Reconstruction from two views using approximate calibration

The problem of Euclidean reconstruction from two perspec-tive images 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 ma-trix, however, it is quite sensitive to the computed fundamen-tal 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 reconstruc-tion. Weak bounds on the principal point locations, and the focal lengths of the cameras and the condition that points must lie in front of the cameras give enough constraint to compute a fundamental matrix that always leads to a plau-sible focal length estimate, and hence Euclidean reconstruc-tion that suffers only a very small degradation in residual point-reprojection error. 1