Using stereo geometry towards accurate 3D reconstruction

This paper addresses the problem of threedimensional reconstruction and how the geometry of the stereo vision system affects the quality of such a reconstruction. We have considered the general case of non calibrated cameras with approximately known intrinsic parameters. The latter could be known either from previous experiments or from the manufacturer´s specifications. In particular, the paper aims at finding the best geometric configuration of the stereo vision system(rotation and translation between the two cameras) that is the least sensitive to errors on the intrinsic parameters. Given that in most cases, in robotics for instance, we have the freedom to set-up the geometry of the stereo vision system, finding how cameras´ geometry interacts with errors from different sources is a central issue. Furthermore, when the intrinsic parameters are completely unknown, we have used a single constraint from the scene that has allowed us to calculate the focal length and therefore, the Euclidean reconstruction. We have used extensive simulations where the stereo vision geometry has ranged from pure translation to general 3D motion. The obtained results have clearly shown that a pure translation is always better, as it is not significantly affected by errors on the intrinsic parameters. When assuming that the intrinsic parameters are not known, the use of the perpendicularity constraint from the scene has made it possible to avoid the classical and tedious calibration process.