Von Kries Coefficient Law

The von Kries coefficient law in color adaptation describes the relationship between the illuminant and the human visual system sensitivity. The law accounts for the approximate color constancy in the human visual system. It is the oldest and most widely used law to quantify color adaptation, and is used widely in the field of vision and chromatic adaptation.

The von Kries coefficient law compensates for the illumination change using a purely diagonal scaling of the cone absorptions. While the law does not provide a precise indication of the correction, it typically provides a reasonable approximation.

The von Kries coefficient law built upon theories and research done by Hermann von Helmholtz. A German physicist and physician, Helmholtz asserted that “the nervous substance in question is less sensitive to reacting light falling on it than the rest of the retina that was not previously stimulated”. Helmholtz, along with Thomas Young, proposed the trichromatic theory, or the Young–Helmholtz theory, that stated that the retina contains three types of cones, which respond to light of three different wavelengths, corresponding to red, green, or blue. Activation of these cones in different combinations and to different degrees results in the perception of other colors.

While von Kries and the other researchers did not have the means to test out the results of his stated law, others tested out his coefficient law by estimating the eigenvectors of the measured linear transformations. Many researchers, including Eileen Wassof (1959), Burnham et al. (1957), and Macadam [12] rejected his law as being insufficiently accurate. There were frequently reported systematic discrepancies between prediction and experiment.

The law assumes that although the responses of the three cone types (R, G, and B) are affected differently by chromatic adaptation, the spectral sensitivities of each of the three cone mechanisms remains unchanged. Therefore, if one of the three cones are less stimulated than the others, the sensitivity is proportionally reduced. The specific amount that this number is reduced by is inversely related to the relative strengths of activation by the energy distribution of the particular light in question.

The von Kries coefficient law can be expressed by the following equations:

, where ${\displaystyle R_{c},G_{c},}$ and ${\displaystyle B_{c}}$ are the cone responses of the same observer, and ${\displaystyle R,G,}$ and ${\displaystyle B}$ are all cone responses of the same observer; the only difference is that ${\displaystyle R_{c},G_{c},}$ and ${\displaystyle B_{c}}$ are viewed under a reference illuminant while the other set of values is experimental. α, β, and γ are the von Kries coefficients corresponding to the reduction in sensitivity of the three cone mechanisms due to chromatic adaptation.

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