Single-view recognition: the perspective case

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

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