Commutative Algebra and Algebraic Geometry: Changing Views on Curves and Surfaces

Seminar | September 12 | 3:45-4:45 p.m. | 939 Evans Hall

 Bernd Sturmfels, UC Berkeley

 Department of Mathematics

We present work with Kathlen Kohn and Matthew Trager on visual events in computer vision. Given an algebraic curve or surface in 3-space, the image or contour curve arises by projecting from a viewpoint. Qualitative changes in that curve occur when the viewpoint crosses the visual event surface. The components of this ruled surface are iterated singular loci of the coisotropic hypersurfaces associated with the original curve or surface. We present formulas, due to Salmon and Petitjean, for the degrees of these surfaces, and show how to compute visual event surfaces using algebraic tools.