Area-Based Medial Axis of Planar Curves

Authors:
Marc Niethammer;Santiago Betelu;Guillermo Sapiro;Allen Tannenbaum;Peter J. Giblin
Affiliations:
Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, USA;Department of Mathematics, University of North Texas, Denton, TX 76203, USA;Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA. guille@ece.umn.edu;Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, USA;Department of Mathematics, University of Liverpool, Liverpool L69 3BX, UK
Venue:
International Journal of Computer Vision
Year:
2004

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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.