Figure 10.

Blur gradients and perception of planar 3D shape. (A) Response icons for five of the nine possible responses. These are the five planar responses. There were also four wedge responses (Figure 11A). (B) Experimental results with vertical and horizontal blur gradients; the upper panel is for vertical gradients and the lower for horizontal gradients. In both panels, the proportion of responses of a particular category (green for ground plane, black for ceiling plane, red for right-side forward, and blue for left-side forward) is plotted as a function of the magnitude of the blur gradient. The abscissa values are the maximum values of σ in Equation 6. The data have been averaged across the five observers. We calculated the departure of the data from equal distribution of responses among the geometrically plausible alternatives for each value of m. Specifically, we computed goodness-of-fit χ² for the observed responses relative to responses distributed equally among five alternatives. When the blur gradient was vertical, we considered observed responses relative to the alternatives of “flat,” “ground,” “ceiling,” “convex” (horizontal vertex), and “concave” (horizontal vertex). When the gradient was horizontal, we considered responses relative to “flat,” “left,” “right,” “convex” (vertical vertex), and “concave” (vertical vertex). All χ² values were statistically significant (p < 0.01), except for m = 1, horizontal gradient, sharp center. This means that responses were not randomly distributed among the planar alternatives.