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Rekha Thomas: Multiview Chirality, Two Cameras and a Cubic Surface

Time: Tue 2021-02-09 15.45

Location: Zoom, meeting ID: 625 8662 8413

Participating: Rekha Thomas, University of Washington

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Abstract

The set of images captured by an arrangement of pinhole cameras is usually modeled by an algebraic variety called the multiview variety. The true set is in fact a semialgebraic subset of this variety, arising from the physical restriction that cameras can only image points in front of them. I will discuss this set for multiple cameras. 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. We will see that the combinatorics and arithmetic information of this minimal case is carried by a cubic surface with 27 real lines.

Joint work with Sameer Agarwal, Andrew Pryhuber and Rainer Sinn
 

About the speaker

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 under the supervision of Bernd Sturmfels. Her research interests are in optimization and applied algebraic geometry.
sites.math.washington.edu/~thomas/