Grey-scale morphology based on fuzzy logic
Tingquan Deng, Henk J.A.M. Heijmans · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2000
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 definition 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 Classification: 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 first author to CWI. He gratefully acknowledges financial support of the Netherlands Organi...