A formal classification of 3D medial axis points and their local geometry

IEEE Transactions on Pattern Analysis and Machine Intelligence
Peter J Giblin, Benjamin B Kimia

Abstract

This paper proposes a novel hypergraph skeletal representation for 3D shape based on a formal derivation of the generic structure of its medial axis. By classifying each skeletal point by its order of contact, we show that, generically, the medial axis consists of five types of points, which are then organized into sheets, curves, and points: 1) sheets (manifolds with boundary) which are the locus of bitangent spheres with regular tangency A1(2) (Ak(n) notation means n distinct k-fold tangencies of the sphere of contact, as explained in the text); two types of curves, 2) the intersection curve of three sheets and the locus of centers of tritangent spheres, A1(3), and 3) the boundary of sheets, which are the locus of centers of spheres whose radius equals the larger principal curvature, i.e., higher order contact A3 points; and two types of points, 4) centers of quad-tangent spheres, A1(4), and 5) centers of spheres with one regular tangency and one higher order tangency, A1A3. The geometry of the 3D medial axis thus consists of sheets (A1(2)) bounded by one type of curve (A3) on their free end, which corresponds to ridges on the surface, and attached to two other sheets at another type of curve (A1(3)), which support a generali...Continue Reading

References

Feb 1, 1973·Journal of Theoretical Biology·H Blum
Oct 6, 2004·IEEE Transactions on Pattern Analysis and Machine Intelligence·Thomas B SebastianBenjamin B Kimia

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Citations

Apr 27, 2005·NeuroImage·Sylvain BouixKaleem Siddiqi
Apr 2, 2016·Computers in Biology and Medicine·Robert S Bradley, Philip J Withers
Apr 17, 2015·IEEE Transactions on Medical Imaging·Punam K SahaGunilla Borgefors
Apr 20, 2013·IEEE Transactions on Pattern Analysis and Machine Intelligence·Andrei C JalbaAlexandru C Telea
Dec 16, 2006·IEEE Transactions on Pattern Analysis and Machine Intelligence·Frederic F Leymarie, Benjamin B Kimia
Jan 17, 2007·IEEE Transactions on Pattern Analysis and Machine Intelligence·David Coeurjolly, Annick Montanvert
Mar 21, 2009·IEEE Transactions on Pattern Analysis and Machine Intelligence·Peter J GiblinAnthony J Pollitt
Dec 8, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Yong-Jin Liu Kai Tang
Aug 21, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Qi GuoJiaqing Shao
Dec 16, 2006·IEEE Transactions on Medical Imaging·Paul A YushkevichJames C Gee
Jan 15, 2008·IEEE Transactions on Visualization and Computer Graphics·Dennie ReniersAlexandru Telea
Dec 15, 2015·IEEE Transactions on Pattern Analysis and Machine Intelligence·Andrei C JalbaAlexandru C Telea
Apr 28, 2006·CNS Spectrums·In Kyoon LyooPerry F Renshaw

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