Are two rotational flows sufficient to calibrate a smooth non-parametric sensor?

We present an attempt to determine whether the shape of a generic central-projection camera, such as the eye of an insect or a log-polar camera, can be determined from two motion flows resulting from purely rotational motions with non-collinear axes. Our first contribution is to write the smooth non-parametric calibration problem as a differential equation. It is unclear at present whether this problem has unique solution, up to an orthogonal transformation. Our second contribution is a discretized version of this smooth problem, for which we give a calibration algorithm - a third contribution. Using this algorithm, we explore numerically the properties of the discrete self-calibration problem, giving some insight on the nature of the problem. We show examples of successful self-calibration, but cannot give a definite affirmative answer to the question in the title.