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Proceedings Paper

A unifying retinex model based on non-local differential operators
Author(s): Dominique Zosso; Giang Tran; Stanley Osher
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Paper 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’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.

Paper Details

Date Published: 14 February 2013
PDF: 16 pages
Proc. SPIE 8657, Computational Imaging XI, 865702 (14 February 2013); doi: 10.1117/12.2008839
Show Author Affiliations
Dominique Zosso, The Univ. of California, Los Angeles (United States)
Giang Tran, The Univ. of California, Los Angeles (United States)
Stanley Osher, The Univ. of California, Los Angeles (United States)


Published in SPIE Proceedings Vol. 8657:
Computational Imaging XI
Charles A. Bouman; Ilya Pollak; Patrick J. Wolfe, Editor(s)

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