On fuzzy distances and their use in image processing under imprecision

This paper proposes a classification of fuzzy distances with respect to the requirements needed for applications in image processing under imprecision. We distinguish, on the one hand, distances that basically compare only the membership functions representing the concerned fuzzy objects, and, on the other hand, distances that combine spatial distance between objects and membership functions. To our point of view, the second class of methods finds more general applications in image processing since these methods take into account both spatial information and information related to the imprecision attached to the image objects. New distances based on mathematical morphology are proposed in this second class. (C) 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.