Aspect graphs of bodies of revolution with algorithms of real algebraic geometry

Marie-Françoise Roy, Thierry Van Effelterre
IRMAR, Université de Rennes I
Campus de Beaulieu, 35042 Rennes Cedex, France

email: costeroy@univ-rennes1.fr, vaneffel@emmy.univ-rennes1.fr

Abstract:

An Aspect graph represents a 3-d object with all the topologically stable visible contours we may get by projecting the object onto a "retinal" plane, and by the visual events that change the topology of the visible contours. Such a representation could have some relevance for visual object recognition. We study the visible contours of bodies of revolution, whose generating curve is piecewise polynomial, under perspective projection. We show that the visual events locus of bodies of revolution is the union of a finite number of hyperboloids and cones of revolution, and that a body of revolution generated by a polynomial curve of degree d has at most distinct aspects, where . Eventually, we show how the Aspect graph of bodies of revolution may be computed exactly by using methods of real algebraic geometry.

• Introduction
• Structure of the Visual Events Locus
• Complexity of the Aspect graph
• Exact computation of the Aspect graph
• About this document ...