Point cloud normal estimation method based on asymmetric twin network

Abstract

The invention discloses a point cloud normal estimation method based on an asymmetric twin network, and the method comprises the steps: constructing a multi-view normal estimation data set, and forming a noiseless point cloud data set and a noise point cloud data set; performing point cloud rotation on the data set to obtain a rotated data set; constructing an asymmetric twin network, wherein the asymmetric twin network comprises two normal estimators with the same structure; inputting the rotated noiseless point cloud data set into one normal estimator for training to obtain a noiseless normal estimation model; inputting the rotated noise point cloud data set into another normal estimator for training to obtain a noise normal estimation model; obtaining a feature matching loss function, and adjusting parameters of the noise normal estimation model to obtain an optimized noise normal estimation model; inputting the test set into the optimized noise normal estimation model to obtain a normal estimation value of the point cloud; according to the method, the relevance of different noise level feature representations in point cloud normal estimation is obtained, the performance of the model is improved, and the problem of overfitting is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of point cloud normal estimation, and in particular to a point cloud normal estimation method based on an asymmetric twin network. Background Art

[0002] Point cloud normal estimation is a fundamental task in the field of digital geometry processing. Its estimation results can be widely applied to a variety of downstream tasks, such as surface reconstruction, point cloud denoising, and semantic segmentation. Due to the lack of universal parameter settings applicable to diverse point clouds in traditional methods, data-driven normal estimation methods have emerged as an effective research direction to solve this problem and have achieved remarkable results.

[0003] The most classical normal estimation algorithms include Principal Component Analysis (PCA) proposed by Hoppe et al. (1992) and Singular Value Decomposition (SVD) proposed by Klasing et al. (2009). These methods estimate the normal of each point by sampling neighborhood points with a fixed scale on a given model and fitting the local tangent plane of the normal vector. Thanks to their simplicity and efficiency, a large number of improved methods based on this paradigm have emerged subsequently, such as Moving Least Squares (MLS) (Levin, 1998), Truncated Taylor Expansion (Jets) (Cazals & Pouget, 2005), etc. These improvement schemes aim to fit higher-order local surfaces at a larger sampling scale to improve the robustness of normal estimation. Despite significant progress, these methods are sensitive to the sampling scale and difficult to preserve local details. To solve the above problems, Mitra & Nguyen (2003) combined local information such as noise level, curvature, and sampling density to find a more reasonable sampling radius and gave theoretical guarantees. Subsequently, Pauly et al. (2003) assigned Gaussian weights to each neighborhood point. In addition, to preserve sharp features and local details, Voronoi cell analysis or Hough Transform was introduced into the normal estimation task (Mérigot et al., 2010; Amenta & Bern, 1998; Alliez et al., 2007; Boulch & Marlet, 2012). In fact, as mentioned above, traditional methods have improved performance through more heuristic designs, but the existence of a large number of additional interference parameters makes it difficult to generalize these algorithms to more general application scenarios. In recent years, with the rise of deep learning, data-driven methods have made significant breakthroughs in the robust point cloud normal estimation task.

[0004] Inspired by PointNet (Qi et al., 2017), Guerrero et al. (2018) proposed a point cloud network called PCPNet. This network takes local blocks as input and outputs the normal estimation value of the block center point. This architecture can be regarded as a milestone in the field of normal estimation, and its structure can be roughly divided into three parts: input block alignment, point feature extraction, and normal estimation module. Based on this paradigm, Zhou et al. (2020) adopted a multi-scale architecture in the feature extraction stage and introduced an additional constraint loss in the normal estimation stage. Cao et al. (2021) designed a differentiable classification RANSAC module to predict the implicit tangent plane, which can replace the original multi-layer fully connected normal estimation module in the PCPNet architecture. Similarly, DeepFit (Ben-Shabat & Gould, 2020) uses the n-th order Jet of weighted points to fit the local surface and predict the center point normal. This estimation module can constrain the solution space to obtain high-quality normal estimation. Subsequently, to improve the reliability of the n-Jet module, Zhang et al. (2022) introduced geometric weight guidance, while Zhou et al. (2023) and Zhu et al. (2021) considered updating the point positions before surface fitting. In addition, Zhu et al. (2021) also integrated multi-neighborhood scale features through a new aggregation layer, improving the network's feature extraction ability. In recent years, with the help of more powerful feature extraction networks such as point transformers (Zhao et al., 2021) and graph convolutional networks (Wang et al., 2019), Hsurf (Li et al., 2022) and GraphFit (Li et al., 2022) have further improved the performance of point cloud normal estimation.

[0005] The above methods are sensitive to the sampling scale and difficult to maintain local details. Moreover, although traditional methods have improved performance through more heuristic designs, the existence of a large number of additional interference parameters makes it difficult to generalize these algorithms to more general application scenarios. Summary of the Invention

[0006] The present invention provides a method for normal estimation of point clouds based on an asymmetric twin network to overcome the technical problems that in the existing models for normal estimation of point clouds, due to differences in different noise levels and noise patterns, the model performance is affected, resulting in poor data processing effects of the model.

[0007] To achieve the above objective, the technical solution of the present invention is as follows:

[0008] A method for normal estimation of point clouds based on an asymmetric twin network, comprising:

[0009] S1: Construct a multi - perspective normal estimation dataset, which is divided into a training set and a test set. Extract the point cloud data in the training set to form a noise - free point cloud dataset. At the same time, add noise to the noise - free point cloud dataset to form a noisy point cloud dataset. Perform the first point cloud rotation operation on the noise - free point cloud dataset and the noisy point cloud dataset to obtain the rotated noise - free point cloud dataset and the rotated noisy point cloud dataset;

[0010] S2: Construct an asymmetric Siamese network, and the asymmetric Siamese network includes two normal estimators with the same structure. The normal estimator includes a spatial transformation module, a feature encoder module, and a normal prediction module, which are used to predict the point cloud data to obtain the normal estimation value of the point cloud data;

[0011] S3: Input the rotated noise - free point cloud dataset into one of the normal estimators for training, obtain the normal estimation loss function, update the normal estimator to obtain a noise - free normal estimation model. The noise - free normal estimation model is used to extract the feature representation of the noise - free point cloud data;

[0012] S4: Input the rotated noisy point cloud dataset into the other normal estimator for training to obtain a noisy normal estimation model. The noisy normal estimation model is used to extract the feature representation of the noisy point cloud data;

[0013] S5: Perform feature matching on the feature representation of the noise - free point cloud data and the feature representation of the noisy point cloud data, obtain the feature matching loss function, and adjust the model parameters of the noisy normal estimation model based on the feature matching loss function to obtain an optimized noisy normal estimation model;

[0014] S6: Input the test set into the optimized noisy normal estimation model to obtain the normal estimation value of the point cloud.

[0015] Furthermore, the normal estimator is constructed based on the PCPNet neural network or the AdaFit neural network.

[0016] Furthermore, the spatial transformation module of the normal estimator includes a first MLPs module and a fully - connected layer;

[0017] The first MLPs module includes multiple MLPs layers, which are used to perform multi - layer non - linear transformation on the input rotated noise - free point cloud dataset or the rotated noisy point cloud dataset, and extract the first latent feature of the rotated noise - free point cloud dataset or the second latent feature of the rotated noisy point cloud dataset;

[0018] The fully connected layer is used to perform a dimensionality reduction operation on the first latent feature or the second latent feature output by the first MLPs module to obtain the quaternion of the noise-free point cloud data or the quaternion of the noisy point cloud data; the quaternion of the noise-free point cloud data includes the rotation matrix of the noise-free point cloud data, and the quaternion of the noisy point cloud data includes the rotation matrix of the noisy point cloud data;

[0019] Use the rotation matrices of the two quaternions to perform a second point cloud rotation operation on the corresponding point cloud data respectively to obtain the preliminarily predicted normal data of the noise-free point cloud and the preliminarily predicted normal data of the noisy point cloud.

[0020] Further, the feature encoder module of the normal estimator constructed based on the PCPNet neural network includes a second MLPs module with the same structure as the first MLPs module. The second MLPs module is used to perform a non-linear transformation on the input preliminarily predicted normal data of the noise-free point cloud or the preliminarily predicted normal data of the noisy point cloud to obtain the third latent feature of the preliminarily predicted normal data of the noise-free point cloud or the fourth latent feature of the preliminarily predicted normal data of the noisy point cloud.

[0021] Further, the feature encoder module of the normal estimator constructed based on the AdaFit neural network is a dynamic graph convolutional neural network block; the dynamic graph convolutional neural network block includes a local fusion layer and a third MLPs module with the same structure as the first MLPs module and the second MLPs module;

[0022] Input the input preliminarily predicted normal data of the noise-free point cloud or the preliminarily predicted normal data of the noisy point cloud into the local fusion layer, perform a k-nearest neighbor search on the points of each point cloud, and fuse the features of the neighboring points to obtain a first feature block or a second feature block with the same dimension as the corresponding latent feature. Input the first feature block or the second feature block into the third MLPs module to obtain the fifth latent feature of the preliminarily predicted normal data of the noise-free point cloud or the sixth latent feature of the preliminarily predicted normal data of the noisy point cloud.

[0023] Further, the normal prediction module of the normal estimator constructed based on the PCPNet neural network includes a first fully connected layer module;

[0024] The first fully connected layer module includes multiple fully connected layers and is used to perform multiple linear transformations on the input third latent feature or fourth latent feature to obtain the finally predicted normal data of the noise-free point cloud or the finally predicted normal data of the noisy point cloud.

[0025] Further, the normal prediction module of the normal estimator constructed based on the AdaFit neural network includes a weighted least squares solver;

[0026] The least squares solver is used to calculate the distance from each point in the point cloud to the tangent plane perpendicular to the normal vector for the fifth latent feature or the sixth latent feature, and with the goal of minimizing the sum of the distances from each point to the tangent plane perpendicular to the normal vector, the normal vector is continuously optimized until the goal is reached. The optimized normal vector is the finally predicted normal data of the noise-free point cloud or the finally predicted normal data of the noisy point cloud.

[0027] Further, obtain the normal estimation loss function, including:

[0028] Obtain the sine center loss function, as shown in formula (1),

[0029]

[0030] where L center represents the sine center loss function, represents the true normal of point p; n p represents the output normal of point p;

[0031] Obtain the consistency loss function for updating the weight-based least squares solver, as shown in formula (2),

[0032]

[0033] In the formula, L con represents the consistency loss function, N represents the number of points in the point cloud, q i represents any point in the point cloud, λ1 represents the regularization term weight, j is a constant, ω j represents the weight of each point in the least squares solver, λ2 represents the point cloud normal estimation weight, gt represents the true value, n gt,j represents the true normal vector of a certain point cloud, represents the predicted normal;

[0034] Obtain the regularization loss function to update the spatial transformation module, as shown in formula (3),

[0035] L reg =|I - AA T | (3)

[0036] In the formula, L reg represents the regularization loss, I represents the identity matrix, and A represents the feature alignment matrix;

[0037] Construct the normal estimation loss function of the finally constructed normal estimator based on the PCPNet neural network based on the sine center loss function and the regularization loss function, as shown in formula (4),

[0038] L total1 =L center +α2Lreg (4)

[0039] Based on the sine center loss function, the consistency loss function, and the regularization loss function, construct the normal estimation loss function of the final normal estimator constructed based on the AdaFit neural network, as shown in Equation (5).

[0040] L total2 = L center + α1L con + α2L reg (5)

[0041] In Equations (4) and (5), α1 and α2 are hyperparameters used to balance the influence of all subterms on the optimization behavior; L total1 is the normal estimation loss function of the final normal estimator constructed based on the PCPNet neural network, and L total2 is the normal estimation loss function of the final normal estimator constructed based on the AdaFit neural network.

[0042] Furthermore, perform feature matching on the feature representations of the noise-free point cloud data and the noisy point cloud data to obtain the feature matching loss function, including:

[0043] Use the Euclidean distance for feature matching, as shown in Equation (6).

[0044]

[0045] In the formula, l represents the l-th normal estimator, l = 1, 2; l = 1 represents the normal estimator used to train the noise-free point cloud dataset, l = 2 represents the normal estimator used to train the noisy point cloud dataset, C is the dimension of the extracted features; m is a constant;

[0046] and respectively represent all potential features extracted from the rotated noise-free point cloud dataset and the rotated noisy point cloud dataset.

[0047] Furthermore, construct a multi-view normal estimation dataset, including:

[0048] Introduce the denoising synthetic dataset and the ABC dataset. Select multiple mesh models from the denoising synthetic dataset and multiple CAD models from the ABC dataset. For each mesh model and CAD model, uniformly select r camera poses on the unit sphere, and sample the point cloud based on the camera poses to form a multi-view normal estimation dataset.

[0049] Beneficial effects: The present invention provides a method for estimating point cloud normal based on an asymmetric twin network. The proposed asymmetric twin network trains the noise-free point cloud data and the noisy point cloud data through two normal estimators respectively, ensuring that the multi-scale features are consistent with or without noise, obtaining the correlation of feature representations at different noise levels in point cloud normal estimation, improving the performance of the model and solving the overfitting problem; by constructing a large-scale multi-view normal estimation dataset for point cloud normal estimation, the scope of the dataset is expanded and the accuracy of point cloud estimation is improved. Description of the Drawings

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0051] Figure 1 It is a flowchart of a method for estimating point cloud normal based on an asymmetric twin network provided by the present invention;

[0052] Figure 2 It is a process diagram of constructing a multi-view normal estimation database of the present invention;

[0053] Figure 3 It is a structural diagram of the asymmetric twin network provided by the present invention;

[0054] Figure 4 It is a comparison chart of AUC result curves of an embodiment of the present invention;

[0055] Figure 5 It is a qualitative result diagram of the conventional dataset of the present invention;

[0056] Figure 6 It is a qualitative result diagram of the dataset of the present invention;

[0057] Figure 7 It is a visualization comparison chart of the improvement effect of multi-view training data based on the CAD model of the test set in the present invention;

[0058] Figure 8 It is a visualization comparison chart of the improvement effect of multi-view training data based on the fine model of the test set in the present invention;

[0059] Figure 9 It is a visualization comparison chart of the point cloud distribution across datasets in an embodiment of the present invention;

[0060] Figure 10 It is a t-SNE visualization result diagram of feature extraction of the spatial transformation module of the present invention. Specific Embodiments

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0062] This embodiment provides a point cloud normal estimation method based on an asymmetric siamese network, as Figure 1 shown, including:

[0063] S1: Construct a multi-view normal estimation dataset, which is divided into a training set and a test set. Extract the point cloud data in the training set to form a noise-free point cloud dataset, and at the same time add noise to the noise-free point cloud dataset to form a noisy point cloud dataset; perform a first point cloud rotation operation on the noise-free point cloud dataset and the noisy point cloud dataset to obtain a rotated noise-free point cloud dataset and a rotated noisy point cloud dataset;

[0064] S2: Construct an asymmetric siamese network, which includes two normal estimators with the same structure; the normal estimator includes a spatial transformation module, a feature encoder module, and a normal prediction module, and is used to predict the point cloud data to obtain the normal estimation value of the point cloud data;

[0065] S3: Input the rotated noise-free point cloud dataset into one of the normal estimators for training, obtain the normal estimation loss function, update the normal estimator, and obtain a noise-free normal estimation model; the noise-free normal estimation model is used to extract the feature representation of the noise-free point cloud data;

[0066] S4: Input the rotated noisy point cloud dataset into the other normal estimator for training to obtain a noisy normal estimation model; the noisy normal estimation model is used to extract the feature representation of the noisy point cloud data;

[0067] S5: Perform feature matching on the feature representation of the noise-free point cloud data and the feature representation of the noisy point cloud data, obtain the feature matching loss function, and adjust the model parameters of the noisy normal estimation model based on the feature matching loss function to obtain an optimized noisy normal estimation model;

[0068] S6: Input the test set into the optimized noisy normal estimation model to obtain the normal estimation value of the point cloud.

[0069] Specifically, first, a multi-view normal estimation dataset is constructed, which is divided into a training set and a test set. The point cloud data in the training set is extracted to form a noise-free point cloud dataset. At the same time, the noise-free point cloud dataset is added with noise to form a noisy point cloud dataset. A first point cloud rotation operation is performed on the noise-free point cloud dataset and the noisy point cloud dataset to obtain the rotated noise-free point cloud dataset and the rotated noisy point cloud dataset, which can enhance the richness of the normal estimation dataset, accurately simulate the real scanned point cloud affected by self-occlusion. Performing PCA operation on the point cloud data can eliminate the direction deviation. By rotation, the main axis (PCA eigenvector) of the point cloud is aligned with the coordinate axis, eliminating the arbitrary rotation posture of the original data, which is convenient for subsequent unified processing;

[0070] Secondly, an asymmetric Siamese network is constructed. The asymmetric Siamese network includes two normal estimators with the same structure. The normal estimator includes a spatial transformation module, a feature encoder module, and a normal prediction module, which are used to predict the point cloud data to obtain the normal estimation value of the point cloud data. The asymmetric Siamese network can extract multiple global features related to a given block at different stages. By introducing a symmetric Siamese training mechanism, the noisy data and the noise-free data are trained. Among them, the noise-free information can effectively guide the model training process and improve the model's representation ability for noisy blocks, thereby improving the prediction accuracy of the model;

[0071] Thirdly, the rotated noise-free point cloud dataset is input into one of the normal estimators for training to obtain a normal estimation loss function, and the normal estimator is updated to obtain a noise-free normal estimation model. The noise-free normal estimation model is used to extract the feature representation of the noise-free point cloud data. The rotated noisy point cloud dataset is input into another normal estimator for training to obtain a noisy normal estimation model. The noisy normal estimation model is used to extract the feature representation of the noisy point cloud data and perform feature matching to obtain a feature matching loss function. Based on the feature matching loss function, the model parameters of the noisy normal estimation model are adjusted to obtain an optimized noisy normal estimation model, which can adapt to the real scene and improve the accuracy of normal estimation of actual point cloud data;

[0072] Finally, the test set is input into the optimized noisy normal estimation model to obtain the normal estimation value of the point cloud, and the obtained data can avoid the direct interference of noise and adapt to the real scene.

[0073] In a specific embodiment, the scheme for constructing a multi-view normal estimation dataset, dividing it into a training set and a test set, extracting the point cloud data in the training set to form a noise-free point cloud dataset, and at the same time adding noise to the noise-free point cloud dataset to form a noisy point cloud dataset, and performing a first point cloud rotation operation on the noise-free point cloud dataset and the noisy point cloud dataset to obtain the rotated noise-free point cloud dataset and the rotated noisy point cloud dataset is as follows:

[0074] S11. Introduce the denoised synthetic dataset and the ABC dataset. Select multiple mesh models from the denoised synthetic dataset and multiple CAD models from the ABC dataset. For each mesh model and CAD model, uniformly select r camera poses on the unit sphere, and sample the point cloud based on the camera poses to form a multi-view normal estimation dataset:

[0075] To construct a more comprehensive point cloud normal estimation training and evaluation dataset, introduce the denoised synthetic dataset, select 11 feature-rich models, and select 56 CAD models from the ABC dataset;

[0076] For each mesh model, uniformly select 20 camera poses on the unit sphere, and sample the rendered point cloud based on these poses, as Figure 2 shown in the schematic diagram of the camera distribution in

[0077] This rendering process is implemented by Blender. The virtual camera resolution is set to 640×480, the sensor width and focal length are set to 36 and 40 respectively, and the true normal of the sampling surface is marked for each point of the virtual scan shape. The multi-view rendered point cloud effectively enhances the diversity of the sampling density;

[0078] To simulate the noise that may be introduced in virtual scanning, referring to the settings of PCPNet, add multiple levels of Gaussian noise to the multi-view scan shape to form noise data, and its standard deviations are 0.0025, 0.012, and 0.024 times the diagonal length of the shape bounding box, as Figure 2 shown. The figure shows examples of different noise levels. The noise only acts on the position information of the points, the true normal remains unchanged, and the points sampled from different noisy point clouds have corresponding relationships;

[0079] S12. Perform the first point cloud rotation operation on the noiseless point cloud dataset and the noisy point cloud dataset to obtain the rotated noiseless point cloud dataset and the rotated noisy point cloud dataset:

[0080] As Figure 3 shown, perform PCA operations on the noiseless point cloud dataset and the noisy point cloud dataset, and rotate the point cloud through the PCA operations:

[0081] The first step, given a point cloud block of N points N*3, first calculate the center position c of the point cloud block through the addition and averaging operation, and perform a translation operation on the original point cloud block to obtain the centered point cloud;

[0082] In the second step, calculate the covariance matrix of the centered point cloud, and perform SVD decomposition on the covariance matrix to obtain the component values of the point cloud block in three directions. We take the direction with the lowest component as the vertical direction of the point cloud block, align the point cloud block to obtain a 3*3 rotation transformation matrix, and perform matrix multiplication with the centered point cloud to align the direction of the point cloud block with the z-axis, completing the rotation of the point cloud block.

[0083] The multi-view virtual scanning dataset proposed in this solution has the following significant advantages:

[0084] 1) It contains both CAD models and synthetic models with richer details, enhancing the richness of the normal estimation dataset compared to the PCPNet dataset;

[0085] 2) By using a small number of 3D mesh models, scanning shapes with a wide sampling density coverage range and various shape types can be obtained;

[0086] 3) The dataset contains a large number of high-quality synthetic local scanned point clouds, which can accurately simulate real scanned point clouds affected by self-occlusion;

[0087] Performing PCA operation on the point cloud data can eliminate direction deviation. By rotating, the main axis (PCA eigenvector) of the point cloud is aligned with the coordinate axis, eliminating any rotation posture of the original data, which is convenient for subsequent unified processing.

[0088] In a specific embodiment, an asymmetric twin network is constructed. The asymmetric twin network includes two normal estimators with the same structure; the normal estimator includes a spatial transformation module, a feature encoder module, and a normal prediction module, and the solution for predicting the point cloud data to obtain the normal estimation value of the point cloud data is:

[0089] The normal estimator is constructed based on the PCPNet neural network or the AdaFit neural network;

[0090] As Figure 3 shown, the spatial transformation module of the normal estimator includes a first MLPs module and a fully connected layer; the quaternion space transformation layer in the figure is the spatial transformation module;

[0091] The first MLPs module includes multiple MLPs layers, which are used to perform multi-layer nonlinear transformation on the input rotated noiseless point cloud dataset or the rotated noisy point cloud dataset, extract the first latent feature of the rotated noiseless point cloud dataset or extract the second latent feature of the rotated noisy point cloud dataset; the latent feature is the multi-dimensional vector of the obtained point cloud data;

[0092] The fully connected layer is used to perform a dimensionality reduction operation on the first latent feature or the second latent feature output by the first MLPs module to obtain the quaternion of the noise-free point cloud data or the quaternion of the noisy point cloud data; the quaternion of the noise-free point cloud data includes the rotation matrix of the noise-free point cloud data, and the quaternion of the noisy point cloud data includes the rotation matrix of the noisy point cloud data;

[0093] The feature encoder module of the normal estimator based on the PCPNet neural network includes a second MLPs module with the same structure as the first MLPs module. The second MLPs module is used to perform a non-linear transformation on the initially predicted noise-free point cloud normal data or the initially predicted noisy point cloud normal data input, to obtain the third latent feature of the initially predicted noise-free point cloud normal data or the fourth latent feature of the initially predicted noisy point cloud normal data;

[0094] The feature encoder module of the normal estimator based on the AdaFit neural network is a dynamic graph convolutional neural network block; the dynamic graph convolutional neural network block includes a local fusion layer and a third MLPs module with the same structure as the first MLPs module and the second MLPs module;

[0095] Input the initially predicted noise-free point cloud normal data or the initially predicted noisy point cloud normal data into the local fusion layer, perform a k-nearest neighbor search on the points of each point cloud, and fuse the features of the neighboring points to obtain a first feature block or a second feature block with the same dimension as the corresponding latent feature. Input the first feature block or the second feature block into the third MLPs module to obtain the fifth latent feature of the initially predicted noise-free point cloud normal data or the sixth latent feature of the initially predicted noisy point cloud normal data;

[0096] The normal prediction module of the normal estimator based on the PCPNet neural network includes a first fully connected layer module;

[0097] The first fully connected layer module includes multiple fully connected layers, and is used to perform multiple linear transformations on the input third latent feature or fourth latent feature to obtain the finally predicted noise-free point cloud normal data or the finally predicted noisy point cloud normal data.

[0098] The normal prediction module of the normal estimator based on the AdaFit neural network includes a weighted least squares solver;

[0099] The least squares solver is used to calculate the distance from each point of the point cloud in the fifth latent feature or the sixth latent feature to the tangent plane perpendicular to the normal vector, and with the goal of minimizing the sum of the distances from each point to the tangent plane perpendicular to the normal vector, continuously optimize the normal vector until the goal is reached. The optimized normal vector is the finally predicted noise-free point cloud normal data or the finally predicted noisy point cloud normal data. The optimization steps are as follows:

[0100] Obtain the normal vectors of a certain point and the points within its neighborhood in the point cloud, and construct an objective function with the goal of minimizing the sum of the distances from all neighborhood points to the tangent plane perpendicular to the normal vector;

[0101] Convert this objective function into a linear least squares problem to obtain a linear least squares function;

[0102] Solve the linear least squares function: calculate the local covariance matrix and perform eigenvalue decomposition on the matrix. The smallest eigenvalue obtained from the decomposition is the optimal normal vector;

[0103] Perform optimization and solution for each point in the point cloud to obtain the finally predicted normal data of the noisy point cloud.

[0104] The estimator designed in this solution can extract multiple global features related to a given block at different stages. By introducing a symmetric twin training mechanism, it trains on noisy data and noise-free data. The noise-free information can effectively guide the model training process and improve the model's representation ability for noisy blocks, thereby improving the prediction accuracy of the model.

[0105] In a specific embodiment, the rotated noise-free point cloud dataset is input into one of the normal estimators for training. Calculate the normal estimation loss function and update the normal estimator to obtain a noise-free normal estimation model; The scheme for the noise-free normal estimation model to extract the feature representation of the noise-free point cloud data is as follows:

[0106] S31. Input the rotated noise-free point cloud dataset into one of the normal estimators for training. Perform multi-layer non-linear transformation on the input rotated noise-free point cloud dataset through a spatial transformation module to extract the first latent feature of the rotated noise-free point cloud dataset. Through dimensionality reduction operation on the first latent feature, obtain the quaternion of the noise-free point cloud data;

[0107] Perform a second point cloud rotation operation on the rotated noise-free point cloud dataset through the rotation matrix of the quaternion to obtain the preliminarily predicted noise-free point cloud normal data, that is, multiply the rotation matrix by the rotated noise-free point cloud dataset to obtain the preliminarily predicted noise-free point cloud normal data;

[0108] S32. Input the initially predicted normal data of the noise-free point cloud into the feature encoder module of the normal estimator constructed based on the PCPNet neural network or the feature encoder module of the normal estimator constructed based on the AdaFit neural network for processing to obtain the third latent feature or the fifth latent feature, and then input the corresponding latent feature into the normal prediction module of the normal estimator constructed based on the PCPNet neural network or the normal prediction module of the normal estimator constructed based on the AdaFit neural network for processing to obtain the finally predicted normal data of the noise-free point cloud;

[0109] S33. Obtain the normal estimation loss function, update the normal estimator, and obtain the noise-free normal estimation model:

[0110] Obtain the sine center loss function as shown in formula (7).

[0111]

[0112] where L center represents the sine center loss function, represents the true normal of point p; n p represents the output normal of point p;

[0113] Obtain the consistency loss function for updating the weight-based least squares solver as shown in formula (8).

[0114]

[0115] In the formula, L con represents the consistency loss function, N represents the number of points in the point cloud, q i represents any point in the point cloud, λ1 represents the regularization term weight, j is a constant, ω j represents the weight of each point in the least squares solver, λ2 represents the point cloud normal estimation weight, gt represents the true value, and n gt,j represents the true normal vector of a certain point cloud, represents the predicted normal;

[0116] Obtain the regularization loss function to update the spatial transformation module as shown in formula (9).

[0117] L reg = |I - AA T | (9)

[0118] In the formula, L reg represents the regularization loss, I represents the identity matrix, and A represents the feature alignment matrix;

[0119] The normal estimation loss function of the final normal estimator constructed based on the PCPNet neural network is constructed based on the sine center loss function and the regularization loss function, as shown in Equation (10).

[0120] L total1 = L center + α2L reg (10)

[0121] The normal estimation loss function of the final normal estimator constructed based on the AdaFit neural network is constructed based on the sine center loss function, the consistency loss function and the regularization loss function, as shown in Equation (11).

[0122] L total2 = L center + α1L con + α2L reg (11)

[0123] In Equations (10) and (11), α1 and α2 are hyperparameters used to balance the influence of all subterms on the optimization behavior; L total1 is the normal estimation loss function of the final normal estimator constructed based on the PCPNet neural network, and L total2 is the normal estimation loss function of the final normal estimator constructed based on the AdaFit neural network; to ensure fairness, the same loss function parameter settings as DeepFit are adopted, and the weight factors selected according to experience are: α1 = 0.25, α2 = 0.1;

[0124] According to the calculated losses of the two normal estimation loss functions, the gradient changes of each parameter in the outermost layer of the corresponding normal estimator are calculated, and feedback is performed using the chain rule to obtain the gradient changes of each parameter, and the weights of the parameters in the model are updated using the stochastic gradient descent method.

[0125] In this solution, the noise-free point cloud data is first trained to more purely learn the underlying geometric structure of the point cloud (such as shape, curvature, topological relationship), avoiding feature deviation caused by noise interference.

[0126] In a specific embodiment, the rotated noisy point cloud data set is input into another normal estimator for training to obtain a noisy normal estimation model; the scheme for the noisy normal estimation model to extract the feature representation of the noisy point cloud data is as follows:

[0127] S41. Input the rotated noisy point cloud dataset into another normal estimator for training. Perform multi-layer non-linear transformation on the input rotated noisy point cloud dataset through the spatial transformation module, extract the second latent feature of the rotated noisy point cloud dataset, and obtain the quaternion of the noisy point cloud data through dimensionality reduction operation on the second latent feature;

[0128] Perform the second point cloud rotation operation on the rotated noisy point cloud dataset through the rotation matrix of the quaternion to obtain the preliminarily predicted normal data of the noisy point cloud, that is, multiply the rotation matrix by the rotated noisy point cloud dataset to obtain the preliminarily predicted normal data of the noisy point cloud;

[0129] S42. Input the preliminarily predicted normal data of the noisy point cloud into the feature encoder module of the normal estimator constructed based on the PCPNet neural network, or the feature encoder module of the normal estimator constructed based on the AdaFit neural network for processing to obtain the fourth latent feature or the sixth latent feature;

[0130] Then input the corresponding latent feature value into the normal prediction module of the normal estimator constructed based on the PCPNet neural network, or the normal prediction module of the normal estimator constructed based on the AdaFit neural network for processing to obtain the finally predicted normal data of the noisy point cloud.

[0131] In this solution, training the noisy point cloud can adapt to the real scene and improve the accuracy of normal estimation of the actual point cloud data.

[0132] In a specific embodiment, the scheme for performing feature matching on the feature representations of the noise-free point cloud data and the noisy point cloud data, obtaining the feature matching loss function, and adjusting the model parameters of the noisy normal estimation model based on the feature matching loss function to obtain the optimized noisy normal estimation model is as follows:

[0133] S51. Use the Euclidean distance for feature matching, as shown in formula (12),

[0134]

[0135] In the formula, l represents the l-th normal estimator, l = 1, 2; l = 1 represents the normal estimator for training the noise-free point cloud dataset, l = 2 represents the normal estimator for training the noisy point cloud dataset, C is the dimension of the extracted feature; m is a constant;

[0136] and respectively represent all the latent features extracted from the rotated noise-free point cloud dataset and the rotated noisy point cloud dataset;

[0137] S52. Adjust the model parameters of the noise normal estimation model based on the feature matching loss function to obtain an optimized noise normal estimation model:

[0138] Calculate the gradient change of each parameter in the outermost layer of the corresponding model according to the loss of the obtained feature matching loss function, use the chain rule for feedback to obtain the gradient change of each parameter, and use the stochastic gradient descent method to update the weights of the parameters in the model.

[0139] In a specific embodiment, the scheme of inputting the test set into the optimized noise normal estimation model to obtain the normal estimation value of the point cloud is as follows:

[0140] Input the test set into the optimized noise normal estimation model for processing, and output the true normal estimation value.

[0141] To verify the effectiveness of this scheme, compare it with the prior art from the following aspects:

[0142] 1. Evaluate the asymmetric twin network architecture of the present invention using a public dataset:

[0143] 1) Determine the comparison dataset

[0144] The datasets for comparison include PCPNet (Guerrero et al., 2018) and FamousShape (Erler et al., 2020), both of which provide the true normals of the point cloud. The PCPNet dataset consists of a training set and a test set, and strictly follows its original experimental settings, including operations such as training-test division, noise addition, and changes in the density of test data distribution;

[0145] The FamousShape dataset is mainly used for method performance evaluation. In the FamousShape dataset, this dataset contains a total of 5360 point clouds, covering four noise scales, and is divided into a training set and a test set, with the test set accounting for 40%;

[0146] 2) Determine the asymmetric twin network architecture

[0147] To verify the effectiveness of the proposed asymmetric twin network of the invention, a comparative experiment is conducted by comparing the network of the present invention with various mainstream normal estimation algorithms, including DeepFit (Ben-Shabat & Gould, 2020), AdaFit (Zhu et al., 2021), and GraphFit (Li et al., 2022);

[0148] To ensure the fairness of the experiment, all comparative methods adopt determined parameter settings:

[0149] DeepFit: A single-scale model that follows the PCPNet structure. The encoder includes QSTN, MLP, and FTN layers, and the decoder is a four-layer MLP. The n-Jet technology is introduced, with the block size set to 256 points and the Jet order to 3.

[0150] AdaFit: Similar to DeepFit, but adds a cascaded scale aggregation (CSA) module to achieve multi-scale feature extraction. The block size gradually decreases from 700 to 350 and 175, and the Jet order is 3.

[0151] GraphFit: Performs multi-scale graph convolution operations, with the number of k-nearest neighbors set to 20 and 40. Feature aggregation is achieved through the GraphBlock layer and concatenation. The Jet order is 3, and the block size is set to 500.

[0152] Except for adopting a two-branch two-stage training strategy and adding a feature matching loss, the other parameters are the same as the original model:

[0153] First, train using the noise-free data in the PCPNet training set, and then use the complete PCPNet training set to train the asymmetric siamese network:

[0154] Through quantitative and qualitative comparisons, the accuracy improvement before and after introducing the asymmetric siamese network on the PCPNet and FamousShape datasets was evaluated, as shown in Tables 1 and 2.

[0155] Table 1 Comparison table of RMSE angular errors of unoriented normal estimation on the PCPNet dataset

[0156]

[0157] On the PCPNet dataset, the present invention brings improvements to both the DeepFit and AdaFit models. Although the performance of the GraphFit method slightly decreases, for high-noise data, all methods show performance improvement.

[0158] Table 2 Comparison of RMSE angular errors of unoriented normal estimation on the FamousShape dataset

[0159]

[0160]

[0161] Table 2 further shows that after training with the asymmetric siamese network of the present invention, the present invention also improves the performance on the FamousShape dataset with different distribution characteristics, indicating that the method of training the two branches of the model using noise-free data and noisy data respectively can enhance the generalization ability of the model by transmitting the noise-free data pattern information.

[0162] Figure 4 The AUC curves of PCPNet and the FamousShape dataset are shown. The figure presents the curves of three models, DeepFit, AdaFit, and GraphFit, without the asymmetric twin network designed in the present invention and with the asymmetric twin network designed in the present invention under No Noise, Low Noise, Med Noise, High Noise, Striped, and Gradient noises. It can be seen from the figure that the curves with the asymmetric twin network designed in the present invention are always better than the baseline, indicating its significant stability under different angular thresholds; Figure 4 The enlarged area shows that when trained with the asymmetric twin network, the performance improvement is particularly obvious when the error increases; in the figure, Siamese represents the twin network;

[0163] Figure 5 and Figure 6 respectively present the qualitative comparison results of the PCPNet and the FamousShape dataset. To clearly show the improvement brought by the network of the present invention, the normal angle error of each point of the point cloud is visualized through a heat map, and the point distribution ratio in different error intervals is statistically analyzed; Figure 5 is the comparison result of the PCPNet dataset, Figure 6 is the comparison result of the FamousShape dataset. For the PCPNet dataset, the error intervals are set to 5° and 10°, while for the FamousShape dataset, they are set to 10° and 20°; the experiments show that the training method based on the twin network effectively reduces the proportion of high-error points, indicating that the feature constraint successfully transfers the characteristics of noiseless data to high-error samples;

[0164] 2. Using the prior art to compare the influence of the domain difference between the dataset of the present invention and the conventional dataset

[0165] First, the multi-view normal estimation dataset of the present invention is evaluated using existing mainstream methods, and the evaluation results are shown in Tables 3 and 4.

[0166] Table 3 Influence of introducing multi-view training data on the RMSE angular error of normal estimation in the fine model test set

[0167]

[0168] Table 4 Comparison of the training RMSE angular error of normal estimation in the CAD test set

[0169]

[0170]

[0171] As can be seen from Table 3 and Table 4, when testing only using the PCPNet dataset (i.e., the "none" column), the model performs poorly on the dataset proposed in the present invention (including CAD models and detailed models), highlighting the significant differences between the two types of datasets. However, when the model is retrained using some data proposed in the present invention (the "with new data" column), the performance on the multi-view scanning test set is significantly improved, indicating that introducing the training of the constructed dataset can improve the accuracy of the model;

[0172] Figure 7 and Figure 8 The visualization comparison shows the performance improvement effects on the CAD model and the detailed model after training with new data:

[0173] Figure 7 It is a visualization comparison graph of the improvement effect of multi-view training data for the CAD model based on the test set. On the left side of the graph is the point cloud effect diagram with low noise, and on the right side is the comparison graph of the point cloud with high noise. The first row of each point cloud image in the graph shows the results of the existing point cloud estimation method without using this dataset, and the second row presents the optimization effect after introducing this dataset;

[0174] Figure 8 It is a visualization comparison graph of the improvement effect of multi-view training data for the fine model based on the test set. On the left side of the graph is the point cloud effect diagram with low noise, and on the right side is the comparison graph of the point cloud with high noise. The first row of each point cloud image in the graph shows the results of the existing point cloud estimation method without using this dataset, and the second row presents the optimization effect after introducing this dataset;

[0175] Furthermore, the performance of the multi-view point cloud data training model and the original model was compared on the PCPNet dataset, as shown in Table 5,

[0176] Table 5 Comparison of the impact of introducing multi-view training data on the RMSE angular error of normal estimation on the PCPNet test set

[0177]

[0178]

[0179] The results show that introducing multi-view data training significantly improves the performance of the PCPNet and DeepFit models; however, for models with stronger learning ability (such as GraphFit and HSurf), after introducing data training with significant domain differences, their performance on the PCPNet dataset slightly decreases. This indicates a phenomenon worthy of vigilance: high-performance normal estimation models (such as GraphFit and HSurf) may be in an overfitting state. Specifically, as Figure 9 shown, Figure 9Shows a visualization comparison diagram of the point cloud distribution across datasets. On the left is the point cloud distribution of the PCPNet dataset under noiseless, gradient noise, and stripe noise, and on the right is the point cloud distribution in the multi-view normal estimation dataset of the present invention. It can be seen from Figure 9 that the point cloud distribution in the multi-view normal estimation dataset of the present invention is more complex and non-uniform. Models relying on local graph convolution (such as GraphFit and HSurf) tend to learn these complex local patterns and may ignore the simpler distribution rules in the PCPNet dataset.

[0180] 3. In-depth analysis of the asymmetric twin network to determine specific parameters

[0181] Parameter setting analysis

[0182] In the asymmetric twin network, the feature matching weight is used to balance the normal estimation result and the noiseless feature matching degree. Its selection directly affects the generalization ability of the model. In the present invention, both the global feature and the final latent encoding in the rotation process of the spatial transformation module participate in the matching constraint. Comparing the effects of these two matching losses on the model accuracy, as shown in Table 6,

[0183] Table 6 Comparison of RMSE angular errors of asymmetric twin DeepFit under different feature matching weight values

[0184]

[0185] Taking DeepFit as the backbone network, the spatial transformation module learns feature matching at layer l1, and the final block feature matching is at layer l2. The results show that the optimal matching weight for the spatial transformation module layer is 0.5, and the weight of the feature matching term has the best constraint effect when it is 0.5. In addition, the features of the rotation layer have the greatest impact on the model robustness, while matching global features will reduce the performance, proving that the consistency of the QSTN rotation process is crucial;

[0186] 4. Visualization of the feature space drift

[0187] Finally, t-SNE is used to visualize the feature distribution drift extracted by DeepFit and the asymmetric twin network of the present invention. As Figure 10 shown, each group of examples shows the feature drift at low, medium, and high noise levels from left to right. In each group of examples, the first row is the one without adding the asymmetric twin network of the present invention in t-SNE, and the second row is the one with the addition of the asymmetric twin network of the present invention in t-SNE; it can be seen from the figure that after training with the asymmetric twin network, the feature distribution of the noisy data (blue dots) is closer to the noiseless point cloud, and the RMSE angular error is smaller. The visualization experiment shows that a more consistent feature distribution helps to improve the model stability.

[0188] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A point cloud normal estimation method based on an asymmetric twin network, characterized in that: include: S1: construct a multi-view normal estimation dataset, which is divided into a training set and a test set, extract point cloud data in the training set to form a noise-free point cloud dataset, and add noise to the noise-free point cloud dataset to form a noise point cloud dataset; Performing a first point cloud rotation operation on the noise-free point cloud dataset and the noisy point cloud dataset to obtain a rotated noise-free point cloud dataset and a rotated noisy point cloud dataset; S2: constructing an asymmetric twin network, wherein the asymmetric twin network includes two normal estimators with the same structure; the normal estimator includes a spatial transformation module, a feature encoder module and a normal prediction module, which are used to predict the point cloud data to obtain the normal estimation value of the point cloud data; S3: inputting the rotated noise-free point cloud data set into one of the normal estimators for training, obtaining a normal estimation loss function, updating the normal estimator, and obtaining a noise-free normal estimation model; the noise-free normal estimation model is used to extract feature representation of the noise-free point cloud data; S4: inputting the rotated noise point cloud data set into another normal estimator for training to obtain a noise normal estimation model; the noise normal estimation model is used to extract feature representation of the noise point cloud data; S5: performing feature matching on the feature representation of the noise-free point cloud data and the feature representation of the noise point cloud data, obtaining a feature matching loss function, and adjusting the model parameters of the noise normal estimation model based on the feature matching loss function to obtain an optimized noise normal estimation model; S6: Input the test set into the optimized noise normal estimation model to obtain the normal estimation value of the point cloud.

2. According to claim 1, a point cloud normal estimation method based on an asymmetric twin network is characterized in that: The normal estimator is constructed based on the PCPNet neural network or the AdaFit neural network.

3. According to claim 1, a point cloud normal estimation method based on an asymmetric twin network is characterized in that: The spatial transformation module of the normal estimator includes a first MLPs module and a fully connected layer; The first MLPs module includes multiple MLPs layers, which are used to perform multiple nonlinear transformations on the input rotated noise-free point cloud data set or the rotated noisy point cloud data set, and extract the first potential features of the rotated noise-free point cloud data set or extract the second potential features of the rotated noisy point cloud data set; The fully connected layer is used to perform a dimensionality reduction operation on the first potential feature or the second potential feature output by the first MLPs module to obtain a quaternion of noise-free point cloud data or a quaternion of noise point cloud data; the quaternion of noise-free point cloud data includes a rotation matrix of noise-free point cloud data, and the quaternion of noise point cloud data includes a rotation matrix of noise point cloud data; The two quaternion rotation matrices are used to perform a second point cloud rotation operation on the corresponding point cloud data to obtain preliminary predicted noise-free point cloud normal data and preliminary predicted noise point cloud normal data.

4. According to claim 2, a point cloud normal estimation method based on an asymmetric twin network is characterized in that: The feature encoder module of the normal estimator constructed based on the PCPNet neural network includes a second MLPs module with the same structure as the first MLPs module, and the second MLPs module is used to perform a nonlinear transformation on the input preliminary predicted noise-free point cloud normal data or the preliminary predicted noisy point cloud normal data to obtain the third potential feature of the preliminary predicted noise-free point cloud normal data or the fourth potential feature of the preliminary predicted noisy point cloud normal data.

5. The point cloud normal estimation method based on an asymmetric twin network according to claim 2, characterized in that: The feature encoder module of the normal estimator constructed based on the AdaFit neural network is a dynamic graph convolutional neural network block; the dynamic graph convolutional neural network block includes a local fusion layer and a third MLPs module with the same structure as the first MLPs module and the second MLPs module; The input preliminary predicted noise-free point cloud normal data or the preliminary predicted noisy point cloud normal data is input into the local fusion layer, a k-neighbor search is performed on each point cloud point, and the neighboring points are feature fused to obtain a first feature block or a second feature block of the same dimension as the corresponding potential feature, and the first feature block or the second feature block is input into the third MLPs module to obtain the fifth potential feature of the preliminary predicted noise-free point cloud normal data or the sixth potential feature of the preliminary predicted noisy point cloud normal data.

6. The point cloud normal estimation method based on an asymmetric twin network according to claim 4, characterized in that: The normal prediction module of the normal estimator built based on the PCPNet neural network includes a first fully connected layer module; The first fully connected layer module includes multiple layers of fully connected layers, which are used to perform multiple linear transformations on the input third potential feature or the fourth potential feature to obtain the final predicted noise-free point cloud normal data or the final predicted noisy point cloud normal data.

7. The point cloud normal estimation method based on an asymmetric twin network according to claim 5, characterized in that: The normal prediction module of the normal estimator built on the AdaFit neural network includes a weighted least squares solver; The least squares solver is used to calculate the distance from each point in the point cloud in the fifth potential feature or the sixth potential feature to the tangent plane perpendicular to the normal vector, and takes the minimum sum of the tangent plane distances from each point to the normal vector as the goal, and continuously optimizes the normal vector until the goal is reached. The optimized normal vector is the final predicted noise-free point cloud normal data or the final predicted noise point cloud normal data.

8. The point cloud normal estimation method based on an asymmetric twin network according to claim 7, characterized in that: Get the normal estimation loss function, including: Obtain the sinusoidal center loss function, as shown in formula (1), Among them, L center represents the sinusoidal center loss function, Represents the true value normal of point p; n p Represents the output normal direction of point p; Obtain the consistency loss function for updating the weighted least squares solver, as shown in formula (2), Where, L con represents the consistency loss function, N represents the number of points in the point cloud, and q i represents any point in the point cloud, λ1 represents the regularization term weight, j is a constant, ω j represents the weight of each point in the least squares solver, λ2 represents the point cloud normal estimation weight, gt represents the true value, and n gt,j Represents the true normal vector of a point cloud, represents the predicted normal direction; Obtain the regularized loss function and update the spatial transformation module, as shown in formula (3): L reg =|I-AA T | (3) Where, L reg represents the regularization loss, I represents the identity matrix, and A represents the feature alignment matrix; Based on the sine center loss function and the regularization loss function, the final normal estimation loss function of the normal estimator based on the PCPNet neural network is constructed, as shown in formula (4): L total1 =L center +α2L reg (4) Based on the sine center loss function, consistency loss function and regularization loss function, the final normal estimation loss function of the normal estimator based on the AdaFit neural network is constructed, as shown in formula (5): L total2 =L center +α1L con +α2L reg (5) In formulas (4) and (5), α1 and α2 are hyperparameters used to balance the impact of all sub-items on the optimization behavior; L total1 is the normal estimation loss function of the final normal estimator based on the PCPNet neural network, L total2 is the normal estimation loss function of the final normal estimator built based on the AdaFit neural network.

9. The point cloud normal estimation method based on an asymmetric twin network according to claim 1, characterized in that: Perform feature matching on the feature representation of the noise-free point cloud data and the feature representation of the noise point cloud data to obtain and calculate the feature matching loss function, including: Use Euclidean distance for feature matching, as shown in formula (6): Where, l represents the lth normal estimator, l = 1, 2; l = 1 represents the normal estimator used to train the noise-free point cloud dataset, l = 2 represents the normal estimator used to train the noisy point cloud dataset, C is the dimension of the extracted features; m is a constant; and Represent all potential features extracted from the rotated noise-free point cloud dataset and the rotated noisy point cloud dataset, respectively.

10. The point cloud normal estimation method based on an asymmetric twin network according to claim 1, characterized in that: Construct a multi-view normal estimation dataset, including: A denoising synthetic dataset and an ABC dataset are introduced. Multiple mesh models are selected from the denoising synthetic dataset, and multiple CAD models are selected from the ABC dataset. For each mesh model and CAD model, r camera poses are uniformly selected on the unit sphere. The point cloud is sampled based on the camera poses to form a multi-view normal estimation dataset.

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