Three-dimensional grid filtering and denoising method and system and computing equipment

Abstract

The invention discloses a three-dimensional grid filtering and denoising method and system and computing equipment, and the method comprises the steps: firstly obtaining a three-dimensional grid M0 of a to-be-denoised scene, and then carrying out the definition and redefinition of the three-dimensional grid M0, so as to obtain a grid vertex set v, a grid surface set f, a grid surface normal set n and a grid surface centroid set p; constructing an undirected graph structure H0 by utilizing the grid vertex set v and the grid surface normal set n, acquiring a filtering parameter set theta, and updating by adopting a bilateral filtering method, a normal vector updating method and a grid vertex updating formula to obtain a filtered and denoised grid surface normal set ng and a grid vertex set vg; and finally, performing splicing operation to obtain a denoised three-dimensional grid Mend. According to the method, the advantages of a traditional optimization algorithm and deep learning are combined, more efficient and accurate three-dimensional grid denoising capacity is provided, and high interpretation and controllability are achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of computer graphics, and in particular to a three-dimensional mesh filtering and denoising method and system. Background Art

[0002] The three-dimensional mesh denoising technology has profound application significance in the fields of computer graphics, computer vision, computer-aided design, etc. Its main purpose is to remove noise or measurement errors while maintaining the geometric shape and detailed features of the three-dimensional model, thereby improving the quality and accuracy of the mesh data. Noise usually manifests as distortions on the mesh surface, inaccurate vertex positions, or errors in surface normals. If these problems are not handled in a timely manner, they will lead to a decrease in the accuracy of the three-dimensional model, and further affect its performance in practical applications. Therefore, the three-dimensional mesh denoising technology plays an irreplaceable role in enhancing the visual effect and functionality of the three-dimensional model, and improving the reliability and accuracy of the model.

[0003] At present, the technical methods for three-dimensional mesh denoising are mainly divided into the following categories:

[0004] 1. Geometric processing-based methods: such as Laplacian smoothing, bilateral filtering, etc. This type of method usually removes noise based on the geometric characteristics of the mesh. Noise removal is easy to implement and has a low computational cost, but it may lead to the loss of model details while removing noise;

[0005] 2. Statistical and optimization-based methods: such as the least squares method, total variation, etc. This type of method usually establishes a mathematical model and uses global optimization techniques to remove noise, which can retain the geometric details of the model to a certain extent, but has a high computational complexity;

[0006] 3. Deep learning-based methods: such as convolutional neural networks (CNNs), graph neural networks (GNNs), etc. With the development of deep learning, the neural network-based denoising technology will gradually become a hot research direction. It can automatically learn and extract complex features and achieve efficient noise removal, and has significant advantages in dealing with complex noise. However, this type of method usually requires a large amount of labeled data for training and has poor generalization performance. Summary of the Invention

[0007] To overcome the above defects in the existing three-dimensional mesh denoising technology, the present invention provides a three-dimensional mesh filtering and denoising method and system, aiming to process noisy three-dimensional meshes. It effectively improves the problem of detail loss of three-dimensional meshes existing in geometric processing methods, makes up for the defects such as high computational complexity caused by statistical optimization methods, and further improves the problem of poor generalization performance of deep learning-based methods, which is conducive to outputting a high-quality denoised model. To achieve the above objectives, the present invention is realized through the following technical solutions:

[0008] A three-dimensional mesh filtering and denoising method, comprising the steps of:

[0009] Step S1: Use a three-dimensional space scanning device to scan the scene to be denoised, and obtain a three-dimensional mesh M0 of the scene to be denoised;

[0010] Step S2: Define the three-dimensional mesh M0, obtain the mesh vertex set v and mesh face set f of the three-dimensional mesh M0, and re-define the mesh face normal set n and mesh face centroid set p of the three-dimensional mesh M0;

[0011] Step S3: Use the obtained mesh vertex set v and mesh face normal set n to construct an undirected graph structure H0, and use a graph neural network to obtain a filtering parameter set θ, where θ = {σ s , N f , N v}; where σ s represents the spatial weight factor, N f represents the number of iterations for updating the mesh face normal, and N v represents the number of iterations for updating the vertices after each filtering of the mesh face normal;

[0012] Step S4: Perform bilateral filtering operations on each individual mesh face in the mesh face set f using the bilateral filtering method; update the mesh face normal set n using the normal vector update method to obtain an updated normal vector set n'; use the updated normal vector set n' to perform N v iterative updates on the mesh vertex set v according to the mesh vertex update formula; define it as one mesh face normal filtering; after iteratively filtering the mesh face normal N f times, obtain the filtered and denoised mesh face normal set n g and mesh vertex set v g ;

[0013] Step S5: According to the filtered and denoised mesh vertex set v g and mesh face normal set n g , use the splicing operation to obtain the denoised three-dimensional mesh M end .

[0014] Preferably, the three-dimensional space scanning device in step S1 is a three-dimensional laser scanner, and the file formats supported by the three-dimensional laser scanner for printing include STL and OBJ.

[0015] Preferably, the implementation manner of defining the three-dimensional mesh M0 in step S2 includes:

[0016] Define the three-dimensional mesh M0 such that M0 = {v, f}; where v = {v a |a = 1, 2,..., A}, f = {fa |a = 1, 2, …, A}, where v a represents any grid vertex within the set of grid vertices, and f a represents any grid face within the set of grid faces, and A represents a non - zero natural number;

[0017] The implementation manner of re - defining the set of grid - face normals n and the set of grid - face centroids p of the three - dimensional grid M0 in step S2 includes:

[0018] Redefine n = {n a |a = 1, 2, …, A}, p = {p a |a = 1, 2, …, A}; where n a represents any grid - face normal within the set of grid - face normals, and A represents a non - zero natural number; p in the set p p a is the centroid of the currently selected grid face f a , and v a1 , v a2 , v a3 are the three vertices of the currently selected grid face f a respectively.

[0019] Preferably, the specific implementation manner of step S3 includes:

[0020] Step S31: Define an undirected graph structure H0 composed of A nodes, and each node is represented by the following formula;

[0021]

[0022] where v a represents any vertex, n ak represents the grid - face normal of the grid face f a where the vertex v ak is located, k ∈ {1, 2, …, K}, a ∈ {1, 2, …, A}, and both A and K represent non - zero natural numbers;

[0023] Step S32: Use a graph neural network to perform multiple iterative updates on the undirected graph structure H0; the method is as follows:

[0024] H1 = β(H0)

[0025] H2 = β(H1)

[0026] …

[0027] H l = β(H L-1 )

[0028] In the formula, β represents the graph neural network, L represents the number of updates, and H L represents the undirected graph structure after each update;

[0029] Step S33: Use a fully connected neural network for global mapping to obtain the set of filtering parameters θ, in the following way:

[0030]

[0031] In the formula, MLP σs , MLP Nf , MLP Nv respectively represent three fully connected neural networks used to map H L to the set of filtering parameters;

[0032] Step S34: Through the calculation in Step S33, obtain the set of filtering parameters θ = {σ s , N f , N v}, where σ s represents the spatial weight factor, N f represents the iteration times of grid surface normal update, and N v represents the iteration times of vertex update after each filtering of the grid surface normal.

[0033] Preferably, the implementation method of performing bilateral filtering operation on each individual grid surface in the grid surface set f in Step S4 includes:

[0034] Perform bilateral filtering operation on each individual grid surface in the grid surface set f by using the bilateral filtering formula. The bilateral filtering formula is as follows:

[0035]

[0036] In the formula, w s (p d , p e ) represents the spatial weight, w r (n d , n e ) represents the geometric similarity weight; σ s represents the spatial weight factor; σ r represents the geometric similarity weight factor; p d represents the centroid of the individual grid surface f d ; p e represents the centroid of the individual grid surface f e ; n d represents the normal vector of the grid surface f d , n e represents the normal vector of the grid surface f e , n dT is the normal vector n d transpose, and f r is set to 1.

[0037] Preferably, in step S4, the normal vector update method is used to update the grid surface normal vector set n to obtain the updated normal vector set n'. The implementation method includes:

[0038] By using the normal vector update formula to update the grid surface normal vector set n, a new normal vector set n' is obtained. The normal vector update formula is as follows:

[0039]

[0040] n' = {n' d , d ∈ (1, A)}

[0041] In the formula, n' d represents the updated normal vector of the grid surface f d ; represents the set of adjacent grid surfaces f d composed of the adjacent grid surfaces f e of the grid surface f, and A represents a non-zero natural number.

[0042] Preferably, in step S4, the updated normal vector set n' is used to perform N v iterative updates on the grid vertex set v according to the grid vertex update formula. The implementation method includes:

[0043] The obtained normal vector set n' is used to perform multiple iterative updates on the grid vertex set v according to the vertex update formula. The vertex update formula is as follows:

[0044]

[0045] v' = {v' a , a ∈ (1, A)}

[0046] In the formula, v a represents any grid vertex in the grid vertex set, v a represents the updated grid vertex, v' represents the updated grid vertex set, A is a non-zero natural number, represents the set of adjacent grid surfaces f d composed of the adjacent grid surfaces f e of the grid surface f, p d represents the centroid of the individual grid surface f d ; p e represents the centroid of the individual grid surface f e ; n' d represents the grid surface f dUpdated normal vector.

[0047] Preferably, in step S4, iterate N f times of grid surface normal filtering to obtain the filtered and denoised grid surface normal set n g and the grid vertex set v g The implementation manner includes:

[0048] By repeatedly executing the grid surface normal filtering process multiple times, and defining the grid surface normal set after the m-th grid surface normal filtering process as n (m) When m = N f it means that the grid surface normal set n has been iterated N f times to obtain the finally denoised grid surface normal set n g and the grid vertex set v g .

[0049] A 3D grid filtering and denoising system for running a 3D grid filtering and denoising method, the 3D grid filtering and denoising system includes:

[0050] A 3D scanning module for scanning a scene and obtaining a 3D grid M0 of the scene;

[0051] A definition module for performing a definition operation on the obtained 3D grid M0;

[0052] A network module, the network module includes a graph neural network module and a fully connected neural network module, the graph neural network module is used for the process of multiple iterative updates, and the fully connected neural network module is used for the process of global mapping;

[0053] An update module, the update module includes a bilateral filtering module, a normal vector update module and a grid surface normal filtering module, the bilateral filtering module is used for the bilateral filtering update process, the normal vector update module is used for the normal vector update process, and the grid surface normal filtering module is used for the grid surface normal filtering process;

[0054] A stitching output module for performing a stitching operation and outputting the denoised 3D grid M end .

[0055] A computing device includes a memory and a processor, the memory is used for storing an instruction set of a 3D grid filtering and denoising method and an instruction set for the normal operation of the processor, and the processor is used for executing at least one instruction set stored in the memory.

[0056] The present invention has the following advantages and beneficial effects compared with the prior art:

[0057] 1. The present invention provides a more interpretable and controllable 3D mesh denoising method by using graph neural networks. Each module in the combination plays an important role in the denoising work, making the internal process of the model more transparent and facilitating understanding and debugging.

[0058] 2. The present invention makes full use of the advantages of deep learning. It aims to effectively remove the noise introduced by scanning devices through deep learning techniques and restore a smoother and more accurate 3D surface. Through an end-to-end training process, it realizes the adaptive learning and adjustment of various parameters in the 3D mesh denoising process, not only improving the training efficiency, but also being able to quickly and effectively process noise during the inference stage, retaining the original features and meeting the requirements of real-time applications.

[0059] 3. The present invention not only combines the advantages of traditional optimization algorithms and deep learning, provides a more efficient and accurate 3D mesh denoising ability, but also has strong interpretability and controllability, providing an innovative and effective solution for computer graphics and computer vision applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flowchart of the execution of the 3D mesh filtering and denoising method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] Next, in combination with the drawings and specific embodiments, the present invention will be further described:

[0062] To make the purpose, technical solutions and advantages of the present invention clearer and more definite, the following examples are given with reference to the drawings to further illustrate the present invention.

[0063] Example 1:

[0064] As Figure 1 shown, a 3D mesh filtering and denoising method includes the following steps:

[0065] Step S1: Use a 3D space scanning device to scan the scene to be denoised to obtain a 3D mesh M0 of the scene to be denoised; the 3D space scanning device is a 3D laser scanner, and the file formats supported by the 3D laser scanner include STL, OBJ, etc.

[0066] Step S2: Define the 3D mesh M0, obtain the mesh vertex set v and mesh face set f of the 3D mesh M0, and redefine the mesh face normal set n and mesh face centroid set p of the 3D mesh M0; wherein, the implementation manners of the definition and redefinition in this step include the following steps:

[0067] First, define the 3D mesh M0 so that M0 = {v, f}; wherein, v = {v a |a = 1, 2,..., A}, f = {fa |a = 1, 2, …, A}, and secondly, re - define n = {n a |a = 1, 2, …, A}, p = {p a |a = 1, 2, …, A}; where, v a represents any grid vertex within the set of grid vertices, f a represents any grid face within the set of grid faces, n a represents any grid - face normal within the set of grid - face normals, and A represents a non - zero natural number.

[0068] Furthermore, in the above - mentioned set p, p a is the centroid of the currently selected grid face f a , and v a1 , v a2 , v a3 are respectively the three vertices of the currently selected grid face f a .

[0069] Step S3: Construct an undirected graph structure H0 using the obtained set of grid vertices v and the set of grid - face normals n. This undirected graph structure is composed of multiple nodes and edges without weights; and use a graph neural network to obtain the most suitable set of filtering parameters θ, where θ = {σ s , N f , N v}.

[0070] The specific implementation of this step includes:

[0071] Step S31: Define an undirected graph structure H0 composed of A nodes; and each node is represented by the following formula;

[0072]

[0073] where, v a represents any vertex, n ak represents the grid - face normal of the grid face f a where the vertex v ak is located, k ∈ {1, 2, …, K}, a ∈ {1, 2, …, A}, both A and K represent non - zero natural numbers, and K is the number of grid faces around the vertex v a , and avg represents the averaging operation, that is, the node is obtained by concatenating the vertex coordinate v a and the mean value of its grid - face normal.

[0074] Step S32: Use the graph neural network to perform multiple iterative updates on the undirected graph structure H0; specifically as follows:

[0075] H1 = β(H0)

[0076] H2 = β(H1)

[0077] …

[0078] H l = β(H L-1 )

[0079] where β represents a graph neural network, L represents the number of updates, and H L represents the undirected graph structure after each update.

[0080] Step S33: Use a fully connected neural network for global mapping to obtain the most suitable set of filtering parameters θ, in the following specific manner:

[0081]

[0082] where MLP σs , MLP Nf , and MLP Nv respectively represent three fully connected neural networks used to map H L to the most suitable set of filtering parameters. Through the above calculations, the most suitable set of filtering parameters θ = {σ s , N f , N v} is obtained, where σ s represents the spatial weight factor, N f represents the number of iterations for updating the grid surface normal, and N v represents the number of iterations for updating the vertices after each filtering of the grid surface normal.

[0083] Step S4: Perform bilateral filtering operations on each individual grid surface in the grid surface set f using the bilateral filtering method, update the grid surface normal set n using the normal vector update method to obtain the updated normal vector set n', and use the updated normal vector set n' to perform N v iterative updates on the grid vertex set v according to the grid vertex update formula, and this process is called one grid surface normal filtering; after continuing to iterate the process of grid surface normal filtering N f times, finally obtain the filtered and denoised grid surface normal set n g and the grid vertex set v g . It should be noted that the grid vertex set required for each grid surface normal filtering comes from the grid vertex set output by the previous grid surface normal filtering.

[0084] In the above steps, the specific implementation of performing bilateral filtering operation on individual mesh surfaces using the bilateral filtering method is to perform bilateral filtering operation on each individual mesh surface in the mesh surface set f using the bilateral filtering formula, and the bilateral filtering formula is as follows:

[0085]

[0086] In the formula, w s (p d ,p e ) represents the spatial weight, w r (n d ,n e ) represents the geometric similarity weight; σ s represents the spatial weight factor; σ r represents the geometric similarity weight factor; p d represents the centroid of the individual mesh surface f d ; p e represents the centroid of the individual mesh surface f e ; n d represents the normal vector of the mesh surface f d , n e represents the normal vector of the mesh surface f e , n d T is the transpose of the normal vector n d , and the value of σ r is set to 1, and the mesh surface f d and the mesh surface f e are two adjacent mesh surfaces.

[0087] In the above steps, the specific implementation of obtaining the updated normal vector set n′ using the normal vector update method is to update the mesh surface normal set n using the normal vector update formula to obtain a new normal vector set n′, and the normal vector update formula is as follows:

[0088]

[0089] n′={n′ d , d∈(1, A)}

[0090] In the formula, n′ d represents the updated normal vector of the mesh surface f d ; represents the set of adjacent mesh surfaces composed of the adjacent mesh surface f d of the mesh surface f e , and A represents a non-zero natural number.

[0091] In the above steps, using the updated normal vector set n′ to perform N on the mesh vertex set v vThe specific implementation of the secondary iterative update is to perform multiple iterative updates on the mesh vertex set v according to the vertex update formula using the obtained normal vector set n′. The vertex update formula is as follows:

[0092]

[0093] v′ = {v′ a , a ∈ (1, A)}

[0094] In the formula, v a represents any mesh vertex within the mesh vertex set, that is, the vertex before the mesh vertex is updated. v a represents the updated mesh vertex. v η represents the updated mesh vertex set. A is a natural number not equal to 0. represents the adjacent face mesh surface set composed of the adjacent face mesh surfaces f d of the mesh surface f e . p d represents the centroid of the individual mesh surface f d . p e represents the centroid of the individual mesh surface f e . n′ d represents the updated normal vector of the mesh surface f d .

[0095] In the above steps, after the mesh surface normal filtering process is iterated N f times, the filtered and denoised mesh surface normal set n g and the mesh vertex set v g are obtained in the following way:

[0096] The process of mesh surface normal filtering is repeatedly executed multiple times, and the mesh surface normal set after the m-th mesh surface normal filtering process is defined as n (m) . When m = N f , that is, when the mesh surface normal set n is iterated N f times and each mesh surface normal filtering process is fully executed, the finally denoised mesh surface normal set n g and the mesh vertex set v g are obtained.

[0097] Step S5, according to the finally filtered and denoised mesh vertex set v g and the mesh surface normal set n g , the denoised three-dimensional mesh M end is obtained through a splicing operation, which is the finally output denoised three-dimensional mesh data. The splicing is preferably performed by combining the finally denoised mesh vertex set v g and the face normal set n gSave using a txt file and convert it to an OBJ file.

[0098] Embodiment 2:

[0099] The present invention also discloses a three-dimensional mesh filtering and denoising system for running the above three-dimensional mesh filtering and denoising method. Among them, the three-dimensional mesh filtering and denoising system includes the following modules:

[0100] A three-dimensional scanning module for scanning a scene and obtaining a three-dimensional mesh M0 of the scene;

[0101] A definition module for performing a definition operation on the obtained three-dimensional mesh M0;

[0102] A network module, the network module includes a graph neural network module and a fully connected neural network module. The graph neural network module is used for the process of multiple iterative updates, and the fully connected neural network module is used for the process of global mapping;

[0103] An update module, the update module includes a bilateral filtering module, a normal vector update module, and a mesh surface normal filtering module. The bilateral filtering module is used for the bilateral filtering update process, the normal vector update module is used for the normal vector update process, and the mesh surface normal filtering module is used for the process of mesh surface normal filtering;

[0104] A stitching output module for implementing a stitching operation and outputting the denoised three-dimensional mesh M end .

[0105] Embodiment 3:

[0106] The present invention also discloses a computing device, which includes a memory and a processor. Among them, the memory is used to store the instruction set of the three-dimensional mesh filtering and denoising method and the instruction set for the normal operation of the processor, and the processor is used to execute at least one instruction set stored in the memory, and the instruction set for the normal operation of the processor is an essential item.

[0107] Generally speaking, the present invention not only combines the advantages of traditional optimization algorithms and deep learning, provides more efficient and accurate three-dimensional mesh denoising capabilities, but also has strong interpretability and controllability, providing an innovative and effective solution for computer graphics and computer vision applications.

[0108] In summary, the method proposed in this application realizes a complete mesh denoising process through the advantages of deep learning and can perform denoising processing on 3D meshes. This method combines the strengths of traditional optimization methods and deep learning techniques, providing a more accurate and efficient denoising solution. At the same time, this method has good interpretability and controllability, becoming an innovative and effective technical path in the fields of computer graphics and computer vision.

Claims

1. A three-dimensional grid filtering and denoising method, characterized in that Including the steps: Step S1: Use a three-dimensional space scanning device to scan the scene to be denoised, and obtain the three-dimensional mesh M0 of the scene to be denoised; Step S2: Define the three-dimensional mesh M0, obtain the set of mesh vertices v and the set of mesh faces f of the three-dimensional mesh M0, and re-define the set of mesh face normals n and the set of mesh face centroids p of the three-dimensional mesh M0; Step S3: Construct an undirected graph structure H0 using the obtained grid vertex set v and grid face normal set n, and use a graph neural network to obtain a set of filtering parameters θ, where θ = {σ s , N f , N v}, σ s represents the spatial weight factor, N f represents the number of iterations for updating the grid face normal, and N v represents the number of iterations for updating the vertices after each filtering of the grid face normal; Step S4: Perform bilateral filtering operations on each individual mesh surface in the mesh surface set f, and update the mesh surface normal vector set n using the normal vector update method to obtain the updated normal vector set n ′ , and use the updated normal vector set n ′ to perform N v iterative updates on the mesh vertex set v according to the mesh vertex update formula, which is defined as one mesh surface normal filtering; after iteratively performing N f times of mesh surface normal filtering, the filtered and denoised mesh surface normal vector set n g and the mesh vertex set v g are obtained; Step S5. According to the set of grid vertices v after filtering and denoising g and the set of grid face normals n g , a three-dimensional grid M after denoising is obtained by using the splicing operation end .

2. The three-dimensional grid filtering and denoising method according to claim 1, wherein The three-dimensional space scanning device in step S1 is a three-dimensional laser scanner, and the file formats supported by the three-dimensional laser scanner for printing include STL and OBJ.

3. A three-dimensional grid filtering and denoising method according to claim 1, characterized in that The implementation manner of defining the three-dimensional mesh M0 in step S2 includes: Define a three-dimensional mesh M0 such that M0 = {v, f}; where v = {v a | a = 1, 2, …, A}, f = {f a | a = 1, 2, …, A}, where v a represents any mesh vertex within the mesh vertex set, and f a represents any mesh face within the mesh face set, and A represents a non-zero natural number; The implementation manner of re-defining the set of mesh face normals n and the set of mesh face centroids p of the three-dimensional mesh M0 in step S2 includes: Redefine \(n = \{n a |a = 1,2,\ldots,A\}\), \(p=\{p a |a = 1,2,\ldots,A\}\); where \(n a represents any grid surface normal in the set of grid surface normals, and \(A\) represents a non-zero natural number; \(p\) in the set \(p p a is the centroid of the currently selected grid surface \(f a \), and \(v a1 \), \(v a2 \), \(v a3 are the three vertices of the currently selected grid surface \(f a respectively.

4. A three-dimensional grid filtering and denoising method according to claim 1, characterized in that The specific implementation manner of step S3 includes: Step S31: Define an undirected graph structure H0 composed of A nodes, and each node is represented by the following formula; where v a represents any vertex, n ak represents the grid surface f a where the vertex v ak is located, k ∈ {1, 2, …, K}, a ∈ {1, 2, …, A}, both A and K represent non-zero natural numbers; Step S32: Use a graph neural network to perform multiple iterative updates on the undirected graph structure H0; the method is as follows: H1 = β(H0) H2 = β(H1) … H l = β(H L-1 ) where β represents the graph neural network, L represents the number of updates, and H L represents the undirected graph structure after each update; Step S33: Use a fully connected neural network for global mapping to obtain the set of filtering parameters θ, the method is as follows: where MLP σs , MLP Nf , and MLP Nv respectively represent three fully connected neural networks for mapping H L to the set of filtering parameters; Step S34: Through the calculation in step S33, obtain the set of filtering parameters θ = {σ s , N f , N v}, where σ s represents the spatial weight factor, N f represents the iteration times of grid surface normal update, and N v represents the iteration times of vertex update after each filtering of the grid surface normal.

5. A three-dimensional grid filtering and denoising method according to claim 1, characterized in that The implementation manner of performing bilateral filtering operations on each individual mesh face in the set of mesh faces f in step S4 using the bilateral filtering method includes: Perform bilateral filtering operations on each individual mesh face in the set of mesh faces f by using the bilateral filtering formula, and the bilateral filtering formula is as follows: where, w s (p d , p e ) represents the spatial weight, and w r (n d , n e ) represents the geometric similarity weight; σ s represents the spatial weight factor; σ r represents the geometric similarity weight factor; p d represents the centroid of the individual grid face f d ; p e represents the centroid of the individual grid face f e ; n d represents the normal vector of the grid face f d , and n e represents the normal vector of the grid face f e ; n d T is the transpose of the normal vector n d , and the value of σ r is set to 1.

6. A three-dimensional grid filtering and denoising method according to claim 1, characterized in that In the step S4, the normal vector update method is used to update the grid surface normal vector set n, and the updated normal vector set n is obtained. ′ The implementation manner includes: By using the normal vector update formula to update the set of grid surface normals \(n\), a new set of normal vectors \(n\) is obtained. ′ , and the normal vector update formula is as follows: n′ = {n′ d , d ∈ (1, A)} where n′ d represents the updated normal vector of the mesh surface f d ; represents the set of adjacent mesh surfaces composed of the adjacent mesh surfaces f d of the mesh surface f, and A represents a natural number other than 0. e ​ 7. A three-dimensional grid filtering and denoising method according to claim 1, characterized in that In step S4, the vertex set v of the grid is updated N times according to the grid vertex update formula by using the updated normal vector set n'. v The implementation method of the N - time iterative update includes: Iteratively update the set of mesh vertices v multiple times according to the vertex update formula with the obtained set of normal vectors n′, and the vertex update formula is shown as follows: v′ = {v′ a , a ∈ (1, a)} where, v a represents any grid vertex within the set of grid vertices, v a represents the updated grid vertex, v' represents the updated set of grid vertices, A is a natural number not equal to 0, represents the set of adjacent grid faces composed of the adjacent grid face f d of the grid face f e ; p d represents the centroid of the individual grid face f d ; p e represents the centroid of the individual grid face f e ; n' d represents the updated normal vector of the grid face f d .​ 8. A three-dimensional grid filtering and denoising method according to claim 1, wherein, In the step S4, iterate N f times of grid surface normal filtering to obtain a filtered and denoised set of grid surface normals n g and a set of grid vertices v g The implementation manner includes: By repeatedly executing the grid surface normal filtering process multiple times, and defining the grid surface normal set after the m-th grid surface normal filtering process as n (m) , when m = N f , it means that the grid surface normal set n has been iterated N f times to obtain the finally denoised grid surface normal set n g and the grid vertex set v g .

9. A three-dimensional mesh filtering and denoising system for running the three-dimensional mesh filtering and denoising method according to any one of claims 1-8, characterized in that The three-dimensional mesh filtering and denoising system includes: A three-dimensional scanning module, which is used to scan the scene and obtain the three-dimensional mesh M0 of the scene; A definition module, which is used to perform definition operations on the obtained three-dimensional mesh M0; A network module, the network module includes a graph neural network module and a fully connected neural network module, the graph neural network module is used for the process of performing multiple iterative updates, and the fully connected neural network module is used for the process of performing global mapping; An update module, the update module includes a bilateral filtering module, a normal vector update module, and a mesh face normal filtering module, the bilateral filtering module is used for the process of bilateral filtering update, the normal vector update module is used for the process of normal vector update, and the mesh face normal filtering module is used for the process of mesh face normal filtering; The splicing output module is used to implement the splicing operation and output the denoised three-dimensional mesh M end .

10. A computing device, including a memory and a processor, the memory is used to store the instruction set of the three-dimensional mesh filtering and denoising method according to any one of claims 1-8 and the instruction set for the normal operation of the processor, and the processor is used to execute at least one instruction set stored in the memory.

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