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Proceedings Paper

Reconstruction of convex sets using an involution over admissible sets
Author(s): Francois Pointet
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Paper Abstract

There is an application GAff which sends an admissible subset M of Pn+1 to an admissible subset GAff(M) of Pn+1. The application GAff is an involution, but the most useful property of GAff is to transform the profile of M in the direction (nu) (epsilon) Pn into an intersection of GAff(M) with an affine hyperplane of Pn+1. We denote by i:Pn yields Pn+1 the application defined by i([x1,...,xn+1]) equals [x1,...,xn+1,0], and C(nu)M the profile in the direction (nu) (epsilon) Pn. We can generalize the application GAff to convex n-polytopes, written GPAff, and it gives a dual application from n-polytopes to n-polytopes which reverses inclusion of faces. The main property of GPAff is that if A is a polytope close to an analytic convex hypersurface M, then GPAff (A) is close to GAff(M). We can deduce an algorithm of reconstruction of convex sets using this map.

Paper Details

Date Published: 30 September 1996
PDF: 8 pages
Proc. SPIE 2826, Vision Geometry V, (30 September 1996); doi: 10.1117/12.251799
Show Author Affiliations
Francois Pointet, Univ. de Lausanne (Switzerland)

Published in SPIE Proceedings Vol. 2826:
Vision Geometry V
Robert A. Melter; Angela Y. Wu; Longin Jan Latecki, Editor(s)

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