Changing Views on Curves and Surfaces - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Acta Mathematica Vietnamica Year : 2018

Changing Views on Curves and Surfaces


Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint. Qualitative changes in that curve occur when the viewpoint crosses the visual event surface. We examine the components of this ruled surface, and observe that these coincide with the iterated singular loci of the coisotropic hypersurfaces associated with the original curve or surface. We derive formulas, due to Salmon and Petitjean, for the degrees of these surfaces, and show how to compute exact representations for all visual event surfaces using algebraic methods.

Dates and versions

hal-01676208 , version 1 (05-01-2018)



Kathlén Kohn, Bernd Sturmfels, Matthew Trager. Changing Views on Curves and Surfaces. Acta Mathematica Vietnamica, 2018, ⟨10.1007/s40306-017-0240-1⟩. ⟨hal-01676208⟩
179 View
0 Download



Gmail Facebook Twitter LinkedIn More