Connections between Retinex, neural models and variational methods

Abstract

This paper explores the interrelations between Retinex, neural models and variational methods by making an overview of relevant related works in the past few years. Taking all the essential elements of the Retinex theory as postulated by Land and McCann (channel independence, the ratio reset mechanism, local averages, non-linear correction), it has been shown that we can obtain a Retinex algorithm implementation that is intrinsically 2D, whose results comply with all the expected properties of the original, one-dimensional path-based Retinex algorithm (such as approximating color constancy while being unable to deal with overexposed images) but don't suffer from common shortcomings such as sensitivity to noise, appearance of halos, etc. An iterative application of this 2D Retinex algorithm takes the form of a partial differential equation (PDE) that it's proven not to minimize any energy functional, and this fact is linked to its limitations regarding over-exposed pictures. It was proposed to modify in this regard the iterative method in a certain way so that it is able to handle both under and over-exposed images, the resulting PDE now has a number of very relevant properties which allow to connect Retinex with variational models, histogram equalization and efficient coding, perceptual color correction algorithms, and computational neuroscience models of cortical activity and retinal models.