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. Representations of these window operators are given here 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. The minimal elements of on-set and the maximal elements of off-set of any positive Boolean function are shown to be equivalent to the simplest sum-of-product form and product-of-sum form of that positive Boolean function, respectively. A fast algorithm for finding the representation of stack filters is designed