相关论文: Spherical Authalic Energy Minimization for Area-Pr…

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-dimensional parameter space. This process allows for the…

This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…

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 gradient descent method, the projected conjugate gradient…

We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…

In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically…

For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy $\gamma(\boldsymbol{n})$ in three dimensions (3D), where $\boldsymbol{n}$ is the unit outward normal vector, by introducing…

Spherical microphone arrays (SMAs) are widely used for sound field analysis, and sparse recovery (SR) techniques can significantly enhance their spatial resolution by modeling the sound field as a sparse superposition of dominant plane…

Density-equalizing maps are a class of mapping methods in which the shape deformation is driven by prescribed density information. In recent years, they have been widely used for data visualization on planar domains and planar…

We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…

We show that in the setting of proper metric spaces one obtains a solution of the classical two-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area (in the sense of convex geometry) has…

We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero…

Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…

We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

Surface parameterization is a fundamental task in geometry processing and plays an important role in many science and engineering applications. In recent years, the density-equalizing map, a shape deformation technique based on the physical…

Surface parameterizations are widely applied in computer graphics, medical imaging and transformation optics. In this paper, we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical…

Recent progress in self-supervised representation learning has resulted in models that are capable of extracting image features that are not only effective at encoding image level, but also pixel-level, semantics. These features have been…

Sharpness-Aware Minimization (SAM) has emerged as a powerful method for improving generalization in machine learning models by minimizing the sharpness of the loss landscape. However, despite its success, several important questions…

Conformal energy minimization is an efficient approach to compute conformal parameterization. In this paper, we develop a stable algorithm to compute conformal parameterization of simply connected open surface, termed Stable Discrete…

Sharpness-aware minimization (SAM), which searches for flat minima by min-max optimization, has been shown to be useful in improving model generalization. However, since each SAM update requires computing two gradients, its computational…

We consider the surface Stokes equation on a smooth closed hypersurface in three-dimensional space. For discretization of this problem a generalization of the surface finite element method (SFEM) of Dziuk-Elliott combined with a Hood-Taylor…