Abstract
Luminance is the standard for measuring the intensity of lights, and the luminous efficiency curve V(l) defines how radiance is weighted across different wavelengths. Yet, luminance is defined mainly by procedures that emphasize high temporal (minimum flicker) or high spatial (minimum border) frequencies, where the S-cones are known to be much less sensitive. It has long been known that human heterochromatic brightness perception deviates markedly from luminance. For example, colorful patches look brighter than achromatic patches of equal luminance, and hue also has an effect on brightness (the Helmholtz-Kohlrausch effect). Some appearance models take this into account, but they typically take luminance as their starting point and typically are computationally rather complex.
We collected behavioural data from 16 participants making judgements of perceived brightness. Participants ranked, in each trial, 16 patches varying in hue, saturation and intensity. We compared the empirical rankings with that predicted by luminance, a simple non-linear model taking the weighted maximum of three color channels (maxRGB), and several common color appearance models.
The simple nonlinear model maxRGB predicts the rankings significantly better than luminance (82% correct predictions for maxRGB compared to 77.8% for luminance (t(15)=4.56, p<0.0005). The various color appearance models have intermediate accuracies. Visible radiance performed about equally well as luminance. The weights fitted to the maxRGB model differ strongly from the weights used by luminance. They closely agree with weights describing perceptually unique yellow.
We conclude that a simple non-linear model can serve as an improvement over the V(l) defined luminance for describing the brightness of hetero-chromatic stimuli.