Journal of Mathematical Imaging and Vision

, Volume 43, Issue 3, pp 206–213

Euclidean Signature Curves


DOI: 10.1007/s10851-011-0303-1

Cite this article as:
Hickman, M.S. J Math Imaging Vis (2012) 43: 206. doi:10.1007/s10851-011-0303-1


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 C3 that have a given signature curve.


Euclidean transformations Signature curves Equivalence problems for planar curves Image recognition 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of CanterburyChristchurchNew Zealand

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