Invariant Signatures of Closed Planar Curves

Authors:
Emilio Musso;Lorenzo Nicolodi
Affiliations:
Dipartimento di Matematica, Politecnico di Torino, Torino, Italy 10129;Dipartimento di Matematica, Università degli Studi di Parma, Parma, Italy 43100
Venue:
Journal of Mathematical Imaging and Vision
Year:
2009

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Abstract

We prove that any subset of 驴2 parametrized by a C 1 periodic function and its derivative is the Euclidean invariant signature of a closed planar curve. This solves a problem posed by Calabi et al. (Int. J. Comput. Vis. 26:107---135, 1998). Based on the proof of this result, we then develop some cautionary examples concerning the application of signature curves for object recognition and symmetry detection as proposed by Calabi et al.