Distortion Varieties

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.
Author(s): Joe Kileel [sup.1] , Zuzana Kukelova [sup.2] , Tomas Pajdla [sup.3] , Bernd Sturmfels [sup.1] Author Affiliations: (Aff1) 0000 0001 2181 7878, grid.47840.3f, Department of Mathematics, University of California, [...]