SOME REPRESENTATION PROPERTIES OF STACK FILTERS

Stack filters are a class of nonlinear filters which are based on positive Boolean functions as the window operators. In this paper, the representations of these window operators are presented via the structures of on-set and off-set of the positive Boolean functions which can be expressed as a Boolean expression containing no complements of the input variables. Although several researchers have analyzed the existence of those representation forms, for the application consideration we need an algorithmic method to find those representation forms. In this paper, a fast algorithm for finding the representation of stack filters is designed. This algorithm can be easily extended to find the representation of morphological filters mentioned in [7].