(Universitat Politècnica de Catalunya, 2001) Burillo López, Pedro; Frago Paños, Noé Natalio; Fuentes González, Ramón; Automática y Computación; Automatika eta Konputazioa
Fuzzy Mathematical Morphology aims to extend the binary morphological
operators to grey-level images. In order to define the basic morphological
operations fuzzy erosion, dilation, opening and closing, we introduce a
general method based upon fuzzy implication and inclusion grade operators,
including as particular case, other ones existing in related literature
In the definition of fuzzy erosion and dilation we use several fuzzy
implications (Annexe A, Table of fuzzy implications), the paper includes a
study on their practical effects on digital image processing. We also present
some graphic examples of erosion and dilation with three different structuring
elements B(i,j)=1, B(i,j)=0.7, B(i,j)=0.4, i,j∈{1,2,3} and various fuzzy
implications.
(Universitat Politècnica de Catalunya, 2003) Burillo López, Pedro; Frago Paños, Noé Natalio; Fuentes González, Ramón; Automática y Computación; Automatika eta Konputazioa
First of all, in this paper we propose a family of fuzzy implication operators,
which the generalised Luckasiewicz´s one, and to analyse the impacts of Smets
and Magrez properties on these operators. The result of this approach will be a
characterisation of a proposed family of inclusion grade operators (in Bandler and
Kohout´s manner) that satisfies the axioms of Divyendu and Dogherty. Second,
we propose a method to define fuzzy morphological operators (erosions and
dilations). A family of fuzzy implication operators and the inclusion grade are the
basis for this method.
