Computational representation of lattice operators

摘要

Abstract: Computational mathematical morphology is extended to provide computational representations of increasing and nonincreasing windowed translation-invariant operators of the form $psi : L$+N$/ $YLD M, where L and M are complete lattices. Representations are grounded on the Riemann zeta function and provide lattice-valued extensions of the classical disjunctive- normal-form, reduced, and positive logical representations. Both direct and dual representations are given. Representations are morphological because they involve elemental forms of erosion, dilation, or the hit-or-miss transform. !12