Design of Boolean LUM Smoothers through Permutation Coloring Concept

Rank-order based LUM (lower-upper-middle) smoothers distinguishes bywide range of smoothing characteristics given by filter parameter.Thus, for the capability to achieve the best balance between noisesuppression and signal details preservation, the LUM smoothers arepreferred in smoothing applications. Thanks to threshold decompositionand stacking properties, the LUM smoothers belong to the class of stackfilters. This paper is focused to the derivation of minimal positiveBoolean function for LUM smoothers through permutation groups and acoloring concept.