On the relation of order-statistics filters and template matching: Optimalmorphological pattern recognition

In this paper, we investigate methods for optimal morphological pattern rec ognition. The task of optimal pattern recognition is posed as a solution to a hypothesis testing problem. A minimum probability of error decision rule -maximum a posteriori filter-is sought. The classical solution to the minim um probability of error hypothesis testing problem, in the presence of inde pendent and identically distributed noise degradation, is provided by templ ate matching (TM), A modification of this task, seeking a solution to the m inimum probability of error hypothesis testing problem, in the presence of composite (mixed) independent and identically distributed noise degradation , is demonstrated to be given by weighted composite template matching (WCTM ). As a consequence of our investigation, the relationship of the order-sta tistics filter (OSF) and TM-in both the standard as well as the weighted an d composite implementations-is established. This relationship is based on t he thresholded cross-correlation representation of the OSF. The optimal ord er and weights of the OSF for pattern recognition are subsequently derived. An additional outcome of this representation is a fast method for the impl ementation of the OSF.