Our perception of color is often considered to be a by--product of visual perception rather than an intrinsic property of the reflectance spectra in the environment . The world of electromagnetic stimuli in which we are immersed would seem to have a much more rich and varied structure than our visual system can process. To begin with, we only perceive a limited range of frequencies of electromagnetic radiation, the narrow band of ``visible light'' which ranges in wavelength from approximately 400nm to 680nm. Furthermore, the visible wavelengths of light that are reflected from the objects in our everyday world are composed of mixtures of thousands of separate and distinct wavelengths of light. We represent this distribution of wavelengths of visible light as a single percept which we call a color. In doing so, it would seem that we have lost a great deal of the information that was originally present in light. One consequence of this loss of information is that many different distributions of visible light can produce the same subjective color percept .
The visual system reduces a very high dimensional input, the distribution of energy values of the photons arriving at each point on the retina, into a low dimensional percept, one in which each point in visual space appears to be mapped to its own single color. It has been suggested that the visual system attempts to preserve as much of the information in the input as possible during this process of reduction of dimension [3,4]. If this hypothesis holds, the visual system should attempt to preserve patterns of covariance in the distributions of photon energies generated by the product of the illuminant spectra with reflectance spectra from objects present in the environment.
Cohen  and Vrhel  present principal components analyses and Maloney  presents a multiple regression analysis each of which demonstrate that spectral distributions from the environment can be efficiently reproduced using linear combinations of a small number of components. The present work describes a method for measuring the correspondence between the low dimensional structure of spectral distributions in the environment and the low dimensional structure of the perception of color.
The visual system adapts to different brightness and overall spectral content of the illumination source such that a perception of color constancy is maintained within a wide range of environmental lighting conditions [8,9]. Thus it would make sense for the visual system to attempt to remove the overall mean illuminance from the input spectral distributions while preserving an accurate but low dimensional estimate of their covariance structure.
For example, suppose that the spectral distribution of the light source illuminating a scene was skewed toward the red end of the spectrum. By extracting the mean value for each wavelength over the entire visual scene, the effect of the skewed spectral distribution of the lighting source would be removed.
Statistical techniques such as factor analysis are designed to perform exactly this task of finding an efficient reduction in the dimension of data while preserving covariance relations among the input variables . As long as certain distributional and modeling assumptions are met, factor analysis is considered to perform an optimal linear reduction in dimension with respect to a specified cost function (e.g. least squares or maximum likelihood). Confirmatory factor analysis, a form of maximum likelihood latent variable modeling with constraints, allows measurement of goodness of fit of a particular model to a particular data set [11,12]. The premise of this paper is that the goodness of fit of the visual system's solution to the problem of reduction of dimension in the perception of distributions of photon energies can be estimated through confirmatory factor analysis, and consequently the structure of the perceptual representation of color can be better understood by studying these factor models.