Distortion Varieties
This provides a new framework for multi-view geometry in computer vision, addressing camera models with image distortion, but it appears incremental as it builds on existing mathematical tools.
The paper tackles the problem of formulating and solving minimal problems for camera models with image distortion in computer vision by studying distortion varieties, obtaining exact formulas for degrees and defining equations in one-parameter cases using Chow polytopes and Gröbner bases, and extending to multi-parameter cases with tropical geometry.
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.