Modified Akaike Information Criterion for Selecting the Numbers of Mixture Components: An Application to Initial Lung Segmentation

Nonetheless, a proper number of components for a mixture are typically selected manually, in spite of multiple existing criteria for automatic selection [5-16]. Each deterministic criterion, such as the Akaike’s information (AIC) [5-7], Schwarz’s Bayesian inference [8], minimum message length (MML) [9,10], classication likelihood [11], mutual information between the components [12], or greedy mixture learning [13,14], can be applied to decrease sequentially a large initial set of the candidate components or increase their initial small set. However, these methods are too computationally expensive: for instance, the AIC requires the recalculation of the model’s log-likelihood for all the exclusions or inclusions of the individual candidates. A few known stochastic techniques, for example, based on resampling [15] or crossvalidation [16], are also computationally expensive.