Extremal edges (EEs) are projections of viewpoint-specific horizons of self-occlusion on smooth convex surfaces. An ecological analysis of viewpoint constraints suggests that an EE surface is likely to be closer to the observer than the non-EE surface on the other side of the edge. In two experiments, one using shading gradients and the other using texture gradients, we demonstrated that EEs operate as strong cues to relative depth perception and figure-ground organization. Image regions with an EE along the shared border were overwhelmingly perceived as closer than either flat or equally convex surfaces without an EE along that border. A further demonstration suggests that EEs are more powerful than classical figure-ground cues, including even the joint effects of small size, convexity, and surroundedness.