Preprint 39/2017

Changing Views on Curves and Surfaces

Kathlén Kohn, Bernd Sturmfels, and Matthew Trager

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Submission date: 07. Jul. 2017
published in: Acta mathematica Vietnamica, 43 (2018) 1, p. 1-29 
DOI number (of the published article): 10.1007/s40306-017-0240-1
MSC-Numbers: 14Q10, 65D19, 68W30, 53A05
Link to arXiv: See the arXiv entry of this preprint.

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.

16.03.2021, 02:15