Are Gaussian spectra a viable perceptual assumption in color appearance?

Natural illuminant and reflectance spectra can be roughly approximated by a linear model with as few as three basis functions, and this has suggested that the visual system might construct a linear representation of the spectra by estimating the weights of these functions. However, such models do not accommodate nonlinearities in color appearance, such as the Abney effect. Previously, we found that these nonlinearities are qualitatively consistent with a perceptual inference that stimulus spectra are instead roughly Gaussian, with the hue tied to the inferred centroid of the spectrum [J. Vision 6(9), 12 (2006)]. Here, we examined to what extent a Gaussian inference provides a sufficient approximation of natural color signals. Reflectance and illuminant spectra from a wide set of databases were analyzed to test how well the curves could be fit by either a simple Gaussian with three parameters (amplitude, peak wavelength, and standard deviation) versus the first three principal component analysis components of standard linear models. The resulting Gaussian fits were comparable to linear models with the same degrees of freedom, suggesting that the Gaussian model could provide a plausible perceptual assumption about stimulus spectra for a trichromatic visual system.