Probabilistic distance measures of the Dirichlet and Beta distributions

We give the analytical definitions of the Chernoff, Bhattacharyya and Jeffreys–Matusita probabilistic distances between two Dirichlet distributions and two Beta distributions as its special case. For all other known probabilistic distances we show their inappropriateness in the analytical case. We discuss the parameter learning of the Dirichlet distribution from a finite sample set and present an application for split-and-merge image segmentation.