Monday, September 26, 2016 - 15:05
1 hour (actually 50 minutes)
This talks presents two projects at the interface of computer vision and algebraic geometry. Work with Zuzana Kukelova, Tomas Pajdla and Bernd Sturmfels introduces the distortion varieties of a given projective variety. These 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, the case of most interest for modeling cameras with image distortion. Single-authored work determines the algebraic degree of minimal problems for the calibrated trifocal variety. Our techniques rely on numerical algebraic geometry, and the homotopy continuation software Bertini.