An interpretation of discrete Choquet integrals in morphological image processing

Mathematical morphology has been widely used for shape analysis and feature extraction in digital images. Morphological filters are based on morphological transformations of signals by crisp sets. Their sensitivity to noise led researchers define morphological operations on fuzzy sets. Choquet integrals provide another means of generalizing binary morphological operators. They operate on crisp sets. But, they are referred to as fuzzy integrals because they integrate a real function with respect to a fuzzy measure. An interpretation of a fuzzy measure in terms of fuzzy fitting has led us to generalize gray-scale morphological operators based on Choquet integrals. These operators are called Choquet Morphological Operators (CMO). We used them for domain learning, feature selection, information fusion and, feature extraction. CMOs have been shown to provide better results than conventional morphological operators. In this paper, we give a detailed discussion of the fuzzy fitting concept that leads us to generalizing gray-scale morphological operators using Choquet integrals.