Exact Computation of the Aspect Graph of Semi-algebraic 3-d Objects

An Overview

Marie-Françoise Roy, Thierry Van Effelterre
IRMAR Université de Rennes I
Campus de Beaulieu, 35042 Rennes Cedex, France
Emails: Marie-Francoise.Coste-Roy@univ-rennes1.fr, vaneff@can.nl

Abstract:

The aspect graph is a viewer-centered representation of a 3-d object by the total set of its stable visible contours under diffeomorphism of the retinal plane (called its aspects) as well as by the visual events that make the visible contours switch from one aspect to another.
We compute the exact aspect graph of bounded semi-algebraic 3-d objects under perspective projection. More precisely, we deal with objects that are bounded by a finite union of smooth algebraic surface patches, the patches intersecting each other transversally at the edges and at most three patches intersecting at isolated triple points. We illustrate this computation for the bodies of revolution.

• Contours and Aspects

• Generic Singularities and Visual Events
  • Generic singularities of the image contour

  • Visual events

  • Global visual events locus and cells in viewspace

  • Case of the bodies of revolution

• Exact Computation of the Aspect Graph

• Theoretical Complexity of the Aspect Graph

• Example

• References

Go to:
Exact Computation of Aspect Graphs with Computer Algebra
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