, Volume 30, Issue 2, pp 144-163

First online:

A One-Step Crust and Skeleton Extraction Algorithm

  • C. GoldAffiliated withDepartment of Land Surveying and Geo-Informatics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, and Department of Geomatics, Laval University, Quebec City, Quebec, Canada.
  • , J. SnoeyinkAffiliated withDepartment of Computer Science, University of North Carolina at Chapel Hill, NC 27599-3125, USA, and Department of Computer Science, University of British Columbia, Vancouver, BC, Canada.

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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.

Key words. Curve reconstruction, Medial axis, Voronoi diagram, Planar subdivision, Scanned maps, Topology building in GIS.