PDE Surface-Represented Facial Blendshapes
Partial differential equation (PDE)-based geometric modelling and computer animation has been extensively investigated in the last three decades. However, the PDE surface-represented facial blendshapes have not been investigated. In this paper, we propose a new method of facial blendshapes by using...
Guardado en:
| Autores principales: | , , , , , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/990267f55d7941ebaba82b61565a00ce |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:doaj.org-article:990267f55d7941ebaba82b61565a00ce |
|---|---|
| record_format |
dspace |
| spelling |
oai:doaj.org-article:990267f55d7941ebaba82b61565a00ce2021-11-25T18:17:04ZPDE Surface-Represented Facial Blendshapes10.3390/math92229052227-7390https://doaj.org/article/990267f55d7941ebaba82b61565a00ce2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2905https://doaj.org/toc/2227-7390Partial differential equation (PDE)-based geometric modelling and computer animation has been extensively investigated in the last three decades. However, the PDE surface-represented facial blendshapes have not been investigated. In this paper, we propose a new method of facial blendshapes by using curve-defined and Fourier series-represented PDE surfaces. In order to develop this new method, first, we design a curve template and use it to extract curves from polygon facial models. Then, we propose a second-order partial differential equation and combine it with the constraints of the extracted curves as boundary curves to develop a mathematical model of curve-defined PDE surfaces. After that, we introduce a generalized Fourier series representation to solve the second-order partial differential equation subjected to the constraints of the extracted boundary curves and obtain an analytical mathematical expression of curve-defined and Fourier series-represented PDE surfaces. The mathematical expression is used to develop a new PDE surface-based interpolation method of creating new facial models from one source facial model and one target facial model and a new PDE surface-based blending method of creating more new facial models from one source facial model and many target facial models. Some examples are presented to demonstrate the effectiveness and applications of the proposed method in 3D facial blendshapes.Haibin FuShaojun BianEhtzaz ChaudhryShuangbu WangLihua YouJian Jun ZhangMDPI AGarticlefacial blendshapescurve extraction and correspondencepartial differential equationsFourier series representationsanalytical solutionPDE surface-based facial shape creation and animationMathematicsQA1-939ENMathematics, Vol 9, Iss 2905, p 2905 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
facial blendshapes curve extraction and correspondence partial differential equations Fourier series representations analytical solution PDE surface-based facial shape creation and animation Mathematics QA1-939 |
| spellingShingle |
facial blendshapes curve extraction and correspondence partial differential equations Fourier series representations analytical solution PDE surface-based facial shape creation and animation Mathematics QA1-939 Haibin Fu Shaojun Bian Ehtzaz Chaudhry Shuangbu Wang Lihua You Jian Jun Zhang PDE Surface-Represented Facial Blendshapes |
| description |
Partial differential equation (PDE)-based geometric modelling and computer animation has been extensively investigated in the last three decades. However, the PDE surface-represented facial blendshapes have not been investigated. In this paper, we propose a new method of facial blendshapes by using curve-defined and Fourier series-represented PDE surfaces. In order to develop this new method, first, we design a curve template and use it to extract curves from polygon facial models. Then, we propose a second-order partial differential equation and combine it with the constraints of the extracted curves as boundary curves to develop a mathematical model of curve-defined PDE surfaces. After that, we introduce a generalized Fourier series representation to solve the second-order partial differential equation subjected to the constraints of the extracted boundary curves and obtain an analytical mathematical expression of curve-defined and Fourier series-represented PDE surfaces. The mathematical expression is used to develop a new PDE surface-based interpolation method of creating new facial models from one source facial model and one target facial model and a new PDE surface-based blending method of creating more new facial models from one source facial model and many target facial models. Some examples are presented to demonstrate the effectiveness and applications of the proposed method in 3D facial blendshapes. |
| format |
article |
| author |
Haibin Fu Shaojun Bian Ehtzaz Chaudhry Shuangbu Wang Lihua You Jian Jun Zhang |
| author_facet |
Haibin Fu Shaojun Bian Ehtzaz Chaudhry Shuangbu Wang Lihua You Jian Jun Zhang |
| author_sort |
Haibin Fu |
| title |
PDE Surface-Represented Facial Blendshapes |
| title_short |
PDE Surface-Represented Facial Blendshapes |
| title_full |
PDE Surface-Represented Facial Blendshapes |
| title_fullStr |
PDE Surface-Represented Facial Blendshapes |
| title_full_unstemmed |
PDE Surface-Represented Facial Blendshapes |
| title_sort |
pde surface-represented facial blendshapes |
| publisher |
MDPI AG |
| publishDate |
2021 |
| url |
https://doaj.org/article/990267f55d7941ebaba82b61565a00ce |
| work_keys_str_mv |
AT haibinfu pdesurfacerepresentedfacialblendshapes AT shaojunbian pdesurfacerepresentedfacialblendshapes AT ehtzazchaudhry pdesurfacerepresentedfacialblendshapes AT shuangbuwang pdesurfacerepresentedfacialblendshapes AT lihuayou pdesurfacerepresentedfacialblendshapes AT jianjunzhang pdesurfacerepresentedfacialblendshapes |
| _version_ |
1718411397811929088 |