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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