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Communication Dans Un Congrès Année : 2010

Reconstructing Shapes with Guarantees by Unions of Convex Sets

Résumé

A simple way to reconstruct a shape A from a sample P is to output an offset P + r B, where B designates the unit Euclidean ball centered at the origin. Recently, it has been proved that the output P + r B is homotopy equivalent to the shape A, for a dense enough sample P of A and for a suitable value of the parameter r. In this paper, we extend this result and find convex sets C, besides the unit Euclidean ball B, for which P + r C reconstructs the topology of A. This class of convex sets includes in particular N-dimensional cubes. We proceed in two steps. First, we establish the result when P is an offset of A. Building on this first result, we then consider the case when P is a finite noisy sample of A.
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Dates et versions

hal-00427035 , version 1 (28-10-2009)
hal-00427035 , version 2 (10-12-2009)
hal-00427035 , version 3 (31-03-2010)

Identifiants

Citer

Dominique Attali, André Lieutier. Reconstructing Shapes with Guarantees by Unions of Convex Sets. SoCG 2010 - 26th Annual Symposium on Computational Geometry, Jun 2010, Snowbird, Utah, United States. pp.344-353, ⟨10.1145/1810959.1811015⟩. ⟨hal-00427035v3⟩
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