By Rekha R. Thomas
A key problem in computer vision is the estimation of the three-dimensional shape of a world scene from images and the parameters of the cameras that captured them. This problem, studied under the name structure from motion or multiview geometry, has its origins in photogrammetry and perspective drawings. The modeling language for these problems is projective geometry, which naturally leads to polynomial models for multiview geometry. While the needed polynomials are clear in some instances, they may be harder to identify in others. Up to this point, algebraic vision’s focus has been in multiview geometry and its immediate relatives.
In my talk at the 2018 SIAM Annual Meeting, to be held July 9-13 in Portland, Ore., I will convey the main philosophy of algebraic vision and illustrate the impact of algebraic methods on some of the foundational problems in vision.