Multiscale Medial Loci and Their Properties

  • Authors:

  • Stephen M. Pizer;Kaleem Siddiqi;Gabor Székely;James N. Damon;Steven W. Zucker

  • Affiliations:

  • Computer Science, University of N.C., Chapel Hill, NC;Computer Science, McGill University, Montreal, Canada;Electr. Engineering, E.T.H., Zürich, Switzerland;Mathematics, University of N.C., Chapel Hill, NC;Computer Science, Yale University, New Haven, CT

  • Venue:
  • International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
  • Year:
  • 2003

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Abstract

Blum's medial axes have great strengths, in principle, inintuitively describing object shape in terms of a quasi-hierarchyof figures. But it is well known that, derived from a boundary,they are damagingly sensitive to detail in that boundary. Thedevelopment of notions of spatial scale has led to some definitionsof multiscale medial axes different from the Blum medial axis thatconsiderably overcame the weakness. Three major multiscale medialaxes have been proposed: iteratively pruned trees of Voronoi edges(Ogniewicz, 1993- Székely, 1996- Näf, 1996), shock lociof reaction-diffusion equations (Kimia et al., 1995- Siddiqi andKimia, 1996), and height ridges of medialness (cores) (Fritsch etal., 1994- Morse et al., 1993- Pizer et al., 1998). These aredifferent from the Blum medial axis, and each has differentmathematical properties of generic branching and ending properties,singular transitions, and geometry of implied boundary, and theyhave different strengths and weaknesses for computing objectdescriptions from images or from object boundaries. Thesemathematical properties and computational abilities are laid outand compared and contrasted in this paper.