One type of model which has attempted to extend the representation of color space into four dimensions postulates that white and black are orthogonal rather than being opponent ends of the same dimension. While this may seem counterintuitive at first, the point is argued by Heggelund [Heggelund 1992] that the color white consists primarily of intensity information carried by an excitatory combination of the three cone types, whereas black and ``luminous'' are two opposing ends of another dimension which carries contrast information from center/surround antagonistic combinations of the cones.
Figure 15. (A) Projection of spectral and white color points connected by lines of equiluminance onto the chromatic (Z_1,Z_2) plane. Note that equiluminance lines describe the outline of the CIE chromaticity diagram. (B) Projection of spectral and white color points connected by lines of equal wavelength onto the (Z_3,Z_4) achromatic plane. The spherical coordinate of a point on the (Z_3,Z_4) plane describes its brightness [from Izmailov & Sokolov 1991].
Another group which has presented evidence supporting a model of orthogonal white and black dimensions is that of Izmailov and Sokolov [Izmailova et al. 1990, Izmailov & Sokolov 1991, Paramei et al. 1991]. They performed a series of experiments in which subjects rated differences between paired stimuli at much greater than just noticeable differences from each other in color space. They then analyzed these data using both multidimensional scaling and factor analysis with essentially the same results: the brightness dimension is curved and is better fit using two orthogonal axes than with a single axis consisting of the opponents black and white. They have replicated these findings [Izmailov & Sokolov 1992] using a method similar to Boynton and Gordon Boynton65a, and with primates using a novel approach of learning curves [Sokolov 1993]. Sokolov and colleagues have constructed a model for a uniform color space with a Riemann metric which suggests that the perceptual color space may be four dimensional and may also be normalized onto the surface of a four dimensional hypersphere (see Figure 15).
The structure of the representational space of color is at least in part determined by the need to adapt to the topology and metric of the information in the photic environment. At least as important to the construction of the perceptual color space are the constraints supplied by the neurological mechanisms which comprise the biological mechanism that performs the mapping between the photic space and color space.