Amodal completion of coincidentally occluded angles: a matter of visual approximation

In the Gerbino illusion a regular but coincidentally occluded polygon appears distorted. Such a display represents a critical condition for amodal completion (AC), in which the smooth continuations of contour fragments—however small—conflict with their possible monotonic interpolation. Smoothness and monotonicity are considered the fundamental constraints of AC at the contour level. To account for the Gerbino illusion we contrasted two models derived from alternative AC frameworks: visual interpolation, based on the literal representation of contour fragments, vs. visual approximation, which tolerates a small misorientation of contour fragments, compatible with smoothness and monotonicity constraints. To measure the perceived misorientation of sides of coincidentally occluded angles we introduced a novel technique for analyzing data from a multiple probe adjustment task. An unsupervised cluster analysis of errors in extrapolation and tilt adjustments revealed that the distortion observed in the Gerbino illusion is consistent with visual approximation and, in particular, with the concatenation of misoriented and locally shrinked amodally completed angles. Implications of our technique and obtained results shed new light on visual completion processes.