Distortion Varieties
Joe Kileel, Zuzana Kukelova, Tomas Pajdla, Bernd Sturmfels
TL;DR
This paper introduces a mathematical framework for understanding distortion varieties in projective geometry, deriving formulas for degrees and equations, with applications to camera models in computer vision.
Contribution
It provides exact formulas for one-parameter distortions and a tropical geometry approach for multi-parameter distortions, advancing the theoretical understanding of distortion varieties.
Findings
Formulas for degrees of one-parameter distortion varieties
Equations derived using Chow polytopes and Gröbner bases
A new framework for minimal problems in camera models with distortion
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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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Vision and Imaging · Advanced Numerical Analysis Techniques