Distant surfaces are occluded by nearer surfaces to different extents in the two eyes, leading to the existence of unpaired image points visible in one eye and not the other. An ecological analysis of the real world situation that could have given rise to such unpaired points indicates the presence of a depth constraint zone, defined by visibility lines between which possible real world points must lie. The leading edge of this zone starts at the edge of a fused binocular occluding surface and recedes linearly with increases in horizontal distance to the unpaired point. Psychophysical evidence indicates that the human visual system makes use of this unpaired information in a remarkably adaptive manner, showing an increase in perceived depth for increasing horizontal separations between the unpaired target and fused edge, at least over a significant angular range (approx. 25-40 min arc). We also show that unpaired points in binocular images can lead to the formation of subjective occluding contours and surface having the qualitatively appropriate sign of depth. Furthermore, we show that the visual system could not recover depth of unpaired points camouflaged from the other eye against silhouettes. Our findings indicate that the visual system makes use of occlusive relations in the real world to recover depth, contour, and surface from unpaired points. The fact that such processes must utilize eye-of-origin information implies that they share this essential characteristic with classical or Wheatstone stereopsis. The necessity of eye-of-origin information also suggests that the processing may begin relatively early in cortical visual processing, possibly as early as V1. Finally, the novel emergence of subjective occluding contours from unpaired monocular stimuli raises the possibility that this process is mediated by visual experience, built up by the association of unpaired points and occluding contours.