Calculating the output distribution of stack filters that are erosion-dilation cascades, in particular LU LU -filters

摘要

Two procedures to compute the output distribution (phi)S(of certain stack)filters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields phi(S) for some important LU LU -operators S. Properties of phi(S) can be used to characterize smoothing properties of S. Also, in the same way as our polynomials phi(S) are computed one could compute the reliability polynomial of a connected graph, or more generally the reliability polynomial w.r.t. any positive Boolean function.