Output distributions of stack filters based on mirrored threshold decomposition

The output distribution formula for stack filters based on mirrored threshold decomposition is derived. This formula allows one to compute the cumulative distribution function of the output of a stack filter for a given independent and identically distributed (i.i.d.) input noise distribution. Mirrored threshold decomposition permits us to analyze the input–output characteristics of the stack filter in the binary domain. The sliding window operation of the stack filter is modeled by a deterministic finite automaton. The output distribution of the filter is obtained by interpreting the automaton as a Markov chain whose transition probabilities depend on the probabilistic description of the binary input signal. An example illustrating the use of the output distribution formula is provided.