In this talk I will briefly present our journal paper:
Kileel J., Kukelova Z., Pajdla T., Sturmfels B., "Distortion Varieties",
Foundations of Computational Mathematics, 2017.
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.