Methods and Applications of Analysis

Volume 21 (2014)

Number 1

Automatic correction of image intensity non-uniformity by the simplest total variation model

Pages: 91 – 104

DOI: http://dx.doi.org/10.4310/MAA.2014.v21.n1.a4

Authors

Ana Belén Petro (Department of Mathematics and Computer Sciene, Universitat de les Illes Balears, Palma de Mallorca, Spain)

Catalina Sbert (Department of Mathematics and Computer Sciene, Universitat de les Illes Balears, Palma de Mallorca, Spain)

Jean-Michel Morel (Centre de Mathématiques et leur applications (CMLA), ENS Cachan, Paris, France)

Abstract

Extending if possible the spectacular applications of the total variation model in image processing, this paper proposes an extension of the TV model to attenuate the effects of non-uniform illumination in digital images. We compare the simplest possible linear algorithm and the simplest possible total-variation based algorithm. The comparison demonstrates once again that the total variation model improves images with minimal halo artifacts. We show that with a single contrast parameter (which keeps the same value in most experiments), the total variation model delivers state of the art results. They compare favourably to results obtained with more complex algorithms. Our algorithm is designed for all kinds of images, but with the special specification of making minimal image detail alteration thanks to a first order fidelity term, instead of the usual zero order term. Experiments on non-uniform medical images and on hazy images images illustrate significant perception gain.

Keywords

total variation, Poisson equation, gradient-based methods, non-uniform illumination, color perception theory

2010 Mathematics Subject Classification

35Jxx, 42-xx, 49-xx

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