Related papers: Distortion Varieties
We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…
Two-parameter perturbation theory is a scheme tailor-made to consistently include nonlinear density contrasts on small scales ($<100\; \mathrm{Mpc}$), whilst retaining a traditional approach to cosmological perturbations in the…
The paper surveys variational approaches for image reconstruction in dynamic inverse problems. Emphasis is on methods that rely on parametrised temporal models. These are here encoded as diffeomorphic deformations with time dependent…
In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate…
Multidimensional factorization method is formulated in arbitrary curvilinear coordinates. Particular cases of polar and spherical coordinates are considered and matrix potentials with separating variables are constructed. A new class of…
A single Panorama can be drawn perspectively without distortions in arbitrary viewing directions and field-of-views when the camera position is at the origin. This is a key advantage in VR and virtual tour applications because it enables…
Although recent learning-based calibration methods can predict extrinsic and intrinsic camera parameters from a single image, the accuracy of these methods is degraded in fisheye images. This degradation is caused by mismatching between the…
Tropical algebraic geometry offers new tools for elimination theory and implicitization. We determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus.
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…
Estimating the depth of omnidirectional images is more challenging than that of normal field-of-view (NFoV) images because the varying distortion can significantly twist an object's shape. The existing methods suffer from troublesome…
Although all members of the ophthalmic community agree that distortion is an aberration affecting the geometry of an image produced by the periphery of an ophthalmic lens, there are several approaches for analyzing and quantifying this…
We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in…
This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…
We study the notion of consistency between a 3D shape and a 2D observation and propose a differentiable formulation which allows computing gradients of the 3D shape given an observation from an arbitrary view. We do so by reformulating view…
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal…
Monocular depth predictors are typically trained on large-scale training sets which are naturally biased w.r.t the distribution of camera poses. As a result, trained predictors fail to make reliable depth predictions for testing examples…
Previous literature suggests that perceptual similarity is an emergent property shared across deep visual representations. Experiments conducted on a dataset of human-judged image distortions have proven that deep features outperform…
We discuss existence and regularity results for multi-channel images in the setting of isotropic and anisotropic variants of the TV-model.
Three-dimensional (3D) reconstruction from a single image is an ill-posed problem with inherent ambiguities, i.e. scale. Predicting a 3D scene from text description(s) is similarly ill-posed, i.e. spatial arrangements of objects described.…