A mathematical theory of optical illusions and figural aftereffects

If it is assumed that spurious enhancement of receptive field excitations near the intersection of image lines on the retina contributes to the cortical determination of the geometry of two-dimensional figures, an equation based on the least-squares fit of data points to a straight line-can be obtained to represent theapparent line. Such a fit serves as anextreemum on the precision with which a data set can be represented by a straight line. The disparity between theapparent line and the actual line that occurs in the case of peripheral (and to a lesser degree in more central regions of the retina) vision is sufficient to produce the perceptual errors that occur in the Poggendorff, Hering, and Mueller-Lyer illusions. The magnitude of the Poggendorff illusion as a function of the line angle is derived and experimentally tested. Blakemore, Carpenter, and Georgeson’s (1970) experimental data on angle perception are shown to fit this same function. Theapparent curve is derived for the Hering illusion. The Mueller-Lyer illusion is found to be a variation of the Poggendorff illusion. The equations are further developed and used to derive Pollack’s (1958) experimental results on figural aftereffects. The results involve onlyone experimentally determined coefficient that can be evaluated, within the limits of experimental error, in terms of physiological data. The use of these concepts provides a foundation for the abstract modeling of the initial phases of the central nervous system data reduction processes, including receptive field structure, that is consistent with the physiological limitations of the retina as a source of visual data, as well as with the findings of Hubel and Wiesel (1962).