A closed-form solution for a two-view self-calibration problem under fixation

It is well known that the epipolar geometry between two uncalibrated perspective views is completely encapsulated in the fundamental matrix. Since the fundamental matrix has seven degrees of freedom (DOF), self-calibration is possible if at most seven of the intrinsic or extrinsic camera parameters are unknown by extracting them from the fundamental matrix. This work presents a linear algorithm for self-calibrating a perspective camera which undergoes fixation, that is, a special motion in which the camera's optical axis is confined in a plane. Since this fixation has four degrees of freedom, which is one smaller than that of general motion, we can extract at most three intrinsic parameters from the fundamental matrix. We here assume that the focal length (1 DOF) and the principal point (2 DOF) are unknown but fixed for two views. It will be shown that these three parameters are obtained from the fundamental matrix in an analytical fashion and a closed-form solution is derived. We also characterize all the degenerate motions under which there exists an infinite set of solutions.