Output distributions of stack filters based on mirrored threshold decomposition

The output distribution formula for stack biters based on mirrored threshol d decomposition is derived. This formula allows one to compute the cumulati ve distribution function of the output of a stack filter for a given indepe ndent and identically distributed (i.i.d.) input noise distribution. Mirror ed threshold decomposition permits us to analyze the input-output character istics of the stack filter in the binary domain, The sliding window operati on 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 probabilist ic description of the binary input signal, An example illustrating the use of the output distribution formula is provided.