MODELS of stereopsis typically assume that all the information about stereoscopic depth is contained in the disparity field, that is, the positional differences of image features that arise from surfaces visible to both eyes. But such models have difficulty in resolving image regions containing occlusions, because a portion of the occluded surface is visible to only one of the two eyes (’half-occlusions’)1. Here I present displays revealing an unexpected relationship between interocular differences in image position and occluding contours. The partial occlusion of contours can give rise to both horizontal and vertical image differences that are not disparities. The results show that the visual system interprets these image differences as signalling the presence of occluding contours. Even when a single line segment serves as a binocular target, subjective contours form that can appear both oriented and in depth. These local subjective contours have a strong tendency to interact cooperatively and form global contours not present in the monocular images. These and other findings2-4 show that stereoscopic processing actively decomposes vertical and horizontal image differences into disparities and half-occlusions. The two sources of information are complementary : while disparity provides relative depth information about surface features visible to both eyes, half-occlusions provide information to segment the visual world into coherent objects at object boundaries.