Arc feature automatic extraction and fitting method and system based on three-dimensional point cloud

Abstract

The invention provides a three-dimensional point cloud-based arc feature automatic extraction and fitting method. The method comprises the steps of collecting and preprocessing target three-dimensional point cloud data; converting the point cloud data into a triangular mesh model; extracting an outer boundary point cloud from the triangular mesh model; thirdly, projecting the three-dimensional outer boundary point cloud to an optimal two-dimensional plane by adopting principal component analysis, detecting an arc section based on a self-adaptive sliding window, performing quality optimization on the extracted arc section point cloud through endpoint trimming, angle continuity inspection and quality evaluation, screening high-quality arc section point cloud, and obtaining a high-quality arc section point cloud; and carrying out overall circle fitting on the optimized arc segment point cloud to realize accurate extraction of arc features. The method solves the problems that a traditional method is low in arc detection precision and poor in noise immunity in complex point clouds, the accuracy and robustness of arc feature extraction are remarkably improved, and the method can be widely applied to the fields of industrial detection, reverse engineering and three-dimensional modeling.

Description

Technical Field

[0001] This invention relates to the fields of computer vision and 3D point cloud processing technology, specifically to a method and system for automated extraction and fitting of circular arc features based on 3D point clouds. Background Technology

[0002] In fields such as 3D scanning, reverse engineering, and computer vision, point cloud data serves as the primary carrier of geometric information about object surfaces, making its processing and analysis crucial. Accurately extracting specific geometric features, such as arcs, from point clouds is of core value for applications like industrial inspection, workpiece recognition, dimensional measurement, and 3D reconstruction. However, existing point cloud arc extraction technologies face a series of significant challenges, often resulting in extraction results that fail to meet practical requirements in terms of accuracy, robustness, and usability.

[0003] First, the inherent characteristics of point cloud data present a fundamental challenge to arc extraction. Due to factors such as scanning equipment precision, object surface material, and environmental interference, the acquired point clouds often contain noise, uneven density, or even missing data, which severely interfere with the recognition of arc features. More importantly, real-world arc features are often not mathematically perfect complete circles, but rather partial arc segments that are incomplete, occluded, or connected to other geometric features. This makes traditional detection methods based on complete circle models (such as the standard Hough transform) difficult to apply directly, as they have excessively high requirements for data integrity and quality, high computational complexity, and are prone to false positives and false negatives.

[0004] Existing methods also have shortcomings in the arc fitting stage. Commonly used methods such as Random Sample Consensus (RANSAC) or least squares fitting are very sensitive to initial parameter settings and have poor robustness to outliers (such as boundary points that do not belong to the arc). Especially for shorter arc segments, the fitting results are extremely unstable, and the estimated values ​​of the center and radius are prone to large deviations. More importantly, there is a lack of an effective mechanism to automatically evaluate the quality of the extracted arc segments, making it impossible to determine whether a set of points truly originates from a geometric arc or is just randomly arranged into an arc. This often leads to invalid fitting results being mistakenly identified as successful in subsequent processing.

[0005] Another key challenge lies in the adaptive adjustment of parameters. Point cloud data vary greatly in size, density, and distribution, while existing arc extraction algorithms typically rely on a fixed set of parameters. This leads to unstable performance and a lack of generalization ability when processing data from different scenarios. For example, for sparse point clouds, an excessively large window may fail to capture effective arc segments; while for dense point clouds, an excessively small window may fail to obtain stable fitting results, requiring repeated manual adjustment of parameters, a tedious process that relies heavily on experience.

[0006] Furthermore, when the target circle is composed of multiple discontinuous arc segments, how to automatically identify and merge these segments belonging to the same circle is a problem that has not yet been well solved. Existing methods usually process each arc segment in isolation, lacking a global perspective, and it is difficult to correctly associate multiple scattered arc segments that may come from the same circumference, thus failing to reconstruct a complete and accurate circle.

[0007] Therefore, there is an urgent need in this field for a point cloud arc extraction method that can overcome the above-mentioned defects. This method should be able to automatically adapt to different point cloud characteristics, robustly identify partial arc segments from noisy data, intelligently evaluate the fitting quality, and effectively fuse multiple arc segments to fit a complete circle. Summary of the Invention

[0008] To address the problems of low accuracy, poor adaptability, and strong parameter dependence in existing point cloud arc feature extraction methods, this invention proposes an automated arc feature extraction and fitting method and system based on 3D point clouds. This method combines adaptive sliding window and topology analysis. The core of the method is to use an adaptive sliding window algorithm to traverse a 2D boundary point sequence, dynamically detect, expand, and optimize arc segments. Then, the quality of the arc segments is optimized, low-quality segments are filtered out, and finally, the extracted high-quality arc segments are merged to fit a complete circle, obtaining relevant parameters such as the center coordinates and radius, thus achieving accurate detection of the current arc.

[0009] This invention aims to effectively improve the automation, accuracy, and robustness of point cloud arc feature extraction, so that it can be widely applied to fields with high requirements for geometric feature extraction, such as industrial inspection, cultural relic digitization, and reverse engineering.

[0010] To achieve the above-mentioned technical objectives, the present invention provides the following technical solution: An automated method for extracting and fitting circular arc features based on 3D point clouds, specifically including: Manually select a point cloud region containing the target arc from the existing point cloud, and obtain the three-dimensional point cloud data of the target arc from it; Completeness and validity checks are performed on the 3D point cloud data of the target arc; A greedy projection triangulation algorithm is used to mesh the 3D point cloud data that has undergone integrity and validity checks, resulting in a triangular mesh model. Extract the three-dimensional outer boundary point cloud representing the outer contour of the target circular arc from the triangular mesh model; Principal component analysis is performed on the 3D outer boundary point cloud to determine the optimal 2D projection plane; the 3D outer boundary point cloud is then projected onto the optimal 2D projection plane to obtain a 2D planar point cloud sequence. An adaptive algorithm based on a sliding window is used to perform initial detection on a two-dimensional planar point cloud sequence to extract arc segment point clouds under different point cloud states; Each extracted arc segment point cloud is subjected to quality optimization to obtain a high-quality arc segment point cloud; the quality optimization includes endpoint trimming, angle continuity check and quality assessment; The optimized arc segment point cloud is fitted with a whole circle to calculate the center coordinates, radius, and fitting residual of the circle containing the target arc. The fitting quality is evaluated to achieve accurate extraction of the target arc.

[0011] Furthermore, the extraction of the three-dimensional outer boundary point cloud representing the outer contour of the target circular arc from the triangular mesh model specifically involves: Traverse all edges of the triangular mesh and count the number of times each edge is shared by adjacent triangles; determine the edge that is shared by only one triangle as a boundary edge; connect all boundary edges according to their adjacency to form one or more closed loops; select the closed loop with the most points from all closed loops as the outer boundary of the target elliptical groove point cloud, and extract the corresponding points from the mesh vertices to form a three-dimensional outer boundary point cloud. It detects hole areas in the triangular mesh and automatically determines whether they need to be filled based on the hole size and geometric features; for hole areas that need to be filled, it uses planar interpolation or surface fitting methods for intelligent filling.

[0012] Furthermore, the step of performing principal component analysis on the three-dimensional outer boundary point cloud to determine the optimal two-dimensional projection plane, and then projecting the three-dimensional outer boundary point cloud onto the optimal two-dimensional projection plane to obtain the two-dimensional plane point cloud sequence, specifically involves: Each point in the 3D outer boundary point cloud is decentered. The covariance matrix of the 3D outer boundary point cloud is calculated based on the 3D components of the coordinates of the decentered points. The eigenvalues ​​and corresponding eigenvectors are obtained by solving the covariance matrix. The eigenvector corresponding to the largest eigenvalue is taken as the first principal direction, and the eigenvector corresponding to the second largest eigenvalue is taken as the second principal direction. The 2D plane spanned by the first and second principal directions is taken as the optimal 2D projection plane. Each point after decentering is projected onto the optimal 2D projection plane, thereby transforming the shape information of the 3D outer boundary point cloud into a 2D planar curve, which yields the 2D planar point cloud sequence.

[0013] Furthermore, the initial detection of the two-dimensional planar point cloud sequence using an adaptive algorithm based on a sliding window, and the extraction of arc segment point clouds under different point cloud states, specifically includes: Based on the size, total number of points, point cloud density, shape complexity, and spatial continuity of the two-dimensional planar point cloud sequence, the initial detection parameters are dynamically estimated. The initial detection parameters include: the window size of the sliding window, the maximum allowable fitting residual, the expected range of the arc radius, and the maximum allowable gap for expansion. The sliding windows are slid sequentially on the two-dimensional plane point cloud sequence. For the point set in each sliding window, the least squares method is used to fit a circle to obtain the initial center coordinates, initial radius and fitting residual of the fitted circle for the point set in each sliding window. Candidate arc segments are selected. For each set of points in a sliding window, if the circle is successfully fitted and the fitting residual is less than the maximum allowable fitting residual, and the initial radius of the fitted circle is within the expected arc radius range, then the set of points in the current window is determined to be a candidate arc segment. For each candidate arc segment, a bidirectional expansion strategy is implemented to expand the sliding window. During the expansion of the sliding window, a progressive verification mechanism and a gap tolerance mechanism are introduced to include adjacent points that meet the candidate conditions into the candidate arc segment. Repeat the process of sliding the window, filtering candidate arc segments, and expanding the window until the entire point cloud sequence is traversed and multiple arc segment point clouds are extracted.

[0014] More specifically, the dynamic estimation of initial detection parameters based on the size, total number of points, point cloud density, shape complexity, and spatial continuity of the two-dimensional planar point cloud sequence is as follows: The bounding box of the two-dimensional planar point cloud sequence is determined by obtaining the extreme values ​​of the x-coordinate and y-coordinate of the point cloud range included in the sequence. The total number of points in the two-dimensional planar point cloud sequence is counted, and the point cloud density is obtained by dividing the total number of points by the area of ​​the bounding box. The size of the sliding window is adaptively set according to the total number of points, shape complexity, and spatial continuity. The maximum allowable fitting residual is set according to the point cloud density; the higher the density, the smaller the residual threshold. The desired arc radius range is determined according to the diagonal length of the point cloud bounding box.

[0015] More specifically, the implementation of the bidirectional expansion strategy for each candidate arc segment to expand the sliding window is as follows: starting from the starting point of the current candidate arc segment, expand in the reverse direction, and at the same time start from the ending point of the current candidate arc segment, expand in the forward direction, and add adjacent points to the point set in the sliding window in sequence.

[0016] More specifically, the incremental verification mechanism and the gap tolerance mechanism are respectively: The progressive verification mechanism is as follows: according to the expansion order, each time a new adjacent point is added, the candidate arc segment screening is performed again to determine whether the new adjacent point meets the candidate conditions. If it does, the new adjacent point is included in the candidate arc segment. The gap tolerance mechanism is as follows: if a new adjacent point does not meet the candidate conditions, the gap number is recorded once, and expansion stops only when the gap number exceeds the maximum allowable gap.

[0017] Furthermore, the endpoint trimming, angle continuity check, and quality assessment specifically include: For each arc segment point cloud extracted in the initial detection, a reference circle is obtained by refitting the circle; the distance from each point in the arc segment point cloud to the reference circle is calculated, and a dynamic threshold is set based on the mean and standard deviation of the distance; starting from both ends of the arc segment point cloud, points whose distance to the reference circle exceeds the dynamic threshold are regarded as outliers, and all outliers are removed from the arc segment point cloud to complete the endpoint trimming. An angular continuity test is performed on the point cloud of the arc segment after the endpoints are trimmed. The angle value of each point relative to the center of the circle is calculated, and jump points with discontinuous angle values ​​are detected. The point cloud of the arc segment between the jump points is retained as the effective arc range. Next, the point cloud of the arc segment after endpoint trimming and angle continuity test is evaluated for quality. Specifically, the weighted sum of fitting accuracy, point continuity, arc opening angle and average distance error is used as the comprehensive quality score, and low-quality point cloud segments with comprehensive quality scores below the preset threshold are filtered out.

[0018] Furthermore, the step of performing overall circle fitting on the optimized arc segment point cloud, calculating the center coordinates, radius, and fitting residual of the circle containing the target arc, and evaluating the fitting quality to achieve accurate extraction of the target arc specifically involves: If only one arc segment point cloud is saved, then the overall circle fitting is performed directly, and the center coordinates, radius, and fitting residual of the circle containing the target arc are calculated. If there are multiple arc segment point clouds, the arc segment point clouds are grouped based on geometric similarity, and the overall circle fitting is performed uniformly on the arc segment point clouds in the same group. The center coordinates, radius, and fitting residual of the circle containing the arc segment point clouds in each group are output. During the fitting process, the weighted least squares method is used to determine the influence of each arc segment point cloud on the overall circle fitting result of the group based on the quality assessment results of each arc segment point cloud. After the overall circle is fitted, the fitting residual analysis and error assessment are performed to calculate the overall fitting accuracy. For multiple independent arcs obtained from point clouds of different groups of arc segments, an additional relative position analysis is performed. Based on the center coordinates and radius of the circle in which each independent arc is located, it is determined whether the spatial position association and geometric constraints between multiple independent arcs meet the preset design rules. The final output is the evaluation result of the fitting quality, and the target arc is accurately extracted based on the obtained center coordinates and radius.

[0019] This invention also discloses an application system for the above method, which specifically includes a data input module, a mesh processing module, a boundary calculation module, a projection transformation module, a core detection module, an optimization filtering module, and a fitting output module, wherein: The data input module is used to collect and preprocess 3D point cloud data; The mesh processing module is used to convert 3D point cloud data into a triangular mesh model; The boundary calculation module is used to extract the three-dimensional outer boundary point cloud from the triangular mesh model; The projection transformation module is used to project the three-dimensional boundary point cloud onto a two-dimensional plane; The core detection module is used to perform adaptive detection and extract point clouds of arc segments; The optimized filtering module is used to trim endpoints and evaluate the point cloud quality of arc segments; The fitting output module is used to fuse high-quality circular arc segment point clouds and fit and output circle parameters.

[0020] Based on the above technical solution, the present invention has at least the following beneficial effects: The method proposed in this invention achieves high-precision, high-robustness, and high-efficiency arc feature recognition in point cloud data processing through innovative arc extraction and fitting methods. By employing adaptive parameter optimization technology, the sliding window size, fitting residual threshold, and radius range are dynamically adjusted based on features such as point cloud density and size distribution, ensuring optimal arc extraction results under different data conditions. Principal component analysis projection technology projects the 3D point cloud onto the optimal 2D plane, preserving key geometric features while facilitating subsequent verification and adjustment. The least squares-based circle fitting algorithm can quickly calculate the center coordinates and radius, and supports multi-arc segment fusion fitting to reconstruct a complete circular structure, making it particularly suitable for scenarios with partial occlusion or missing data. A multi-stage quality assessment system effectively filters out noise points and invalid arc segments, improving the reliability of the extraction results. This invention utilizes an intelligent endpoint detection mechanism, based on angle change analysis and distance threshold judgment, to accurately identify the start and end points of the arc, avoiding misclassification of straight lines or noise points as arc segments. Overall, this invention significantly improves the accuracy and efficiency of arc extraction, reduces the need for manual intervention, and provides reliable technical support for applications such as industrial inspection and reverse engineering. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of a triangular mesh model for the 3D point cloud transformation of the target arc in this invention; Figure 2 This is a schematic diagram of the outer boundary of the three-dimensional point cloud extracted in this invention; Figure 3 This invention aims to extract point clouds from arc segments. Figure 4 This is a schematic diagram of the overall circle fitting result based on the extracted arc segment point cloud; Figure 5 This is a schematic diagram of a sub-process of the automatic extraction and fitting method for circular arc features based on 3D point clouds proposed in this invention. Figure 6This is a schematic diagram of sub-process two of the specific process of the automated extraction and fitting method of circular arc features based on three-dimensional point clouds proposed in this invention; Figure 7 This is an overall flowchart of the method proposed in this invention. Detailed Implementation

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the following description is provided in conjunction with the accompanying drawings. Figure 1-7 The present invention will be further described in detail with reference to the embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0023] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0024] The automated extraction and fitting method for circular arc features based on 3D point clouds proposed in this invention mainly includes five core stages: point cloud collection and preprocessing, boundary extraction, projection transformation, circular arc detection, extraction and optimization, and circle fitting. The corresponding application system of this method is divided into seven modules, specifically including a data input module, a mesh processing module, a boundary calculation module, a projection transformation module, a core detection module, an optimization filtering module, and a fitting output module. The data input module is used to collect and preprocess 3D point cloud data; The mesh processing module is used to convert 3D point cloud data into a triangular mesh model; The boundary calculation module is used to extract the three-dimensional outer boundary point cloud from the triangular mesh model; The projection transformation module is used to project the three-dimensional boundary point cloud onto a two-dimensional plane; The core detection module is used to perform adaptive detection and extract point clouds of arc segments; The optimized filtering module is used to trim endpoints and evaluate the point cloud quality of arc segments; The fitting output module is used to fuse high-quality circular arc segment point clouds and fit and output circle parameters.

[0025] The system receives raw 3D point cloud data as input, processes it through multiple stages, and finally outputs accurate circular arc geometric parameters (geometric parameters of the circle containing the arc) and complete circle fitting results (such as...). Figure 4 (As shown).

[0026] Manually select a point cloud region containing the target arc from the existing point cloud, and obtain the three-dimensional point cloud data of the target arc from it; Completeness and validity checks are performed on the 3D point cloud data of the target arc; In this embodiment, the system automatically searches for 3D point cloud files of the target arc in PCD format in a specified directory and verifies the file integrity. After the integrity verification is completed and the file is successfully loaded, the system analyzes the basic characteristics of the point cloud data, such as the point cloud scale, spatial distribution range, and density distribution, to detect the validity of the point cloud data. This step ensures the quality of the initial input data and lays the foundation for subsequent processing.

[0027] A greedy projection triangulation algorithm is used to mesh the 3D point cloud data after integrity and validity checks, resulting in a triangular mesh model. This process includes key steps such as normal vector estimation, projection plane calculation, and local connectivity reconstruction. In this embodiment, by setting reasonable triangulation parameters, such as search radius, maximum neighbor count, and surface angle threshold, the generated triangular mesh model is ensured to maintain both geometric features and a good topological structure. The triangular mesh model of the target ellipse obtained in this step is shown below. Figure 1 As shown.

[0028] Extract the three-dimensional outer boundary point cloud representing the outer contour of the target circular arc from the triangular mesh model; In a preferred embodiment, the extraction of the three-dimensional outer boundary point cloud representing the outer contour of the target circular arc from the triangular mesh model specifically involves: Traverse all edges of the triangular mesh and count the number of times each edge is shared by adjacent triangles; identify edges shared by only one triangle as boundary edges; connect all boundary edges according to their adjacency to form one or more closed loops (using a depth-first search strategy to ensure the continuity and integrity of the loops); select the closed loop with the most points from all closed loops as the outer boundary of the target elliptical groove point cloud, and extract the corresponding points from the mesh vertices to form a shape like... Figure 2 The three-dimensional outer boundary point cloud is shown.

[0029] Principal component analysis is performed on the 3D outer boundary point cloud to determine the optimal 2D projection plane; the 3D outer boundary point cloud is then projected onto the optimal 2D projection plane to obtain a 2D planar point cloud sequence. This step is a crucial preprocessing step for arc extraction. By using principal component analysis, the centroid and covariance matrix of the boundary point cloud are calculated, and its eigenvalues ​​and eigenvectors are solved. The point cloud is then projected onto the corresponding two-dimensional plane. This transforms the arc extraction problem into a more manageable two-dimensional curve fitting problem while preserving the original spatial distribution characteristics to the greatest extent, significantly improving computational efficiency and accuracy.

[0030] An adaptive algorithm based on a sliding window is used to perform initial detection on a two-dimensional planar point cloud sequence to extract arc segment point clouds under different point cloud states; In a preferred embodiment, the step of using an adaptive algorithm based on a sliding window to perform initial detection on the two-dimensional planar point cloud sequence and extracting the arc segment point cloud under different point cloud states specifically includes: Based on the size, total number of points, point cloud density, shape complexity, and spatial continuity of the two-dimensional planar point cloud sequence, initial detection parameters are dynamically estimated. These initial detection parameters include: the window size of the sliding window, the maximum allowable fitting residual, the desired arc radius range, and the maximum allowable gap for expansion. The initial detection parameters are set to transition from fixed parameters to dynamic adaptive parameters, overcoming the shortcomings of traditional methods in adapting to different point clouds. In this embodiment, the dynamic estimation of initial detection parameters based on the size, total number of points, point cloud density, shape complexity, and spatial continuity of the two-dimensional planar point cloud sequence specifically involves: The bounding box of the 2D planar point cloud sequence is determined by obtaining the extreme values ​​of the x-coordinate and y-coordinate of the point cloud area included in the sequence. The total number of points in the 2D planar point cloud sequence is counted, and the point cloud density is obtained by dividing the total number of points by the area of ​​the bounding box. The size of the sliding window is adaptively set according to the total number of points, shape complexity, and spatial continuity. The maximum allowable fitting residual is set according to the point cloud density. The higher the density, the smaller the residual threshold (i.e., a smaller window and stricter threshold are used for dense point clouds, while the conditions are appropriately relaxed for sparse point clouds to ensure that the algorithm adapts to different data characteristics). The desired arc radius range is determined based on the diagonal length of the point cloud bounding box.

[0031] In this embodiment, shape complexity is used to quantify the curvature, curvature change frequency, or nonlinearity of the local or overall geometric structure of a two-dimensional planar point cloud sequence. Spatial continuity describes the degree of connection between the two-dimensional planar point cloud sequence in space, i.e., whether there are obvious breaks, sparse intervals, or outliers between points. The higher the shape complexity and the lower the spatial continuity, the larger the window should be set to avoid interruption during the sliding window process.

[0032] The sliding windows are sequentially slid across the two-dimensional planar point cloud sequence. For each point set within a sliding window, a circle is fitted using the least squares method to obtain the initial center coordinates, initial radius, and fitting residual of the fitted circle for each point set within the sliding window. Candidate arc segments are then selected. For each point set within a sliding window, if the circle fitting is successful (the fitted circle is geometrically reasonable and numerically stable), the fitting residual is less than the maximum allowable fitting residual, and the initial radius of the fitted circle is within the expected arc radius range, then the point set within the current window is determined to be a candidate arc segment. In this embodiment, each candidate arc segment is required to simultaneously satisfy the triple constraints of successful circle fitting, residual threshold, and reasonable radius to ensure the reliability of the detection results.

[0033] For each candidate arc segment, a bidirectional expansion strategy is implemented to expand the sliding window. During the expansion of the sliding window, a progressive verification mechanism and a gap tolerance mechanism are introduced to include adjacent points that meet the candidate conditions into the candidate arc segment. In this embodiment, the bidirectional expansion strategy is specifically as follows: starting from the starting point of the current candidate arc segment, expand in the reverse direction, and at the same time start from the ending point of the current candidate arc segment, expand in the forward direction, and add adjacent points to the point set in the sliding window in sequence; The progressive verification mechanism is as follows: according to the expansion order, each time a new adjacent point is added, the candidate arc segment screening is performed again to determine whether the new adjacent point meets the candidate conditions. If it does, the new adjacent point is included in the candidate arc segment. The gap tolerance mechanism is as follows: if a new adjacent point does not meet the candidate conditions, the gap number is recorded once, and expansion stops only when the gap number exceeds the maximum allowable gap.

[0034] This embodiment uses a bidirectional expansion strategy to obtain the most complete and continuous point cloud of circular arc segments. During the expansion process, a progressive verification mechanism monitors the changes in fitting quality in real time to ensure the consistency of the quality of candidate circular arc segments at all times, and immediately backs down when an anomaly is detected. The gap tolerance mechanism allows crossing a limited data missing region, thereby enabling the handling of discontinuous boundary data.

[0035] Repeat the process of sliding the window, filtering candidate arc segments, and expanding the window until the entire point cloud sequence is traversed and multiple arc segment point clouds are extracted.

[0036] In this embodiment, the point cloud of the arc segment extracted after preliminary detection is as follows: Figure 3 As shown, the extracted point cloud of each arc segment is then subjected to quality optimization to obtain a high-quality point cloud of the arc segment, thereby further improving the accuracy of arc segment detection; the quality optimization includes endpoint trimming, angle continuity verification, and quality assessment; In this preferred embodiment, the endpoint trimming, angle continuity check, and quality assessment specifically refer to: For each arc segment point cloud extracted in the initial detection, a reference circle is obtained by refitting the circle; the distance from each point in the arc segment point cloud to the reference circle is calculated, and a dynamic threshold is set based on the mean and standard deviation of the distance; starting from both ends of the arc segment point cloud, points whose distance to the reference circle exceeds the dynamic threshold are regarded as outliers, and all outliers are removed from the arc segment point cloud to complete the endpoint trimming. An angular continuity test is performed on the point cloud of the arc segment after the endpoints are trimmed. The angle value of each point relative to the center of the circle is calculated, and jump points with discontinuous angle values ​​are detected. The point cloud of the arc segment between the jump points is retained as the effective arc range (i.e., the part that is not considered to belong to the target arc is removed). Endpoint trimming and angle continuity testing significantly improve the geometric purity of the arc segment point cloud. Then, the quality of the arc segment point cloud after endpoint trimming and angle continuity testing is evaluated. Specifically, the comprehensive quality score is the weighted sum of fitting accuracy, inter-point continuity, arc opening angle, and average distance error. Low-quality point cloud segments with a comprehensive quality score below a preset threshold are filtered out. This ensures that the final retained arc segment has high geometric accuracy and broad applicability to industrial scenarios.

[0037] It should be noted that: the fitting accuracy is the normalized root mean square residual of the circle fitting; the continuity between points measures the uniformity and lack of breakage of the distance between adjacent points within the candidate arc segment; the arc opening angle is defined as the central angle corresponding to the arc, reflecting geometric significance; and the average distance error reflects the average absolute deviation of the point cloud from the fitted circle.

[0038] The optimized point cloud of the arc segment is fitted with a global circle. The center coordinates, radius, and fitting residual of the circle containing the target arc are calculated. The fitting quality is evaluated to achieve accurate extraction of the target arc. As a preferred implementation, this step specifically involves: The center coordinates, radius, and fitting residual of the circle containing the target arc are calculated, and the fitting quality is evaluated to achieve accurate extraction of the target arc. If only one arc segment point cloud is saved, then the overall circle fitting is performed directly, and the center coordinates, radius, and fitting residual of the circle containing the target arc are calculated. If there are multiple arc segment point clouds, the arc segment point clouds are grouped based on geometric similarity, and the overall circle fitting is performed uniformly on the arc segment point clouds in the same group. The center coordinates, radius, and fitting residual of the circle containing the arc segment point clouds in each group are output. During the fitting process, the weighted least squares method is used to determine the influence of each arc segment point cloud on the overall circle fitting result of the group based on the quality assessment results of each arc segment point cloud. After overall circle fitting, residual analysis and error assessment are performed to calculate the overall fitting accuracy. The results of overall circle fitting are as follows: Figure 4 As shown; for multiple independent arcs obtained from point clouds of different sets of arc segments, additional relative position analysis is performed. Based on the center coordinates and radius of the circle in which each independent arc is located, it is determined whether the spatial position relationship and geometric constraints between multiple independent arcs meet the preset design rules. The final output is the evaluation result of the fitting quality, and the target arc is accurately extracted based on the obtained center coordinates and radius.

[0039] In summary, the method proposed in this invention achieves high-precision, high-robustness, and high-efficiency arc feature recognition in point cloud data processing through innovative arc extraction and fitting methods. Overall, this invention significantly improves the accuracy and efficiency of arc extraction, reduces the need for manual intervention, and provides reliable technical support for applications such as industrial inspection and reverse engineering.

[0040] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0041] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. An automated method for extracting and fitting circular arc features based on 3D point clouds, characterized in that, Specifically, the following steps are included: Manually select a point cloud region containing the target arc from the existing 3D point cloud, and obtain the 3D point cloud data of the target arc from it; Completeness and validity checks are performed on the 3D point cloud data of the target arc; A greedy projection triangulation algorithm is used to mesh the 3D point cloud data that has undergone integrity and validity checks, resulting in a triangular mesh model. Extract the 3D outer boundary point cloud representing the outer contour of the target circular arc from the triangular mesh model; Principal component analysis is performed on the 3D outer boundary point cloud to determine the optimal 2D projection plane; the 3D outer boundary point cloud is then projected onto the optimal 2D projection plane to obtain a 2D planar point cloud sequence. An adaptive algorithm based on a sliding window is used to perform initial detection on a two-dimensional planar point cloud sequence to extract arc segment point clouds under different point cloud states; Each extracted arc segment point cloud is subjected to quality optimization to obtain a high-quality arc segment point cloud; the quality optimization includes endpoint trimming, angle continuity check and quality assessment; The optimized arc segment point cloud is fitted with a whole circle to calculate the center coordinates, radius, and fitting residual of the circle containing the target arc. The fitting quality is evaluated to achieve accurate extraction of the target arc.

2. The automated extraction and fitting method for circular arc features based on 3D point clouds according to claim 1, characterized in that, The extraction of the 3D outer boundary point cloud representing the outer contour of the target circular arc from the triangular mesh model specifically involves: Traverse all edges of the triangular mesh and count the number of times each edge is shared by adjacent triangles; determine the edge that is shared by only one triangle as a boundary edge; connect all boundary edges according to their adjacency to form one or more closed loops; select the closed loop with the most points and the largest enclosed area from all closed loops as the outer boundary of the target elliptical groove point cloud, and extract the corresponding points from the mesh vertices to form a three-dimensional outer boundary point cloud. It also detects hole areas in the triangular mesh and automatically determines whether they need to be filled based on the hole size and geometric features; for hole areas that need to be filled, it uses planar interpolation or surface fitting methods for intelligent filling.

3. The automated extraction and fitting method for circular arc features based on three-dimensional point clouds according to claim 1, characterized in that, The process of performing principal component analysis on the 3D outer boundary point cloud to determine the optimal 2D projection plane, and then projecting the 3D outer boundary point cloud onto the optimal 2D projection plane to obtain the 2D plane point cloud sequence, is as follows: Each point in the 3D outer boundary point cloud is decentered. The covariance matrix of the 3D outer boundary point cloud is calculated based on the 3D components of the coordinates of the decentered points. The eigenvalues ​​and corresponding eigenvectors are obtained by solving the covariance matrix. The eigenvector corresponding to the largest eigenvalue is taken as the first principal direction, and the eigenvector corresponding to the second largest eigenvalue is taken as the second principal direction. The 2D plane spanned by the first and second principal directions is taken as the optimal 2D projection plane. Each point after decentering is projected onto the optimal 2D projection plane, thereby transforming the shape information of the 3D outer boundary point cloud into a 2D planar curve, which yields the 2D planar point cloud sequence.

4. The automated extraction and fitting method for circular arc features based on three-dimensional point clouds according to claim 1, characterized in that, The step of using an adaptive algorithm based on a sliding window to perform initial detection on a two-dimensional planar point cloud sequence and extracting arc segment point clouds under different point cloud states specifically includes: Based on the size, total number of points, point cloud density, shape complexity, and spatial continuity of the two-dimensional planar point cloud sequence, the initial detection parameters are dynamically estimated. The initial detection parameters include: the window size of the sliding window, the maximum allowable fitting residual, the expected range of the arc radius, and the maximum allowable gap for expansion. The sliding windows are slid sequentially on the two-dimensional plane point cloud sequence. For the point set in each sliding window, the least squares method is used to fit a circle to obtain the initial center coordinates, initial radius and fitting residual of the fitted circle for the point set in each sliding window. Candidate arc segments are selected. For each set of points in a sliding window, if the circle is successfully fitted and the fitting residual is less than the maximum allowable fitting residual, and the initial radius of the fitted circle is within the expected arc radius range, then the set of points in the current window is determined to be a candidate arc segment. For each candidate arc segment, a bidirectional expansion strategy is implemented to expand the sliding window. During the expansion of the sliding window, a progressive verification mechanism and a gap tolerance mechanism are introduced to include adjacent points that meet the candidate conditions into the candidate arc segment. Repeat the process of sliding the window, filtering candidate arc segments, and expanding the window until the entire point cloud sequence is traversed and multiple arc segment point clouds are extracted.

5. The automated extraction and fitting method for circular arc features based on three-dimensional point clouds according to claim 4, characterized in that, The specific steps for dynamically estimating the initial detection parameters based on the size, total number of points, point cloud density, shape complexity, and spatial continuity of the two-dimensional planar point cloud sequence are as follows: Obtain the extreme values ​​of the x-coordinate and y-coordinate of the point cloud range included in the two-dimensional planar point cloud sequence to determine the bounding box of the two-dimensional planar point cloud sequence; count the total number of points in the two-dimensional planar point cloud sequence, divide the total number of points by the area of ​​the bounding box to obtain the point cloud density; The sliding window size is adaptively set based on the total number of points, shape complexity, and spatial continuity; the maximum allowable fitting residual is set based on the point cloud density, with a smaller residual threshold for higher density; and the desired arc radius range is determined based on the diagonal length of the point cloud bounding box.

6. The automated extraction and fitting method for circular arc features based on three-dimensional point clouds according to claim 4, characterized in that, The implementation of the bidirectional expansion strategy for each candidate arc segment to expand the sliding window specifically involves: expanding backward from the starting point of the current candidate arc segment, and simultaneously expanding forward from the ending point of the current candidate arc segment, adding adjacent points to the point set within the sliding window in sequence.

7. The automated extraction and fitting method for circular arc features based on three-dimensional point clouds according to claim 4, characterized in that, The incremental verification mechanism and the gap tolerance mechanism are respectively: The progressive verification mechanism is as follows: according to the expansion order, each time a new adjacent point is added, the candidate arc segment screening is performed again to determine whether the new adjacent point meets the candidate conditions. If it does, the new adjacent point is included in the candidate arc segment. The gap tolerance mechanism is as follows: if a new adjacent point does not meet the candidate conditions, the gap number is recorded once, and expansion stops only when the gap number exceeds the maximum allowable gap.

8. The method for automated extraction and fitting of circular arc features based on three-dimensional point clouds according to claim 1, characterized in that, The endpoint trimming, angle continuity check, and quality assessment specifically include: For each arc segment point cloud extracted in the initial detection, a reference circle is obtained by re-fitting the circle; the distance from each point in the arc segment point cloud to the reference circle is calculated, and a dynamic threshold is set based on the mean and standard deviation of the distance. Starting from both ends of the arc segment point cloud, points whose distance to the reference circle exceeds the dynamic threshold are considered outliers. All outliers are removed from the arc segment point cloud to complete the endpoint trimming. An angular continuity test is performed on the point cloud of the arc segment after the endpoints are trimmed. The angle value of each point relative to the center of the circle is calculated, and jump points with discontinuous angle values ​​are detected. The point cloud of the arc segment between the jump points is retained as the effective arc range. Next, the point cloud of the arc segment after endpoint trimming and angle continuity test is evaluated for quality. Specifically, the weighted sum of fitting accuracy, point continuity, arc opening angle and average distance error is used as the comprehensive quality score, and low-quality point cloud segments with comprehensive quality scores below the preset threshold are filtered out.

9. The automated extraction and fitting method for circular arc features based on three-dimensional point clouds according to claim 1, characterized in that, The process of performing overall circle fitting on the optimized arc segment point cloud, calculating the center coordinates, radius, and fitting residual of the circle containing the target arc, and evaluating the fitting quality to achieve accurate extraction of the target arc specifically involves: If only one arc segment point cloud is saved, then the overall circle fitting is performed directly, and the center coordinates, radius, and fitting residual of the circle containing the target arc are calculated. If there are multiple arc segment point clouds, the arc segment point clouds are grouped based on geometric similarity, and the overall circle fitting is performed uniformly on the arc segment point clouds in the same group. The center coordinates, radius, and fitting residual of the circle containing the arc segment point clouds in each group are output. During the fitting process, the weighted least squares method is used to determine the influence of each arc segment point cloud on the overall circle fitting result of the group based on the quality assessment results of each arc segment point cloud. After the overall circle is fitted, the fitting residual analysis and error assessment are performed to calculate the overall fitting accuracy. For multiple independent arcs obtained from point clouds of different groups of arc segments, an additional relative position analysis is performed. Based on the center coordinates and radius of the circle in which each independent arc is located, it is determined whether the spatial position association and geometric constraints between multiple independent arcs meet the preset design rules. The final output is the evaluation result of the fitting quality, and the target arc is accurately extracted based on the obtained center coordinates and radius.

10. The application system of the automated extraction and fitting method for circular arc features based on three-dimensional point clouds according to any one of claims 1-9, characterized in that, It includes a data input module, a mesh processing module, a boundary calculation module, a projection transformation module, a core detection module, an optimization filtering module, and a fitting output module, among which: The data input module is used to collect and preprocess 3D point cloud data; The mesh processing module is used to convert 3D point cloud data into a triangular mesh model; The boundary calculation module is used to extract the three-dimensional outer boundary point cloud from the triangular mesh model; The projection transformation module is used to project the three-dimensional boundary point cloud onto a two-dimensional plane; The core detection module is used to perform adaptive detection and extract point clouds of arc segments; The optimized filtering module is used to trim endpoints and evaluate the point cloud quality of arc segments; The fitting output module is used to fuse high-quality circular arc segment point clouds and fit and output circle parameters.

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