Direct Methods for Self-Calibration of a Moving Stereo Head

. We consider the self-calibration problem in the special context of a stereo head, where the two cameras are arranged on a lateral rig with coplanar optical axes, each camera being free to vary its angle of vergence. Under various constraints, we derive explicit forms for the epipolar equation, and show that a static stereo head constitutes a degenerate camera configuration for carrying out self-calibration in the sense of Hartley [4]. The situation is retrieved by consideration of a special kind of motion of the stereo head in which the baseline remains confined to a plane. New closed-form solutions for self-calibration are thereby obtained, inspired by an earlier discrete motion analysis of Zhang et al. [11]. Key factors in our approach are the development of explicit, analytical forms of the fundamental matrix, and the use of the vergence angles in the parameterisation of the problem. Keywords: Self-calibration, stereo head, degeneracy, epipolar equation, fundamental matrix, ego-mo..