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Voronoi-Based Medial Axis Approximation from Samples: Issues and Solutions

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Transactions on Computational Science XX

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 8110))

Abstract

Continuous curves are approximated by sample points, which carry the shape information of the curve. If sampling is sufficiently dense, the sample points can be used to extract the structural properties of the curve (e.g., crust, medial axis, etc.). This article focuses on approximation of medial axis from sample points. Especially, we review the methods that approximate the medial axis using Voronoi diagram. Such methods are extremely sensitive to noise and boundary perturbations. Thus, a pre- or post-processing step is needed to filter irrelevant branches of the medial axis, which are introduced in this article. We, then, propose a new medial axis approximation algorithm that automatically avoids irrelevant branches through labeling sample points. The results indicate that our method is stable, easy to implement, robust and able to handle sharp corners, even in the presence of significant noise and perturbations.

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Author information

Authors and Affiliations

  1. Department of Surveying and Geomatics Engineering, College of Engineering, University of Tehran, Iran

    Farid Karimipour & Mehran Ghandehari

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  1. Farid Karimipour
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  2. Mehran Ghandehari
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Editors and Affiliations

  1. University of Calgary, Calgary, AB, Canada

    Marina L. Gavrilova

  2. CloudFabriQ Ltd., Warnford Court, 29 Throgmorton Street, EC2N 2AT, London, UK

    C. J. Kenneth Tan

  3. Rutgers University, New Brunswick, NJ, USA

    Bahman Kalantari

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Karimipour, F., Ghandehari, M. (2013). Voronoi-Based Medial Axis Approximation from Samples: Issues and Solutions. In: Gavrilova, M.L., Tan, C.J.K., Kalantari, B. (eds) Transactions on Computational Science XX. Lecture Notes in Computer Science, vol 8110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41905-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-41905-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41904-1

  • Online ISBN: 978-3-642-41905-8

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