An algorithm is proposed for solving the stereoscopic matching problem. The algorithm consists of five steps: (1) Each image is filtered at different orientations with bar masks of four sizes that increase with eccentricity; the equivalent filters are one or two octaves wide. (2) Zero-crossings in the filtered images, which roughly correspond to edges, are localized. Positions of the ends of lines and edges are also found. (3) For each mask orientation and size, matching takes place between pairs of zero-crossings or terminationss of the same sign in the two images, for a range of disparities up to about the width of the mask's central region. (4) Wide masks can control vergence movements, thus causing small masks to come into correspondence. (5) When a correspondence is achieved, it is stored in a dynamic buffer, called the 2 1/2-D sketch. It is shown that this proposal provides a theoretical framework for most existing psychophysical and neurophysiological data about stereopsis. Several critical experimental predictions are also made, for instance about the size of Panum's area under various conditions. The results of such experiments would tell us whether, for example, cooperativity is necessary for the matching process.