Unconstrained stereoscopic matching of lines

The computation of horizontal binocular disparities used in stereoscopic depth perception depends upon the identification of corresponding features in the two retinal images. In principle, binocular matching is a two-dimensional problem that considers matches in all possible meridians. Normally, constraints such as end points or crossing points limit the direction and magnitude of matches. If matching is unconstrained, such as is the case with long lines, it is completely ambiguous. Under these conditions the default match will be determined by the operating range, or upper disparity limit, of matchable vertical and horizontal disparities. We computed the operating range of vertical matches for stereoscopic depth as a function of line orientation. Our results suggest that the two-dimensional operating range is anisotropic for vertical and horizontal disparity and that unconstrained matches are not based upon either epipolar geometry or nearest neighbor constraints, but rather the mean of disparity estimates within the operating range for binocular matches. This operating range can be extended vertically when matches are constrained by image primitives.