Self-calibration of a rotating camera with a translational offset

Camera self calibration, based on a purely rotational movement of the camera, receives the most attention among different camera self-calibration methods due to its algorithmic simplicity. The existing purely rotational methods, however, assume camera rotates around its optical center, therefore yielding no translation offset. This assumption is not realistic, since in practice, the precise location of the optical center is often unknown, and the rotation is often performed about an unknown but fixed point near the optical center. The conventional methods tend to ignore the offset, and therefore, could lead to significant errors with the estimated camera parameters. In this paper, we introduce a new rotation-based camera self-calibration method, which explicitly accounts for the unknown translation offset. To this end, the problem is mathematically formulated and solved for differently taking the translation into consideration. To obtain the camera parameters with unknown camera rotations, our algorithm requires the camera to rotate around an unknown but fixed axis twice, by the same yet unknown angle. This is not an unreasonable assumption for precalibrating a camera on an active head. Experiments with both synthetic and real data show that the systematic errors caused by ignoring the translational offset will be effectively eliminated by our approach.