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Distortion Varieties
October 06, 2016 Β· Declared Dead Β· π Foundations of Computational Mathematics
"No code URL or promise found in abstract"
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Authors
Joe Kileel, Zuzana Kukelova, Tomas Pajdla, Bernd Sturmfels
arXiv ID
1610.01860
Category
math.AG
Cross-listed
cs.CV
Citations
12
Venue
Foundations of Computational Mathematics
Last Checked
3 months ago
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 GrΓΆbner 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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