Barycentric distribution estimation for texture clustering based on information-geometry tools

The goal of the paper
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is to propose a new method for texture clustering based on the information-geometry tools. Considering textured images as a collection of heavy-tailed prior probability distributions related to some space/scale decomposition, an average of distributions, i.e. a barycentric distribution, is proposed for characterizing each cluster. We suggest the use of the Jeffrey divergence as a dissimilarity measure for the clustering of textured images. Taking into account the geometry of the probabilistic manifold associated to the prior family, we provide the steepest descent method used to estimate the barycentric distribution. The descent exploits the Fisher information matrix, which is the expected value of the Hessian matrix and the local metric to the manifold. The results of experimental evaluation conducted on well-known texture databases show that the Fisher information matrix approach provides a convergence speed significantly higher than the convergence speed of conventional methods of steepest descent.