Fuzzy logic and mathematical morphology
Ting Deng · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2000
In this report we investigate the general theory of grey-scale morphology within the framework of complete lattices and fuzzy logic. This includes grey-scale granulometries, hit-or-miss operators for grey-scale images, rank operators, and connected operators. We also show that the Matheron's representation theory does not hold for general grey-scale images and we present some results related to the representation theory. Besides these, in this report, we put forward a new approach to fuzzy morphology through the extension of infimum, supremum, and conjunction. 2000 Mathematics Subject Classification: 03B52, 03E72, 68U10 Keywords and Phrases: Mathematical morphology, image processing, fuzzy logic, complete lattice, adjunction, conjunction, implication, dilation, erosion, negation, fuzzy adjunction. Note: This work was carried out during a one-year visit of the author to CWI. He gratefully acknowledges financial support of the Netherlands Organization for International Cooperation in H...