Droplet model driven entropy optimization individual wood skeletonization method

Abstract

The invention discloses an entropy optimization individual tree skeletonization method driven by a water drop model, and belongs to the technical field of forest three-dimensional reconstruction and laser point cloud processing. According to the method, single-tree point cloud is regarded as a water drop model with mass difference, contraction, merging and evaporation are carried out under the action of attractive force, repulsive force and equivalent surface tension, and a preliminary framework with local details reserved is generated; a skeleton entropy is defined based on water drop evolution geometric feature distribution, and entropy reduction optimization is utilized to enable a water drop model to converge from disorder to a low-entropy ordered skeleton. And iteratively minimizing the residual sum of squares of the point cloud and the skeleton edge, and reconstructing the topology, so that the skeleton point is more centered, and the topology is more reasonable. According to the method, skeleton points and topological edges can be output at the same time, and a reliable basis is provided for accurate individual tree modeling, biomass estimation and forestry application.

Description

Technical Field

[0001] This invention relates to the field of forest 3D reconstruction and laser point cloud processing technology, and in particular to an entropy optimization method for single-tree skeletonization driven by a water droplet model. Background Technology

[0002] The purpose of tree skeletonization is to simplify complex 3D tree point clouds into a low-dimensional, structured representation, generating a simplified topological structure to represent the tree trunk, branches, and their relationships. Tree skeletonization is a fundamental task in forestry remote sensing, and the obtained skeleton provides basic input for downstream applications such as 3D tree modeling, volume and biomass estimation, trunk and crown segmentation, and forest phenotypic parameter analysis. Methods for obtaining such high-quality skeletons rely on the large amounts of high-density point clouds acquired by Terrestrial Laser Scanning (TLS) technology and robust tree skeletonization algorithms for TLS point clouds. However, due to the inherent properties of TLS data and the inherent accuracy and robustness issues of tree skeletonization methods, the skeletonization results have significant problems in terms of detail fidelity, topological rationality, and centering.

[0003] The main challenge in preserving detail fidelity in individual tree skeletonization is retaining the details of local branches during the process. Due to the complexity of forest site conditions, the acquired individual tree TLS point clouds not only contain a large amount of noise and outliers, but also exhibit density heterogeneity in the canopy region far from the TLS device, where the point cloud is sparse. Furthermore, the complexity of forest scenes and the extension of branches within individual tree canopies, with trees often intertwined and entangled, leads to occlusion or self-occlusion between branches, resulting in missing point cloud data. Classic graph topology optimization methods such as AdTree typically use smoothing and pruning as post-processing to improve the fidelity of the geometric representation of individual tree skeletons. However, this also makes the skeletonization results heavily reliant on rule-based prior constraints (branch length or angle thresholds, etc.). Uniform prior constraints cannot be applied to point clouds with varying densities and noise. Inappropriate threshold settings can incorrectly remove local details such as treetops and twigs. Conversely, insufficient optimization of individual tree skeletons, or lenient post-processing constraints, can lead to "undersimplification" of the individual tree point cloud, resulting in a skeleton containing numerous redundant branch points. Local feature optimization algorithms struggle to balance optimization intensity. In treetop regions with low point cloud density or high density heterogeneity, improper optimization often overlooks fine branch structures. In areas with density variations due to missing data and at tree branching points with complex topologies, over-optimization frequently leads to skeleton breakage, compromising its integrity. Furthermore, recently emerging deep feature representation (DL) methods, which extract point cloud features in blocks, cannot capture fine features in sparse, high-density, heterogeneous point clouds, resulting in skeletons that fail to preserve local details.

[0004] The main challenge in ensuring the rationality of individual tree topologies lies in constructing a skeleton topology that conforms to the growth pattern of individual trees. Graph topology optimization methods rely on path traversal on the neighborhood graph constructed from the point cloud. This strategy is prone to generating topological shortcuts or redundant loops that do not conform to the tree growth pattern in areas with branch intersections, noise, or density variations. Subsequent pruning algorithms used to break these erroneous connections may then incorrectly remove true branches from sparse areas of the point cloud, compromising topological integrity. Local feature optimization methods, such as L1-medial, construct topologies in a fragmented manner, first extracting a discrete skeleton point set before attempting to reconstruct the topology. In areas with missing data, uneven density, or noise interference, the quality of the extracted skeleton point set deteriorates or erroneous skeleton points are generated, easily leading to topological breaks or the establishment of false topological branches. While deep learning methods are better at learning the geometric features of individual trees, their skeleton point extraction process is also affected by density heterogeneity. Ultimately, they still rely on traditional graph theory algorithms as a post-processing step to construct the individual tree topology, inheriting the inherent defects of the fragmented construction strategy.

[0005] Regarding the centering of individual tree skeletons, true centering is required. Ideally, the individual tree skeleton should be located at the center of the surrounding point cloud, which can be interpreted as the distance from the surrounding point cloud to the skeleton should be consistent (i.e., the sum of squared residuals should be minimized). This consistency can reduce biases caused by noise, occlusion, or uneven point cloud density, thus better capturing the tree's geometry and branching patterns when dealing with complex branching regions. However, existing methods generally do not adopt this optimization criterion. Graph topology optimization methods focus on the rationality of the skeleton topology, lacking optimization for skeleton centering. Local feature optimization methods rely on a geometrically based definition of centering. For example, centroid-based methods such as WoodSKE are highly sensitive to noise and uneven distribution of point clouds, causing the skeleton results to fail to align the branch centers in noisy and missing point clouds. Although L1-medial-based methods are more robust to noisy and unevenly distributed point clouds, they still cannot align the branch centers in cases of missing point clouds. Furthermore, the above methods define the center based on geometry, rather than minimizing the sum of squared residuals, and therefore cannot strictly align the branch centers. The deep learning method implicitly learns the centering criterion from biased truth values ​​and prior knowledge, and the skeleton result also cannot be aligned with the strict branch center. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide an entropy-optimized single-wood skeletonization method driven by a water droplet model. Through entropy-controlled iterative optimization, adaptive evolution of the water droplet model, and a skeleton geometry-topology collaborative enhancement mechanism, the method achieves accurate centering of the skeleton, preservation of details, topological stability, and overall compactness.

[0007] Technical solution: A water droplet model-driven entropy optimization method for single-wood skeletonization, comprising the following steps: S1, regard the single-tree TLS point cloud as a water droplet model with different masses in 3D space, and realize the shrinkage of the water droplet by balancing the forces of the water droplet model; S2, during the process of water droplet shrinkage, merges with water droplets in the vicinity of the space, initially forming a skeletal structure that retains local details; S3 iteratively evaporates water droplets with small mass that deviate from the optimal path of a single tree, removing erroneous or redundant small branches generated during the shrinkage and merging stages; S4 introduces skeleton entropy as a global constraint. By calculating the entropy value of the geometric feature distribution of water droplets during the skeletonization process, iterative entropy reduction optimization is performed on shrinkage, merging and evaporation, so that the water droplets converge from a scattered and "disordered" distribution to a stable and "ordered" state. S5, through a process that combines geometry and topology optimization, enhances the centrality and topological consistency of the skeleton, ultimately constructing a single-tree topology that conforms to the tree growth pattern.

[0008] Furthermore, the steps to achieve the shrinkage of water droplets include: S11, calculate the surface tension of a single water droplet; The sum of the attractive and repulsive forces acting on a single water droplet is defined as the equivalent surface tension of that single water droplet. This is used to drive the contraction, merging, and evaporation of water droplets, and its expression is as follows: , in, Represented as water droplets The attraction, Represents water droplets The repulsive force experienced; attraction To minimize the sum of Euclidean distances between water droplets, the expression is as follows: , in, Indicates the attractiveness weight. Represents the Euclidean distance between vectors. These are water droplets that need optimization. yes The neighboring water droplets; N(i) is the water droplets in the neighborhood; Centered on, within radius The collection of all neighboring water droplets within the affected area; Each water droplet initially The radius is half the diagonal distance of the bounding box of the water droplet found by searching with the square root of the Euclidean distance between it and its nearest water droplet. express quality, initial , and These are the maximum and minimum values ​​of the number of water droplets in the corresponding neighborhood of all water droplets. yes The number of water droplets in the neighborhood; It is an adjustable parameter used to control the mass; The expression for the Huber loss function is as follows: , in, For the threshold, Represents water droplets and L2 distance between them; when When, it indicates It is not a noisy water droplet; it uses a secondary method to enhance the noise level. The attraction; when At that time, the influence of noise water droplets is limited using an L1 linear form; threshold Calculated using the absolute deviation of the median: , Where median represents the median; Represents the neighborhood centroid. express To the neighboring centroid Euclidean distance; The repulsive force is defined by minimizing the sum of squared residuals. The calculation formula is as follows: , , , in, As the weight of the repulsive force, The weighted average distance; Indicates from the neighborhood centroid To neighboring water droplets The quality-weighted average distance; S12, calculates the global surface tension of water droplets; Based on the attractive and repulsive forces of individual water droplets, it will contain The surface tension of a single water droplet's TLS point cloud is defined as the sum of the surface tensions of all water droplets, as expressed below: , in, This represents the sum of the surface tensions of all water droplets; By minimizing the surface tension of a single-tree TLS point cloud, the surface tension effect of a real-world water droplet system is simulated, driving the single-tree TLS point cloud to shrink from the outer layer towards the center of the branch.

[0009] Furthermore, in step S2, water droplets in spatial proximity and The conditions for merging are as follows: , , in, yes and The Euclidean distance between them for physical radius, for physical radius, It is a scaling factor that scales Euclidean distance and physical radius to the same scale.

[0010] Furthermore, in step S3, based on the optimal path for a single tree and the properties of the water droplets themselves, water droplets with small evaporation mass, insignificant geometric features, or far from the optimal path are selected. The extraction of the optimal path for a single tree includes the following steps: S311, confirm the single-tree reference point; select in the single-tree TLS point cloud. The point with the lowest value, and within the height range [ , Filter candidate points within [+h]; project candidate points onto [h]. The plane is then fitted with a center point by minimizing the sum of squared residuals. , ), and with the corresponding Combining to obtain ( , , ) as the root point; S312, construct an undirected graph of a single tree and generate paths; based on the fact that the nutrient transport process of a tree follows the optimal path allocation law from the root to each branch, in each water droplet... A local Delaunay partition is constructed on the nearest neighbors, and combined with the edges of the global Delaunay partition to form the final connected undirected graph; the weight of the edge in the undirected graph is defined as: , in, water droplets and The average planar features, water droplets and The average dispersion characteristics, water droplets and The average linear characteristics, water droplets and The average mass; , , , These are the corresponding weighting coefficients; water droplets and The Euclidean distance between them; To adjust the parameters and control the influence of geometric features in the exponential term on the total weight; S313, Select the optimal path for a single tree; based on the spatial competition concept, iteratively select the optimal path from the single tree paths; for each water droplet, obtain its path to the root point and calculate its relative path length. : , in, This is the path from the current water droplet to the treetop. This is the path length from the current water droplet to the root of the tree; Then based on the relative path length Sort, smaller This indicates that the water droplets are closer to the treetops and have a longer path, thus having a higher priority. Subsequently, a greedy strategy was used to iteratively select... The smallest water droplet has the corresponding optimal path, and this smallest water droplet is marked as a skeleton point, while other water droplets in the neighborhood are marked as non-skeleton points; this process is repeated until all water droplets are classified. Finally, all optimal paths are combined with skeleton points to obtain the final optimal path for a single tree and its corresponding skeleton points.

[0011] Furthermore, in step S4, a normalized skeleton entropy reduction process is used to constrain the intensity of water droplet shrinkage, merging, and evaporation, thereby gradually transforming a disordered and scattered single-tree TLS point cloud into an ordered single-tree skeleton. The specific process is as follows: First, the initial skeleton entropy is calculated based on the geometric features of the discrete water droplets; Subsequently, the skeletal entropy is recalculated after each iteration of water droplet shrinkage, merging, and evaporation; when the entropy value decreases to a steady state or reaches the maximum number of iterations, it indicates linearity. planar features With scattered characteristics If the distribution has stabilized, stop iterating; otherwise, continue optimizing.

[0012] Furthermore, in step S5, the steps of the geometry and topology intertwining optimization process are as follows; S51, assign the single-tree TLS point cloud to the nearest neighbor edge of the preliminary skeleton generated by the normalized skeleton entropy constraint for geometric optimization; subsequently, during the iterative optimization process, fine-tune the two endpoints of the skeleton edge using the following optimization equation: , in, and These represent the optimized skeleton edge endpoints; , The endpoints before optimization; For the TLS point cloud of a single tree within the neighborhood; This represents the distance from a point to an edge; This represents the average distance from neighboring points to the skeleton edges; S52, after completing a single iteration, uses the DMST algorithm to correct the skeleton topology on the optimized skeleton points to obtain a refined skeleton topology; S53, the obtained refined skeleton topology is used as the input for the geometric optimization stage of the next iteration. The single-tree TLS point cloud is reassigned to the nearest skeleton edge, and then the second geometric optimization is performed. After the geometric optimization is completed, the DMST algorithm is applied again to refine the single-tree skeleton topology. Steps S51 and S52 are performed alternately until the cumulative change of the skeleton edge position drops below the predefined threshold or the maximum number of iterations is reached.

[0013] Furthermore, in step S51, when fine-tuning the two endpoints of the skeleton edge, the following constraints must be satisfied: Geometric length constraints: Ensure that the skeleton edges maintain their original length; Directional constraints: Limit the angle between the old and new sides to no more than a threshold. , where "·" represents the dot product between vectors; Neighborhood range constraint: and This ensures that the optimized endpoints remain within the single-tree point cloud, guaranteeing that the skeleton is anchored within the single-tree point cloud; among which, and These are the centroid of the neighboring TLS point cloud and the radius of the boundary sphere, respectively.

[0014] Furthermore, to ensure the smoothness and convergence stability of the optimization process, a step rate is introduced. Control the geometry and topology optimization process; after obtaining the theoretical target result through the following formula, update the skeleton result: , in, ∈ [0, 1], Indicates the endpoint after a single iteration update; For endpoints located in multiple neighborhoods, the average of the optimization results of each neighborhood is taken as the update value; within a single iteration, relying on... Iterate over all skeleton edges Second-rate.

[0015] Compared with the prior art, the significant advantages of this invention are as follows: 1. This invention proposes a water droplet model to guide the single-tree skeletonization process: the discrete TLS point cloud of a single tree is regarded as a water droplet model with varying masses in space, which evolves under the equivalent surface tension defined by attraction, repulsion, and their resultant force. The surface tension between water droplets is defined by minimizing the Huber loss and the sum of squared residuals. Minimizing the surface tension drives the water droplet contraction, and the radius of the water droplet is dynamically solved according to its mass, achieving adaptive merging with spatially adjacent water droplets and eliminating redundant water droplets. In addition, based on the geometric relationship between the water droplet's own properties and the optimal path of the single tree, outlier water droplets that deviate from the optimal path are evaporated, ultimately generating a preliminary single-tree skeleton that retains local branch details; 2. This invention proposes an adaptive skeleton generation framework with entropy control: The entire skeletonization process is designed as an entropy reduction optimization process. By calculating the distribution of linear, planar, and scattered features of all water droplets during shrinkage, merging, and evaporation, the orderliness of the entropy reduction optimization process is quantified, enabling adaptive control of the "shrinkage-merging-evaporation" process of the water droplet model. This iterative skeletonization framework guides the single-tree point cloud from a high-entropy disordered state to a low-entropy compact single-tree skeleton. 3. This invention proposes a geometric and topological interleaving optimization strategy to center a single-tree skeleton: This strategy corrects the skeleton by alternately performing geometric and topological optimizations. In geometric optimization, skeleton points are updated by minimizing the sum of squared residuals between the single-tree TLS point cloud and the nearest skeleton edge. In topological optimization, the optimal connection relationship on the skeleton points is reconstructed using the minimum spanning tree. In interleaving optimization, the single-tree skeleton refined by topological optimization is used as input for geometric optimization, and geometric and topological optimizations are performed again. The interleaving between skeleton points and skeleton lines is enhanced, generating skeleton points with stronger centering and a more reasonable skeleton topology through mutual iterative optimization. Attached Figure Description

[0016] Figure 1 This is a rough flowchart of the present invention; Figure 2 This is a detailed flowchart of a tree as an example in this embodiment, where (a) is a water droplet model with different masses, (b) is the shrinkage of water droplets, (c) is the merging of spatially adjacent water droplets, (d) is the iterative evaporation of water droplets, (e) is the convergence to a stable "ordered" state, and (f) is the optimization process of geometric and topological interweaving. Figure 3 This is a schematic diagram of the shrinking, merging, and evaporation of water droplets in nature. (a)-(c) and (e) show the process of water droplet shrinking, while (d) and (f) show the process of water droplet merging. Figure 4This diagram illustrates the attraction, repulsion, and resultant force between the water droplet to be optimized and its neighboring water droplets. (a) shows the attraction force with only neighboring water droplets, (b) shows the repulsion force with only neighboring water droplets, and (c) shows the attraction and repulsion forces (resultant force) with neighboring water droplets. Water droplets 1, 2, 3, and 4 are far from the water droplet to be optimized, and their repulsion and attraction forces are in the same direction, both directed from the water droplet to be optimized towards them. The resultant force is in the same direction as the attraction force. Water droplets 5, 6, and 7 have repulsion and attraction forces in opposite directions, but because they are close to the water droplet to be optimized, their repulsion forces are greater than their attraction forces, so the resultant force is directed towards the repulsion force. Figure 5 This is a schematic diagram of evaporation. The water droplets to be evaporated are circled in blue, red dots represent individual tree skeleton points, black dots represent the results of water droplet shrinkage and merging, and blue topological connecting lines represent the optimal path for individual trees. (a) indicates that the water droplet is far from the optimal path and has a small mass; (b) indicates that the water droplet has a large mass and linear characteristics, but small random and planar characteristics, and is far from the optimal path; (c) indicates that the water droplet has a large mass, large random and planar characteristics, but small linear characteristics, and is far from the optimal path. Figure 6 This is a flowchart of water droplet evaporation; where red dots are skeleton points, black dots are the results of water droplet shrinkage and merging, and green lines represent the connection edges between the TLS point cloud and the nearest optimal path of a single tree; (a) is the result of water droplet shrinkage and merging, (b) is the optimal path of a single tree, (c) is the index relationship between the result of water droplet shrinkage and merging and the optimal path of a single tree, and (d) is the result of water droplet evaporation; Figure 7 This is a graph of tree growth and spatial competition, where black dots represent the results of water droplet shrinkage and merging, and red dots represent skeleton points; (a) is the result of water droplet shrinkage and merging, (b) is an undirected graph, with green representing edges in the undirected graph; (c) is a single tree path, with green lines representing connections; (d) is the optimal single tree path, with blue lines representing connections. Figure 8 This is a schematic diagram of tree growth and spatial competition. In it, (a) is an undirected graph at the bottom of the tree, with green representing connecting edges; (b) is the path at the bottom of the tree and the optimal path; (c) is an enlarged subgraph of the optimal path at the bottom of the tree; (d) is an undirected graph at the branch point; (e) is the path at the branch point and the optimal path; and (f) is an enlarged subgraph of the optimal path at the branch point. Figure 9 This is a flowchart of entropy reduction optimization; Figure 10 This is a flowchart of the optimization process involving geometry and topology; where (a) is the unoptimized single-tree skeleton, (b) is the nearest neighbor index result of the single-tree skeleton and the TLS point cloud, and the green line indicates the correspondence; (c) is the optimization result of a single iteration, and (d) is the final single-tree skeleton. The enlarged sub-graph overlays the single-tree point cloud and the unoptimized skeleton. Figure 11 These are the skeleton results of 24 individual trees using different methods in the test dataset used in this invention. (a) is the TLS single tree point cloud, (b) is AdTree, (c) is WoodSKE, (d) is LBC, (e) is L1-medial, (f) is Dijkstra-enhanced L1-medial, (g) is the WDTS of this invention (only skeleton points), and (h) is the WDTS of this invention (including skeleton points and topology) (a total of 8 individual trees). Figure 12 These are the skeleton results of 24 individual trees using different methods in the test dataset used in this invention. (a) is the TLS single tree point cloud, (b) is AdTree, (c) is WoodSKE, (d) is LBC, (e) is L1-medial, (f) is Dijkstra-enhanced L1-medial, (g) is the WDTS of this invention (only skeleton points), and (h) is the WDTS of this invention (including skeleton points and topology) (a total of 8 individual trees). Figure 13 These are the skeleton results of 24 individual trees using different methods in the test dataset used in this invention. (a) is the TLS single tree point cloud, (b) is AdTree, (c) is WoodSKE, (d) is LBC, (e) is L1-medial, (f) is Dijkstra-enhanced L1-medial, (g) is the WDTS of this invention (only skeleton points), and (h) is the WDTS of this invention (including skeleton points and topology) (a total of 8 individual trees). Figure 14 These are enlarged detail images of the skeletonization methods of different methods of Tree_1 in the test dataset used in this invention. (a) is AdTree, (b) is WoodSKE, (c) is LBC, (d) is L1-medial, (e) is Dijkstra-enhanced L1-medial, and (f) is WDTS of this invention. Detailed Implementation

[0017] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0018] like Figure 1 The diagram shown is the overall flowchart of the water droplet model-driven entropy optimization single-wood skeletonization method (WDTS) of this invention. The specific implementation process is as follows: Figure 2 As shown, this invention treats the single-tree TLS point cloud as a model of water droplets of varying masses in 3D space, such as... Figure 2As shown in (a) of the diagram. The shrinkage of the water droplet is achieved through force balance in the water droplet model. Figure 2 (b)). During the process of water droplet contraction, adjacent water droplets in space merge ( Figure 2 In (c) of the diagram, a preliminary skeletal structure retaining local details is formed. Water droplets with small mass and deviating from the optimal path of a single tree are iteratively evaporated, such as... Figure 2 As shown in (d), erroneous or redundant small branches generated during the shrinkage and merging stages are removed. Specifically, a weighted undirected graph is constructed on the results of water droplet shrinkage and merging. Based on the ideas of tree growth and spatial competition, the optimal path of a single tree is extracted from the undirected graph, and the water droplets are iteratively evaporated according to the geometric relationship between the water droplet attributes and the optimal path of a single tree, thereby simplifying the skeleton structure. Furthermore, skeleton entropy is introduced as a global constraint. By calculating the entropy value of the geometric feature distribution of water droplets during the skeletonization process, iterative entropy reduction optimization is performed on shrinkage, merging, and evaporation. Figure 2 (b)- Figure 2 (d) in the middle, so that it converges from a scattered "disordered" distribution to a stable "ordered" state. Figure 2 (e)). Finally, a geometry and topology interleaving optimization process was designed (corresponding to...). Figure 2 (f) further improves the centering and topological rationality of the single-tree skeleton. This geometric and topological intertwined optimization process first minimizes the single-tree TLS point cloud (f) Figure 2 (a) in the middle to the nearest skeleton edge ( Figure 2 The residual sum of squares in (e) is used, and then the skeleton topology is fine-tuned using DMST (Minimum Distance Spanning Tree). The point and topology are iteratively interleaved to optimize the centering of the skeleton points and the rationality of the topology. The specific implementation steps are as follows: Step 1 involves creating water droplet models of varying masses and then achieving droplet shrinkage through force balance within these models. Discrete water droplet systems in nature tend to spontaneously evolve by minimizing their surface tension until they reach an energy-stable state, preserving local details, such as... Figure 3 As shown. During evolution, water droplets shrink along the direction that minimizes local surface tension until a dynamic equilibrium is reached (e.g., ...). Figure 3 (a)-(c) and (e)). Secondly, during the contraction process, when the radii of the water droplets overlap, they merge to form larger new water droplets (such as...). Figure 3 (d) and (f) in the text). Meanwhile, during this process, smaller, isolated water droplets are removed by the system due to energy dissipation (e.g., ...). Figure 3 Treatment of small and medium-sized water droplets).

[0019] Step 11, calculate the surface tension of a single water droplet; Drawing inspiration from the shrinking, merging, and evaporation phenomena of water droplet systems in nature, this invention views the single-tree TLS point cloud as a series of discrete water droplet models with varying masses attached to the tree's topology. By simulating its dynamic evolution process, the single-tree skeleton, preserving local details, is accurately extracted. Assuming that each point in the single-tree TLS point cloud is a discrete water droplet model with equal physical density, an attractive force is first defined to simulate the water droplet shrinkage phenomenon, such as... Figure 4 As shown in (a) above. If only attractive forces exist, each water droplet will move toward the water droplet with the largest mass in its neighborhood until they merge. To prevent global collapse of the water droplets, a repulsive force exerted by neighboring water droplets is defined, such as... Figure 4 As shown in (b) above. If only repulsive force exists, the water droplet will be pushed far away. Finally, the attractive and repulsive forces combine to form a resultant force, as shown in (b). Figure 4 As shown in (c) in the diagram.

[0020] The sum of the attractive and repulsive forces acting on a single water droplet is defined as its equivalent surface tension. The expression for driving water droplet contraction, merging, and evaporation is as follows:

[0021] in, Represented as water droplets The attraction, and Represents water droplets The repulsive force experienced.

[0022] The attraction is designed to minimize the sum of the Euclidean distances between the water droplets, in order to help push the water droplet system to a lower energy state, as shown below:

[0023] in, Indicates the attractiveness weight. Represents the Euclidean distance between vectors. These are water droplets that need optimization. yes The neighboring water droplets; N(i) is the water droplets in the neighborhood; Centered on, within radius The collection of all neighboring water droplets within the affected area.

[0024] Each water droplet initially The radius is half the diagonal distance of the bounding box of the water droplet found by searching with the square root of the Euclidean distance between it and its nearest neighboring water droplet. express quality, initial , and These are the maximum and minimum values ​​of the number of water droplets in the corresponding neighborhood of all water droplets. yes The number of water droplets in the neighborhood, It is an adjustable parameter used to control the mass. This invention introduces the reciprocal of the mass of a neighboring water droplet. Weighting by attraction makes water droplets with larger masses more attractive to each other. Smaller water droplets have weaker attractive forces and stronger repulsive forces. Therefore, in a state of force equilibrium, smaller water droplets have stronger attractive forces and weaker repulsive forces. It will tend to move towards the neighborhood center.

[0025] In addition, the Huber loss function is introduced into the attraction factor to control its magnitude. This function combines L2 (Euclidean) and L1 (Manhattan) distances, effectively suppressing extreme attractive forces. When the Huber loss value is too large, it indicates that the distance between water droplets is relatively large, resulting in a strong attractive force and a weak repulsive force; the net force manifests as an attractive force. Conversely, a small Huber loss value indicates a weak attractive force and a strong repulsive force. Therefore, in force equilibrium, the water droplets... It will be located at the center of the neighborhood. The specific form of Huber loss is as follows:

[0026] in, The threshold value is used. Time (i.e., water droplets) and (The L2 distance between them is less than the threshold), indicating that It is not a noisy water droplet; it uses a secondary method to enhance the noise level. The attraction. The influence of noise droplets is limited using a linear approach. Threshold Calculated using the absolute deviation of the median:

[0027] Where median represents the median; Represents the neighborhood centroid. express To the neighboring centroid Euclidean distance.

[0028] To further adapt the attraction to different local scales and neighborhood densities, this invention uses an attraction scaling factor. Normalize it. Defined as neighborhood centroid With neighboring water droplets The sum of the total attraction between them can be scaled using an attraction scaling factor. Its appeal makes It should become a relative metric that is robust to changes in the neighborhood scale.

[0029] Unlike attraction, repulsion forces repel neighboring water droplets. With the current water droplets Separation is achieved to prevent global collapse under the influence of attraction. This invention defines the repulsive force by minimizing the sum of squared residuals, calculated as follows:

[0030] in, As the weight of the repulsive force, It is a weighted average distance. The repulsive force is based on... and The distance between and The direction is adaptively adjusted based on the difference. If the distance is less than... ,illustrate Too close, need to move away , direction from point to , making When the forces are in equilibrium, they naturally move to the center of the neighborhood.

[0031] Similar to attraction, repulsion Scaling factor based on repulsive force Normalization is applied to ensure it adapts to the local neighborhood scale. This repulsive scaling factor represents the basic weighted sum of the squared residuals in the neighborhood. Wherein, Indicates from the neighborhood centroid To neighboring water droplets Quality-weighted average distance (i.e.) ).

[0032] Step 12, calculate the global surface tension of the water droplets; Based on the attractive and repulsive forces of individual water droplets, it will contain The surface tension of a single-water droplet TLS point cloud is defined as the sum of the surface tensions of all water droplets. This approach transforms the complex skeleton extraction problem into a well-defined energy minimization problem, as shown below:

[0033] in, This represents the sum of the surface tensions of all water droplets.

[0034] By minimizing the surface tension of a single-tree TLS point cloud, the surface tension effect of a real-world water droplet system is simulated, driving the single-tree TLS point cloud to shrink from the outer layer towards the center of the branch. Equation (6) is continuously differentiable overall, but still belongs to a highly nonlinear high-dimensional optimization problem. Therefore, the L-BFGS algorithm is used to efficiently minimize the surface tension until all water droplets reach force equilibrium. In the iteration, the surface tension of each water droplet is minimized. and according to Update the geometric features:

[0035] in, , It is the initial The scope and quality of the impact, , The next iteration The scope and quality of its impact. , , They are linear characteristics ( ), planar features ( ) and scattered characteristics ( ).in, The three eigenvalues ​​are calculated from the covariance matrix (Equation (8)) composed of N(i), and satisfy the following conditions: .

[0036]

[0037] in, It is the centroid of N(i). It is the number of water droplets in the neighborhood; Let N(i) represent the covariance matrix, and T represent the matrix transpose. Represents water droplets The X, Y, and Z coordinates.

[0038] Step 2: During the shrinking process of water droplets, merge the water droplets in the space that are adjacent to each other to initially form a skeletal structure that retains local details; During the solution of equation (6), the water droplets gradually move inward. When the forces are balanced, the water droplets are close to each other but do not overlap, resulting in redundancy in the results. To solve this problem, this invention introduces water droplet merging, simulating the phenomenon in nature where water droplets that are too close together will directly merge, while adaptively adjusting the attractive and repulsive forces. Specifically, when two water droplets... and When elements overlap, a merge will be triggered. This condition is defined as follows:

[0039] in, yes and The Euclidean distance between them. physical radius Due to its quality Therefore, assuming the physical density of all water droplets is constant, the radius-mass relationship is determined as follows:

[0040] in, It is a scaling factor that scales Euclidean distance and physical radius to the same scale.

[0041] if and If the conditions in equation (9) are met, they are merged into a new water droplet. All properties of the new water droplet are weighted and averaged, and the attractive and repulsive forces are adaptively updated accordingly.

[0042] Step 3: Iteratively evaporate water droplets with small mass that deviate from the optimal path of a single tree to remove erroneous or redundant small branches generated during the shrinkage and merging stages; The shrinkage and coalescence of water droplets is a process of finding a local optimum of surface tension, which may lead to convergence to a non-ideal local minimum, thus generating erroneous or redundant small branches, such as... Figure 5 As shown. Furthermore, the processes of water droplet shrinkage, merging, and evaporation rely on skeletal entropy for regulation, and these erroneous branches cause instability in the calculation of skeletal entropy. Therefore, drawing inspiration from the evaporation phenomenon of isolated small water droplets in nature, and combining the optimal path of a water droplet with that of a single tree (defined as a set of paths with the lowest overall cost connecting all other nodes in the point set starting from the node with the lowest Z-value, such as...), we propose a method to address this issue. Figure 5 The geometric relationships shown in (a)-(c) in the figure are used to perform evaporation treatment on the water droplet system.

[0043] In nature, easily evaporating water droplets are typically small in mass, and there are no larger water droplets in their neighborhood. Under the geometry of a single-path optimality, easily evaporating water droplets usually have the following characteristics: they are far from the single-path optimality, such as... Figure 5 As shown in (a) in the figure; the linear features are smaller while the scattered features and planar features are larger, such as Figure 5 As shown in (b) and (c) above. Based on the above analysis, this invention designs a water droplet evaporation mechanism, as... Figure 6 As shown: First, regarding the results of water droplet shrinkage and merging (such as...) Figure 6 As shown in (a), the optimal path for a single tree from the root node to every other node is extracted, such as... Figure 6 As shown in (b) above. Subsequently, the shrinking and merging results (as shown in...) Figure 6 (as shown in (a)) is mapped to the nearest optimal path (e.g.) Figure 6 As shown in (b) in the figure, the results are as follows: Figure 6 (c) Based on the optimal path for a single tree and the properties of the water droplet itself, the surface area of ​​the water droplet is defined. This method is used for water droplets with small evaporation mass, insignificant geometric features, or far from the optimal path, and the results are as follows: Figure 6 As shown in (d) in the diagram. The specific implementation steps are as follows: Step 31, Extract the optimal path for a single tree; In areas where water droplets are unevenly distributed (such as at the branching point of a tree trunk), errors can easily occur in the force balance process, often leading to the formation of incorrect or redundant small branches in the shrinkage and merging process (such as...). Figure 5 and Figure 6 As shown in (a)). These abnormal water droplets clearly do not conform to the definition of a single tree skeleton. Therefore, a tree growth and spatial competition method was designed to extract the optimal path for a single tree (e.g., Figure 7 (As shown). The process includes three steps: confirmation of single-tree benchmark points, construction of undirected graphs of single trees and path generation, and selection of optimal single-tree paths guided by spatial competition.

[0044] Step 311, Single-tree reference point confirmation; select in the single-tree TLS point cloud The point with the lowest value, and within the height range [ , Filter candidate points within [+h]. Project the candidate points onto... The plane is then fitted with a center point by minimizing the sum of squared residuals. , ), and with the corresponding Combining to obtain ( , , ( ) as the root point of the tree.

[0045] Step 312, Construction of Undirected Graph for Single Tree and Path Generation; In nature, the nutrient transport process of trees usually follows the optimal (approximately shortest) path allocation law from the root to each branch. Therefore, a connected undirected graph (such as...) is constructed based on the results of water droplet shrinkage and merging. Figure 8 (a) and (d) in the graph). Starting from the root point, the shortest path to other water droplets can be obtained by following the path in the undirected graph (e.g., ...). Figure 8 (b) and (e) in the text.

[0046] In the early stages of contraction, due to the planar characteristics of water droplets... With scattered characteristics Larger, can be fixed The K-Nearest Neighbors (KNN) method is used to construct a connected undirected graph. However, as the contraction continues, the linear features of the water droplets... Enlargement and merging can lead to localized discontinuity of the skeleton (e.g.) Figure 7 As shown in (a)). At this point, KNN struggles to balance the overall connectivity and local refinement of the undirected graph. Currently, there are two approaches to address this problem. One is to use the local Delaunay method. This method focuses on the local Delaunay method within the water droplets. A Delaunay triangulation is constructed on the nearest neighbors, retaining the edges connected to the current water droplet, and merging the edges connecting all water droplets to construct an undirected graph. Secondly, a combination of global Delaunay and local KNN methods is employed. This allows for the creation of a more efficient and efficient graph. The method obtains local KNN edges, then superimposes them with global Delaunay triangulation to generate edges (and performs percentile pruning to remove overly long connections). The former reduces the number of edges but introduces excessively long edges. The latter ensures detailed connectivity but increases the number of edges and computational complexity. This invention combines the advantages of both methods, achieving optimal connectivity for each water droplet. A local Delaunay partition is constructed on the nearest neighbors, and combined with the global Delaunay partition edges (after percentile pruning) to form the final connected graph, as shown below. Figure 7 As shown in (b), the optimal path for a single tree should have linear characteristics. Large, planar features With scattered characteristics Due to characteristics such as small size, the weight of an edge in an undirected graph is defined as:

[0047] in, , , , Water droplets and Average areal characteristics, average random characteristics, average linear characteristics, and average quality; , , , These are the corresponding weighting coefficients; water droplets and The Euclidean distance between them; To adjust the parameters, the influence of geometric features in the exponential term on the total weight is controlled.

[0048] In an undirected graph, the larger the average mass and average linearity of the water droplets at the edge endpoints, the smaller the average randomness and average planarity, the smaller the Euclidean distance between the water droplets at the endpoints, and the smaller the edge weights. This makes it easier to obtain a single-tree topology that better conforms to the tree growth pattern (e.g., using the Minimum Spanning Tree (DMST)). Figure 7 (as shown in (c)).

[0049] Step 313, optimal path selection for a single tree under spatial competition guidance; the paths from the root point to each water droplet are highly redundant (e.g., Figure 8(c) and (f) in the text). Based on the spatial competition concept, this invention iteratively selects the optimal path from single-tree paths. The spatial competition concept originates from the spatial colony tree modeling algorithm. Its core idea lies in the exclusive occupation of spatial regions by branch growth. Once a branch extends and occupies a specific region, that region shields other branches, causing them to lose the competitiveness to grow in that direction. Extending this to optimal path generation, once an optimal path is determined, it will inhibit the extension of other optimal paths in the neighborhood, such as... Figure 8 As shown in (c) and (f) in the diagram. For each water droplet, the present invention obtains its path to the root point and calculates its relative path length ( ),Right now Then sort them. Among them, This is the path from the current water droplet to the treetop. That is the path length from the current water droplet to the root of the tree. Clearly, the smaller one... This indicates that water droplets closer to the treetop and with longer paths have higher priority. Subsequently, this invention uses a greedy strategy to iteratively select... The path of the smallest water droplet is the corresponding optimal path, and this droplet is marked as a skeleton point. Other water droplets in its neighborhood are marked as non-skeleton points. This process is repeated until all water droplets are classified. All optimal paths and skeleton points are combined to obtain the final optimal path for a single tree and its corresponding skeleton point (e.g., ...). Figure 7 (as shown in (d)).

[0050] Step 32, taking into account the evaporation of water droplets along the optimal path for a single tree; The processes of water droplet shrinkage, merging, and evaporation are constrained by skeletal entropy. However, the uneven distribution of geometric features of outlier water droplets can lead to overestimation of entropy values, thus slowing down the convergence speed of water droplet shrinkage, merging, and evaporation. Furthermore, water droplets that do not conform to the optimal path for a single tree may continue to shrink and merge, potentially getting trapped in erroneous or redundant small branches, forming an incorrect single-tree skeleton. To address these issues, this invention provides a framework for each water droplet... Define an equivalent surface area ( This measures the stability of a water droplet. The higher the value, the more closely the droplet follows the optimal path for a single tree, and the less likely it is to evaporate. The specific definition is as follows:

[0051] in, It is an intrinsic structural factor, ( ) is a local environmental factor. It is a very small constant to avoid the denominator being zero. Used to depict water droplets The inherent properties of water droplets are taken into account in the calculation. quality linear features planar features With scattered characteristics and its nearest branch on the optimal path. The average mass of the water droplets at both ends Average linear characteristics Mean plane characteristics and average dispersion characteristics And through weighting coefficients ( , , , Adjustments are made in accordance with equation (11). Local environmental factors are determined by... and Composition, respectively representing all those consisting of The candidate water droplets of the most recent branch are set to The mean and standard deviation of the distance distribution are used to characterize the dispersion of local water droplets. During optimization, water droplets with the smallest surface area are preferentially eliminated. Evaporation is achieved. When the minimum... When the surface area of ​​the water droplets is no longer lower than the average surface area of ​​all current candidate water droplets, the iteration stops, and the core water droplets that are highly coupled with the optimal path of a single tree are adaptively retained, while isolated, tiny or geometrically abnormal water droplets are effectively evaporated.

[0052] Step 4, Entropy Reduction Optimization: Introduce skeleton entropy as a global constraint. By calculating the entropy value of the geometric feature distribution of water droplets during the skeletonization process, iterative entropy reduction optimization is performed on shrinkage, merging, and evaporation to make the water droplets converge from a scattered and "disordered" distribution to a stable and "ordered" state. If the water droplets are allowed to shrink, merge, and evaporate uncontrollably, it will eventually lead to the erroneous merging of different branch skeletons and the loss of details. If the shrinkage, merging, and evaporation are prematurely terminated, redundant single-piece skeletons will be generated. Therefore, this invention introduces entropy, derived from information theory, as a constraint metric. Entropy is an important parameter for measuring the degree of disorder in a system; systems in nature typically exhibit an increasing entropy trend as they transition from order to disorder. However, when a discrete water droplet system gradually evolves from a scattered distribution into a single-piece skeleton... It shows a gradual upward trend, while and The distribution gradually decreases, exhibiting a shift from disorder to order, which is contrary to the natural law of entropy change. Based on this, this invention designs a normalized skeleton entropy reduction process to constrain the forces of water droplet contraction, merging, and evaporation, thereby gradually transforming a disordered and scattered single-tree TLS point cloud into an ordered single-tree skeleton.

[0053] For continuous variables Differential entropy is defined as .in ( ) for The probability density function. Based on this definition, the skeleton entropy is defined as follows:

[0054] in, ( ) represents the normalized skeleton entropy, while ( ) indicates as by , and The sum of negative differential entropies calculated from the three sets of water droplet features. This invention designs the range of skeleton entropy between [0, 1], so that the skeleton entropy monotonically decreases during the iteration process and eventually converges.

[0055] In mathematics, expectation can be defined as Therefore, the differential entropy can also be transformed into h( ) = [log( ( Combining the Monte Carlo approximation idea, when the sample size When the sample size is sufficiently large and the samples are independent and identically distributed, the expected value can be approximated by the sample mean, i.e. .because , and All TLS point cloud data originate from the same tree, satisfying independent and identically distributed characteristics, and the scale of a single tree's TLS point cloud is typically in the tens of thousands to hundreds of thousands. Therefore, equation (13) can be transformed into:

[0056] in, , and Obtained through kernel density estimation (KDE), reflecting the water droplets respectively. exist , and Probability density in a given dimension. KDE is a nonparametric statistical method that analyzes discrete geometric feature samples of a single tree point cloud and fits the distribution of these features to a continuous probability density function. It is defined as: .in, Here, h represents the number of TLS point cloud nodes, and h represents the bandwidth. Estimation is performed using Silverman's rule of thumb, specifically defined as follows: .in, express standard deviation For h, the first sample points . (·) is the kernel function. This invention selects the Gaussian distribution, which is the most common distribution in nature, as the kernel function, and its definition is... . and The calculation method and Consistent.

[0057] This invention first calculates the initial skeleton entropy based on the geometric characteristics of discrete water droplets. Then, after each iteration of droplet shrinkage, merging, and evaporation, the skeleton entropy is recalculated (e.g., ...). Figure 9 As shown). When the entropy value decreases to a steady state (less than the change threshold), ) or reach the maximum number of iterations ( ),illustrate , and The distribution of the water droplets has stabilized; at this point, iteration stops. Otherwise, optimization continues. In the early stages of iteration, the distribution of each water droplet... , and The differences are significant (dispersed distribution), corresponding to a disordered state. The calculated values ​​at this point are... , and The smaller the value, the smaller the corresponding log value, thus leading to... ( Smaller ( The effect is relatively large. As contraction, merging, and evaporation continue, , and The gradual convergence (concentration of distribution) corresponds to an ordered state. At this point, the calculated probability density function value gradually increases, and the corresponding log value also increases, making... ( Increase and push ( The water continued to drop. Eventually, as the water droplets gradually contracted to form a compact single-wooden skeleton, ( If the water droplets converge and remain stable, it indicates that the geometric distribution of the water droplets has reached an ordered state, and the iteration should be stopped at this point.

[0058] Step 5, Geometric and Topological Interleaving Optimization; Through the geometric and topological interleaving optimization process, the centrality and topological consistency of the skeleton are enhanced, and finally a single-tree topology that is more in line with the tree growth pattern is constructed. The iterative shrinkage, merging, and evaporation of the water droplet model are essentially about finding a local minimum of surface tension. Therefore, while the resulting skeleton can retain higher detail fidelity, it often fails to be located at the center of the branches, significantly reducing its compatibility with downstream applications, such as the inability to reconstruct high-precision 3D tree models and extract more accurate single-tree structural parameters.

[0059] Unlike existing skeletonization methods that define diversity, this invention proposes that skeleton centrality should be measured by minimizing the sum of squared residuals between skeleton edges and the nearest TLS point cloud. Based on this, this invention designs an interwoven geometry and topology optimization strategy to enhance the centrality and topological consistency of the skeleton, such as... Figure 10 As shown. Each major iterative phase of this interleaved optimization consists of two consecutive steps: geometric optimization and topology optimization. The invention repeats the entire process until the cumulative change in the skeleton edge positions drops to a predefined threshold. Below, or reaching the maximum number of iterations. .

[0060] Step 51, geometry optimization; Specifically, the single-tree TLS point cloud is first assigned to the preliminary skeleton generated by the normalized skeleton entropy constraint. Figure 9 The nearest neighbor edge in (a) is used. Here, the mean and one standard deviation are used to remove excessively long connection edges, preventing TLS point clouds from different branches from being assigned to the same skeleton edge, such as... Figure 10 As shown in (b) of the diagram. Subsequently, during the iterative optimization process, the two endpoints of the skeleton edge are fine-tuned using the following optimization equation:

[0061] in, and These represent the optimized skeleton edge endpoints. , The endpoint before optimization. This represents the single-tree TLS point cloud within the neighborhood. This represents the distance from a point to an edge. Let be the average distance from neighboring points to the skeleton edges. This optimization aims to minimize the sum of squared residuals from neighboring points to the nearest skeleton edge, thereby driving the skeleton edges to gradually approach the branch center, achieving a uniform distribution of single-tree point clouds around the skeleton. Furthermore, the optimization process is subject to three constraints: 1) Geometric length constraint: Ensure that the skeleton edges maintain their original length to avoid unnecessary stretching during the optimization process.

[0062] 2) Directional constraints: Limit the angle between the old and new sides to no more than a threshold. This avoids excessive distortion of the skeleton and maintains the overall topological structure. Here, "·" represents the dot product between vectors.

[0063] 3) Neighborhood range constraint: and The optimized endpoints must still be within the range of the single-tree point cloud, ensuring the skeleton is anchored within the single-tree point cloud. and These are the centroid of the neighborhood TLS point cloud and the radius of the boundary sphere, respectively. Furthermore, to ensure the smoothness and convergence stability of the optimization process, a step rate is introduced (…). Control the geometry and topology optimization process. After obtaining the theoretical target result through equation (15), update the skeleton result using the following equation:

[0064] in, ∈ [0, 1], This represents the endpoint after a single iteration update. For endpoints located in multiple neighborhoods, the average of the optimization results for each neighborhood is taken as the update value. Within a single iteration, relying on... Iterate over all skeleton edges Next, such as Figure 10 As shown in (c) in the figure.

[0065] Step 52, Topology optimization; After a single iteration, this invention uses DMST to correct the skeleton topology at the optimized skeleton points. DMST considers the total path length and the length to the root point when constructing the minimum spanning tree, and can construct a single-tree topology that is more in line with the tree growth pattern.

[0066] Step 53, Interleaving Optimization The refined skeleton topology obtained through topology optimization is used as input for the geometry optimization stage of the next iteration, such as... Figure 10 As shown in (a) above, the monotree TLS point cloud is reassigned to the nearest skeleton edge (e.g., ...). Figure 10 (b))) then performs a second geometric optimization. After completing the geometric optimization, the DMST algorithm is applied again to refine the single-wood skeleton topology. These two steps are performed alternately until the interleaving optimization converges (i.e., the cumulative change at the skeleton edge positions drops below a predefined threshold or the maximum number of iterations is reached), as shown in (b)). Figure 10 As shown in (d) in the diagram.

[0067] To comprehensively evaluate the performance of the proposed WDTS, a relatively complete single-tree TLS point cloud dataset was selected, as shown in Table 1. The dataset consists of multi-station registered real single-tree TLS point clouds of 24 trees in a leafless state. The average tree height is approximately 21.8 m, and the average diameter at breast height (DBH) is approximately 28.6 cm. The point cloud integrity is high, and the canopy complexity is simple, but there is still strong geometric complexity in the branch bifurcation area, although the overall complexity is relatively simple. The point cloud density of the dataset is given by formula ( Definition ). Where n is the total number of point clouds, and These represent point clouds in The extreme values ​​of coordinates of a plane projection.

[0068] Table 1. Detailed description of tree point clouds in the dataset

[0069] This embodiment implements WDTS using the Python language. All comparative experiments were performed on the same desktop computer with the following hardware configuration: Intel(R) Core(TM) i7-10700K CPU (3.80GHz), 32 GB RAM, and NVIDIA GeForce RTX 3070 GPU. The software environment was a 64-bit Windows 11 Home operating system. CloudCompare and MeshLab were used to visualize all subsequent single-tree skeletonization results.

[0070] The key parameter settings involved in this embodiment are detailed in Table 2.

[0071] Table 2 WDTS Specific Parameter Settings

[0072] This embodiment selects five commonly used and open-source skeleton extraction algorithms for comparison: the skeleton extraction part of the AdTree algorithm, L1-medial, LBC, KNN mean shrinkage (WoodSKE), and the L1-medial skeleton extraction method derived from L1-Tree with Dijkstra enhancement. WoodSKE is a shrinkage method that considers the skeleton point as the mean point within the neighborhood of the single-tree TLS point cloud, iteratively shrinking the local point cloud inward until the maximum number of iterations is reached. The Dijkstra-enhanced L1-medial optimizes the selection of initial seed points using Dijkstra's shortest path algorithm. Except for AdTree and WDTS, the other comparison methods only output skeleton points in their public implementations and do not directly provide topology information. To ensure comparability and avoid the influence of different post-processing strategies on topology evaluation, this invention does not restore the topology for these methods. Furthermore, while AdTree can generate topologies according to its method definition, the format of the obtained open-source implementation is inconsistent with the topology import specification of Mesh-Lab / CloudCompare. Therefore, the topology information could not be loaded in the visualization environment, and thus the AdTree topology is not shown in the illustration. Although the comparison methods do not display the complete topology structure in the illustration, this does not affect the qualitative evaluation in this section, as the qualitative evaluation only requires TLS single-tree point clouds. For the skeleton extraction results of different methods on 24 trees in the dataset, see [link to relevant documentation]. Figures 11-14 .

[0073] The results show that on datasets with relatively complete point clouds and low complexity, the WDTS method of this invention is generally able to reconstruct topologically reasonable single-tree skeletons while preserving details (see...). Figures 11-13 ).

[0074] Figure 14The results show that AdTree and WoodSKE fail to generate tree skeleton structures suitable for downstream applications in complete single-tree point clouds. AdTree misclassifies a large number of point clouds as skeletons at trunk bifurcation points and in the canopy region, while WoodSKE forms planar and scattered skeleton structures in bifurcation areas. Compared to single-station single-tree TLS point clouds, neither shows improved performance on complete point clouds. In contrast, the LBC algorithm can also generate compact skeleton results on complete single-tree TLS point clouds, but it loses skeleton details of local canopy branches. Because the density inhomogeneity problem of complete point clouds is improved compared to single-station TLS point clouds, the problem of losing skeleton details in local branches is somewhat alleviated in LBC. L1-medial significantly outperforms the previous three in terms of compactness and preservation of local details, and its performance on complete single-tree TLS point clouds is significantly improved compared to single-station single-tree TLS point clouds (the point cloud branch structure and point density are clearer and more uniform), but it still loses skeleton details at trunk bifurcation points and canopy branches (requiring optimization based on the initial seed point). Dijkstra's enhanced L1-medial skeleton produces results similar to the L1-medial skeleton. However, due to issues with initial seed point selection, it also suffers from the loss of skeleton details at trunk bifurcation and canopy branching. Unlike all the comparison methods, WDTS, while shrinking the single-tree TLS point cloud into a compact single-tree skeleton, also retains more skeleton details at trunk bifurcation and small canopy branches, maintaining the consistency and rationality of the topology. Furthermore, in comparisons of single-station and multi-station complete single-tree TLS point clouds, the skeleton results of WDTS show little difference, demonstrating the stability and robustness of WDTS at both geometric and topological levels under different data acquisition conditions.

[0075] Ideally, a single tree skeleton should be located at the center of the branch point cloud, meaning the distance from the skeleton to the TLS point cloud of neighboring single trees should be consistent. Based on this, this embodiment uses the point cloud as the ground truth, calculates the distance to the nearest skeleton edge, and calculates the mean absolute error (MAE) and standard deviation (SD) according to equation (17) as the accuracy index for measuring the centering of the skeleton. Since the definition of this accuracy index depends on the skeleton edge, i.e. the topological structure of the skeleton, and some comparison methods only output a skeleton point set without topology, the centering cannot be evaluated without restoring the topology. Therefore, in order to ensure the fairness and consistency of the evaluation and avoid the influence of different topology restoration strategies on the results, this embodiment uniformly adopts the DMST algorithm to restore the skeleton topology before evaluating the centering accuracy of single trees for all comparison methods that only output skeleton points. Furthermore, to verify the effectiveness of the geometry and topology interleaving optimization strategy in WDTS, this embodiment also calculated the accuracy indices before (w / o Opt. in Table 3) and after (w / Opt. in Table 3) geometry and topology interleaving optimization. Additionally, since the skeletons generated by AdTree and WoodSKE are not compact on most individual trees and do not meet the prerequisites for accuracy evaluation, their indices were not calculated.

[0076]

[0077] in, This represents the total number of points in the point cloud. For the first The Euclidean distance from a point to the nearest edge of the skeleton. All distances belonging to the uniform skeleton edge The mean. MAE The smaller the value, the more centered the overall skeleton is. SD The smaller the value, the more uniform the distance from the skeleton to each point.

[0078] Table 3 presents the evaluation results and comparisons of skeleton centering. The results show that WDTS already achieves good performance without interleaving optimization, with average MAE and SD reaching 0.014 and 0.024, respectively. Furthermore, adding an interleaving optimization strategy can further improve skeleton centering. Specifically, WDTS using interleaving optimization will average... MAE and SD They decreased by 0.003 respectively. And 0.005 In Table 3, w / o Opt. and w / Opt. represent the WDTS values ​​before and after the interleaving optimization in Table 3, respectively. MAE and SD .

[0079] Table 3. Entropy of different methods across all trees MAE and SD

[0080] Compared to other methods, even without interleaving optimization, the WDTS of this invention has already demonstrated comparable or superior performance. This trend indicates that, with high-quality data as input, entropy-reduction optimized WDT implicitly promotes skeleton centering by minimizing the repulsive force defined by the sum of squared residuals. By introducing an interleaving optimization strategy, WDTS explicitly optimizes centering, exhibiting significantly better centering performance than all other methods. Specifically, WDTS will average... and Decrease by 0.003 respectively And 0.005 The results show that the proposed interleaving optimization strategy is particularly effective in correcting skeleton offsets, especially in regions with missing points or uneven local point density. However, for a few trees, such as Tree_24, WDTS performs slightly worse than the Dijkstra-enhanced L1-medial method. This is mainly attributed to the smaller number of interleaving points used in the optimization strategy. To maintain the compactness of the optimized interleaving skeleton and avoid extreme oscillations that could compromise topological rationality, WDTS, while maintaining the overall optimal centrality of the trunk skeleton for most trees, demonstrates the robustness and effectiveness of the proposed method.

Claims

1. A water droplet model-driven entropy optimization method for single-wood skeletonization, characterized in that, The steps include the following: S1, regard the single-tree TLS point cloud as a water droplet model with different masses in 3D space, and realize the shrinkage of the water droplet by balancing the forces of the water droplet model; S2, during the process of water droplet shrinkage, merges with water droplets in the vicinity of the space, initially forming a skeletal structure that retains local details; S3 iteratively evaporates water droplets with small mass that deviate from the optimal path of a single tree, removing erroneous or redundant small branches generated during the shrinkage and merging stages; S4 introduces skeleton entropy as a global constraint. By calculating the entropy value of the geometric feature distribution of water droplets during the skeletonization process, iterative entropy reduction optimization is performed on shrinkage, merging and evaporation, so that the water droplets converge from a scattered "disordered" distribution to a stable "ordered" state. S5, through a process that combines geometry and topology optimization, enhances the centrality and topological consistency of the skeleton, ultimately constructing a single-tree topology that conforms to the tree growth pattern.

2. The entropy optimization single-wood skeletonization method driven by the water droplet model according to claim 1, characterized in that, The steps to shrink water droplets include: S11, calculate the surface tension of a single water droplet; The sum of the attractive and repulsive forces acting on a single water droplet is defined as the equivalent surface tension of that single water droplet. This is used to drive the contraction, merging, and evaporation of water droplets, and its expression is as follows: in, Represented as water droplets The attraction, Represents water droplets The repulsive force experienced; attraction To minimize the sum of Euclidean distances between water droplets, the expression is as follows: in, Indicates the attractiveness weight. Represents the Euclidean distance between vectors. These are water droplets that need optimization. yes The neighboring water droplets; N(i) is the water droplets in the neighborhood; Centered on, within radius The collection of all neighboring water droplets within the affected area; Each water droplet initially The radius is half the diagonal distance of the bounding box of the water droplet found by searching with the square root of the Euclidean distance between it and its nearest water droplet. express quality, initial , and These are the maximum and minimum values ​​of the number of water droplets in the corresponding neighborhood of all water droplets. yes The number of water droplets in the neighborhood; It is an adjustable parameter used to control the mass; The expression for the Huber loss function is as follows: in, For the threshold, Represents water droplets and L2 distance between them; when When, it indicates It is not a noisy water droplet; it uses a secondary method to enhance the noise level. The attraction; when At that time, the influence of noise water droplets is limited using an L1 linear form; threshold Calculated using the absolute deviation of the median: Where median represents the median; Represents the neighborhood centroid. express To the neighboring centroid Euclidean distance; The repulsive force is defined by minimizing the sum of squared residuals. The calculation formula is as follows: in, As the weight of the repulsive force, The weighted average distance; Indicates from the neighborhood centroid To neighboring water droplets The quality-weighted average distance; S12, calculates the global surface tension of water droplets; Based on the attractive and repulsive forces of individual water droplets, it will contain The surface tension of a single water droplet's TLS point cloud is defined as the sum of the surface tensions of all water droplets, as expressed below: in, This represents the sum of the surface tensions of all water droplets; By minimizing the surface tension of a single-tree TLS point cloud, the surface tension effect of a real-world water droplet system is simulated, driving the single-tree TLS point cloud to shrink from the outer layer towards the center of the branch.

3. The entropy optimization single-wood skeletonization method driven by the water droplet model according to claim 1, characterized in that, In step S2, water droplets in the vicinity of space and The conditions for merging are as follows: in, yes and The Euclidean distance between them for physical radius, for physical radius, It is a scaling factor that scales Euclidean distance and physical radius to the same scale.

4. The entropy optimization single-wood skeletonization method driven by the water droplet model according to claim 1, characterized in that, In step S3, based on the optimal path for a single tree and the properties of the water droplets themselves, water droplets with small evaporation mass, insignificant geometric features, or far from the optimal path are selected. The extraction of the optimal path for a single tree includes the following steps: S311, confirm the single-tree reference point; select in the single-tree TLS point cloud. The point with the lowest value, and within the height range [ , Filter candidate points within [+h]; project candidate points onto [h]. The plane is then fitted with a center point by minimizing the sum of squared residuals. , ), and with the corresponding Combining to obtain ( , , ) as the root point; S312, construct an undirected graph of a single tree and generate paths; based on the fact that the nutrient transport process of a tree follows the optimal path allocation law from the root to each branch, in each water droplet... A local Delaunay partition is constructed on the nearest neighbors, and combined with the edges of the global Delaunay partition to form the final connected undirected graph; the weight of the edge in the undirected graph is defined as: in, water droplets and The average planar features, water droplets and The average dispersion characteristics, water droplets and The average linear characteristics, water droplets and The average mass; , , , These are the corresponding weighting coefficients; water droplets and The Euclidean distance between them; To adjust the parameters and control the influence of geometric features in the exponential term on the total weight; S313, Select the optimal path for a single tree; based on the spatial competition concept, iteratively select the optimal path from the single tree paths; for each water droplet, obtain its path to the root point and calculate its relative path length. : in, This is the path from the current water droplet to the treetop. This is the path length from the current water droplet to the root of the tree; Then based on the relative path length Sort, smaller This indicates that the water droplets are closer to the treetops and have a longer path, thus having a higher priority. Subsequently, a greedy strategy was used to iteratively select... The smallest water droplet has the corresponding optimal path, and this smallest water droplet is marked as a skeleton point, while other water droplets in the neighborhood are marked as non-skeleton points; this process is repeated until all water droplets are classified. Finally, all optimal paths are combined with skeleton points to obtain the final optimal path for a single tree and its corresponding skeleton points.

5. The entropy optimization single-wood skeletonization method driven by the water droplet model according to claim 1, characterized in that, In step S4, a normalized skeleton entropy reduction process is used to constrain the intensity of water droplet shrinkage, merging, and evaporation, thereby gradually transforming a disordered and scattered single-tree TLS point cloud into an ordered single-tree skeleton. The specific process is as follows: First, the initial skeleton entropy is calculated based on the geometric features of the discrete water droplets; Subsequently, the skeletal entropy is recalculated after each iteration of water droplet shrinkage, merging, and evaporation; when the entropy value decreases to a steady state or reaches the maximum number of iterations, it indicates linearity. planar features With scattered characteristics If the distribution has stabilized, stop iterating; otherwise, continue optimizing.

6. The entropy optimization single-wood skeletonization method driven by the water droplet model according to claim 1, characterized in that, In step S5, the steps of the geometry and topology intertwined optimization process are as follows; S51, assign the single-tree TLS point cloud to the nearest neighbor edge of the preliminary skeleton generated by the normalized skeleton entropy constraint for geometric optimization; subsequently, during the iterative optimization process, fine-tune the two endpoints of the skeleton edge using the following optimization equation: in, and These represent the optimized skeleton edge endpoints; , The endpoints before optimization; For the TLS point cloud of a single tree within the neighborhood; This represents the distance from a point to an edge; This represents the average distance from neighboring points to the skeleton edges; S52, after completing a single iteration, uses the DMST algorithm to correct the skeleton topology on the optimized skeleton points to obtain a refined skeleton topology; S53, the obtained refined skeleton topology is used as the input for the geometric optimization stage of the next iteration. The single-tree TLS point cloud is reassigned to the nearest skeleton edge, and then the second geometric optimization is performed. After the geometric optimization is completed, the DMST algorithm is applied again to refine the single-tree skeleton topology. Steps S51 and S52 are performed alternately until the cumulative change of the skeleton edge position drops below the predefined threshold or the maximum number of iterations is reached.

7. The entropy optimization single-wood skeletonization method driven by the water droplet model according to claim 6, characterized in that, In step S51, when fine-tuning the two endpoints of the skeleton edge, the following constraints must be satisfied: Geometric length constraints: Ensure that the skeleton edges maintain their original length; Directional constraints: Limit the angle between the old and new sides to no more than a threshold. , where "·" represents the dot product between vectors; Neighborhood range constraint: and This ensures that the optimized endpoints remain within the single-tree point cloud, guaranteeing that the skeleton is anchored within the single-tree point cloud; among which, and These are the centroid of the neighboring TLS point cloud and the radius of the boundary sphere, respectively.

8. The entropy optimization single-wood skeletonization method driven by the water droplet model according to claim 6, characterized in that, To ensure the smoothness and convergence stability of the optimization process, a step rate is introduced. Control the geometry and topology optimization process; after obtaining the theoretical target result through the following formula, update the skeleton result: in, ∈ [0, 1], Indicates the endpoint after a single iteration update; For endpoints located in multiple neighborhoods, the average of the optimization results of each neighborhood is taken as the update value; within a single iteration, relying on... Iterate over all skeleton edges Second-rate.

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