Formalizations of the retinex model and its variants with variational principles and partial differential equations

Abstract

Land and McCann introduced the retinex model as a computational theory of color vision. However, retinex details were described algorithmically rather than mathematically. Soon after the birth of retinex, Horn proposed a drastic simplification of the model, which, however, had the merit of being mathematically explicit and rigorous. As a consequence, at least two different interpretations of retinex appeared in the literature almost at the same time. This generated a lot of confusion about the name retinex that persists even now. The aim of this paper is to present an overview about the different interpretations and the corresponding mathematical formalizations of retinex in terms of variational principles and partial differential equations.