Links between mathematical morphology, rough sets, fuzzy logic and higher order neural networks

In this paper we present some remarks on dependence and similarity between morphological operations and other modern techniques of image treatment i.e. high-order neural networks, rough sets and fuzzy logic as well as its realization. Two basic morphological operations: erosion and dilation can be realized in many different ways including approaches based on precise mathematics of polynomial higher order neural nets (pi-sigma or functional link) or imprecise notions of uncertainty (fuzzy or rough sets). These concepts can be extended from binary images (sets) to gray level pictures (functions).