Theoretical Models for Color Conversion

The simple color shift, described in Section 11.2, is not the only theory that fits the data of Helson. Theoretical models are also given by Judd (1940) and Richards and Parks (1971). Judd (1940) describes the hue of a sample as the orientation of a vector that points from the achromatic point [nr, ng, rib]T to the given color [cy, cg, cy]r. 

All colors are represented as trilinear coordinates where the amounts of the three primary stimuli are expressed as fractions of their total, i.e. the colors are normalized. In the model, the achromatic point is a function of the illuminant, the particular sample fixated, and the samples near the fixation point in the immediate past  

AGREEMENT WITH DATA FROM EXPERIMENTAL PSYCHOLOGY 

Note that, in order to explain the experimental data, Judd also incorporated factors into his equations that depend on the size of the samples relative to the background and the amount of time for which the samples were fixated. The equations given by Judd are quite complicated. In fact, Land (1960) criticized the formulation of Judd for being wavelength-rich and time-dependent. According to Land, the formulation should be nearly independent of wavelength and fully independent of time. 

Compared to the formulation of Judd, our use of simple color shifts is much more elegant. A temporal effect is introduced when we assume that the local averaging, as described in Chapter 10, takes a finite amount of time. It takes some time until the process converges. Of course, intermediate results can still be obtained at any point in time. The computed output color would then depend on outdated information about local space average color, which is stored in the parallel network. This would explain why afterimages occur when the focus of fixation is suddenly moved to a different location. 

---