A case against epipolar geometry

Abstract

We discuss briefly a number of areas where epipolar geometry is currently central in carrying out visual tasks. In contrast we demonstrate configurations for which 3D projective invariants can be computed from perspective stereo pairs, but epipolar geometry (and full projective structure) cannot. We catalogue a number of these configurations which generally involve isotropies under the 3D projective group, and investigate the connection with camera calibration. Examples are given of the invariants recovered from real images. We also indicate other areas where a strong reliance on epipolar geometry should be avoided, in particular for image transfer.