Article

International Journal of Computer Vision

, Volume 60, Issue 3, pp 203-224

First online:

Area-Based Medial Axis of Planar Curves

  • Marc NiethammerAffiliated withDepartment of Electrical and Computer Engineering, Georgia Institute of Technology
  • , Santiago BeteluAffiliated withDepartment of Mathematics, University of North Texas
  • , Guillermo SapiroAffiliated withUniversity of Minnesota
  • , Allen TannenbaumAffiliated withDepartment of Electrical and Computer Engineering, Georgia Institute of Technology
  • , Peter J. GiblinAffiliated withDepartment of Mathematics, University of Liverpool

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Abstract

A new definition of affine invariant medial axis of planar closed curves is introduced. A point belongs to the affine medial axis if and only if it is equidistant from at least two points of the curve, with the distance being a minimum and given by the areas between the curve and its corresponding chords. The medial axis is robust, eliminating the need for curve denoising. In a dynamical interpretation of this affine medial axis, the medial axis points are the affine shock positions of the affine erosion of the curve. We propose a simple method to compute the medial axis and give examples. We also demonstrate how to use this method to detect affine skew symmetry in real images.

medial axis affine invariant symmetry area shape pattern recognition