Triangular mesh reconstruction method based on region expansion

Abstract

The present disclosure is about a triangular mesh reconstruction method based on regional expansion. The method includes: constructing a tree structure to manage the point cloud data set; selecting seed points in the point cloud data set and constructing seed triangles; mapping the point cloud data set to a two-dimensional plane, taking one of the three sides of the seed triangle as the reference side in turn, and determining the candidate point set of the reference side from the point cloud data set according to the two vertices of the reference side; mapping the candidate point set back to three-dimensional space, selecting the optimal point from the candidate point set as the expansion point through the candidate point evaluation function to expand and obtain a mesh area; mapping the point cloud data set to a two-dimensional plane, taking one of the multiple sides of the mesh area as the reference side in turn, selecting the optimal point as the expansion point for regional expansion, until all points in the point cloud data set are constructed and the mesh reconstruction is completed.

Description

Technical Field

[0001] The present disclosure relates to the field of data processing and application technology, and in particular to a triangular mesh reconstruction method based on region expansion. Background Art

[0002] In recent years, surface model reconstruction from point cloud data has been widely used in reverse engineering, 3D city modeling, computer animation and 3D model reconstruction.

[0003] In the related technologies, the commonly used research directions of point cloud surface reconstruction are mainly: one is based on Delaunay triangle reconstruction, which maps three-dimensional data to a two-dimensional plane for Delaunay triangulation, restricts it through triangulation and related constraints, and finally maps the two-dimensional data back to a three-dimensional structure to construct a surface mesh with a relatively clear structural hierarchy. However, this method requires a large amount of data and the efficiency of model reconstruction is low. Another type of surface reconstruction is based on mesh growth. This method continuously grows outward from seed points to eventually form a surface mesh. This method is relatively simple, but there are still certain difficulties in selecting seed points, determining the growth direction, and formulating growth rules.

[0004] Therefore, it is necessary to provide a new technical solution to improve one or more problems existing in the above solutions.

[0005] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to ordinary technicians in the field. Summary of the invention

[0006] The purpose of the present disclosure is to provide a triangular mesh reconstruction method based on region expansion, thereby overcoming one or more problems caused by limitations and defects of related technologies at least to a certain extent.

[0007] According to an embodiment of the present disclosure, a triangular mesh reconstruction method based on region expansion is provided, comprising:

[0008] Construct a tree structure to manage point cloud datasets;

[0009] Selecting seed points in the point cloud data set and constructing seed triangles;

[0010] Mapping the point cloud data set onto a two-dimensional plane, and according to the position distribution of the point cloud data in the two-dimensional plane and the three-dimensional space, taking one of the three sides of the seed triangle as a reference side in turn, and determining a candidate point set of the reference side from the point cloud data set according to two vertices of the reference side and a preset constraint principle;

[0011] Mapping the candidate point set back to the three-dimensional space, selecting the best point from the candidate point set as the expansion point through the candidate point evaluation function to expand and obtain a grid area;

[0012] The point cloud data set is mapped onto a two-dimensional plane, and one of the multiple edges of the grid area is used as the reference edge in turn, and the optimal point is selected as the extension point to expand the area until all points in the point cloud data set are constructed and the grid reconstruction is completed.

[0013] In an embodiment of the present disclosure, the tree structure is a KD-Tree or an octree.

[0014] In an embodiment of the present disclosure, when the point cloud data in the point cloud data set is less than a preset value, the tree structure is a KD-Tree; when the point cloud data in the point cloud data set is greater than a preset value, the tree structure is an octree.

[0015] In an embodiment of the present disclosure, the step of selecting a seed point in the point cloud data set includes:

[0016] Selecting the point with the smallest value on the X-axis in the point cloud data set as the initial point, and performing neighborhood search using a tree structure to obtain a neighborhood point set of the initial point;

[0017] Calculate the normal vector size of the initial point and the normal vector size of each neighboring point in the neighborhood point set;

[0018] The normal vector angles of each of the neighborhood points and the initial point are calculated respectively. When the normal vector angles are all less than 90°, the initial point is the seed point. When any normal vector angle is greater than 90°, the second smallest point on the X-axis in the point cloud data set is selected as the initial point for calculation and judgment until the seed point is determined.

[0019] In an embodiment of the present disclosure, the step of calculating the normal vector size of the initial point and the normal vector size of each neighborhood point in the neighborhood point set includes:

[0020] Calculate the normal vector of the initial point, where the normal vector of the initial point is the average of the normal vectors of multiple triangles formed by the initial point and any two neighboring points in its neighboring point set;

[0021] A tree structure is used to perform neighborhood searches respectively to obtain a second neighborhood point set of each neighborhood point in the neighborhood point set of the initial point;

[0022] The normal vector of each neighborhood point in the neighborhood point set is calculated, and the normal vector of each neighborhood point in the neighborhood point set is the average of the normal vectors of multiple triangles formed by the neighborhood point in the neighborhood point set and any two neighborhood points in the corresponding second neighborhood point set.

[0023] In an embodiment of the present disclosure, the step of constructing a seed triangle includes:

[0024] Select a second point in the point cloud data set that has the closest Euclidean distance to the seed point and forms an edge with the seed point;

[0025] A tree structure is used to perform neighborhood search to obtain neighborhood point sets of the seed point and the second point respectively;

[0026] Calculate the intersection of the neighborhood point set of the seed point and the neighborhood point set of the second point, and select a point from the intersection that can be connected with the seed point and the second point to form an acute triangle and has the smallest sum of distances to the seed point and the second point as the third point;

[0027] The third point is connected with the seed point and the second point to form a seed triangle.

[0028] In an embodiment of the present disclosure, the step of determining a candidate point set of the reference edge from the point cloud data set according to two vertices of the reference edge and by a preset constraint principle includes:

[0029] A tree structure is used to perform neighborhood search to obtain neighborhood point sets of two vertices of the reference edge respectively;

[0030] Calculate the intersection of the neighborhood point sets of two vertices;

[0031] Candidate points are selected from the intersection to form a candidate point set according to a preset constraint principle, wherein the preset constraint principle is: combining the minimum inner angle principle, the empty circumscribed circle principle and the dihedral angle constraint principle, the minimum inner angle principle and the empty circumscribed circle principle are the selection principles when the point cloud data set is mapped on a two-dimensional plane, and the dihedral angle constraint principle is the selection principle when the point cloud data set is in three-dimensional space.

[0032] In the embodiment of the present disclosure, the minimum interior angle principle is to select a neighborhood point whose interior angle θ formed by the two vertices in the intersection in a two-dimensional coordinate system satisfies 30°<θ<90°;

[0033] The empty circumscribed circle principle is to select a neighboring point in the intersection set in a two-dimensional coordinate system that is outside the circumscribed circle of the seed triangle and whose minimum distance from the circumscribed circle is less than the diameter of the circumscribed circle;

[0034] The dihedral angle constraint principle is to select a point in the three-dimensional coordinate system where the dihedral angle β between the triangle formed by the two vertices and the seed triangle satisfies π / 3≤β≤π.

[0035] In the embodiment of the present disclosure, the candidate point evaluation function is: Wherein, D is the ratio of the length of the reference side to the sum of the distances from the candidate point to the two vertices of the reference side.

[0036] In the embodiment of the present disclosure, the optimal point is the candidate point in the candidate point set whose H is the largest by calculation of the candidate point evaluation function.

[0037] The technical solution provided by the embodiments of the present disclosure may have the following beneficial effects:

[0038] In one embodiment of the present disclosure, through the above-mentioned triangular mesh reconstruction method based on region expansion, on the one hand, the idea of ​​projection is used to transform the three-dimensional space problem into a two-dimensional plane for solution, which greatly improves the computational efficiency in the model reconstruction process; on the other hand, the candidate point set is determined by a preset constraint principle and the optimal point is selected from the candidate point set for expansion through a designed candidate point evaluation function, which promotes the quality of the reconstructed triangles and can express the physical structure of the model in more detail.

[0039] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A flowchart of a triangular mesh reconstruction method based on region expansion in an exemplary embodiment of the present disclosure is schematically shown;

[0041] Figure 2 Schematically showing a schematic diagram of constructing a seed triangle in an exemplary embodiment of the present disclosure;

[0042] Figure 3 Schematically showing the minimum interior angle principle, the dihedral angle constraint principle and the empty circumscribed circle principle in the exemplary embodiment of the present disclosure;

[0043] Figure 4 The diagram schematically shows the best point selection in the exemplary embodiment of the present disclosure. DETAILED DESCRIPTION

[0044] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0045] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0046] In this example implementation, a triangular mesh reconstruction method based on region expansion is first provided. Figure 1 As shown in , the method may include:

[0047] Step S101: construct a tree structure to manage the point cloud data set;

[0048] Step S102: selecting seed points in the point cloud data set and constructing seed triangles;

[0049] Step S103: mapping the point cloud data set onto a two-dimensional plane, and according to the position distribution of the point cloud data in the two-dimensional plane and the three-dimensional space, taking one of the three sides of the seed triangle as a reference side, and determining a candidate point set of the reference side from the point cloud data set according to two vertices of the reference side and a preset constraint principle;

[0050] Step S104: mapping the candidate point set back to the three-dimensional space, and selecting the best point from the candidate point set as the expansion point through the candidate point evaluation function to expand and obtain a grid area;

[0051] Step S105: Map the point cloud data set onto a two-dimensional plane, take one of the multiple edges of the grid area as the reference edge, select the optimal point as the expansion point to expand the area, until all points in the point cloud data set are constructed, and the grid reconstruction is completed.

[0052] Specifically, in step S101, a tree structure is constructed to facilitate the management of point cloud data. The point cloud data set may be an optimized point cloud data set after being processed by a preset algorithm; the point cloud data set may also be an unprocessed point cloud data set. After the tree structure is constructed to manage the point cloud data set, it may be optimized through filtering processing as needed.

[0053] In step S102, when building a model, seed points must first be selected in the point cloud data set, and a seed triangle is constructed based on the selected seed points.

[0054] In step S103, after the seed triangle is constructed, it is necessary to perform region expansion based on the seed triangle. The specific expansion principle is to take one side of the seed triangle as the reference side, determine the candidate point set of the reference side from the point cloud data set according to the two vertices of the reference side and the preset constraint principle, and then determine the candidate point set with the second side of the seed triangle as the reference side, and finally determine the candidate point set with the third side as the reference side.

[0055] In step S104, the candidate point set is mapped back to the three-dimensional space, and when the optimal point is selected from the candidate point set by the candidate point evaluation function, an optimal point can be determined after each candidate set of one edge of the seed triangle is obtained, or the optimal point of each edge can be determined in sequence after the candidate set of three edges of the seed triangle is obtained, and each time an optimal point is determined, the optimal point is locked so that other edges cannot select the optimal point as the optimal point, that is, the candidate points in each candidate point set cannot be repeatedly used as the optimal points of multiple edges. After the optimal point is determined, the optimal point is used as the expansion point to expand to obtain the grid area.

[0056] In step S105, the edges of the mesh area are continuously searched for the optimal point for peripheral expansion in the same manner as in step S104 until all points in the point cloud data set are constructed, and the mesh reconstruction is completed.

[0057] Through the above-mentioned triangular mesh reconstruction method based on region expansion, on the one hand, the idea of ​​projection is used to transform the three-dimensional space problem into a two-dimensional plane for solution, which greatly improves the computational efficiency in the model reconstruction process; on the other hand, the best point is selected from the candidate point set for expansion through the designed candidate point evaluation function, which promotes the quality of the reconstructed triangle and can express the physical structure of the model more delicately.

[0058] Next, we will refer to Figure 1 to Figure 4 Each step of the above method in this example implementation is described in more detail.

[0059] In one embodiment, the tree structure is a KD-Tree or an octree. Specifically, the KD-Tree is a tree data structure that stores instance points in a k-dimensional space for rapid retrieval, and is mainly used for searching key data in a multidimensional space. An octree is a tree data structure for describing a three-dimensional space. Each node of an octree represents a volume element of a cube, and each node has eight child nodes. The volume elements represented by the eight child nodes are added together to equal the volume of the parent node.

[0060] In one embodiment, when the point cloud data in the point cloud data set is less than a preset value, the tree structure is a KD-Tree; when the point cloud data in the point cloud data set is greater than a preset value, the tree structure is an octree. Specifically, the octree structure is suitable for situations where there is more data in the point cloud data set, and the KD-Tree is suitable for situations where there is less data in the point cloud data set. The corresponding preset value can be set according to its applicability. For example, the preset value can be 100,000. When the point cloud data is greater than 100,000, the octree is used, and when the point cloud data is less than 100,000, the KD-Tree is used. Of course, the setting of the preset value is not limited to the above value.

[0061] In one embodiment, the step of selecting a seed point in the point cloud data set includes:

[0062] Selecting the point with the smallest value on the X-axis in the point cloud data set as the initial point, and performing neighborhood search using a tree structure to obtain a neighborhood point set of the initial point;

[0063] Calculate the normal vector size of the initial point and the normal vector size of each neighboring point in the neighborhood point set;

[0064] The normal vector angles of each of the neighborhood points and the initial point are calculated respectively. When the normal vector angles are all less than 90°, the initial point is the seed point. When any normal vector angle is greater than 90°, the second smallest point on the X-axis in the point cloud data set is selected as the initial point for calculation and judgment until the seed point is determined.

[0065] Specifically, when selecting a seed point, first select the point with the smallest value on the X-axis in the point cloud data set as the initial point, and use a tree structure such as KD-Tree or octree to perform neighborhood search to obtain the neighborhood point set of the initial point. Exemplarily, the number of neighborhood points in the neighborhood point set can be set in advance according to demand, for example, the search amount of neighborhood points can be set to 10, 20, etc. After determining the neighborhood point set, calculate the size of the normal vector of the initial point and the size of the normal vector of each neighborhood point in the neighborhood point set, and calculate the angle between the normal vector of the initial point and the normal vectors of multiple neighborhood points respectively. Only when all calculated angles are less than 90°, the initial point is identified as a seed point. When any angle is greater than 90°, the initial point is abandoned, and the point with the second smallest value on the X-axis in the point cloud data set is selected as the initial point to re-perform the above calculation until the seed point is determined.

[0066] In one embodiment, the step of calculating the normal vector size of the initial point and the normal vector size of each neighborhood point in the neighborhood point set includes:

[0067] Calculate the normal vector of the initial point, where the normal vector of the initial point is the average of the normal vectors of multiple triangles formed by the initial point and any two neighboring points in its neighboring point set;

[0068] A tree structure is used to perform neighborhood searches respectively to obtain a second neighborhood point set of each neighborhood point in the neighborhood point set of the initial point;

[0069] The normal vector of each neighborhood point in the neighborhood point set is calculated, and the normal vector of each neighborhood point in the neighborhood point set is the average of the normal vectors of multiple triangles formed by the neighborhood point in the neighborhood point set and any two neighborhood points in the corresponding second neighborhood point set.

[0070] Specifically, the normal vector of the initial point is the average of the normal vectors of multiple triangles formed by the initial point as a vertex and any two points in the neighborhood point set as the other two vertices. Similar to the initial point, the normal vector of each neighboring point in the neighborhood point set is the average of the normal vectors of multiple triangles formed by the neighborhood point and its corresponding second neighborhood point set.

[0071] In one embodiment, the step of constructing a seed triangle includes:

[0072] Select a second point in the point cloud data set that has the closest Euclidean distance to the seed point and forms an edge with the seed point;

[0073] Using a tree structure to perform neighborhood search to obtain neighborhood point sets of the seed point and the second point respectively;

[0074] Calculate the intersection of the neighborhood point set of the seed point and the neighborhood point set of the second point, and select a point from the intersection that can be connected with the seed point and the second point to form an acute triangle and has the smallest sum of distances to the seed point and the second point as the third point;

[0075] The third point is connected with the seed point and the second point to form a seed triangle.

[0076] Specifically, first select the point with the closest Euclidean distance to the seed point as the second point and connect it to the seed point to form an edge, then perform neighborhood search on the seed point and the second point respectively to obtain a neighborhood point set, find the intersection of the seed point neighborhood point set and the second point neighborhood point set, select a point from the intersection to form a seed triangle with the seed point and the second point, and the selection principle is to select a point, the triangle formed by the point, the seed point and the second point is an acute triangle, on this basis, the distance between the point and the seed point plus the distance between the point and the second point must be the minimum. For example, refer to Figure 2 As shown in 1 is the seed point, p 2 For the second point, p 4 Although the distance p 1 and p 2 The closest, but the triangle formed is an obtuse triangle, so choose p 3 For the third point, it can be1 and p 2 When forming an acute triangle, the distance p 1 and p 2 It's the most recent.

[0077] In one embodiment, the step of determining a candidate point set of the reference edge from the point cloud data set according to two vertices of the reference edge includes:

[0078] A tree structure is used to perform neighborhood search to obtain neighborhood point sets of two vertices of the reference edge respectively;

[0079] Calculate the intersection of the neighborhood point sets of two vertices;

[0080] Candidate points are selected from the intersection to form a candidate point set according to a preset constraint principle, wherein the preset constraint principle is: combining the minimum inner angle principle, the empty circumscribed circle principle and the dihedral angle constraint principle, the minimum inner angle principle and the empty circumscribed circle principle are the selection principles when the point cloud data set is mapped on a two-dimensional plane, and the dihedral angle constraint principle is the selection principle when the point cloud data set is in three-dimensional space.

[0081] Specifically, the method for obtaining the candidate point set of the reference edge is to perform a neighborhood search to obtain the neighborhood point sets of the two vertices of the reference edge and calculate the intersection, and select candidate points from the intersection to form a candidate point set by combining the minimum interior angle principle, the dihedral angle constraint principle and the empty circumscribed circle principle, that is, to select neighborhood points that simultaneously meet the above three principles from the intersection as candidate points to form a candidate point set.

[0082] In one embodiment, the minimum interior angle principle is to select a neighborhood point whose interior angle θ formed by the two vertices in the intersection in a two-dimensional coordinate system satisfies 30°<θ<90°;

[0083] The empty circumscribed circle principle is to select a neighboring point in the intersection set in a two-dimensional coordinate system that is outside the circumscribed circle of the seed triangle and whose minimum distance from the circumscribed circle is less than the diameter of the circumscribed circle;

[0084] The dihedral angle constraint principle is to select a point in the three-dimensional coordinate system where the dihedral angle β between the triangle formed by the two vertices and the seed triangle satisfies π / 3≤β≤π.

[0085] Specifically, refer to Figure 3 As shown in Figure 3 In (a), the minimum interior angle principle means that the interior angle θ formed by the selected point such as C and the two vertices A and B of the reference side must satisfy 30°<θ<90°, and the optimal value of θ is 60°; Figure 3In (b), the dihedral angle constraint principle is that the dihedral angle β between the selected point E and the two vertices A and B of the reference side, triangle △ABE, and the seed triangle △ABC must satisfy π / 3≤β≤π. Figure 3 Point D in (b) does not meet the above conditions and therefore cannot be selected as a candidate point. The reason for this selection is that the larger the dihedral angle, the smoother the transition between the two surfaces. Figure 3 In (c), the empty circumscribed principle means that the selected point, such as C, must be outside the circumscribed circle of the seed triangle △ABD. Figure 3 Point C in the left figure in (c) satisfies the empty circumscribed principle, while point C in the right figure does not satisfy the empty circumscribed principle.

[0086] In one embodiment, the candidate point evaluation function is: Wherein, D is the ratio of the length of the reference edge to the sum of the distances from the candidate point to the two vertices of the reference edge. Figure 4 As shown in the figure, AB is the reference side, △ABC is the seed triangle, D1 and D2 are the candidate points in the candidate point set, and D 1 For example, θ is the internal angle ∠AD formed by the connection between D1 and A and B in the candidate point set. 1 B, β is △ABC and △ABD 1 The dihedral angles formed,

[0087] In one embodiment, the optimal point is the candidate point in the candidate point set whose H is the largest by calculation of the candidate point evaluation function.

[0088] Through the above-mentioned triangular mesh reconstruction method based on region expansion, on the one hand, the idea of ​​projection is used to transform the three-dimensional space problem into a two-dimensional plane for solution, which greatly improves the computational efficiency in the model reconstruction process; on the other hand, the candidate point set is determined by the preset constraint principle and the optimal point is selected from the candidate point set for expansion through the designed candidate point evaluation function, which promotes the quality of the reconstructed triangles and can express the physical structure of the model more delicately.

[0089] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0090] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, a magnetic disk, or an optical disk), and includes a number of instructions for enabling a terminal (which can be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to execute the methods described in each embodiment of the present invention.

[0091] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A triangular mesh reconstruction method based on region expansion, characterized in that: include: Construct a tree structure to manage point cloud datasets; Selecting seed points in the point cloud data set and constructing seed triangles; Mapping the point cloud data set onto a two-dimensional plane, and according to the position distribution of the point cloud data in the two-dimensional plane and the three-dimensional space, taking one of the three sides of the seed triangle as a reference side in turn, and determining a candidate point set of the reference side from the point cloud data set according to two vertices of the reference side and a preset constraint principle; Mapping the candidate point set back to the three-dimensional space, selecting the best point from the candidate point set as the expansion point through the candidate point evaluation function to expand and obtain a grid area; Mapping the point cloud data set onto a two-dimensional plane, taking one of the multiple edges of the grid area as a reference edge, selecting the optimal point as an extension point to perform area expansion, until all points in the point cloud data set are constructed, and grid reconstruction is completed; The step of determining a candidate point set of the reference edge from the point cloud data set according to two vertices of the reference edge and through a preset constraint principle comprises: A tree structure is used to perform neighborhood search to obtain neighborhood point sets of two vertices of the reference edge respectively; Calculate the intersection of the neighborhood point sets of two vertices; Selecting candidate points from the intersection to form a candidate point set according to a preset constraint principle, wherein the preset constraint principle is: combining a minimum inner angle principle, an empty circumscribed circle principle and a dihedral angle constraint principle, wherein the minimum inner angle principle and the empty circumscribed circle principle are selection principles when the point cloud dataset is mapped on a two-dimensional plane, and the dihedral angle constraint principle is a selection principle when the point cloud dataset is in a three-dimensional space; The candidate point evaluation function is: Among them, D is the ratio of the length of the reference side to the sum of the distances from the candidate point to the two vertices of the reference side, θ is the interior angle formed by the two vertices in the intersection in the two-dimensional coordinate system, and β is the dihedral angle between the triangle formed by the two vertices in the intersection in the three-dimensional coordinate system and the seed triangle.

2. The triangular mesh reconstruction method based on region expansion according to claim 1, characterized in that: The tree structure is a KD-Tree or an octree.

3. The triangular mesh reconstruction method based on region expansion according to claim 2, characterized in that: When the point cloud data in the point cloud data set is less than a preset value, the tree structure is a KD-Tree; when the point cloud data in the point cloud data set is greater than a preset value, the tree structure is an octree.

4. The triangular mesh reconstruction method based on region expansion according to claim 1, characterized in that: The step of selecting a seed point in the point cloud data set includes: Selecting the point with the smallest value on the X-axis in the point cloud data set as the initial point, and performing neighborhood search using a tree structure to obtain a neighborhood point set of the initial point; Calculate the normal vector size of the initial point and the normal vector size of each neighboring point in the neighborhood point set; The normal vector angles of each of the neighborhood points and the initial point are calculated respectively. When the normal vector angles are all less than 90°, the initial point is the seed point. When any normal vector angle is greater than 90°, the second smallest point on the X-axis in the point cloud data set is selected as the initial point for calculation and judgment until the seed point is determined.

5. The triangular mesh reconstruction method based on region expansion according to claim 4, characterized in that: The steps of calculating the normal vector size of the initial point and the normal vector size of each neighboring point in the neighboring point set include: Calculate the normal vector of the initial point, where the normal vector of the initial point is the average of the normal vectors of multiple triangles formed by the initial point and any two neighboring points in its neighboring point set; A tree structure is used to perform neighborhood searches respectively to obtain a second neighborhood point set of each neighborhood point in the neighborhood point set of the initial point; The normal vector of each neighborhood point in the neighborhood point set is calculated, and the normal vector of each neighborhood point in the neighborhood point set is the average of the normal vectors of multiple triangles formed by the neighborhood point in the neighborhood point set and any two neighborhood points in the corresponding second neighborhood point set.

6. The triangular mesh reconstruction method based on region expansion according to claim 4, characterized in that: The steps to construct the seed triangle include: Select a second point in the point cloud data set that has the closest Euclidean distance to the seed point and forms an edge with the seed point; A tree structure is used to perform neighborhood search to obtain neighborhood point sets of the seed point and the second point respectively; Calculate the intersection of the neighborhood point set of the seed point and the neighborhood point set of the second point, and select a point from the intersection that can be connected with the seed point and the second point to form an acute triangle and has the smallest sum of distances to the seed point and the second point as the third point; The third point is connected with the seed point and the second point to form a seed triangle.

7. The triangular mesh reconstruction method based on region expansion according to claim 1, characterized in that: The minimum interior angle principle is to select a neighborhood point whose interior angle θ formed by the two vertices in the intersection in the two-dimensional coordinate system satisfies 30°<θ<90°; The empty circumscribed circle principle is to select a neighboring point in the intersection set in a two-dimensional coordinate system that is outside the circumscribed circle of the seed triangle and whose minimum distance from the circumscribed circle is less than the diameter of the circumscribed circle; The dihedral angle constraint principle is to select a point in the three-dimensional coordinate system where the dihedral angle β between the triangle formed by the two vertices and the seed triangle satisfies π / 3≤β≤π.

8. The triangular mesh reconstruction method based on region expansion according to claim 7, characterized in that: The optimal point is the candidate point in the candidate point set whose H is the largest by calculation of the candidate point evaluation function.

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