A recent variational implementation of Land\&$\#$39;s Retinex theory of color vision can improve the appearance of images without introducing artifacts (Bertalm\ío et al. 2009). Through anti-symmetrization of the resulting partial differential equation, this methodology emulates color constancy on both under and over exposed images. Remarkably, this formulation of Retinex is formally equivalent to local histogram equalization and has the same form as the Wilson-Cowan equations that model the response of populations of cortical neurons. The model cannot predict the phenomena of color assimilation because it can only increase the contrast of an image. However an addition to the model, designed to allow it to reach a steady state in a constant time regardless of stimulus structure, can predict assimilation. This approach weights the magnitude of each convergence step by computing the ratio of image variance and histogram uniformity. This model can predict the perception of achromatic induction from the data of Rudd (2010) investigating the perceived lightness of a disk-and-ring stimulus. In particular the model predicts when contrast switches to assimilation, and it can also predict how the slope and curvature of such functions vary with ring width and polarity.

}, author = {Marcelo Bertalm{\'\i}o} }