Land and water terrain mapping method using UAV laser / shipborne multi-beam data

Abstract

The present invention belongs to the field of marine surveying and mapping technology, and discloses a method for mapping land and water terrain using unmanned aerial vehicle laser / shipborne multi-beam data. The method roughly extracts data overlap areas through virtual grids, and finely extracts overlap areas using an alpha-shape algorithm to obtain boundary points, and removes edge triangles in an irregular triangulated network constructed by unmanned aerial vehicle laser bathymetry data and shipborne multi-beam bathymetry data; calculates vertex normal vectors, uses the vertex tangent plane of the multi-beam irregular triangulated network as a registration primitive, and performs weight distribution based on the distance from point to vertex, and performs rough registration through an ICP registration algorithm from point to plane; constructs a fine registration model based on point-to-plane distance, and eliminates elevation differences in overlapping areas by minimizing the normal distance from unmanned aerial vehicle laser bathymetry points to multi-beam bathymetry triangle face elements. The point cloud fusion model of the present invention is used for processing, and the phenomenon of inconsistent elevations of point clouds from different sources in overlapping areas is effectively improved, and underwater terrain data fusion is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of marine surveying and mapping, and in particular relates to a method for surveying land and water terrain using unmanned aerial vehicle laser / shipborne multi-beam data. Background Art

[0002] UAV laser sounding and multi-beam sounding systems have developed rapidly and become an important source of underwater topographic data. UAV laser sounding can efficiently obtain high-precision, high-density integrated water and underwater data in shallow water areas. However, due to the limitations of water transparency, water scattering and absorption, UAV laser sounding cannot obtain underwater topographic information in deep water areas. Multi-beam sounding uses high-frequency sound waves for detection, with less propagation loss in water, and can obtain large-scale underwater topographic data in deep water areas. However, due to the limitation of ship draft, survey ships cannot conduct underwater topographic measurements of shallow water areas and complex terrains such as islands and reefs, and measurement blank areas are prone to occur. UAV laser sounding and multi-beam sounding point clouds use different platforms, and their operating areas and ranges are complementary. Fusion of these two types of data can fill the measurement gaps.

[0003] However, there are significant differences in data acquisition platforms, measurement media and methods between drone laser bathymetry and multi-beam bathymetry point clouds, which often lead to elevation differences in underwater terrain data obtained by these two technologies. Existing fusion algorithms usually assume that there is a simple rotation and translation relationship between the point cloud as a whole, which makes it difficult to handle local distortion caused by complex factors and thus cannot meet the requirements of high-precision underwater terrain mapping. Therefore, it is necessary to propose a method for water and land terrain mapping using drone laser / shipborne multi-beam data.

[0004] For existing technologies, the fusion of drone laser depth sounding and multi-beam sonar depth sounding can be divided into the following three steps:

[0005] Step 1: Use the ICP algorithm to perform initial registration of the UAV laser bathymetry and multi-beam sonar bathymetry point clouds; Step 2: Construct a virtual grid covering the entire study area according to the pre-set virtual grid unit size parameter cs, so as to identify the overlapping and non-overlapping areas of the UAV laser bathymetry and multi-beam sonar bathymetry point clouds; Step 3: Construct a seamless integration model based on non-overlapping blocks to eliminate the data gap at the junction of the UAV laser bathymetry and multi-beam sonar bathymetry point clouds.

[0006] However, the above technologies have the following limitations:

[0007] (1) Initial registration has limitations: The current technical step 1 first uses the ICP algorithm for initial rough registration, which does not take into account the large differences in the distribution of underwater acoustic and optical data and the uneven distribution of point cloud density. The point-to-point registration algorithm has poor stability.

[0008] (2) Pseudo nodes cause loss of terrain details: In the current technical step 2, virtual grids are used to identify overlapping areas and form pseudo nodes. The process of constructing pseudo nodes is essentially a uniform thinning process, which results in the loss of some terrain detail information. In addition, pseudo nodes have poor stability at the boundaries of multi-beam data and cannot reflect the real terrain information measured by multi-beam data.

[0009] (3) Point cloud interpolation destroys the integrity of the point cloud: The current technical step 3 uses TPS interpolation to fuse the UAV laser depth measurement and multi-beam sonar depth measurement point cloud. However, the point cloud is a whole. Interpolating the point cloud onto a plane destroys the integrity of the UAV laser depth measurement point cloud.

[0010] Through the above analysis, the problems and defects of the prior art are as follows:

[0011] (1) UAV laser depth sounding cannot obtain underwater topographic information in deep water areas, while survey ships cannot conduct underwater topographic measurements in shallow water areas and complex terrains such as islands and reefs, which easily leads to measurement blank areas.

[0012] (2) There are significant differences between UAV laser bathymetry and multi-beam bathymetry point cloud in data acquisition platform, measurement medium and method, which leads to elevation differences in the underwater terrain data obtained by these two technologies.

[0013] (3) Existing fusion algorithms usually assume that there is a simple rotation and translation relationship between the point cloud as a whole, which makes it difficult to deal with local distortion caused by complex factors and cannot meet the requirements of high-precision underwater terrain mapping. Summary of the invention

[0014] In order to overcome the problem of inconsistent elevation and ground feature expression in overlapping areas due to system errors, refraction errors, etc. in the process of fusion of UAV laser bathymetry and multi-beam bathymetry data, the disclosed embodiment of the present invention provides a method for water and land topography mapping using UAV laser / shipborne multi-beam data. The purpose of the present invention is to fuse the UAV laser bathymetry point cloud with the shipborne multi-beam bathymetry point cloud to obtain integrated terrain information above and below the water, use a more sophisticated overlapping area recognition method to identify the overlapping area, use TIN to reflect the terrain details, and reduce the influence of the terrain edge; use a more stable rigid registration model to register the two heterogeneous data; construct a point cloud fusion model, and correct the UAV laser bathymetry point cloud under the premise of multi-beam data as a constraint, instead of performing direct interpolation.

[0015] The technical solution is as follows: A method for land and water terrain mapping using UAV laser / shipborne multi-beam data, comprising the steps of:

[0016] S1, determination of overlapping areas and TIN construction by combining virtual grid topology and alpha-shape algorithm: coarse extraction of data overlapping areas through virtual grid, fine extraction of overlapping areas using alpha-shape algorithm, obtaining boundary points, and using boundary points to remove edge triangles in irregular triangulated network TIN constructed by UAV laser bathymetry data and shipborne multi-beam bathymetry data;

[0017] S2, coarse registration based on the tangent plane of the TIN grid vertex: calculate the vertex normal vector, use the tangent plane of the multi-beam irregular triangulated network vertex as the registration primitive, assign weights based on the distance from the point to the corresponding vertex, and perform coarse registration through the point-to-plane ICP registration algorithm;

[0018] S3, precise registration based on the normal distance from point to triangulated mesh face: Construct a precise registration model based on point-to-face distance to eliminate the elevation difference in the overlapping area by minimizing the normal distance from the UAV laser bathymetric point to the corresponding multi-beam bathymetric triangulated face.

[0019] In step S1, the data overlap area is roughly extracted through the virtual grid, including:

[0020] Merge UAV laser bathymetry and multibeam bathymetry point clouds and set grid size , the number of rows and columns of the virtual grid is calculated according to the maximum and minimum horizontal and vertical coordinates of the merged point cloud. The expression is:

[0021] ;

[0022] In the formula, is the number of grid rows and columns, To round up, To round down, are the maximum and minimum horizontal and vertical coordinates in the point cloud data, respectively. is the grid size;

[0023] After merging any point Divide into virtual grids. If there are UAV laser bathymetry and multi-beam bathymetry point cloud points in the grid, the grid will be retained and marked as an overlapping area.

[0024] Use low-density point cloud to search for adjacent points, take twice the distance of the largest neighboring point as the grid size ; The value is obtained by rounding up the point cloud density, and the grid size The calculation formula is:

[0025] ;

[0026] In the formula, To search for point clouds The nearest neighbor of each point The distance of the points, For point cloud data with low density, is the corresponding density, To get the maximum value.

[0027] In step S1, the overlap area determination and TIN construction of the combined virtual grid topology and alpha-shape algorithm include:

[0028] When there is a discrete point cloud ,right Normalize the elevation and project it onto the same plane to get a two-dimensional point set ; In a two-dimensional point set Pick any point , find Zhongyu Point spacing is less than Point set ; Connection point With point set Find the points in the alpha-shape rule and mark them as boundary points; traverse All points in get the final boundary point index ;

[0029] The alpha-shape algorithm is used to extract the overlapping areas and boundaries of the UAV laser bathymetry and multi-beam bathymetry point clouds, respectively. The boundary points of the constructed triangulated network are detected, and the boundary triangles are eliminated by judging the positional relationship of the boundary points contained in the triangle vertices.

[0030] Furthermore, the constructed triangulated network is subjected to boundary point detection, and boundary triangles are eliminated by determining the positional relationship of boundary points contained in the triangle vertices, including:

[0031] (1) Eliminate triangulated networks with edges longer than The triangles get a new TIN network;

[0032] (2) For any triangle in the TIN network , search whether its three vertices are boundary points;

[0033] (3) If there is no boundary point or only one vertex is a boundary point, store the triangle to vertex index matrix Vertices If there are two or more boundary points, execute step (4);

[0034] (4) Determine the positional relationship between boundary points. For a triangle containing two boundary points, if the two boundary points are not adjacent boundary points, the triangle is discarded. If the two boundary points are adjacent, the triangle is stored in the vertex index matrix. Vertices For a triangle whose three vertices are all boundary points, if the three boundary points are not three adjacent continuous boundary points, the triangle is removed. If the three boundary points are adjacent, the triangle is stored in the vertex index matrix. Vertices ;

[0035] (5) Repeat steps (2) to (4) until all triangles have been traversed.

[0036] In step S2, the vertex normal vector is calculated, including:

[0037] Calculate the normal vector for each triangle separately. , , The surface normal vector is calculated by the following formula:

[0038] ;

[0039] In the formula, is the triangle face normal vector;

[0040] The vertex normal vector is obtained by weighted average of the adjacent face normal vectors. The vertex normal vector is expressed as:

[0041] ;

[0042] In the formula, is the vertex normal vector, is the number of vertices in the triangulated network, For the The area of ​​adjacent triangles, is the normal vector of the triangle.

[0043] In step S2, a rough registration is performed using a point-to-plane ICP registration algorithm, including:

[0044] The weight is assigned according to the distance between the source point and the matched target point. For points with large deviations, small weights are assigned. The weight calculation formula is:

[0045] ;

[0046] In the formula, is a discrete point cloud, is the distance from the source point to the corresponding target point;

[0047] After constructing the weight matrix, point to plane ICP is used for coarse registration to correct the overall offset between the source point cloud and the target point cloud.

[0048] In step S3, the precise registration based on the normal distance from the point to the triangulated mesh element includes:

[0049] Loss function for non-rigid registration model for:

[0050] ;

[0051] In the formula, is the distance term, which represents the distance difference between the nearest points of the source point cloud and the target point cloud; is a rigid term used to penalize the difference in the affine transformation matrices of adjacent vertices; is a feature item, which indicates the distance difference between feature points and is used for initialization guidance; , is the weight factor, which is used to control the influence of the error term;

[0052] A non-rigid registration model based on the normal distance from the point to the corresponding triangle surface element is constructed. By establishing a one-to-one correspondence between the UAV laser bathymetry points and the triangles in the multi-beam bathymetry irregular triangulation network, the distance between the UAV laser bathymetry points and the corresponding triangle surface elements is minimized, and the elevation difference in the overlapping area after the registration of the UAV laser bathymetry and multi-beam bathymetry point clouds is eliminated.

[0053] Furthermore, the rotation and translation of the point cloud is shown as follows:

[0054] ;

[0055] In the formula, is the target point cloud, Reason , , The rotation matrix is ​​formed, , , are three Euler angles, representing the axis, Axis and Rotation of the axis; is the source point cloud, is the spatial translation parameter;

[0056] Taylor expansion is performed on the rotation and translation formula of the point cloud and the first-order term is taken to obtain the corresponding error equation group, which is expressed as follows:

[0057] ;

[0058] In the formula, is the difference between the transformed point cloud and the target point cloud, is the Jacobian matrix, which represents the influence of rotation and translation parameters on point cloud transformation; is a parameter vector, containing rotation and translation parameters, , is the observation vector, which represents the distance from each target point to the closest point after the source point cloud is transformed; , , They are the translation amounts on the X-axis, Y-axis, and Z-axis respectively;

[0059] The distance term from the calculated point to the triangle source normal is:

[0060] ;

[0061] In the formula is the distance term, which represents the distance difference between the nearest points of the source point cloud and the target point cloud; is the laser depth measurement point cloud, For a laser depth point The corresponding triangular face plane parameters, , is the unit normal vector of the plane, is the distance from the plane to the origin; Delaunay triangulation constructed for multibeam bathymetric point clouds, is the distance function, used to calculate the distance between points and surfaces; is a laser sounding point, for The rotation matrix of for The translation vector of

[0062] According to the error equations, the distance term It is expressed by the following formula:

[0063] ;

[0064] In the formula, For the general The sparse matrix of the matrix mapping, is composed of rotation and translation parameters The parameter matrix, Constant term.

[0065] Furthermore, a non-rigid registration model based on the normal distance from the point to the corresponding triangle surface element is constructed, including: In non-rigid registration, the rigid term prevents excessive deformation of the local area by penalizing the transformation difference between adjacent source points, and introduces the weight matrix , Used to balance the proportion of rotation and translation parameters, and get the rigid term , the expression is:

[0066] ;

[0067] In the formula, For the Neighboring triangles of the source point to be corrected The vertex on is the index of the source point cloud to be corrected, and is the corresponding parameter matrix;

[0068] Use the source point cloud to construct a Delaunay triangulation network, and use the edge triangle elimination method to construct a triangulation network, obtain all edge indexes in the triangulation network; according to the vertex relationship of each edge, construct The sparse matrix , is the number of edges in the triangulated network, and the loss function is expressed as:

[0069] ;

[0070] In the formula, is the weight factor, for The weight matrix of is the cross product, is the weight matrix of boundary relations, is the Jacobian matrix;

[0071] Convert the loss function into the indirect adjustment equation form:

[0072] ;

[0073] The unknown parameters are continuously calculated to determine whether the average value of the point-to-surface distance is less than the preset value; if the termination condition is not met, the transformation parameters are applied to the source point cloud, and the precise alignment based on the normal distance from the point to the triangulated surface element is performed again.

[0074] Combining all the above technical solutions, the advantages and positive effects of the present invention are as follows:

[0075] First, the present invention roughly extracts the data overlap area through virtual grid, and uses alpha-shape algorithm to finely extract the overlap area, obtains boundary points, and removes edge triangles in the irregular triangulated network (TIN) constructed by UAV laser bathymetry data and shipborne multi-beam bathymetry data; calculates vertex normal vectors, uses the vertex tangent plane of the multi-beam irregular triangulated network as the registration primitive, and distributes weights based on the distance from the point to the corresponding vertex, and performs rough registration through the point-to-plane ICP registration algorithm; constructs a fine registration model based on point-to-plane distance, and eliminates the elevation difference in the overlapping area by minimizing the normal distance from the UAV laser bathymetry point to the corresponding multi-beam bathymetry triangle face element. The present invention effectively realizes the underwater terrain data fusion of UAV laser bathymetry data and multi-beam bathymetry data, and provides an effective solution for obtaining a high-precision integrated terrain model above and below the water.

[0076] Compared with the prior art, the present invention combines the virtual grid topology with the alpha-shape algorithm to determine the overlapping area, and uses the alpha threshold and the boundary point dual constraints to remove the edge single-sided large triangles from the TIN network constructed by the UAV laser bathymetry and the multi-beam bathymetry point cloud; the vertex normal vectors of the obtained multi-beam bathymetry TIN network are calculated, and the vertex normal vectors are weightedly calculated through the area constraints of adjacent triangles, and all vertices are traversed. Based on the multi-beam bathymetry point cloud as a reference, the weight matrix is ​​calculated using the distance between the UAV laser bathymetry point and the matched multi-beam bathymetry point, and the calculated vertex normal vector and point to plane are used to calculate the weight matrix. The ICP algorithm calculates the rotation and translation parameters and applies them to all UAV laser bathymetric point clouds to achieve coarse alignment; the correspondence between the UAV laser bathymetric point cloud and the multi-beam bathymetric triangulation network is established, and the traditional point-to-point distance term is improved into a more noise-resistant point-to-triangle surface normal distance term by constructing a non-rigid registration model based on the normal distance from the point to the corresponding TIN triangle element. A rigid term based on the point cloud triangulation network constraint is established to correct the elevation discrepancy of the point clouds in the overlapping area, thereby achieving precise alignment.

[0077] Second, the present invention considers the characteristics of drone laser sounding and multi-beam sounding data and the limitations of measurement operations, taking into account that the two heterogeneous data are only partially overlapping, introduces the overlap area determination and TIN construction of the joint virtual grid topology and alpha-shape algorithm, and reduces the impact of edge triangles and non-overlapping areas on data fusion; in view of the position offset phenomenon between heterogeneous data, the TIN grid vertex tangent plane is used as the registration primitive, and the distance between the point and the grid vertex is used to constrain the overall position offset; in view of the fact that there is still inconsistent elevation expression in the data overlap area after rigid registration, resulting in inaccurate expression of the ground objects, a one-to-one correspondence relationship is established between the drone laser sounding point and the triangle in the irregular triangulated network constructed by multi-beam sounding, and correction is made based on the precise registration of the normal distance from the point to the triangulated network face element. The underwater terrain acoustic and optical data fusion of drone laser sounding and multi-beam sounding data is effectively realized, providing an effective solution for obtaining a high-precision integrated terrain model above and below the water.

[0078] Third, the present invention uses the drone laser bathymetry data of Yunnan lakes and the ship-borne multi-beam bathymetry data as the data basis to perform data fusion. The present invention can be applied to the nearshore underwater topography measurement of islands and reefs, to build a seamless above-water and underwater integrated model, and can also be applied to the underwater topography measurement of plateau lakes and to calculate the volume of plateau lakes.

[0079] After being processed by the point cloud fusion model of the present invention, the inconsistency of elevations of point clouds from different sources in the overlapping area can be effectively improved, providing an effective solution for obtaining a high-precision UAV laser bathymetry and multi-beam bathymetry point cloud above-and-underwater integrated terrain model.

[0080] Fourth, the present invention improves surveying and mapping efficiency and accuracy: This technical solution reduces the time for determining data overlap areas and constructing TINs in marine surveying and mapping by optimizing the data processing process, while improving the accuracy of the results, which is particularly important for industries that require fast and accurate surveying and mapping data.

[0081] Reduce costs: By automating and optimizing data processing, the need for manual intervention is reduced, thereby reducing labor costs and time costs, making marine mapping projects more cost-effective.

[0082] Enhanced data fusion capability: This technical solution can better fuse data from different measurement equipment, such as drone laser bathymetry and ship-borne multi-beam bathymetry data, to provide a more comprehensive view of the seabed topography, which is of great value in fields such as marine resource exploration, environmental monitoring and seabed infrastructure construction.

[0083] The present invention effectively processes and fuses data from different sources (such as drone laser sounding and ship-borne multi-beam sounding) in marine surveying. The normal distance from the drone laser sounding point to the corresponding multi-beam sounding triangle surface is minimized through the precise registration model, and the elevation difference in the overlapping area is eliminated, thereby improving the accuracy of data fusion. The dependence on a single data source is overcome, and data complementarity and optimization are achieved by combining two different measurement technologies. This method reduces the bias against a single measurement technology and improves the reliability and comprehensiveness of marine surveying results. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0085] Figure 1 It is a flow chart of a method for land and water topography mapping using UAV laser / shipborne multi-beam data provided by an embodiment of the present invention;

[0086] Figure 2 is a schematic diagram of a fine extraction process of overlapping regions provided by an embodiment of the present invention;

[0087] Figure 3 It is a schematic diagram of point to plane rough registration based on the tangent plane of the triangular facet vertex provided by an embodiment of the present invention;

[0088] Figure 4 is a schematic diagram of matching a source point cloud and a cutting plane provided by an embodiment of the present invention;

[0089] Figure 5 It is a schematic diagram of precise registration based on the normal distance from a point to a triangulated mesh element provided by an embodiment of the present invention;

[0090] Figure 6 It is a schematic diagram of the fusion result provided by an embodiment of the present invention; wherein, (a) is the comparison of the experimental area 1 before and after fusion; (b) is the comparison of the experimental area 2 before and after fusion; and (c) is the comparison of the experimental area 3 before and after fusion. DETAILED DESCRIPTION

[0091] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0092] The innovation of the present invention is:

[0093] (1) The present invention combines overlapping grids with the alpha-shape algorithm to extract overlapping areas and boundary points, and removes edge triangles through the boundary points;

[0094] (2) The present invention allocates weights based on the distance from a point to the corresponding vertex, and performs coarse registration using the point-to-plane ICP registration algorithm;

[0095] (3) The present invention constructs a refined fusion model and eliminates the elevation difference in the overlapping area by minimizing the normal distance from the ALB point to the corresponding MBES triangle surface element.

[0096] Application example 1: for the measurement of islands and reefs, due to the existence of reefs in shallow water areas, the survey ship cannot get close and cannot obtain shallow water terrain information. Therefore, UAV laser depth sounding is used to obtain shallow water terrain information, and the ship-borne multi-beam depth sounding data is used to complement the survey area. However, there is a certain spatial offset in the data obtained by the two carriers, and the terrain expression is inconsistent. The present invention can reduce the spatial offset of multi-beam and UAV laser depth sounding, and obtain seamless point cloud data in the overlapping area, which can realize the refined acquisition of island and reef terrain.

[0097] Application example 2: for water resource surveys, there is a large amount of silt in the shallow water areas of lakes and reservoirs, and survey ships cannot conduct safe measurements. The present invention can obtain shallow water area data and merge it with multi-beam sounding deep water area data to obtain terrain information in the lake, calculate the water resource volume in the lake, and achieve rapid water resource surveys.

[0098] Example 1: Figure 1 As shown, the method for land and water terrain mapping using UAV laser / shipborne multi-beam data provided by the embodiment of the present invention specifically includes the following steps:

[0099] S1, determination of overlapping areas and TIN construction by combining virtual grid topology and alpha-shape algorithm: coarse extraction of data overlapping areas through virtual grid, fine extraction of overlapping areas using alpha-shape algorithm, obtaining boundary points, and using boundary points to remove edge triangles in irregular triangulated network TIN constructed by UAV laser bathymetry data and shipborne multi-beam bathymetry data;

[0100] Since the UAV laser bathymetry and multi-beam bathymetry point cloud data only partially overlap, directly constructing a Delaunay triangulation network for the multi-beam bathymetry point cloud and fusing it is easy to cause local convergence and cause non-overlapping UAV laser bathymetry points to be incorrectly matched to triangles with too large a single side. In order to avoid the influence of edge triangles and non-overlapping areas on data fusion, it is necessary to determine the overlapping area, such as Figure 2 As shown, the triangles with one side that are too large in TIN are removed.

[0101] As a preferred embodiment, step S1 of the present invention specifically includes the following steps:

[0102] Step 1.1: Construct a virtual grid to roughly extract the overlapping area of ​​the point cloud;

[0103] Merge UAV laser bathymetry and multibeam bathymetry point clouds and set grid size , the number of rows and columns of the virtual grid is calculated according to the maximum and minimum horizontal and vertical coordinates of the merged point cloud, as shown in formula (1). Then, any point after the merger Divide into virtual grids. If there are UAV laser bathymetry and multi-beam bathymetry point cloud points in the grid, the grid will be retained and marked as an overlapping area.

[0104] (1);

[0105] In the formula, is the number of grid rows and columns, To round up, To round down, are the maximum and minimum horizontal and vertical coordinates in the point cloud data, respectively. is the grid size;

[0106] Formula (1) can be obtained by , Coordinates are calculated by row and column numbers to quickly build a virtual grid.

[0107] In order to ensure data integrity and reduce data volume, a point cloud with lower density is used to search for adjacent points, take twice the distance between the largest neighboring points as the grid size . The value is obtained by rounding up the point cloud density, and the grid size calculation formula is shown in formula (2):

[0108] (2);

[0109] In the formula, To search for point clouds The nearest neighbor of each point The distance of the points, For point cloud data with low density, is the corresponding density, To get the maximum value.

[0110] Formula (2) calculates the grid size according to the specific conditions of the two types of data, ensures the integrity of the proposed overlapping area data, and reduces the amount of data, thereby eliminating the problem of multiple manual attempts to determine the existing grid size and reducing the workload.

[0111] Step 1.2: Use alpha-shape algorithm to extract overlapping areas and construct TIN network;

[0112] Assume a discrete point cloud ,right Normalize the elevation and project it onto the same plane to get a two-dimensional point. When there is a discrete point cloud ,right Normalize the elevation and project it onto the same plane to get a two-dimensional point set ; In a two-dimensional point set Pick any point , find Zhongyu Point spacing is less than Point set ; Connection point With point set Find the points in the alpha-shape rule and mark them as boundary points; traverse All points in get the final boundary point index ;

[0113] The point clouds of UAV laser bathymetry and multi-beam bathymetry are only partially overlapped, so the alpha-shape algorithm is used to extract the overlapping area and boundaries of the UAV laser bathymetry and multi-beam bathymetry point clouds respectively.

[0114] In the process of constructing TIN, there are often too large triangles in the boundary area. These triangles lack terrain information, which affects the fusion effect. Therefore, the present invention performs boundary point detection on the constructed triangulated network and removes the boundary triangles by judging the positional relationship of the boundary points contained in the triangle vertices. The specific steps are as follows:

[0115] Step 1: Eliminate the triangle mesh with an edge length greater than The triangles get a new TIN network;

[0116] Step 2: For any triangle in the TIN network , search whether its three vertices are boundary points;

[0117] Step 3: If there is no boundary point or only one vertex is a boundary point, store the triangle to the vertex index matrix Vertices If there are two or more boundary points, proceed to the next step;

[0118] Step 4: Determine the positional relationship between boundary points. For a triangle containing two boundary points, if the two boundary points are not adjacent boundary points, the triangle is removed. If the two boundary points are adjacent, the triangle is stored in the vertex index matrix. Vertices For a triangle whose three vertices are all boundary points, if the three boundary points are not three adjacent continuous boundary points, the triangle is removed. If the three boundary points are adjacent, the triangle is stored in the vertex index matrix. Vertices ;

[0119] Step5: Repeat Step2-Step4 until all triangles are traversed.

[0120] For UAV laser bathymetry and multi-beam bathymetry, oversized triangles in the TIN boundary area are removed based on boundary point detection.

[0121] S2, coarse registration based on the tangent plane of the TIN grid vertex: calculate the vertex normal vector, use the tangent plane of the multi-beam irregular triangulated network vertex as the registration primitive, assign weights based on the distance from the point to the corresponding vertex, and perform coarse registration through the point-to-plane ICP registration algorithm;

[0122] The density, accuracy and ground object expression of underwater acoustic and optical point cloud data are different, which makes it difficult to extract feature points and is easily affected by water noise, resulting in the difficulty of traditional ICP algorithm registration accuracy to meet the requirements. Therefore, a point-to-plane registration algorithm with stronger noise resistance is selected to calculate the vertex normal vector and assign weights based on the distance from the point to the corresponding tangent plane. Coarse registration is performed based on the point-to-plane ICP registration algorithm, see Figure 3 .

[0123] As a preferred embodiment, step S2 of the present invention specifically includes the following steps:

[0124] Step 2.1: Vertex normal vector calculation;

[0125] The calculation of normal vectors by principal component analysis (PCA) and quadratic surface fitting usually requires setting neighborhood thresholds, and different neighborhood search ranges are required for data with different point cloud densities. However, due to the uneven distribution of point cloud density, the calculation of normal vectors in different areas may be biased. The calculation of vertex normal vectors using triangular meshes can be directly calculated based on the TIN triangulation network, which is more efficient and robust than the other two methods.

[0126] For each triangle, calculate its normal vector. Assume that the triangulated network consists of three vertices , , The surface normal vector can be calculated by the following formula:

[0127] (3);

[0128] In the formula, is the triangle face normal vector;

[0129] Formula (3) is used to calculate the face normal vector, which facilitates the subsequent calculation of the vertex normal vector.

[0130] The vertex normal vector can be obtained by weighted average of the adjacent face normal vectors. In the present invention, the area weighted method is used, and the vertex normal vector can be expressed as:

[0131] (4);

[0132] In the formula, is the vertex normal vector, is the number of vertices in the triangulated network, For the The area of ​​adjacent triangles, is the normal vector of the triangle.

[0133] Formula (4) is used to calculate the vertex normal vector, which is constrained by the normal vectors of adjacent triangles and area weighting. This method is faster and more accurate in calculating the vertex normal vector. Compared with other methods, this method has a faster calculation speed.

[0134] Step 2.2: Determine the weight matrix;

[0135] After calculating the normal vector of the target point cloud, find the target point corresponding to the minimum distance between the source point cloud and the target point cloud tangent plane. If the coarse registration is performed directly, the distance between the source point and the corresponding target tangent plane is calculated. Some source points are matched to the tangent plane with the minimum distance, but the corresponding target points are far away. Figure 4 .

[0136] Therefore, the weight is assigned according to the distance between the source point and the matched target point. For points with large deviations, a smaller weight is assigned. The weight formula is shown in formula (5):

[0137] (5);

[0138] In the formula, is a discrete point cloud, is the distance from the source point to the corresponding target point;

[0139] Formula (5) is used to weight the coarse registration and enhance the robustness of the registration model, thus solving the difficult problem of coarse registration between UAV laser depth sounding point cloud and multi-beam data.

[0140] After constructing the weight matrix, point to plane ICP is used for coarse registration to correct the overall offset between the source point cloud and the target point cloud.

[0141] Step S3, correcting the elevation inconsistency in the data overlap area based on the precise registration of the normal distance from the point to the triangulated surface element.

[0142] After rigid registration, there will still be some elevation differences in the overlapping areas of the two data. In order to achieve the fusion of UAV laser bathymetry and multi-beam bathymetry underwater terrain data and obtain seamless underwater terrain data, further precise registration should be performed. Therefore, by minimizing the normal distance from the UAV laser bathymetry point to the corresponding multi-beam bathymetry point cloud triangle element, the elevation difference in the overlapping area is eliminated, such as Figure 5 shown.

[0143] As a preferred embodiment, step S3 of the present invention specifically includes the following steps:

[0144] After rigid registration, there will still be some elevation differences in the overlapping areas of the two data. In order to realize the fusion of UAV laser bathymetry and multi-beam bathymetry point cloud underwater terrain data and obtain seamless underwater terrain data, further precise registration should be performed.

[0145] The loss function of the classic non-rigid registration model is as follows:

[0146] (6);

[0147] In the formula, is the distance term, which represents the distance difference between the nearest points of the source point cloud and the target point cloud; is a rigid term used to penalize the difference in the affine transformation matrices of adjacent vertices; is a feature item, which indicates the distance difference between feature points and is used for initialization guidance; , is the weight factor, which is used to control the influence of the error term;

[0148] Formula (6) shows the traditional non-rigid registration model, which facilitates comparison with the non-rigid registration model proposed in the present invention.

[0149] The Non-Rigid ICP algorithm is relatively mature, but it is based on the nearest point iteration algorithm. It is easy to make mismatches for heterogeneous point clouds with different point cloud accuracy and distribution. In addition, underwater point clouds often have various noise interferences, which seriously affect the accuracy of data fusion. In order to better match data features and enhance the noise resistance of the model, the present invention proposes a non-rigid registration model based on the normal distance from the point to the corresponding triangular surface element. By establishing a one-to-one correspondence between the drone laser depth measurement point and the triangle in the multi-beam depth measurement irregular triangulation network, the distance between the drone laser depth measurement point and its corresponding triangular surface element is minimized, thereby eliminating the elevation difference in the overlapping area after the drone laser depth measurement and multi-beam depth measurement point cloud are registered. The rotation and translation of the point cloud is expressed as formula (7):

[0150] (7);

[0151] In the formula, is the target point cloud, Reason , , The rotation matrix is ​​formed, , , are three Euler angles, representing the axis, Axis and Rotation of the axis; is the source point cloud, is the spatial translation parameter; Formula (7) shows the principle of point cloud registration.

[0152] By performing Taylor expansion on formula (7) and taking its first-order term, we can obtain the corresponding error equation group:

[0153] (8);

[0154] In the formula, is the difference between the transformed point cloud and the target point cloud, is the Jacobian matrix, which represents the influence of rotation and translation parameters on point cloud transformation; is a parameter vector, containing rotation and translation parameters, , is the observation vector, which represents the distance from each target point to the closest point after the source point cloud is transformed; , , They are the translation amounts on the X-axis, Y-axis, and Z-axis respectively;

[0155] The normal distance term from the point to the triangle source is calculated as:

[0156] (9);

[0157] In the formula is the distance term, which represents the distance difference between the nearest points of the source point cloud and the target point cloud; is the laser depth measurement point cloud, For a laser depth point The corresponding triangular face plane parameters, , is the unit normal vector of the plane, is the distance from the plane to the origin; Delaunay triangulation constructed for multibeam bathymetric point clouds, is the distance function, used to calculate the distance between points and surfaces; is a laser sounding point, for The rotation matrix of for The translation vector of

[0158] Formula (9) constrains non-rigid registration based on the distance from point to plane, replacing the distance loss from point to nearest point in the traditional non-rigid registration model; compared with the traditional distance term, this formula avoids the problem of excessive difference in point cloud density distribution before and after non-rigid registration caused by inconsistent point cloud distribution between heterogeneous point clouds because it uses the point-to-plane distance as a constraint. It can be expressed by formula (10):

[0159] ;

[0160] In the formula, For the general The sparse matrix of the matrix mapping, is composed of rotation and translation parameters The parameter matrix, is a constant term.

[0161] Rigid terms based on point cloud triangulation constraints: In non-rigid registration, the rigid terms can prevent excessive deformation of local areas by penalizing the transformation difference between adjacent source points. The weight matrix is ​​introduced To balance the weight of rotation and translation parameters, we can get the rigid term for:

[0162] (11);

[0163] In the formula, For the Neighboring triangles of the source point to be corrected The vertex on is the source point cloud index to be corrected, , is the corresponding parameter matrix;

[0164] Formula (11) is used to correct the error of the point cloud. The deformation is constrained by adjacent triangle vertices to prevent excessive deformation. In order to effectively calculate the rigid term, the source point cloud is used to construct a Delaunay triangulation network. The edge triangle elimination method proposed in the patent is used to construct the triangulation network. All edge indices in the triangulation network are obtained. According to the vertex relationship of each edge, the triangulation network is constructed. The sparse matrix , is the number of edges in the triangulated network, and the loss function is expressed as:

[0165] (12);

[0166] In the formula, is the weight factor, for The weight matrix of is the cross product, is the weight matrix of boundary relations, is the Jacobian matrix;

[0167] Formula (12) realizes the fusion of UAV laser bathymetry and multi-beam bathymetry data, and solves the problem that the existing non-rigid registration model is not suitable for heterogeneous point cloud registration. It is difficult to extract homonymous points in non-homologous underwater point clouds, and after rough registration, there is a good initial state, so the patent model abandons the classic feature point term. The loss function is converted into the indirect adjustment method equation form:

[0168] ;

[0169] The unknown parameters are calculated continuously, and finally it is determined whether the average distance between points and surfaces is less than the preset value. If the termination condition is not met, the transformation parameters are applied to the source point cloud, and the precise alignment based on the normal distance from the point to the triangulated surface element is performed again.

[0170] In summary, the present invention considers the characteristics of drone laser sounding and multi-beam sounding data and the limitations of measurement operations, takes into account that the two heterogeneous data are only partially overlapped, introduces the overlap area determination and TIN construction of the joint virtual grid topology and alpha-shape algorithm, and reduces the influence of edge triangles and non-overlapping areas on data fusion; in view of the position offset phenomenon between heterogeneous data, the TIN grid vertex tangent plane is used as the registration primitive, and the distance between the point and the grid vertex is used to constrain the overall position offset; in view of the fact that there is still inconsistent elevation expression in the data overlap area after rigid registration, resulting in inaccurate expression of the ground objects, a one-to-one correspondence relationship between the drone laser sounding point and the triangle in the irregular triangulated network constructed by multi-beam sounding is established, and correction is made based on the precise registration of the normal distance from the point to the triangulated network face element. The underwater terrain acoustic and optical data fusion of drone laser sounding and multi-beam sounding data is effectively realized, providing an effective solution for obtaining a high-precision integrated terrain model above and below the water.

[0171] Embodiment 2, the embodiment of the present invention also provides a drone laser / shipborne multi-beam data water and land topography mapping system, the system specifically includes:

[0172] The overlap area determination and TIN construction module of the combined virtual grid topology and alpha-shape algorithm is used to roughly extract the data overlap area through the virtual grid, and finely extract the overlap area using the alpha-shape algorithm to obtain the boundary points, and use the boundary points to eliminate the edge triangles in the irregular triangulated network TIN constructed by the UAV laser bathymetric data and the shipborne multi-beam bathymetric data;

[0173] The rough registration module based on the vertex tangent plane of the TIN grid is used to calculate the vertex normal vector, use the vertex tangent plane of the multi-beam irregular triangulated network as the registration primitive, assign weights based on the distance from the point to the corresponding vertex, and perform rough registration through the point-to-plane ICP registration algorithm;

[0174] The precise registration module based on the normal distance from point to triangulated mesh face is used to construct a precise registration model based on point-to-face distance. It eliminates the elevation difference in overlapping areas by minimizing the normal distance from the drone laser sounding point to the corresponding multi-beam sounding triangulated face.

[0175] In order to further demonstrate the positive effects of the above embodiment, the present invention conducts the following experiments based on the above technical solution.

[0176] In order to verify the performance of the proposed UAV laser bathymetry and multi-beam bathymetry point cloud fusion algorithm, experiments were conducted using UAV laser bathymetry and multi-beam bathymetry data collected from a lake in China. The UAV laser bathymetry data used in the experiment was obtained by a vertical fixed-wing UAV equipped with a Mapper 20KU laser bathymetry system. The shipborne multi-beam bathymetry data was measured by the Haizhuo MS8200 and the Xingtian Technology Cubeam One multi-beam sonar. As shown in Table 1, three sample data were selected from the lake dataset.

[0177] Table 1 Overview of experimental areas:

[0178]

[0179] The UAV laser bathymetry and shipborne multi-beam bathymetry data from three experimental areas were selected to verify the algorithm of the present invention. The shipborne multi-beam bathymetry data was used as the target data, and the UAV laser bathymetry data was used as the data to be fused. The fusion results are shown in Figure 2. Figure 6 As shown. From the terrain shadow map, the multi-beam bathymetric point cloud and the UAV laser bathymetric point cloud have been effectively fused. After the fusion, there is no deformation at the boundaries of the three regions, the terrain changes are relatively consistent, and the inconsistent point cloud elevation in the overlapping area has been significantly improved. The four regions A, B, and C are located at the boundary of the UAV laser bathymetric data and the multi-beam bathymetric data. After the fusion, the elevation difference of the point cloud in the overlapping area has been significantly improved, and there is no obvious elevation difference at the junction of the data. The data of the overlapping area and the non-overlapping area are well connected, but due to the density difference between the multi-beam bathymetric point cloud and the UAV laser bathymetric point cloud, the data junction is more obvious.

[0180] In order to quantify the fusion effect of the proposed algorithm, the mean, mean absolute error (MAE) and root mean squared error (RMSE) of UAV laser bathymetry and shipborne multi-beam C2T (Cloud-to-TIN) before and after fusion are calculated as evaluation criteria. A TIN model is constructed for the shipborne multi-beam bathymetry data, and the C2T distance from the UAV laser bathymetry data to the multi-beam bathymetry TIN model is calculated. Table 2 lists the Mean, MAE, and RMSE of the C2T distance before and after the fusion of UAV laser bathymetry data and shipborne multi-beam bathymetry data in the three experimental areas, and the algorithm processing results are compared and analyzed with the Non-Rigid ICP registration algorithm processing results.

[0181] Table 2 Accuracy statistics before and after fusion:

[0182]

[0183] In general, the three algorithms have made corrections to the three experimental areas to varying degrees. From the perspective of the mean C2T distance, the C2T distance of the algorithm proposed in the present invention is smaller and less than 1 cm, which is more stable. For MAE and RMSE, the accuracy of Non-Rigid ICP and the algorithm proposed in the present invention is at the centimeter level. From the perspective of MAE and RMSE alone, the two algorithms have similar performances, but Non-Rigid ICP uses a point-to-point matching strategy. When processing point clouds of different accuracies of UAV laser depth sounding and multi-beam depth sounding sensors, it is easy to have inconsistent point cloud density before and after correction in the overlapping area of ​​UAV laser depth sounding, resulting in the loss of some terrain details. The technology proposed in the present invention adopts a point-to-surface matching strategy and introduces a rigid term based on the point cloud triangulation constraint, which is more robust when dealing with different accuracies and different distribution data of UAV laser depth sounding and multi-beam depth sounding sensors.

[0184] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for land and water terrain mapping using unmanned aerial vehicle laser / shipborne multi-beam data, characterized in that: The method comprises the steps of: S1, determination of overlapping areas and TIN construction by combining virtual grid topology and alpha-shape algorithm: coarse extraction of data overlapping areas through virtual grid, fine extraction of overlapping areas using alpha-shape algorithm, obtaining boundary points, and using boundary points to remove edge triangles in irregular triangulated network TIN constructed by UAV laser bathymetry data and shipborne multi-beam bathymetry data; S2, coarse registration based on the tangent plane of the TIN grid vertex: calculate the vertex normal vector, use the tangent plane of the multi-beam irregular triangulated network vertex as the registration primitive, assign weights based on the distance from the point to the corresponding vertex, and perform coarse registration through the point-to-plane ICP registration algorithm; S3, precise registration based on the normal distance from point to triangulated mesh surface element: Construct a precise registration model based on the distance between point and surface, and eliminate the elevation difference in the overlapping area by minimizing the normal distance from the UAV laser bathymetric point to the corresponding multi-beam bathymetric triangulated surface element; In step S2, the vertex normal vector is calculated, including: Calculate the normal vector for each triangle separately. , , The surface normal vector is calculated by the following formula: ； In the formula, is the triangle face normal vector; The vertex normal vector is obtained by weighted average of the adjacent face normal vectors. The vertex normal vector is expressed as: ； In the formula, is the vertex normal vector, is the number of vertices in the triangulated network, For the The area of ​​adjacent triangles, is the normal vector of the triangle.

2. The method for land and water terrain mapping using unmanned aerial vehicle laser / shipborne multi-beam data according to claim 1, characterized in that: In step S1, the data overlap area is roughly extracted through the virtual grid, including: Merge UAV laser bathymetry and multibeam bathymetry point clouds and set grid size , the number of rows and columns of the virtual grid is calculated according to the maximum and minimum horizontal and vertical coordinates of the merged point cloud. The expression is: ； In the formula, is the number of grid rows and columns, To round up, To round down, are the maximum and minimum horizontal and vertical coordinates in the point cloud data, respectively. is the grid size; Any point after merging Divide into virtual grids. If there are UAV laser bathymetry and multi-beam bathymetry point cloud points in the grid, the grid will be retained and marked as an overlapping area. Use low-density point cloud to search for adjacent points, take twice the distance of the largest neighboring point as the grid size ; The value is obtained by rounding up the point cloud density, and the grid size The calculation formula is: ； In the formula, To search for point clouds The nearest neighbor of each point The distance of the points, For point cloud data with low density, is the corresponding density, To get the maximum value.

3. The method for land and water terrain mapping using UAV laser / shipborne multi-beam data according to claim 1, characterized in that: In step S1, the overlap area determination and TIN construction of the combined virtual grid topology and alpha-shape algorithm include: When there is a discrete point cloud ,right Normalize the elevation and project it onto the same plane to get a two-dimensional point set ; In a two-dimensional point set Pick any point , find Zhongyu Point spacing is less than Point set ; Connection point With point set Find the points in the alpha-shape rule and mark them as boundary points; traverse All points in get the final boundary point index The alpha-shape algorithm is used to extract the overlapping areas and boundaries of the drone laser depth sounding and multi-beam depth sounding point clouds, and the boundary points of the constructed triangulated network are detected. The boundary triangles are eliminated by judging the positional relationship of the boundary points contained in the triangle vertices.

4. The method for land and water terrain mapping using unmanned aerial vehicle laser / shipborne multi-beam data according to claim 3 is characterized in that: The constructed triangulated network is subjected to boundary point detection, and boundary triangles are eliminated by determining the positional relationship of boundary points contained in triangle vertices, including: (1) Eliminate triangulated networks with edges longer than The triangles get a new TIN network; (2) For any triangle in the TIN network , search whether its three vertices are boundary points; (3) If there is no boundary point or only one vertex is a boundary point, store the triangle to vertex index matrix Vertices If there are two or more boundary points, execute step (4); (4) Determine the positional relationship between boundary points. For a triangle containing two boundary points, if the two boundary points are not adjacent boundary points, the triangle is discarded. If the two boundary points are adjacent, the triangle is stored in the vertex index matrix. Vertices For a triangle whose three vertices are all boundary points, if the three boundary points are not three adjacent continuous boundary points, the triangle is removed. If the three boundary points are adjacent, the triangle is stored in the vertex index matrix. Vertices ; (5) Repeat steps (2) to (4) until all triangles have been traversed.

5. The method for land and water terrain mapping using unmanned aerial vehicle laser / shipborne multi-beam data according to claim 1, characterized in that: In step S2, a rough registration is performed using a point-to-plane ICP registration algorithm, including: The weight is assigned according to the distance between the source point and the matched target point. For points with large distance deviation, a small weight is assigned. The weight calculation formula is: ； In the formula, is a discrete point cloud, is the distance from the source point to the corresponding target point; After constructing the weight matrix, point to plane ICP is used for coarse registration to correct the overall offset between the source point cloud and the target point cloud; Loss function for non-rigid registration model for: ； In the formula, is the distance term, which represents the distance difference between the nearest points of the source point cloud and the target point cloud; is a rigid term used to penalize the difference in the affine transformation matrices of adjacent vertices; is a feature item, which indicates the distance difference between feature points and is used for initialization guidance; , is the weight factor, which is used to control the influence of the error term; A non-rigid registration model based on the normal distance from the point to the corresponding triangle surface element is constructed. By establishing a one-to-one correspondence between the UAV laser bathymetry points and the triangles in the multi-beam bathymetry irregular triangulation network, the distance between the UAV laser bathymetry points and the corresponding triangle surface elements is minimized, and the elevation difference in the overlapping area after the registration of the UAV laser bathymetry and multi-beam bathymetry point clouds is eliminated.

6. The method for land and water terrain mapping using unmanned aerial vehicle laser / shipborne multi-beam data according to claim 5, characterized in that: The rotation and translation of the point cloud is shown as follows: ； In the formula, is the target point cloud, Reason , , The rotation matrix is ​​formed, , , are three Euler angles, representing the axis, Axis and Rotation of the axis; is the source point cloud, is the spatial translation parameter; Taylor expansion is performed on the rotation and translation formula of the point cloud and the first-order term is taken to obtain the corresponding error equation group, which is expressed as follows: ； In the formula, is the difference between the transformed point cloud and the target point cloud, is the Jacobian matrix, which represents the influence of rotation and translation parameters on point cloud transformation; is a parameter vector, containing rotation and translation parameters, , is the observation vector, which represents the distance from each target point to the triangle surface element; , , They are the translation amounts on the X-axis, Y-axis, and Z-axis respectively; The distance term from the calculated point to the triangle source normal is: ； In the formula is the distance term, which represents the distance difference between the nearest points of the source point cloud and the target point cloud; is the laser depth measurement point cloud, For a laser depth point The corresponding triangular face plane parameters, , is the unit normal vector of the plane, is the distance from the plane to the origin; Delaunay triangulation constructed for multibeam bathymetric point clouds, is the distance function, used to calculate the distance between points and surfaces; is a laser sounding point, for The rotation matrix of for The translation vector of According to the error equations, the distance term It is expressed by the following formula: ； In the formula, For the general The sparse matrix of the matrix mapping, is composed of rotation and translation parameters The parameter matrix, is a constant term.

7. The method for land and water terrain mapping using unmanned aerial vehicle laser / shipborne multi-beam data according to claim 6, characterized in that: Construct a non-rigid registration model based on the normal distance from the point to the corresponding triangle surface element, including: In non-rigid registration, the rigid term prevents excessive deformation of the local area by penalizing the transformation difference between adjacent source points, and introduces a weight matrix , Used to balance the proportion of rotation and translation parameters, and get the rigid term , the expression is: ； In the formula, For the Neighboring triangles of the source point to be corrected The vertex on is the source point cloud index to be corrected, , is the corresponding parameter matrix; Use the source point cloud to construct a Delaunay triangulation network, and use the edge triangle elimination method to construct a triangulation network, obtain all edge indexes in the triangulation network; according to the vertex relationship of each edge, construct The sparse matrix , is the number of edges in the triangulated network, and the loss function is expressed as: ； In the formula, is the weight factor, for The weight matrix of is the cross product, is the weight matrix of boundary relations, is the Jacobian matrix; Convert the loss function into the indirect adjustment equation form: ； The unknown parameters are continuously calculated to determine whether the average value of the point-to-surface distance is less than the preset value; if the termination condition is not met, the transformation parameters are applied to the source point cloud, and the precise alignment based on the normal distance from the point to the triangulated surface element is performed again.

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