The output distribution of important LULU-operators
Abstract
Two procedures to compute the output distribution phiS 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 phiS for some important LULU-operators S. Properties of phiS can be used to characterize smoothing properties of S. One of the methods discussed also allows for the calculation of the reliability polynomial of any positive Boolean function (e.g. one derived from a connected graph).
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.