A general axiomatic theory of intrinsically fuzzy mathematical morphologies

Author

Sinha, Divyendu ; Dougherty, Edward R.

Author_Institution

Graduate Center, City Univ. of New York, Staten Island, NY, USA

Volume

3

Issue

4

fYear

1995

fDate

11/1/1995 12:00:00 AM

Firstpage

389

Lastpage

403

Abstract

Intrinsic fuzzification of mathematical morphology is grounded on an axiomatic characterization of subset fuzzification. The result is an axiomatic formulation of fuzzy Minkowski algebra. Part of the Minkowski algebra results solely from the axioms themselves and part results from a specific postulated form of a subsethood indicator function. There exists an infinite number of fuzzy morphologies satisfying the axioms; in particular, there are uncountably many indicators satisfying the postulated form. This paper develops fuzzy Minkowski algebra, with special emphasis on fitting characterizations of fuzzy erosion and opening, examines key properties of the indicator function, and provides fuzzy extensions of the basic binary Matheron representations for openings and increasing, translation-invariant operators

Keywords

algebra; fuzzy set theory; mathematical morphology; minimisation; binary Matheron representations; fuzzy Minkowski algebra; fuzzy erosion; fuzzy opening; general axiomatic theory; indicator function; intrinsically fuzzy mathematical morphologies; subset fuzzification; translation-invariant operators; Algebra; Computer science; Fuzzy set theory; Fuzzy sets; Fuzzy systems; Morphological operations; Morphology; Pixel; Uncertainty;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/91.481948

Filename

481948