The calibration of a generic central camera can be described non-parametrically by a map assigning to each image pixel a 3D projection ray. We address the determination of this map and the motion of a camera that performs two infinitesimal rotations about linearly independent axes. A complex closed-form solution exists, which in practice allows to visually identify the geometry of a range of sensors, but it only works at the center of the image domain and not accurately. We present a new two-step method to solve the stated self-calibration problem that overcomes these drawbacks. Firstly, the Gram matrix of the camera rotation velocities is estimated jointly with the Lie bracket of the two rotational flows computed from the data images. Secondly, the knowledge that such Lie bracket is also a rotational flow is exploited to provide a solution for the calibration map which is defined on the whole image domain. Both steps are essentially linear, being robust to the noise inherent to the computation of optical flow from images. The accuracy of the proposed method is quantitatively demonstrated for different noise levels, rotation pairs, and imaging geometries. Several applications are exemplified, and possible extensions and improvements are also considered.
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