Design of Boolean LUM Smoothers through Permutation Coloring Concept

Abstract

Rank-order based LUM (lower-upper-middle) smoothers distinguishes by wide range of smoothing characteristics given by filter parameter. Thus, for the capability to achieve the best balance between noise suppression and signal details preservation, the LUM smoothers are preferred in smoothing applications. Thanks to threshold decomposition and stacking properties, the LUM smoothers belong to the class of stack filters. This paper is focused to the derivation of minimal positive Boolean function for LUM smoothers through permutation groups and a coloring concept.