Active contours on statistical manifolds and texture segmentation

A new approach to active contours on statistical manifolds is presented. The statistical manifolds are 2-dimensional Riemannian manifolds that are statistically defined by maps that transform a parameter domain onto a set of probability density functions. In this novel framework, color or texture features are measured at each image point and their statistical characteristics are estimated. This is different from statistical representation of bounded regions. A modified Kullback-Leibler divergence, that measures dissimilarity between two density distributions, is added to the statistical manifolds so that a geometric interpretation of the manifolds becomes possible. With this framework, we can formulate a metric tensor on the statistical manifolds. Then, a geodesic active contour is evolved with the aid of the metric tensor. We show that the statistical manifold framework provides more robust and accurate texture segmentation results.