Stevens's brightness law, contrast gain control, and edge integration in achromatic color perception: a unified model.

The brightness of an isolated test patch is related to its luminance by a power law having an exponent of about 1/3, a result known as Stevens's brightness law. The brightness law exponent characterizes the rate at which brightness grows with luminance and can thus be thought of as an "exponential" gain factor. We studied changes in this gain factor for incremental and decremental test squares as a function of the size of a surrounding frame of homogeneous luminance. For incremental targets, the gain decreased as an approximately linear function of the frame width. For decremental targets, the gain increased as an approximately linear function of the frame width. We modeled the brightness of the frame-embedded target with a quantitative theory based on the assumption that the target brightness is determined by the sum of achromatic color induction signals originating from the inner and outer edges of the surround, a theory that has previously been used to account for the results of several other brightness matching experiments. To account for the frame-width-dependent gain changes observed in the present study, we elaborate this edge integration theory by proposing the existence of a cortical contrast gain control mechanism by which the gains applied to neural edge detectors are influenced by the responses of other edge detectors responding to the nearby edges.