B. Debaets et al., THE FUNDAMENTALS OF FUZZY MATHEMATICAL MORPHOLOGY .2. IDEMPOTENCE, CONVEXITY AND DECOMPOSITION, International journal of general systems, 23(4), 1995, pp. 307-322
Citations number
6
Categorie Soggetti
Ergonomics,"System Science","Computer Science Theory & Methods",Ergonomics
Fuzzy mathematical morphology is an alternative extension of binary ma
thematical morphology to gray-scale images. This paper discusses some
of the more advanced properties of the fuzzy morphological operations.
The possible extensivity of the fuzzy closing, anti-extensivity of th
e fuzzy opening and idempotence of the fuzzy closing and fuzzy opening
are studied in detail. It is demonstrated that these properties only
partially hold. On the other hand, it is shown that the fuzzy morpholo
gical operations satisfy the same translation invariance and have the
same convexity properties as the binary morphological operations. Fina
lly, the paper investigates the possible decomposition, by taking (str
ict) alpha-cuts, of the fuzzy morphological operations into binary mor
phological operations.