Three Characterizations of 3D Reconstruction Uncertainty with Bounded Error

Considering a stereoscopic visual system, this paper deals with the error involved by a 3D reconstruction process. If image pixels are seen as surfaces instead of points, interval analysis provides bounding boxes in which the reconstructed 3D point lies with certainty. This paper presents a method which refine this bounding box and gives a tighter approximation of the error. Using bisection, and a reprojection test in the image planes, the space in which the 3D reconstructed point may be located is given as an octree. This is achieved through the resolution of a set inversion problem using the SIVIA algorithm. For a lighter manipulation of the result, an englobing ellipsoid is deduced from this approximation. Finally the three models are tested on a recognition process for a humanoid robot.