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Perceptual contrast in the Receptor Noise Limited (RNL) model is calculated as the response of opponent processes which themselves are ‘fed’ by the stimulation of each receptor channel in relation to the channel specific noise (or Weber fraction in the case of the log-transformed RNL model used in QCPA):

in the case of two opponent mechanisms X1 & X2 (i.e. a trichromatic visual system) we can calculate them as above where ω is the weber fraction (or channel specific noise in the linear RNL model!) of each the M(medium wave), L(long wave) and S(short wave) receptor channels and f(i)=ln(qi). From Kelber et al. 2003.

This means that we can plot any colour perceived by a trichromat in a XY coordinate system where each axis corresponds to the stimulation of an opponent channel:

The tri-chromatic RNL colour space. For a tetra-chromatic colour space an additional Z-axis is added or in the case of di-chromacy the space becomes a line. The distance between any two points can be expressed as the Euclidian distance (ΔS).


Kelber, A., Vorobyev, M. & Osorio, D. 2003. Animal colour vision – behavioural tests and physiological concepts. 81–118.

The Receptor Noise Limited Colour Space
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