The Chern-Mather class of the multiview variety. Issue 6 (3rd June 2018) - Harris, Corey; Lowengrub, Daniel
ABSTRACT: The multiview varietyassociated to a collection of N cameras records which sequences of image points in ℙ 2 N can be obtained by taking pictures of a given world point x ∈ 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 ∈ ℙ 2 N 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.