Related papers: A Numerical Framework for Efficient Motion Estimat…
High-quality scene reconstruction and novel view synthesis based on Gaussian Splatting (3DGS) typically require steady, high-quality photographs, often impractical to capture with handheld cameras. We present a method that adapts to camera…
We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…
Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and…
In this paper we present a numerical method for the Boltzmann equation. It is a spectral discretization in the velocity and a discontinuous Galerkin discretization in physical space. To obtain uniform approximation properties in the mach…
We present a general abstract framework for the systematic numerical approximation of dissipative evolution problems. The approach is based on rewriting the evolution problem in a particular form that complies with an underlying energy or…
We develop structure-preserving numerical methods for the compressible Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxes designed to ensure the conservation of entropy and total…
A new moving mesh scheme based on the Lagrange-Galerkin method for the approximation of the one-dimensional convection-diffusion equation is studied. The mesh movement, which is prescribed by a discretized dynamical system for the nodal…
This paper introduces a novel framework for the automated tracking of cells, with a particular focus on the challenging situation of phase contrast microscopic videos. Our framework is based on a topology preserving variational segmentation…
We use light microscopy to investigate the aging dynamics of a glass made of closely packed soft spheres, following a rapid transition from a fluid to a solid-like state. By measuring time-resolved, coarse-grained displacements fields, we…
Event-based structured light systems have recently been introduced as an exciting alternative to conventional frame-based triangulation systems for the 3D measurements of diffuse surfaces. Important benefits include the fast capture speed…
We present a computational approach for solving reaction-diffusion equations on evolving surfaces which have been obtained from cell image data. It is based on finite element spaces defined on surface triangulations extracted from time…
In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…
We propose a meshless conservative Galerkin method for solving Hamiltonian wave equations. We first discretize the equation in space using radial basis functions in a Galerkin-type formulation. Differ from the traditional RBF Galerkin…
Video Motion Magnification (VMM) aims to break the resolution limit of human visual perception capability and reveal the imperceptible minor motion that contains valuable information in the macroscopic domain. However, challenges arise in…
A general framework for the numerical approximation of evolution problems is presented that allows to preserve exactly an underlying Hamiltonian- or gradient structure. The approach relies on rewriting the evolution problem in a particular…
The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
Myocardial motion and deformation are rich descriptors that characterize cardiac function. Image registration, as the most commonly used technique for myocardial motion tracking, is an ill-posed inverse problem which often requires prior…
This paper presents a novel approach of representing dynamic visual scenes with static maps generated from video/image streams. Such representation allows easy visual assessment of motion in dynamic environments. These maps are 2D matrices…
Reconstructing dynamic 3D scenes from 2D images and generating diverse views over time is challenging due to scene complexity and temporal dynamics. Despite advancements in neural implicit models, limitations persist: (i) Inadequate Scene…