Visual interpolation is not scale invariant

According to the scale-dependence hypothesis, the visual interpolation of contour fragments depends on the retinal separation of endpoints: as the retinal size of a partially occluded angle increases, the interpolated contour gradually deviates from the shortest connecting path and approaches the shape of the unoccluded angle. In the field model (Fantoni and Gerbino, 2003 and Fantoni et al., 2005), as the retinal size increases the strength of good continuation increases while the strength of the minimal-path tendency decreases. To test the scale-dependence hypothesis—as well as other hypotheses connected to inclusion, support-ratio dependence, and extended relatability—we ran two experiments using the probe localization technique. Stimuli were regular polygons with rectilinear contours bounding symmetrically occluded angles. Retinal size was manipulated by changing viewing distance. Observers were asked to judge if a probe, briefly superposed on the occlusion region, was inside or outside the amodally completed angle. Retinal size strongly influenced the penetration of interpolated trajectories in the predicted direction. However, support ratio and interpolated angle size interacted with retinal size, consistently with the idea that unification factors are effective within a spatial window. We modified the field model to include the size of such a window as a new parameter and generated model-based trajectories that fitted empirical data closely.