Representation Theorems In A L-Fuzzy Set Theory Based Algebra For Morphology
Divyendu Sinha, Charles R. Giardina · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
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].