Cluster validation criteria for image segmentation

In this paper cluster validation criteria for piecewise constant image segmentation are proposed. All the criteria are based on the maximum a posteriori (MAP) principle and derived and implemented by four different, but related approaches. They are obtained by using Taylor expansions and three of them are derived by Bayesian predictive densities. The third and fourth criteria are implemented by the bootstrap technique, and their evaluations are, therefore, computationally more intensive than the evaluations of the first two. The proposed rules are compared by computer simulations with the widely used Akaike's information criterion (AIC) and the minimum description length (MDL) criteria.