Stack filters: theory and applications

Stack filters are a large class of nonlinear filters which obey a weak superposition property called the threshold decomposition and an ordering property called the stacking property. They contain such other well-known nonlinear filters as median filters, rank-order filters, weighted median filters, weighted order statistic filters, and increasing morphological filters with flat structuring elements. In this paper, the theory of MMAE stack filtering is reviewed, and a new, fast algorithm for adaptive stack filtering is introduced. Examples showing the output of optimal stack filters are provided