A test of a perspective theory of geometrical illusions.

Three-dimensional Miiller-Lyer figures were used in three experiments to test a perspective theory of geometrical illusions. The real depth cues were in one of two orientations, designed either to support or to oppose the action of the perspective depth cues hypothesized by the perspective theory. If any illusion is obtained with these three-dimensional figures, the theory implies, its magnitude should be different in the two orientations. In fact, a substantial illusion was obtained, but the difference between the two orientations was small and opposite to the prediction of perspective theory. Perspective explanations of geometrical illusions have a long history,' but only recently has this approach received the conceptual clarification needed to open it to experimental analysis. Gregory's formulation of perspective theory rests on two main assumptions.2 First, geometrical-illusion figures such as the MiillerLyer ones in Figure lab are considered two-dimensional projections of three-dimensional figures; thus, they contain perspective cues for depth. Second, these cues are assumed to trigger a constancy-scaling mechanism that corrects for decrease in the retinal image with increasing distance. Those parts of the figure that would be more distant in the three-dimensional representation are enlarged and those that would be closer are diminished, in accord with size constancy. This version of perspective theory has been applied especially to Received for publication April 27, 1970. The first author, who is now at the University of Wisconsin, was supported by a postdoctoral fellowship, MH39369-02, from the National Institute of Mental Health. Support was also provided by a National Science Foundation grant, GB-6666, to the second author. The authors thank Susan Keeve for her help. 1 R. S. Woodworth, Experimental Psychology, 1938, 644-645; R. L. Gregory, Eye and Brain, 1966, 141-156. 2R. L. Gregory, Distortion of visual space as inappropriate constancy scaling, Nature, 199, 1963, 678-680; R. L. Gregory. Seeing in depth, Nature, 207, 1965, 16-19.