An important problem in computer vision is to understand the space of  images that can be captured by an arrangement of cameras. A description of this space allows for statistical estimation methods to reconstruct  three-dimensional models of the scene that was imaged. The set of images captured by an arrangement of pinhole cameras is usually modeled as an  algebraic variety. The true set however is a semialgebraic subset of  this variety, arising from the physical restriction that cameras can only image points in front of them, a requirement called “chirality”.  For a pair of cameras, the minimal problem in this semialgebraic setting is given by 5 point pairs, which even in general position, can fail to have a “chiral” 3-dimensional reconstruction. These problems have surprising connections to classical mathematics. In particular, we will see that the combinatorics and arithmetic information of the minimal case of 5 point pairs are carried by a cubic surface with 27 real lines.

Joint work with Sameer Agarwal, Andrew Pryhuber and Rainer Sinn

Short Bio:
Rekha Thomas is the Walker Family Endowed Professor in Mathematics at the University of Washington.  She received her Ph.D. in Operations Research in 1994 from Cornell University. Her research interests are in Optimization and Applied Algebraic Geometry.
https://sites.math.washington.edu/~thomas/

Organizer: Dmitry Zenkov