The effect of luminance variation on the apparent position of an edge

A gray outline against a white (or black) ground appears to deviate when one of the divided regions turns into black (white). The direction of shift is not predictable on the basis of luminance profile and polarity contrast of this part of contour, called gray edge (to indicate a stepwise gradient from black to gray and from gray to white). Rather, it appears to depend on the luminance profiles of the collinear regions: A gray edge shifts toward the dark side whenever collinear with a gray line traversing a white ground. The same gray edge takes the opposite direction whenever it extends against a black ground. This rule proved to be successful in predicting the illusory convergence of the sides of a square that formed the stimuli of the first experiment, but the magnitude of the phenomenon was affected by luminance ratios and polarity contrasts of the gray edges, in agreement with the findings of the experiments on gray or blurred edge misalignment. A second experiment tested some hypotheses predicting the combined effects of two or more distorting sources. These hypotheses, suggested by the physical theory of vector sum, were partially disproved. A new model is proposed that assumes different ways of integrating local distortions. The third experiment tested predictions of how distorting pulses in opposite directions combine. The illusory misplacement of edge studied in this experiment is proposed as the underlying phenomena of the café wall illusion, the hollow square illusion, and other illusory phenomena observed with blurred areas. A connection with the induction grid phenomena is hypothesized.