Fuzzy mathematical morphology

Review paper Image Algebra for Electron Images

“…We cannot go into detail here and refer to [10,16,[62][63][64]66], where recent thinking on these questions is to be found.…”

Fuzzy soft mathematical morphology

“…Also, fuzzy soft morphological operation should preserve the notion of fuzzy fitting [7]. Thus, the definitions for fuzzy soft erosion and fuzzy soft dilation are derived in this paper for the first time as far as we know, as follows :…”

“…This framework leads to an i nfinity of fuzzy mathematical morphologies, which are constructed in families with specific properties. In this paper the approach described by Sinha and Dougherty [7] has been used. This is a special case of the framework presented in [8].…”

“…Sinha and Dougherty [7] have introduced fuzzy mathematical morphology. In this approach the images are not treated as crisp binary sets, but as fuzzy sets.…”

Lattice Fuzzy Signal Operators and Generalized Image Gradients

“…As an earlier example, the use of min/max to extend the intersection/union of ordinary (crisp) sets to fuzzy sets [14] has also been used to extend the set-theoretic morphological shrink/expand operations on binary images to min/max filtering on graylevel images [11,3]. While the field of morphological image analysis was maturing, several researchers developed various other approaches using fuzzy logic ideas for extending or generalizing the morphological image operations [13,1]. The main ingredients of these approaches have been to (1) map the max-plus structure of Minkowski signal dilation to a sup-T signal convolution, where T is some fuzzy intersection norm, and (2) use duality to map the inf-minus structure of Minkowski signal erosion to a inf-T convolution, where T is a dual fuzzy union norm.…”