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Changing views on curves and surfaces
Zitatschlüssel KST-Changing-Views-On-Curves-And-Surfaces
Autor Kathlén Kohn and Bernd Sturmfels and Matthew Trager
Seiten 1–29
Jahr 2018
DOI 10.1007/s40306-017-0240-1
Journal Acta Math. Vietnam.
Jahrgang 43
Nummer 1
Monat 01
Zusammenfassung 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.
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