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.

Additive and multiplicative structuring functions, Adjunctions, Boolean lattices, Dilations, Erosions, Lift operator, Polar morphology, Projection operator, Self-dual lattices, Translation invariance, Translation-rotation morphology
Advances in Imaging and Electron Physics
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

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