Adjunctions, dilations, and erosions

Heijmans, Henk J.A.M.

doi:10.1016/bs.aiep.2020.07.005

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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Keywords	Additive and multiplicative structuring functions, Adjunctions, Boolean lattices, Dilations, Erosions, Lift operator, Polar morphology, Projection operator, Self-dual lattices, Translation invariance, Translation-rotation morphology
Persistent URL	doi.org/10.1016/bs.aiep.2020.07.005
Organisation	Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands
Citation APA Style AAA Style APA Style Cell Style Chicago Style Harvard Style IEEE Style MLA Style Nature Style Vancouver Style American-Institute-of-Physics Style Council-of-Science-Editors Style BibTex Format Endnote Format RIS Format CSL Format DOIs only Format	Heijmans, H. (2020). Adjunctions, dilations, and erosions. In Advances in Imaging and Electron Physics (pp. 121–176). doi:10.1016/bs.aiep.2020.07.005

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