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.

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Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Heijmans, H.J.A.M. (2020). Lattice representations of functions. In Advances in Imaging and Electron Physics (pp. 331–354). doi:10.1016/bs.aiep.2020.07.010