Theory and practice on the self-calibration of a rotating and zooming camera from two views

The paper deals with first the uniqueness of the self-calibration of a rotating and zooming camera, mathematically, given two views. It is assumed that the principal point and the aspect ratio are fixed but the focal length changes as the camera rotates. In this case, theoretically at least one inter-image homography is enough to compute the internal calibration parameters as well as the rotation, and the self-calibration is unique up to a rotation. Secondly, it is shown that the calibration parameters can be obtained through a linear computation, even though the original problem is highly nonlinear, when the principal point is given a priori. Finally, the authors analyse the effects of the deviation of the principal point on the linear computation of the focal lengths and the rotation. From the mathematical analysis, it is found that the more the camera changes its zoom the larger the effects are, and the larger the rotation angle the smaller the effects are. Thus, the image centre may be taken as the principal point in practical applications. Experimental results using real images are also given