Ambiguity in reconstruction from image correspondences

摘要

In certain cases, reconstruction from point correspondences between two images is ambiguous, in that two or more surfaces are obtained, each of which can give rise to the correspondences. These ambiguous surfaces are examples of rectangular hyperboloids. Each ambiguous surface is invariant under a rotation through 180° that interchanges the two possible positions for the optical centre of the camera taking the second image. As a result, the ambiguous surfaces are subject to a cubic polynomial constraint. We use this constraint to give a new proof that there are, in general, exactly ten different reconstructions compatible with five image correspondences.