Relative Spatial Expansion and Contraction within the Müller-Lyer and Judd Illusions

The shaft portions of Müller-Lyer (M-L) figures, one-ended M-L figures, Judd figures, and their respective control (tails-up) figures were divided by subjects into eight equal-appearing intervals by means of successive bisections. For most of the control stimuli the length of the left half of the shaft tended to be overestimated relative to the length of the right side. For the tails-out version of the M-L figure, there was relative overestimation of segments of the shaft adjacent to the tails, while for the tails-in version there was relative underestimation of these segments. These results indicate that the distortion of perceived length in the M-L illusion is not distributed evenly along the shaft. For the one-ended M-L figures the apparent overestimations and underestimations extended further along the shaft than for the standard figures. For the Judd figure perceived length varied systematically along the length of the shaft from underestimation near the tails-in end of the figure to overestimation near the tails-out end. These results are contradictory to the hypothesis that the M-L illusion results from inappropriate size scaling produced through the operation of size-constancy mechanisms, since this conjecture would predict uniform expansion or contraction. The results are compared with findings that localization responses are accurate for M-L figures but biased for one-ended M-L figures and Judd figures.