Applied Algebra Seminar: Scene reconstruction and a resolution of the multiview variety

Seminar | February 9 | 5:15-6:15 p.m. | 891 Evans Hall

 Daniel Lowengrub, University of California, Berkeley

 Department of Mathematics

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 $x\in P^3$ 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 $u\in P^{2N}$ and the multiview variety. In this paper 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.