As is well known, camera calibration in photogrammetry and with the use of Bundle Adjustment with self-calibration, the coordinates of the principal points cannot be recovered from parallel images. This situation calls for convergent images to recover the coordinates of the principal point. A common explanation is attributed to the algebraic correlation between the exterior orientation parameters and the calibration parameters. Now the question in other words, Is there is any deep explanation about the nature or the type of this algebraic correlation? Is there is any analytical proof for this correlation? or we have to accept this empirical finding (we need convergent images for camera calibration)
Your question is about camera-self-calibration, without any control point information, what is a really tough topic. So, if you ask, why the parameters of the exterior orientation (EO) and the interior orientation (IO) are highly correlated, then let us make a short thought experiment:
If one consider the pinhole camera model, and one slightly pans (rotation in the horizontal plane) the camera around the projection centre (which is the pinhole), lets say to the right direction, then the mapped image content slightly shifts with it. This is a small change of the EO angle around the zenith axis (pointing upwards) in terrestial case. Now let's slightly move the pinhole into the same direction. Since the principle point is directly connected to the projection centre, it is the same as shifting the principle point (at least for the pinhole camera model). Then, again, the image content is slightly shifted, in the same direction like before.
The conclusion is, that it is impossible for infinite small changes in the orientation of a camera to distinguish between some of the parameters, because the effect on the image is very the same.
I don't know, what your goal is. But if it is possible, then I recommend to perform a camera calibration in beforehand.
Regarding literature, there exist a deep investigation of Wester-Ebbinghaus (1985):
"Verfahren zur Feldkalibrierung von Photogrammetrischen Aufnahmekammern im Nahbereich." DGK Reihe B 275", but it is only in German.
I found a good paper (in English) by Fabio Remondino and Clive Fraser (2006) . It gives a good overview of different kinds of camera calibration as well as recommendations on "how to do it". One important point is to roll the camera in steps of 90° around the viewing axis. This disconnects the principle point from the exterior orientation during camera calibration.
I hope this helps you.
Kind Regards
Olaf Peters
Article Digital camera calibration methods: Considerations and comparisons
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