CN116778027A - Curved surface parameterization method and device based on neural network - Google Patents

Curved surface parameterization method and device based on neural network Download PDF

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CN116778027A
CN116778027A CN202311055288.8A CN202311055288A CN116778027A CN 116778027 A CN116778027 A CN 116778027A CN 202311055288 A CN202311055288 A CN 202311055288A CN 116778027 A CN116778027 A CN 116778027A
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CN116778027B (en
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庞宇飞
慕茹霜
刘杨
陈波
陈浩
谢冬香
胡月凡
滕凡
陈超
张千一
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The application relates to a curved surface parameterization method and a curved surface parameterization device based on a neural network, belonging to the technical field of curved surface parameterization, wherein the method comprises the following steps: giving a grid curved surface S and target curvatures of grid vertexes on the grid curved surface S; calculating the weight of each grid edge in the grid curved surface S and the curvature corresponding to each grid vertex; constructing and training a neural network, and obtaining a neural network with optimized parameters; the method comprises the steps of obtaining conformal factor variation of each grid vertex on a grid curved surface S; and obtaining the target measurement of the two-dimensional grid corresponding to the grid curved surface S, and mapping the target measurement to the two-dimensional parameter domain. The method and the device provided by the application acquire the conformal factor variation of each grid vertex on the grid curved surface through the neural network with optimized parameters, thereby acquiring the target measurement of the two-dimensional grid corresponding to the grid curved surface, mapping the target measurement to the two-dimensional parameter domain, and avoiding the problems that the calculation error and the calculation time cost are influenced by the increase of the complexity of the grid scale.

Description

Curved surface parameterization method and device based on neural network
Technical Field
The application relates to the technical field of surface parameterization, in particular to a surface parameterization method and device based on a neural network.
Background
In the existing curved surface parameterization technology, discrete Ricci flows are solved mainly through an iteration method, a curved surface is paved to a two-dimensional parameter domain according to solving results, however, with the development of information technology, the grid scale of requirements is gradually increased, high-specification curved surfaces are increasingly used, and the problems of long time consumption and mapping deformation of the existing curved surface parameterization technology are gradually revealed. The increase in mesh size increases the number of mesh points to be calculated, meaning that a partial differential equation with a large coefficient matrix is required to be solved, and the increase in complexity affects the calculation error, which increases the overall calculation time cost.
Disclosure of Invention
The application aims to provide a curved surface parameterization method and device based on a neural network, which solve the defects in the prior art.
The curved surface parameterization method based on the neural network provided by the application comprises the following steps:
giving a grid curved surface S and a target curvature of each grid vertex on the grid curved surface S;
calculating the weight of each grid edge in the grid curved surface S and the curvature corresponding to each grid vertex on the grid curved surface S;
constructing and training a neural network through target curvatures corresponding to all grid vertexes on the grid curved surface S, weights of all grid edges in the grid curved surface S and curvatures corresponding to all grid vertexes on the grid curved surface S, and obtaining a neural network with optimized parameters;
obtaining conformal factor variation of each grid vertex on the grid curved surface S through a neural network with optimized parameters;
and obtaining the target measurement of the two-dimensional grid corresponding to the grid curved surface S through the conformal factor variation, and mapping the target measurement to a two-dimensional parameter domain.
In the above scheme, the target curvature of each mesh vertex on the mesh surface S satisfies the Gauss-Bonnet condition:
wherein->For grid vertex v on source grid surface S i Corresponding target curvature->Is the euler descriptive number of the source mesh surface S.
In the above solution, constructing and training a neural network through a target curvature corresponding to each grid vertex on the grid curved surface S, a weight of each grid edge in the grid curved surface S, and a curvature corresponding to each grid vertex on the grid curved surface S, where obtaining the neural network with optimized parameters includes:
constructing a neural network capable of calculating the conformal factor variation of each grid vertex on the grid curved surface S;
inputting target curvatures corresponding to all grid vertexes on the grid curved surface S, weights of all grid edges in the grid curved surface S and curvatures corresponding to all grid vertexes on the grid curved surface S into the neural network, training the neural network, and obtaining conformal factor variation obtained by training;
and constructing a loss function through the conformal factor variation obtained through training.
In the above solution, constructing and training a neural network through the target curvature corresponding to each grid vertex on the grid curved surface S, the weight of each grid edge in the grid curved surface S, and the curvature corresponding to each grid vertex on the grid curved surface S, where obtaining the neural network with optimized parameters further includes:
inputting the loss function to a combination of an Adam optimization optimizer and a random gradient descent optimization optimizer to obtain a loss function value;
acquiring parameters of the neural network corresponding to the minimum loss function value;
and taking the neural network corresponding to the minimum loss function value as the neural network with optimized parameters.
In the above scheme, the calculation formula of the conformal factor variation corresponding to each grid vertex on the grid curved surface S is:
;
wherein H is formed by the weights of each grid edge in the grid curved surface SIs the number of grid vertices on the grid surface S, n is +.>Is the mesh vertex v on the mesh surface S i Corresponding conformal factor variation, +.>For grid vertex v on source grid surface S i Corresponding target curvature->Mesh vertices on a source mesh surface S v i Corresponding curvature.
In the above scheme, the expression of the loss function is:
;
wherein M is the number of input grid vertices, and H is the weight of each grid edge in the grid curved surface SHesse matrix, u n Is the conformal factor of the nth mesh vertex, +.>For the conformal factor variation of the nth mesh vertex, +.>K is the target curvature of the input nth mesh vertex n For the curvature of the input nth mesh vertex,represents the 2-norm, u 0 Is the initial conformal factor of the mesh vertices on the mesh surface S.
The curved surface parameterization device based on the neural network provided by the application adopts the curved surface parameterization method based on the neural network to carry out curved surface parameterization, and comprises the following steps:
the information providing module is used for giving a grid curved surface S and target curvatures of grid vertexes on the grid curved surface S, and calculating weights of grid edges in the grid curved surface S and curvatures corresponding to the grid vertexes on the grid curved surface S;
the neural network acquisition module is used for constructing and training a neural network through the target curvature corresponding to each grid vertex on the grid curved surface S, the weight of each grid edge in the grid curved surface S and the curvature corresponding to each grid vertex on the grid curved surface S, and acquiring a neural network with optimized parameters;
the conformal factor variation acquisition module is used for acquiring the conformal factor variation of each grid vertex on the grid curved surface S through the neural network with optimized parameters;
and the mapping module is used for acquiring the target measurement of the two-dimensional grid corresponding to the grid curved surface S through the conformal factor variation and mapping the target measurement to the two-dimensional parameter domain.
In the above solution, the neural network acquisition module includes:
the neural network construction unit is used for constructing a neural network capable of calculating the conformal factor variation of each grid vertex on the grid curved surface S;
the neural network training unit is used for inputting target curvatures corresponding to all grid vertexes on the grid curved surface S, weights of all grid edges in the grid curved surface S and curvatures corresponding to all grid vertexes on the grid curved surface S into the neural network, training the neural network and obtaining conformal factor variation obtained by training;
the loss function construction unit is used for constructing a loss function through the conformal factor variation obtained through training;
the parameter optimization neural network acquisition unit is used for inputting the loss function to the combination of the Adam optimization optimizer and the random gradient descent optimization optimizer to acquire a loss function value, acquiring the parameters of the neural network corresponding to the minimum loss function value, and taking the neural network corresponding to the minimum loss function value as the parameter optimization neural network.
The application also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the neural network-based surface parameterization method as described above when executing the program.
The present application also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the neural network-based surface parameterization method as described above.
The embodiment of the application has the following advantages:
according to the curved surface parameterization method and device based on the neural network, the neural network with optimized parameters is obtained through construction and training, the conformal factor variation of each grid vertex on the grid curved surface is obtained through the neural network with optimized parameters, so that the target measurement of the two-dimensional grid corresponding to the grid curved surface is obtained, the target measurement is mapped onto the two-dimensional parameter domain, the efficiency is faster, the time cost is low, and the problem that calculation errors and calculation time cost are affected due to the increase of the grid scale complexity is avoided.
Drawings
Fig. 1 is a step diagram of a curved surface parameterization method based on a neural network according to the present application.
Fig. 2 is a step diagram of the neural network of the present application for obtaining parameter optimization.
Fig. 3 is a schematic diagram of the composition of the curved surface parameterization device based on the neural network.
Fig. 4 is a schematic diagram of the components of the neural network acquisition module of the present application.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The application will be described in detail below with reference to the drawings in connection with embodiments.
As shown in fig. 1, the present application provides a curved surface parameterization method based on a neural network, including:
step S1: given a mesh surface S, a target curvature of each mesh vertex on the mesh surface S.
Specifically, the target curvature of each grid vertex on the grid curved surface S satisfies the Gauss-Bonnet condition:
wherein->For grid vertex v on source grid surface S i Corresponding target curvature->Is the euler descriptive number of the source mesh surface S.
Step S2: and calculating the weight of each grid edge in the grid curved surface S and the curvature corresponding to each grid vertex on the grid curved surface S.
Step S3: and constructing and training a neural network through the target curvature corresponding to each grid vertex on the grid curved surface S, the weight of each grid edge in the grid curved surface S and the curvature corresponding to each grid vertex on the grid curved surface S, and obtaining the neural network with optimized parameters.
As shown in fig. 2, step S3 includes:
step S31: constructing a neural network capable of calculating the conformal factor variation of each grid vertex on the grid curved surface S;
step S32: inputting target curvatures corresponding to all grid vertexes on the grid curved surface S, weights of all grid edges in the grid curved surface S and curvatures corresponding to all grid vertexes on the grid curved surface S into the neural network, training the neural network, and obtaining conformal factor variation obtained by training, wherein a conformal factor variation calculation formula corresponding to all grid vertexes on the grid curved surface S is as follows:
;
wherein H is formed by the weights of each grid edge in the grid curved surface SIs the number of grid vertices on the grid surface S, n is +.>Is the mesh vertex v on the mesh surface S i The corresponding amount of variation of the conformal factor,for grid vertex v on source grid surface S i Corresponding target curvature->For grid vertex v on source grid surface S i Corresponding target curvature.
Step S33: constructing a loss function through conformal factor variation obtained through training, wherein the expression of the loss function is as follows:
;
wherein M is the number of input grid vertices, and H is the weight of each grid edge in the grid curved surface SHesse matrix, u n Is the conformal factor of the nth mesh vertex, +.>For the conformal factor variation of the nth mesh vertex, +.>K is the target curvature of the input nth mesh vertex n For the curvature of the input nth mesh vertex, < ->Represents the 2-norm, u 0 Initial conformal factors of grid vertexes on the grid curved surface S;
step S34: inputting the loss function to a combination of an Adam optimization optimizer and a random gradient descent optimization optimizer to obtain a loss function value;
step S35: acquiring parameters of the neural network corresponding to the minimum loss function value;
step S36: and taking the neural network corresponding to the minimum loss function value as the neural network with optimized parameters.
Specifically, in step S32, the number of iterations of training the neural network is 20000, and the initial learning rate set in the training process is 1e-3, and the attenuation is 0.9 every 1000 cycles.
Step S4: and obtaining the conformal factor variation of each grid vertex on the grid curved surface S through the neural network with optimized parameters.
Step S5: and obtaining the target measurement of the two-dimensional grid corresponding to the grid curved surface S through the conformal factor variation, and mapping the target measurement to a two-dimensional parameter domain.
As shown in fig. 3, the present application provides a curved surface parameterization device based on a neural network, which performs curved surface parameterization by adopting the curved surface parameterization method based on the neural network, including:
the information providing module is used for giving a grid curved surface S and target curvatures of grid vertexes on the grid curved surface S, and calculating weights of grid edges in the grid curved surface S and curvatures corresponding to the grid vertexes on the grid curved surface S;
the neural network acquisition module is used for constructing and training a neural network through the target curvature corresponding to each grid vertex on the grid curved surface S, the weight of each grid edge in the grid curved surface S and the curvature corresponding to each grid vertex on the grid curved surface S, and acquiring a neural network with optimized parameters;
the conformal factor variation acquisition module is used for acquiring the conformal factor variation of each grid vertex on the grid curved surface S through the neural network with optimized parameters;
and the mapping module is used for acquiring the target measurement of the two-dimensional grid corresponding to the grid curved surface S through the conformal factor variation and mapping the target measurement to the two-dimensional parameter domain.
As shown in fig. 4, the neural network acquisition module includes:
the neural network construction unit is used for constructing a neural network capable of calculating the conformal factor variation of each grid vertex on the grid curved surface S;
the neural network training unit is used for inputting target curvatures corresponding to all grid vertexes on the grid curved surface S, weights of all grid edges in the grid curved surface S and curvatures corresponding to all grid vertexes on the grid curved surface S into the neural network, training the neural network and obtaining conformal factor variation obtained by training;
the loss function construction unit is used for constructing a loss function through the conformal factor variation obtained through training;
the parameter optimization neural network acquisition unit is used for inputting the loss function to the combination of the Adam optimization optimizer and the random gradient descent optimization optimizer to acquire a loss function value, acquiring the parameters of the neural network corresponding to the minimum loss function value, and taking the neural network corresponding to the minimum loss function value as the parameter optimization neural network.
The application also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the neural network-based surface parameterization method as described above when executing the program.
The present application also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the neural network-based surface parameterization method as described above.
It should be noted that the foregoing detailed description is exemplary and is intended to provide further explanation of the application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, the singular is intended to include the plural unless the context clearly indicates otherwise. Furthermore, it will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, steps, operations, devices, components, and/or groups thereof.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present application and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the application described herein are capable of operation in sequences other than those illustrated or otherwise described herein.
Furthermore, the terms "comprise" and "have," as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those elements but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Spatially relative terms, such as "above … …," "above … …," "upper surface at … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial location relative to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "above" or "over" other devices or structures would then be oriented "below" or "beneath" the other devices or structures. Thus, the exemplary term "above … …" may include both orientations of "above … …" and "below … …". The device may also be positioned in other different ways, such as rotated 90 degrees or at other orientations, and the spatially relative descriptors used herein interpreted accordingly.
In the above detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, like numerals typically identify like components unless context indicates otherwise. The illustrated embodiments described in the detailed description, drawings, and claims are not meant to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented herein.
The above description is only of the preferred embodiments of the present application and is not intended to limit the present application, but various modifications and variations can be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims (10)

1. A method for parameterizing a curved surface based on a neural network, the method comprising:
giving a grid curved surface S and a target curvature of each grid vertex on the grid curved surface S;
calculating the weight of each grid edge in the grid curved surface S and the curvature corresponding to each grid vertex on the grid curved surface S;
constructing and training a neural network through target curvatures corresponding to all grid vertexes on the grid curved surface S, weights of all grid edges in the grid curved surface S and curvatures corresponding to all grid vertexes on the grid curved surface S, and obtaining a neural network with optimized parameters;
obtaining conformal factor variation of each grid vertex on the grid curved surface S through a neural network with optimized parameters;
and obtaining the target measurement of the two-dimensional grid corresponding to the grid curved surface S through the conformal factor variation, and mapping the target measurement to a two-dimensional parameter domain.
2. The neural network-based surface parameterization method of claim 1, wherein the target curvature of each mesh vertex on the mesh surface S satisfies a Gauss-Bonnet condition:
wherein->For grid vertex v on source grid surface S i Corresponding target curvature->Is the euler descriptive number of the source mesh surface S.
3. The neural network-based surface parameterization method of claim 1, wherein the obtaining the neural network with optimized parameters by constructing and training the neural network with the target curvature corresponding to each grid vertex on the grid surface S, the weight of each grid edge in the grid surface S, and the curvature corresponding to each grid vertex on the grid surface S comprises:
constructing a neural network capable of calculating the conformal factor variation of each grid vertex on the grid curved surface S;
inputting target curvatures corresponding to all grid vertexes on the grid curved surface S, weights of all grid edges in the grid curved surface S and curvatures corresponding to all grid vertexes on the grid curved surface S into the neural network, training the neural network, and obtaining conformal factor variation obtained by training;
and constructing a loss function through the conformal factor variation obtained through training.
4. The neural network-based surface parameterization method of claim 3, wherein the obtaining the neural network with optimized parameters by constructing and training the neural network with the target curvature corresponding to each grid vertex on the grid surface S, the weight of each grid edge in the grid surface S, and the curvature corresponding to each grid vertex on the grid surface S further comprises:
inputting the loss function to a combination of an Adam optimization optimizer and a random gradient descent optimization optimizer to obtain a loss function value;
acquiring parameters of the neural network corresponding to the minimum loss function value;
and taking the neural network corresponding to the minimum loss function value as the neural network with optimized parameters.
5. The neural network-based surface parameterization method of claim 3, wherein the conformal factor variation calculation formula corresponding to each grid vertex on the grid surface S is:
;
wherein H is formed by the weights of each grid edge in the grid curved surface SIs the number of grid vertices on the grid surface S, n is +.>Is the mesh vertex v on the mesh surface S i Corresponding conformal factor variation, +.>For grid vertex v on source grid surface S i Corresponding target curvature->For grid vertex v on source grid surface S i Corresponding curvature.
6. A neural network based surface parameterization method according to claim 3, wherein the expression of the loss function is:
;
wherein M is the number of input grid vertices, and H is the weight of each grid edge in the grid curved surface SHesse matrix, u n Is the conformal factor of the nth mesh vertex, +.>For the conformal factor variation of the nth mesh vertex, +.>K is the target curvature of the input nth mesh vertex n For the curvature of the input nth mesh vertex, < ->Represents the 2-norm, u 0 Is the initial conformal factor of the mesh vertices on the mesh surface S.
7. A neural network-based surface parameterization apparatus for performing surface parameterization using the neural network-based surface parameterization method according to any one of claims 1-6, the apparatus comprising:
the information providing module is used for giving a grid curved surface S and target curvatures of grid vertexes on the grid curved surface S, and calculating weights of grid edges in the grid curved surface S and curvatures corresponding to the grid vertexes on the grid curved surface S;
the neural network acquisition module is used for constructing and training a neural network through the target curvature corresponding to each grid vertex on the grid curved surface S, the weight of each grid edge in the grid curved surface S and the curvature corresponding to each grid vertex on the grid curved surface S, and acquiring a neural network with optimized parameters;
the conformal factor variation acquisition module is used for acquiring the conformal factor variation of each grid vertex on the grid curved surface S through the neural network with optimized parameters;
and the mapping module is used for acquiring the target measurement of the two-dimensional grid corresponding to the grid curved surface S through the conformal factor variation and mapping the target measurement to the two-dimensional parameter domain.
8. The neural network-based surface parameterization apparatus of claim 7, wherein the neural network acquisition module comprises:
the neural network construction unit is used for constructing a neural network capable of calculating the conformal factor variation of each grid vertex on the grid curved surface S;
the neural network training unit is used for inputting target curvatures corresponding to all grid vertexes on the grid curved surface S, weights of all grid edges in the grid curved surface S and curvatures corresponding to all grid vertexes on the grid curved surface S into the neural network, training the neural network and obtaining conformal factor variation obtained by training;
the loss function construction unit is used for constructing a loss function through the conformal factor variation obtained through training;
the parameter optimization neural network acquisition unit is used for inputting the loss function to the combination of the Adam optimization optimizer and the random gradient descent optimization optimizer to acquire a loss function value, acquiring the parameters of the neural network corresponding to the minimum loss function value, and taking the neural network corresponding to the minimum loss function value as the parameter optimization neural network.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the neural network-based surface parameterization method of any of claims 1-6 when the program is executed.
10. A non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor, implements the steps of the neural network-based surface parameterization method of any of claims 1-6.
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