Share Email Print

Proceedings Paper

Characterization of fuzzy Minkowski algebra
Author(s): Divyendu Sinha; Edward R. Dougherty
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

Paper 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.

Paper Details

Date Published: 1 June 1992
PDF: 11 pages
Proc. SPIE 1769, Image Algebra and Morphological Image Processing III, (1 June 1992); doi: 10.1117/12.60632
Show Author Affiliations
Divyendu Sinha, CUNY/College of Staten Island (United States)
Edward R. Dougherty, Rochester Institute of Technology (United States)

Published in SPIE Proceedings Vol. 1769:
Image Algebra and Morphological Image Processing III
Paul D. Gader; Edward R. Dougherty; Jean C. Serra, Editor(s)

© SPIE. Terms of Use
Back to Top