A Mathematical Model of Perception with Reference to Peripheral Vision and its Application to the Hermann Grid Illusion

Central vision and peripheral vision are two of main components of visual perception. The functional differences between the two visions are considered with two points of view: the physiological receptive field and the psychological perceptive field.

The authors propose a retinal model of lateral inhibition. The output is discrete summation of ganglion cell responses through the Difference of Gaussian (DOG) function of the coupling width. The coupling width is given by the size of receptive field, according to Fisher’s findings that the distribution of the ganglion cell density decreases from the fovea to the peripheral area. Sampling points of the summation correspond to the positions of the ganglion cells, so that a number of points in all the same in each receptive field. The coupling width was determined by the data of Jung and Spillmann’s (1970) psychological experiment. As an application of this model, the Hermann grid illusion is quantitatively explained.