# Area-Based Medial Axis of Planar Curves

Marc Niethammer, Santiago BetelĂș, Guillermo Sapiro, Allen R. Tannenbaum, Peter J. Giblin

January 2004
### 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.

Publication

*Int. J. Comput. Vis.*

###### Professor of Computer Science

My research interests include image registration, image segmentation, shape analysis, machine learning, and biomedical applications.