Von Kries coefficient law

Helmholtz and the Young–Helmholtz theory 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. Experiments 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. == Chromatic adaptation ==

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. Equations The von Kries coefficient law can be expressed by the following equations: :R_c = R α :G_c = G β :B_c = B γ , where R_c, G_c, and B_c are the cone responses of the same observer, and R, G, and B are all cone responses of the same observer; the only difference is that R_c, G_c, and 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. == Evaluation/effectiveness of the law ==

Many studies have been conducted to study the precision and applicability of the law. Most studies conclude that the law is a general approximation that cannot take into account all of the specificity needed to get a precise answer; different studies and their results will be summarized below. Wirth, in research done from 1900 to 1903, demonstrated through his studies that the law can be considered “nearly valid for reacting lights that are not too weak”. However, this might be seen as a way to moderate color constancy - models display color constancy only as far as the von Kries coefficient law displays color constancy. Therefore, any discrepancies in calculations are due to the visual system behaving in accordance with newer models Further research by Brian Wandell on Wassof's findings revealed that when objects analyzed by the coefficient law are in the same context, the rates of cone absorption as realized by the law match up with experimental values. However, when the two objects are seen under different illuminants, the cone absorptions do not correlate with the true values. Within each context the observer uses the pattern of cone absorption to infer color appearance, probably by comparing the relative cone absorption rates. Color appearance is an interpretation of the physical properties of the objects in the image. == Prevalence ==

Applications Despite the various inconsistencies seen in the von Kries coefficient law, the law is widely used in many color and vision applications and papers. For example, many chromatic adaptation platforms (CATs) are based on the von Kries coefficient law. :c'=D_1\,S^T\,f_1 = D_2\,S^T\,f_2 where S is the cone sensitivity matrix and f is the spectrum of the conditioning stimulus. This leads to the von Kries transform for chromatic adaptation in LMS color space (responses of long-, medium-, and short-wavelength cone response space): :D = D_1^{-1} D_2=\begin{bmatrix} L_2/L_1 & 0 & 0 \\ 0 & M_2/M_1 & 0 \\ 0 & 0 & S_2/S_1 \end{bmatrix} ==References==