Extremal edges: A powerful cue to depth and figure-ground organization

Extremal edges (EEs) are viewpoint-specific tangent points of self-occlusion on smoothly curved, convex surfaces. A simple ecological analysis of viewpoint constraints shows that the curved surface producing an EE is likely to be closer to the observer than the surface on the other, non-EE side. Four experiments examined whether EEs and 3D surface convexity operate as cues to depth and figure-ground organization. Experiment 1 used simple luminance profiles (the positive half of a sinusoid) to simulate shading gradients in simple bipartite displays. The results showed that observers are very likely to perceive EEs as closer and figural, and that EEs are more potent than surface convexity alone. Because the argument from general viewpoint is strictly about the geometry of the scene, independent of the kind of visual information that specifies the existence of an extremal edge, it follows that the bias toward perceiving EE surfaces as closer should hold regardless of what visual property specifies the extremal edge. To test this hypothesis, Experiment 2 used EEs rendered via texture gradients of checkerboard surfaces that contained neither shading and nor occlusion cues. The results of this experiment showed a strong bias toward perceiving the EE side as closer and figural from texture gradients. Experiment 3 used ray-traced images of EE shading patterns on simple convex "pillow-like" surfaces to study the combination of EEs with Gestalt cues of smaller size and 2D edge convexity. EEs largely dominated the other figural cues (2D edge convexity, size, and their combination) studied in this experiment. Experiment 4 used shading gradients in ray-traced images of surfaces of revolution to study the effects of EEs versus other individual figure-ground cues (region size, 2D edge convexity, surroundedness, and familiarity). The results show that EEs produce stronger effects than all of these factors. The data clearly demonstrate that extremal edges are among the most powerful cues to depth across a contour and to figure-ground organization.