A method for evaluating the accuracy of a triangular mesh model

Abstract

This invention provides a method for evaluating the accuracy of a triangular mesh model, comprising: Step 1, resampling the point cloud data to be evaluated from the modeled triangular mesh model using a uniform sampling method; Step 2, constructing a multi-dimensional geometric feature set for each point in the point cloud data to be evaluated, and identifying salient feature regions; Step 3, further adaptively and dynamically adjusting the local sampling point density according to the importance of each point in the point cloud to be evaluated; Step 4, extracting the geometric features of the sampled point cloud data, and constructing a geometric feature-aware Gaussian mixture model to achieve high-precision point cloud registration; Step 5, identifying outliers in the registered point cloud based on multi-dimensional features; Step 6, constructing an accuracy evaluation index. The evaluation index of this invention can flexibly adapt to changes in multi-dimensional features, combining geometric features, topological features, and density distribution features to achieve a comprehensive evaluation of the point cloud model.

Description

Technical Field

[0001] This invention belongs to the field of 3D modeling and data analysis, and in particular relates to a method for evaluating the accuracy of triangular mesh models. Background Technology

[0002] Triangulated Irregular Network (TIN), as a modeling method based on irregular grid space, has been widely used in fields such as geographic information systems, digital twin modeling, and medical image reconstruction due to its geometric feature preservation and adaptive topology construction capabilities. To ensure the accuracy of the TIN model, it is usually necessary to evaluate the accuracy of the constructed TIN model. However, the current accuracy evaluation of TIN models faces two major problems: (1) Multi-dimensional feature coupling problem: The feature regions of the target usually have strong spatial correlation between geometric features and semantic attributes, and traditional single-dimensional error indices cannot effectively decouple multi-source errors; (2) Uneven weight distribution: The weight distribution of complex feature regions exhibits significant non-Gaussian properties, and existing weight calculation methods are difficult to apply to dynamic weight requirements. These pose challenges to the construction of accuracy evaluation indices. The focus of this invention is to achieve adaptive construction of accuracy evaluation indices for TIN models that fuse multi-dimensional features.

[0003] Accuracy evaluation of triangulation models has been a widely studied topic by scholars both domestically and internationally. To address the problem of multi-dimensional feature coupling, researchers proposed a multi-band InSAR coupling error separation model. While this model solves the problem of confusion between geometric errors and deformation signals in traditional triangulation accuracy evaluation, its reliance on fixed frequency band division parameters reduces its adaptability to multi-scale coupling features. Researchers utilized Generative Adversarial Networks (GANs) to decouple geometric and semantic features, separating the coupling effects of terrain complexity and data acquisition errors by generating synthetic terrain data. However, this method requires massive amounts of heterogeneous data to support model training. Researchers designed a coupling sensitivity-driven Bayesian validation model to quantitatively separate errors generated by geological structure coupling and interpolation algorithms. Although it achieved an 82% accuracy rate in error tracing during landslide monitoring, its network topology construction relies on prior geological knowledge, limiting its applicability. Researchers developed a coupling feature quantification method based on supervoxel segmentation, automatically identifying the coupling feature strength of abrupt terrain changes through supervoxel clustering. This method improved the accuracy of edge areas by 18% in urban 3D modeling, but the supervoxel size is sensitive to the results, requiring repeated parameter tuning to optimize computational efficiency.

[0004] Regarding weight optimization, researchers proposed a residual weighting method to address the InSAR phase unwrapping problem and allocate weights reasonably for constructing a model accuracy evaluation index. This method outperforms the traditional LP norm algorithm, but it doesn't consider spatial heterogeneity, leading to significant errors in large deformation gradient regions. Researchers introduced a triangular fuzzy number hierarchical analysis method to optimize the weights of distribution network investment evaluation indicators, thus mitigating subjectivity. However, this method still relies on expert experience, resulting in insufficient objectivity of the weights. Researchers established a triangular fuzzy number dynamic multi-attribute decision model to optimize distribution network investment and address regional differences, but its computational complexity is high, making it difficult to apply to large-scale systems. Researchers proposed a weighted iterative 3D line segment reconstruction method that can optimize the edge accuracy of point cloud models to within 1 pixel, but this method has limited adaptability to complex buildings and low computational efficiency. Researchers developed a TIN-based C1 smooth interpolation model to improve DEM surface accuracy, but pre-calculation of node curvature weights leads to time-consuming model construction, making it unsuitable for large-scale scenarios.

[0005] In conclusion, developing an index construction method for adaptive evaluation of multidimensional features remains an urgent problem to be solved. Summary of the Invention

[0006] Objective of the Invention: The technical problem to be solved by the present invention is to address the shortcomings of existing technologies by providing a method for evaluating the accuracy of triangular mesh models, comprising the following steps:

[0007] Step 1: Use the uniform sampling method to resample the point cloud data to be evaluated from the modeled triangular network model to be evaluated;

[0008] Step 2: For the point cloud data to be evaluated, construct a multi-dimensional geometric feature set for each point and identify regions with significant features;

[0009] Step 3: Based on the importance of each point in the point cloud to be evaluated, further adaptively and dynamically adjust the local sampling point density;

[0010] Step 4: Extract the geometric features of the sampled point cloud data and construct a geometric feature-aware Gaussian mixture model to achieve high-precision point cloud registration;

[0011] Step 5: Identify outliers in the registered point cloud based on multidimensional features;

[0012] Step 6: Construct the accuracy assessment index.

[0013] In step 1, a 3D laser scanner is used to perform high-precision scanning of the spatial target to obtain point cloud data, which is used as the ground truth point cloud.

[0014] For the triangular mesh model to be evaluated after modeling, a uniform sampling method is used to resample and generate an indirect point cloud: First, the area of ​​each triangle is calculated based on the vertices of each triangle, and then the number of sampling points is allocated according to the proportion of each triangle to the total surface area.

[0015] G1 = round(H1 * H2)

[0016] H1 = H3,

[0017] H2 = H4 / H5

[0018] H5 = Σ(H6),

[0019] Where G1 represents the number of sampling points of the first triangle, H1 represents the total number of sampling points, H2 represents the area ratio of the first triangle, H3 represents the number of point clouds scanned by the lidar, H4 represents the area of ​​the first triangle, H5 represents the total area, and H6 represents the area of ​​all triangles.

[0020] The triangular mesh model records the vertex coordinates of each triangle on the surface. Then, sampling points are uniformly generated inside the plane of each triangle using the centroid coordinate method, while retaining the vertices of the original triangular mesh, to generate a resampled point cloud that covers the model surface and contains the geometric features of the target.

[0021] In step 2, the normal vector and curvature of each point in the indirect point cloud are calculated. A covariance matrix is ​​constructed from the K nearest neighbors of each point. The eigenvector corresponding to the smallest eigenvalue of the covariance matrix is ​​calculated as the normal vector. The normal vector is propagated using the region growing method. Based on the eigenvalues ​​of the covariance matrix of each point, assuming λ1≥λ2≥λ3, the approximate value of curvature c is calculated.

[0022] (1),

[0023] Wherein, λ1 represents the degree of dispersion of the point cloud in the principal direction (i.e., the point distribution is most dispersed / has the greatest variation in this direction); λ2 represents the degree of dispersion of the point cloud in the secondary principal direction; and λ3 represents the degree of dispersion of the point cloud in the normal vector direction (i.e., the point distribution is most concentrated / has the least variation in this direction).

[0024] Analyze the histogram distribution of three angular features α, φ, and θ:

[0025] (2),

[0026] (3),

[0027] (4),

[0028] in, and They are unit normal vector and Unit normal vector; characteristic angle Reflects the relative tilt of neighboring points; characteristic angle The vertical elevation angle of a neighboring point; characteristic angle It represents the curvature change of a local surface; each angular feature is divided into 11 intervals, forming a 33-dimensional feature vector. It doesn't necessarily have to be 11 intervals; the number of intervals can be adjusted according to actual needs (e.g., 8, 16, etc.), but 11 is an empirically common compromise, ensuring feature resolution without leading to excessively high dimensionality; 33 is 11 intervals * 3 features (…). , , ); It is the spatial coordinate of a neighboring point (a three-dimensional point, containing x, y, and z components). These are the spatial coordinates of the center point (a three-dimensional point, containing x, y, and z components). It is the unit normal vector of the k-th point (usually the normal vector of the center point or a neighboring point). It is the z-coordinate (elevation) of the neighboring points. It is the z-coordinate (elevation) of the center point. It is the x-coordinate of a neighboring point. It is the x-coordinate of the center point. It is the y-coordinate of a neighboring point. It is the y-coordinate of the center point;

[0029] Points with curvature values ​​greater than a threshold are considered feature points, and points with abrupt changes in the angle between their neighborhood normal vectors are considered edge features. A curvature consistency parameter (CCP) is also introduced.

[0030] (5),

[0031] in, The neighborhood average value represents the curvature; by setting a threshold for the feature combination parameters, salient regions in the indirect point cloud are identified.

[0032] In step 3, the sampling density is dynamically adjusted according to the importance of features to obtain the point cloud to be evaluated: in regions with significant features, the point density of the original point cloud is increased; in transition regions, the original point density is maintained; and in flat regions, the point density of the original point cloud is decreased.

[0033] During resampling, new points are generated inside the triangle surface using the centroid coordinate method; the triangular mesh model to be evaluated in step 1 includes the labeled triangle vertices, which are retained as key topological points and do not participate in the resampling process.

[0034] In step 4, point cloud registration is achieved by constructing a geometric feature-aware Gaussian mixture model. The ground truth point cloud is used as the source point cloud, and the resampled point cloud to be evaluated is used as the target point cloud. Each point in the target point cloud is regarded as the center of a Gaussian distribution, which is used as the point set Y, and the points in the original point cloud are used as the point set X. N and M are the number of points in point set X and point set Y, respectively. D is the dimension of point set X and point set Y.

[0035] The probability density function of the Gaussian mixture model is:

[0036] (6),

[0037] Where v represents a point in the point set X; ;in Exp represents the variance; exp represents the natural exponential function. This represents the probability density value of point v appearing under the entire Gaussian mixture distribution;

[0038] M is the number of Gaussian distributions, with each target point serving as the center of a Gaussian distribution;

[0039] p(v|m) represents the probability model of v using the m-th Gaussian distribution, reflecting the likelihood that v belongs to the m-th Gaussian distribution;

[0040] This represents the mean vector (center point) of the m-th Gaussian component. It is a D-dimensional vector (D is the dimension of the data) used to describe the position of the m-th Gaussian distribution in space.

[0041] Introduce a uniform distribution , which describes noise and outliers; where N represents the number of points in the point set X, i.e. the number of points in the source point cloud (the ground truth point cloud);

[0042] The uniformly distributed weights are expressed as , The Gaussian mixture model considering noise and outliers is as follows:

[0043] (7),

[0044] At this point, the negative logarithmic form of the likelihood function is:

[0045] (8),

[0046] in The negative logarithmic form of the likelihood function is the objective function used for optimization in the expectation-maximization (EM) algorithm, reflecting the goodness of fit of the observed data under model parameters (such as transformation parameters and variance).

[0047] The parameters representing a rigid spatial transformation typically include a rotation matrix and a displacement vector, used to transform a point set Y to a spatial position of a point set X.

[0048] The covariance of the Gaussian distribution (usually assumed to be isotropic, i.e., a scalar) reflects the distribution range of the point cloud matching error, that is, the magnitude of the fitting error between points.

[0049] By minimizing Find the parameters Covariance σ 2 This makes the point set X most likely generated from the transformed source point cloud Y;

[0050] The expected value maximization algorithm is used to iteratively solve the problem: the curvature characteristics of the target point cloud after coordinate transformation are calculated using formula (1). Calculate the curvature characteristics of the coordinate positions of the source point cloud after coordinate transformation. In the E-step computation, the posterior probability density of the introduced curvature difference is calculated for each point based on the given parameters. :

[0051] (9),

[0052] Wherein, the normalization constant ; This represents the mean vector of the m-th Gaussian component. Perform parameters Coordinate transformation under; Represents the spatial coordinates (usually three-dimensional coordinates) of the nth point in the target point cloud, i.e., the observation point or the point to be registered;

[0053] Next, we proceed to M steps (M being an abbreviation for MAX in the EM expectation-maximization algorithm), which involves finding new parameters by minimizing the perfect negative logarithm function:

[0054] (10)

[0055] Among them, intermediate parameters ; This represents the objective function in Gaussian mixture model (GMM) point cloud registration, which measures the performance of a point cloud under given parameters. (such as transformation parameters like rotation and translation) and covariance The following describes the degree of matching between the source and target point clouds. The goal of optimizing this function is to find the optimal registration parameters.

[0056] The centroid transformation of the Gaussian mixture model is defined as: R represents the rotation matrix, t represents the translation vector, and s represents the scale factor;

[0057] The objective function can be further written as:

[0058] (11),

[0059] in This represents the objective function in point cloud registration based on a Gaussian mixture model (GMM), also known as the likelihood function or loss function. It measures the likelihood of a point cloud under given rotation matrix R, translation vector t, scale factor s, and covariance. Under the given conditions, the degree of matching between the source point cloud and the target point cloud;

[0060] The parameters are obtained through singular value decomposition:

[0061] (12)

[0062] (13)

[0063] (14)

[0064] (15)

[0065] Where C is the covariance matrix, typically used to describe the correlation between point sets; A is the weighted correlation matrix, reflecting the correlation between the source and target point sets. d(P) is the diagonal matrix of P, where P is a probability matrix used to describe the matching relationship between point pairs; tr represents the trace of the matrix.

[0066] It is the weighted centroid (center) of the target point cloud Y, that is, the coordinates of the weighted average of all target points. ;

[0067] ; Denotes the weighted centroid of point set X;

[0068] It is the point set matrix of the source point cloud. Based on the point set X, each point has its weighted center coordinates of the point cloud subtracted: ; It is the weighted centroid (center) of the point set X, that is, the coordinates of the weighted average of all source points;

[0069] It is the point set matrix of the target point cloud. Based on the point set Y, each point has its weighted center coordinates of the point cloud subtracted: T denotes matrix transpose, and P denotes posterior probability density. The set of all points; the sum of the matching probabilities of all point pairs. U and V are the unitary matrices formed by the left singular vectors and the right singular vectors, respectively. ;in Represents the computation matrix The determinant value;

[0070] Then, using the obtained rotation matrix R, translation vector t, scale factor s, and covariance... The original point cloud is transformed to obtain the registered point cloud.

[0071] In step 5, during the outlier identification process of the registered point cloud, error statistics are first obtained: by calculating the average error... and maximum error The overall deviation between the two point clouds is obtained; where, and These represent the points in the point cloud to be evaluated and the corresponding nearest neighbors in the ground truth point cloud, respectively. Indicates all The maximum value in;

[0072] Using KL divergence Quantify the difference between two curvature distributions; where P(x) represents the probability density value of the probability distribution of the source point cloud at point x, and Q(x) represents the probability density value of the probability distribution of the target point cloud at point x; x represents the independent variable of the probability distribution function;

[0073] Then, calculate the angle between the normal vectors. Evaluate the consistency of the normal vector, where n i and m i These are the normal vectors of the corresponding points in the point cloud to be evaluated and the normal vectors of the corresponding points in the ground truth point cloud, respectively.

[0074] In addition to calculating the features mentioned above, the space is also divided into grids, and the point density differences within each grid are calculated. ;in, and Let represent the point density of the point cloud to be evaluated in the j-th grid and the point density of the ground truth point cloud in the j-th grid, respectively.

[0075] Finally, abnormal regions are identified by setting judgment criteria. When a region W meets the criteria... , or If any of the conditions are met, W will be defined as an abnormal region. , and These are the thresholds for distance, normal vector difference, and point density difference, respectively. This represents the average distance in region W. This represents the difference in point density between region W and the surrounding region. This represents the angular deviation of the normal vector within region W.

[0076] In step 6, a three-dimensional labeling matrix [a,b,c] is established to label each point cloud identified as an anomaly. Each position in the matrix corresponds to a specific anomaly type: position a represents geometric anomaly; position b represents topological consistency anomaly; and position c represents density distribution anomaly.

[0077] At the same time, an assignment rule is established: if the point cloud has an anomaly of a certain type, the corresponding position is assigned a value of 1; if the point cloud does not have an anomaly, the corresponding position is assigned a value of 0.

[0078] Two constraints are established as the basis for evaluating the modeling accuracy: outliers are classified according to the number of non-zero elements in the 3D marker matrix.

[0079] First-level spatial feature set: The matrix has only one non-zero element, i.e., |a,b,c|[1,1,1]^T = 1, which means that the point cloud has anomalies in only one aspect;

[0080] Second-level spatial feature set: The matrix has two non-zero elements, namely |a,b,c|[1,1,1]^T = 2, which indicates that the point cloud has anomalies in two aspects;

[0081] Three-level spatial feature set: The matrix has three non-zero elements, namely |a,b,c|[1,1,1]^T = 3, which indicates that the point cloud has anomalies in all three aspects;

[0082] Two constraints are established to evaluate the modeling accuracy:

[0083] Condition 1: If the total number of first-level and second-level spatial feature sets exceeds the threshold of all feature sets, the modeling accuracy is deemed unqualified.

[0084] Condition 2: If the proportion of the third-level spatial feature set to all feature sets exceeds the threshold, the modeling accuracy is deemed unqualified.

[0085] In step 6, the accuracy evaluation index TOW is constructed under the condition that two constraints are satisfied:

[0086] (16)

[0087] in, , , and Let these represent the normalized standard deviation of distance, the normalized standard deviation of curvature, the normalized standard deviation of normal vector, and the normalized standard deviation of density, respectively. The calculation formulas are as follows: , , , ,in, , , and These are the original distance, curvature, normal vector, and density standard deviation, respectively. , , and They are , , and The maximum possible value; To distinguish quantities in space; These are the valid sampling points after identifying outliers; This represents the distance from the outlier points; The number of outliers in curvature or normal vector; W1 represents the number of density outliers; W2 are weighting coefficients, satisfying W1+W2=1.

[0088] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0089] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0090] Beneficial Effects: This invention significantly improves the quality assessment capability of 3D models by constructing an adaptive accuracy evaluation index. Unlike traditional methods, the evaluation index of this invention can flexibly adapt to changes in multi-dimensional features, combining geometric features, topological features, and density distribution features to achieve a comprehensive evaluation of point cloud models. By dynamically adjusting weights and parameters, the evaluation index can accurately identify abnormal regions in the model and provide targeted optimization suggestions. This evaluation method not only improves the accuracy and reliability of the model but also provides strong support for point cloud processing in complex scenes. Evaluation results show that this invention demonstrates excellent practical value in various complex scenarios and can effectively guide subsequent model optimization and improvement. Attached Figure Description

[0091] Figure 1 This is a flowchart illustrating a method according to an embodiment of the present invention.

[0092] Figure 2 This is an example diagram of downsampling results in an embodiment of the present invention.

[0093] Figure 3This is an example diagram of the anomaly point identification results in an embodiment of the present invention.

[0094] Figure 4 This is an example diagram illustrating the spatial feature set differentiation criteria in an embodiment of the present invention. Detailed Implementation

[0095] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0096] refer to Figure 1 This invention provides a method for evaluating the accuracy of a triangular mesh model, comprising the following steps:

[0097] Step 1: Use the uniform sampling method to resample the point cloud data to be evaluated from the modeled triangular network model to be evaluated;

[0098] Step 2: For the point cloud data to be evaluated, construct a multi-dimensional geometric feature set for each point and identify regions with significant features;

[0099] Step 3: Based on the importance of each point in the point cloud to be evaluated, further adaptively and dynamically adjust the local sampling point density;

[0100] Step 4: Extract the geometric features of the sampled point cloud data and construct a geometric feature-aware Gaussian mixture model to achieve high-precision point cloud registration;

[0101] Step 5: Identify outliers in the registered point cloud based on multidimensional features;

[0102] Step 6: Construct the accuracy assessment index.

[0103] In step 1, a 3D laser scanner is used to perform high-precision scanning of the spatial target to obtain point cloud data, which is used as the ground truth point cloud.

[0104] For the triangular mesh model to be evaluated after modeling, a uniform sampling method is used to resample and generate an indirect point cloud: First, the area of ​​each triangle is calculated based on the vertices of each triangle, and then the number of sampling points is allocated according to the proportion of each triangle to the total surface area.

[0105] G1 = round(H1 * H2)

[0106] H1 = H3,

[0107] H2 = H4 / H5

[0108] H5 = Σ(H6),

[0109] Where G1 represents the number of sampling points of the first triangle, H1 represents the total number of sampling points, H2 represents the area ratio of the first triangle, H3 represents the number of point clouds scanned by the lidar, H4 represents the area of ​​the first triangle, H5 represents the total area, and H6 represents the area of ​​all triangles.

[0110] The triangular mesh model records the vertex coordinates of each triangle on the surface. Then, sampling points are uniformly generated inside the plane of each triangle using the centroid coordinate method, while retaining the vertices of the original triangular mesh, to generate a resampled point cloud that covers the model surface and contains the geometric features of the target.

[0111] In step 2, the normal vector and curvature of each point in the indirect point cloud are calculated. A covariance matrix is ​​constructed from the K nearest neighbors of each point. The eigenvector corresponding to the smallest eigenvalue of the covariance matrix is ​​calculated as the normal vector. The normal vector is propagated using the region growing method. Based on the eigenvalues ​​of the covariance matrix of each point, assuming λ1≥λ2≥λ3, the approximate value of curvature c is calculated.

[0112] (1),

[0113] Wherein, λ1 represents the degree of dispersion of the point cloud in the principal direction (i.e., the point distribution is most dispersed / has the greatest variation in this direction); λ2 represents the degree of dispersion of the point cloud in the secondary principal direction; and λ3 represents the degree of dispersion of the point cloud in the normal vector direction (i.e., the point distribution is most concentrated / has the least variation in this direction).

[0114] Analyze the histogram distribution of three angular features α, φ, and θ:

[0115] (2),

[0116] (3),

[0117] (4),

[0118] in, and They are unit normal vector and Unit normal vector; characteristic angle Reflects the relative tilt of neighboring points; characteristic angle The vertical elevation angle of a neighboring point; characteristic angle It represents the curvature change of a local surface; each angular feature is divided into 11 intervals, forming a 33-dimensional feature vector. It doesn't necessarily have to be 11 intervals; the number of intervals can be adjusted according to actual needs (e.g., 8, 16, etc.), but 11 is an empirically common compromise, ensuring feature resolution without leading to excessively high dimensionality; 33 is 11 intervals * 3 features (…). , , ); It is the spatial coordinate of a neighboring point (a three-dimensional point, containing x, y, and z components). These are the spatial coordinates of the center point (a three-dimensional point, containing x, y, and z components). It is the unit normal vector of the k-th point (usually the normal vector of the center point or a neighboring point). It is the z-coordinate (elevation) of the neighboring points. It is the z-coordinate (elevation) of the center point. It is the x-coordinate of a neighboring point. It is the x-coordinate of the center point. It is the y-coordinate of a neighboring point. It is the y-coordinate of the center point;

[0119] Points with curvature values ​​greater than a threshold (0.03 in this embodiment based on experience) are considered feature points, and points with abrupt changes in the angle between their neighborhood normal vectors are considered edge features. A curvature consistency parameter (CCP) is also introduced.

[0120] (5),

[0121] in, The neighborhood average value represents the curvature; by setting a threshold for the feature combination parameters, salient regions in the indirect point cloud are identified.

[0122] In step 3, the sampling density is dynamically adjusted according to the importance of features to obtain the point cloud to be evaluated: in regions with significant features, the point density of the original point cloud is increased; in transition regions, the original point density is maintained; and in flat regions, the point density of the original point cloud is decreased.

[0123] During resampling, new points are generated inside the triangle surface using the centroid coordinate method; the triangular mesh model to be evaluated in step 1 includes the labeled triangle vertices, which are retained as key topological points and do not participate in the resampling process.

[0124] In step 4, point cloud registration is achieved by constructing a geometric feature-aware Gaussian mixture model. The ground truth point cloud is used as the source point cloud, and the resampled point cloud to be evaluated is used as the target point cloud. Each point in the target point cloud is regarded as the center of a Gaussian distribution, which is used as the point set Y, and the points in the original point cloud are used as the point set X. N and M are the number of points in point set X and point set Y, respectively. D is the dimension of point set X and point set Y.

[0125] The probability density function of the Gaussian mixture model is:

[0126] (6),

[0127] Where v represents a point in the point set X; ;in Exp represents the variance; exp represents the natural exponential function. This represents the probability density value of point v appearing under the entire Gaussian mixture distribution;

[0128] M is the number of Gaussian distributions, with each target point serving as the center of a Gaussian distribution;

[0129] p(v|m) represents the probability model of v using the m-th Gaussian distribution, reflecting the likelihood that v belongs to the m-th Gaussian distribution;

[0130] This represents the mean vector (center point) of the m-th Gaussian component. It is a D-dimensional vector (D is the dimension of the data) used to describe the position of the m-th Gaussian distribution in space.

[0131] Introduce a uniform distribution , which describes noise and outliers; where N represents the number of points in the point set X, i.e. the number of points in the source point cloud (the ground truth point cloud);

[0132] The uniformly distributed weights are expressed as , The Gaussian mixture model considering noise and outliers is as follows:

[0133] (7),

[0134] At this point, the negative logarithmic form of the likelihood function is:

[0135] (8),

[0136] in The negative logarithmic form of the likelihood function is the objective function used for optimization in the expectation-maximization (EM) algorithm, reflecting the goodness of fit of the observed data under model parameters (such as transformation parameters and variance).

[0137] The parameters representing a rigid spatial transformation typically include a rotation matrix and a displacement vector, used to transform a point set Y to a spatial position of a point set X.

[0138] The covariance of the Gaussian distribution (usually assumed to be isotropic, i.e., a scalar) reflects the distribution range of the point cloud matching error, that is, the magnitude of the fitting error between points.

[0139] By minimizing Find the parameters Covariance σ 2 This makes the point set X most likely generated from the transformed source point cloud Y;

[0140] The expected value maximization algorithm is used to iteratively solve the problem: the curvature characteristics of the target point cloud after coordinate transformation are calculated using formula (1). Calculate the curvature characteristics of the coordinate positions of the source point cloud after coordinate transformation. In the E-step computation, the posterior probability density of the introduced curvature difference is calculated for each point based on the given parameters. :

[0141] (9),

[0142] Wherein, the normalization constant ; This represents the mean vector of the m-th Gaussian component. Perform parameters Coordinate transformation under; Represents the spatial coordinates (usually three-dimensional coordinates) of the nth point in the target point cloud, i.e., the observation point or the point to be registered;

[0143] Next, we proceed to M steps (M being an abbreviation for MAX in the EM expectation-maximization algorithm), which involves finding new parameters by minimizing the perfect negative logarithm function:

[0144] (10)

[0145] Among them, intermediate parameters ; This represents the objective function in Gaussian mixture model (GMM) point cloud registration, which measures the performance of a point cloud under given parameters. (such as transformation parameters like rotation and translation) and covariance The following describes the degree of matching between the source and target point clouds. The goal of optimizing this function is to find the optimal registration parameters.

[0146] The centroid transformation of the Gaussian mixture model is defined as: R represents the rotation matrix, t represents the translation vector, and s represents the scale factor;

[0147] The objective function can be further written as:

[0148] (11),

[0149] in This represents the objective function in point cloud registration based on a Gaussian mixture model (GMM), also known as the likelihood function or loss function. It measures the likelihood of a point cloud under given rotation matrix R, translation vector t, scale factor s, and covariance. Under the given conditions, the degree of matching between the source point cloud and the target point cloud;

[0150] The parameters are obtained through singular value decomposition:

[0151] (12)

[0152] (13)

[0153] (14)

[0154] (15)

[0155] Where C is the covariance matrix, typically used to describe the correlation between point sets; A is the weighted correlation matrix, reflecting the correlation between the source and target point sets. d(P) is the diagonal matrix of P, where P is a probability matrix used to describe the matching relationship between point pairs; tr represents the trace of the matrix.

[0156] It is the weighted centroid (center) of the target point cloud Y, that is, the coordinates of the weighted average of all target points. ;

[0157] ; Denotes the weighted centroid of point set X;

[0158] It is the point set matrix of the source point cloud. Based on the point set X, each point has its weighted center coordinates of the point cloud subtracted: ; It is the weighted centroid (center) of the point set X, that is, the coordinates of the weighted average of all source points;

[0159] It is the point set matrix of the target point cloud. Based on the point set Y, each point has its weighted center coordinates of the point cloud subtracted: T denotes matrix transpose, and P denotes posterior probability density. The set of all points; the sum of the matching probabilities of all point pairs. U and V are the unitary matrices formed by the left singular vectors and the right singular vectors, respectively. ;in Represents the computation matrix The determinant value;

[0160] Then, using the obtained rotation matrix R, translation vector t, scale factor s, and covariance... The original point cloud is transformed to obtain the registered point cloud.

[0161] In step 5, during the outlier identification process of the registered point cloud, error statistics are first obtained: by calculating the average error... and maximum error The overall deviation between the two point clouds is obtained; where, and These represent the points in the point cloud to be evaluated and the corresponding nearest neighbors in the ground truth point cloud, respectively. Indicates all The maximum value in;

[0162] Using KL divergence Quantify the difference between two curvature distributions; where P(x) represents the probability density value of the probability distribution of the source point cloud at point x, and Q(x) represents the probability density value of the probability distribution of the target point cloud at point x; x represents the independent variable of the probability distribution function;

[0163] Then, calculate the angle between the normal vectors. Evaluate the consistency of the normal vector, where n i and m i These are the normal vectors of the corresponding points in the point cloud to be evaluated and the normal vectors of the corresponding points in the ground truth point cloud, respectively.

[0164] In addition to calculating the features mentioned above, the space is also divided into grids, and the point density differences within each grid are calculated. ;in, and Let represent the point density of the point cloud to be evaluated in the j-th grid and the point density of the ground truth point cloud in the j-th grid, respectively.

[0165] Finally, abnormal regions are identified by setting judgment criteria. When a region W meets the criteria... , or If any of the conditions are met, W will be defined as an abnormal region. , and These are the threshold values ​​for distance (3mm based on experience in this embodiment), normal vector difference (6° based on experience in this embodiment), and point density difference (4% based on experience in this embodiment). This represents the average distance in region W. This represents the difference in point density between region W and its surrounding regions. This represents the angular deviation of the normal vector within region W.

[0166] In step 6, a three-dimensional labeling matrix [a,b,c] is established to label each point cloud identified as an anomaly. Each position in the matrix corresponds to a specific anomaly type: position a represents geometric anomaly; position b represents topological consistency anomaly; and position c represents density distribution anomaly.

[0167] At the same time, an assignment rule is established: if the point cloud has an anomaly of a certain type, the corresponding position is assigned a value of 1; if the point cloud does not have an anomaly, the corresponding position is assigned a value of 0.

[0168] Two constraints are established as the basis for evaluating the modeling accuracy: outliers are classified according to the number of non-zero elements in the 3D marker matrix.

[0169] First-level spatial feature set: The matrix has only one non-zero element, i.e., |a,b,c|[1,1,1]^T = 1, which means that the point cloud has anomalies in only one aspect;

[0170] Second-level spatial feature set: The matrix has two non-zero elements, namely |a,b,c|[1,1,1]^T = 2, which indicates that the point cloud has anomalies in two aspects;

[0171] Three-level spatial feature set: The matrix has three non-zero elements, namely |a,b,c|[1,1,1]^T = 3, which indicates that the point cloud has anomalies in all three aspects;

[0172] Two constraints are established to evaluate the modeling accuracy:

[0173] Condition 1: If the total number of first-level and second-level spatial feature sets accounts for more than the threshold of all feature sets (in this embodiment, the value is taken as 20% based on experience), then the modeling accuracy is deemed unqualified.

[0174] Condition 2: If the proportion of the third-level spatial feature set to all feature sets exceeds the threshold (in this embodiment, the value is taken as 10% based on experience), then the modeling accuracy is deemed unqualified.

[0175] In step 6, the accuracy evaluation index TOW is constructed under the condition that two constraints are satisfied:

[0176] (16)

[0177] in, , , and Let these represent the normalized standard deviation of distance, the normalized standard deviation of curvature, the normalized standard deviation of normal vector, and the normalized standard deviation of density, respectively. The calculation formulas are as follows: , , , ,in, , , and These are the original distance, curvature, normal vector, and density standard deviation, respectively. , , and They are , , and The maximum possible value; To distinguish quantities in space; These are the valid sampling points after identifying outliers; This represents the distance from the outlier points; The number of outliers in curvature or normal vector; W1 represents the number of density outliers; W2 are weighting coefficients, satisfying W1+W2=1.

[0178] This method can be implemented automatically using computer software, and specifically includes the following steps:

[0179] Step 1: Given a freeform surface target (e.g., a statue), obtain the laser point cloud model of the statue and preprocess it and the triangular mesh model to be evaluated. Use a 3D laser scanning device to perform a high-precision scan of the target object to obtain the laser point cloud model, i.e., the ground truth point cloud data. Next, perform mean resampling on the model to be evaluated to obtain the indirect point cloud. Specifically, allocate the number of sampling points by calculating the area of ​​each triangle. Based on the area of ​​each triangle, determine the number of points to be sampled on that triangle. Set a total number of sampling points, and then allocate the number of sampling points according to the proportion of the area of ​​each triangle to the total area. Use the centroid coordinate method to generate uniformly distributed points inside the triangles.

[0180] Step 2: Obtain key features in the point cloud model after mean resampling. Calculate the curvature and normal vector of the indirect point cloud. Use Principal Component Analysis (PCA) to fit the local neighborhood of each point to a plane. Specifically, select the K nearest neighbors (usually K values ​​are between 10 and 30) or points within the radius neighborhood of each point to construct the covariance matrix. To ensure the consistency of the normal vector direction, the region growing method can be used for normal vector propagation. Use formula (1) to describe the curvature feature of the model. The larger the value, the higher the curvature of the local surface. In addition, use formulas (2) to (4) to calculate the FPFH descriptor, and statistically analyze the histogram distribution of the three angular features (α, φ, θ). Divide each angular feature into 11 intervals to form a 33-dimensional feature vector. This effectively reduces the computational complexity while preserving the key geometric information of the point cloud. Then, use formula (5) to introduce the curvature consistency parameter (CCP). Set a threshold (e.g., CCP > 0.25) to identify the significant feature regions.

[0181] Step 3: Based on the features obtained above, calculate their importance and dynamically adjust the sampling density to obtain the point cloud to be evaluated: In regions with significant features (such as edges, corners, and high curvature areas), increase the sampling density to 1.5 to 2 times the original density; in transitional regions, maintain the original density; in flat regions (such as planes and low curvature areas), decrease the sampling density to 0.3 to 0.5 times the original density. During sampling, use the centroid coordinate method to generate new points inside the triangle to ensure uniform point distribution. Figure 2 As shown. Note that the triangle vertices labeled in step 1 are retained as key topological points and do not participate in the resampling process to maintain the integrity of the model's topological structure.

[0182] Step 4: Extract the geometric features of the point cloud to be evaluated and construct a geometric feature-aware Gaussian mixture model to achieve high-precision point cloud registration. Specifically, substitute the curvature parameters of the coordinate positions of the target point cloud and the source point cloud after coordinate transformation into formulas (8) and (9) to obtain the expectation-maximum (EM) algorithm that introduces the curvature difference. Iteratively solve the transformation parameters and variance σ. 2 This ensures that the target point cloud X is most likely generated from the transformed source point cloud Y. Then, the parameters required for the objective function (10) are obtained through singular value decomposition (SVD), as shown in equations (11) to (14), and the centroid transformation of the Gaussian mixture model is performed. The registered point cloud is then obtained.

[0183] Step 5: During the outlier identification process of the registered point cloud, error statistics are first obtained: by calculating the average error... and maximum error The overall deviation between the two point clouds is obtained; where, and These represent the points in the point cloud to be evaluated and the corresponding nearest neighbors in the ground truth point cloud, respectively. Indicates all The maximum value in;

[0184] Using KL divergence Quantify the difference between two curvature distributions; where P(x) represents the probability density value of the probability distribution of the source point cloud at point x, and Q(x) represents the probability density value of the probability distribution of the target point cloud at point x; x represents the independent variable of the probability distribution function;

[0185] Then, calculate the angle between the normal vectors. Evaluate the consistency of the normal vector, where n i and m i These are the normal vectors of the corresponding points in the point cloud to be evaluated and the normal vectors of the corresponding points in the ground truth point cloud, respectively.

[0186] In addition to calculating the features mentioned above, the space is also divided into grids, and the point density differences within each grid are calculated. ;in, and Let represent the point density of the point cloud to be evaluated in the j-th grid and the point density of the ground truth point cloud in the j-th grid, respectively.

[0187] Finally, abnormal regions are identified by setting judgment criteria. When a region W meets the criteria... , or If any of the conditions are met, W will be defined as an abnormal region. , and These are the thresholds for distance, normal vector, and point density, respectively. This represents the average distance in region W. This represents the difference in point density between region W and the surrounding region. This represents the angular deviation of the normal vector within region W.

[0188] These thresholds are set based on experience regarding point cloud quality requirements and the needs of practical application scenarios. The results of outlier identification are determined by... Figure 3 As shown.

[0189] Step 6: Construct the accuracy evaluation index. First, establish a 3D label matrix [ABC] to label each point cloud element identified as an anomaly. Each position in the matrix corresponds to a specific anomaly type: position A (first position) represents geometric anomaly; position B (second position) represents topological consistency anomaly; and position C (third position) represents density distribution anomaly. Simultaneously, establish the assignment rule: if a point cloud contains a certain type of anomaly, the corresponding position is assigned a value of 1; if the point cloud does not contain a certain type of anomaly, the corresponding position is assigned a value of 0. Then, set two constraints to form the basis for evaluating modeling accuracy. Specifically, outliers are first classified according to the number of non-zero elements in the label matrix: Level 1 spatial feature set: the matrix has only one non-zero element, i.e., |A,B,C|[1,1,1]^T = 1, indicating that the point cloud has anomalies in only one aspect; Level 2 spatial feature set: the matrix has two non-zero elements, i.e., |A,B,C|[1,1,1]^T = 2, indicating that the point cloud has anomalies in two aspects; Level 3 spatial feature set: the matrix has three non-zero elements, i.e., |A,B,C|[1,1,1]^T = 3, indicating that the point cloud has anomalies in all three aspects. The classification result is determined by... Figure 4 Colors are used to visually represent information.

[0190] Based on the above classification, two constraints are established to evaluate the modeling accuracy:

[0191] Condition 1: If the total number of primary and secondary spatial feature sets accounts for more than 5% of all feature sets, it is determined that the modeling accuracy is unqualified;

[0192] Condition 2: If the proportion of the tertiary spatial feature set in all feature sets exceeds 5%, it is determined that the modeling accuracy is unqualified.

[0193] Finally, under the condition of passing the above two constraints, a more specific and standardized evaluation is realized relying on formula (15). According to the value of TOW, the model quality is divided into five levels: when TOW ≤ 0.2, the model quality is excellent; when 0.2 < TOW ≤ 0.4, the model quality is good; when 0.4 < TOW ≤ 0.6, the model quality is qualified; when 0.6 < TOW ≤ 0.8, the model quality is poor; and when TOW > 0.8, the model quality is unqualified and the triangular mesh model needs to be reconstructed.

[0194] The present invention provides a method for evaluating the accuracy of a triangular mesh model. There are many methods and ways to specifically implement this technical solution. The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by existing technologies.

Claims

1. A method for evaluating the accuracy of a triangular mesh model, characterized in that, Includes the following steps: Step 1: Use the uniform sampling method to resample the point cloud data to be evaluated from the modeled triangular network model to be evaluated; Step 2: For the point cloud data to be evaluated, construct a multi-dimensional geometric feature set for each point and identify regions with significant features; Step 3: Based on the importance of each point in the point cloud to be evaluated, further adaptively and dynamically adjust the local sampling point density; Step 4: Extract the geometric features of the sampled point cloud data and construct a geometric feature-aware Gaussian mixture model to achieve high-precision point cloud registration; In step 4, point cloud registration is achieved by constructing a geometric feature-aware Gaussian mixture model. The ground truth point cloud is used as the source point cloud, and the resampled point cloud to be evaluated is used as the target point cloud. Each point in the target point cloud is regarded as the center of a Gaussian distribution, which is used as the point set Y, and the points in the original point cloud are used as the point set X. N and M are the number of points in point set X and point set Y, respectively. D is the dimension of point set X and point set Y. The probability density function of the Gaussian mixture model is: （6）， Where v represents a point in the point set X; ;in Exp represents the variance; exp represents the natural exponential function. This represents the probability density value of point v appearing in the entire Gaussian mixture distribution; p(v|m) represents the probability model of v using the m-th Gaussian distribution, reflecting the likelihood that v belongs to the m-th Gaussian distribution; Let represent the mean vector of the m-th Gaussian component; Introduce a uniform distribution , which describes noise and outliers; where N represents the number of points in the point set X; The uniformly distributed weights are expressed as , The Gaussian mixture model considering noise and outliers is as follows: （7）， The negative logarithmic form of the likelihood function is: （8）， in Represents the negative logarithmic form of the likelihood function; Parameters representing rigid transformations in space; The covariance of the Gaussian distribution is represented by . By minimizing Find the parameters Covariance σ 2 This makes the point set X most likely generated from the transformed source point cloud Y; Iteratively solve using the expectation-maximization algorithm: Calculate the curvature characteristics of the target point cloud after coordinate transformation. Calculate the curvature characteristics of the coordinate positions of the source point cloud after coordinate transformation. In the E-step computation, the posterior probability density of the introduced curvature difference is calculated for each point based on the given parameters. : （9）， Wherein, the normalization constant ; This represents the mean vector of the m-th Gaussian component. Perform parameters Coordinate transformation under; Represents the spatial coordinates of the nth point in the target point cloud; Next, we perform an M-step to find new parameters by minimizing the complete negative logarithm function: （10）， Among them, intermediate parameters ; This represents the objective function in Gaussian mixture model point cloud registration, which measures the performance of a point cloud under given parameters. Covariance Below, the degree of matching between the source point cloud and the target point cloud; The centroid transformation of the Gaussian mixture model is defined as: R represents the rotation matrix, t represents the translation vector, and s represents the scale factor; The objective function can be further written as: （11）， in This represents the objective function based on the Gaussian mixture model in point cloud registration. The parameters are obtained through singular value decomposition: （12）， （13）， （14）， （15）， Where C is the covariance matrix; A is the weighted correlation matrix. d(P) is the diagonal matrix of P, where P is the probability matrix; tr represents the trace of the matrix. It is the weighted centroid of the target point cloud Y. ; ; Denotes the weighted centroid of point set X; It is the point set matrix of the source point cloud. ; It is the weighted centroid of point set X; It is the point set matrix of the target point cloud. T denotes matrix transpose, and P denotes posterior probability density. The set of all points; the sum of the matching probabilities of all point pairs. U and V are the unitary matrices formed by the left singular vectors and the right singular vectors, respectively. ;in Represents the computation matrix The determinant value; Then, using the obtained rotation matrix R, translation vector t, scale factor s, and covariance... The original point cloud is transformed to obtain the registered point cloud. Step 5: Identify outliers in the registered point cloud based on multidimensional features; Step 6: Construct the accuracy evaluation index; In step 6, a three-dimensional labeling matrix [a,b,c] is established to label each point cloud identified as an anomaly. Each position in the matrix corresponds to a specific anomaly type: position a represents a geometric anomaly; position b represents a topological consistency anomaly; and position c represents a density distribution anomaly. At the same time, an assignment rule is established: if the point cloud has an anomaly of a certain type, the corresponding position is assigned a value of 1; if the point cloud does not have an anomaly, the corresponding position is assigned a value of 0. Two constraints are established as the basis for evaluating the modeling accuracy: outliers are classified according to the number of non-zero elements in the 3D marker matrix. First-level spatial feature set: The matrix has only one non-zero element, i.e., |a,b,c|[1,1,1]^T = 1, which means that the point cloud has anomalies in only one aspect; Second-level spatial feature set: The matrix has two non-zero elements, namely |a,b,c|[1,1,1]^T = 2, which indicates that the point cloud has anomalies in two aspects; Three-level spatial feature set: The matrix has three non-zero elements, namely |a,b,c|[1,1,1]^T = 3, which indicates that the point cloud has anomalies in all three aspects; Two constraints are established to evaluate the modeling accuracy: Condition 1: If the total number of first-level and second-level spatial feature sets exceeds the threshold of all feature sets, the modeling accuracy is deemed unqualified. Condition 2: If the proportion of the third-level spatial feature set to all feature sets exceeds the threshold, the modeling accuracy is deemed unqualified. In step 6, the accuracy evaluation index TOW is constructed under the condition that two constraints are satisfied: （16）， in, , , and Let these represent the normalized standard deviation of distance, the normalized standard deviation of curvature, the normalized standard deviation of normal vector, and the normalized standard deviation of density, respectively. The calculation formulas are as follows: , , , ,in, , , and These are the original distance, curvature, normal vector, and density standard deviation, respectively. , , and They are , , and The maximum possible value; To distinguish quantities in space; These are the valid sampling points after identifying outliers; This represents the distance from the outlier points; The number of outliers in curvature or normal vector; W1 represents the number of density outliers; W2 are weighting coefficients, satisfying W1+W2=1.

2. The method according to claim 1, characterized in that, In step 1, a 3D laser scanner is used to perform high-precision scanning of the spatial target to obtain point cloud data, which is used as the ground truth point cloud. For the triangular mesh model to be evaluated after modeling, a uniform sampling method is used to resample and generate an indirect point cloud: First, the area of ​​each triangle is calculated based on the vertices of each triangle, and then the number of sampling points is allocated according to the proportion of each triangle to the total surface area. G1 = round(H1 * H2) H1 = H3, H2 = H4 / H5 H5 = Σ(H6), Where G1 represents the number of sampling points of the first triangle, H1 represents the total number of sampling points, H2 represents the area ratio of the first triangle, H3 represents the number of point clouds scanned by the lidar, H4 represents the area of ​​the first triangle, H5 represents the total area, and H6 represents the area of ​​all triangles. The triangular mesh model records the vertex coordinates of each triangle on the surface. Then, sampling points are uniformly generated inside the plane of each triangle using the centroid coordinate method, while retaining the vertices of the original triangular mesh, to generate a resampled point cloud that covers the model surface and contains the geometric features of the target.

3. The method according to claim 2, characterized in that, In step 2, the normal vector and curvature of each point in the indirect point cloud are calculated. A covariance matrix is ​​constructed from the K nearest neighbors of each point. The eigenvector corresponding to the smallest eigenvalue of the covariance matrix is ​​calculated as the normal vector. The normal vector is propagated using the region growing method. Based on the eigenvalues ​​of the covariance matrix of each point, assuming λ1≥λ2≥λ3, the approximate value of curvature c is calculated. （1）， Where λ1 represents the degree of dispersion of the point cloud in the principal direction; λ2 represents the degree of dispersion of the point cloud in the secondary principal direction; and λ3 represents the degree of dispersion of the point cloud in the normal vector direction. Analyze the histogram distribution of three angular features α, φ, and θ: （2）， （3）， （4）， in, and They are unit normal vector and Unit normal vector; characteristic angle Reflects the relative tilt of neighboring points; characteristic angle The vertical elevation angle of a neighboring point; characteristic angle Characterizes the curvature changes of a local surface; These are the spatial coordinates of neighboring points. These are the spatial coordinates of the center point. It is the unit normal vector of the k-th point. It is the z-coordinate of a neighboring point. It is the z-coordinate of the center point. It is the x-coordinate of a neighboring point. It is the x-coordinate of the center point. It is the y-coordinate of a neighboring point. It is the y-coordinate of the center point; Points with curvature values ​​greater than a threshold are considered feature points, and points with abrupt changes in the angle between their neighborhood normal vectors are considered edge features. A curvature consistency parameter (CCP) is also introduced. （5）， in, The neighborhood average value represents the curvature; by setting a threshold for the feature combination parameters, salient regions in the indirect point cloud are identified.

4. The method according to claim 3, characterized in that, In step 3, the sampling density is dynamically adjusted according to the importance of features to obtain the point cloud to be evaluated: in regions with significant features, the point density of the original point cloud is increased; in transition regions, the original point density is maintained; and in flat regions, the point density of the original point cloud is decreased. During resampling, new points are generated inside the triangle surface using the centroid coordinate method; the triangular mesh model to be evaluated in step 1 includes the labeled triangle vertices, which are retained as key topological points and do not participate in the resampling process.

5. The method according to claim 4, characterized in that, In step 4, the curvature features of the target point cloud after coordinate transformation are calculated using formula (1). .

6. The method according to claim 5, characterized in that, In step 5, during the outlier identification process of the registered point cloud, error statistics are first obtained: by calculating the average error... and maximum error The overall deviation between the two point clouds is obtained; where, and These represent the points in the point cloud to be evaluated and the corresponding nearest neighbors in the ground truth point cloud, respectively. Indicates all The maximum value in; Using KL divergence Quantify the difference between two curvature distributions; where P(x) represents the probability density value of the probability distribution of the source point cloud at point x, and Q(x) represents the probability density value of the probability distribution of the target point cloud at point x; x represents the independent variable of the probability distribution function; Then, calculate the angle between the normal vectors. Evaluate the consistency of the normal vector, where n i and m i These are the normal vectors of the corresponding points in the point cloud to be evaluated and the normal vectors of the corresponding points in the ground truth point cloud, respectively. This is achieved by dividing the space into grids and calculating the point density differences within each grid. ;in, and Let represent the point density of the point cloud to be evaluated in the j-th grid and the point density of the ground truth point cloud in the j-th grid, respectively. Finally, abnormal regions are identified by setting judgment criteria. When a region W meets the criteria... , or If any of the conditions are met, W will be defined as an abnormal region. , and These are the thresholds for distance, normal vector difference, and point density difference, respectively. This represents the average distance in region W. This represents the difference in point density between region W and its surrounding regions. This represents the angular deviation of the normal vector within region W.

7. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 6.

8. A storage medium, characterized in that, It stores a computer program or instructions that, when run on a computer, perform the steps of the method as described in any one of claims 1 to 6.

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