Computational morphology and representation of operators between complete lattices

摘要

The representations of translation-invariant mappings in the context of computational morphology are in terms of elementary binary erosions and dilations. The general representations in the context of complete lattices are in terms of abstract dilations and antidilations. The present paper considers the relationship between the specialized computational and general lattice representations. The computational and lattice-based representations are directly demonstrated to be equivalent in the computational setting.