SIAM News Blog

Algebraic Vision

By Rekha R. Thomas

Rekha R. Thomas, University of Washington.
Algebraic vision is an emerging viewpoint of geometric problems in computer vision that aims to examine polynomial models through the lens of algebra. Modeled as problems in applied algebraic geometry, the fundamental questions take on a new life that makes them amenable to algebraic methods in both geometry and optimization. These formulations have resulted in a greater understanding of the structural properties of problems in vision, thus enabling the design of algorithms that exploit structure. Moreover, they have brought the role of real algebraic geometry in such applied problems to the forefront. Problems in vision have also led to exciting and novel advances in mathematics because of questions that might not have been asked or answered without this external stimulus. A diverse group of researchers—including experts from vision, computational algebraic geometry, classical algebraic geometry, combinatorics, numerics, linear algebra, and optimization—have come together to collaborate on algebraic vision problems.

Rekha R. Thomas will discuss algebraic vision and its application to geometry and optimization at the 2018 SIAM Annual Meeting.

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.

Rekha R. Thomas, a professor of mathematics at the University of Washington in Seattle, works in optimization and computational algebra.
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