Casting deformation compensation method based on point cloud

Abstract

The invention provides a casting deformation compensation method based on point cloud, and belongs to the crossing field of three-dimensional digital detection and precision casting technology, and the method comprises the steps: carrying out the Gaussian filtering and edge point detection of a casting point cloud, sampling an edge point detection result to obtain a source point cloud, registering the source point cloud to a template point cloud coordinate system of a casting through ICP registration, and obtaining a point cloud coordinate system of the casting; obtaining an initial registration point cloud; respectively acquiring a registration feature point set and a template feature point set of the initial registration point cloud and the template point cloud by using SIFT, acquiring a rough matching pair set according to the feature point distance, and performing robust matching on the rough matching pair set to obtain a fine registration point cloud; performing deformation compensation on the fine registration point cloud based on local affine transformation and multi-scale deformation mapping to obtain a final registration point cloud; dividing the final registration point cloud into a rigid layer point cloud and a non-rigid layer point cloud; and transforming the final registration point cloud by using the global transformation matrix to obtain a compensation point cloud. The deformation compensation precision and efficiency of the casting can be effectively improved.

Description

Technical Field

[0001] The present invention belongs to the cross - field of three - dimensional digital detection and precision casting technology, and particularly relates to a method for compensating casting deformation based on point cloud. Background Technique

[0002] During the solidification and cooling process of castings, due to differences in alloy shrinkage rates, the constraint effect of the mold shell, and uneven temperature gradient distribution, complex deformation phenomena such as overall shrinkage and local warping generally exist. Traditional anti - deformation compensation methods rely on empirical formulas or finite - element simulations to predict the deformation amount, and achieve deformation cancellation by presetting reverse compensation amounts during the mold design stage. However, for complex - surface castings such as turbine blades, the deformation shows highly non - linear characteristics. It is difficult to accurately match the actual deformation amount with only single - displacement - field compensation, and multiple trial - mold iterations are often required for correction.

[0003] With the development of three - dimensional scanning technology, deformation analysis based on measured point clouds has gradually become the mainstream. However, it still faces the following multiple technical bottlenecks in engineering applications: In the point - cloud pre - processing stage, the surface of castings often has interference features such as burrs and oxide scales, and the scanned data is mixed with high - frequency noise and redundant points. Existing technologies have defects such as blurring geometric edge details or limited effects in removing irregular burrs when filtering noise and redundant points; In the deformation - modeling stage, traditional global rigid - transformation models cannot represent the gradient characteristics of casting shrinkage, while pure non - rigid algorithms have high computational complexity and are prone to excessive deformation. About 60% of casting deformation belongs to global rigid displacement and 40% is local plastic deformation. Therefore, a hybrid modeling strategy is required. However, existing methods mostly divide rigid regions through curvature analysis but do not establish a dynamic weight mechanism, resulting in discontinuous phenomena in the transition region of the compensation matrix. This makes the accuracy and efficiency of existing technologies for compensating casting deformation unsatisfactory. Summary of the Invention

[0004] The purpose of the present invention is to propose a method for compensating casting deformation based on point cloud, which can effectively improve the accuracy and efficiency of casting deformation compensation.

[0005] The present invention is realized through the following technical solutions: A method for compensating casting deformation based on point cloud, comprising the following steps: Step S1: Perform Gaussian filtering and edge - point detection on the casting point cloud, sample the edge - point detection results using a dynamic sampling rate to obtain a source point cloud, and register the source point cloud to the coordinate system of the template point cloud of the casting using ICP registration to obtain an initial registered point cloud; Step S2: Use SIFT to respectively obtain the registered feature - point set of the initial registered point cloud and the template feature - point set of the template point cloud, obtain a set of rough - matching pairs based on the feature - point distance, and perform robust matching on this set of rough - matching pairs to obtain a precisely registered point cloud; Step S3. Perform deformation compensation on the finely registered point cloud based on local affine transformation and multi-scale deformation mapping to obtain the final registered point cloud; Step S4. Calculate the standard deviation of curvature of each point cloud in the final registered point cloud, and perform clustering on the final registered point cloud based on the KD tree to obtain multiple clusters of point clouds. For each cluster of point clouds, if the standard deviation of curvature of each point cloud is less than the set curvature threshold and the included angle between the normal vectors of the point clouds is less than the set first included angle threshold, then classify this cluster of point clouds as rigid layer point clouds; otherwise, classify them as non-rigid layer point clouds; Step S5. Use the global transformation matrix to transform the final registered point cloud to obtain the compensated point cloud. The global transformation matrix is obtained by weighted fusion of the homogeneous transformation matrix and the local affine transformation matrix. The homogeneous transformation matrix is obtained according to the rigid layer point clouds, and the local affine transformation matrix is obtained according to the non-rigid layer.

[0006] Further, in the step S1, the edge point detection of the cast point cloud after Gaussian filtering specifically includes: for the i -th point cloud of the cast point cloud after Gaussian filtering, calculate the covariance matrix of the point cloud coordinates in its neighborhood, perform eigenvalue decomposition on this covariance matrix to obtain three eigenvalues λ1, λ2, λ3 sorted by size. If λ1 > k 1·λ2 and λ2 ≤ k 2·λ3, then determine that the i -th point cloud is a candidate edge point. If the variance of the included angles between the normal vectors of the points in the neighborhood and the normal vector of the center point is greater than the set second included angle threshold, then determine that the i -th point cloud is an edge point. After attaching an edge point mark to this point cloud, place it in the edge point set, where n is the number of point clouds in the neighborhood, q j is the j -th point cloud in the neighborhood, and μ is the mean value of the point clouds in the neighborhood.

[0007] Further, in the step S1, the sampling of the edge point detection result using the dynamic sampling rate specifically includes: recursively divide the edge point set to obtain multiple point sets. Each time of division, calculate the variances of the current point set on the X / Y / Z coordinate axes respectively, select the coordinate axis corresponding to the maximum variance as the splitting axis, sort the current point set according to the splitting axis coordinate, select the median in the sorting as the splitting point, and divide the current point set into two point sets. For each point set, determine it as a high-density area or a low-density area according to its point density, and perform sampling at a lower sampling rate in the high-density area and at a higher sampling rate in the low-density area.

[0008] Further, in the step S1, in the ICP registration, iterate with an iteration step size , in each iteration, for the template point cloud P t the point cloud in p t , search for the nearest neighbor points of the point cloud P s in the source point cloud p t . If the included angle between the normal vectors of the point cloud p s and the point cloud p s is less than the set third included angle threshold, then ( p t , p s , p t ) is used as a valid matching pair. After the iteration ends, the transformation matrix T is obtained. According to the formula the initial registered point cloud is obtained . Among them, is the set large step size, is the set small step size, is the error change rate of the current iteration, E k is the error of the current iteration.

[0009] Furthermore, the step S2 includes the following steps: Step S21: Use SIFT to obtain the set of registration feature points of the initial registered point cloud and the set of template feature points of the template point cloud; Step S22: For the template feature points in the set of template feature points, select the registration feature points in the registered point cloud whose distance from the template feature point is less than the set distance threshold, and form an initial matching pair with the selected registration feature points; Step S23: When the number of initial matching pairs is greater than one, calculate the distances between the template feature points and the registration feature points corresponding to each initial matching pair to obtain the nearest neighbor distance D 1 and the second nearest neighbor distance D 2. If D 1 / D 2 is less than the set ratio threshold, then retain the initial matching pair corresponding to the nearest neighbor distance; otherwise, delete all the initial matching pairs corresponding to the template feature point to obtain the set of rough matching pairs; Step S24: Use the RANSAC algorithm to remove the mismatches in the set of rough matching pairs, and use the Geman-McClure kernel function to optimize the set of rough matching pairs after removing the mismatches to obtain the optimal transformation matrix, and then obtain the accurately registered point cloud according to the initial registered point cloud and the optimal transformation matrix .

[0010] Further, the specific steps of step S3 are as follows: Step S31: Optimize the local affine transformation matrix through random gradient descent iteration A i , where the loss function is , where , , represents the point in the template point cloud that matches the point cloud p i , is the set threshold; Step S32: Use the Laplace - Beltrami operator to calculate the curvature of the finely registered point cloud transformed by the local affine transformation matrix, separate the high - curvature region and the low - curvature region, construct a Gaussian pyramid, gradually reduce the point cloud resolution, extract geometric features from coarse to fine to achieve multi - scale filtering, and obtain the filtered point cloud; Step S33: Define the energy function , and optimize the transformation matrix T' to minimize the Wasserstein distance between the filtered point cloud and the template point cloud to obtain the final registered point cloud , where p i' represents the filtered point cloud, p j' is the point cloud in the template point cloud that matches p i' , and inf represents the infimum.

[0011] Further, in step S4, according to the formula calculate the standard deviation of the curvature of the point cloud p i'' in the final registered point cloud , where m is the number of points in the neighborhood of the point cloud p i'' , is the Gaussian curvature of the point cloud p j'' in the neighborhood, is the average Gaussian curvature in the neighborhood.

[0012] Further, the curvature threshold is set to 0.05, and the first included - angle threshold is set to 10°.

[0013] Further, in step S5, for the point cloud in the final registered point cloud p i'' , its corresponding global transformation matrix is expressed as , optimize the weights through the Levenberg-Marquardt algorithm w i'' , where is a homogeneous transformation matrix, is a local affine transformation matrix, and when optimizing the weights w i'' , its initial value is obtained by the formula , K i'' represents the point cloud of the non-rigid layer p i'' of the Gaussian curvature, represents the point cloud of the non-rigid layer p i'' of the Gaussian curvature gradient, , are set weight factors, .

[0014] Furthermore, in the step S5, for the point cloud of the non-rigid layer p i'' , use the least squares method to obtain and , where the error function is defined as , is the point cloud in the template point cloud, and N is the number of point clouds in the template point cloud.

[0015] The present invention has the following beneficial effects: 1. The present invention performs Gaussian filtering and edge point detection on the cast part point cloud, can eliminate local perturbations while retaining geometric features, ensure that key structures such as edges and corners are not blurred, uses a dynamic sampling rate to sample the edge point detection results to obtain the source point cloud, and uses ICP registration to register the source point cloud to the coordinate system of the cast part template point cloud to obtain the initial registered point cloud, which can achieve data reduction and registration optimization, and effectively improve the quality of the point cloud; uses SIFT to obtain the registration feature point set of the initial registered point cloud and the template feature point set of the template point cloud respectively, obtains the rough matching pair set based on the feature point distance, performs robust matching on the rough matching pair set to obtain the fine registered point cloud, and performs deformation compensation on the fine registered point cloud based on local affine transformation and multi-scale deformation mapping to obtain the final registered point cloud, which can achieve fine adjustment of local deformation and enhance the ability to retain details. Finally, it is judged whether each point cloud in the final registered point cloud belongs to the rigid layer point cloud or the non-rigid layer point cloud, and the global transformation matrix is used to transform the final registered point cloud to obtain the compensated point cloud. The global transformation matrix is obtained by weighted fusion of the homogeneous transformation matrix and the local affine transformation matrix. The homogeneous transformation matrix is obtained according to the rigid layer point cloud, and the local affine transformation matrix is obtained according to the non-rigid layer, effectively solving the compensation problem of coexistence of rigid and non-rigid deformations in the cast part, and thus effectively improving the compensation accuracy and efficiency. Description of the Drawings

[0016] The present invention will be further described in detail below with reference to the accompanying drawings.

[0017] Figure 1 It is a flowchart of the present invention.

[0018] Figure 2 It is the casting point cloud of the present invention.

[0019] Figure 3 It is the template point cloud of the present invention.

[0020] Figure 4 It is the final registration schematic diagram of the casting point cloud and the template point cloud of the present invention.

[0021] Figure 5 It is the schematic diagram of the casting compensation point cloud of the present invention. Specific embodiments

[0022] As Figure 1 shown, the method for compensating casting deformation based on point cloud includes the following steps: Step S1: Perform Gaussian filtering and edge point detection on the casting point cloud, sample the edge point detection result using a dynamic sampling rate to obtain a source point cloud, and register the source point cloud to the coordinate system of the template point cloud of the casting using ICP registration to obtain an initial registered point cloud; Specifically, the casting point cloud is as Figure 2 shown, and the template point cloud is as Figure 3 shown. The template point cloud is obtained from the standard CAD model of the casting; In Gaussian filtering, the weights of each point in the neighborhood are calculated through a Gaussian function, and these points are weighted and averaged to update the coordinates of the center point; The edge point detection for the Gaussian-filtered casting point cloud specifically includes: for the i th point cloud of the Gaussian-filtered casting point cloud, calculate the covariance matrix of the point cloud coordinates in its neighborhood, perform eigenvalue decomposition on this covariance matrix to obtain three eigenvalues λ1, λ2, λ3 sorted by size. If λ1 > k 1 ⋅ λ2 and λ2 ≤ k 2 ⋅ λ3, then determine that the i th point cloud is a candidate edge point. If the variance of the included angle between the normal vectors of each point in the neighborhood and the normal vector of the center point is greater than a set second included angle threshold, then determine that the i th point cloud is an edge point, add an edge point mark to this point cloud and place it in the edge point set, where n is the number of point clouds in the neighborhood, q j is the j th point cloud in the neighborhood, μis the mean of the point cloud in the neighborhood, k 1 = 4, k 2 = 1.5.

[0023] Sampling the edge point detection results using a dynamic sampling rate specifically includes: recursively dividing the edge point set to obtain multiple point sets. Each time of division, calculate the variance of the current point set on the X / Y / Z coordinate axes respectively, select the coordinate axis corresponding to the maximum variance as the splitting axis, sort the current point set according to the splitting axis coordinate, select the median in the sorting as the splitting point, and divide the current point set into left and right point sets. For each point set, determine whether it is a high-density area or a low-density area according to its point density. Sample at a lower sampling rate (such as 10%) in the high-density area and at a higher sampling rate (such as 30%) in the low-density area. During the sampling process, for the feature areas (such as edge points or regions with significant curvature) identified by curvature or the change rate of the normal vector, all points are forced to be retained. Compared with uniform sampling, the dynamic sampling of the present invention compresses by more than 20% while maintaining the feature integrity. Among them, the point density calculation formula is , and define the area as the high-density area, and define the area as the low-density area, is the global average density, l 1 = 1.5, l 2 = 1.8.

[0024] In ICP registration, iterate with the iteration step size , in each iteration, for the template point cloud P t in the point cloud p t , search for the nearest neighbor point of the point cloud P s in the source point cloud p t . If the included angle between the normal vectors of the point cloud p s and the point cloud p s is less than the set third included angle threshold, then take ( p t , p s ) as a valid matching pair. After the iteration ends, obtain the transformation matrix T, and according to the formula p t get the initial registered point cloud where, is the set large step size, is the set small step size, is the error change rate of the current iteration, is, Ek is the error of the current iteration. Among them, the third included angle threshold is set to 15° - 30°, the large step size is 0.5, and the small step size is 0.1.

[0025] Step S2: Use SIFT to respectively obtain the registration feature point set of the initial registration point cloud and the template feature point set of the template point cloud, obtain the set of rough matching pairs based on the distance between feature points, and perform robust matching on the set of rough matching pairs to obtain the precisely registered point cloud; Specifically, it includes the following steps: Step S21: Use SIFT (Scale-Invariant Feature Transform) to obtain the registration feature point set of the initial registration point cloud and the template feature point set of the template point cloud; in the parameter settings of SIFT, min_scale = 0.01 defines the minimum scale space resolution, n_octaves = 3 indicates constructing three scale pyramid layers, and each layer contains n_scales_per_octave = 4 sub-levels to cover the feature changes at different scales.

[0026] Step S22: For the template feature points in the template feature point set, select the registration feature points in the registration point cloud whose distance from the template feature point is less than the set distance threshold, and form an initial matching pair with the selected registration feature points; Step S23: When the number of initial matching pairs is greater than one, calculate the distances between the template feature points and the registration feature points corresponding to each initial matching pair to obtain the nearest neighbor distance D 1 and the second nearest neighbor distance D 2. If D 1 / D 2 is less than the set ratio threshold, then retain the initial matching pair corresponding to the nearest neighbor distance; otherwise, delete all the initial matching pairs corresponding to the template feature point to obtain the set of rough matching pairs ; among them, the ratio threshold is set to 0.6; Geometric combination constraints can also be added. Let the original triangle side length be , and after matching it is . If , then it is considered to satisfy geometric similarity. The 5% error threshold refers to the actual sensor noise level and balances robustness and computational efficiency.

[0027] Step S24: Use the RANSAC algorithm to eliminate the mismatches in the set of rough matching pairs, use the Geman-McClure kernel function to optimize the set of rough matching pairs after eliminating the mismatches to obtain the optimal transformation matrix, and then obtain the precisely registered point cloud according to the initial registration point cloud and the optimal transformation matrix ; When RANSAC eliminates the mismatches, calculate according to the formula the number of iterationsN , randomly sample at each iteration m = 3 matching pairs, calculate the transformation matrix, and count the number of inliers T inlier , when , terminate the iteration in advance and output the optimal transformation matrix and the inlier set ; In the optimization of the Geman-McClure kernel function, according to the residuals in the inlier set , calculate the error function and the weight function (this weight function comes from the Geman-McClure kernel function, is a dynamically adjusted scale parameter), then the robust matching pair set is , where is the estimated optimal rigid body transformation matrix, τ = 0.1mm is the residual threshold for judging whether it is an inlier, is the set of matching point pairs with high consistency that are retained, and the optimal transformation matrix , is the Euclidean distance between the transformed source point and the target point, and this minimization problem is solved by weighted least squares or nonlinear optimization.

[0028] Through a complete robust optimization from coarse to fine, the accuracy is significantly improved while maintaining the algorithm efficiency.

[0029] Step S3, perform deformation compensation on the finely registered point cloud based on local affine transformation and multi-scale deformation mapping to obtain the final registered point cloud; Specifically, it includes the following steps: Step S31, optimize the point cloud by random gradient descent iteration p i corresponding local affine transformation matrix A i , where the loss function is , where , , represents the point in the template point cloud that matches the point cloud p i matching, is the set threshold; Step S32, use the Laplace-Beltrami operator to calculate the curvature of the finely registered point cloud transformed by the local affine transformation matrix, separate the high-curvature region and the low-curvature region, construct a Gaussian pyramid, gradually reduce the point cloud resolution layer by layer, extract geometric features from coarse to fine to achieve multi-scale filtering, and obtain the filtered point cloud; Step S33, define the energy function Optimize the transformation matrix to minimize the Wasserstein distance between the filtered point cloud and the template point cloud T' to obtain the final registered point cloud as shown in Figure 4 , where p i' represents the filtered point cloud, p j' is the point cloud in the template point cloud that matches p i' , and inf represents the infimum.

[0030] Step S4: Calculate the standard deviation of the curvature of each point cloud in the final registered point cloud, and cluster the final registered point cloud based on the KD tree to obtain multiple clusters of point clouds. For each cluster of point clouds, if the standard deviation of the curvature of each point cloud is less than the set curvature threshold and the included angle between the normal vectors of the point clouds is less than the set first included angle threshold, then classify this cluster of point clouds as rigid layer point clouds; otherwise, classify them as non-rigid layer point clouds; According to the formula calculate the standard deviation of the curvature of the point cloud p i'' in the final registered point cloud , where m is the number of point clouds in the neighborhood of the point cloud p i'' , is the Gaussian curvature of the point cloud p j'' in the neighborhood, is the average Gaussian curvature in the neighborhood. The curvature threshold is set to 0.05, and the first included angle threshold is set to 10°. The calculation processes of the Gaussian curvature and the average Gaussian curvature are prior arts.

[0031] Step S5: Use the global transformation matrix to transform the final registered point cloud to obtain the compensated point cloud. The global transformation matrix is obtained by weighted fusion of the homogeneous transformation matrix and the local affine transformation matrix. The homogeneous transformation matrix is obtained according to the rigid layer point cloud, and the local affine transformation matrix is obtained according to the non-rigid layer; For the point cloud in the final registered point cloud p i'' , its corresponding global transformation matrix is expressed as , and optimize the weight w i'' through the Levenberg-Marquardt algorithm, where is the homogeneous transformation matrix, is the local affine transformation matrix. When optimizing the weight w i'' , its initial value is obtained from the formula Get, K i'' Representing non-rigid layer point clouds p i'' The Gaussian curvature of Representing non-rigid layer point clouds p i'' The Gaussian curvature gradient of , is the weight factor set based on experience, .

[0032] For non-rigid layer point clouds p i'' , using the least squares method to obtain and , where the error function is defined as , is the point cloud in the template point cloud, and N is the number of point clouds in the template point cloud. The final compensated point cloud is as follows Figure 5 shown.

[0033] The above description is only a preferred embodiment of the present invention, and therefore cannot be used to limit the scope of implementation of the present invention. That is, equivalent changes and modifications made according to the scope of the patent application of the present invention and the contents of the specification should still fall within the scope covered by the patent of the present invention.

Claims

1. A method for compensating the deformation of a casting based on point cloud, characterized in that: It includes the following steps: Step S1: Perform Gaussian filtering and edge point detection on the cast part point cloud, sample the edge point detection results using a dynamic sampling rate to obtain the source point cloud, and register the source point cloud to the coordinate system of the template point cloud of the cast part using ICP registration to obtain the initial registered point cloud; Step S2: Use SIFT to obtain the registered feature point set of the initial registered point cloud and the template feature point set of the template point cloud respectively, obtain the set of rough matching pairs based on the distance between feature points, and perform robust matching on the set of rough matching pairs to obtain the precisely registered point cloud; Step S3: Perform deformation compensation on the precisely registered point cloud based on local affine transformation and multi-scale deformation mapping to obtain the final registered point cloud; Step S4: Calculate the standard deviation of the curvature of each point cloud in the final registered point cloud, and perform clustering on the final registered point cloud based on the KD tree to obtain multiple clusters of point clouds. For each cluster of point clouds, if the standard deviation of the curvature of each point cloud is less than the set curvature threshold and the included angle between the normal vectors of the point clouds is less than the set first included angle threshold, then classify this cluster of point clouds as rigid layer point clouds, otherwise classify them as non-rigid layer point clouds; Step S5: Transform the final registered point cloud using the global transformation matrix to obtain the compensated point cloud. The global transformation matrix is obtained by weighted fusion of the homogeneous transformation matrix and the local affine transformation matrix. The homogeneous transformation matrix is obtained based on the rigid layer point cloud, and the local affine transformation matrix is obtained based on the non-rigid layer.

2. The method for compensating casting deformation based on point cloud according to claim 1, wherein: In the step S1, the edge point detection of the cast part point cloud after Gaussian filtering specifically includes: for the i th point cloud of the cast part point cloud after Gaussian filtering, calculate the covariance matrix of the point cloud coordinates within its neighborhood, perform eigenvalue decomposition on the covariance matrix to obtain three eigenvalues λ1, λ2, λ3 sorted by size. If λ1 > k 1 ⋅ λ2 and λ2 ≤ k 2 ⋅ λ3, then determine that the i th point cloud is a candidate edge point. If the variance of the angles between the normal vectors of each point within the neighborhood and the normal vector of the center point is greater than the set second angle threshold, then determine that the i th point cloud is an edge point. After attaching an edge point marker to the point cloud, place it in the edge point set, where n is the number of point clouds within the neighborhood, q j is the j th point cloud within the neighborhood, μ is the mean value of the point clouds within the neighborhood.

3. A method for compensating for the deformation of a casting based on point cloud according to claim 2, characterized in that: In the said step S1, specifically sampling the edge point detection results using a dynamic sampling rate includes: recursively dividing the edge point set to obtain multiple point sets. Each time of division, calculate the variance of the current point set on the X / Y / Z coordinate axes respectively, select the coordinate axis corresponding to the maximum variance as the splitting axis, sort the current point set according to the splitting axis coordinate, select the median in the sorting as the splitting point, divide the current point set into two point sets. For each point set, determine it as a high-density area or a low-density area according to its point density, sample at a lower sampling rate in the high-density area, and sample at a higher sampling rate in the low-density area.

4. A method for compensating for the deformation of a casting based on point cloud according to claim 3, characterized in that: In the step S1, in the ICP registration, iteration is performed with an iteration step size. , in each iteration, for the template point cloud P t the point cloud p t , search for the nearest neighbor points of the point cloud P s in the source point cloud p t . If the included angle between the normal vectors of the point cloud p s and the point cloud p s is less than the set third included angle threshold, then ( p t , p s ) is used as a valid matching pair. After the iteration ends, the transformation matrix T is obtained. According to the formula p t , the initial registered point cloud is obtained. Among them, is the set large step size, is the set small step size, is the error change rate of the current iteration, E k is the error of the current iteration.

5. A method for compensating for the deformation of a casting based on point cloud according to claim 4, characterized in that: The said step S2 includes the following steps: Step S21: Use SIFT to obtain the registered feature point set of the initial registered point cloud and the template feature point set of the template point cloud; Step S22: For the template feature points in the template feature point set, select the registered feature points in the registered point cloud whose distance from the template feature point is less than the set distance threshold, and form an initial matching pair by combining the template feature point and the selected registered feature point; Step S23: When there is more than one initial matching pair, calculate the distances between the template feature points and the registration feature points corresponding to each initial matching pair to obtain the nearest neighbor distance D 1 and the second nearest neighbor distance D 2. If D 1 / D 2 is less than the set ratio threshold, retain the initial matching pair corresponding to the nearest neighbor distance; otherwise, delete all the initial matching pairs corresponding to this template feature point to obtain a set of rough matching pairs Step S24: Use the RANSAC algorithm to eliminate the mismatches in the set of rough matching pairs, and use the Geman-McClure kernel function to optimize the set of rough matching pairs after eliminating the mismatches to obtain the optimal transformation matrix. Furthermore, obtain the precisely registered point cloud based on the initial registered point cloud and the optimal transformation matrix .

6. A method for compensating for casting deformation based on point cloud according to claim 5, characterized in that: The said step S3 specifically includes the following steps: Step S31: Iteratively optimize the local affine transformation matrix through stochastic gradient descent A i , where the loss function is , where , , represents the point in the template point cloud that matches the point cloud p i , is the set threshold; Step S32: Use the Laplace-Beltrami operator to calculate the curvature of the precisely registered point cloud transformed by the local affine transformation matrix, separate the high-curvature area and the low-curvature area, construct a Gaussian pyramid, gradually reduce the point cloud resolution layer by layer, extract geometric features from coarse to fine to achieve multi-scale filtering, and obtain the filtered point cloud; Step S33: Define an energy function to optimize the transformation matrix by minimizing the Wasserstein distance between the filtered point cloud and the template point cloud T' to obtain the final registered point cloud where p i' represents the filtered point cloud, p j' is the point cloud in the template point cloud that matches p i' and inf represents the infimum.

7. A method for compensating for casting deformation based on point cloud according to claim 6, characterized in that: In the step S4, according to the formula calculate the final registered point cloud the midpoint cloud p i'' the standard deviation of curvature , where m is the number of points in the neighborhood of the point cloud p i'' , is the Gaussian curvature of the point cloud in the neighborhood p j'' , is the average Gaussian curvature in the neighborhood.

8. A method for compensating casting deformation based on point cloud according to claim 7, characterized in that: The curvature threshold is set to 0.05, and the first included angle threshold is set to 10°.

9. A method for compensating for the deformation of a casting based on point cloud according to claim 8, characterized in that: In the step S5, for the finally registered point cloud the point cloud p i'' , its corresponding global transformation matrix is expressed as , and the weight is optimized by the Levenberg-Marquardt algorithm w i'' , where is the homogeneous transformation matrix, is the local affine transformation matrix. When optimizing the weight w i'' , its initial value is obtained by the formula , K i'' represents the Gaussian curvature of the non-rigid layer point cloud p i'' , represents the Gaussian curvature gradient of the non-rigid layer point cloud p i'' , and are the set weight factors, .

10. A method for compensating for casting deformation based on point cloud according to claim 9, characterized in that: In the step S5, for the non-rigid layer point cloud p i'' , the least squares method is used to obtain and , where the error function is defined as , is the point cloud in the template point cloud, and N is the number of point clouds in the template point cloud.

Images