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Image segmentation-the process of defining objects in images-remains the most challenging problem in image processing despite decades of research. Many general methodologies have been proposed to date to tackle this problem. An emerging framework that has shown considerable promise recently is that of fuzzy connectedness. Images are by nature fuzzy. Object regions manifest themselves in images with a heterogeneity of image intensities owing to the inherent object material heterogeneity, and artifacts such as blurring, noise and background variation introduced by the imaging device. In spite of this gradation of intensities, knowledgeable observers can perceive object regions as a gestalt. The fuzzy connectedness framework aims at capturing this notion via a fuzzy topological notion called fuzzy connectedness which defines how the image elements hang together spatially in spite of their gradation of intensities. In defining objects in a given image, the strength of connectedness between every pair of image elements is considered, which in turn is determined by considering all possible connecting paths between the pair. In spite of a high combinatorial complexity, theoretical advances in fuzzy connectedness have made it possible to delineate objects via dynamic programming at close to interactive speeds on modern PCs. This paper gives a tutorial review of the fuzzy connectedness framework delineating the various advances that have been made. These are illustrated with several medical applications in the areas of Multiple Sclerosis of the brain, magnetic resonance (MR) and computer tomographic (CT) angiography, brain tumor, mammography, upper airway disorders in children, and colonography.