Related papers: Distortion Varieties
The commonly used radial distortion model for camera calibration is in fact an assumption or a restriction. In practice, camera distortion could happen in a general geometrical manner that is not limited to the radial sense. This paper…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…
We present a generalization of multiview varieties as closures of images obtained by projecting subspaces of a given dimension onto several views, from the photographic and geometric points of view. Motivated by applications in Computer…
Most distortion correction methods focus on simple forms of distortion, such as radial or linear distortions. These works undistort images either based on measurements in the presence of a calibration grid, or use multiple views to find…
In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…
Common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial…
We present some results on projective toric varieties which are relevant in Diophantine geometry. We interpret and study several invariants attached to these varieties in geometrical and combinatorial terms. We also give a B\'ezout theorem…
Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera…
Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an…
We tackle the problem of automatic calibration of radially distorted cameras in challenging conditions. Accurately determining distortion parameters typically requires either 1) solving the full Structure from Motion (SfM) problem involving…
This is a survey of the language of polyhedral divisors describing T-varieties. This language is explained in parallel to the well established theory of toric varieties. In addition to basic constructions, subjects touched on include…
An observer surrounded by sufficiently small spherical light sources at a fixed distance will see a pattern of elliptical images distributed over the sky, owing to the distortion effect (shearing effect) of the spacetime geometry upon light…
In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…
We study algebraic varieties associated with the camera resectioning problem. We characterize these resectioning varieties' multigraded vanishing ideals using Gr\"obner basis techniques. As an application, we derive and re-interpret…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
Low isometric distortion is often required for mesh parameterizations. A configuration of some vertices, where the distortion is concentrated, provides a way to mitigate isometric distortion, but determining the number and placement of…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
We study algebraic and combinatorial aspects of (classical) projections of $m$-dimensional tropical varieties onto $(m+1)$-dimensional planes. Building upon the work of Sturmfels, Tevelev, and Yu on tropical elimination as well as the work…
We discuss an experimental approach to open problems in toric geometry: are smooth projective toric varieties (i) projectively normal and (ii) defined by degree 2 equations? We discuss the creation of lattice polytopes defining smooth toric…