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Euclidean Signature Curves

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Abstract

It is well known that two planar curves that are related by a Euclidean transformation possess the same signature curve. Recently Musso and Nicolodi (J. Math. Imaging Vis. 35:68–85, 2009) gave examples of non-congruent curves that possess the same Euclidean signature curve. In this paper we show how to construct all planar curves of class C 3 that have a given signature curve.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand

    Mark S. Hickman

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  1. Mark S. Hickman
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Correspondence to Mark S. Hickman.

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Hickman, M.S. Euclidean Signature Curves. J Math Imaging Vis 43, 206–213 (2012). https://doi.org/10.1007/s10851-011-0303-1

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  • DOI: https://doi.org/10.1007/s10851-011-0303-1

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