Projective Structure from two Uncalibrated Images: Structure from Motion and Recognition

This paper addresses the problem of recovering relative structure, in the form of an invariant, from two views of a 3D scene. The invariant structure is computed without any prior knowledge of camera geometry, or internal calibration, and with the property that perspective and orthographic projections are treated alike, namely, the system makes no assumption regarding the existence of perspective distortions in the input images. We show that, given the location of epipoles, the projective structure invariant can be constructed from only four corresponding points projected from four non-coplanar points in space (like in the case of parallel projection). This result leads to two algorithms for computing projective structure. The rst algorithm requires six corresponding points, four of which are assumed to be projected from four coplanar points in space. Alternatively, the second algorithm requires eight corresponding points, without assumptions of coplanarity of object points. Our study of projective structure is applicable to both structure from motion and visual recognition. We use projective structure to re-project the 3D scene from two model images and six or eight corresponding points with a novel view of the scene. The re-projection process is well-de ned under all cases of central projection, including the case of parallel projection. Copyright c Massachusetts Institute of Technology, 1992 This report describes research done at the Arti cial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's arti cial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under O ce of Naval Research contract N00014-85-K-0124. A. Shashua was also supported by NSF-IRI8900267.