Shape analysis and symmetry detection in gray-level objects using the analytical Fourier-Mellin representation

Authors:
Stéphane Derrode;Faouzi Ghorbel
Affiliations:
Groupe Signaux Multi-dimensionnels, Institut Fresnel (UMR 6133), École Nationale Supérieure de Physique de Marseille, Domaine Universitaire de Saint Jérôme, 13013 Marseille Ced ...;Groupe de Recherceh Images et Formes de Tunisie, Laboratoire Cristal, École Natinale des Sciences de l'Informatique, Domaine Universitaire de La Manuba, 2010 Manuba, Tunisia
Venue:
Signal Processing
Year:
2004

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Abstract

The analytical Fourier-Mellin transform is used in order to assess motion parameters between gray-level objects having the same shape with distinct scale and orientation. From results on commutative harmonic analysis, a functional is constructed in which the location of the minimum gives an estimation of the size and orientation parameters. Furthermore, when the set of geometrical transformations is restricted to the compact rotation group, we show that this minimum is exactly the Hausdorff distance between shapes represented in the Fourier-Mellin domain. This result is used for the detection and the estimation of both all rotation and reflection symmetries in objects.