A model for contrast discrimination with incremental and decremental test patches

Whittle [Vision Research, 26, 1677 (1986)] has shown that the metric of contrast W = delta L/Lmin (delta L = difference in luminance between test patch and background, Lmin = the smaller of the luminance of the background or test patch) is able to provide a unifying description of the pattern of contrast discrimination thresholds for pairs of test patches set against a common background. In particular the metric W unifies the pattern of discrimination thresholds for both increment and decrement pairs. We argue that while W provides a good mathematical description of Whittle's data it is functionally implausible since it implies that the component of the stimulus which sets the adaptational level for increments is different from that which sets the adaptational level for decrements. We argue that the metric G = ln(L/Lb) (L = test patch luminance, Lb = background luminance) is physiologically more plausible than W and show that G can provide at least as good a fit as W to Whittle's data when incorporated in a transfer function of the form RG = kG1-n, with n set to 0.69. The fit to the data can be improved still further if a parameter representing the non-linearity in the gain-luminance function at low luminances is included in the RG equation. The theoretical implications for retinal gain mechanisms are discussed.