The computation of various geometrical and topological properties of objects, as well as the inter-relationships among them, is useful and important in image processing and computer vision problems. Many of these properties and relations are ill-defined and presented here are some approaches to define them using fuzzy set theoretic concepts. It is assumed that the objects are segmented into a two-tone mask from a grey tone image. The properties considered are bigness, position, convexity, circularity, elongatedness, straightness and angular orientation. The relationships considered are relative position, relative orientation, degree of surroundedness and the degree of between ness. A man-machine interaction based on these proper-lies is also proposed and illustrative examples of the results of executed algorithms are presented.