Diffusion on Statistical Manifolds

This paper presents a new diffusion scheme on statistical manifolds for the detection of texture boundaries. The technique derives from our previous work, in which 2-dimensional Riemannian manifolds were statistically defined by maps that transform a parameter domain onto a set of probability density functions. In the earlier approach, a modified Kullback-Leibler divergence, measuring dissimilarity between two density distributions, was added to the statistical manifolds so that a geometric interpretation of the manifolds becomes possible. Although the previous framework produced good segmentation results, the approach led to offsets in texture boundaries for some situations. This paper introduces a diffusion scheme on statistical manifolds that leads to substantially improved localization accuracy in segmentation of textured images.