In binocular viewing of natural three-dimensional scenes, occlusion relationships between objects at different depths create regions of the background that are visible to only one eye. These monocular regions can support depth perception. There are two viewing conditions in which a monocular region can be on the nasal side of a binocular surface-(a) when a background surface is viewed through an aperture and (b) when a region is camouflaged against the background in one eye's view. We created stimuli with a monocular region using complex textures in which camouflage was not possible, and for which there was no physical aperture. For these stimuli, observers perceived a strong phantom contour in near depth at the edge of the monocular region, with the monocular texture perceived behind at the depth of the binocular surface. Depth-matching with a probe showed that the depth of the phantom occluding surface was as precise as for stimuli with regular binocular disparity. Monocular regions of texture on the opposite (temporal) side of the binocular surface were perceived behind, as predicted by occlusion geometry, and there was no phantom surface. We discuss the implications for models of da Vinci stereopsis and stereoscopic edge processing, and consider the involvement of a form of Panum's limiting case. We conclude that the visual system uses a combination of occlusion geometry and complex matching to precisely locate edges in depth that lack a luminance contour.