On Model Selection for an Urban Area, by the AIC Criterion

The paper concludes the issue of constructing a statistical model for a satellite image of an urban area. In a previous study (2006) we have introduced the Gaussian mixture as an appropriate model for an urban area when treated as a single object. Here the choice of the number of components of the mixture is addressed as a model selection problem. The Akaike Information Criterion (AIC) is used for choosing the best fitting Gaussian mixture. The EM algorithm is used for the estimation of the parameter and the optimal, parsimonious model is obtained by minimizing the AIC value, under some supplementary conditions on the weights of the different mixture components, so that the identified components are significant and well separated.