Geometry Seminar

Date: April 24, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Corey Harris, Florida State

Title: Chern-Mather class of the multiview variety

Abstract: The multiview variety associated to a collection of N cameras records which sequences of image points in P^2N can be obtained by taking pictures of a given world point x∈P3 with the cameras. In order to reconstruct a scene from its picture under the different cameras it is important to be able to find the critical points of the function which measures the distance between a general point u∈P^2N and the multiview variety. We calculate a specific degree 3 polynomial that computes the number of critical points as a function of N. In order to do this, we construct a resolution of the multiview variety, and use it to compute its Chern-Mather class.