Finding, solving, and simplifying minimal problems in computer vision

I will describe recent research on the intersection of algebraic geometry and computer vision, beginning with a discussion of the basics of 3D computer vision from a geometric point of view. The talk will touch on joint work with Kathlén Kohn, Viktor Korotynskiy, Anton Leykin, Tomas Pajdla, and Maggie Regan. The focus is on solving "minimal cases" for the problem of reconstruction of a configuration of points and lines in space. Under various natural hypotheses we can enumerate all minimal problems (basic dimension counting) and compute the number of complex solutions (symbolic/numerical methods.) Time-permitting, I will explain a fun connection between the five-point problem (a workhorse of modern RANSAC-based reconstruction pipelines) and the Coxeter group D_10, and how this relates to the general program of whether or not minimal problems "simplify".