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Foundations of Computational Mathematics
Erschienen in: Foundations of Computational Mathematics 4/2018

07.07.2017

Distortion Varieties

verfasst von: Joe Kileel, Zuzana Kukelova, Tomas Pajdla, Bernd Sturmfels

Erschienen in: Foundations of Computational Mathematics | Ausgabe 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.
Vorheriger Artikel An Explicit Isometric Reduction of the Unit Sphere into an Arbitrarily Small Ball

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Metadaten
Titel
Distortion Varieties
verfasst von
Joe Kileel
Zuzana Kukelova
Tomas Pajdla
Bernd Sturmfels
Publikationsdatum
07.07.2017
Verlag
Springer US
Erschienen in
Foundations of Computational Mathematics / Ausgabe 4/2018
Print ISSN: 1615-3375
Elektronische ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-017-9361-0

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