A gain-control theory of binocular combination.

In binocular combination, light images on the two retinas are combined to form a single "cyclopean" perceptual image, in contrast to binocular rivalry which occurs when the two eyes have incompatible ("rivalrous") inputs and only one eye;s stimulus is perceived. We propose a computational theory for binocular combination with two basic principles of interaction: in every spatial neighborhood, each eye (i) exerts gain control on the other eye's signal in proportion to the contrast energy of its own input and (ii) additionally exerts gain control on the other eye's gain control. For stimuli of ordinary contrast, when either eye is stimulated alone, the predicted cyclopean image is the same as when both eyes are stimulated equally, coinciding with an easily observed property of natural vision. The gain-control theory is contrast dependent: Very low-contrast stimuli to the left- and right-eye add linearly to form the predicted cyclopean image. The intrinsic nonlinearity manifests itself only as contrast increases. To test the theory more precisely, a horizontal sine wave grating of 0.68 cycles per degree is presented to each eye. The gratings differ in contrast and phase. The predicted (and perceived) cyclopean grating also is a sine wave; its apparent phase indicates the relative contribution of the two eyes to the cyclopean image. For 48 measured combinations of phase and contrast, the theory with only one estimated parameter accounts for 95% of the variance of the data. Therefore, a simple, robust, physiologically plausible gain-control theory accurately describes an early stage of binocular combination.