Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation

Images are by nature fuzzy. Approaches to object information extraction from images should attempt to use this fact and retain fuzziness as realistically as possible. In past image segmentation research, the notion of “hanging togetherness” of image elements specified by their fuzzy connectedness has been lacking. We present a theory of fuzzy objects forn-dimensional digital spaces based on a notion of fuzzy connectedness of image elements. Although our definitions lead to problems of enormous combinatorial complexity, the theoretical results allow us to reduce this dramatically, leading us to practical algorithms for fuzzy object extraction. We present algorithms for extracting a specified fuzzy object and for identifying all fuzzy objects present in the image data. We demonstrate the utility of the theory and algorithms in image segmentation based on several practical examples all drawn from medical imaging.