Algebraic Geometry for Computer Vision

Series: 
Algebra Seminar
Monday, September 26, 2016 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
UC Berkeley
Organizer: 
This talks presents two projects at the interface of computer vision and algebraic geometry. Work with Zuzana Kukelova, Tomas Pajdla and Bernd Sturmfels introduces the distortion varieties of a given projective variety. These are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter distortions, the case of most interest for modeling cameras with image distortion. Single-authored work determines the algebraic degree of minimal problems for the calibrated trifocal variety. Our techniques rely on numerical algebraic geometry, and the homotopy continuation software Bertini.