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Area-Based Medial Axis of Planar Curves

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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.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0250, USA

    Marc Niethammer & Allen Tannenbaum

  2. Department of Mathematics, University of North Texas, Denton, TX, 76203, USA

    Santiago Betelu

  3. University of Minnesota, Minneapolis, MN, 55455, USA

    Guillermo Sapiro

  4. Department of Mathematics, University of Liverpool, Liverpool, L69 3BX, UK

    Peter J. Giblin

Authors
  1. Marc Niethammer
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  2. Santiago Betelu
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  3. Guillermo Sapiro
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  4. Allen Tannenbaum
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  5. Peter J. Giblin
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Niethammer, M., Betelu, S., Sapiro, G. et al. Area-Based Medial Axis of Planar Curves. International Journal of Computer Vision 60, 203–224 (2004). https://doi.org/10.1023/B:VISI.0000036835.28674.d0

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