Single tree diameter estimation method based on double-constraint convex hull algorithm

Abstract

The invention provides an individual tree diameter estimation method based on a double-constraint convex hull algorithm, and belongs to the field of individual tree diameters. According to the experiment, masson pine is taken as a main research object, 71 single trees are taken as samples, true values of different height diameters are destructively acquired, and the accuracy of the algorithm for inverting different height diameters of trunks is verified and discussed. Experimental results show that the extracted diameter at breast height is compared with a true value, R2 is 0.995, and RMSE is 0.55 cm; and compared with a real value, the extracted different height diameters are gradually reduced in inversion precision along with the increase of the point cloud height. The inversion R2 is greater than 0.9 at the 4 / 10 position or below; from the 4 / 10 position to the 6 / 10 position, the inversion R2 is reduced but is still greater than 0.5; the inversion precision at 6 / 10 or above is low, and the precision is reduced due to data loss caused by the fact that a ground-based laser radar cannot scan point cloud at a high position. When the point cloud data is sufficient, the result of extracting different height diameters by the algorithm is reliable.

Description

[0001] Citation of Related Applications

[0002] This application claims all rights and interests in the invention patent application with application number 202510656504.7 filed with the State Intellectual Property Office of the People's Republic of China on May 21, 2025, entitled "Single Tree Diameter Estimation Method Based on Double Constrained Convex Hull Algorithm", and incorporates its entire contents into this article by reference. Technical Field

[0003] The present invention relates to the field of tree trunk algorithms, and in particular to a single tree diameter estimation method based on a double-constrained convex hull algorithm. Background Art

[0004] Traditionally, quantifying the diameter of individual trees at different heights relies on manual measurement, which is time-consuming, labor-intensive, and requires destructive sampling. This makes the results irreproducible and hinders the development of forest resource surveys. With the continuous advancement of LiDAR technology, forestry survey methods are gradually changing. Ground-based LiDAR, which can non-destructively obtain high-precision three-dimensional point cloud information about trees, is widely used in small-scale forestry surveys.

[0005] At present, the main methods for inverting the DBH are allometric equation simulation, Hough transform, and circle fitting algorithms such as RANSAC. The latter directly uses point cloud distribution features to fit the DBH of individual trees, achieving better results. Existing technologies use Hough transform and RANSAC fitting algorithms to extract the DBH of individual trees, respectively. The results show that both methods can achieve high DBH extraction accuracy, with root mean square errors (RMSE) of 1.17 cm and 3.1 cm, respectively. The convex hull is the smallest polygon containing a set of planar points that can accurately describe the outer contour of the trunk. However, the traditional convex hull boundary produces many gaps, resulting in its boundary calculation being still not accurate enough, and it is impossible to more accurately describe the trunk shape. Therefore, there is still a need to explore more accurate boundary descriptions and algorithms that are suitable for extracting trunk diameters at different heights. Summary of the Invention

[0006] This patent provides a method for estimating the diameter of a single tree based on a double-constrained convex hull algorithm. Based on the two-dimensional convex hull algorithm, this patent proposes a double-constrained convex hull algorithm. This algorithm optimizes the convex hull boundary in the algorithm to ensure a close fit between the boundary and the tree crown point cloud. A distance threshold is also added to improve computational efficiency while maintaining accuracy, thereby enhancing the model's accurate description of tree trunk shape.

[0007] Focusing on the above goals, this patent mainly completes the following tasks:

[0008] 1) Extracting single tree trunk point cloud based on ground-based lidar system.

[0009] 2) The double-constrained convex hull algorithm is used to accurately calculate the trunk diameters of trees at different heights and compare the accuracy with the actual values.

[0010] The technical solution of the present invention provides: a method for estimating the diameter of a single tree based on a double-constrained convex hull algorithm, comprising the following steps:

[0011] S101: Data Collection

[0012] The main tree species studied was Pinus massoniana. The point cloud was collected using a FARO Focus3D terrestrial 3D laser scanner, using a multi-station stitching method based on a public target sphere.

[0013] S102: Data Preprocessing

[0014] Point cloud preprocessing is done using the Python point cloud processing library Open3D. To avoid the reduction in computational efficiency caused by the large amount of data from ground-based lidar, voxel downsampling is used to process the original ground-based lidar. The specific principle of this method is as follows (Formula (1-3)):

[0015] Step 1: First, based on the point cloud coordinate set, obtain the maximum and minimum boundary coordinates X of the point cloud 3D max ,Y max ,Z max ,X min ,Y min ,Z min , and set the voxel side length r;

[0016] Step 2: Solve the minimum bounding box side length L based on the extreme values ​​of each dimension coordinate x ,L y ,L z ;

[0017]

[0018] Step 3: Calculate the voxel grid size D based on the bounding box side length and voxel side length x ,D y ,D z :

[0019]

[0020] in Indicates rounding down;

[0021] Step 4: Calculate the index M of each point in the voxel unit:

[0022]

[0023] Step 5: Calculate the centroid of each voxel unit and use the centroid coordinates to replace all points in the unit to complete point cloud downsampling while ensuring that the point cloud distribution characteristics remain unchanged.

[0024] In this patent, based on the distribution of points, the voxel side length r is set to 0.1m;

[0025] The open-source point cloud processing software CloudCompare was then used to manually crop the sampled ground-based point cloud data to ensure that the branch and leaf point clouds were separated and the trunk point clouds were preserved. Through morphological comparison and screening, 71 typical trees with different morphologies were finally selected as experimental subjects.

[0026] S103: Tree Trunk Point Cloud Layered Slicing Algorithm

[0027] In order to extract the trunk diameters at different heights, a tree trunk point cloud hierarchical slicing algorithm is designed using Python. The pseudo code of the algorithm is as follows:

[0028]

[0029]

[0030] The point cloud slices are intercepted by judging the relative position between the point cloud coordinates and different heights and the slice thickness;

[0031] S104: Double Constrained Convex Hull Algorithm

[0032] Based on the Graham convex hull algorithm, a double-constrained convex hull algorithm is proposed. This algorithm mainly improves the Graham convex hull algorithm. The point cloud obtained by slicing in step S103 is input into the optimization algorithm one by one to complete the precise extraction of the boundary and fit the trunk diameter at that location according to the area.

[0033] Preferably, step S104: the convex hull optimization algorithm controlled by the distance threshold in the double-constrained convex hull algorithm is specifically:

[0034] In a given space R n For a set of finite points S, the convex hull Conv(S) is the set of all convex combinations of S, that is (Formula (4)):

[0035]

[0036] Where S={x1,x2,...,x k} is a set of points, point x i Located in R n ;λ i is satisfied The non-negative coefficient of ;

[0037] The convex hull describes the boundary of a scattered point set well due to its geometric properties. The convex hull calculation methods include Graham scanning method and Jarvis stepping method.

[0038] Step 1: Use Graham to establish the original convex hull and optimize the convex hull shape based on it; the Graham scanning method is established as follows;

[0039] For a scattered point set S, find a point P1 such that P1 is the outermost point of the entire point set; starting from point P1, calculate the polar angle between P1 and other points respectively, and sort them according to the polar angle size and the distance from P1; connect the points in order, and determine the concavity of the next point according to the vector cross product (Equation (5)):

[0040]

[0041] Wherein, vectors AB and AC represent the vectors consisting of the starting scanning point and any two fixed points. When CP>0, AB rotates counterclockwise along AC, and when CP<0, AB rotates clockwise along AC. According to the above process, the outermost convex hull boundary is determined point by point, all boundary points are obtained, and finally the Graham convex hull is established.

[0042] Step 2: Optimize the convex hull algorithm. Based on the original Graham convex hull boundary points, further characterize the distribution boundary of the points. The core idea of ​​the algorithm is to use the point set X(P1, P2, ..., P n ) in the convex hull set S formed by , continuously searching for new boundary points according to the operation rules until no new boundary points are generated, thereby optimizing the convex hull;

[0043] 1) Obtain two adjacent boundary points one by one in a cyclic manner, and draw a circle with the Euclidean distance between the two points as the radius;

[0044] 2) Add the non-boundary points contained in the circle to the set of undetermined internal points, find the outermost internal point by comparing the cosine value of the angle between the vectors, add it to the set of boundary points, and generate new boundary points (Equation (6));

[0045]

[0046] 3) Gradually approximate the convex hull shape in the same way until there are no internal points in the circle established by the two points; at the same time, in order to improve the efficiency of the algorithm, the side lengths of the two boundary points are introduced as thresholds to improve the accuracy of the convex hull while ensuring the running speed;

[0047] Following the above process, an improved convex hull is generated. The black line in the figure represents the original Graham convex hull, and the red line represents the optimized convex hull.

[0048] Step 3: Based on the optimized convex hull boundary points, calculate the area of ​​the single-layer convex hull using the discretized Green's theorem. Green's theorem describes the relationship between the interior of a figure enclosed by a curve on a plane and the integral on the curve, and is often used to calculate the area enclosed by a curve. The discretized Green's theorem is a discretized expression of Green's theorem.

[0049] Sort the generated convex hull in counterclockwise direction. At this time, for the S vertices of the convex set (x1,y1),(x2,y2),...,(x n ,y n ), the area calculation formula is (Formula (7)):

[0050]

[0051] Where, Area is the convex hull area calculated by the optimized convex hull algorithm, (x i ,y i ) The coordinates of the convex hull vertices are arranged in counterclockwise order, and n is the number of convex hull points; the initial point is usually repeatedly added to the end of the point set to close the polygon.

[0052] Step 4: Based on the single-layer point cloud area of ​​the tree trunk solved above, the diameter of the single layer of the tree trunk is inversely calculated according to the circle area formula. The diameter solution formula is (Equation (8)):

[0053]

[0054] Where d is the diameter of a single-layer trunk, and Area is the convex hull area of ​​a single layer.

[0055] Beneficial effects of the present invention:

[0056] Based on the Graham algorithm, this application proposes a new algorithm for accurately calculating the trunk diameters at different heights from TLS (Terrain LiDAR Systems) data - the double constraint (DB) algorithm. The experiment uses Pinus massoniana as the main research object and 71 single trees as samples. The real values ​​of the diameters at different heights are destructively collected to verify and discuss the accuracy of the algorithm in inverting the trunk diameters at different heights. The experimental results show that the extracted diameter at breast height is R higher than the real value. 2 The inversion accuracy of the extracted diameters at different heights is 0.995 and the RMSE is 0.55cm. Compared with the true values, the inversion accuracy decreases with the increase of the point cloud height. 2 are all greater than 0.9; between 4 / 10 and 6 / 10, the inverted R 2 The inversion accuracy is low at more than 6 / 10 locations, mainly because the ground-based lidar cannot scan the point cloud at high altitudes, resulting in data loss and reduced accuracy. When there is sufficient point cloud data, the algorithm can reliably extract diameters at different altitudes. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] To more clearly illustrate the technical solutions of the present disclosure, the following briefly introduces the drawings required for use in some embodiments of the present disclosure. Obviously, the drawings described below are only drawings of some embodiments of the present disclosure, and those skilled in the art can also derive other drawings based on these drawings. Furthermore, the drawings described below are schematic diagrams and are not intended to limit the actual dimensions of the products, actual processes of the methods, actual timing of signals, and the like involved in the embodiments of the present disclosure.

[0058] Figure 1 Flowchart of the proposed DB algorithm; (a) preprocessing; (b) trunk extraction; (c) calculation of diameters at different heights.

[0059] Figure 2 Schematic diagram for constructing the Graham convex hull; (a) a set of discrete points distributed in two-dimensional space; (b) sorting by polar angle and distance; (c) determining convexity; (d) connecting boundary points to complete the Graham convex hull.

[0060] Figure 3 Schematic diagram for optimizing the Graham convex hull; (a) Graham convex hull origin boundary; (b) internal point traversal process; (c) adding convex hull edge length threshold; (d) connecting boundary points and completing the optimized convex hull.

[0061] Figure 4 is the accuracy of the extracted DBH, and the black dashed line represents the 1:1 line.

[0062] Figure 5 The accuracy of trunk diameter extraction at different heights is shown in Figure 2. The black dashed line represents the 1:1 line. DETAILED DESCRIPTION

[0063] In order to enable those skilled in the art to better understand the technical solutions in this application, the following will provide a clear and complete description of the technical solutions in the embodiments of this application in conjunction with the drawings in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0064] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making creative efforts are within the scope of protection of this application.

[0065] The present invention is described in further detail below by way of examples.

[0066] In an embodiment, a method for estimating the diameter of a single tree based on a double-constrained convex hull algorithm comprises the following steps:

[0067] Data collection

[0068] The study area covers 14 cities (prefectures) in Hunan Province, and a total of 153 Masson pine trees were surveyed. The diameter at breast height, diameter at ground level, tree height, diameter at different relative positions, height below branches, crown width, and trunk, root, branch, leaf, wood, and bark samples were collected for each tree. The point cloud was collected using a FARO Focus3D terrestrial 3D laser scanner. The point cloud was collected using a multi-station splicing method based on a public target sphere to obtain point cloud data in a relative coordinate system. The average point density of the point cloud was 4410 points / m 2 , which satisfies the trunk diameter calculation.

[0069] Data preprocessing

[0070] Point cloud preprocessing is done using the Python point cloud processing library Open3D. To avoid the reduction in computational efficiency caused by the large amount of data from ground-based lidar, voxel downsampling is used to process the original ground-based lidar. The specific principle of this method is as follows (Formula (9-11)):

[0071] Step 1: First, based on the point cloud coordinate set, obtain the maximum and minimum boundary coordinates X of the point cloud 3D max ,Y max ,Z max ,X min ,Y min ,Z min , and set the voxel side length r;

[0072] Step 2: Solve the minimum bounding box side length L based on the extreme values ​​of each dimension coordinate x ,L y ,L z ;

[0073]

[0074] Step 3: Calculate the voxel grid size D based on the bounding box side length and voxel side length x ,D y ,D z :

[0075]

[0076] in Indicates rounding down;

[0077] Step 4: Calculate the index M of each point in the voxel unit:

[0078]

[0079] Step 5: Calculate the centroid of each voxel unit and use the centroid coordinates to replace all points in the unit to complete point cloud downsampling while ensuring that the point cloud distribution characteristics remain unchanged.

[0080] In this patent, based on the distribution of points, the voxel side length r is set to 0.1m;

[0081] The open-source point cloud processing software CloudCompare was then used to manually crop the sampled ground-based point cloud data to ensure that the branch and leaf point clouds were separated and the trunk point clouds were preserved. Through morphological comparison and screening, 71 typical trees with different morphologies were finally selected as experimental subjects.

[0082] Tree trunk point cloud layered slicing algorithm

[0083] In order to extract the trunk diameters at different heights, a tree trunk point cloud hierarchical slicing algorithm was designed using Python. The pseudo code of the algorithm is as follows:

[0084]

[0085]

[0086] The point cloud slices are intercepted by judging the relative position between the point cloud coordinates and different heights and the slice thickness;

[0087] Double-constrained convex hull algorithm

[0088] Considering that most of the existing tree trunk diameter extraction algorithms use circle fitting algorithms such as Hough and Ransac, they cannot accurately describe the shape of the outer boundary of the tree trunk. Based on the Graham convex hull algorithm, a double-constrained convex hull algorithm is proposed. This algorithm mainly improves the Graham convex hull algorithm, optimizes Graham's convex hull boundary to make it closer to the outer periphery of the trunk, and introduces a side length threshold to balance accuracy and efficiency. The point cloud is obtained by slicing at a certain thickness and input into the optimization algorithm one by one to complete the accurate extraction of the boundary and fit the trunk diameter according to the area.

[0089] In a given space R n For a set of finite points S, the convex hull Conv(S) is the set of all convex combinations of S, that is (Formula (12)):

[0090]

[0091] Where S={x1,x2,...,x k} is a set of points, point xi Located in R n ;λ i is satisfied The non-negative coefficient of ;

[0092] The convex hull describes the boundary of a scattered point set well due to its geometric properties. The convex hull calculation methods include Graham scanning method and Jarvis stepping method.

[0093] Step 1: Use Graham to establish the original convex hull and optimize the convex hull shape based on it; the Graham scanning method is established as follows ( Figure 2 );

[0094] For a scattered point set S, find a point P1 such that P1 is the outermost point of the entire point set; starting from point P1, calculate the polar angle between P1 and other points respectively, and sort them according to the polar angle size and the distance from P1; connect the points in order, and determine the concavity of the next point according to the vector cross product (Equation (13)):

[0095]

[0096] Wherein, vectors AB and AC represent the vectors consisting of the starting scanning point and any two fixed points. When CP>0, AB rotates counterclockwise along AC, and when CP<0, AB rotates clockwise along AC. According to the above process, the outermost convex hull boundary is determined point by point, all boundary points are obtained, and finally the Graham convex hull is established.

[0097] Step 2: Optimize the convex hull algorithm. Based on the original Graham convex hull boundary points, further characterize the distribution boundary of the points. The core idea of ​​the algorithm is to use the point set X(P1, P2, ..., P n ) in the convex hull set S, and continuously search for new boundary points according to the operation rules until no new boundary points are generated, thereby optimizing the convex hull ( Figure 3 );

[0098] 1) Obtain two adjacent boundary points one by one in a cyclic manner, and draw a circle with the Euclidean distance between the two points as the radius;

[0099] 2) Add the non-boundary points contained in the circle to the set of undetermined internal points, find the outermost internal point by comparing the cosine value of the angle between the vectors, add it to the set of boundary points, and generate new boundary points (Equation (14));

[0100]

[0101] 3) Gradually approximate the convex hull shape in the same way until there are no internal points in the circle established by the two points; at the same time, in order to improve the efficiency of the algorithm, the side lengths of the two boundary points are introduced as thresholds to improve the accuracy of the convex hull while ensuring the running speed;

[0102] Following the above process, an improved convex hull is generated. The black line in the figure represents the original Graham convex hull, and the red line represents the optimized convex hull.

[0103] Step 3: Based on the optimized convex hull boundary points, calculate the area of ​​the single-layer convex hull using the discretized Green's theorem. Green's theorem describes the relationship between the interior of a figure enclosed by a curve on a plane and the integral on the curve, and is often used to calculate the area enclosed by a curve. The discretized Green's theorem is a discretized expression of Green's theorem.

[0104] Sort the generated convex hull in counterclockwise direction. At this time, for the S vertices of the convex set (x1,y1),(x2,y2),...,(x n ,y n ), the area calculation formula is (Formula (15)):

[0105]

[0106] Where, Area is the convex hull area calculated by the optimized convex hull algorithm, (x i ,y i ) The coordinates of the convex hull vertices are arranged in counterclockwise order, and n is the number of convex hull points; the initial point is usually repeatedly added to the end of the point set to close the polygon.

[0107] Step 4: Based on the single-layer point cloud area of ​​the tree trunk solved above, the diameter of the single-layer tree trunk is inversely calculated according to the circle area formula. The diameter solution formula is (Equation (16)):

[0108]

[0109] Where d is the diameter of a single-layer trunk, and Area is the convex hull area of ​​a single layer.

[0110] Performance evaluation of DB (double constraint) algorithm

[0111] Diameter at breast height and accuracy evaluation of diameters at different heights

[0112] The DBH values ​​and diameters at different heights of 71 trees surveyed in the field were used as the true values ​​to compare with the values ​​extracted by the DB algorithm. 2 ) and the root mean square error (RMSE) were used to evaluate the results (Formula (17-18)).

[0113]

[0114] Among them, Y i represents the true value of the field survey; represents the diameter calculated by the DB algorithm; n represents the number of trees; and Y max Y min The mean, maximum, and minimum values ​​of Y i .

[0115] Calculation results of diameter at breast height and diameters at different heights

[0116] The extracted DBH is compared with the true value ( Figure 4 ), R 2 is 0.995, and the RMSE is 0.55cm. Compared with the true values, the inversion accuracy of the extracted diameters at different heights gradually decreases with the increase of the point cloud height ( Figure 5 ). Below 4 / 10, the inverted R 2 are all greater than 0.9; between 4 / 10 and 6 / 10, the inverted R 2 The inversion accuracy is low at more than 6 / 10 locations, mainly because the ground-based lidar cannot scan the point cloud at high altitudes, resulting in data loss and reduced accuracy. When there is sufficient point cloud data, the algorithm can reliably extract diameters at different altitudes.

[0117] The above describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, from all points of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and range of equivalents of the claims are included in the present invention. Any reference signs in the claims should not be construed as limiting the claim to which they relate.

[0118] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A single tree diameter estimation method based on a double-constrained convex hull algorithm, characterized by: The following steps are involved: S101: Data Collection The main tree species studied was Pinus massoniana. The point cloud was collected using a FARO Focus3D terrestrial 3D laser scanner, using a multi-station stitching method based on a public target sphere. S102: Data Preprocessing Point cloud preprocessing is completed using the Python point cloud processing library Open3D. To avoid the reduction in computational efficiency caused by the large amount of data from the ground-based lidar, voxel downsampling is used to process the original ground-based lidar. The specific principle of this method is as follows: Formulas (1)-(3): Step 1: First, based on the point cloud coordinate set, obtain the maximum and minimum boundary coordinates X of the point cloud 3D max ,Y max ,Z max ,X min ,Y min ,Z min , and set the voxel side length r; Step 2: Solve the minimum bounding box side length L based on the extreme values ​​of each dimension coordinate x ,L y ,L z ; Step 3: Calculate the voxel grid size D based on the bounding box side length and voxel side length x ,D y ,D z : in Indicates rounding down; Step 4: Calculate the index M of each point in the voxel unit: Step 5: Calculate the centroid of each voxel unit and use the centroid coordinates to replace all points in the unit to complete point cloud downsampling while ensuring that the point cloud distribution characteristics remain unchanged; Based on the distribution of points, the voxel side length r is set to 0.1m; The open-source point cloud processing software CloudCompare was then used to manually crop the sampled ground-based point cloud data to ensure that the branch and leaf point clouds were separated and the trunk point cloud was preserved. Through morphological comparison and screening, 71 typical trees with different morphologies were finally selected as experimental subjects; S103: Tree Trunk Point Cloud Layered Slicing Algorithm In order to extract the trunk diameters at different heights, a tree trunk point cloud hierarchical slicing algorithm was designed using Python. The pseudo code of the algorithm is as follows: The point cloud slices are intercepted by judging the relative position between the point cloud coordinates and different heights and the slice thickness; S104: Double Constrained Convex Hull Algorithm Based on the Graham convex hull algorithm, a double-constrained convex hull algorithm is proposed, which mainly improves the Graham convex hull algorithm. The point cloud obtained by slicing in step S103 is input one by one into the optimization algorithm to complete the precise extraction of the boundary and fit the trunk diameter at that location according to the area.

2. The method according to claim 1, wherein: Step S104: The convex hull optimization algorithm controlled by the distance threshold in the double-constrained convex hull algorithm is specifically as follows: In a given space R n For a set of finite points S, the convex hull Conv(S) is the set of all convex combinations of S, that is (Formula (4)): Where S={x1,x2,...,x k } is a set of points, point x i Located in R n ;λ i is satisfied The non-negative coefficient of ; The convex hull describes the boundary of a scattered point set well due to its geometric properties. The convex hull calculation methods include Graham scanning method and Jarvis stepping method. Step 1: Use Graham to establish the original convex hull and optimize the convex hull shape based on it; the Graham scanning method is established as follows; For a scattered point set S, find a point P1 such that P1 is the outermost point of the entire point set; starting from point P1, calculate the polar angle between P1 and other points respectively, and sort them according to the polar angle size and the distance from P1; connect the points in order, and determine the concavity of the next point according to the vector cross product (Equation (5)): Wherein, vectors AB and AC represent the vectors consisting of the starting scanning point and any two fixed points; when CP>0, AB rotates counterclockwise along AC, and when CP<0, AB rotates clockwise along AC; according to the above process, the outermost convex hull boundary is determined point by point, all boundary points are obtained, and finally the Graham convex hull is established; Step 2: Optimize the convex hull algorithm. Based on the original Graham convex hull boundary points, further characterize the distribution boundary of the points. The core idea of ​​the algorithm is to use the point set X(P1, P2, ..., P n ) in the convex hull set S formed by , continuously searching for new boundary points according to the operation rules until no new boundary points are generated, thereby optimizing the convex hull; 1) Obtain two adjacent boundary points one by one in a cyclic manner, and draw a circle with the Euclidean distance between the two points as the radius; 2) Add the non-boundary points contained in the circle to the set of undetermined internal points, find the outermost internal point by comparing the cosine value of the angle between the vectors, add it to the set of boundary points, and generate new boundary points (Equation (6)); 3) Gradually approximate the convex hull shape in the same way until there are no internal points in the circle established by the two points; at the same time, in order to improve the efficiency of the algorithm, the side lengths of the two boundary points are introduced as thresholds to improve the accuracy of the convex hull while ensuring the running speed; Step 3: Based on the optimized convex hull boundary points, calculate the area of ​​the single-layer convex hull using the discretized Green's theorem. Green's theorem describes the relationship between the interior of a figure enclosed by a curve on a plane and the integral on the curve, and is often used to calculate the area enclosed by a curve. The discretized Green's theorem is a discretized expression of Green's theorem. Sort the generated convex hull in counterclockwise direction. At this time, for the S vertices of the convex set (x1,y1),(x2,y2),...,(x n ,y n ), the area calculation formula is (Formula (7)): Where, Area is the convex hull area calculated by the optimized convex hull algorithm, (x i ,y i ) The coordinates of the convex hull vertices arranged in counterclockwise order, where n is the number of convex hull points; the initial point is usually repeatedly added to the end of the point set to close the polygon; Step 4: Based on the single-layer point cloud area of ​​the tree trunk solved above, the diameter of the single layer of the tree trunk is inversely calculated according to the circle area formula. The diameter solution formula is (Equation (8)): Where d is the diameter of a single-layer trunk, and Area is the convex hull area of ​​a single layer.

Images