A General Theory of Single View Recognition -- the Affine Case -- with Applications to Indexing Image Databases for Content Based Retrieval

Using the theory of correspondences from algebraic geometry, we develop methods to relate 3-D objects to 2-D images and vice versa. In effect, we provide a very general framework for the use of geometric invariants in image recognition. At the most concrete level, our techniques yield a system of polynomial equations in variables which represent both the 3-D invariants of the features on an object and the 2-D invariants of features in an image. These equations will be satisfied if and only if the object can produce the image up to affine transformations of both the object and the image. The case of projective invariants will be dealt with in a forthcoming paper. The applications considered are to single view recognition and to indexing image databases for content based retrieval