Morphological operations on fuzzy sets

One can analyse the structure of a binary image by looking at patterns of a certain shape at different places on the image. This idea of describing the image by looking at similar patterns at various locations is quantified in mathematical morphology by the concept of a structuring element. Binary images can be regarded as subsets of Euclidean or digital space. Fuzzy sets have proven to be useful to model grey-tone images. As shown by Werman and Peleg (1985), morphology techniques used for analysis of binary images can be applied to grey-tone images using fuzzy logic. In the present paper a redefinition of Werman and Peleg´s fuzzy morphology operations is given. This redefinition employs the more general indicator framework, given by Sinha and Dougherty (1992)