Before revision: A general procedure to compute the output distribution D for certain nonlinear operators S (so called erosion-dilation cascades) is given. A refinement of the procedure yields D for some important LULU-operators S. Properties of D can also be used to characterize smoothing properties of a nonlinear operator S.
After revision: A general procedure to compute the output distribution D for certain nonlinear operators 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 LULU-operators S. Properties of D can also be used to characterize smoothing properties of a nonlinear operator S.