The Chern-Mather class of the multiview variety. Issue 6 (3rd June 2018)

• Record Type: Journal Article
• Authors: Harris, Corey; Lowengrub, Daniel
• Is Part Of: Communications in algebra. Volume 46:Issue 6(2018)
• Page Start: 2488
• Page End: 2499
• Publication Date: 2018-06-03
• Subjects: Chern-Mather class -- Chern-Schwartz-MacPherson class -- Computer vision -- Euclidean distance degree -- Higher discriminants; Primary: 14C17 -- Secondary: 14E05 -- 14N10 -- 51N35 -- 57R20; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1392545
• Languages: English
• ISSNs: 0092-7872

Abstract

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.