Bernd Sturmfels, Berkeley: Cameras and their Distortions
Abstract: We discuss two current projects at the interface of computer vision and algebraic geometry. Work with Joe Kileel, Zuzana Kukelov and Tomas Pajdla 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. Work with Jean Ponce and Matthew Trager develops multi-view geometry for algebraic cameras that are represented by congruences in the Grassmannian of lines in 3-space.