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Foundations of Computational Mathematics

Distortion Varieties

  • 07-07-2017
Published in:
Authors
Joe Kileel
Zuzana Kukelova
Tomas Pajdla
Bernd Sturmfels
Published in
Foundations of Computational Mathematics | Issue 4/2018

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Abstract

The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter distortions. These are based on Chow polytopes and Gröbner bases. Multi-parameter distortions are studied using tropical geometry. The motivation for distortion varieties comes from multi-view geometry in computer vision. Our theory furnishes a new framework for formulating and solving minimal problems for camera models with image distortion.

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previous article An Explicit Isometric Reduction of the Unit Sphere into an Arbitrarily Small Ball
Title
Distortion Varieties
Authors
Joe Kileel
Zuzana Kukelova
Tomas Pajdla
Bernd Sturmfels
Publication date
07-07-2017
Publisher
Springer US
Published in
Foundations of Computational Mathematics / Issue 4/2018
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-017-9361-0
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Other articles of this Issue 4/2018

Optimal Rates for Regularization of Statistical Inverse Learning Problems

Computing the Homology of Real Projective Sets

An Explicit Isometric Reduction of the Unit Sphere into an Arbitrarily Small Ball

A Lagrangian Scheme à la Brenier for the Incompressible Euler Equations

Numerical Computation of Galois Groups

Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies

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