Complex curved surface forming deviation evaluation method and system based on equidistant mapping
By extracting point cloud boundaries, constructing adjacency graphs, and performing dimensionality reduction using the equidistant mapping method, the problem of point cloud matching for complex surfaces is solved, achieving efficient and accurate deviation assessment. This method is suitable for complex surface forming in high-end manufacturing.
Patent Information
- Application Number
- CN202411290191.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-14
- Publication Date
- 2026-02-03
AI Technical Summary
Existing technologies struggle to accurately assess the matching between target point clouds and measured point clouds of complex, small-curvature surfaces with no obvious geometric features. This results in inaccurate assessment of forming deviations in complex surfaces, failing to meet the precision forming requirements of high-end manufacturing.
A method based on isometric mapping is adopted. The point cloud boundaries are extracted for coarse registration, an adjacency graph is constructed to calculate the shortest path matrix, and the point cloud is unfolded into a low-dimensional space for fine registration, finally obtaining the deviation cloud map.
It achieves efficient and accurate deviation assessment for complex curved surfaces, and is particularly suitable for surface features with weak texture and large curvature. It improves the data support capability for secondary processing and enhances the stability and computational efficiency of registration.
Smart Images
Figure CN121458768A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of complex surface component manufacturing, in particular to a complex surface forming deviation evaluation method and system based on isometric mapping. BACKGROUND
[0002] Complex surface integral components are widely used in aerospace, shipbuilding, high-speed transportation and other high-end manufacturing fields, which are difficult to manufacture and have high requirements on surface precision and surface quality. Flexible forming processes such as shot forming and incremental forming are the main process means to realize the forming of integral components, and have significant advantages in processing efficiency, manufacturing cost and geometric shape adaptability. However, due to metal springback in the forming process and many inevitable unstable factors in the process, complex surface flexible forming usually cannot achieve the surface precision requirement in one forming. Therefore, the formed surface must be measured, and the forming deviation of the surface is evaluated by comparing with the target surface, which provides guidance for subsequent secondary or multiple processing, so as to gradually approach the target shape and finally meet the processing precision requirement. Accurate evaluation method of complex surface integral component forming surface deviation is an important link to realize precision forming manufacturing.
[0003] Complex three-dimensional surface forming deviation evaluation includes target surface measurement and matching of measured point cloud and standard point cloud. Among them, the complex surface measurement method is relatively mature, such as structured light three-dimensional measurement, binocular stereo vision method, time flight method, etc. For complex surface components with weak texture and large curvature, traditional point cloud registration algorithm is not applicable, and ICP and its improved algorithm is easy to fall into local optimum, and NDT algorithm also has poor registration effect due to no significant geometric features of point cloud, and non-rigid registration algorithm has large degree of freedom, which may lead to unstable algorithm and invalid forming deviation result in the absence of constraints. At present, the matching of target point cloud and measured point cloud of small curvature continuous complex surface with no obvious geometric features is still an important technical challenge in precision forming manufacturing. SUMMARY
[0004] In view of the defects in the prior art, the purpose of the present application is to provide a complex surface forming deviation evaluation method and system based on isometric mapping.
[0005] According to one aspect of the present application, a complex surface forming deviation evaluation method based on isometric mapping is provided, comprising:
[0006] Extracting the boundaries of the measured point cloud and the standard point cloud, and performing rough registration of the point clouds with the respective boundaries as references;
[0007] Constructing an adjacent graph for the original high-dimensional measured point cloud and the standard point cloud, respectively;
[0008] Based on the adjacency graph, geodesic distances are calculated, and the shortest path matrix is obtained;
[0009] The shortest path matrix is equidistantly mapped to a low-dimensional space, and the surface of the measured point cloud and the standard point cloud is unfolded to obtain a planar point cloud.
[0010] Fine registration is performed on the basis of coarse registration using the planar point clouds developed from the measurement point cloud and the target point cloud respectively;
[0011] The measured point cloud that has been precisely registered is compared with the target point cloud to obtain a deviation cloud map.
[0012] Preferably, the step of extracting the boundaries between the measured point cloud and the standard point cloud, and performing coarse registration of the point clouds using their respective boundaries as references, includes:
[0013] A point cloud boundary recognition method based on normal vector estimation is used to extract the boundaries of the measured point cloud and the standard point cloud, specifically:
[0014] For each point p in the point cloud P i Use a KD-tree to find its K nearest neighbors, and the neighborhood set is represented as N(p i );
[0015] For the neighborhood point set N(p) of point Pi i ), calculate the covariance matrix C:
[0016]
[0017] in It is N(p) i The center of mass of )
[0018] The covariance matrix C is decomposed into eigenvalues to obtain eigenvalues and eigenvectors;
[0019] The eigenvector with the smallest eigenvalue is used as the normal vector n. i ;
[0020] For point p i Calculate the normal vector and the neighborhood point set N(p) i The angle θ between the normal vectors of neighboring points in the equation ij ;
[0021] Set a normal change threshold θ th ;
[0022] Calculate point p i The normal change of a point relative to all its neighboring points is considered. If the maximum change exceeds a threshold, the point is determined to be an edge point.
[0023] Boundary identification was performed on the measured point cloud P and the standard point cloud Q respectively, resulting in two boundary point sets P. edgeand Q edge ;
[0024] Coarse registration is performed by applying the ICP method to the boundary point cloud, specifically as follows:
[0025] For the standard point cloud boundary point set Q edge Each point q in edge In the boundary point set P of the measured point cloud edge Find its nearest point p in the middle edge ;
[0026] Iterative estimation of rotation matrix R edge Translation vector t edge And transform the measured point cloud, so that
[0027]
[0028] Convergence yields the rotation matrix R. edge Translation vector t edge ;
[0029] Using the rotation matrix R edge Translation vector t edge The measured point cloud is transformed to complete the coarse registration of the standard point cloud and the measured point cloud in the initial state.
[0030] Preferably, in the process of extracting the boundary between the measured point cloud and the standard point cloud using the point cloud boundary identification method based on normal vector estimation, 30° is selected as the normal change threshold for boundary extraction.
[0031] Preferably, the construction of an adjacency graph for the original high-dimensional measurement point cloud and the standard point cloud includes:
[0032] Calculate the distance between each pair of data points in the measured point cloud or standard point cloud data to form a distance matrix D;
[0033] For each data point x i Find the k nearest data points from the distance matrix D to form a neighbor set N(x) i )
[0034] Initialize the adjacency matrix A, where A[i][j] = 0 represents node x. i and x j Not adjacent; if x j It is x i Let A[i][j] be one of the k nearest neighbors of point x. i and point x j Euclidean distance;
[0035] Use the adjacency matrix A to generate an adjacency graph.
[0036] Preferably, the Dijkstra method is used to calculate the geodesic distances on the adjacency graph, and the calculated shortest path lengths are used to form a shortest path matrix D. Dijkstra .
[0037] Preferably, the step of mapping the shortest path matrix to a low-dimensional space and unfolding the surfaces of the measured point cloud and the standard point cloud to obtain a planar point cloud includes:
[0038] The shortest path matrix D Dijkstra Transformed into a bi-centered matrix in, J is a one-dimensional matrix;
[0039] The eigenvalue decomposition of the bicentric matrix B yields the eigenvector Λ and the eigenvector matrix V.
[0040] Select the two largest eigenvalues to form a diagonal matrix Λ2 and the corresponding eigenvector matrix V2, and calculate the two-dimensional coordinate matrix X, X = V2Λ2. 1 / 2 Each row of matrix X represents the coordinates of a three-dimensional data point reduced to a two-dimensional plane.
[0041] Preferably, the precise registration using the planar point clouds unfolded from the measurement point cloud and the target point cloud includes:
[0042] Search the flattened measurement point cloud P in the flattened standard point cloud Q' using a KD-tree. i The nearest point Q' i P i ′ and Q′ i Points form corresponding point pairs;
[0043] Find P based on the point cloud. i ′ and Q′ i At the corresponding point P in the original point cloud P and Q i and Q i P i and Q i Form corresponding point pairs;
[0044] Based on the corresponding point pair P i and Q i Calculate the rotation matrix R and the translation vector t:
[0045] Calculate the centroids of point clouds P and Q and
[0046]
[0047]
[0048] Peer-to-peer decentralization:
[0049]
[0050]
[0051] Calculate the covariance matrix:
[0052]
[0053] Perform singular value decomposition on the covariance matrix H:
[0054] H=U∑V T
[0055] Calculate the rotation matrix R and the translation vector t:
[0056] R = VU T
[0057]
[0058] Calculate the mean square error d of the rotation matrix R and the translation vector t. t By making Minimize the rotation matrix R and translation vector t;
[0059] Based on the determined rotation matrix R and translation vector t, the measured point cloud is transformed to complete the fine registration.
[0060] According to a second aspect of the present invention, a system for evaluating the forming deviation of complex curved surfaces based on isometric mapping is provided, comprising:
[0061] Coarse registration module: Extracts the boundaries between the measured point cloud and the standard point cloud, and performs coarse registration of the point clouds using their respective boundaries as references;
[0062] Adjacency Graph Module: Constructs an adjacency graph for both the original high-dimensional measurement point cloud and the standard point cloud;
[0063] Shortest path matrix module: Calculates geodesic distances based on the adjacency graph and obtains the shortest path matrix;
[0064] Dimensionality reduction module: Maps the shortest path matrix equidistantly to a low-dimensional space, and unfolds the surfaces of the measured point cloud and the standard point cloud to obtain a planar point cloud;
[0065] Fine registration module: Based on coarse registration, fine registration is performed using the planar point clouds developed from the measurement point cloud and the target point cloud respectively;
[0066] Deviation assessment module: compares the finely registered measurement point cloud with the target point cloud to obtain a deviation cloud map.
[0067] According to a third aspect of the present invention, a terminal is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, can be used to perform any of the methods described herein, or to run the system described herein.
[0068] According to a fourth aspect of the invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, can be used to perform any of the methods described herein, or to run the system described herein.
[0069] Compared with the prior art, the embodiments of the present invention have at least one of the following beneficial effects:
[0070] The method and system for evaluating the forming deviation of complex curved surfaces based on equidistant mapping in this invention can efficiently and accurately evaluate the deviation between the measured point cloud and the standard digital model through point cloud registration based on equidistant mapping, providing reliable data support for secondary processing planning. It is particularly suitable for integral wall panels with weak texture and variable curvature surface features. Attached Figure Description
[0071] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:
[0072] Figure 1 This is a flowchart of a method for evaluating the forming deviation of complex curved surfaces based on equidistant mapping in one embodiment of the present invention.
[0073] Figure 2 The following are diagrams showing the point cloud boundary extraction results in a preferred embodiment of the present invention: (a) shows the boundary extracted from the standard point cloud, and (b) shows the boundary extracted from the measured point cloud.
[0074] Figure 3 The following are the results of applying the ICP algorithm to the boundary points in a preferred embodiment of the present invention. Figures (a), (b), (c), and (d) are the isometric view, top view, front view, and left view of the measured point cloud after coarse registration, respectively.
[0075] Figure 4 In a preferred embodiment of the present invention, a planar point cloud is obtained based on an adjacency graph and isometric unfolding. (a) represents the isometric unfolded adjacency graph and planar point cloud corresponding to the standard point cloud K=5; (b) represents the isometric unfolded adjacency graph and planar point cloud corresponding to the measured point cloud K=5; (c) represents the isometric unfolded adjacency graph and planar point cloud corresponding to the standard point cloud K=20; and (d) represents the isometric unfolded adjacency graph and planar point cloud corresponding to the measured point cloud K=20.
[0076] Figure 5The diagram shows a comparison of the registration effects of different methods in a specific embodiment of the present invention. (a) represents the present invention; (b) represents the ICP method; and (c) represents the NDT method.
[0077] Figure 6 This is a measurement point cloud and a standard profile surface deviation cloud map in a specific embodiment of the present invention. Detailed Implementation
[0078] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.
[0079] In one embodiment of the present invention, a method for evaluating the forming deviation of complex curved surfaces based on isometric mapping is provided, such as... Figure 1 As shown, the main steps are as follows:
[0080] S100: Extract the boundaries between the measured point cloud and the standard point cloud, and perform coarse registration of the point clouds using their respective boundaries as references.
[0081] S200, construct an adjacency graph for the original high-dimensional measurement point cloud and the standard point cloud respectively;
[0082] S300: Based on the adjacency graph constructed from S200, geodesic distances are calculated, and the shortest path matrix is obtained.
[0083] S400 maps the shortest path matrix obtained from S300 to a low-dimensional space at equal intervals, and unfolds the surface of the measured point cloud and the standard point cloud to obtain a planar point cloud.
[0084] S500 performs fine registration based on coarse registration using planar point clouds developed from the measurement point cloud and the target point cloud, respectively.
[0085] The S600 compares the precisely registered measurement point cloud with the target point cloud to obtain a deviation cloud map.
[0086] The above embodiments effectively solve the problem of evaluating the forming deviation of complex three-dimensional surfaces, providing an accurate basis for subsequent correction processes.
[0087] To provide a favorable initial relative pose for fine registration and increase registration stability, in a preferred embodiment of the present invention, coarse registration is used to roughly align the standard point cloud and the measurement point cloud in their initial state. Specifically, the following steps can be taken:
[0088] S101 employs a point cloud boundary recognition method based on normal vector estimation to extract the boundaries of the measured point cloud and the standard point cloud. Specifically:
[0089] For each point p in the point cloud P i The K-nearest neighbor is found using the KD-tree method, and the neighborhood set is represented as N(p i ).
[0090] Principal component analysis is used to estimate the normal vector of each point. For the neighborhood point set N(p) of point Pi, ... i ), calculate the covariance matrix C:
[0091]
[0092] in It is N(p) i Find the centroid of the covariance matrix C, and perform eigenvalue decomposition on the covariance matrix C to obtain eigenvalues and eigenvectors. Normal vector n i It is the eigenvector corresponding to the smallest eigenvalue.
[0093] For point p i Calculate its normal vector and its neighborhood point set N(p) i The angle θ between the normal vectors of the nearest points of ) ij Set a normal change threshold θ th Calculate point p i The point is considered an edge point if the maximum change in its normal vector relative to all neighboring points exceeds a threshold. Boundary identification is then performed on the measured point cloud P and the standard point cloud Q, resulting in two boundary point clouds P. edge and Q edge .
[0094] To determine the optimal normal change threshold θ for point cloud boundary recognition th When the normal change threshold θ th If the threshold is too small, it may detect a large number of non-edge points, leading to an increase in false positives; when the normal change threshold θ... th If the threshold is too large, some edge points may be missed. Therefore, in some specific embodiments, by comparing different normal change thresholds, 30° is selected as the normal change threshold for boundary extraction. The result of boundary extraction of the point cloud is as follows: Figure 2 As shown.
[0095] S102, applying the ICP algorithm to the boundary points to achieve coarse registration of the point cloud, specifically:
[0096] For the standard point cloud boundary point set Q edge Each point q in edge In the boundary point set P of the measured point cloud edge Find its nearest point p in the middle edge Iterative estimation of the rotation matrix R edge Translation vector t edge And transform the measured point cloud, and make
[0097]
[0098] Convergence yields the rotation matrix R. edge Translation vector t edge ;
[0099] Using the rotation matrix R edge Translation vector t edge The measured point cloud is transformed to complete the coarse registration of the standard point cloud and the measured point cloud in the initial state.
[0100] The above embodiment performs boundary identification on the measured point cloud P and the standard point cloud Q to obtain two boundary point clouds P. edge and Q edge Applying ICP to P edge and Q edge Registration is performed to obtain the transformation matrix R and translation vector t. The measured point cloud P is then transformed to obtain the coarsely registered point cloud P', as shown below. Figure 3 As shown in the figure. Compared with applying the ICP algorithm to all points, the coarse registration time is reduced from 5.2s to 0.2s due to the significant reduction in data volume, and the relative pose of the point cloud is good. The relative pose of the point cloud after coarse registration is shown in the figure. Figure 3 As shown.
[0101] To reflect the local proximity relationships of the data and preserve its geometric structure during dimensionality reduction, it is first necessary to construct an adjacency graph from the original high-dimensional data point set. In one embodiment of the present invention, step S200 involves selecting a suitable parameter k and finding the k nearest neighbors of each data point in the high-dimensional space. An adjacency graph is then constructed based on these k nearest neighbors, where nodes represent data points and edge weights represent the distances between data points. The specific steps are as follows:
[0102] S201, Calculate the distance matrix: Calculate the distance between each pair of data points in the dataset to form the distance matrix D.
[0103] S202, Finding the k-nearest neighbor: For each data point x i Find the k nearest data points from the distance matrix D to form a neighbor set N(x) i ).
[0104] S203, Construct the adjacency matrix: Initialize the adjacency matrix A, where A[i][j] = 0 represents node x. i and x j Not adjacent. If x j It is x i Let A[i][j] be one of the k nearest neighbors of point x. i and point x j Euclidean distance.
[0105] S204, Generate Adjacency Graph: Generate an adjacency graph using adjacency matrix A.
[0106] In the aforementioned embodiments, an adjacency graph was constructed by identifying the K nearest points. This adjacency graph ensures that the internal geometry of the point cloud is preserved during dimensionality reduction, thereby guaranteeing the accuracy of registration.
[0107] In a preferred embodiment of the present invention, step S300 involves using Dijkstra's algorithm to calculate the geodesic distance (geodetic distance refers to the shortest path distance between two points on the surface of a manifold) on the adjacency graph, and then forming a distance matrix D using the calculated shortest path lengths. Dijkstra Dijkstra's algorithm uses a greedy strategy to progressively expand the known shortest paths to ensure that the current optimal node is selected at each step. Finally, it calculates the shortest path from the source node to all other nodes.
[0108] The shortest path matrix D obtained in the above embodiment Dijkstra Building upon this, in another embodiment of the present invention, a multidimensional scaling method (Classical MDS) is used to map distances to a low-dimensional space, achieving low-dimensional embedding, i.e., surface flattening, to obtain a two-dimensional planar point cloud. Specifically,
[0109] S401, the shortest path matrix D Dijkstra Transformed into a bi-centered matrix in, J is a matrix consisting entirely of one elements.
[0110] S402, perform eigenvalue decomposition on the bicenter matrix B to obtain eigenvectors Λ and eigenvector matrix V, and select the two largest eigenvalues to form a diagonal matrix Λ2 and the corresponding eigenvector matrix V2;
[0111] S403, Calculate the two-dimensional coordinate matrix X, X = V2Λ2 1 / 2 Each row of matrix X represents the coordinates of a three-dimensional data point reduced to a two-dimensional plane.
[0112] In the process of forming a three-dimensional curved surface while ignoring extension, the blank can be regarded as a two-dimensional point cloud. The target surface and the measurement point cloud are different deformations that maintain the geodesic distance between a point on the two-dimensional point cloud and its neighboring points. In the above embodiment, when reducing the dimensionality of the three-dimensional curved surface point cloud, the geodesic distance between point pairs remains unchanged, and the two-dimensional point clouds obtained after dimensionality reduction of the target surface and the measurement point cloud are the same. Therefore, by reducing the dimensionality, corresponding point pairs can be found through the two-dimensional point cloud for registration.
[0113] In some specific embodiments, the standard digital model and the measured point cloud of the irregularly bounded cylinder are respectively subjected to equidistant unfolding, resulting in shape deviations between the measured point cloud and the standard digital model. Adjacency graphs are constructed using different K values, such as... Figure 4 As shown in (a) and (b), when the K value is <10, the point cloud shape changes significantly; finally, K=20 was chosen as the parameter for constructing the neighborhood graph, without changing the scale, thus preserving the point cloud features, such as... Figure 4 As shown in (c) and (d), the residuals of the isometric expansion are all less than 10e-5.
[0114] Once the unfolded measurement point cloud and target point cloud are obtained, they can be used as input for fine registration. By aligning the shaped target surface with the corresponding planar point cloud of the measurement point cloud, the nearest points between the two point clouds are found to obtain registration control point pairs. The coordinates of the registration control point pairs are reflected into the 3D point cloud. The sum of the Euclidean distances between all matching point pairs is used as the objective function to solve for the optimal relative pose of the two point clouds. In a preferred embodiment, step 5400 can be specifically described as follows:
[0115] S501, Finding corresponding point pairs: Using a KD-tree, search the flattened measured point cloud P in the standard point cloud Q'. i The nearest point Q' i P i ′ and Q′ i Points form corresponding point pairs.
[0116] S502, find P based on the point cloud. i ′ and Q′ i At the corresponding point P in point cloud P and Q i and Q i P i and Q i Form corresponding point pairs.
[0117] S503, calculate the rotation matrix R and the translation vector t, and calculate the mean square error d corresponding to the transformation matrix. t , making d t Minimum, of which
[0118]
[0119] Calculate the centroids of point clouds P and Q and
[0120]
[0121]
[0122] Peer-to-peer decentralization:
[0123]
[0124]
[0125] Calculate the covariance matrix:
[0126]
[0127] Perform singular value decomposition on the covariance matrix H:
[0128] H=U∑V T
[0129] Calculate the rotation matrix R and the translation vector t:
[0130] R = VU T
[0131]
[0132] Transform the measured point cloud to complete the transformation.
[0133] After the transformation is completed in the above-mentioned point cloud, the distance between corresponding point pairs is calculated as the forming deviation.
[0134] Based on the same inventive concept, other embodiments of the present invention also provide a complex surface forming deviation evaluation system based on equidistant mapping, comprising:
[0135] Coarse registration module: Extracts the boundaries between the measured point cloud and the standard point cloud, and performs coarse registration of the point clouds using their respective boundaries as references;
[0136] Adjacency Graph Module: Constructs an adjacency graph for both the original high-dimensional measurement point cloud and the standard point cloud;
[0137] Shortest path matrix module: Calculates geodesic distances based on the adjacency graph and obtains the shortest path matrix;
[0138] Dimensionality reduction module: Maps the shortest path matrix equidistantly to a low-dimensional space, and unfolds the surfaces of the measured point cloud and the standard point cloud to obtain a planar point cloud;
[0139] Fine registration module: Based on coarse registration, fine registration is performed using the planar point clouds developed from the measurement point cloud and the target point cloud respectively;
[0140] Deviation assessment module: compares the finely registered measurement point cloud with the target point cloud to obtain a deviation cloud map.
[0141] This system, based on the rapid coarse registration of the point cloud by applying the ICP method to the boundary points of the measured point cloud, reduces the dimensionality of the measured point cloud and the target surface by the equidistant mapping method to obtain geometrically corresponding point pairs. Finally, it solves the transformation matrix corresponding to the minimum mean square error of the Euclidean distance of each corresponding point pair by the least square method to achieve fine registration of the point cloud. The mean square error is used as the evaluation index of the forming accuracy, and the final deviation cloud map is output.
[0142] The specific implementation techniques of each module / unit in the above examples of the present invention can be referred to the steps of the complex surface forming deviation evaluation method based on equidistant mapping in the above embodiments, and will not be repeated here.
[0143] To verify the feasibility and effectiveness of the complex surface forming deviation evaluation method based on isometric mapping in the above embodiments, in a specific embodiment of the present invention, the evaluation method of complex surface forming deviation based on isometric mapping in the present invention is compared with other ICP and NDT methods. The registration threshold ε of the ICP and NDT methods is set to 0.01 and the maximum number of iterations K is set to... max For 50 iterations, fine registration was performed on a given point cloud using ICP, NDT methods, and the method described in this embodiment of the invention, respectively. The comparison results are as follows: Figure 5 As shown.
[0144] After precise registration, the point cloud is imported into Geomagic Wrap and compared with the target surface to obtain:
[0145] The point cloud deviation and root mean square error (RMSE) after registration according to the method of this invention embodiment are 17.3269 mm, which can be found in [reference needed]. Figure 6 The RMSE values for the ICP and NDT methods were 14.1375 mm and 46.9477 mm, respectively.
[0146] Although the root mean square error of the method in this embodiment is slightly larger than that of the ICP method, the pose of the registered point cloud is closer to the pose obtained during actual surface processing than that of the ICP method. (Traditional point cloud registration algorithms are not suitable for complex surface components with weak texture and large curvature; ICP and its improved algorithms are prone to getting trapped in local optima, leading to registration errors.) The comparison results show that the complex surface forming deviation evaluation method based on equidistant mapping exhibits higher accuracy and stability in point cloud registration and deviation evaluation, demonstrating superior overall performance. Furthermore, it eliminates the need for iterative solutions, significantly improving computational efficiency and demonstrating a clear advantage in the registration of complex curved surfaces.
[0147] Table 1 Comparison of Registration Methods
[0148]
[0149] Based on the same inventive concept, in other embodiments of the present invention, a terminal is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it can be used to perform the above-described method or to run the above-described system.
[0150] Optionally, the memory is used to store programs; the memory may include volatile memory, such as random-access memory (RAM), such as static random-access memory (SRAM), double data rate synchronous dynamic random-access memory (DDR SDRAM), etc.; the memory may also include non-volatile memory, such as flash memory. The memory is used to store computer programs (such as application programs, functional modules, etc. that implement the above methods), computer instructions, etc., and the above-mentioned computer programs, computer instructions, etc., may be partitioned and stored in one or more memories.
[0151] A processor is used to execute a computer program stored in memory to implement the various steps of the methods involved in the above embodiments. For details, please refer to the relevant descriptions in the preceding method embodiments.
[0152] The processor and memory can be separate structures or integrated structures. When the processor and memory are separate structures, they can be coupled together via a bus.
[0153] Based on the same inventive concept, in other embodiments of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, can be used to perform the above-described method or to run the above-described system.
[0154] Computer-readable media include computer storage media and communication media, wherein communication media include any medium that facilitates the transfer of computer programs from one place to another. Storage media can be any available medium accessible to a general-purpose or special-purpose computer. An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and storage medium can reside in an ASIC. Alternatively, the ASIC can reside in a user device. Of course, the processor and storage medium can also exist as discrete components in a communication device.
[0155] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied 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.
[0156] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0157] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0158] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0159] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.
Claims
1. A method for evaluating the forming deviation of complex curved surfaces based on isometric mapping, characterized in that, include: Extract the boundaries between the measured point cloud and the standard point cloud, and perform coarse registration of the point clouds using their respective boundaries as references; Construct an adjacency graph for both the original high-dimensional measurement point cloud and the standard point cloud; Based on the adjacency graph, geodesic distances are calculated, and the shortest path matrix is obtained; The shortest path matrix is equidistantly mapped to a low-dimensional space, and the surface of the measured point cloud and the standard point cloud is unfolded to obtain a planar point cloud. Fine registration is performed on the basis of coarse registration using the planar point clouds developed from the measurement point cloud and the target point cloud respectively; The measured point cloud that has been precisely registered is compared with the target point cloud to obtain a deviation cloud map.
2. The method for evaluating the forming deviation of complex curved surfaces based on equidistant mapping according to claim 1, characterized in that, The step of extracting the boundaries between the measured point cloud and the standard point cloud, and performing coarse registration of the point clouds using their respective boundaries as references, includes: A point cloud boundary recognition method based on normal vector estimation is used to extract the boundaries of the measured point cloud and the standard point cloud, specifically: For each point p in the point cloud P i Use a KD-tree to find its K nearest neighbors, and the neighborhood set is represented as N(p i ); For the neighborhood point set N(p) of point Pi i ), calculate the covariance matrix C: in It is N(p) i The center of mass of ) The covariance matrix C is decomposed into eigenvalues to obtain eigenvalues and eigenvectors; The eigenvector with the smallest eigenvalue is used as the normal vector n. i ; For point p i Calculate the normal vector and the neighborhood point set N(p) i The angle θ between the normal vectors of neighboring points in the region ij ; Set a normal change threshold θ th ; Calculate point p f The normal change of a point relative to all its neighboring points is considered. If the maximum change exceeds a threshold, the point is determined to be an edge point. Boundary identification was performed on the measured point cloud P and the standard point cloud Q respectively, resulting in two boundary point sets P. edge and Q edge ; Coarse registration is performed by applying the ICP method to the boundary point cloud, specifically as follows: For the standard point cloud boundary point set Q edg Each point q in e edge In the boundary point set P of the measured point cloud edge Find its nearest point p in the middle edge ; Iterative estimation of rotation matrix R edge Translation vector t edge And transform the measured point cloud, so that Convergence yields the rotation matrix R. edge Translation vector t edge ; Using the rotation matrix R edge Translation vector t edge The measured point cloud is transformed to complete the coarse registration of the standard point cloud and the measured point cloud in the initial state.
3. The method for evaluating the forming deviation of complex curved surfaces based on isometric mapping according to claim 2, characterized in that, In the process of extracting the boundary between the measured point cloud and the standard point cloud using a point cloud boundary identification method based on normal vector estimation, 30° is selected as the normal change threshold for boundary extraction.
4. The method for evaluating the forming deviation of complex curved surfaces based on isometric mapping according to claim 1, characterized in that, The construction of an adjacency graph for both the original high-dimensional measurement point cloud and the standard point cloud includes: Calculate the distance between each pair of data points in the measured point cloud or standard point cloud data to form a distance matrix D; For each data point x i Find the k nearest data points from the distance matrix D to form a neighbor set N(x) i ) Initialize adjacency matrix A: node x i and x j If they are not adjacent, A[i][j] = 0; x j It is x i Let A[i][j] be the k nearest neighbor of point x. i and point x j Euclidean distance; Use the adjacency matrix A to generate an adjacency graph.
5. The method for evaluating the forming deviation of complex curved surfaces based on equidistant mapping according to claim 1, characterized in that, The Dijkstra method is used to calculate the geodesic distances on the adjacency graph, and the calculated shortest path lengths are used to form a shortest path matrix D. Dijkstra .
6. The method for evaluating the forming deviation of complex curved surfaces based on isometric mapping according to claim 1, characterized in that, The step of mapping the shortest path matrix to a low-dimensional space and unfolding the surfaces of the measured point cloud and the standard point cloud to obtain a planar point cloud includes: The shortest path matrix D Dijkstra Transformed into a bi-centered matrix in, J is a matrix consisting entirely of one elements; The eigenvalue decomposition of the bicentric matrix B yields the eigenvector Λ and the eigenvector matrix V. Select the two largest eigenvalues to form a diagonal matrix Λ2 and the corresponding eigenvector matrix V2, and calculate the two-dimensional coordinate matrix X, X = V2Λ2. 1 / 2 Each row of matrix X represents the coordinates of a three-dimensional data point reduced to a two-dimensional plane.
7. The method for evaluating the forming deviation of complex curved surfaces based on equidistant mapping according to claim 1, characterized in that, The fine registration process, which utilizes the planar point clouds developed from the measurement point cloud and the target point cloud respectively, based on coarse registration, includes: Search the flattened measurement point cloud P in the flattened standard point cloud Q' using a KD-tree. i The nearest point Q' i P i ′ and Q′ i Points form corresponding point pairs; Find P based on the point cloud. i ′ and Q′ i At the corresponding point P in the original point cloud P and Q i and Q f P i and Q i Form corresponding point pairs; Based on the corresponding point pair P i and Q i Calculate the rotation matrix R and the translation vector t: Calculate the centroids of point clouds P and Q and N is the number of point clouds; Peer-to-peer decentralization: Calculate the covariance matrix: Perform singular value decomposition on the covariance matrix H: H=U∑V T Calculate the rotation matrix R and the translation vector t: R=VU T Calculate the mean square error d of the rotation matrix R and the translation vector t. t By making Minimize the rotation matrix R and translation vector t; Based on the determined rotation matrix R and translation vector t, the measured point cloud is transformed to complete the fine registration.
8. A system for evaluating the forming deviation of complex curved surfaces based on isometric mapping, characterized in that, include: Coarse registration module: Extracts the boundaries between the measured point cloud and the standard point cloud, and performs coarse registration of the point clouds using their respective boundaries as references; Adjacency Graph Module: Constructs an adjacency graph for both the original high-dimensional measurement point cloud and the standard point cloud; Shortest path matrix module: Calculates geodesic distances based on the adjacency graph and obtains the shortest path matrix; Dimensionality reduction module: Maps the shortest path matrix equidistantly to a low-dimensional space, and unfolds the surfaces of the measured point cloud and the standard point cloud to obtain a planar point cloud; Fine registration module: Based on coarse registration, fine registration is performed using the planar point clouds developed from the measurement point cloud and the target point cloud respectively; Deviation assessment module: compares the finely registered measurement point cloud with the target point cloud to obtain a deviation cloud map.
9. A terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it can be used to perform the method of any one of claims 1-7, or to run the system of claim 8.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program can be used to perform the method of any one of claims 1-7, or to run the system of claim 8.