Abstract

Given two well-defined and reasonable assumptions, all nonlinear color vision models reduce to the form of a vector model under constraints imposed by conditions required for measurement of color luminance difference thresholds. The first assumption is linearization of the visual transformation equations. This assumption applies to small (threshold-level) perturbations in vision. Linearization is equivalent to saying that the linear weighting coefficients of the resultant vector model are partial derivatives of the nonlinear functions. The second assumption is that the variance in visual sensation is the same for test stimulus conditions as it is for reference stimulus conditions in a difference threshold experiment. Although this assumption is known to fail for individual observers, it is valid for the average observer if between-observer variability outweighs within-observer variability. This second assumption leads to an analytic form of the detectability index (d') that is equivalent to a vector magnitude. The present paper reports how these two assumptions formally constrain nonlinear color vision models to generate a unique set of predictions for a wide variety of color and luminance difference threshold data. An important consequence of the theory is that any nonlinear color vision model, once defined, is constrained to predict chromaticity discrimination contours, Stiles’s field sensitivity curves, threshold-vs-radiance curves, threshold-vs-wavelength functions, etc., with no additional assumptions or degrees of freedom. This constraint is illustrated for a general logarithmic color vision model.

© 1985 Optical Society of America