Lightness scale from image intensity distributions

A lightness scale is derived from a theoretical estimate of the probability distribution of image intensities for natural scenes. The derived image intensity distribution considers three factors: reflectance; surface orientation and illumination; and surface texture (or roughness). The convolution of the effects of these three factors yields the theoretical probability distribution of image intensities. A useful lightness scale should be the integral of this probability density function, for then equal intervals along the scale are equally probable and carry equal information. The result is a scale similar to that used in photography or by the nervous system as its transfer function.