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On the Geometry of Multivariate Generalized Gaussian Models

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Abstract

This paper concerns the geometry of the zero-mean multivariate generalized Gaussian distribution (MGGD) and the calculation of geodesic distances on the MGGD manifold. The MGGD is a suitable distribution for the modeling of multivariate (color, multispectral, vector and tensor images, etc.) image wavelet statistics. Expressions are derived for the Fisher-Rao metric for the zero-mean MGGD model. A closed-form expression is obtained for the geodesic distance on the submanifolds characterized by a fixed MGGD shape parameter. Suitable approximate solutions to the geodesic equations are presented in the case of MGGDs with varying shape parameters. An application to image texture similarity measurement in the wavelet domain is briefly discussed, comparing the performance of the geodesic distance and the Kullback-Leibler divergence.

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Authors and Affiliations

  1. Department of Applied Physics, Ghent University, J. Plateaustraat 22, 9000, Gent, Belgium

    Geert Verdoolaege

  2. IBBT-Visionlab, Department of Physics, University of Antwerp, Universiteitsplein 1, 2610, Wilrijk, Belgium

    Paul Scheunders

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  1. Geert Verdoolaege
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  2. Paul Scheunders
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Correspondence to Geert Verdoolaege.

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Verdoolaege, G., Scheunders, P. On the Geometry of Multivariate Generalized Gaussian Models. J Math Imaging Vis 43, 180–193 (2012). https://doi.org/10.1007/s10851-011-0297-8

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