Gradient attenuation as an emergent property of reset-based Retinex models

The Retinex image filtering algorithms have been inspired by experimental findings on the behavior of the Human Vision System. They are known to locally adjust image color and contrast by preserving edges and attenuating gradients. In a reference formulation of the algorithm by Land and McCann, edge preservation and gradient attenuation are granted by two ad-hoc mechanisms: called respectively reset (the distinctive feature of all the Retinex algorithms) and thresholding. A somehow unanticipated finding is that gradient attenuation is also observed with algorithm variants that do not include the latter mechanism, which was explicitly devised to implement gradient attenuation. In this work, we provide an analytic demonstration of the capability of Retinex models to attenuate gradients using only the "reset" mechanism, combined with the local character of the mutual pixel influences. We show that this capability is an emergent property of all the reset-based Retinex models.