Reconstruction from two views using approximate calibration

We consider the problem of Euclidean reconstruction from two perspective images. This problem is well studied for calibrated cameras, and good algorithms are known. On the other hand, if the cameras are known to have square pixels (no skew and unit aspect ratio) then the problem is also theoretically solvable, provided an estimate of the principal point is provided. The focal lengths of the cameras may be computed from the fundamental matrix, and then a calibrated reconstruction algorithm applied. In reality, however, it has been shown that this process is quite sensitive to the computed fundamental matrix and the assumed position of the principal point. In fact, sometimes the estimate of the focal length fails, and so Euclidean reconstruction is impossible using this method. In this paper, we investigate the cause of this problem, and suggest an algorithm that more reliably leads to a reconstruction. It is unnecessary to know the exact location of the principal point, provided weak bounds on the principal point locations, and the focal lengths of the cameras are provided. The condition that points must lie in front of the cameras gives a further constraint. It is shown that by suffering only a very small degradation in residual pointreprojection error, it is possible to compute a fundamental matrix that always leads to a plausible focal length estimate, and hence Euclidean reconstruction.