Fusion of Numerical and Structural Image Information in Medical Imaging in the Framework of Fuzzy Sets

Fuzzy sets theory provides a good theoretical basis to represent imprecision of the information, at different levels of representation. It constitutes an unified framework for representing and processing both numerical and symbolic information, as well as structural information (constituted mainly by spatial relationships in image processing). We show that this theory can achieve tasks at several levels, from low level (e.g. grey-level based classification) to high level (e.g. model based structural pattern recognition and scene interpretation). We describe the use of fuzzy set at low level, for processing the basic numerical information contained in the images. Then we go to the object level, and show how to represent objects or structures in the images as fuzzy objects, and we present some operations on such fuzzy objects. At higher level, we are concerned by structural information and spatial relationships between objects, as distances, adjacency, and relative position between fuzzy objects. Finally, we address the problem of combining and fusing information. We show examples at low level for multi-source classification, and at high level for recognition of brain structures based on an atlas.