Polynomials in Multiview Geometry

Abstract

We study multiview geometry and some of its applications through the use of polynomials. A three-dimensional world point gives rise to n ≥ 2 two-dimensional projections in n given cameras. The object of focus in this thesis is the multiview variety, the space of all possible n-tuples of such projections. By applying tools and techniques from algebraic geometry, representation theory, optimization, and others, we are able to provide a more complete picture of the multiview variety than has existed before. We apply this understanding to solving triangulation, the problem of reconstructing a world point from noisy projections.