Carina Geldhauser


Last Name

Geldhauser

First Name

Carina

ORCID

0000-0002-9997-6710

Organisational unit

09565 - Figalli, Alessio / Figalli, Alessio

Filters

2024 - 20254
Reset filters

Search Results

Publications 1 - 4 of 4
  • All’s Well That FID’s Well? Result Quality and Metric Scores in GAN Models for Lip-Synchronization Tasks
    Item type: Journal Article
    Geldhauser, Carina; Liljegren, Johan; Nordqvist, Pontus (2025)
    Electronics
    This exploratory study investigates the usability of performance metrics for generative adversarial network (GAN)-based models for speech-driven facial animation. These models focus on the transfer of speech information from an audio file to a still image to generate talking-head videos in a small-scale “everyday usage” setting. Two models, LipGAN and a custom implementation of a Wasserstein GAN with gradient penalty (L1WGAN-GP), are examined for their visual performance and scoring according to commonly used metrics: Quantitative comparisons using FID, SSIM, and PSNR metrics on the GRIDTest dataset show mixed results, and metrics fail to capture local artifacts crucial for lip synchronization, pointing to limitations in their applicability for video animation tasks. The study points towards the inadequacy of current quantitative measures and emphasizes the continued necessity of human qualitative assessment for evaluating talking-head video quality.
  • Travelling waves for discrete stochastic bistable equations
    Item type: Journal Article
    Geldhauser, Carina; Kuehn, Christian (2024)
    Partial Differential Equations and Applications
    Many physical, chemical and biological systems have an inherent discrete spatial structure that strongly influences their dynamical behaviour. Similar remarks apply to internal or external noise. In this paper we study the combined effect of spatial discretization and stochastic perturbations on travelling waves in the Nagumo equation, which is a prototypical model for bistable reaction-diffusion partial differential equations (PDEs). We prove that under suitable parameter conditions, various discrete-stochastic variants of the Nagumo equation have solutions, which stay close on long time scales to the classical monotone Nagumo front with high probability if the noise covariance and spatial discretization are sufficiently small.
  • Traveling Phase Interfaces in Viscous Forward-Backward Diffusion Equations
    Item type: Journal Article
    Geldhauser, Carina; Herrmann, Michael; Janssen, Dirk (2024)
    Journal of Dynamics and Differential Equations
    The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical understanding of the intricate multiscale evolution is still missing. We shed light on the fine structure of propagating phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone profile and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit.
  • Regularizations of forward-backward parabolic PDEs
    Item type: Review Article
    Geldhauser, Carina (2024)
    GAMM-Mitteilungen
    Forward-backward parabolic equations have been studied since the 1980s, but a mathematically rigorous picture is still far from being established. As quite a number of new papers have appeared recently, we review in this work the current state of the art. We focus our analysis on the status quo regarding the three most common types of regularizations, namely semidiscretization, the viscous approximation, and regularization with higher order spatial derivatives.
Publications 1 - 4 of 4