A computational approach to fisher information geometry with applications to image analysis

Abstract. We develop a computational approach to non-parametric Fisher information geometry and algorithms to calculate geodesic paths in this geometry. Geodesics are used to quantify divergence of probabil-ity density functions and to develop tools of data analysis in information manifolds. The methodology developed is applied to several image anal-ysis problems using a representation of textures based on the statistics of multiple spectral components. Histograms of filter responses are viewed as elements of a non-parametric statistical manifold, and local texture patterns are compared using information geometry. Appearance-based object recognition experiments, as well as region-based image segmen-tation experiments are carried out to test both the representation and metric. The proposed representation of textures is also applied to the development of a spectral cartoon model of images.