Representation Theorems In A L-Fuzzy Set Theory Based Algebra For Morphology

Divyendu Sinha; Charles R. Giardina

doi:10.1117/12.970055

1 November 1989 Representation Theorems In A L-Fuzzy Set Theory Based Algebra For Morphology

Divyendu Sinha, Charles R. Giardina

Proceedings Volume 1199, Visual Communications and Image Processing IV; (1989) https://doi.org/10.1117/12.970055
Event: 1989 Symposium on Visual Communications, Image Processing, and Intelligent Robotics Systems, 1989, Philadelphia, PA, United States

Abstract

Perhaps the most promising area of morphological image processing is that dealing with morphological filters. An image to image mapping is called a morphological filter if it is increasing and translation compatible. In other words, morphological filters preserve the natural set theoretic ordering and are space invariant. Examples of such filters are the convex hull operator, the topological closure, the umbra transform and various other topological algorithms [2-4]. Matheron showed that all such mappings can be characterized by the set theoretic operations erosion and dilation. His representation theorems has been adapted to digital images with great success [4].

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Divyendu Sinha and Charles R. Giardina "Representation Theorems In A L-Fuzzy Set Theory Based Algebra For Morphology", Proc. SPIE 1199, Visual Communications and Image Processing IV, (1 November 1989); https://doi.org/10.1117/12.970055

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