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Discrete & Computational Geometry

, Volume 41, Issue 3, pp 461–479 | Cite as

A Sampling Theory for Compact Sets in Euclidean Space

  • Frédéric Chazal
  • David Cohen-Steiner
  • André Lieutier
Article

Abstract

We introduce a parameterized notion of feature size that interpolates between the minimum of the local feature size and the recently introduced weak feature size. Based on this notion of feature size, we propose sampling conditions that apply to noisy samplings of general compact sets in euclidean space. These conditions are sufficient to ensure the topological correctness of a reconstruction given by an offset of the sampling. Our approach also yields new stability results for medial axes, critical points, and critical values of distance functions.

Keywords

Distance function Sampling Surface and manifold reconstruction 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Frédéric Chazal
    • 1
  • David Cohen-Steiner
    • 2
  • André Lieutier
    • 3
  1. 1.INRIA FutursOrsay CedexFrance
  2. 2.INRIA Sophia-AntipolisSophia-Antipolis CedexFrance
  3. 3.Dassault Systèmes and LMC/IMAGGrenobleFrance

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