Geometry Seminar

Date: September 28, 2020

Time: 3:00PM - 3:50PM

Location: zoom

Speaker: Timothy Duff, Georgia Tech

Title: Structured polynomial systems in algebraic vision

Abstract: Minimal problems arise in 3D reconstruction pipelines that attempt to recover the 3D geometry of a scene from data in several images. Solving minimal problems comes down to solving systems of polynomial equations of a very particular structure. Structure can be understood in terms of an associated branched cover and its birational invariants (degree, Galois/monodromy group.) Classical solutions to well-known problems of camera registration, homography estimation, and five-point relative pose implicitly exploit this structure. In work with Kohn, Leykin, and Pajdla, we identify a large zoo of new minimal problems, and in ongoing work with Korotynskiy, Pajdla, and Regan, we identify and further study those problems with special (eg. imprimitive) Galois/monodromy groups.