Three-dimensional mesh filtering denoising method, system and computing device

Abstract

The application discloses a three-dimensional grid filtering denoising method and system and a computing device, wherein the method comprises the following steps: firstly, obtaining a three-dimensional grid M0 of a scene to be denoised; secondly, defining and redefining the three-dimensional grid M0 to obtain a grid vertex set v, a grid face set f, a grid face normal set n and a grid face centroid set p; thirdly, constructing a undirected graph structure H0 by using the grid vertex set v and the grid face normal set n, and obtaining a filtering parameter set θ; fourthly, updating by using a bilateral filtering method, a normal vector updating method and a grid vertex updating formula to obtain a filtered and denoised grid face normal set n g and a grid vertex set v g ; and finally, obtaining a denoised three-dimensional grid M end by using a splicing operation. The application not only combines the advantages of a traditional optimization algorithm and deep learning, provides a more efficient and accurate three-dimensional grid denoising capability, but also has strong interpretability and controllability.

Description

TECHNICAL FIELD

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

[0002] Three-dimensional mesh denoising technology has far-reaching application significance in the fields of computer graphics, computer vision, and computer-aided design, etc. Its main purpose is to remove noise or measurement errors while preserving the geometric shape and detail features of the three-dimensional model, thereby improving the quality and accuracy of the mesh data. Noise usually manifests as distortion of the mesh surface, inaccuracy of vertex position, or error of face normal. If not promptly addressed, these issues will lead to a decrease in the accuracy of the three-dimensional model, which in turn affects its performance in practical applications. Therefore, 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 mainly fall 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, and the noise removal is easy to implement and has low computational cost, but it may lead to loss of model details when removing noise;

[0005] 2. Statistical and optimization-based methods: such as least squares, total variation, etc. This type of method usually removes noise by establishing a mathematical model and using global optimization techniques, which can preserve the geometric details of the model to some extent, but has 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, denoising techniques based on neural networks will gradually become a hot research direction. They can automatically learn and extract complex features and achieve efficient noise removal, and have significant advantages in handling complex noise; but this type of method usually requires a large amount of labeled data for training and has poor generalization. SUMMARY

[0007] To overcome the above-mentioned defects in existing three-dimensional mesh denoising technology, the present application provides a three-dimensional mesh filtering denoising method and system, which aims to process noisy three-dimensional meshes. It effectively improves the problem of loss of three-dimensional mesh details existing in geometric processing-based methods, makes up for the defects of high computational complexity caused by statistical optimization-based methods, and further improves the poor generalization of deep learning-based methods, which is beneficial to output high-quality denoised models. To achieve the above purpose, the present application is implemented through the following technical solutions:

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

[0009] Step S1, scanning a scene to be denoised by using a three-dimensional space scanning device to obtain a three-dimensional mesh M0 of the scene to be denoised;

[0010] Step S2, defining the three-dimensional mesh M0 to obtain a mesh vertex set v, a mesh face set f, and redefining a mesh face normal set n and a mesh face centroid set p of the three-dimensional mesh M0;

[0011] Step S3, constructing an undirected graph structure H0 by using the obtained mesh vertex set v and the mesh face normal set n, and obtaining a filtering parameter set θ by using a graph neural network, wherein θ={σ s ,N f ,N v}; wherein σ s represents a spatial weight factor, N f represents the number of iterations of mesh face normal updates, and N v represents the number of iterations of vertex updates after each filtering of the mesh face normal;

[0012] Step S4, performing a bilateral filtering operation on each individual mesh face in the mesh face set f by using a bilateral filtering method; updating the mesh face normal set n by using a normal vector updating method to obtain an updated normal vector set n'; updating the mesh vertex set v according to a mesh vertex update formula by using the updated normal vector set n' for N v times; defining one mesh face normal filtering; and after N f times of mesh face normal filtering, obtaining a mesh face normal set n g and a mesh vertex set v g after filtering and denoising;

[0013] Step S5, obtaining a denoised three-dimensional mesh M g by using a splicing operation according to the mesh vertex set v g and the mesh face normal set n end after filtering and denoising.

[0014] Preferably, the three-dimensional space scanning device in step S1 is a three-dimensional laser scanner, and the three-dimensional laser scanner supports printed file formats including STL and OBJ.

[0015] Preferably, the embodiment of defining the three-dimensional mesh M0 in step S2 comprises:

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

[0017] The implementation methods for redefining the set of mesh surface normals n and the set of mesh surface centroids p of the three-dimensional mesh M0 in step S2 include:

[0018] Redefining n = {n a |a=1,2,…,A},p={p a |a=1,2,…,A};where, n a Let A represent any grid surface normal within the set of grid surface normals, where A represents a non-zero natural number; in set p... p a For the currently selected mesh surface f a The center of mass, v a1 v a2 v a3 f represents the currently selected mesh surface. a The three vertices.

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

[0020] Step S31: Define an undirected graph structure H0 consisting of A nodes, and each node... This can be expressed by the following formula;

[0021]

[0022] In the formula, v a Represents any vertex, n ak Representing vertex v a The grid surface f ak The normals of the grid surface, k∈{1,2,…,K}, a∈{1,2,…,A}, where A and K both represent non-zero natural numbers;

[0023] Step S32: Iterate and update the undirected graph structure H0 multiple times using a graph neural network; the method is as follows:

[0024] H1 = β(H0)

[0025] H2 = β(H1)

[0026] …

[0027] H l =β(H L-1 )

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

[0029] Step S33, global mapping is performed using a fully connected neural network to obtain a filter parameter set θ, in the following manner:

[0030]

[0031] wherein MLP σs , MLP Nf , and MLP Nv represent three fully connected neural networks for mapping H L to the filter parameter set, respectively;

[0032] Step S34, through the calculation of step S33, a filter parameter set θ = {σ s , N f , N v} is obtained, wherein σ s represents a spatial weight factor, N f represents the number of iterations of the mesh surface normal update, and N v represents the number of iterations of the vertex update after each filtering of the mesh surface normal.

[0033] Preferably, the implementation of step S4 in which bilateral filtering is performed on each individual mesh surface in the mesh surface set f includes:

[0034] Bilateral filtering is performed on each individual mesh surface in the mesh surface set f by using a bilateral filtering formula, which is as follows:

[0035]

[0036] wherein w s (p d , p e ) represents a spatial weight, w r (n d , n e ) represents a geometric similarity weight; σ s represents a spatial weight factor; σ r represents a 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 ; and n dT Let n be the normal vector d The transpose of f r The value is set to 1.

[0037] Preferably, the implementation method for updating the set of normal vectors n of the mesh surface using the normal vector update method in step S4 to obtain the updated set of normal vectors n′ includes:

[0038] The set of normal vectors n on the mesh surface is updated using the normal vector update formula to obtain a new set of normal vectors n′. The normal vector update formula is as follows:

[0039]

[0040] n′={n′ d ,d∈(1,A)}

[0041] In the formula, n′ d Represents the mesh surface f d Updated normal vector; Represented by the mesh surface f d adjacent mesh face f e The set of adjacent mesh faces, where A represents a non-zero natural number.

[0042] Preferably, in step S4, the updated normal vector set n′ is used to perform N operations on the mesh vertex set v according to the mesh vertex update formula. v The implementation methods for this iteration update include:

[0043] The obtained set of normal vectors n′ is used to iteratively update the set of mesh vertices v multiple times according to the vertex update formula, which is shown below:

[0044]

[0045] v′={v′ a ,a∈(1,A)}

[0046] In the formula, v a v represents any grid vertex within the set of grid vertices. a Let v' represent the updated set of grid vertices, and let A be a non-zero natural number. Represented by the mesh surface f d adjacent mesh face f e The set of adjacent mesh faces, p d Represents a single mesh surface f d The center of mass; p e Represents a single mesh surface f e The center of mass; n′ d Represents the mesh surface f dUpdated normal vector.

[0047] Preferably, the step S4 iterates N f The mesh face normal filtering is performed for a plurality of times to obtain a filtered and denoised mesh face normal set n g and a mesh vertex set v g The embodiments of the step S4 include:

[0048] The mesh face normal filtering is performed for a plurality of times to obtain a filtered and denoised mesh face normal set n (m) When m = N f , it indicates that the mesh face normal set n has been iterated N f times to obtain a final filtered and denoised mesh face normal set n g and a mesh vertex set v g .

[0049] A three-dimensional mesh filtering and denoising system for running a three-dimensional mesh filtering and denoising method, the three-dimensional mesh filtering and denoising system comprising:

[0050] A three-dimensional scanning module for scanning a scene and obtaining a three-dimensional mesh M0 of the scene;

[0051] A definition module for performing a definition operation on the obtained three-dimensional mesh M0;

[0052] A network module, the network module comprising a graph neural network module and a fully connected neural network module, the graph neural network module being configured to perform a plurality of iterations of an updating process, and the fully connected neural network module being configured to perform a global mapping process;

[0053] An updating module, the updating module comprising a bilateral filtering module, a normal vector updating module and a mesh face normal filtering module, the bilateral filtering module being configured to perform a bilateral filtering updating process, the normal vector updating module being configured to perform a normal vector updating process, and the mesh face normal filtering module being configured to perform a mesh face normal filtering process;

[0054] A splicing output module for performing a splicing operation and outputting a denoised three-dimensional mesh M end .

[0055] A computing device comprising a memory and a processor, the memory being configured to store a set of instructions of a three-dimensional mesh filtering and denoising method and a set of instructions for normal operation of the processor, and the processor being configured to execute at least one set of instructions stored in the memory.

[0056] The present application has the following advantages and beneficial effects over the prior art:

[0057] 1. The application provides a three-dimensional mesh denoising method with better interpretability and controllability by using a graph neural network. Each module plays an important role in the denoising process, making the internal process more transparent and easy to understand and debug.

[0058] 2. The application takes full advantage of deep learning to effectively remove noise introduced by scanning devices and restore a smoother and more accurate three-dimensional surface. Through an end-to-end training process, adaptive learning and adjustment of various parameters in the three-dimensional mesh denoising process are achieved, improving training efficiency and quickly and effectively processing noise in the inference stage while preserving original features to meet real-time application requirements.

[0059] 3. The application combines the advantages of traditional optimization algorithms and deep learning to provide more efficient and accurate three-dimensional mesh denoising capabilities, and has strong interpretability and controllability, providing an innovative and effective solution for computer graphics and computer vision applications. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 The execution flowchart of the three-dimensional mesh filtering denoising method of the application. DETAILED DESCRIPTION

[0061] In the following, the application will be further described in conjunction with the drawings and specific embodiments:

[0062] To make the purpose, technical scheme and advantages of the application clearer and more explicit, the following embodiments will be described with reference to the drawings.

[0063] Embodiment 1:

[0064] As shown in the drawings, a three-dimensional mesh filtering denoising method includes the following steps: Figure 1

[0065] Step S1, using a three-dimensional space scanning device to scan a scene to be denoised, obtaining a three-dimensional mesh M0 of the scene to be denoised; the three-dimensional space scanning device is a three-dimensional laser scanner, which can support printing file formats including STL, OBJ, etc.

[0066] Step S2, defining the three-dimensional mesh M0, obtaining the mesh vertex set v, the mesh face set f of the three-dimensional mesh M0, and redefining the mesh face normal set n and the mesh face centroid set p of the three-dimensional mesh M0; wherein the implementation of the definition and redefinition in this step includes the following steps:

[0067] First, define the three-dimensional mesh M0, so that M0={v,f}; wherein v={v a |a=1,2,…,A},f={f​a a = 1,2,..., A}, secondly, redefine n = {n a a = 1,2,..., A}, p = {p a a = 1,2,..., A}; in the formula, v a represents any grid vertex in the grid vertex set, f a represents any grid face in the grid face set, n a represents any grid face normal in the grid face normal set, and A represents a natural number not equal to 0.

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

[0069] Step S3, construct a directed graph structure H0 using the obtained grid vertex set v and the grid face normal set n, and obtain the most suitable filter parameter set θ using a graph neural network, where θ = {σ s , N f , and N v}.

[0070] The specific implementation of this step includes:

[0071] Step S31, define a directed graph structure H0 composed of A nodes; and each node is represented by the following formula:

[0072]

[0073] In the formula, 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}, A and K represent natural numbers not equal to 0, and K is the number of grid faces around the vertex v a , and avg represents an average operation, i.e., the node is obtained by splicing the vertex coordinates v a and the average of the grid face normals where it is located.

[0074] Step S32, update the directed graph structure H0 multiple times using a graph neural network; 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, H L represents the updated undirected graph structure after each update.

[0080] Step S33, global mapping is performed using a fully connected neural network to obtain the most suitable filter parameter set θ, in the following specific manner:

[0081]

[0082] wherein MLP σs , MLP Nf , and MLP Nv represent three fully connected neural networks for mapping H L to the most suitable filter parameter set, and through the above calculation, the most suitable filter parameter set θ = {σ s , N f , N v} is obtained, wherein σ s represents a spatial weight factor, N f represents the number of iterations for updating the mesh surface normal, and N v represents the number of iterations for updating the mesh vertex after each filtering of the mesh surface normal.

[0083] Step S4, bilateral filtering is performed on each individual mesh surface in the mesh surface set f, the mesh surface normal set n is updated using the normal vector updating method to obtain an updated normal vector set n', the mesh vertex set v is updated N v times according to the mesh vertex updating formula using the updated normal vector set n', and this process is referred to as one mesh surface normal filtering; after N f times of mesh surface normal filtering, the mesh surface normal set n g and the mesh vertex set v g after filtering and denoising are finally obtained. It should be noted that the mesh vertex set required for each mesh surface normal filtering is obtained from the mesh vertex set output by the last mesh surface normal filtering.

[0084] In the above steps, the specific implementation of the bilateral filtering method for each individual mesh surface is as follows: The bilateral filtering formula is used to perform a bilateral filtering operation on each individual mesh surface within the mesh surface set f. The bilateral filtering formula is as follows:

[0085]

[0086] In the formula, w s (p d ,p e ) represents spatial weight, w r (n d ,n e ) represents the geometric similarity weight; σ s Represents the spatial weighting factor; σ r p represents the geometric similarity weighting factor. d Represents a single mesh surface f d The center of mass; p e Represents a single mesh surface f e The center of mass; n d Represents the mesh surface f d The normal vector, n e Represents the mesh surface f e The normal vector, n d T Let n be the normal vector d The transpose of σ r The value is set to 1, and the mesh face f d and mesh surface f e These are two adjacent grid faces.

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

[0088]

[0089] n′={n′ d ,d∈(1,A)}

[0090] In the formula, n′ d Represents the mesh surface f d Updated normal vector; Represented by the mesh surface f d adjacent mesh face f e The set of adjacent mesh faces, where A represents a non-zero natural number.

[0091] In the above steps, the updated set of normal vectors n′ is used to perform N operations on the set of mesh vertices v. vThe specific embodiment of the secondary iteration update is that the obtained normal vector set n' is used to perform multiple iteration updates on the mesh vertex set v according to a vertex update formula, and the vertex update formula is as follows:

[0092]

[0093] v' = {v' a , a e (1, A)}

[0094] In the formula, v a represents any mesh vertex in 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 greater than 0, represents the adjacent mesh face set composed of the adjacent mesh faces f d of the mesh face f e , p d represents the centroid of the single mesh face f d ; p e represents the centroid of the single mesh face f e ; n' represents the normal vector of the mesh face f d . d

[0095] In the above steps, after the mesh face normal filtering process is performed for N f times, the filtered and denoised mesh face normal set n g and the mesh vertex set v g are obtained.

[0096] The process of the mesh face normal filtering is repeatedly performed multiple times, and the mesh face normal set after the mth mesh face normal filtering process is defined as n (m) When m = N f , that is, the mesh face normal set n is iterated N f times, and after each mesh face normal filtering process is completely performed, the final denoised mesh face normal set n g and the mesh vertex set v g are obtained.

[0097] In step S5, the final filtered and denoised mesh vertex set v g and the mesh face normal set n g are used to obtain the denoised three-dimensional mesh M end through a splicing operation, that is, the denoised three-dimensional mesh data to be finally output. The splicing is preferably performed by splicing the final denoised mesh vertex set v g and the face normal set n g ​Save using txt file and convert to OBJ file.

[0098] Embodiment 2

[0099] The application further discloses a three-dimensional mesh filtering denoising system for running the three-dimensional mesh filtering denoising method, wherein the three-dimensional mesh filtering denoising system comprises the following modules.

[0100] A three-dimensional scanning module is configured to scan a scene and acquire a three-dimensional mesh M0 of the scene.

[0101] A defining module is configured to perform a defining operation on the acquired three-dimensional mesh M0.

[0102] A network module comprises a graph neural network module and a fully connected neural network module, the graph neural network module is configured to perform a multi-iteration updating process, and the fully connected neural network module is configured to perform a global mapping process.

[0103] An updating module comprises a bilateral filtering module, a normal vector updating module and a mesh face normal filtering module, the bilateral filtering module is configured to perform a bilateral filtering updating process, the normal vector updating module is configured to perform a normal vector updating process, and the mesh face normal filtering module is configured to perform a mesh face normal filtering process.

[0104] A splicing output module is configured to perform a splicing operation and output a denoised three-dimensional mesh M end .

[0105] Embodiment 3

[0106] The application further discloses a computing device comprising a memory and a processor, wherein the memory is configured to store an instruction set of the three-dimensional mesh filtering denoising method and an instruction set for normal operation of the processor, the processor is configured to execute at least one instruction set stored in the memory, and the instruction set for normal operation of the processor is an indispensable item.

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

[0108] In summary, the method proposed in this application takes advantage of deep learning to achieve a complete mesh denoising process, capable of denoising three-dimensional 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 field of computer graphics and computer vision.

Claims

1. A method of denoising by three-dimensional grid filtering, characterized in that, The method comprises the steps of: Step S1, scanning a scene to be denoised by using a three-dimensional space scanning device to obtain a three-dimensional mesh M0 of the scene to be denoised; Step S2, defining the three-dimensional mesh M0 to obtain a mesh vertex set v, a mesh face set f, and redefining a mesh face normal set n and a mesh face centroid set p of the three-dimensional mesh M0; Step S3, constructing an undirected graph structure H0 using the obtained mesh vertex set v and the mesh face normal set n, and obtaining a filtering parameter set θ using a graph neural network, wherein θ = {σ s , N f , N v} , σ s represents a spatial weight factor, N f represents the number of mesh face normal update iterations, and N v represents the number of vertex update iterations after each filtering of the mesh face normal. Step S4: Perform bilateral filtering on each individual mesh surface in the mesh surface set f, and update the mesh surface normal set n using the normal vector update method to obtain the updated normal vector set n. ′ Using the updated set of normal vectors n ′ Based on the grid vertex update formula, perform N on the grid vertex set v. v Each iteration update is defined as one mesh surface normal filtering; then N iterations... f After filtering the mesh surface normals, we obtain the set of filtered and denoised mesh surface normals n. g and the set of grid vertices v g ; Step S5, obtaining the denoised mesh vertex set v according to the filtering g and the mesh face normal set n g , and obtaining the denoised three-dimensional mesh M by using a stitching operation end ; The specific implementation of the step S3 comprises: Step S31, define a undirected graph structure H0 composed of A nodes, and each node is expressed by the following equation; wherein v a represents any vertex, n ak represents vertex v a wherein f ak is a grid face normal, k∈{1,2,…,K}, a∈{1,2,…,A}, A and K both represent natural numbers not equal to 0; Step S32, performing multiple iteration updates on the undirected graph structure H0 by using a graph neural network; the method is as follows: H1=β(H0) H2=β(H1) … H l = β(H L-1 ) In the formula, β represents a graph neural network, L represents the number of updates, H L represents the undirected graph structure after each update; Step S33, performing global mapping by using a fully connected neural network to obtain a filter parameter set θ; the method is as follows: MLP σs MLP Nf MLP Nv represent three fully connected neural networks for mapping the H L to a set of filter parameters, respectively. Step S34, obtaining the filter parameter set θ = {σ s ,N f ,N v} through the calculation of step S33, wherein σ s represents a spatial weight factor, N f represents the number of iterations of the normal update of the mesh surface, and N v represents the number of iterations of the vertex update after each filtering of the normal of the mesh surface.

2. The method of claim 1, wherein, The three-dimensional space scanning device in the step S1 is a three-dimensional laser scanner, and the three-dimensional laser scanner supports printed file formats including STL and OBJ.

3. The method of claim 1, wherein, The implementation of the step S2 of defining the three-dimensional mesh M0 comprises: A three-dimensional mesh M0is defined as M0={v,f}, wherein v={v a |a=1,2,…,A}, f={f a |a=1,2,…,A}, wherein v a represents any mesh vertex in the mesh vertex set, f a represents any mesh face in the mesh face set, and A represents a natural number not equal to 0. The implementation of the step S2 of redefining the mesh face normal set n and the mesh face centroid set p of the three-dimensional mesh M0 comprises: Redefined n = {n a |a = 1, 2, …, A}, p = {p a |a = 1, 2, …, A}; in the formula, n a represents any grid surface normal in the set of grid surface normals, and A represents a natural number not equal to 0; p p a is the centroid of the currently selected grid surface f a , v a1 , v a2 , v a3 are respectively three vertices of the currently selected grid surface f a .

4. The method of claim 1, wherein, The implementation of the step S4 of performing a bilateral filtering operation on each individual mesh face in the mesh face set f by using a bilateral filtering method comprises: The bilateral filtering operation is performed on each individual mesh face in the mesh face set f by using a bilateral filtering formula, and the bilateral filtering formula is as follows: where 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 face f d ; p e represents the centroid of the individual mesh face f e ; n d represents the normal vector of the mesh face f d ; n e represents the normal vector of the mesh face f e ; n d T is the transpose of the normal vector n d , and σ r is set to 1.

5. The method of claim 1, wherein, The implementation of the step S4 of updating the mesh face normal set n by using a normal vector updating method to obtain an updated normal vector set n' comprises: The normal vector set n is updated by using a normal vector updating formula to obtain a new normal vector set n', and the normal vector updating formula is as follows: n' = {n' | n' < n, n' e (1, A)} d , d e (1, A)} wherein n' d represents the mesh face f d updated normal vector; represents the adjacent mesh face set consisting of the adjacent mesh face f d of the mesh face f e A represents a natural number other than 0.

6. The method of claim 1, wherein, The step S4 uses the updated normal vector set n' to update the mesh vertex set v according to the mesh vertex update formula v Embodiments of the secondary iteration update include: The normal vector set n' obtained is used to perform multiple iteration updates on the mesh vertex set v according to a vertex updating formula, and the vertex updating formula is as follows: v' = {v', a e (1, A)} a ,a∈(1,A)} where v a represents any vertex of the set of vertices of the mesh, v a represents the updated vertex, v' represents the set of updated vertices, A is a natural number not equal to 0, represents the set of neighboring faces of the mesh face f d , p e represents the set of neighboring faces of the mesh face f d ; p d represents the centroid of the individual mesh face f e ; p e represents the centroid of the individual mesh face f ′ d represents the normal of the mesh face f d ; n' represents the updated normal.

7. The method of claim 1, wherein, The step S4 iterates N f Sub-grid face normal filtering to obtain a filtered denoised set of grid face normals n g and a set of grid vertices v g The embodiments of the application include: The grid face normal filtering process is repeatedly performed multiple times, and a set of grid face normals after the mth grid face normal filtering process is defined as n (m) When m = N f , it indicates that the set of grid face normals n has been iterated N f times to obtain a final denoised set of grid face normals n g and a set of grid vertices v g .

8. A three-dimensional grid filtering denoising system for running the three-dimensional grid filtering denoising method of any one of claims 1-7, characterized in that, The three-dimensional mesh filtering and denoising system comprises: A three-dimensional scanning module for scanning a scene and obtaining a three-dimensional mesh M0 of the scene; A definition module for defining the obtained three-dimensional mesh M0; A network module comprising a graph neural network module and a fully connected neural network module, the graph neural network module being used for a multiple iteration update process, and the fully connected neural network module being used for a global mapping process; An update module comprising a bilateral filtering module, a normal vector updating module, and a mesh face normal filtering module, the bilateral filtering module being used for a bilateral filtering update process, the normal vector updating module being used for a normal vector updating process, and the mesh face normal filtering module being used for a mesh face normal filtering process; The splicing output module is configured to realize splicing operation and output the three-dimensional mesh M after noise reduction. end .

9. A computing device comprising a memory and a processor, the memory being used to store an instruction set of the three-dimensional mesh filtering and denoising method of any one of claims 1-7 and an instruction set for normal operation of the processor, and the processor being used to execute at least one instruction set stored in the memory.

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