate output resolution, take the nearest integer from the result, and then multiply it by the coordinate output resolution to obtain the quantized target point coordinates. When the result is exactly at the midpoint between two adjacent integers, take the integer with the larger absolute value to unify the quantization boundary processing results.

[0170] All quantized target points of the first source point cloud data to be converted are collected in the order of the original valid point records to obtain the quantized first converted point cloud data; all quantized target points of the second source point cloud data to be converted are collected in the order of the original valid point records to obtain the quantized second converted point cloud data.

[0171] The coordinate transformation processor extracts quantized target points corresponding to the points within the verification trusted spatial unit determined in step S4 from the quantized first and second transformed point cloud data, based on the correspondence between the original point record numbers. Using the quantized target points and the points within the verification trusted spatial unit of the target reference point cloud data, three sets of verification occupied grids are re-established. Following the common coverage verification point selection rules in step S7, the three quantized verification root mean square errors and the three quantized actual verification overlap rates are recalculated. Points within trusted and untrusted spatial units are not included in the post-quantization re-verification.

[0172] When the root mean square error of the three quantized verifications is not greater than the corresponding allowable root mean square error, and the actual verification overlap rate of the three quantized verifications is not lower than the corresponding minimum overlap rate, the output includes two sets of original coordinate transformation matrices, coordinate output resolution, coordinate quantization rules, quantized first transformed point cloud data, quantized second transformed point cloud data, the correspondence between the original point record numbers of the two sets of source point cloud data to be transformed, the quantized verification results, and the target calculation coordinate reference system definition data.

[0173] If any of the post-quantization verification conditions are not met, output a state indicating that the post-quantization verification of coordinates has failed, and do not output the two sets of original coordinate transformation matrices and the two sets of quantized transformed point cloud data.

[0174] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A global optimization method for 3D coordinate transformation parameters of multi-source 3D data for reliable spatial assessment, characterized in that, Includes the following steps: Acquire two sets of source point cloud data to be converted, as well as target reference point cloud data, conversion quality constraint data, and conversion parameter constraint range, and determine the coordinate output resolution; Three sets of point cloud data were assigned to a spatial grid. Confidential spatial units were determined based on the number of points, point cloud density, and covariance eigenvalues. The grid was divided into search-confidential spatial units and verification-confidential spatial units. The joint transformation parameter search domain and parameter box are formed by the constraint interval of the transformation parameters. The lower bound of the distance error and the upper bound of the overlap rate between each pair of the three sets of point cloud data are determined by the search confidence spatial unit. The data is pruned according to the transformation quality constraint data. The parameter box is sorted and subdivided according to the point cloud density and the local three-dimensional dispersion determined by the covariance eigenvalue until the change of the source point coordinates is no greater than the coordinate output resolution, and candidate joint transformation parameters are obtained. The error, overlap rate and parameter identifiability of the candidate joint transformation parameters are verified by the verification confidence spatial unit to determine the joint transformation parameters to be output. The two sets of source point cloud data to be transformed are transformed using the joint transformation parameters to be output to obtain the original coordinate transformation matrix and the transformed point cloud data.

2. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 1, characterized in that: The two sets of source point cloud data to be converted are photogrammetric point cloud data and UAV laser point cloud data, respectively. Ground-based local laser point cloud data is acquired, the above three sets of point cloud data are cleaned, and the original valid point records and their corresponding numbers are saved. A coordinate standardization matrix is ​​established based on the coordinate units, coordinate component order, and positive coordinate axis direction of each of the two sets of source point cloud data to be converted, resulting in the first and second standardized source point cloud data. The corresponding source point cloud centers are then subtracted from each, yielding the first and second standardized centered source point cloud data. The minimum coordinate recording interval required by the project and the maximum value among the point position uncertainties of the above three sets of point cloud data are determined as the coordinate output resolution. The minimum number of valid points in the spatial grid cells of each of the three sets of point cloud data read from the point cloud acquisition technology design data is determined by the maximum value in step 3, which is then used as the minimum number of points in the reliable spatial cell.

3. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 2, characterized in that: Acquire the coordinate data of the corresponding control points, the target coordinate reference system definition data, and the target evaluation space boundary data. Establish a target calculation coordinate reference system with meters as the unit of length based on the target coordinate reference system definition data. Simultaneously standardize the local ground laser point cloud data and the coordinates of the local ground laser control points. Pair the local ground laser control point coordinates and the target control point coordinates according to the control point identifier. Perform singular value decomposition and reflection correction on the cross-covariance matrix of the paired control points to determine the control point orientation rotation matrix and the control point orientation translation vector. When the root mean square error of the control point orientation is not greater than the allowable root mean square error of the control point orientation, orient the local ground laser point cloud data and trim it according to the target evaluation space boundary data to obtain the target reference point cloud data and the target space origin. Use the sum of the uncertainty of the local ground laser point cloud position and the root mean square error of the control point orientation as the conservative uncertainty of the target reference point cloud position.

4. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 3, characterized in that: For each spatial grid cell, calculate and sort the three eigenvalues ​​of the point coordinate covariance in descending order, and project the points onto the local principal plane formed by the first two eigenvectors. When the convex hull area of ​​the projected points is greater than 0, the point cloud density is obtained by dividing the number of points by the convex hull area of ​​the projected points. When the sum of the three covariance eigenvalues ​​is greater than 0, the local three-dimensional dispersion is obtained by dividing three times the third covariance eigenvalue by the sum of the eigenvalues. A spatial grid cell with an actual number of points not less than the minimum number of points in a reliable spatial cell, a point cloud density not less than the corresponding minimum point cloud density, a square root of the second covariance eigenvalue greater than the larger of the coordinate output resolution and the corresponding point cloud position uncertainty, and a sum of eigenvalues ​​greater than 0 is determined as a reliable spatial cell. The target reference point cloud data adopts the conservative point position uncertainty of the target reference point cloud; the search credible spatial units and the verification credible spatial units are divided according to the parity of the grid index.

5. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 4, characterized in that: The transformation parameter constraint interval includes the original coordinate origin translation constraint interval, the rotation vector component constraint interval, and the scaling ratio constraint interval for each set of source point cloud data to be transformed. Substituting the rotation vector component constraint interval into the transformation relationship between the rotation vector and the rotation matrix, and using outward rounding interval operations to enclose the sine, cosine, and matrix operation results, the rotation matrix element interval used to generate the source point coordinate interval box is obtained. Candidate scaling and candidate rotation are performed on the source point cloud center, added to the original coordinate origin translation constraint interval, and the target space origin is subtracted to obtain the center translation parameter interval. The center translation parameter interval, rotation vector component constraint interval, and scaling ratio constraint interval of the two sets of source point cloud data to be transformed are combined using a Cartesian combination to obtain the joint transformation parameter search domain. The maximum center radius of the source point cloud is the maximum Euclidean distance from the standardized source point to the corresponding source point cloud center.

6. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 5, characterized in that: Take the midpoint of each parameter interval in the parameter box to form a representative transformation parameter, determine the three search distance errors, the three actual search overlap rates, and the search target value; record the representative transformation parameter that satisfies the transformation quality constraint data as the search feasible transformation parameter and record the parameter box identifier; take the smallest search target value as the current feasible upper bound parameter, and take its search target value as the current feasible upper bound. When there are no feasible transformation parameters, the current feasible upper bound is positive infinity; round out the possible transformation coordinates of the source point within the parameter box to form the source point coordinate interval box, determine the lower bounds of three search distance errors and the upper bounds of two source-target search overlap rates, and set the upper bound of the inter-source search overlap rate to 1 to determine the lower bound of the search target value in the parameter box; if any search distance error lower bound is greater than the corresponding allowable root mean square error, any source-target search overlap rate upper bound is less than the corresponding minimum overlap rate, or the lower bound of the search target value in the parameter box is greater than the current feasible upper bound, delete the parameter box.

7. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 6, characterized in that: Divide the coordinate output resolution by the sum of the ratios obtained by dividing the three allowable root mean square errors by 6 to obtain the search target value comparison tolerance; determine the processing order in ascending order of the lower bound of the search target value in the parameter box; when the lower bound difference is not greater than the search target value comparison tolerance, determine the processing order in descending order of the number of corresponding point pairs whose distance is not greater than the corresponding allowable root mean square error, the median of the smaller local three-dimensional dispersion at both ends of the point pair, and the median of the smaller ratio of the point cloud density to the lowest point cloud density; determine the equivalent displacement width of each parameter component based on the width of each parameter interval and the maximum center radius of the source point cloud, and bisect the parameter interval corresponding to the largest one; The terminating parameter boxes are assigned to the parameter connected regions according to their intersection or connection relationships. The current feasible upper bound parameters are assigned to the corresponding parameter connected regions according to the parameter box identifier and subdivision relationship. The parameter vector with the smallest search target value and which satisfies the transformation quality constraint data is selected from each region as the candidate joint transformation parameters.

8. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 7, characterized in that: The candidate joint transformation parameters are used to transform the verifiable credible spatial unit points of two sets of standardized centralized source point cloud data. The three actual verification overlap rates and the three verification root mean square errors are calculated. Those that meet the corresponding minimum overlap rate and allowable root mean square error pass the basic verification. The smaller of the source-target allowable root mean square error and the source-to-source allowable geometric consistency root mean square error and the larger of the coordinate output resolution are used as the target inspection displacement; With the remaining parameter components fixed, trial parameters are generated along the decreasing and increasing directions of the parameter being tested. The maximum Euclidean distance between the transformed coordinates of the same verification point and the original candidate joint transformation parameters is recorded. The maximum value is bisected until the target verification displacement is reached, thus obtaining the direction verification parameter. The larger of the absolute changes in the source-target verification root mean square error and the source-to-source verification geometric consistency root mean square error relative to the original candidate joint transformation parameters is taken as the change in direction error.

9. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 8, characterized in that: The maximum value among the coordinate output resolution, the sum of the corresponding source point cloud position uncertainty and the conservative position uncertainty of the target reference point cloud, and the sum of the position uncertainties of the two sets of source point clouds is taken as the parameter identifiable change threshold. When the root mean square error of the three verification parameters in any direction is not greater than the corresponding allowable root mean square error, the actual overlap rate of the three verification parameters is not lower than the corresponding minimum overlap rate, and the change in direction error is not greater than the parameter identifiable change threshold, the original candidate joint transformation parameter is excluded. Processing stops when all candidate joint transformation parameters are excluded. The average of the three verification root mean square errors of the non-excluded parameters is taken as the comprehensive verification error. When there are two or more candidate joint transformation parameters that have not been excluded, and the error difference between the two candidate joint transformation parameters with the smallest comprehensive verification error is not greater than the coordinate output resolution, the output shows a state where there are multiple indistinguishable parameter regions. Otherwise, the parameter with the smallest overall verification error will be determined as the joint conversion parameter to be output.

10. The global optimization method for 3D coordinate transformation parameters of multi-source three-dimensional data for reliable spatial assessment as described in claim 9, characterized in that: Point coordinates are represented by homogeneous column vectors. For each set of source point cloud data to be transformed, the origin recovery matrix, center translation matrix, scaling and rotation matrix, source point cloud center subtraction matrix, and coordinate normalization matrix are multiplied sequentially to obtain the original coordinate transformation matrix from the original source point coordinates to the target computational coordinate reference system. The original valid point records are then processed using the original coordinate transformation matrix. The transformed point coordinates are quantized according to the coordinate output resolution. Based on the correspondence of the original point record numbers, the quantized target point coordinates corresponding to the points in the reliable spatial unit are extracted and verified. The root mean square error of the three quantized verification items and the actual verification overlap rate of the three quantized items are redefined. When the quantized verification results meet the transformation quality constraints, two sets of original coordinate transformation matrices, two sets of quantized transformed point cloud data, and the definition data of the target computational coordinate reference system are output; otherwise, processing stops.

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