Mental rotation in depth as the optical difference of pictures

Abstract

Mental rotation in depth is a facile interpretation of the Shepard-Metzler effect for perspective pictures. Evidence for that interpretation is given by the linear trends of mean response times over depicted angular disparity, as is found for pairs of pictures of complex solids. Numeric simulation has shown how angular disparity in depth correlates with difference in the profiles of figures in picture pairs. (The profile of a figure is the area contained in its outline against the background, somewhat like its solid angle from a normal view.) Depicted angular disparities in three dimensions are tightly linked to differences in profile across picture pairs, which can be quantified as the autocorrelation coefficient of their difference image. This simple statistic predicts differences in response times for judgments of ‘same’ and ‘different’, and numeric averages over the same statistic mimic the linearity of trend which is characteristic of the Shepard-Metzler effect. The difference in picture profiles is an intervening variable between angular disparity and mean response times which accounts for ‘mental rotation in depth’. An extended demonstration is given of this experimental artifact.