Projective rotations applied to a pan-tilt stereo head

A non-metric pan-tilt stereo head consists of a weakly calibrated stereo rig mounted on a pan-tilt mechanism. It is called non-metric since neither the kinematics of the mechanism, nor the camera calibration are required. The Lie group of “projective rotations”-homographies of projective space corresponding to rotational displacements is a new, formalism that is introduced in this article to model the geometry of such a pan-tilt system. A Rodrigues-like formula as well as a minimal parameterization of projective rotations are introduced. Based on this, the practical part of the article devises a numerical optimization technique for accurately estimating projective rotations from stereo point correspondences along trial motions. This procedure recovers sufficient geometry to operate the system. The experiments validate and evaluate the proposed approach on real image data. They evaluate weak calibration, image prediction, and homing of a non-metric pan-tilt stereo head