Abstract for the talk on 07.12.2022 (14:00 h)Seminar on Nonlinear Algebra
Elima Shehu (University of Osnabrück + MPI MiS, Leipzig)
Average degree of the essential variety!
07.12.2022, 14:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, E1 05 (Leibniz-Saal)
The essential variety is an algebraic subvariety of dimension \(5\) in \(\mathbb RP^3.\) It encodes the relative pose of two calibrated cameras, where a calibrated camera is a matrix of the form \([R,t]\) with \(R\in SO(3)\) and \(t\in \mathbb R^3\). Since the degree of this variety is \(10\), there can only be at most \(10\) complex solutions. We compute the expected number of real points in the intersection of the essential variety with a random linear space of codimension \(5\). My aim is to tell you about these computations and our results. This is joint work with Paul Breiding, Samantha Fairchild, and Pierpaola Santarsiero.