Image regions corresponding to partially hidden objects are enclosed by two types of bounding contour: those inherent to the object itself (intrinsic) and those defined by occlusion (extrinsic). Intrinsic contours provide useful information regarding object shape, whereas extrinsic contours vary arbitrarily depending on accidental spatial relationships in scenes. Because extrinsic contours can only degrade the process of surface description and object recognition, it is argued that they must be removed prior to a stage of template matching. This implies that the two types of contour must be distinguished relatively early in visual processing and we hypothesize that the encoding of depth is critical for this task. The common border is attached to and regarded as intrinsic to the closer region, and detached from and regarded as extrinsic to the farther region. We also suggest that intrinsic borders aid in the segmentation of image regions and thus prevent grouping, whereas extrinsic borders provide a linkage to other extrinsic borders and facilitate grouping. Support for these views is found in a series of demonstrations, and also in an experiment where the expected superiority of recognition was found when partially sampled faces were seen in a back rather than a front stereoscopic depth plane.