A new information theoretic criterion for detecting the number of image region

The joint differential entropy of a random variable and the parameter vector of its pdf can be maximized by ML estimate of this parameter vector. When this joint differential entropy is parameterized on the dimension of this parameter vector, then, based on Jaynes´ Principle, minimizing maximum joint differential entropy over the dimension of parameter vector provides means for detecting the number of parameters from the observed data. By linking the dimension of parameter vector to the image regions, a minimizing maximum entropy (MME) criterion for detecting the number of image regions in the image characterized by Finite Normal Mixture (FNM) is developed. The results obtained by applying MME to the simulated and real phantom images demonstrate that MME works consistently with other information theoretic criteria such as AIC and MDL, and also possesses its own meanings.