A One‐Step Crust and Skeleton Extraction Algorithm

A One‐Step Crust and Skeleton Extraction Algorithm

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Article ID: iaor20121030
Volume: 30
Issue: 2
Start Page Number: 144
End Page Number: 163
Publication Date: Jun 2001
Journal: Algorithmica
Authors: ,
Keywords: graphical methods, maps, topology
Abstract:

We wish to extract the topology from scanned maps. In previous work [GNY] this was done by extracting a skeleton from the Voronoi diagram, but this required vertex labelling and was only useable for polygon maps. We wished to take the crust algorithm of Amenta et al. [ABE] and modify it to extract the skeleton from unlabelled vertices. We find that by reducing the algorithm to a local test on the original Voronoi diagram we may extract both a crust and a skeleton simultaneously, using a variant of the Quad‐Edge structure of [GS]. We show that this crust has the properties of the original, and that the resulting skeleton has many practical uses. We illustrate the usefulness of the combined diagram with various applications.

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