Feature detection and tracking in optical flow on non-flat manifolds

Authors:
Sheraz Khan;Julien Lefevre;Habib Ammari;Sylvain Baillet
Affiliations:
Department of Neurology, Medical College of Wisconsin, Milwaukee, USA and Center of Applied Mathematics, Ecole Polytechnique, France and Department of Neurology, MGH/Harvard Medical School, Boston ...;Aix-Marseille Univ, Département d'Informatique de Luminy /CNRS, LSIS, UMR 6168, 13397 Marseille, France;Center of Applied Mathematics, Ecole Polytechnique, France;Department of Neurology, Medical College of Wisconsin, Milwaukee, USA and Montreal Neurological Institute, McGill University, Montreal, Canada
Venue:
Pattern Recognition Letters
Year:
2011

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Abstract

Optical flow is a classical approach to estimating the velocity vector fields associated to illuminated objects traveling onto manifolds. The extraction of rotational (vortices) or curl-free (sources or sinks) features of interest from these vector fields can be obtained from their Helmholtz-Hodge decomposition (HHD). However, the applications of existing HHD techniques are limited to flat, 2D domains. Here we demonstrate the extension of the HHD to vector fields defined over arbitrary surface manifolds. We propose a Riemannian variational formalism, and illustrate the proposed methodology with synthetic and empirical examples of optical-flow vector field decompositions obtained on a variety of surface objects.