3 citations · 8 across the 13 of their papers we have counts for
16 papers
A Discrete-to-Continuum Variational Theory for Area-Preserving Surface Parameterization
Shu-Yung Liu, Kento Sakai, Mei-Heng Yueh
We establish a discrete-to-continuum variational theory for area-preserving parameterization of surfaces based on the stretch energy. For orientation-preserving diffeomorphisms bet…
DiffRGD: An Inference-Time Diffusion Guidance Through Riemannian Gradient Descent
Jia-Wei Liao, Li-Xuan Peng, Mei-Heng Yueh +3
Recently, diffusion models have been widely adopted in generative modeling and have served as foundational models for many image generation tasks. To control the generation without…
Square-Domain Area-Preserving Parameterization for Genus-Zero and Genus-One Closed Surfaces
Shu-Yung Liu, Mei-Heng Yueh
The parameterization of closed surfaces typically requires either multiple charts or a non-planar domain to achieve a seamless global mapping. In this paper, we propose a numerical…
Toroidal area-preserving parameterizations of genus-one closed surfaces
Marco Sutti, Mei-Heng Yueh
We consider the problem of computing toroidal area-preserving parameterizations of genus-one closed surfaces. We propose four algorithms based on Riemannian geometry: the projected…
Energy-Based Distortion-Balancing Parameterization for Open Surfaces
Shu-Yung Liu, Mei-Heng Yueh
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two…
Spherical Area-Preserving Parameterization via Energy Minimization
Shu-Yung Liu, Mei-Heng Yueh
We propose a novel method, called spherical authalic energy minimization (SAEM), for computing spherical area-preserving parameterizations of genus-zero closed surfaces, with stron…
An Improved Variational Method for Image Denoising
Jing-En Huang, Jia-Wei Liao, Ku-Te Lin +2
The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel inte…
Volume-Preserving Parameterizations via Preconditioned Nonlinear Conjugate Gradient Method
Shu-Yung Liu, Tsung-Ming Huang, Wen-Wei Lin +1
A volume-preserving parameterization is a bijective mapping that maps a 3-manifold onto a canonical domain while preserving local volume. We formulate this problem as an unconstrai…
Riemannian gradient descent for spherical area-preserving mappings
Marco Sutti, Mei-Heng Yueh
We propose a new Riemannian gradient descent method for computing spherical area-preserving mappings of topological spheres using a Riemannian retraction-based framework with theor…
Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations
Shu-Yung Liu, Mei-Heng Yueh
An area-preserving parameterization is a bijective mapping that maps a surface onto a specified domain and preserves the local area. This paper formulates the computation of disk a…
Convergence Analysis of Volumetric Stretch Energy Minimization and its Associated Optimal Mass Transport
Tsung-Ming Huang, Wei-Hung Liao, Wen-Wei Lin +2
The volumetric stretch energy has been widely applied to the computation of volume-/mass-preserving parameterizations of simply connected tetrahedral mesh models. However, this app…
Convergence Analysis of Dirichlet Energy Minimization for Spherical Conformal Parameterizations
Wei-Hung Liao, Tsung-Ming Huang, Wen-Wei Lin +1
In this paper, we first derive a theoretical basis for spherical conformal parameterizations between a simply connected closed surface and a unit sphere $\mathbb{S}^2…
Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Mappings
Mei-Heng Yueh
The stretch energy is a fully nonlinear energy functional that has been applied to the numerical computation of area-preserving mappings. However, this approach lacks theoretical s…
A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations
Mei-Heng Yueh, Wen-Wei Lin, Chin-Tien Wu +1
Surface parameterizations have been widely applied to computer graphics and digital geometry processing. In this paper, we propose a novel stretch energy minimization (SEM) algorit…
Conformal Surface Morphing with Applications on Facial Expressions
Mei-Heng Yueh, Xianfeng David Gu, Wen-Wei Lin +2
Morphing is the process of changing one figure into another. Some numerical methods of 3D surface morphing by deformable modeling and conformal mapping are shown in this study. It…
Graph invariants from ideas in physics and number theory
An Huang, Shing-Tung Yau, Mei-Heng Yueh
We study free scalar field theory on a graph, which gives rise to a modified version of discrete Green's function on a graph studied in \cite{CY}. We show that this gives rise to a…