Distortion Varieties
Algebraic Geometry
2016-10-07 v1 Computer Vision and Pattern Recognition
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.
Cite
@article{arxiv.1610.01860,
title = {Distortion Varieties},
author = {Joe Kileel and Zuzana Kukelova and Tomas Pajdla and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1610.01860},
year = {2016}
}
Comments
25 pages