CN114419275A - Method for denoising triangular mesh based on dual-graph neural network - Google Patents

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

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CN114419275A
CN114419275A CN202111521604.7A CN202111521604A CN114419275A CN 114419275 A CN114419275 A CN 114419275A CN 202111521604 A CN202111521604 A CN 202111521604A CN 114419275 A CN114419275 A CN 114419275A
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张英奎
王琼
赵保亮
孙寅紫
王平安
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Shenzhen Institute of Advanced Technology of CAS
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Abstract

The application discloses a method, a device, equipment and a storage medium for denoising triangular meshes based on a dual graph neural network, wherein the method comprises the following steps: simultaneously constructing graph data structures for vertexes and triangular patches in the triangular mesh to form a dual graph, and then inputting the vertex graph and the patch graph into a corresponding graph neural network; the graph structure established based on the vertex is used for pre-denoising the noise vertex in the neural network, and the graph structure established based on the patch is used for denoising the normal direction of the patch in the neural network; and updating the pre-denoised vertexes according to the denoised surface patch method to output the final triangular mesh. According to the scheme, the topological structure of the triangular mesh is better utilized, the denoising effect is better, the retention of geometric details is better, and in quantization errors, the average error of a normal angle of a surface patch and the average error of a vertex distance are smaller.

Description

Method for denoising triangular mesh based on dual-graph neural network
Technical Field
The invention relates to computer software, in particular to a method, a device and equipment for denoising a triangular mesh based on a dual-graph neural network and a storage medium thereof.
Background
In the fields of three-dimensional reconstruction, augmented reality, medicine and the like, the scanning reconstruction of a grid model on an object or a human body is an indispensable step. However, due to the accuracy of devices such as a scanning sensor and the like, ambient light and the like, the reconstructed grid inevitably contains noise, so that the effects of later visualization and the like are greatly influenced.
A triangular mesh is one of the most common forms of representation of three-dimensional geometry, and comprises a set of three-dimensional points and a set of patches, each triangular patch being made up of an index of three points. Due to the noise triangular mesh generated by various reasons, the three-dimensional vertex is deviated, so that the local geometric structure cannot be accurately represented, and noise is formed. The triangular mesh denoising aims to correct the offset of the vertex, simultaneously reserve the original surface patch topological structure, and accurately remove the noise and simultaneously reserve potential geometric details.
The existing triangle mesh denoising method can be mainly divided into a traditional filtering or optimizing-based method and a learning-based method. Traditional filtering and derived methods can obtain good denoising effect, but are difficult to retain fine geometric details, and optimization-based methods, such as L0 minimization, low rank recovery and the like, are generally not thorough in noise removal and are also low in efficiency. Recently, a learning-based method obtains a more prominent denoising effect. For example, from the existing normal filter descriptors, patch normal regression is then performed with a single-layer neural network. And an iterative denoising algorithm is realized by combining three-dimensional voxelization and a 3D convolutional neural network. And (3) constructing a normal matrix block with non-local similarity, and learning by using a convolutional neural network to output the normal of the denoised surface patch.
The noise offset can cause inaccuracy of the normal direction of the triangular patch, thereby affecting the local smooth property of the triangular mesh. The method is a two-step method: firstly, performing normal regression on a triangular surface patch to obtain a normal direction of the denoised surface patch, and then updating a noise vertex coordinate according to the normal direction to output a final denoised grid. However, these methods ignore two points: (1) because the vertexes of the noise mesh contain noise, it is difficult to perform normal regression directly from these noisy attributes, (2) after obtaining the denoised patch normal direction, it is also difficult to directly update the original noise vertexes and retain their potential geometric attributes.
Disclosure of Invention
In view of the foregoing drawbacks and deficiencies of the prior art, it is desirable to provide a method, an apparatus, a device and a storage medium for denoising a triangular mesh based on a dual-graph neural network.
In a first aspect, an embodiment of the present application provides a method for denoising a triangular mesh based on a dual-graph neural network, where the method includes:
simultaneously constructing graph data structures for vertexes and triangular patches in the triangular mesh to form a dual graph, and then inputting the vertex graph and the patch graph into a corresponding graph neural network;
the graph structure established based on the vertex is used for pre-denoising the noise vertex in the neural network, and the graph structure established based on the patch is used for denoising the normal direction of the patch in the neural network;
and updating the pre-denoised vertexes according to the denoised surface patch method to output the final triangular mesh.
In one embodiment, the vertices in the triangular mesh are nodes of a vertex graph in the dual graph, edges between the vertices are edges of the vertex graph in the dual graph, and an adjacency matrix of the vertex graph in the dual graph is Nv*NvWherein N isvThe number of vertices in the triangular mesh.
In one embodiment, the constructing the graph data structure for the triangular patches in the triangular mesh forms a patch graph in a dual graph, including: calculating the mass center and the normal direction of each triangular patch through the vertexes in the triangular mesh; judging whether each triangular patch and surrounding patches have a shared vertex, and if so, retrieving to obtain a neighborhood patch set of the triangular patches; each triangular patch is taken as a node in the patch graph, and an edge in the dual graph is formed by the triangular patch and each patch in the neighborhood of the triangular patch.
In one embodiment, before the graph data structure is constructed for the vertices and the triangular patches in the triangular mesh simultaneously to form the dual graph, the method further comprises: and translating all the triangular meshes to the position taking the mesh centroid as the origin, carrying out normalization processing according to the average length of the edges in the triangular meshes, and scaling the three-dimensional coordinates of the triangular meshes to the average edge length of 1.
In one embodiment, after the graph structure built based on the vertices is used for pre-denoising the noise vertices in the neural network, the method further includes: and calculating new centroid coordinates and normal directions of the surface patches according to the pre-denoised vertexes.
In one embodiment, the vertex graph and the patch graph adopt the same network structure, and a graph convolution unit in the network structure adopts a convolution module:
Figure BDA0003407556870000031
wherein b is a bias term, xiAnd xjFeatures of nodes i and j, respectively, N (i) is a set of adjacent nodes corresponding to node i in the graph structure, WmRepresenting m learnable feature transformations, qmAn assignment function is used to assign weights to the different neighboring nodes.
In one embodiment, after updating the pre-denoised vertices according to the denoised patch normal, the method further includes:
updating the pre-denoised vertex to optimize the final vertex position, wherein the algorithm of the updating process is as follows:
Figure BDA0003407556870000032
wherein, v'iFor the result of vertex pre-denoising, Nf(i) All contiguous patches of vertex i, ckAnd nk' are the centroid of patch k and the denoised normal, respectively.
In a second aspect, an embodiment of the present application further provides a device for denoising a triangular mesh based on a dual-graph neural network, where the device includes:
the construction unit is used for simultaneously constructing graph data structures for vertexes and triangular patches in the triangular mesh to form a dual graph, and then inputting the vertex graph and the patch graph into a corresponding graph neural network;
the denoising unit is used for pre-denoising the noise peak in the neural network based on the graph structure established by the peak, and denoising the normal direction of the patch in the neural network based on the graph structure established by the patch;
and the output unit is used for updating the pre-denoised vertex according to the denoised surface patch normal direction so as to output the final triangular mesh.
In a third aspect, an embodiment of the present application further provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the computer program to implement the method according to any one of the descriptions in the embodiment of the present application.
In a fourth aspect, an embodiment of the present application further provides a computer device, which is a computer-readable storage medium, and a computer program is stored thereon, where the computer program is configured to: which when executed by a processor implements a method as described in any of the embodiments of the present application.
The invention has the beneficial effects that:
the method for denoising the triangular mesh based on the dual-graph neural network provided by the invention better utilizes the topological structure of the triangular mesh, has better denoising effect and better retention of geometric details, and has smaller average errors of the normal angle and the vertex distance of a surface patch in quantization errors.
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Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
fig. 1 is a schematic flowchart illustrating a method for denoising a triangular mesh based on a dual-graph neural network according to an embodiment of the present application;
FIG. 2 is a block diagram illustrating an exemplary structure of an apparatus 200 for denoising a triangular mesh based on a dual-graph neural network according to an embodiment of the present application;
FIG. 3 illustrates a schematic structural diagram of a computer system suitable for use in implementing a terminal device of an embodiment of the present application;
FIG. 4 is a flowchart illustrating a mesh denoising process provided by an embodiment of the present application;
FIG. 5 shows a U-Net form diagram neural network structure provided by the embodiment of the application.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and are not to be considered limiting of the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "over," and "above" a second feature may be directly or diagonally above the second feature, or may simply indicate that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
It will be understood that when an element is referred to as being "secured to" or "disposed on" another element, it can be directly on the other element or intervening elements may also be present. 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. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and the like as used herein are for illustrative purposes only and do not denote a unique embodiment.
Referring to fig. 1 in conjunction with fig. 4, fig. 1 is a schematic flowchart illustrating a method for denoising a triangular mesh based on a dual-graph neural network according to an embodiment of the present disclosure.
As shown in fig. 1, the method includes:
step 110, simultaneously constructing graph data structures for vertexes and triangular patches in the triangular mesh to form a dual graph, and then inputting the vertex graph and the patch graph into a corresponding graph neural network;
step 120, the graph structure established based on the vertex is used for pre-denoising the noise vertex in the neural network, and the graph structure established based on the patch is used for denoising the patch in the normal direction in the neural network;
and step 130, updating the pre-denoised vertex according to the denoised surface patch method to output a final triangular mesh.
By adopting the technical scheme, the topological structure of the triangular mesh is better utilized, the denoising effect is better, the retention of geometric details is better, and the average error of the normal angle of the surface patch and the average error of the vertex distance are smaller in quantization error.
In some embodiments, the vertices in the triangular mesh are nodes of a vertex graph in the dual graph, the edges between the vertices are edges of the vertex graph in the dual graph, and the adjacency matrix of the vertex graph in the dual graph is Nv*NvWherein N isvThe number of vertices in the triangular mesh. In the adjacency matrix, the ith row and the jth column of the element with the value of 0 indicate that the ith vertex and the jth vertex in the mesh are not connected, otherwise, the ith vertex and the jth vertex are connected by edges if the value of 1.
In some embodiments, constructing the graph data structure for triangular patches in the triangular mesh forms a patch graph in a dual graph, including: calculating the mass center and the normal direction of each triangular patch through the vertexes in the triangular mesh; judging whether each triangular patch and surrounding patches have a shared vertex, and if so, retrieving to obtain a neighborhood patch set of the triangular patches; each triangular patch is taken as a node in the patch graph, and an edge in the dual graph is formed by the triangular patch and each patch in the neighborhood of the triangular patch.
Specifically, each triangular patch formed by vertices in the triangular mesh may be retrieved to obtain a neighborhood patch set of patches according to whether the triangular patch has shared vertices with surrounding patches. Thus, each triangular patch can be used as a node in the patch diagram, and the patch and each patch in the neighborhood thereof can form an edge in the diagram structure, i.e., a corresponding patch diagram structure can be constructed. The adjacency matrix has a size of Nf*NfIn which N isfThe number of patches in the grid is represented by the number of elements with the value of 0 in the adjacency matrix, and the ith row and the jth column in which the elements with the value of 0 are located represent that the ith patch and the jth patch in the grid are not in respective neighborhoods, otherwise, the value of 1 represents that the ith patch and the jth patch are neighborhoods.
In some embodiments, before the graph data structure is constructed for the vertices and the triangular patches in the triangular mesh simultaneously to form the dual graph, the method further comprises: and translating all the triangular meshes to the position taking the mesh centroid as the origin, carrying out normalization processing according to the average length of the edges in the triangular meshes, and scaling the three-dimensional coordinates of the triangular meshes to the average edge length of 1.
After a dual graph structure is constructed in a grid, a vertex graph and a patch graph are respectively input into respective graph neural networks, the node attributes of the vertex graph are the initial coordinates and the normal direction of a vertex, and the node attributes of the patch graph are the coordinates of the centroid of a patch and the normal direction of the patch. Because the coordinate system and spatial scale of each triangular mesh are different, all meshes need to be normalized before the network training. Specifically, all the grids are firstly translated to the position with the grid centroid as the origin, and then normalization processing is performed according to the average length of the edges in the grids, namely, the three-dimensional coordinates of the grids are scaled to the average length of the edges being 1.
In some embodiments, after the graph structure built based on vertices is used in a neural network for pre-denoising noise vertices, the method further comprises: and calculating new centroid coordinates and normal directions of the surface patches according to the pre-denoised vertexes.
Aiming at the problem that the complex noise can increase the difficulty of the direct normal regression of the noise patch, the design further calculates the new centroid coordinate and normal of the patch (namely the centroid coordinate and normal of the patch after the pre-denoising) with the output corresponding to the vertex diagram, namely the pre-denoised vertex, so as to enhance the characteristic that the patch diagram is input into the network:
Figure BDA0003407556870000081
(Ffrepresenting the initial characteristics of the patch of material,
Figure BDA0003407556870000082
representing the new patch features calculated from the pre-de-denoised vertices, | | | represents the concatenation operation in the feature dimension, see V' to GfDotted line connection of). Compared with the input noise vertex, the pre-denoised vertex has a more accurate spatial position, so that the normal regression effect of the patch can be obviously improved, and a more accurate denoising normal is provided for subsequent vertex updating.
In addition, aiming at the problem that the original noise vertex is easy to smooth the geometric details in the vertex updating stage, the pre-denoising result of the vertex map can be used as the initial position of the vertex updating stage. Since the pre-denoised vertices have more accurate geometry than the original noisy vertices, more geometric details can be retained after vertex update.
In some embodiments, referring to fig. 5, the vertex graph and the patch graph use the same network structure, and the graph convolution unit in the network structure uses a convolution module:
Figure BDA0003407556870000091
wherein b is a bias term, xiAnd xjFeatures of nodes i and j, respectively, and N (i) is the corresponding node i in the graph structureSet of adjacent nodes of WmRepresenting m learnable feature transformations, qmAn assignment function is used to assign weights to the different neighboring nodes.
The graph pooling method adopts the edge contraction algorithm of the graph structure proposed in the previous step, and by maximization:
Figure BDA0003407556870000092
where di and dj represent degrees of nodes i and j, respectively, in a graph, and wij represents the edge weight between nodes i and j. The algorithm shrinks and combines a pair of nodes with larger edge weight into 1 node by iteratively executing the maximization process. In the mesh denoising, the calculation of the edge weight is obtained by calculating the distance of the nodes and the normal error:
Figure BDA0003407556870000093
where ε is a small positive value to avoid the first term being negative, viAnd VjThe three-dimensional coordinates or patch centroids of nodes i and j, respectively, and le is the average side length of the whole grid. The method has been described in [11]And verifying the pooling of the de-noising graph of the medium grid. The upsampled (anti-pooling) portion of the graph directly copies the features of the points or faces shrunk in the corresponding pooling operation to restore the graph structure to the corresponding size.
Inputting a vertex diagram and a patch diagram into a neural network to simultaneously output the vertex coordinates and the patch normal of pre-denoising, so that in the network training process, a complete loss function needs to comprise the vertex coordinates and the patch normal:
Loss＝αυLossv+αfLossf
wherein
Figure BDA0003407556870000101
v 'is the coordinate of the vertex of the pre-de-noising, n' is the normal direction of the denoised surface patch correspondingly output by the surface patch diagram, vgAnd ngRespectively corresponding vertex reference values and face normal reference values. Alpha is alphaυAnd alphafThe weights of the two losses are respectively.
In some embodiments, after updating the pre-denoised vertices according to the denoised patch normal, the method further comprises: updating the pre-denoised vertex to optimize the final vertex position, wherein the algorithm of the updating process is as follows:
Figure BDA0003407556870000102
wherein, v'iFor the result of vertex pre-denoising, Nf(i) All contiguous patches of vertex i, ckAnd nk' are the centroid of patch k and the denoised normal, respectively.
Specifically, after the graph neural network training is completed, a dual graph structure is constructed for the tested noise network, and then the dual graph structure is input into a fixed network, so that the pre-denoised vertex coordinates and the denoised surface patch normal direction can be directly output, and at this time, the pre-denoised vertex needs to be further updated to optimize the final vertex position. The algorithm of the updating process is as follows:
Figure BDA0003407556870000103
v 'in other mesh denoising algorithms'iAre all initial noise vertices, and the learning of the dual graph in the design has a more accurate vertex pre-denoising result, so v'iFor the result of vertex pre-denoising, Nf(i) All contiguous patches of vertex i, ckAnd nk' are the centroid of patch k (calculated from the pre-denoised vertices) and the normal after denoising, respectively. The process iterates multiple times to obtain the desired vertex update result.
Further, referring to fig. 2, fig. 2 shows an exemplary structural block diagram of an apparatus 200 for denoising a triangular mesh based on a dual-graph neural network according to an embodiment of the present application.
As shown in fig. 2, the apparatus includes:
the construction unit 210 is configured to construct a graph data structure for vertices and triangular patches in a triangular mesh at the same time to form a dual graph, and then input the vertex graph and the patch graph into a corresponding graph neural network;
the denoising unit 220 is configured to pre-denoise a noise vertex in the neural network based on the graph structure established by the vertex, and denoise a normal direction of the patch in the neural network based on the graph structure established by the patch;
and an output unit 230, configured to update the pre-denoised vertices according to the denoised patch normal direction to output a final triangular mesh.
It should be understood that the units or modules recited in the apparatus 200 correspond to the various steps in the method described with reference to fig. 1. Thus, the operations and features described above for the method are equally applicable to the apparatus 200 and the units included therein, and are not described in detail here. The apparatus 200 may be implemented in a browser or other security applications of the electronic device in advance, or may be loaded into the browser or other security applications of the electronic device by downloading or the like. Corresponding elements in the apparatus 200 may cooperate with elements in the electronic device to implement aspects of embodiments of the present application.
Referring now to FIG. 3, a block diagram of a computer system 300 suitable for implementing a terminal device or server of the embodiments of the present application is shown.
As shown in fig. 3, the computer system 300 includes a Central Processing Unit (CPU)301 that can perform various appropriate actions and processes in accordance with 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. In the RAM 303, various programs and data necessary for the operation of the system 300 are also stored. The CPU 301, ROM 302, and RAM 303 are connected to each other via a bus 304. An input/output (I/O) interface 305 is also connected to bus 304.
The following components are connected to the I/O interface 305: an input portion 306 including a keyboard, a mouse, and the like; an output section 307 including a display such as a Cathode Ray Tube (CRT), a Liquid Crystal Display (LCD), and the like, and a speaker; a storage section 308 including a hard disk and the like; 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, or the like is mounted on the drive 310 as necessary, so that a computer program read out therefrom is mounted into the storage section 308 as necessary.
In particular, the process described above with reference to fig. 1 may be implemented as a computer software program, according to an embodiment of the present disclosure. For example, embodiments of the present disclosure include a method of denoising triangular meshes based on a dual-graph neural network, comprising a computer program tangibly embodied on a machine-readable medium, the computer program containing program code for performing the method of fig. 1. In such an embodiment, the computer program may be downloaded and installed from a network through the communication section 309, and/or installed from the removable medium 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 the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). 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 the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The units or modules described in the embodiments of the present application may be implemented by software or hardware. The described units or modules may also be provided in a processor, and 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. Where the names of these units or modules do not in some cases constitute a definition of the unit or module itself, for example, the display area generating unit may also be described as a "unit for generating a display area of text from the first sub-area and the second sub-area".
As another aspect, the present application also provides a computer-readable storage medium, which may be the computer-readable storage medium included in the foregoing device in the foregoing embodiment; or it may be a separate computer readable storage medium not incorporated into the device. The computer readable storage medium stores one or more programs for use by one or more processors in performing the text generation method applied to the transparent window envelope described in the present application.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by those skilled in the art that the scope of the invention herein disclosed is not limited to the particular combination of features described above, but also encompasses other arrangements formed by any combination of the above features or their equivalents without departing from the spirit of the invention as defined above. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.

Claims (10)

1. A method for denoising a triangular mesh based on a dual-graph neural network is characterized by comprising the following steps:
simultaneously constructing graph data structures for vertexes and triangular patches in the triangular mesh to form a dual graph, and then inputting the vertex graph and the patch graph into a corresponding graph neural network;
the graph structure established based on the vertex is used for pre-denoising the noise vertex in the neural network, and the graph structure established based on the patch is used for denoising the normal direction of the patch in the neural network;
and updating the pre-denoised vertexes according to the denoised surface patch method to output the final triangular mesh.
2. The method of claim 1, wherein the vertices of the triangular mesh are nodes of a vertex map of the dual graph, edges between the vertices are edges of the vertex map of the dual graph, and an adjacency matrix of the vertex map of the dual graph is Nv*NvWherein N isvThe number of vertices in the triangular mesh.
3. The method of claim 2, wherein the constructing the graph data structure for the triangular patches in the triangular mesh to form the patch graph in the dual graph comprises:
calculating the mass center and the normal direction of each triangular patch through the vertexes in the triangular mesh;
judging whether each triangular patch and surrounding patches have a shared vertex, and if so, retrieving to obtain a neighborhood patch set of the triangular patches;
each triangular patch is taken as a node in the patch graph, and an edge in the dual graph is formed by the triangular patch and each patch in the neighborhood of the triangular patch.
4. The method of claim 1, wherein before the constructing the graph data structure for the vertices and the triangular patches in the triangular mesh simultaneously to form the dual graph, the method further comprises:
and translating all the triangular meshes to the position taking the mesh centroid as the origin, carrying out normalization processing according to the average length of the edges in the triangular meshes, and scaling the three-dimensional coordinates of the triangular meshes to the average edge length of 1.
5. The method of claim 1, wherein the graph structure based on vertex building is used in the neural network to pre-denoise the noise vertices, and further comprising:
and calculating new centroid coordinates and normal directions of the surface patches according to the pre-denoised vertexes.
6. The method of claim 1, wherein the vertex graph and the patch graph have the same network structure, and a graph convolution unit in the network structure has a convolution module:
Figure FDA0003407556860000021
wherein b is a bias term, xiAnd xjFeatures of nodes i and j, respectively, N (i) is a set of adjacent nodes corresponding to node i in the graph structure, WmRepresenting m learnable feature transformations, qmAn assignment function is used to assign weights to the different neighboring nodes.
7. The method of claim 1, wherein after updating the pre-denoised vertices according to the denoised patch normal, the method further comprises:
updating the pre-denoised vertex to optimize the final vertex position, wherein the algorithm of the updating process is as follows:
Figure FDA0003407556860000022
wherein, v'iFor the result of vertex pre-denoising, Nf(i) All contiguous patches of vertex i, ckAnd nk' are the centroid of patch k and the denoised normal, respectively.
8. A device for denoising triangular meshes based on a dual-graph neural network is characterized by comprising:
the construction unit is used for simultaneously constructing graph data structures for vertexes and triangular patches in the triangular mesh to form a dual graph, and then inputting the vertex graph and the patch graph into a corresponding graph neural network;
the denoising unit is used for pre-denoising the noise peak in the neural network based on the graph structure established by the peak, and denoising the normal direction of the patch in the neural network based on the graph structure established by the patch;
and the output unit is used for updating the pre-denoised vertex according to the denoised surface patch normal direction so as to output the final triangular mesh.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method according to any of claims 1-7 when executing the program.
10. A computer-readable storage medium having stored thereon a computer program for:
the computer program, when executed by a processor, implementing the method as claimed in any one of claims 1-7.
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