Rigorous accuracy bounds for calibrated stereo reconstruction

We deal with the problem of obtaining rigorous bounds to the position of 3-D points computed by stereo triangulation when both the camera matrix and the image points are affected by uncertainty. By "rigorous bounds" we mean that the true unknown 3-D points are guaranteed to lie within the given intervals. To this end we first model the calibration process by assuming a bounded error in the localization of the reference points in the image, then we narrow the entries of the camera matrix. Finally, we apply triangulation and obtain cuboids that bound points coordinates. We concentrated two state-of-the art methods for the solution of linear system of equations, namely INTLAB's and Shary's methods. Empirical comparison shows that the latter always provides sharper error bounds, in this application.