Eureka-2013. Fourth International Workshop Proceedings Linguistic Interpretation of Mathematical Morphology Agustina Bouchet1,2, Gustavo Meschino3, Marcel Brun1, Rafael Espin Andrade4, Virginia Ballarin1 1 Universidad Nacional de Mar de Plata, Mar de Plata, Argentina. 2 CONICET, Mar de Plata, Argentina. 3 Universidad Nacional de Mar de Plata, Mar de Plata, Argentina. 4 ISPJAE, Universidad Técnica de La Habana, Cuba.
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[email protected] Abstract strains imposed by t-norms and s-norms, which are by themselves also conjunctions and disjunctions. Mathematical Morphology is a theory based on geometry, By replacing t-norm and s-norm by conjunction and algebra, topology and set theory, with strong application disjunction, respectively, we obtain the dilation and ero- to digital image processing. This theory is characterized sion operators for the Compensatory Fuzzy Mathematical by two basic operators: dilation and erosion. In this work Morphology (CMM), called compensatory dilation and we redefine these operators based on compensatory fuzzy compensatory erosion, respectively. Two different im- logic using a linguistic definition, compatible with previ- plementations of the CMM were presented at this moment ous definitions of Fuzzy Mathematical Morphology. A [12,21]. comparison to previous definitions is presented, assessing In this work new operators based on the definition of robustness against noise. the CMM are presented, but replacing the supreme and infimum by logical operators, which allow for a linguistic Keywords: Fuzzy Logic, Compensatory Fuzzy Logic, interpretation of their meaning. We call the New Com- Mathematical Morphology, Fuzzy Mathematical Mor- pensatory Morphological Operators.