Finding a Minimum Medial Axis of a Discrete Shape is NP-hard

Abstract : The medial axis is a classical representation of digital objects widely used in many applications. However, such a set of balls may not be optimal: subsets of the medial axis may exist without changing the reversivility of the input shape representation. In this article, we first prove that finding a minimum medial axis is an NP-hard problem for the Euclidean distance. Then, we compare two algorithms which compute an approximation of the minimum medial axis, one of them providing bounded approximation results.
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Submitted on : Monday, October 20, 2008 - 8:31:34 PM
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David Coeurjolly, Jérôme Hulin, Isabelle Sivignon. Finding a Minimum Medial Axis of a Discrete Shape is NP-hard. Theoretical Computer Science, Elsevier, 2008, 206 (1-2), pp.72-79. ⟨hal-00332406⟩

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