@conference {13771,
	title = {A Unifying Retinex Model Based on Non-Local Differential Operators},
	booktitle = {Computational Imaging XI},
	volume = {8657},
	year = {2013},
	publisher = {International Society for Optics and Photonics},
	organization = {International Society for Optics and Photonics},
	abstract = {In this paper, we present a unifying framework for retinex that is able to reproduce many of the existing retinex implementations within a single model. The fundamental assumption, as shared with many retinex models, is that the observed image is a multiplication between the illumination and the true underlying reflectance of the object. Starting from Morel{\textquoteright}s 2010 PDE model for retinex, where illumination is supposed to vary smoothly and where the reflectance is thus recovered from a hard-thresholded Laplacian of the observed image in a Poisson equation, we define our retinex model in similar but more general two steps. First, look for a filtered gradient that is the solution of an optimization problem consisting of two terms: The first term is a sparsity prior of the reflectance, such as the TV or H1 norm, while the second term is a quadratic fidelity prior of the reflectance gradient with respect to the observed image gradients. In a second step, since this filtered gradient almost certainly is not a consistent image gradient, we then look for a reflectance whose actual gradient comes close. Beyond unifying existing models, we are able to derive entirely novel retinex formulations by using more interesting non-local versions for the sparsity and fidelity prior. Hence we define within a single framework new retinex instances particularly suited for texture-preserving shadow removal, cartoon-texture decomposition, color and hyperspectral image enhancement.},
	author = {Dominique Zosso and Giang Tran and Stanley Osher}
}