Differential thresholds in colour perception: a consequence of retinal processing and photoreceptor non-linearities

D.Alleysson & J.Hérault

Laboratoire des Images et des Signaux, Institut National polytechnique, 46 avenue Félix Viallet, 38031 Grenoble, France.

We propose here a model for just noticeable differences in colour. We start from the data of six observers found in three different studies. Observer PGN described first by DL. MacAdam [1942, Journal of Optical Society of America, 32], observers WRJB and DLM found in Brown & MacAdam [1949, JOSA, 39] and observers GF,AR and GW found in Wyszecki & Fielder [1971, JOSA, 61, 9].

Y.LeGrand [Translated by K. Knoblauch, 1994, Color Research and Application, 19, 4] showed that the differential thresholds of colour in the LMS (Long Middle and Short wavelength) space follows a V-shaped curve for the chromatic variables L and M. This property was confirmed by the study of Nagy & al. [1987, JOSA, 4, 4] for the six observers.

In our model, the stimuli, considered in the LMS space, are converted after photoreceptor non-linearity into a lms space (l=L/(L+L₀),... ). The retinal circuits combine lms signals into a multiplexing of two colour-opposition "c_i" and one achromatic "a" channels, providing a "perceptual space" (a, c1, c2). Supposing that the just-noticeable-differences are uniformly distributed in this space as spheres of constant radii, the backward transformations of these spheres into the LMS space should produce ellipsoids, similar to those observed in perceptual experiments.

By using the experimental data, we parametrize this model in order to find a best fit of the data. We show that this produces the expected behaviour, leading also to the explanation of other results such as the V-shaped differential thresholds.