We identify two forms of error in stereoscopic vision: imprecision, which results from digitization of the images and imperfect knowledge of the system geometry and location in space; and uncertainty, generated by random sensor noise and the correspondence problem. Traditional approaches have either ignored one of the two sources of error or merged them into a single representation, namely a point probability distribution in space. Furthermore, unrealistic assumptions have been made on this distribution, which are constantly violated in practice. We propose a new mathematical framework, based on the random closed set theory, that allows for an explicit representation of both sources of error. Digitization and parameter imprecision produce an imprecision set in space, whereas noise and potential matching errors make the location of this set uncertain, hence probabilistic. We provide a practical method for estimating the probability distribution of this random set and demonstrate the efficiency of this approach on 3-D scene reconstruction from multiple stereoscopic views: errors in the final 3-D map are guaranteed to decrease in a statistical sense as additional views are processed. We introduce a connection machine parallel implementation where the 3-D space is represented in an octree. Experimental results on real images are presented.