Abstract: The study of shape is concerned with properties of geometric configurations, such as collections of points and lines, that are invariant to a particular group of transformations. For example, two collections of points might be viewed as equivalent if they differ by rotation, translation and/or scale. The set of equivalence classes (shapes) often form a Riemannian manifold, where the metric gives a notion of how similar or dissimilarity two shapes are. We will discuss these notions and their application to problems in object recognition. We will also introduce object/image relations which describe constraints on all the image shapes of a particular object shape or constraints on the object shapes capable of producing a specific image shape.