An Interval-Valued Fuzzy Morphological Model Based on Lukasiewicz-Operators

摘要

Mathematical morphology is a well-known theory to process binary, grayscale or color images. In this paper, we introduce interval-valued fuzzy mathematical morphology as an extension of classical and fuzzy morphology. It originates from the observation that the pixel values of a grayscale image are not always certain, and models this uncertainty using interval-valued fuzzy set theory. In this way, we are able to incorporate the uncertainty regarding measured pixel values into the toolbox of morphological operators. We focus our attention on a morphological model whose underlying logical framework is based on the Lukasiewicz-operators. For this model we investigate and discuss general theoretical properties, some computational aspects, as well as its relation to fuzzy morphology and classical grayscale morphology.