WO2023109567A1

WO2023109567A1 - Method for denoising triangular mesh based on dual graph neural network

Info

Publication number: WO2023109567A1
Application number: PCT/CN2022/136755
Authority: WO
Inventors: 张英奎; 王琼; 赵保亮; 孙寅紫; 王平安
Original assignee: 深圳先进技术研究院
Priority date: 2021-12-13
Filing date: 2022-12-06
Publication date: 2023-06-22
Also published as: CN114419275A

Abstract

The present application discloses a method and apparatus for denoising a triangular mesh based on a dual graph neural network, a device, and a storage medium. The method comprises: constructing a graph data structure for vertexes and triangular patches in a triangular mesh at the same time to form a dual graph, and then inputting a vertex graph and a patch graph into a corresponding graph neural network; the graph structure established based on the vertexes being used for pre-denoising noise vertexes in the neural network, and the graph structure established based on the patches being used for denoising the normal direction of the patches in the neural network; and updating the pre-denoised vertexes according to the denoised normal direction of the patches so as to output a final triangular mesh. According to the solution provided by the present application, the topological structure of the triangular mesh is better utilized, the denoising effect is better, geometric details are better kept, and in quantization errors, the average error of the normal angles of the patches and the average error of the vertex distances are smaller.

Description

Method of Denoising Triangular Meshes Based on Dual Graph Neural Network

technical field

The invention relates to computer software, in particular to a method, device, equipment and storage medium for denoising triangular grids based on a dual graph neural network.

Background technique

In the fields of 3D reconstruction, augmented reality, medicine, etc., it is an essential step to scan and reconstruct the mesh model of an object or human body. However, due to the accuracy of scanning sensors and other equipment, ambient light and other reasons, the reconstructed grid will inevitably contain noise, which will greatly affect the subsequent visualization effects.

Triangular mesh is one of the most common representation forms of 3D geometry, which includes a set of 3D point sets and a set of facets, each triangular facet consists of three point indices. Due to the noise triangular mesh generated by various reasons, the three-dimensional vertices are shifted, resulting in the inability to accurately represent the local geometric structure and forming noise. Triangular mesh denoising aims to correct the offset of vertices while preserving the original patch topology, and preserve the underlying geometric details while accurately removing noise.

The existing triangular mesh denoising methods can be mainly divided into traditional filtering or optimization-based methods and learning-based methods. Traditional filtering and its derivative methods can achieve good denoising effects, but it is difficult to preserve fine geometric details, while optimization-based methods, such as L0 minimization, low-rank restoration, etc., usually do not remove noise completely and are less efficient . Recently, learning-based methods have achieved outstanding denoising results. For example, according to the existing normal filter descriptor, and then use a single-layer neural network for patch normal regression. An iterative denoising algorithm is realized by combining 3D voxelization and 3D convolutional neural network. By constructing a normal matrix block of non-local similarity, and learning it with a convolutional neural network to output the denoised patch normal.

Due to the offset of noise, the normal direction of the triangular patch will be inaccurate, which will affect the local smoothness of the triangular mesh. The above method is a two-step method: first, perform normal regression on the triangular patch to obtain the denoised surface normal, and then update the noise vertex coordinates according to the normal to output the final denoised mesh. However, these methods ignore two points: (1) Since the vertices of the noisy grid itself contain noise, it is difficult to perform normal regression directly from these noisy attributes. (2) After obtaining the denoised surface Backward of the slice normal, it is also difficult to directly update the original noise vertices to preserve their underlying geometric properties.

Contents of the invention

In view of the above-mentioned defects or deficiencies in the prior art, it is desired to provide a method, device, device and storage medium for denoising triangular meshes based on a dual graph neural network.

In the first aspect, the embodiment of the present application provides a method for denoising triangular meshes based on a dual graph neural network, the method comprising:

Simultaneously build a graph data structure for the vertices and triangle faces in the triangular mesh to form a dual graph, and then input the vertex graph and the face graph into the corresponding graph neural network;

The graph structure based on the vertices is used in the neural network to pre-denoise the noise vertices, and the graph structure based on the patch is used in the neural network to denoise the normal direction of the patch;

The pre-denoised vertices are updated according to the denoised patch normals to output the final triangle mesh.

In one of the embodiments, the vertices in the triangular mesh are the nodes of the vertex graph in the dual graph, the edges between the vertices are the edges of the vertex graph in the dual graph, and the edges in the dual graph are The adjacency matrix of the vertex graph is N _v *N _v , where N _v is the number of vertices in the triangular mesh.

In one of the embodiments, the triangular patch construction graph data structure in the triangular mesh forms the patch graph in the dual graph, including: calculating the centroid and normal direction of each triangular patch through the vertices in the triangular mesh ;Determine whether each triangle patch has shared vertices with the surrounding patches, if so, retrieve the neighborhood patch set of the triangle patch; use each triangle patch as a node in the patch graph, and pass the triangle surface A patch and every patch in its neighborhood form an edge in the dual graph.

In one of the embodiments, before constructing the graph data structure for the vertices and triangle faces in the triangular meshes to form a dual graph, the method also includes: translating all the triangular meshes to the grid centroid as the origin, according to The average length of the sides in the triangular mesh is normalized, and the three-dimensional coordinates of the triangular mesh are scaled to an average side length of 1.

In one of the embodiments, after the graph structure established based on the vertices is used in the neural network to pre-denoise the noisy vertices, the method further includes: calculating the new centroid coordinates and method of the patch according to the pre-denoised vertices Towards.

In one of the embodiments, the vertex graph and the patch graph adopt the same network structure, and the graph convolution unit in the network structure adopts a convolution module:

Among them, b is a bias item, x _i and x _j are the characteristics of node i and j respectively, N(i) is the set of adjacent nodes of node i in the corresponding graph structure, W _m represents m learnable feature transformations, q _m is an assignment function, which is used to assign weights to different adjacent nodes.

In one of the embodiments, after updating the pre-denoised vertices according to the denoised patch normal, the method further includes:

Update the pre-denoised vertices to optimize the final vertex position. The algorithm of the update process is:

Among them, v′ _i is the result of vertex pre-denoising, N _f (i) is all adjacent patches of vertex i, c _k and n _k ′ are the centroid and denoised normal of patch k, respectively.

In the second aspect, the embodiment of the present application also provides a device for denoising triangular meshes based on a dual graph neural network, the device comprising:

The construction unit is used to simultaneously construct a graph data structure for the vertices and triangle faces in the triangular mesh to form a dual graph, and then input the vertex graph and the face graph into the corresponding graph neural network;

The denoising unit, the graph structure established based on the vertices is used in the neural network to pre-denoise the noise vertices, and the graph structure established based on the patch is used in the neural network to denoise the normal direction of the patch;

The output unit is used to update the pre-denoised vertices according to the denoised patch normal to output the final triangular mesh.

In the third aspect, the embodiment of the present application also provides a computer device, including a memory, a processor, and a computer program stored in the memory and operable on the processor. When the processor executes the program, it implements the The method described in any one of the descriptions of the examples.

In a fourth aspect, the embodiment of the present application also provides a computer device, a computer-readable storage medium, on which a computer program is stored, and the computer program is used for: when the computer program is executed by a processor, the computer program according to the present application is implemented. The method described in any one of the descriptions of the examples.

Beneficial effects of the present invention:

The method for denoising triangular meshes based on the dual graph neural network provided by the present invention makes better use of the topological structure of triangular meshes, has better denoising effects, better retention of geometric details, and less quantization errors than meshes. Both the normal angle average error and the vertex distance average error are smaller.

Description of drawings

Other characteristics, objects and advantages of the present application will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings:

FIG. 1 shows a schematic flowchart of a method for denoising triangular meshes based on a dual graph neural network provided by an embodiment of the present application;

FIG. 2 shows an exemplary structural block diagram of a device 200 for denoising triangular meshes based on a dual graph neural network according to an embodiment of the present application;

FIG. 3 shows a schematic structural diagram of a computer system suitable for implementing a terminal device according to an embodiment of the present application;

Fig. 4 shows the grid denoising flow chart provided by the embodiment of the present application;

Fig. 5 shows the U-Net formal graph neural network structure provided by the embodiment of the present application.

Detailed ways

In order to make the above objects, features and advantages of the present invention more comprehensible, specific implementations of the present invention will be described in detail below in conjunction with the accompanying drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described here, and those skilled in the art can make similar improvements without departing from the connotation of the present invention, so the present invention is not limited by the specific embodiments disclosed below.

In describing the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", " Back", "Left", "Right", "Vertical", "Horizontal", "Top", "Bottom", "Inner", "Outer", "Clockwise", "Counterclockwise", "Axial" , "radial", "circumferential" and other indicated orientations or positional relationships are based on the orientations or positional relationships shown in the drawings, which are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying the referred device or Elements must have certain orientations, be constructed and operate in certain orientations, and therefore should not be construed as limitations on the invention.

In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be interpreted as indicating or implying relative importance or implicitly specifying the quantity of indicated technical features. Thus, the features defined as "first" and "second" may explicitly or implicitly include at least one of these features. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

In the present invention, unless otherwise clearly specified and limited, terms such as "installation", "connection", "connection" and "fixation" should be understood in a broad sense, for example, it can be a fixed connection or a detachable connection , or integrated; it may be mechanically connected or electrically connected; it may be directly connected or indirectly connected through an intermediary, and it may be the internal communication of two components or the interaction relationship between two components, unless otherwise specified limit. Those of ordinary skill in the art can understand the specific meanings of the above terms in the present invention according to specific situations.

In the present invention, unless otherwise clearly specified and limited, the first feature may be in direct contact with the first feature or the first and second feature may be in direct contact with the second feature through an intermediary. touch. Moreover, "above", "above" and "above" the first feature on the second feature may mean that the first feature is directly above or obliquely above the second feature, or simply means that the first feature is higher in level than the second feature. "Below", "beneath" and "beneath" the first feature may mean that the first feature is directly below or obliquely below the second feature, or simply means that the first feature is less horizontally than the second feature.

It should be noted that when an element is referred to as being “fixed on” or “disposed on” another element, it may be directly on the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or intervening elements may also be present. As used herein, the terms "vertical", "horizontal", "upper", "lower", "left", "right" and similar expressions are for the purpose of illustration only and are not intended to represent the only embodiments.

Please refer to FIG. 1 in conjunction with FIG. 4 . FIG. 1 shows a schematic flowchart of a method for denoising triangular meshes based on a dual graph neural network provided by an embodiment of the present application.

As shown in Figure 1, the method includes:

Step 110, simultaneously constructing a graph data structure for the vertices and triangle faces in the triangular mesh to form a dual graph, and then inputting the vertex graph and the face graph into the corresponding graph neural network;

Step 120, the graph structure established based on the vertices is used in the neural network to pre-denoise the noisy vertices, and the graph structure established based on the patch is used in the neural network to denoise the normal direction of the patch;

Step 130, update the pre-denoised vertices according to the denoised patch normal to output the final triangular mesh.

Using the above technical solution, the topology of the triangular mesh is better utilized, the denoising effect is better, the geometric details are better maintained, and the quantization error, the average error of the normal angle of the patch and the average error of the vertex distance are smaller.

In some embodiments, the vertices in the triangular mesh are the nodes of the vertex graph in the dual graph, the edges between the vertices are the edges of the vertex graph in the dual graph, and the vertices in the dual graph are The adjacency matrix of the graph is N _v *N _v , where N _v is the number of vertices in the triangular mesh. In the adjacency matrix, the element with a value of 0, in the i-th row and j-th column, means that the i-th vertex and the j-th vertex in the grid are not connected, otherwise, the value of 1 means that the i-th vertex and the j-th vertex j vertices are connected by an edge.

In some embodiments, the constructing graph data structure for the triangular patches in the triangular mesh to form a patch graph in the dual graph includes: calculating the centroid and normal direction of each triangular patch through the vertices in the triangular mesh ;Determine whether each triangle patch has shared vertices with the surrounding patches, if so, retrieve the neighborhood patch set of the triangle patch; use each triangle patch as a node in the patch graph, and pass the triangle surface A patch and every patch in its neighborhood form an edge in the dual graph.

Specifically, for each triangular patch composed of vertices in the triangular mesh, a neighborhood patch set of the patch can be retrieved according to whether it shares vertices with surrounding patches. In this way, each triangular patch can be used as a node in the patch graph, and the patch and each patch in its neighborhood can form an edge in a graph structure, and a corresponding patch graph structure can be constructed. The size of the adjacency matrix is N _f * N _f , where N _f is the number of patches in the grid. In the adjacency matrix, the element with a value of 0, the i-th row and the j-th column represent the i-th in the grid The i-th patch and the j-th patch are not in their respective neighborhoods. On the contrary, if the value is 1, the i-th patch and the j-th patch are adjacent to each other.

In some embodiments, before constructing the graph data structure for the vertices and triangle patches in the triangular meshes to form a dual graph, the method further includes: translating all the triangular meshes to the grid centroid as the origin, according to the triangle The average length of the edges in the grid is normalized, and the three-dimensional coordinates of the triangular mesh are scaled to an average edge length of 1.

After constructing the dual graph structure in the grid, input the vertex graph and the patch graph into their respective graph neural networks. The node attributes of the vertex graph are the initial coordinates and normal directions of the vertices, and the node attributes of the patch graph are the patch centroids. The coordinates and patch normal of . Since the coordinate system and spatial scale of each triangular mesh are different, all meshes need to be normalized before network training. Specifically, all the grids are first translated to the grid centroid as the origin, and then normalized according to the average length of the edges in the grid, that is, the three-dimensional coordinates of the grid are scaled to an average edge length of 1.

In some embodiments, after the graph structure established based on the vertices is used in the neural network to pre-denoise the noisy vertices, the method further includes: calculating the new centroid coordinates and normal of the patch according to the pre-denoised vertices .

Aiming at the problem that complex noise will increase the difficulty of directly performing normal regression on the noise patch, this design further calculates the new centroid coordinates and normal of the patch from the corresponding output of the vertex map, that is, the pre-denoising vertex (that is, the pre-denoising The final patch centroid coordinates and normal direction) to enhance the features of the patch map input into the network:

(F _f represents the initial feature of the patch,

Indicates the new patch feature calculated based on the pre-denoised vertices, || indicates the concatenation operation in the feature dimension, see the dotted line connection between V' and G ^f ). Since the pre-denoised vertices have more accurate spatial positions than the input noise vertices, the effect of patch normal regression can be significantly improved, thereby providing more accurate denoising normals for subsequent vertex updates.

In addition, in view of the problem that directly updating the original noisy vertices in the vertex update stage is easy to smooth geometric details, the pre-denoising result of the vertex map in the present invention can be used as the initial position of the vertex update stage. Since the pre-denoised vertices have more accurate geometry than the original noise vertices, more geometric details can be preserved after vertex updating.

In some embodiments, as shown in FIG. 5, the vertex graph and the patch graph adopt the same network structure, and the graph convolution unit in the network structure adopts a convolution module:

The graph pooling method adopts the edge shrinkage algorithm of the graph structure proposed in , by maximizing:

Among them, di and dj represent the degrees of nodes i and j in a graph, respectively, and wij represents the edge weight between nodes i and j. The algorithm shrinks and merges a pair of nodes with larger edge weights into one node by iteratively executing the above maximization process. In this grid denoising, the calculation of edge weight is obtained by calculating the distance and normal error of nodes:

Among them, ε is a small positive value to avoid the negative value of the first item, v _i and v _j are the three-dimensional coordinates of nodes i and j respectively or the centroid of the patch, and le is the average side length of the entire grid. This approach has been validated in [11] for graph pooling for mesh denoising. The upsampling (unpooling) part of the graph directly copies the features of the points or surfaces that have shrunk in the corresponding pooling operation to restore the graph structure of the corresponding size.

By inputting the vertex map and the patch map into the graph neural network, the pre-denoised vertex coordinates and the patch normal are output at the same time. Therefore, during the training process of this network, the complete loss function needs to include the vertex coordinates and the patch normal. :

Loss = α _v Loss _v + α _f Loss _f

in

v' is the pre-denoised vertex coordinates, n' is the denoised patch normal direction corresponding to the output of the patch image, v _g and n _g are the corresponding vertex reference value and patch normal reference value respectively. α _v and α _f are the weights of the two losses respectively.

In some embodiments, after updating the pre-denoised vertices according to the denoised patch normal, the method further includes: updating the pre-denoised vertices to optimize the final vertex position, the algorithm of the update process is :

Specifically, after the training of the graph neural network is completed, a dual graph structure is constructed for the tested noise network, and then input into a fixed network, which can directly output the pre-denoised vertex coordinates and the denoised face normal. It is necessary to further update the pre-denoised vertices to optimize the final vertex position. The algorithm for this update process is:

In other grid denoising algorithms, v′ _i are the initial noise vertices, but in this design, the dual graph learning has more accurate vertex pre-denoising results, so v′ _i is the result of vertex pre-denoising, N _f (i) is all adjacent patches of vertex i, c _k and nk _′ are the centroid of patch k (calculated from the pre-denoised vertex) and the normal after denoising, respectively. The process is iterated many times to get the ideal vertex update result.

Further, referring to FIG. 2 , FIG. 2 shows an exemplary structural block diagram of an apparatus 200 for denoising triangular meshes based on a dual graph neural network according to an embodiment of the present application.

As shown in Figure 2, the device includes:

The construction unit 210 is used to simultaneously construct a graph data structure for the vertices and triangle faces in the triangular mesh to form a dual graph, and then input the vertex graph and the face graph into the corresponding graph neural network;

Denoising unit 220, the graph structure established based on the vertices is used in the neural network to pre-denoise the noisy vertices, and the graph structure established based on the patch is used in the neural network to denoise the normal direction of the patch;

The output unit 230 is configured to update the pre-denoised vertices according to the denoised facet normal to output the final triangular mesh.

It should be understood that the units or modules recorded in the device 200 correspond to the steps in the method described with reference to FIG. 1 . Therefore, the operations and features described above for the method are also applicable to the device 200 and the units contained therein, and will not be repeated here. The apparatus 200 may be pre-implemented in the browser of the electronic device or other security applications, and may also be loaded into the browser of the electronic device or its security applications by downloading or other means. The corresponding units in the apparatus 200 may cooperate with the units in the electronic device to implement the solutions of the embodiments of the present application.

Referring now to FIG. 3 , it shows a schematic structural diagram of a computer system 300 suitable for implementing a terminal device or a server according to an embodiment of the present application.

As shown in FIG. 3 , a computer system 300 includes a central processing unit (CPU) 301 that can operate according to a program stored in a read-only memory (ROM) 302 or a program loaded from a storage section 308 into a random-access memory (RAM) 303 Instead, various appropriate actions and processes are performed. In the RAM 303, various programs and data required for the operation of the system 300 are also stored. The CPU 301, ROM 302, and RAM 303 are connected to each other through a bus 304. An input/output (I/O) interface 305 is also connected to the bus 304 .

The following components are connected to the I/O interface 305: an input section 306 including a keyboard, a mouse, etc.; an output section 307 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker; a storage section 308 including a hard disk, etc. and a communication section 309 including a network interface card such as a LAN card, a modem, or the like. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the I/O interface 305 as needed. A removable medium 311, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is mounted on the drive 310 as necessary so that a computer program read therefrom is installed into the storage section 308 as necessary.

In particular, according to an embodiment of the present disclosure, the process described above with reference to FIG. 1 may be implemented as a computer software program. For example, embodiments of the present disclosure include a method for denoising triangular meshes based on a dual graph neural network, which includes a computer program tangibly embodied on a machine-readable medium, the computer program including a method for executing the The program code of the method. In such an embodiment, the computer program may be downloaded and installed from a network via communication portion 309 and/or installed from removable media 311 .

The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, program segment, or part of code that includes one or more logical functions for implementing specified executable instructions. It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or they may sometimes be executed in the reverse order, depending upon the functionality involved. It should also be noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by a dedicated hardware-based system that performs the specified functions or operations , or may be implemented by a combination of dedicated hardware and computer instructions.

The units or modules involved in the embodiments described in the present application may be implemented by means of software or by means of hardware. The described units or modules may also be set in a processor. For example, it may be described as: a processor includes a first sub-region generating unit, a second sub-region generating unit, and a display region generating unit. Wherein, the names of these units or modules do not constitute limitations on the units or modules themselves in some cases, for example, the display area generation unit can also be described as "used to generate The cell of the display area of the text".

As another aspect, the present application also provides a computer-readable storage medium, which may be the computer-readable storage medium contained in the aforementioned devices in the above-mentioned embodiments; computer-readable storage media stored in the device. The computer-readable storage medium stores one or more programs, and the aforementioned programs are used by one or more processors to execute the text generation method applied to transparent window envelopes described in this application.

The above description is only a preferred embodiment of the present application and an illustration of the applied technical principle. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to the technical solution formed by the specific combination of the above-mentioned technical features, and should also cover the technical solutions formed by the above-mentioned technical features or without departing from the aforementioned inventive concept. Other technical solutions formed by any combination of equivalent features. For example, a technical solution formed by replacing the above-mentioned features with technical features with similar functions disclosed in (but not limited to) this application.

Claims

A method for denoising triangular grids based on a dual graph neural network, characterized in that the method comprises:

Simultaneously build a graph data structure for the vertices and triangle faces in the triangular mesh to form a dual graph, and then input the vertex graph and the face graph into the corresponding graph neural network;

The graph structure based on the vertices is used in the neural network to pre-denoise the noise vertices, and the graph structure based on the patch is used in the neural network to denoise the normal direction of the patch;

The pre-denoised vertices are updated according to the denoised patch normals to output the final triangle mesh.
The method for denoising a triangular mesh based on a dual graph neural network according to claim 1, wherein the vertices in the triangular mesh are nodes of the vertex graph in the dual graph, and between the vertices The edges of are the edges of the vertex graph in the dual graph, and the adjacency matrix of the vertex graph in the dual graph is N v *N v , where N v is the number of vertices in the triangular mesh.
The method for denoising triangular mesh based on dual graph neural network according to claim 2, characterized in that, the triangular patch in the triangular mesh constructs a graph data structure to form a patch graph in the dual graph, include:

Calculate the centroid and normal of each triangle patch from the vertices in the triangle mesh;

Determine whether each triangle facet has shared vertices with the surrounding facets, and if so, retrieve the neighborhood facet set of the triangle facet;

Each triangular facet is regarded as a node in the facet graph, and an edge in the dual graph is formed by the triangular facet and each facet in its neighborhood.
The method for denoising a triangular mesh based on a dual graph neural network according to claim 1, characterized in that, before the vertices and triangle faces in the triangular mesh are simultaneously constructed a graph data structure to form a dual graph, the Methods also include:

Translate all the triangular meshes to the grid centroid as the origin, perform normalization according to the average length of the sides in the triangular meshes, and scale the three-dimensional coordinates of the triangular meshes to an average side length of 1.
The method for denoising a triangular mesh based on a dual graph neural network according to claim 1, characterized in that, after the graph structure established based on vertices is used in the neural network to pre-denoise noise vertices, the Methods also include:

Compute the new centroid coordinates and normals of the patch based on the pre-denoised vertices.
The method for denoising a triangular mesh based on a dual graph neural network according to claim 1, wherein the vertex graph and the patch graph adopt the same network structure, and the graph volume in the network structure The product unit uses a convolution module:

Among them, b is a bias item, x i and x j are the characteristics of node i and j respectively, N(i) is the set of adjacent nodes of node i in the corresponding graph structure, W m represents m learnable feature transformations, q m is an assignment function, which is used to assign weights to different adjacent nodes.
The method for denoising triangular meshes based on dual graph neural network according to claim 1, characterized in that, after updating the pre-denoised vertices according to the denoised patch normal, the method also includes :

Update the pre-denoised vertices to optimize the final vertex position. The algorithm of the update process is:

Among them, v′ i is the result of vertex pre-denoising, N f (i) is all adjacent patches of vertex i, c k and n k ′ are the centroid and denoised normal of patch k, respectively.
A device for denoising triangular grids based on a dual graph neural network, characterized in that the device includes:

The construction unit is used to simultaneously construct a graph data structure for the vertices and triangle faces in the triangular mesh to form a dual graph, and then input the vertex graph and the face graph into the corresponding graph neural network;

The denoising unit, the graph structure established based on the vertices is used in the neural network to pre-denoise the noise vertices, and the graph structure established based on the patch is used in the neural network to denoise the normal direction of the patch;

The output unit is used to update the pre-denoised vertices according to the denoised patch normal to output the final triangular mesh.
A computer device, comprising a memory, a processor, and a computer program stored on the memory and operable on the processor, characterized in that, when the processor executes the program, it implements any of claims 1-7 described method.
A computer-readable storage medium having stored thereon a computer program for:

When the computer program is executed by the processor, the method according to any one of claims 1-7 is implemented.