A unification of linear, median, order-statistics and morphological filters under mathematical morphology

This paper presents a summary of a unified theory, based upon mathematical morphology, of all translation-invariant and increasing systems. Examples of such systems are morphological transformations of signals, order-statistics filters and some linear shift-invariant filters. Our theoretical research showed that every such system can be uniquely represented by the minimal elements of its kernel and realized as a minimal combination of morphological erosions.