Grey-Scale Morphology Based on Fuzzy Logic

There exist several methods to extend binary morphology to grey-scale images. One of these methods is based on fuzzy logic and fuzzy set theory. Another approach starts from the complete lattice framework for morphology and the theory of adjunctions. In this paper, both approaches are combined. The basic idea is to use fuzzy conjunctions and implications which are adjoint in the de nition of dilations and erosions, respectively. This gives rise to a large class of morphological operators for grey-scale images. It turns out that this class includes the often used grey-scale Minkowski addition and subtraction. 2000 Mathematics Subject Classi cation: 03B52, 03E72, 68U10 Keywords and Phrases: Mathematical morphology, image processing, fuzzy logic, complete lattice, adjunction, conjunction, implication, dilation, erosion, negation. Note: This work was carried out during a one-year visit of the rst author to CWI. He gratefully acknowledges nancial support of the Netherlands Organization for...

• Type: Journal
• Year: 2002
• Where: JMIV
• Authors: Ting-Quan Deng, Henk J. A. M. Heijmans
• Keywords: Complete Lattice, Fuzzy Logic, Grey-scale Images, JMIV 2002