A simple technique for self-calibration

This paper introduces an extension of Hartley's self-calibration technique based on properties of the essential matrix, allowing for the stable computation of varying focal lengths and principal point. It is well known that the three singular values of an essential must satisfy two conditions: one of them must be zero and the other two must be identical. An essential matrix is obtained from the fundamental matrix by a transformation involving the intrinsic parameters of the pair of cameras associated with the two views. Thus, constraints on the essential matrix can be translated into constraints on the intrinsic parameters of the pair of cameras. This allows for a search in the space of intrinsic parameters of the cameras in order to minimize a cost function related to the constraints. This approach is shown to be simpler than other methods, with comparable accuracy in the results. Another advantage of the technique is that it does not require as input a consistent set of weakly calibrated camera matrices (as defined by Harley) for the whole image sequence, i.e. a set of cameras consistent with the correspondences and known up to a projective transformation.