Symmetrical Appearance of Bright and Dark Mach Bands from an Exponential Illumination Gradient

Observers viewed two families of Mach-band-inducing stimuli in which the luminance distribution G of the gradient region varied among stimuli. In one family, the function G was varied almost continuously from a convex, through a linear and an exponential, to an even more pronounced concave form. The exponential distribution was selected as appearing the most symmetrical in terms of the placement and appearance of the bright and dark Mach bands. The second family was a series of power functions in which the exponent that determines G varied between 1.47 and 12.50. Contrary to possible expectations based on Stevens’s power law for brightness perception, these stimuli appeared considerably less symmetric than the exponential stimulus. These results are consistent with the hypothesis of a logarithmic transformation prior to a linear stage of lateral inhibitory interaction in the human visual system.