English

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.

Keywords

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

R2 v1 2026-06-22T16:13:04.173Z