Related papers: Geodesic Warps by Conformal Mappings
We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV)…
Nonconservative evolution problems describe irreversible processes and dissipative effects in a broad variety of phenomena. Such problems are often characterised by a conservative part, which can be modelled as a Hamiltonian term, and a…
We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in…
We study deformations of the geodesic distances on a domain of R N induced by a function called conformal factor. We show that under a positive reach assumption on the domain (not necessarily a submanifold) and mild assumptions on the…
Generative models have recently gained increasing attention in image generation and editing tasks. However, they often lack a direct connection to object geometry, which is crucial in sensitive domains such as computational anatomy,…
In an influential paper, Tadmor, Nezzar and Vese (Multiscale Model. Simul. (2004)) introduced a hierarchical decomposition of an image as a sum of constituents of different scales. Here we construct analogous hierarchical expansions for…
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…
For offshore structures like wind turbines, subsea infrastructure, pipelines, and cables, it is crucial to quantify the properties of the seabed sediments at a proposed site. However, data collection offshore is costly, so analysis of the…
Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal factors vanishing on a regular hypersurface of a Riemannian…
In this paper we study geodesic mappings of $n$-dimensional surfaces of revolution. From the general theory of geodesic mappings of equidistant spaces we specialize to surfaces of revolution and apply the obtained formulas to the case of…
Template matching is a fundamental task in computer vision and has been studied for decades. It plays an essential role in manufacturing industry for estimating the poses of different parts, facilitating downstream tasks such as robotic…
We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a…
Face morphing is a problem in computer graphics with numerous artistic and forensic applications. It is challenging due to variations in pose, lighting, gender, and ethnicity. This task consists of a warping for feature alignment and a…
In this paper, we target image-based person-to-person virtual try-on in the presence of diverse poses and large viewpoint variations. Existing methods are restricted in this setting as they estimate garment warping flows mainly based on 2D…
We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the…
We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms…
Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific…
We consider families of geometries of D--dimensional space, described by a finite number of parameters. Starting from the De Witt metric we extract a unique integration measure which turns out to be a geometric invariant, i.e. independent…