Two procedures to compute the output distribution ϕS of certain stack
lters 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 ϕS for some important LULU-operators S.
Properties of ϕS can be used to characterize smoothing properties of S. Also, in
the same way as our polynomials ϕS 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.