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

摘要

Two procedures to compute the output distribution ϕS of certain stack lters S (so called erosion-dilation cascades) are given. One rests on the disjunctivenormal form of S and also yields the rank selection probabilities. The other is basedon 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, inthe same way as our polynomials ϕS are computed one could compute the reliabilitypolynomial of a connected graph, or more generally the reliability polynomial w.r.t.any positive Boolean function.