Geometric analysis of planar shapes using geodesic paths
ABSTRACT We propose a differential geometric representation of planar shapes using "direction" functions of their boundaries. Each shape becomes an element of a constrained function space, an infinite-dimensional manifold, and pairwise differences between are quantified using the lengths of geodesics connecting them on this space. A gradient-based shooting method is used for finding geodesics between any two shapes. Some applications of this shape metric are illustrated including clustering of objects based on their shapes and computation of intrinsic mean shapes.
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ABSTRACT: Résumé Une approche variationnelle et robuste est proposée pour le recalage de signaux 1D et appliquée au calcul des géodésiques de formes pour la classification. L'approche est ensuite étendue au recalage d'images de séquences de formes. Cette approche de recalage basé-géométrie est plus adaptée aux images peu contrastées où le recalage basé-intensité trouve toutes ses limites. Une étude de va-lidation est menée sur des signaux et des images issus d'archives biologiques marines, qui présentent une grande variabilité interindividuelle, où les approches de recalage sont d'un intérêt tout particulier. Mots Clef Recalage de signaux, recalage d'images, géodésiques dans l'espace des formes, optimisation, classification de formes, otolithes de poissons. Abstract A robust variational setting is proposed for 1D signal reg-istration and applied to the computation of shape geodesics for shape classification issues. This approach is extended to be applied for matching images of shape sequences. This geometric approach is mainly addressed to poorly contrasted images where the intensity-based registration fails. For validation purposes, experiments are carried out on real signals and images issued from marine biologi-cal archives which depict a high interindividual variability such that registration-based approaches are of particular interest.
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ABSTRACT: The primary goal of this research was to develop representations, models, and algorithms for use in Bayesian automated recognition of objects from their images. Despite focused efforts in the area of image understanding in recent years, a fresh look was needed to highlight the progress and the limitations. Our research was focused along the following three broad themes: (i) development of efficient representations of the objects of interest (or their images) using nonlinear manifolds, (ii) development of parametric probability models for capturing object and clutter variability, and (iii) development of algorithms for solving inference problems on nonlinear manifolds that arise in object recognition.03/2003;