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Foundations of Computational Mathematics

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07-07-2017

Distortion Varieties

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.

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

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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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