For the past hundred years, figure-ground cues (e.g. convexity, area, surroundedness, lower region, familiarity) have been known to affect judgments of which region is “figure” and which is “ground” . Put another way, the shape of the contour influences which region is seen to be the occluding surface and which is seen to be the occluded surface. For nearly this entire period, it has been assumed that figure-ground cues provide only "ordinal depth information"- information about which imaged surface is nearer, but nothing about how much the surfaces are separated in depth. However, recent findings have established that figure-ground cues can affect percepts of "metric depth"- how far two surfaces are separated in depth- when another metric depth cues is present (Burge, Peterson, & Palmer, 2005; Bertamini et al, 2008). This result is surprising because ordinal depth information constrains only the sign of depth between pairs of surfaces, so the ordinal cue is either consistent with the metric cue and provides no additional numerical information, or the cues are inconsistent and it is not obvious how to resolve the conflict.

We reexamined the depth information provided by convexity in the natural environment by performing a statistical analysis of natural scenes. We found that i) metric depth information is available from the shape of image regions and ii) that depth steps across surfaces with convex silhouettes are likely to be larger than depth steps across surfaces with concave silhouettes. Even though there is no geometric relationship between the shape of an occluder's silhouette and metric depth, there exists a probabilistic relationship, presumably because most objects are globally convex.

To find out if humans exploit this relationship we performed a psychophysical experiment. For a given metric depth signaled by binocular disparity, observers perceived more depth when the near surface’s silhouette was convex rather than concave. We estimated the depth distributions observers used in making those judgments: They were similar to the natural-scene distributions. Our findings show that convexity should be reclassified as a quantitative depth cue. They also suggest that the dichotomy between metric and non-metric depth cues is a false one and that many, perhaps all, cues should be evaluated with respect to natural-scene statistics. Finally, the findings provide an ecological explanation for why figure-ground cues modulate disparity-sensitive cells in visual cortex.