Variable cost decision metrics with applications to image processing

The Bayes decision criteria is generalized by incorporating cost functions defined on the underlying probability space. The optimal Bayes decision rule using this cost model is obtained and the standard Bayesian approach is shown to be, under certain conditions the mini-max solution. A generalization of the Neyman-Pearson criterion is also proposed for the case in which the prior probabilities are unknown. The optimal decision rule for this cost model is derived, and a minimax solution is obtained for incompletely specified cost models. These models are then applied to optimizing the resolution of an imaging system and to optimizing parameters of a two stage image processing algorithm.