It is shown that set operators can be extended to function operators. This makes it possible to transfer all the theory of binary morphology to grey-level images. For this, a function must be represented by a family of sets. The set operator is then applied to this family after which a transformed function is reconstructed for the family of transformed sets.

Admissible complete lattices, From sets to functions, Power-Type lattices, Set-based representation of function lattices
Advances in Imaging and Electron Physics
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Heijmans, H.J.A.M. (2020). Lattice representations of functions. Advances in Imaging and Electron Physics. doi:10.1016/bs.aiep.2020.07.010