MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Changing Views on Curves and Surfaces

Kathlén Kohn, Bernd Sturmfels and Matthew Trager


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.

Jul 7, 2017
Jul 10, 2017
MSC Codes:
14Q10, 65D19, 68W30, 53A05

Related publications

2018 Repository Open Access
Kathlén Kohn, Bernd Sturmfels and Matthew Trager

Changing views on curves and surfaces

In: Acta mathematica Vietnamica, 43 (2018) 1, pp. 1-29