MINISTÉRIO DA CIÊNCIA E TECNOLOGIA INSTITUTO NACIONAL DE PESQUISAS ESPACIAIS INPE–7694–NTC/343 Set mapping decomposition by mathematical morphology

This paper presents some general representations for set mappings based on Mathematical Morphology. A generalization of the concept of kernel , proposed originaly by Matheron for translation invariant. mappings, will be presented here in order to prove that any set mapping (not necessarily translation invariant.) can be decomposed by a set of (non-translation invariant.) sup-generating mappings . A generalization of the concept of basis is introduced to simplify the proposed representation. A topological condition for the existence of basis is also stated.