Foundation point cloud filtering method for dense tree scene
By identifying tree trunk breakpoints on the scan line and using the Douglas-Puk algorithm to constrain the ground filtering range, the problem of insufficient ground point cloud filtering accuracy in densely wooded scenes is solved, achieving higher precision forest ground point extraction.
Patent Information
- Application Number
- CN202511409845.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-29
- Publication Date
- 2025-12-30
AI Technical Summary
Existing filtering methods struggle to effectively distinguish between ground and non-ground points in densely wooded scenes, resulting in insufficient ground filtering accuracy in forest scenes.
By identifying the junction of tree trunks and the ground as breakpoints on the scan line, and using projection density and the Douglas-Puk algorithm to constrain the ground filtering range, ground candidate points that meet the height threshold are extracted. Combined with the cloth filtering method, accurate extraction of ground points is achieved.
It significantly improves the ground filtering accuracy in forest scenes, avoids misidentification of distant non-ground points, and optimizes the filtering results.
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Figure CN121236401A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of ground filtering processing, specifically relating to a ground-based point cloud filtering method for densely wooded scenes. Background Technology
[0002] Laser point cloud data refers to the discrete points with three-dimensional coordinate information obtained by LiDAR (Light Detection and Ranging) scanners measuring objects using rapidly emitted laser pulses. Based on different scanning heights, this data can be categorized into spaceborne data, airborne data, and ground-based data. Forest data acquired through different scanning methods emphasizes different information from different perspectives. Ground-based scan data contains rich understory information, such as tree trunks and forest topography, and is typically used for small to medium-scale measurements. It has a relatively high point cloud density, providing more realistic and high-quality point cloud data, which helps to reconstruct the details of the three-dimensional scene. Airborne and spaceborne data have wide coverage areas, including information on the top layer of the tree canopy, and can be used to calculate forest height.
[0003] Point cloud filtering, also known as ground filtering (GF), refers to the process of distinguishing the ground from ground features in massive point clouds acquired by LiDAR. Ground filtering improves data quality; this step filters out noise and outliers in the point cloud data, increasing data accuracy and distinguishing ground points from non-ground points. The filtering results provide reliable data for applications such as terrain reconstruction, power line inspection, and forestry surveys. Existing ground filtering methods are mainly divided into supervised and unsupervised classification methods. Learning-based methods, such as traditional machine learning using manually labeled samples, can achieve ground filtering. Deep learning-based ground filtering research focuses on processing different input data formats such as 2D images, 3D images, and voxels, offering higher processing efficiency.
[0004] Traditional filtering methods are currently the mainstream ground filtering methods. Traditional filtering algorithms are mainly developed from airborne lidar measurement (Airbone-Based LiDAR) and are mainly based on slope, mathematical morphology, segmentation clustering, progressive (refined) triangulation filtering (PTD), cloth filtering (CSF), adaptive threshold filtering methods proposed to address the limitations of single method thresholds, and combined methods proposed to address the limitations of single methods.
[0005] Slope-based filtering methods, after determining the current target point, calculate the slope value point-by-point for neighboring points. The accuracy of the filtering result depends on the reasonableness of the threshold setting. Many scholars have proposed various methods for determining the slope threshold. To improve algorithm efficiency, Shan and...
[0006] Aparajithan (2005) utilized scanline information and slope parameters calculated based on one-dimensional point cloud profiles. Wang and Tseng (2014) transformed the concepts of adaptive slope and directional filtering into a bidirectional slope-based filter to improve the over-filtering problem. Lindenberger of the University of Stuttgart, Germany, proposed a morphological method in 1993, which was then used for ground filtering (PMF). The effectiveness of this algorithm depends on the selected window size. If the window is too small, some large buildings and trees may not be removed; if the window is too large, the result will be too smooth and lose details, and the error result will also be too large. The progressively encrypted triangular mesh filtering (PTD) proposed by Axelsson is also widely used. This method first obtains ground seed points, then builds an irregular triangular mesh and iteratively encrypts it, and judges whether the slope and vertical distance between any point in the triangle and its nearest point meet the threshold requirements, thus filtering ground points in the local plane. The Cloth Simulation Filter (CSF) proposed by Zhang Wuming et al. inverts the point cloud and uses a rigid cloth to cover the inverted surface, analyzing the interactions between grid nodes to obtain an approximate ground and separate ground points from non-ground points. This method has achieved many application results in different scenarios. For example, Yang Anxiu et al. proposed a bilateral cloth filter (Yang A, 2020) BCSF to obtain seabed topography; Chang Bingtao et al. proposed a line element cloth filter (Chang B, 2024) method (ALCSF) for ICESat-2 data. For large-scale spaceborne data, it introduces constraint features such as slope to effectively separate the canopy and achieve tree canopy identification in large-scale spaceborne data.
[0007] Existing filtering methods are typically designed for airborne laser point clouds, with the default horizontal range being similar to the ground range. However, in forest-based laser point clouds, due to severe forward occlusion (mainly from tree trunks) in the forest scene, the ground range in the acquired point cloud is much smaller than the non-ground range. Existing filtering methods will misidentify a large number of non-ground points as ground, resulting in insufficient accuracy. Summary of the Invention
[0008] To address the shortcomings of existing technologies, this invention aims to provide a ground-based point cloud filtering method for densely wooded scenes. This method can effectively adapt to ground filtering tasks in forest scenes, utilizes the occlusion effect of tree trunks to determine the ground filtering range in forest scenes, obtains ground seed points segmented on each scan line primitive to fit the ground reference curve, extracts ground candidate points that meet the height threshold, and finally achieves ground filtering through feature selection, effectively avoiding the influence of misidentification of distant non-ground points and significantly improving filtering accuracy.
[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0010] A ground-based point cloud filtering method for densely treeed scenes, the method specifically includes the following steps:
[0011] S1. Scan line number: Calculate the horizontal angle of the projection point of the original coordinates of the point cloud onto the XY plane, and use the horizontal angular resolution of the scanning device to scan the line point by point and number it;
[0012] S2. Scan line breakpoint identification: The point where the tree trunk meets the ground is called the breakpoint. The breakpoint is identified by using projection density. That is, on each scan line, the projection density is calculated sequentially according to different distance windows. The maximum projection density is found, and the point in the corresponding window is the candidate breakpoint. The candidate breakpoints of each scan line are merged to obtain the candidate breakpoint set.
[0013] S3. Ground filtering with breakpoint partition constraints: The points on the scan line are sorted according to the vertical angle of each point relative to the scan center. The dense point cloud before the first breakpoint directly participates in ground filtering. The point cloud after the last breakpoint usually belongs to the tree trunk and canopy. Due to forward occlusion, no ground points are collected and it is directly removed. For other breakpoint intervals, the Douglas-Peucker Algorithm (DP) is used to perform coarse removal of flat areas to obtain ground candidate points, and then ground points are extracted through ground filtering.
[0014] Furthermore, the scan line numbering in step S1 specifically includes:
[0015] Calculate the horizontal angle of the projection of the original point cloud coordinates (x, y, z) onto the XY plane; for the horizontal angle of each point, use the horizontal angular resolution θ of the scanning device. h If we divide the scan lines point by point, then we have:
[0016]
[0017] In the formula, floor represents the floor operation, and θ hi θ represents the horizontal azimuth angle of the i-th point, where n is the number of points. min SL represents the minimum azimuth angle. i This represents the scan line number corresponding to the i-th point.
[0018] Furthermore, step S2, scan line breakpoint identification, specifically includes:
[0019] The scanning line is non-penetrating and cannot collect ground points behind the tree trunk. The point where the tree trunk meets the ground is called the breakpoint. The breakpoint is identified by the projection density.
[0020] For all points p on a single scan line i Sort by horizontal distance from the origin in ascending order, and set the maximum distance to the search window to SW. max The interval between search windows is ΔSW Number of search windows n SW With each search window size SW i It can be determined by the following formula: For any point p within the scan line, calculate the distance window SW of that point within the corresponding scan line, with p as the center. i Density inside:
[0021]
[0022] In the formula, n(i) is SW i The number of point clouds within the range; for all points p on the scan line i (i.e., any point on the scan line whose horizontal distance from the origin increases sequentially) calculate the projection density and find the window corresponding to the maximum projection density:
[0023]
[0024] In the formula, SW m This represents the window corresponding to the maximum projection density within the scan line; if SW m For the first window SW1, the horizontal distance is in the range [0, SW]. m Points within [SW] are defined as candidate breakpoints; otherwise, [SW] is used as a breakpoint. m-1 SW m Points within the specified range are defined as candidate breakpoints; SW m-1 The distance window SW represents the maximum distance from the projected density. m Horizontal distance difference Δ SW The distance window; by merging the candidate breakpoints of each scan line, a set of candidate breakpoints can be obtained;
[0025] Euclidean clustering is applied to the candidate breakpoint set to obtain multiple point sets C. i , i = 1, 2, 3…m; For each C i Projecting onto the XY plane, calculate the perimeter and area of the projected data, and then calculate its compactness:
[0026]
[0027] In the formula, S i and P i They are point clusters C i Area and perimeter of the projection; Compactness i Represents point cluster C i The compactness value is 1, indicating a standard circle as the projection, while a value close to 0 indicates a linear projection; only compactness is retained. i Clusters of points with a value greater than 0.5 and a number of points not less than 10 are used as breakpoint sets. These sets have a shape similar to the arc of the tree trunk. The points that are removed mainly come from abrupt changes in density on slopes and embankments or discrete noise points.
[0028] Furthermore, the ground filtering for breakpoint partition constraints in step S3 specifically includes:
[0029] After step S2, multiple breakpoints may still be detected on a single scan line, some of which are not defined breakpoints. These breakpoints form different intervals on the scan line, requiring different processing strategies for different breakpoint intervals on the same scan line.
[0030] The points are sorted according to the vertical angle of each point on the scan line relative to the scan center. The point cloud before the first break point usually contains a large number of ground points. This part of the data directly participates in ground filtering and is marked as point set P1. The point cloud after the last break point usually belongs to the tree trunk and canopy. Due to forward occlusion, no ground points are collected and it is directly removed.
[0031] For other breakpoint intervals, the Douglas-Puk algorithm is used to coarsely remove flattened areas; the points between the first and last breakpoints are regarded as the set of curve points to be simplified, and the Douglas-Puk algorithm is applied to simplify them into several line segments.
[0032] Evaluate the angle between each line segment and the horizontal direction. If it is less than the threshold T1, mark it as an approximate ground point and denote it as point set P2; otherwise, discard it.
[0033] Finally, the remaining point cloud set P2 after filtering is merged with the point cloud set P1 before the first breakpoint, and then ground voids caused by tree trunk occlusion and steeply tilted features that are obviously not part of the ground are removed to obtain a candidate ground point set; ground point cloud is extracted by cloth filtering based on the candidate ground point set.
[0034] Furthermore, the Douglas-Puk algorithm simplifies the curve by recursively partitioning it while preserving its overall shape. The specific steps are as follows:
[0035] 1) Connect the first and last points to form a baseline, and find the point among the middle points that is farthest from the baseline;
[0036] 2) If the distance to the point exceeds the threshold, retain the point and split the curve, recursively processing the sub-segments;
[0037] 3) Otherwise, discard all intermediate points and keep only the first and last points.
[0038] The beneficial effects of this invention are as follows:
[0039] 1. This invention addresses ground filtering tasks in forest scenes, taking into full account the occlusion problem caused by trees under the trees. By extracting tree trunk breakpoints on the planar scan line, the horizontal range of ground filtering is constrained, thereby improving filtering accuracy.
[0040] 2. This invention is effectively applicable to forest scenarios, can optimize filtering results, constrain the range of ground filtering based on the tree trunk breakpoints on the scan line, avoid the influence of misidentification of distant non-ground points, and improve accuracy. Attached Figure Description
[0041] Figure 1 This is a diagram illustrating the projection density calculation of the present invention;
[0042] Figure 2 This is a diagram illustrating the compactness calculation of the present invention;
[0043] Figure 3 This invention's partitioning processing strategy diagram;
[0044] Figure 4 This is a forest-based laser point cloud identification map using existing methods. Detailed Implementation
[0045] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are for illustrative purposes only and are not intended to limit the scope of the invention.
[0046] This invention proposes a ground-based point cloud filtering method for densely wooded scenes. Specifically designed for ground filtering tasks in forest scenes, it fully considers the occlusion problem of trees under the canopy. By extracting tree trunk breakpoints along a planar scan line, it constrains the horizontal range of ground filtering, thereby improving filtering accuracy. The method specifically includes the following steps:
[0047] Step S1. Scan Line Numbering: Calculate the horizontal angle of the projection of the original point cloud coordinates onto the XY plane, and number the scan lines point by point using the horizontal angular resolution of the scanning device. Specifically, this includes:
[0048] Calculate the horizontal angle of the projection of the original point cloud coordinates (x, y, z) onto the XY plane; for the horizontal angle of each point, use the horizontal angular resolution θ of the scanning device. h If we divide the scan lines point by point, then we have:
[0049]
[0050] In the formula, floor represents the floor operation, and θ hi θ represents the horizontal azimuth angle of the i-th point, n represents the number of points in the data, and θ min SL represents the minimum azimuth angle. i This represents the scan line number corresponding to the i-th point.
[0051] Step S2. Scan Line Breakpoint Identification: The point where the tree trunk meets the ground is called a breakpoint. Breakpoints are identified using projection density. Specifically, on each scan line, the projection density is calculated sequentially according to different distance windows. The point with the maximum projection density is identified, and the corresponding point within that window is considered a candidate breakpoint. The candidate breakpoints for each scan line are merged to obtain a candidate breakpoint set. This includes:
[0052] The scanning line is non-penetrating and cannot collect ground points behind the tree trunk. The point where the tree trunk meets the ground is called the breakpoint. The breakpoint is identified by the projection density.
[0053] For all points p on a single scan line i Sort the data by horizontal distance from the origin (i.e., the scan center) from smallest to largest, and set the maximum distance from the search window to SW. max The interval between search windows is Δ SW Number of search windows n SW With each search window size SW i It can be determined by the following formula; such as Figure 1 As shown, for any point p within the scan line, calculate the position of that point in SW with p as the center. i Density inside:
[0054]
[0055] In the formula, n(i) is SW i The number of point clouds within the range; for all points p on the scan line i Calculate the projection density and find the window corresponding to the maximum projection density:
[0056]
[0057] In the formula, SW m This represents the window corresponding to the maximum projection density within the scan line; if SW m For the first window SW1, the horizontal distance is in the range [0, SW]. m Points within [SW] are defined as candidate breakpoints; otherwise, [SW] is used as a breakpoint. m-1 SW m Points within the specified range are defined as candidate breakpoints; SW m-1 The distance window SW represents the maximum distance from the projected density. m Horizontal distance difference Δ SW The distance window; by merging the candidate breakpoints of each scan line, a set of candidate breakpoints can be obtained;
[0058] Euclidean clustering is applied to the candidate breakpoint set to obtain multiple point sets C. i , i = 1, 2, 3…m; For each C i Project the data onto the XY plane and calculate the perimeter and area of the projection data, such as... Figure 2 As shown ( Figure 2 (The left side represents the projection of the point cluster, the middle side represents the perimeter, and the right side represents the area), and then its compactness is calculated:
[0059]
[0060] In the formula, S i and P i They are point clusters C i Area and perimeter of the projection; Compactness i Represents point cluster C i The compactness value is 1, indicating a standard circle as the projection, while a value close to 0 indicates a linear projection; only compactness is retained. i Clusters of points with a value greater than 0.5 and a number of points not less than 10 are used as breakpoint sets. These sets have a shape similar to the arc of the tree trunk. The points that are removed mainly come from abrupt changes in density on slopes and embankments or discrete noise points.
[0061] Step S3. Ground filtering with breakpoint partition constraints: Points on the scan line are sorted according to their vertical angle relative to the scan center. Dense point clouds before the first breakpoint directly participate in ground filtering. Point clouds after the last breakpoint typically belong to tree trunks and canopies; due to forward occlusion, no ground points are collected, and these are directly discarded. For other breakpoint intervals, the Douglas-Peucker Algorithm (DP) is used for coarse removal of flat areas to obtain candidate ground points, which are then extracted through ground filtering. Specifically, this includes:
[0062] After step S2, multiple breakpoints may still be detected on a single scan line, some of which are not defined breakpoints. These breakpoints form different intervals on the scan line, requiring different processing strategies for different breakpoint intervals within the same scan line. The partitioning processing strategy is as follows: Figure 3 As shown.
[0063] The points are sorted according to the vertical angle of each point on the scan line relative to the scan center. The point cloud before the first break point usually contains a large number of ground points. This part of the data directly participates in ground filtering and is marked as point set P1. The point cloud after the last break point usually belongs to the tree trunk and canopy. Due to forward occlusion, no ground points are collected and it is directly removed.
[0064] For other breakpoint intervals, the Douglas-Peucker Algorithm (DP) is used for coarse removal of flattened regions. The DP algorithm is a classic algorithm for curve simplification, which simplifies the curve by recursively segmenting it while preserving its overall shape. Its specific steps are as follows:
[0065] 1) Connect the first and last points to form a baseline, and find the point among the middle points that is farthest from the baseline;
[0066] 2) If the distance to the point exceeds the threshold, retain the point and split the curve, recursively processing the sub-segments;
[0067] 3) Otherwise, discard all intermediate points and keep only the first and last points.
[0068] The points between the first and last breakpoints are considered as the set of curve points to be simplified, and the Douglas-Puk algorithm is applied to simplify them into several line segments.
[0069] Evaluate the angle between each line segment and the horizontal direction. If it is less than the threshold T1, mark it as an approximate ground point and denote it as point set P2; otherwise, discard it. Finally, merge the remaining point cloud set P2 with the point cloud set P1 before the first breakpoint, and then remove ground voids caused by tree trunk occlusion and steeply tilted features that are obviously not part of the ground (such as tree trunks) to obtain candidate ground point sets. For candidate ground point sets, use cloth filtering to extract ground point clouds.
[0070] like Figure 4 As shown, due to severe forward occlusion in forest scenes, the ground area in the collected point cloud is much smaller than the non-ground area. Existing filtering methods misidentify a large number of non-ground points as ground, leading to insufficient accuracy. This invention proposes a scanline-based filtering method that utilizes the occlusion effect of tree trunks to determine the ground filtering range in forest scenes. Ground seed points are obtained segmentally on each scanline primitive to fit a ground reference curve, extracting ground candidate points that meet a height threshold, and finally achieving ground filtering through feature selection. This invention is applicable to forest scenes, can optimize filtering results, and constrains the ground filtering range based on tree trunk breakpoints on the scanline, avoiding the influence of misidentification of distant non-ground points and significantly improving filtering accuracy.
[0071] Obviously, the embodiments described above are only some embodiments of this application, not all embodiments. The accompanying drawings show preferred embodiments of this application, but do not limit the patent scope of this application. This application can be implemented in many different forms; rather, the purpose of providing these embodiments is to provide a more thorough and comprehensive understanding of the disclosure of this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this application's specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the scope of patent protection of this application.
Claims
1. A ground point cloud filtering method for tree dense scene, characterized in that: The method specifically comprises the following steps: S1. Scan line numbering: calculating the horizontal angle of the original coordinate of the point cloud in the XY plane projection point, and dividing the scan line point by point by using the horizontal angle resolution of the scanning device; S2. Scan line breakpoint identification: the intersection point of the trunk and the ground is called a breakpoint, and the projection density is used to identify the breakpoint; that is, on each scan line, the projection density is calculated in turn according to different distance windows, and the maximum value of the projection density is found out, and the point in the window is the candidate breakpoint, and the candidate breakpoints of each scan line are combined to obtain the candidate breakpoint set; S3. Breakpoint partition constraint ground filtering: according to the vertical angle of each point on the scan line relative to the scanning center, the dense point cloud before the first breakpoint directly participates in the ground filtering, and the point cloud after the last breakpoint usually belongs to the trunk and the canopy, and the ground points cannot be collected due to the front occlusion, and are directly removed; for other breakpoint intervals, the Douglas-Pok algorithm is used for rough removal of flat areas to obtain ground candidate points, and then the ground points are extracted through ground filtering.
2. The method of filtering a ground point cloud for a tree dense scene according to claim 1, wherein: Step S1 scan line numbering specifically comprises: The horizontal angle of the XY plane projection point of the original coordinate (x, y, z) of the point cloud is calculated; for the horizontal angle of each point, the horizontal angle resolution θ of the scanning device is utilized h Point-by-point scanning line division, then: In the formula, floor represents a down rounding operation, θ hi represents the horizontal azimuth angle of the i-th point, n represents the number of points in the data, θ min represents the minimum azimuth angle, SL i represents the scan line number corresponding to the i-th point.
3. The method of filtering a ground point cloud for a tree dense scene according to claim 2, wherein: Step S2 scan line breakpoint identification specifically comprises: The scan line has non-penetration, and the ground points cannot be collected behind the trunk, and the intersection point of the trunk and the ground is called a breakpoint, and the projection density is used to identify the breakpoint; For all points p on a single scan line i Sort by horizontal distance from the origin in ascending order, and set the maximum distance to the search window to SW. max The interval between search windows is Δ SW Number of search windows n SW With each search window size SW i It can be determined by the following formula: For any point p within the scan line, with p as the center, calculate the position of that point in SW. i Density inside: where n(i) is the SW i number of point clouds in the range; for all points p on the scan line i Calculate the projection density, find the window corresponding to the maximum projection density: where SW m represents the window corresponding to the maximum projection density in the scanning line; if SW m corresponds to the first window SW1, then the points with horizontal distance in [0, SW m ] are defined as candidate breakpoints, otherwise the points with horizontal distance in [SW m-1 , SW m ] are defined as candidate breakpoints; SW m-1 represents the distance window corresponding to the maximum projection density in the scanning line; SW m represents the distance window corresponding to the horizontal distance difference Δ SW ; the candidate breakpoints of each scanning line are combined to obtain a candidate breakpoint set; Euclidean clustering is used on the candidate breakpoint set to obtain multiple point sets C i , i = 1, 2, 3…m; each C i is projected to the XY plane, and the perimeter and area of the projected data are calculated respectively, and then the compactness is calculated. Compactness i = 4πS i / P i 2 (6) In the formula, S i and P i They are point clusters C i Area and perimeter of the projection; Compactness i Represents point cluster C i The compactness value is 1, indicating a standard circle as the projection, while a value close to 0 indicates a linear projection; only compactness is retained. i Clusters of points with a value greater than 0.5 and a number of points not less than 10 are used as breakpoint sets. These sets have a shape similar to the arc of the tree trunk. The points that are removed mainly come from abrupt changes in density on slopes and embankments or discrete noise points.
4. The method of filtering a ground point cloud for a tree dense scene according to claim 3, wherein: Step S3 breakpoint partition constraint ground filtering specifically comprises: After step S2, the next scan line may still detect multiple breakpoints, some of which are not the breakpoints defined; these breakpoints form different intervals on the scan line, and different processing strategies are needed for different breakpoint intervals of the same scan line; According to the vertical angle of each point on the scan line relative to the scanning center, the point cloud before the first breakpoint usually contains a large number of ground points, and this part of data directly participates in the ground filtering and is marked as point set P1; the point cloud after the last breakpoint usually belongs to the trunk and the canopy, and the ground points cannot be collected due to the front occlusion and are directly removed; For other breakpoint intervals, the Douglas-Pok algorithm is used for rough removal of flat areas; the points between the first and last breakpoints are regarded as a to-be-simplified curve point set, and the Douglas-Pok algorithm is applied to simplify it into several line segments; Evaluate the angle between each line segment and the horizontal direction, if it is less than a threshold T1, it is marked as an approximate ground point, and is recorded as point set P2; otherwise, it is removed; Finally, the remaining point cloud set P2 and the point cloud set P1 before the first breakpoint are combined, and then the ground hollow area caused by the trunk occlusion and the large inclination ground objects obviously not belonging to the ground are removed to obtain the candidate ground point set; facing the candidate ground point set, the cloth filtering is used to extract the ground point cloud.
5. The method of filtering a ground point cloud for a tree dense scene according to claim 4, wherein: The Douglas-Pok algorithm simplifies the curve by recursive segmentation, while maintaining the overall shape, and the specific steps are as follows: 1) Connect the first and last points to form a baseline, and find the point farthest from the baseline among the intermediate points; 2) If the distance exceeds the threshold, keep the point and divide the curve, and recursively process the sub-segments; 3) Otherwise, discard all intermediate points and only keep the first and last points.