Fractal growth model and method for refined tree modeling

Abstract

The application discloses a fractal growth model and a fine tree modeling method, and belongs to the technical field of three-dimensional reconstruction, which comprises the following steps: acquiring original point clouds of single trees in a reconstruction area, an image set and ground height information of each spatial position; data preprocessing and point cloud data segmentation; extracting the skeleton of the tree from the non-ground point cloud based on graph theory, Dijkstra algorithm and cubic spline interpolation algorithm; hierarchically reconstructing the tree to generate a three-dimensional grid model of the trunk, a branch cylinder model and a small branch model, and fusing them into a tree model; and performing texture mapping based on NeRF to obtain a comprehensive tree model. The application introduces a graph theory method as a key link in the skeleton extraction process, accurately extracts the tree skeleton from the non-ground point cloud, adopts a hierarchical reconstruction method, realizes accurate extraction of the skeleton and tree modeling, introduces the NeRF technology in texture mapping, and improves the modeling accuracy and texture quality.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional reconstruction technology, and in particular to a fractal growth model and a refined tree modeling method. Background Technology

[0002] With the rapid development of 3D modeling and computer vision technologies, deep learning-based 3D tree modeling and texture mapping have shown great potential in forestry management, ecological protection, and the construction of digital twin forest areas. In forestry modeling and ecological assessment, ensuring the accuracy and detail of tree models is crucial for performing carbon sink assessments, green volume calculations, and planning conflict detection. Refined tree modeling often requires realistic textures, representation of tree growth patterns, and terrain integration to meet the needs of forest resource management and ecological protection.

[0003] Current methods for tree modeling include: For example, patent application CN112634432B. This method relies on manually drawing branch trajectories in a virtual environment, resulting in low modeling efficiency, rigid structural forms, lack of real-world terrain constraints, and inability to achieve automatic reconstruction based on real-world data. Another method, patent application CN104392484B, generates a new model by extracting components from existing tree models and connecting them using interpolation curves. While this simplifies the 3D data acquisition process, it heavily relies on a pre-set model library, lacks adaptability to real-world terrain, cannot reflect the actual tree structure, has limited morphological accuracy and naturalness, and does not support automated modeling.

[0004] Therefore, traditional modeling methods are difficult to handle complex tree shapes and details, and cannot guarantee consistent lighting and natural transitions in textures.

[0005] RANSAC (Random Sample Consensus) is an algorithm that calculates mathematical model parameters for a dataset containing outliers to obtain valid sample data. Point cloud data of a single tree often contains a large number of ground points, leading to a large data volume, cluttered view, and negatively impacting subsequent point cloud data classification and recognition. Therefore, these ground points need to be removed first, and RANSAC is a commonly used method for this purpose.

[0006] NeRF (Neural Radiance Field) is a computer vision technique used to generate high-quality 3D reconstruction models. It models the implicit radiance field (density and color) of a scene using a neural network (MLP). Its inputs are: multi-view 2D images and corresponding camera parameters; the rendering process is: sampling 3D points along the light rays, predicting the density and color of each 3D point through the neural network, and finally using volume rendering to integrate and generate pixel colors.

[0007] Dijkstra's algorithm, also known as Dijkstra's algorithm, is a typical shortest path algorithm used to calculate the shortest paths from a source node to all other target nodes. It generates a tree structure of shortest paths from the source node to all other reachable nodes. The shortest path tree is a set of shortest paths from the source node to all nodes, organized in a tree structure. This tree satisfies the following conditions: every path from the source node to any node is a shortest path, and each node has only one parent node in the tree (no cycles).

[0008] Skeleton curves are widely used in real-time simulation animation compositing, shape recognition, image segmentation, and 3D modeling. A skeleton curve typically consists of a set of interconnected line segments that connect key feature points of an object. Skeleton curves capture the basic shape structure and topological relationships of an object. In computer vision, skeleton curves are used to describe the feature contours of objects, thereby enabling object detection, recognition, and reconstruction.

[0009] Edge splitting is a commonly used technique in mesh processing, primarily used to split edges in a mesh. Specifically, it inserts a new vertex on an edge and splits the original triangle to form a new triangle, thereby increasing the complexity and detail of the mesh.

[0010] Fractal theory, proposed by mathematician B.B. Mandelbrot based on fractal geometry, studies the properties of fractals. Fractals originated from the problem of coastlines: the self-similarity of local and global coastlines. Therefore, Mandelbrot defined such shapes, where parts are similar to the whole in a certain way, as fractals. Because fractals are widespread in nature, fractal theory has found numerous applications in biology, urban studies, and other fields, such as organism growth, urban expansion, and digital image processing. Currently, there are mature methods for modeling tree growth using fractal methods, such as the "Fractal-Based Tree Growth Modeling Method" proposed by Zhang Chengxin, Hu Xiaofang, and others. This method addresses the complexity and challenges of tree growth modeling by using fractals to model the tree growth process. Based on the natural growth characteristics of tree branches and leaves, it simulates the leaf growth process, uses fractal algorithms to generate the main branches of the tree, and employs a Logistic model to simulate the tree's growth process. By changing parameters such as leaf size, tree depth, curvature, and tree size, an interactive dynamic growth model is achieved, which can realistically represent the tree growth process. Summary of the Invention

[0011] The purpose of this invention is to provide a fractal growth model and a refined tree modeling method that solves the above problems, enabling not only to achieve refined tree modeling, but also to learn lighting and color information in three-dimensional space, thereby generating highly realistic texture effects.

[0012] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a fractal growth model and a refined tree modeling method, comprising the following steps;

[0013] S1, acquire the original point cloud, image set, and ground height information h(x,y) of each spatial location of a single tree in the reconstruction area. The image set includes original images from multiple perspectives for NeRF reconstruction, and h(x,y) is the ground height of each spatial location in the area where the tree is located.

[0014] S2, data preprocessing and point cloud data segmentation;

[0015] Preprocess the original image and the original point cloud to obtain a two-dimensional image and a first point cloud;

[0016] Based on the RANSAC algorithm, the ground plane is fitted, and the first point cloud is segmented into ground point cloud and non-ground point cloud.

[0017] Based on the RANSAC algorithm, a cylinder is fitted, and the ground point cloud is divided into trunk point cloud and branch point cloud.

[0018] S3, extracts the tree skeleton from non-ground point cloud, including S31~S33;

[0019] S31. Construct an adjacency graph G=(V,E) of the non-terrestrial point cloud based on the Delaunay triangulation method, where V is the set of vertices and E is the set of edges. For two vertices p i and p j If there is an edge e between the two ij Then e ij The edge weight is w ij , In the formula, , p i and p j In the world coordinate system, the coordinates are Euclidean distances, where |∙|2 is the Euclidean distance.

[0020] S32, select a point close to the ground as the root node, use Dijkstra's algorithm to generate the shortest path tree for that root node, and use the set of nodes in the shortest path tree as the initial skeleton S. initial ;

[0021] S33, the initial skeleton S is generated using a cubic spline interpolation algorithm. initialThe smoothed skeleton curve Q'(t);

[0022] S4, the trees are reconstructed in layers, including S41~S44;

[0023] S41, based on ground height information constraints, Poisson reconstruction is used to model the tree trunk point cloud, generating a 3D mesh model M of the tree trunk. trunk ;

[0024] S42, preset density threshold, divide the points in the branch point cloud that are greater than the density threshold into main branch point cloud P1, and the rest into small branch point cloud P2.

[0025] S43, Reconstruct P1 using cylindrical fitting to generate a branched cylindrical model M. branch ;

[0026] S44, based on fractal theory, simulates the growth of fine branches in P2 to generate a fine branch model M. twig ;

[0027] S5, for M trunk M branch and M twig By merging the components, we obtain the tree model M. tree ;

[0028] S6, for tree model M tree Texture mapping is performed on each point to generate a comprehensive tree model. .

[0029] Preferably, in S2, preprocessing the original image involves transforming the original image to the world coordinate system;

[0030] The preprocessing of the original point cloud involves transforming the original point cloud into the world coordinate system, processing the point cloud data through a clustering algorithm to remove noise points, and obtaining the first point cloud.

[0031] Preferably, in S33, the initial skeleton S is generated. initial The smoothed skeleton curve Q'(t) is specifically as follows;

[0032] Sb1, from S initial Extract discrete point sets from;

[0033] Sb2, using the cubic spline function Q(t) to interpolate and smooth the discrete point set, yields the skeleton curve, where Q(t) = A⋅[t] 3 ,t 2 ,t 1 ,1] T ,t∈[0,1],A is the coefficient matrix, andt is the local normalization parameter;

[0034] Sb3, optimize the solution of the coefficient matrix A to make Q(t) approximate Sinitial The middle node marks the final skeleton curve as the smoothed skeleton curve Q'(t).

[0035] As a preferred option, in S4, the Poisson equation reconstructed from Poisson is... It is obtained from the following formula;

[0036] ,

[0037] In the formula, For volume field, ∇ 2 Let ∇ be the Laplace operator, and ∇ be the divergence operator. Let λ be the normal vector field of the non-ground point cloud, λ be the control coefficient of the terrain conformation intensity, and z be the height of each point within Q'(t).

[0038] As a preferred option, S43 reconstructs P1 using cylindrical fitting to generate a branched cylindrical model M. branch Specifically;

[0039] Sc1, based on a clustering algorithm, divides the main branch point cloud P1 into several sub-point clouds;

[0040] Sc2, for each sub-point cloud, a cylindrical model is generated using a weighted regularized cylindrical fitting method, wherein the objective function F of the weighted regularized cylindrical fitting method is obtained according to the following formula;

[0041] ,

[0042] In the formula, n is the total number of points in the sub-point cloud, and w i For the i-th point p in the dot cloud i The weights, dist(p) i Cylinder(θ) is a point p i The distance to the cylinder, γ is the regularization parameter, θ is the cylinder parameter, and θ is the distance to the cylinder. prior For the prior parameters of the branches, The square of the L2 norm;

[0043] Sc3, the set of cylindrical models of all sub-point clouds constitutes M. branch。

[0044] As a preferred option, S5 is for M. trunk M branch and M twig To integrate, specifically;

[0045] S51, splicing M trunk M branch and M twig And the seams were eliminated using a weighted average fusion method;

[0046] S52 uses an edge segmentation algorithm to segment the merged edges, thereby encrypting the mesh at the splicing point.

[0047] As a preferred option, S6, for the tree model M tree Texture mapping is performed on each point to generate a comprehensive tree model. Specifically;

[0048] M based on the lighting model tree Each point generates illumination intensity under different viewpoints, and the illumination intensity of point p under viewpoint v is L(v,p);

[0049] A NeRF model is pre-trained using an image set to generate M. tree The color of each point in the image is determined by different viewpoints. The color of point p at viewpoint v is C(r).

[0050] Generate texture information for each point from different viewpoints and map it to M. tree The composite tree model is obtained on the mesh surface containing that point. The texture information of point p under viewpoint v is T(v,p), T(v,p)=L(v,p)⋅C(r).

[0051] Compared with the prior art, the advantages of the present invention are as follows:

[0052] (1) Accurate skeleton extraction and tree modeling: Graph theory methods from deep learning are introduced as a key step in the skeleton extraction process to accurately extract tree skeletons from non-ground point clouds. A layered reconstruction method is adopted, first using Poisson reconstruction to model the trunk point cloud and generate a 3D mesh model M of the trunk. trunk Then, the point cloud P1 of the main branches is reconstructed using cylindrical fitting to generate the cylindrical branch model M. branch Then, based on fractal theory, a model M of the fine branches is generated from the point cloud P2. twig The three models are fused to obtain the tree model M. tree This method not only focuses on the accuracy of the trunk and branches, but also accurately processes the fractal growth of small branches, ensuring the natural transition and accurate modeling of the trunk, branches and small branches, and significantly improving the effect of tree modeling.

[0053] (2) Improve modeling accuracy and texture quality: The present invention introduces neural radiation field (NeRF) technology during texture mapping, which not only improves the texture quality of the tree surface, but also ensures the consistency of the lighting and natural transition of the texture. Therefore, it effectively improves the details and lighting effects of the tree model and can provide more realistic data support for forest area management.

[0054] (3) Efficient application and ecological assessment: Through refined tree modeling, the leaf area index (LAI) and biomass of trees can be calculated more accurately, and the green volume of forest areas can be estimated. These indicators have important application value in forestry management, ecological protection and climate change research.

[0055] In summary, this invention automatically completes segmented modeling of tree trunks and branches based on real-world collected laser point cloud and image data. It introduces terrain elevation constraints to improve the ground-hugging nature of the structure and combines multimodal fusion and texture mapping to reconstruct a high-precision, natural-looking 3D tree model. This significantly improves realism and automation, and solves the problems of lack of real-world accuracy, poor versatility, and low automation in traditional model splicing methods. It provides a new technical path for refined tree modeling and biomass assessment and is more suitable for tree modeling in forestry digital scenarios and complex natural environments. Attached Figure Description

[0056] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0057] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0058] Example 1: See Figure 1 A fractal growth model and a refined tree modeling method, comprising the following steps;

[0059] S1, acquire the original point cloud, image set, and ground height information h(x,y) of each spatial location of a single tree in the reconstruction area. The image set includes original images from multiple perspectives for NeRF reconstruction, and h(x,y) is the ground height of each spatial location in the area where the tree is located.

[0060] S2, data preprocessing and point cloud data segmentation;

[0061] Preprocess the original image and the original point cloud to obtain a two-dimensional image and a first point cloud;

[0062] Based on the RANSAC algorithm, the ground plane is fitted, and the first point cloud is segmented into ground point cloud and non-ground point cloud.

[0063] Based on the RANSAC algorithm, a cylinder is fitted, and the ground point cloud is divided into trunk point cloud and branch point cloud.

[0064] S3, extracts the tree skeleton from non-ground point cloud, including S31~S33;

[0065] S31. Construct an adjacency graph G=(V,E) of the non-terrestrial point cloud based on the Delaunay triangulation method, where V is the set of vertices and E is the set of edges. For two vertices p i and pj If there is an edge e between the two ij Then e ij The edge weight is w ij , In the formula, , p i and p j In the world coordinate system, the coordinates are Euclidean distances, where |∙|2 is the Euclidean distance.

[0066] S32, select a point close to the ground as the root node, use Dijkstra's algorithm to generate the shortest path tree for that root node, and use the set of nodes in the shortest path tree as the initial skeleton S. initial ;

[0067] S33, the initial skeleton S is generated using a cubic spline interpolation algorithm. initial The smoothed skeleton curve Q'(t);

[0068] S4, the trees are reconstructed in layers, including S41~S44;

[0069] S41, based on ground height information constraints, Poisson reconstruction is used to model the tree trunk point cloud, generating a 3D mesh model M of the tree trunk. trunk ;

[0070] S42, preset density threshold, divide the points in the branch point cloud that are greater than the density threshold into main branch point cloud P1, and the rest into small branch point cloud P2.

[0071] S43, Reconstruct P1 using cylindrical fitting to generate a branched cylindrical model M. branch ;

[0072] S44, based on fractal theory, simulates the growth of fine branches in P2 to generate a fine branch model M. twig ;

[0073] S5, for M trunk M branch and M twig By merging the components, we obtain the tree model M. tree ;

[0074] S6, for tree model M tree Texture mapping is performed on each point to generate a comprehensive tree model. .

[0075] Example 2: See Figure 1 More specifically, based on Example 1:

[0076] In S2, preprocessing the original image involves transforming it to the world coordinate system;

[0077] The preprocessing of the original point cloud involves transforming the original point cloud into the world coordinate system, processing the point cloud data through a clustering algorithm to remove noise points, and obtaining the first point cloud.

[0078] In S33, the initial skeleton S is generated. initial The smoothed skeleton curve Q'(t) is specifically as follows;

[0079] Sb1, from S initial Extract discrete point sets from;

[0080] Sb2, using the cubic spline function Q(t) to interpolate and smooth the discrete point set, yields the skeleton curve, where Q(t) = A⋅[t] 3 ,t 2 ,t 1 ,1] T ,t∈[0,1],A is the coefficient matrix, andt is the local normalization parameter;

[0081] Sb3, optimize the solution of the coefficient matrix A to make Q(t) approximate S initial The middle node marks the final skeleton curve as the smoothed skeleton curve Q'(t).

[0082] In S4, the Poisson equation reconstructed from Poisson. It is obtained from the following formula;

[0083] ,

[0084] In the formula, For volume field, ∇ 2 Let ∇ be the Laplace operator, and ∇ be the divergence operator. Let λ be the normal vector field of the non-ground point cloud, λ be the control coefficient of the terrain conformation intensity, and z be the height of each point within Q'(t).

[0085] S43 reconstructs P1 using cylindrical fitting, generating a branched cylindrical model M. branch Specifically;

[0086] Sc1, based on a clustering algorithm, divides the main branch point cloud P1 into several sub-point clouds;

[0087] Sc2, for each sub-point cloud, a cylindrical model is generated using a weighted regularized cylindrical fitting method, wherein the objective function F of the weighted regularized cylindrical fitting method is obtained according to the following formula;

[0088] ,

[0089] In the formula, n is the total number of points in the sub-point cloud, and w i For the i-th point p in the dot cloud i The weights, dist(p) iCylinder(θ) is a point p i The distance to the cylinder, γ is the regularization parameter, θ is the cylinder parameter, and θ is the distance to the cylinder. prior For the prior parameters of the branches, The square of the L2 norm;

[0090] Sc3, the set of cylindrical models of all sub-point clouds constitutes M. branch。

[0091] S5 vs M trunk M branch and M twig To integrate, specifically;

[0092] S51, splicing M trunk M branch and M twig And the seams were eliminated using a weighted average fusion method;

[0093] S52 uses an edge segmentation algorithm to segment the merged edges, thereby encrypting the mesh at the splicing point.

[0094] S6, for tree model M tree Texture mapping is performed on each point to generate a comprehensive tree model. Specifically;

[0095] M based on the lighting model tree Each point generates illumination intensity under different viewpoints, and the illumination intensity of point p under viewpoint v is L(v,p);

[0096] A NeRF model is pre-trained using an image set to generate M. tree The color of each point in the image is determined by different viewpoints. The color of point p at viewpoint v is C(r).

[0097] Generate texture information for each point from different viewpoints and map it to M. tree The composite tree model is obtained on the mesh surface containing that point. The texture information of point p under viewpoint v is T(v,p), T(v,p)=L(v,p)⋅C(r).

[0098] Example 3: See Figure 1 Based on Example 1, the specific operations for each step are given.

[0099] Regarding step S1: In 3D modeling of forestry landscapes, point cloud data and image data are the most common basic data sources. Point cloud data, namely the original point cloud described in this invention, can be represented as a 3D point set. , where each point p i It is a three-dimensional coordinate (x) i ,y i,z i The image data refers to the image set described in this invention. Since it is used for NeRF reconstruction, multiple original images from multiple perspectives are acquired using a UAV according to the NeRF method. Ground height information h(x,y) represents the ground height at each spatial location and is used for mapping trees to the terrain.

[0100] Regarding step S2: Both the original image and the original point cloud need to be transformed to a unified world coordinate system. Taking the original point cloud as an example, first transform each point p... i Through rigid transformation matrix This achieves the transformation from the laser scanning coordinate system to the world coordinate system, resulting in p. i The corresponding point in the world coordinate system , , This includes rotation and translation. The original images in the image set need to be registered with the point cloud data so that the points on the original images match the points in the point cloud at the corresponding locations.

[0101] Clustering algorithms: Clustering algorithms are commonly used to remove noise points from point cloud data. Examples include DBSCAN (Density-Based Spatial Clustering of Applications with Noise), RANSAC (Random Sample Consensus), region-growing-based clustering algorithms, and K-Means clustering. Clustering algorithms not only optimize spatial density but also consider the spatial distribution characteristics of the point cloud, such as directionality and shape. Ultimately, they identify and remove noise points from the point cloud data, resulting in the first point cloud.

[0102] Regarding step S3: The goal of this step is to extract the tree skeleton from the non-ground point cloud. Since the tree structure is hierarchical and branched, it is necessary to extract the trunk and main branches using graph theory and shortest path algorithms, and then smooth them. Therefore, this invention uses the Delaunay triangulation method to construct the adjacency graph of the non-ground point cloud, and uses Dijkstra's algorithm to generate the shortest path tree of the root node, obtaining the initial skeleton S. initial。

[0103] Considering the spatial structure and morphology of trees, and the connectivity between adjacent nodes, local smoothing is necessary to remove noise points and enhance the stability of the main framework. The smoothing process ensures the continuity of the framework by minimizing the distance between each point and its neighbors; therefore, this invention utilizes a cubic spline interpolation algorithm for optimization. This method starts from S... initialDiscrete point sets are extracted, and the discrete point sets are interpolated and smoothed using a cubic spline function Q(t) to generate a skeleton curve. The coefficient matrix A in Q(t) is then solved to make Q(t) approximate S as closely as possible. initial By eliminating the nodes and removing irregular discrete errors, a continuous and smooth Q'(t) can be obtained.

[0104] Regarding step S41: Tree trunk modeling is one of the most crucial steps in the terrain fusion process. At this stage, considering the influence of terrain, this invention improves the Poisson equation by combining the tree trunk model with the terrain, that is, based on the original Poisson equation... Based on this, the λ⋅(zh(x,y)) part is introduced, with a default value of 0.1, which can be adjusted according to the actual situation. The optimization goal of Poisson reconstruction is to make the tree trunk surface as smooth as possible while accurately conforming to the terrain data. By solving the Poisson equation, the surface of the tree trunk is optimized to better conform to the terrain. After reconstruction, a model is obtained, and then the moving cube algorithm is used to extract isosurfaces to generate a 3D mesh model M of the tree trunk. trunk The improved Poisson reconstruction in this invention is identical to the existing Poisson reconstruction methods, except for the equation.

[0105] Regarding step S42: The purpose is to divide the branch point cloud into two parts using a density threshold for subsequent reconstruction.

[0106] Regarding step S43: In tree branch modeling, a common method is cylindrical fitting. Weighted regularized cylindrical fitting is used to model the main branches, ensuring natural and smooth connections between branches and the trunk and other branches. Since a tree includes many main branches, the main branch point cloud P1 is also divided into multiple sub-point clouds, each subjected to cylindrical fitting, and then merged to form the branch cylindrical model M. branch When fitting a cylinder, P1 needs to be divided into multiple sub-point clouds using a clustering algorithm, such as the DBSCAN method, which is a spatial connectivity-based clustering algorithm.

[0107] Regarding step S44: Since the growth of twigs exhibits complex fractal characteristics, this invention simulates the natural growth of twigs based on fractal theory, and uses dynamic allometric rules to describe the growth of twigs during the growth process. In these rules, multiple twigs located at the same branching point are grouped into a cluster, where the diameter of the i-th twig is... With the irregular changes in tree growth:

[0108] ,

[0109] Where α(t) is a growth factor that varies with time t, used to simulate the morphological changes that trees undergo as they age, and r sw is the reference initial radius for branch growth. i Let w be the weight of the i-th twig, representing its relative importance at the current growth stage. j This represents the sum of the weights of a cluster of small branches. After simulating all the small branches, the Delaunay triangulation method is used to generate a triangular mesh model of the branches, resulting in the small branch model M. twig。

[0110] Regarding step S5: The purpose is to refine the previously obtained M... trunk M branch and M twig The models are then merged to generate a complete 3D tree model M. tree And ensure that the transitions between the parts are natural.

[0111] Regarding step S6: Borrowing the idea of ​​the NeRF model, a deep neural network is used to learn the lighting and color information in 3D space, thereby generating a highly realistic texture effect. According to the method of this invention, the lighting intensity L(v,p) of point p at viewpoint v is generated by the lighting model, and the color C(r) of point p at viewpoint v is generated by the NeRF model. Combining these two results in the texture information T(v,p) of point p at viewpoint v, which is then mapped to M. tree From This is a complete tree model that includes color and density information and has realistic texture effects.

[0112] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A fractal growth model and a refined tree modeling method, characterized in that, Includes the following steps; S1, acquire the original point cloud, image set, and ground height information h(x,y) of each spatial location of a single tree in the reconstruction area. The image set includes original images from multiple perspectives for NeRF reconstruction, and h(x,y) is the ground height of each spatial location in the area where the tree is located. S2, data preprocessing and point cloud data segmentation; Preprocess the original image and the original point cloud to obtain a two-dimensional image and a first point cloud; Based on the RANSAC algorithm, the ground plane is fitted, and the first point cloud is segmented into ground point cloud and non-ground point cloud. Based on the RANSAC algorithm, a cylinder is fitted, and the ground point cloud is divided into trunk point cloud and branch point cloud. S3, extracts the tree skeleton from non-ground point cloud, including S31~S33; S31. Construct an adjacency graph G=(V,E) of the non-terrestrial point cloud based on the Delaunay triangulation method, where V is the set of vertices and E is the set of edges. For two vertices p i and p j If there is an edge e between the two ij Then e ij The edge weight is w ij , In the formula, , p i and p j In the world coordinate system, the coordinates are Euclidean distances, where |∙|2 is the Euclidean distance. S32, select a point close to the ground as the root node, use Dijkstra's algorithm to generate the shortest path tree for that root node, and use the set of nodes in the shortest path tree as the initial skeleton S. initial ; S33, the initial skeleton S is generated using a cubic spline interpolation algorithm. initial The smoothed skeleton curve Q'(t); S4, the trees are reconstructed in layers, including S41~S44; S41, based on ground height information constraints, Poisson reconstruction is used to model the tree trunk point cloud, generating a 3D mesh model M of the tree trunk. trunk The Poisson equation reconstructed from Poisson It is obtained from the following formula; ， In the formula, For volume field, ∇ 2 Let ∇ be the Laplace operator, and ∇ be the divergence operator. λ is the normal vector field of the non-ground point cloud, λ is the control coefficient of the terrain fitting intensity, and z is the height of each point in Q'(t); S42, preset density threshold, divide the points in the branch point cloud that are greater than the density threshold into main branch point cloud P1, and the rest into small branch point cloud P2. S43, Reconstruct P1 using cylindrical fitting to generate a branched cylindrical model M. branch ; S44, based on fractal theory, simulates the growth of fine branches in P2 to generate a fine branch model M. twig ; S5, for M trunk M branch and M twig By merging the components, we obtain the tree model M. tree ; S6, for tree model M tree Texture mapping is performed on each point to generate a comprehensive tree model. ; The growth of S44 is described using dynamic allometric rules. In these rules, multiple twigs located at the same branching point are grouped into a cluster, where the diameter of the i-th twig is... With the irregular changes in tree growth: ， Where α(t) is a growth factor that varies with time t, used to simulate the morphological changes that trees undergo as they age, and r s w is the reference initial radius for branch growth. i Let w be the weight of the i-th twig, representing its relative importance at the current growth stage. j The sum of the weights of a cluster of small branches; after simulating all the small branches, the Delaunay triangulation method is used to generate a triangular mesh model of the branches, resulting in the small branch model M. twig .

2. The fractal growth model and refined tree modeling method according to claim 1, characterized in that, In S2, preprocessing the original image involves transforming it to the world coordinate system; The preprocessing of the original point cloud involves transforming the original point cloud into the world coordinate system, processing the point cloud data through a clustering algorithm to remove noise points, and obtaining the first point cloud.

3. The fractal growth model and refined tree modeling method according to claim 1, characterized in that, In S33, the initial skeleton S is generated. initial The smoothed skeleton curve Q'(t) is specifically as follows; Sb1, from S initial Extract discrete point sets from; Sb2, using the cubic spline function Q(t) to interpolate and smooth the discrete point set, yields the skeleton curve, where Q(t) = A⋅[t] 3 ,t 2 ,t 1 ,1] T ,t∈[0,1],A is the coefficient matrix, andt is the local normalization parameter; Sb3, optimize the solution of the coefficient matrix A to make Q(t) approximate S initial The middle node marks the final skeleton curve as the smoothed skeleton curve Q'(t).

4. The fractal growth model and refined tree modeling method according to claim 1, characterized in that, S43 reconstructs P1 using cylindrical fitting, generating a branched cylindrical model M. branch Specifically; Sc1, based on a clustering algorithm, divides the main branch point cloud P1 into several sub-point clouds; Sc2, for each sub-point cloud, a cylindrical model is generated using a weighted regularized cylindrical fitting method, wherein the objective function F of the weighted regularized cylindrical fitting method is obtained according to the following formula; ， In the formula, n is the total number of points in the sub-point cloud, and w i For the i-th point p in the dot cloud i The weights, dist(p) i Cylinder(θ) is a point p i The distance to the cylinder, γ is the regularization parameter, θ is the cylinder parameter, and θ is the distance to the cylinder. prior For the prior parameters of the branches, The square of the L2 norm; Sc3, the set of cylindrical models of all sub-point clouds constitutes M. branch .

5. The fractal growth model and refined tree modeling method according to claim 1, characterized in that, S5 vs M trunk M branch and M twig To integrate, specifically; S51, splicing M trunk M branch and M twig And the seams were eliminated using a weighted average fusion method; S52 uses an edge segmentation algorithm to segment the merged edges, thereby encrypting the mesh at the splicing point.

6. The fractal growth model and refined tree modeling method according to claim 1, characterized in that, S6, for tree model M tree Texture mapping is performed on each point to generate a comprehensive tree model. Specifically; M based on the lighting model tree Each point generates illumination intensity under different viewpoints, and the illumination intensity of point p under viewpoint v is L(v,p); A NeRF model is pre-trained using an image set to generate M. tree The color of each point in the image is determined by different viewpoints. The color of point p at viewpoint v is C(r). Generate texture information for each point from different viewpoints and map it to M. tree The composite tree model is obtained on the mesh surface containing that point. The texture information of point p under viewpoint v is T(v,p), T(v,p)=L(v,p)⋅C(r).

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