DESIGN FU - Academia.edu (original) (raw)

Papers by DESIGN FU

Research paper thumbnail of PDE Surface-Represented Facial Blendshapes

Mathematics, 2021

Partial differential equation (PDE)-based geometric modelling and computer animation has been ext... more 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 math...

Research paper thumbnail of Efficient Ordinary Differential Equation-Based Discontinuous Galerkin Method for Viscoelastic Wave Modeling

IEEE Transactions on Geoscience and Remote Sensing, 2017

We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave pro... more We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave propagation in viscous media. To include the attenuation and dispersion due to the quality factor in time domain, several sets of auxiliary ordinary differential equations (AODEs) are added. Unlike the conventional auxiliary partial differential equationbased algorithm, this new method is highly parallel with its lossless counterpart, thus requiring much less time and storage consumption. Another superior property of the AODEbased DG method is that a novel exact Riemann solver can be derived, which allows heterogeneous viscoelastic coupling, in addition to accurate coupling with purely elastic media and fluid. Furthermore, thanks to the nonconformal-mesh technique, adaptive hp-refinement and flexible memory allocation for the auxiliary variables are achieved. Numerical results demonstrate the efficiency and accuracy of our method.

Research paper thumbnail of Recent Developments in Skin Deformation for Character Animation

Proceedings of the 10th International Conference on Computer Graphics Theory and Applications, 2015

Achieving realistic skin deformation efficiently is a very important task for character animation... more Achieving realistic skin deformation efficiently is a very important task for character animation. With the development of skin deformation, the efficiency and effectiveness of character modelling and animation have been obviously enhanced. In this paper, we survey the recent literature on skin deformation according to three types of approaches: purely geometric, physics-based, and data driven. Especially we focus on the work since 2009. We review the problems they primarily tackles, the methodologies they applies, and the advantages and disadvantages they have. At last, we discuss directions for future research.

Research paper thumbnail of 3D Modelling with C2 Continuous PDE Surface Patches

Mathematics, 2022

In this paper, we present a new modelling method to create 3D models. First, characteristic cross... more In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly.

Research paper thumbnail of State-of-the-Art in 3D Face Reconstruction from a Single RGB Image

Since diverse and complex emotions need to be expressed by different facial deformation and appea... more Since diverse and complex emotions need to be expressed by different facial deformation and appearances, facial animation has become a serious and ongoing challenge for computer animation industry. Face reconstruction techniques based on 3D morphable face model and deep learning provide one effective solution to reuse existing databases and create believable animation of new characters from images or videos in seconds, which greatly reduce heavy manual operations and a lot of time. In this paper, we review the databases and state-of-the-art methods of 3D face reconstruction from a single RGB image. First, we classify 3D reconstruction methods into three categories and review each of them. These three categories are: Shape-from-Shading (SFS), 3D Morphable Face Model (3DMM), and Deep Learning (DL) based 3D face reconstruction. Next, we introduce existing 2D and 3D facial databases. After that, we review 10 methods of deep learning-based 3D face reconstruction and evaluate four representative ones among them. Finally, we draw conclusions of this paper and discuss future research directions.

Research paper thumbnail of Efficient C2 Continuous Surface Creation Technique Based on Ordinary Differential Equation

Symmetry

In order to reduce the data size and simplify the process of creating characters’ 3D models, a ne... more In order to reduce the data size and simplify the process of creating characters’ 3D models, a new and interactive ordinary differential equation (ODE)-based C2 continuous surface creation algorithm is introduced in this paper. With this approach, the creation of a three-dimensional surface is transformed into generating two boundary curves plus four control curves and solving a vector-valued sixth order ordinary differential equation subjected to boundary constraints consisting of boundary curves, and first and second partial derivatives at the boundary curves. Unlike the existing patch modeling approaches which require tedious and time-consuming manual operations to stitch two separate patches together to achieve continuity between two stitched patches, the proposed technique maintains the C2 continuity between adjacent surface patches naturally, which avoids manual stitching operations. Besides, compared with polygon surface modeling, our ODE C2 surface creation method can signif...

Research paper thumbnail of Fully Automatic Facial Deformation Transfer

Symmetry

Facial Animation is a serious and ongoing challenge for the Computer Graphic industry. Because di... more Facial Animation is a serious and ongoing challenge for the Computer Graphic industry. Because diverse and complex emotions need to be expressed by different facial deformation and animation, copying facial deformations from existing character to another is widely needed in both industry and academia, to reduce time-consuming and repetitive manual work of modeling to create the 3D shape sequences for every new character. But transfer of realistic facial animations between two 3D models is limited and inconvenient for general use. Modern deformation transfer methods require correspondences mapping, in most cases, which are tedious to get. In this paper, we present a fast and automatic approach to transfer the deformations of the facial mesh models by obtaining the 3D point-wise correspondences in the automatic manner. The key idea is that we could estimate the correspondences with different facial meshes using the robust facial landmark detection method by projecting the 3D model to ...

Research paper thumbnail of Efficient and realistic character animation through analytical physics-based skin deformation

Research paper thumbnail of Automatic Generation of Dynamic Skin Deformation for Animated Characters

Symmetry

Since non-automatic rigging requires heavy human involvements, and various automatic rigging algo... more Since non-automatic rigging requires heavy human involvements, and various automatic rigging algorithms are less efficient in terms of computational efficiency, especially for current curve-based skin deformation methods, identifying the iso-parametric curves and creating the animation skeleton requires tedious and time-consuming manual work. Although several automatic rigging methods have been developed, but they do not aim at curve-based models. To tackle this issue, this paper proposes a new rigging algorithm for automatic generation of dynamic skin deformation to quickly identify iso-parametric curves and create an animation skeleton in a few milliseconds, which can be seamlessly used in curve-based skin deformation methods to make the rigging process fast enough for highly efficient computer animation applications.

Research paper thumbnail of PDE Surface-Represented Facial Blendshapes

Mathematics, 2021

Partial differential equation (PDE)-based geometric modelling and computer animation has been ext... more 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 math...

Research paper thumbnail of Efficient Ordinary Differential Equation-Based Discontinuous Galerkin Method for Viscoelastic Wave Modeling

IEEE Transactions on Geoscience and Remote Sensing, 2017

We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave pro... more We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave propagation in viscous media. To include the attenuation and dispersion due to the quality factor in time domain, several sets of auxiliary ordinary differential equations (AODEs) are added. Unlike the conventional auxiliary partial differential equationbased algorithm, this new method is highly parallel with its lossless counterpart, thus requiring much less time and storage consumption. Another superior property of the AODEbased DG method is that a novel exact Riemann solver can be derived, which allows heterogeneous viscoelastic coupling, in addition to accurate coupling with purely elastic media and fluid. Furthermore, thanks to the nonconformal-mesh technique, adaptive hp-refinement and flexible memory allocation for the auxiliary variables are achieved. Numerical results demonstrate the efficiency and accuracy of our method.

Research paper thumbnail of Recent Developments in Skin Deformation for Character Animation

Proceedings of the 10th International Conference on Computer Graphics Theory and Applications, 2015

Achieving realistic skin deformation efficiently is a very important task for character animation... more Achieving realistic skin deformation efficiently is a very important task for character animation. With the development of skin deformation, the efficiency and effectiveness of character modelling and animation have been obviously enhanced. In this paper, we survey the recent literature on skin deformation according to three types of approaches: purely geometric, physics-based, and data driven. Especially we focus on the work since 2009. We review the problems they primarily tackles, the methodologies they applies, and the advantages and disadvantages they have. At last, we discuss directions for future research.

Research paper thumbnail of 3D Modelling with C2 Continuous PDE Surface Patches

Mathematics, 2022

In this paper, we present a new modelling method to create 3D models. First, characteristic cross... more In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly.

Research paper thumbnail of State-of-the-Art in 3D Face Reconstruction from a Single RGB Image

Since diverse and complex emotions need to be expressed by different facial deformation and appea... more Since diverse and complex emotions need to be expressed by different facial deformation and appearances, facial animation has become a serious and ongoing challenge for computer animation industry. Face reconstruction techniques based on 3D morphable face model and deep learning provide one effective solution to reuse existing databases and create believable animation of new characters from images or videos in seconds, which greatly reduce heavy manual operations and a lot of time. In this paper, we review the databases and state-of-the-art methods of 3D face reconstruction from a single RGB image. First, we classify 3D reconstruction methods into three categories and review each of them. These three categories are: Shape-from-Shading (SFS), 3D Morphable Face Model (3DMM), and Deep Learning (DL) based 3D face reconstruction. Next, we introduce existing 2D and 3D facial databases. After that, we review 10 methods of deep learning-based 3D face reconstruction and evaluate four representative ones among them. Finally, we draw conclusions of this paper and discuss future research directions.

Research paper thumbnail of Efficient C2 Continuous Surface Creation Technique Based on Ordinary Differential Equation

Symmetry

In order to reduce the data size and simplify the process of creating characters’ 3D models, a ne... more In order to reduce the data size and simplify the process of creating characters’ 3D models, a new and interactive ordinary differential equation (ODE)-based C2 continuous surface creation algorithm is introduced in this paper. With this approach, the creation of a three-dimensional surface is transformed into generating two boundary curves plus four control curves and solving a vector-valued sixth order ordinary differential equation subjected to boundary constraints consisting of boundary curves, and first and second partial derivatives at the boundary curves. Unlike the existing patch modeling approaches which require tedious and time-consuming manual operations to stitch two separate patches together to achieve continuity between two stitched patches, the proposed technique maintains the C2 continuity between adjacent surface patches naturally, which avoids manual stitching operations. Besides, compared with polygon surface modeling, our ODE C2 surface creation method can signif...

Research paper thumbnail of Fully Automatic Facial Deformation Transfer

Symmetry

Facial Animation is a serious and ongoing challenge for the Computer Graphic industry. Because di... more Facial Animation is a serious and ongoing challenge for the Computer Graphic industry. Because diverse and complex emotions need to be expressed by different facial deformation and animation, copying facial deformations from existing character to another is widely needed in both industry and academia, to reduce time-consuming and repetitive manual work of modeling to create the 3D shape sequences for every new character. But transfer of realistic facial animations between two 3D models is limited and inconvenient for general use. Modern deformation transfer methods require correspondences mapping, in most cases, which are tedious to get. In this paper, we present a fast and automatic approach to transfer the deformations of the facial mesh models by obtaining the 3D point-wise correspondences in the automatic manner. The key idea is that we could estimate the correspondences with different facial meshes using the robust facial landmark detection method by projecting the 3D model to ...

Research paper thumbnail of Efficient and realistic character animation through analytical physics-based skin deformation

Research paper thumbnail of Automatic Generation of Dynamic Skin Deformation for Animated Characters

Symmetry

Since non-automatic rigging requires heavy human involvements, and various automatic rigging algo... more Since non-automatic rigging requires heavy human involvements, and various automatic rigging algorithms are less efficient in terms of computational efficiency, especially for current curve-based skin deformation methods, identifying the iso-parametric curves and creating the animation skeleton requires tedious and time-consuming manual work. Although several automatic rigging methods have been developed, but they do not aim at curve-based models. To tackle this issue, this paper proposes a new rigging algorithm for automatic generation of dynamic skin deformation to quickly identify iso-parametric curves and create an animation skeleton in a few milliseconds, which can be seamlessly used in curve-based skin deformation methods to make the rigging process fast enough for highly efficient computer animation applications.