Mathematical Analysis of the Visual Illusion

Some geometrical visual illusions are analyzed in terms of the perceptual field. Psychological distance, which differs from physical distance, is introduced to explain the illusions. A theory is proposed in which the psychological distance is represented as a function of the field potential induced by the stimulus figure. By defining the psychological distance and line, the straight line and the length in the figure can be determined, and geometrical visual illusions can be explained as distortions of the metric of the perceptual field.