Finding a minimum medial axis of a discrete shape is NP-hard

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 a NP-hard problem for the Euclidean distance. Then, we compare two algorithms which compute an approximation of the minimum medial axis. Key words: Minimum Medial Axis, NP-completeness, bounded approximation algorithm.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: David Coeurjolly, Jérôme Hulin, Isabelle Sivignon
• Keywords: Input Shape Representation, Medial Axis, Minimum Medial Axis, TCS 2008, Theoretical Computer Science