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arXiv · 1610.01860

Distortion Varieties

Joe Kileel·Zuzana Kukelova·Tomas Pajdla·Bernd Sturmfels
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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 Gr\"obner 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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Joe Kileel, Zuzana Kukelova, Tomas Pajdla, Bernd Sturmfels. 2016-10-06. Distortion Varieties. https://arxiv.org/abs/1610.01860

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