A general axiomatic theory of intrinsically fuzzy mathematical morphologies Academic Article

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. 1995 IEEE

authors

• Dougherty, Edward

published proceedings

• IEEE Transactions on Fuzzy Systems

author list (cited authors)

• Sinha, D., & Dougherty, E. R.

citation count

• 43

complete list of authors

• Sinha, D||Dougherty, ER

publication date

• January 1995

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

published in

• IEEE transactions on fuzzy systems  Journal

Digital Object Identifier (DOI)

• 10.1109/91.481948

start page

• 389

end page

• 403

volume

• 3

issue

• 4

URL

• http://dx.doi.org/10.1109/91.481948