Identifying the visual cues that determine relative depth across an image contour (i.e., figure-ground organization) is a central problem of vision science. In this paper, we compare flat cues to figure-ground organization with the recently discovered cue of extremal edges (EEs), which arise when opaque convex surfaces smoothly curve to partly occlude themselves. The present results show that EEs are very powerful pictorial cues to relative depth across an edge, almost entirely dominating the well-known figure-ground cues of relative size, convexity, shape familiarity, and surroundedness. These results demonstrate that natural shading and texture gradients in an image provide important information about figure-ground organization that has largely been overlooked in the past 75 years of research on this topic.