Characterization of fuzzy Minkowski algebra

Divyendu Sinha; Edward R. Dougherty

doi:10.1117/12.60632

1 June 1992 Characterization of fuzzy Minkowski algebra

Divyendu Sinha, Edward R. Dougherty

Proceedings Volume 1769, Image Algebra and Morphological Image Processing III; (1992) https://doi.org/10.1117/12.60632
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

There are various fuzzy morphologies (Minkowski algebras), these depending on the particular fuzzifification of set inclusion that is employed for the definition of erosion. Set-inclusion fuzzification depends upon the choice of an indicator for set inclusion and, based upon a collection of nine axioms, a class of indicators results such that each indicator in the class yields a Minkowski algebra in which a certain core of the ordinary propositions typically associated with mathematical morphology are valid. By going a bit further and postulating a certain mathematical form for the indicator, one obtains fitting characterizations for the basic operators. In ordinary crisp-set binary morphology, certain fundamental representation theorems hold, specifically the Matheron representations for increasing, translation invariant mappings and for T-openings. The definition of a T-opening extends for fuzzy T-openings. There is also a weakened version of the Matheron kernel representation for increasing, translation invariant mappings.

Citation Download Citation

Divyendu Sinha and Edward R. Dougherty "Characterization of fuzzy Minkowski algebra", Proc. SPIE 1769, Image Algebra and Morphological Image Processing III, (1 June 1992); https://doi.org/10.1117/12.60632

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