Abstract for the talk on 20.06.2017 (10:00 h)Seminar on Non-Linear Algebra
Corey Harris (MPI MIS, Leipzig)
Chern classes of the multiview variety
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.