A consistent algebraic framework is introduced with which the various translations encountered in the discussion of erosions and dilations can be unified. Adjunction is re-examined and the T-invariant operators are defined and discussed in detail. Self-dual and Boolean lattices are defined. Translation-invariant and polar morphology are studied. Additive and multiplicative structuring functions are considered in connection with grey-scale functions. T is examined in the non-Abelian situation, where the projection and lift operators are employed. Translation-rotation morphology is described.

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

Heijmans, H.J.A.M. (2020). Adjunctions, dilations, and erosions. In Advances in Imaging and Electron Physics (pp. 121–176). doi:10.1016/bs.aiep.2020.07.005