Sponges for Generalized Morphology

Mathematical morphology has traditionally been grounded in lattice theory. For non-scalar data lattices often prove too restrictive, however. In this paper we present a more general alternative, sponges, that still allows useful definitions of various properties and concepts from morphological theory. It turns out that some of the existing work on “pseudo-morphology” for non-scalar data can in fact be considered “proper” mathematical morphology in this new framework, while other work cannot, and that this correlates with how useful/intuitive some of the resulting operators are.