Quantitative properties of achromatic color induction: an edge integration analysis.

Edge integration refers to a hypothetical process by which the visual system combines information about the local contrast, or luminance ratios, at luminance borders within an image to compute a scale of relative reflectances for the regions between the borders. The results of three achromatic color matching experiments, in which a test and matching ring were surrounded by one or more rings of varying luminance, were analyzed in terms of three alternative quantitative edge integration models: (1) a generalized Retinex algorithm, in which achromatic color is computed from a weighted sum of log luminance ratios, with weights free to vary as a function of distance from the test (Weighted Log Luminance Ratio model); (2) an elaboration of the first model, in which the weights given to distant edges are reduced by a percentage that depends on the log luminance ratios of borders lying between the distant edges and the target (Weighted Log Luminance Ratio model with Blockage); and (3) an alternative modification of the first model, in which Michelson contrasts are substituted for log luminance ratios in the achromatic color computation (Weighted Michelson Contrast model). The experimental results support the Weighted Log Luminance Ratio model over the other two edge integration models. The Weighted Log Luminance Ratio model is also shown to provide a better fit to the achromatic color matching data than does Wallach's Ratio Rule, which states that the two disks will match in achromatic color when their respective disk/ring luminance ratios are equal.