2017/01/24 by Harris, Corey, Lowengrub, Daniel · 1 citation
#14C17 (Primary) 14E05 #14N10 #51N35 #57R20 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1701.07079
The multiview variety associated to a collection of N cameras records which sequences of image points in ℙ2N 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∈ℙ2N 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.