A Multiple View Approach for Auto-Calibration of a Rotating and Zooming Camera∗

In this paper we deal with the problem of calibrating a rotating and zooming camera, without 3D pattern, whose internal calibration parameters change frame by frame. First, we theoretically show the existence of the calibration parameters up to an orthogonal transformation under the assumption that the skew of the camera is zero. Auto-calibration becomes possible by analyzing inter-image homographies which can be obtained from the matches in images of the same scene, or through direct nonlinear iteration. In general, at least four homographies are needed for auto-calibration. When we further assume that the aspect ratio is known and the principal point is fixed during the sequence then one homography yields camera parameters, and when the aspect ratio is assumed to be unknown with fixed principal point then two homographies are enough. In the case of a fixed principal point, we suggest a method for obtaining the calibration parameters by searching the space of the principal point. If this is not the case, then nonlinear iteration is applied. The algorithm is implemented and validated on several sets of synthetic data. Also experimental results for real images are given. key words: auto-calibration, rotating and zooming camera, camera calibration, homography