Use of threshold decomposition theory to derive basic properties of median filters
Robert W. Hawley, Neal C. Gallagher · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1991
Necessary and sufficient conditions for a binary signal to be invariant to median filtering are derived. Proof is shown that one pass of a recursive median filter on a binary signal results in a new signal that is invariant to further median filtering. A technique is described whereby threshold decomposition theory and the stacking property can be used to generalize these results so that they may be applied to arbitrary k-valued signals.