Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection |
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Authors: | Jean-François Aujol Guy Gilboa Tony Chan Stanley Osher |
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Affiliation: | (1) Department of Mathematics, UCLA, Los Angeles, California 90095, USA;(2) Present address: CMLA (CNRS UMR 8536), ENS Cachan, France |
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Abstract: | This paper explores various aspects of the image decomposition problem using modern variational techniques. We aim at splitting
an original image f into two components u and ρ, where u holds the geometrical information and ρ holds the textural information. The focus of this paper is to study different energy
terms and functional spaces that suit various types of textures. Our modeling uses the total-variation energy for extracting
the structural part and one of four of the following norms for the textural part: L2, G, L1 and a new tunable norm, suggested here for the first time, based on Gabor functions. Apart from the broad perspective and
our suggestions when each model should be used, the paper contains three specific novelties: first we show that the correlation
graph between u and ρ may serve as an efficient tool to select the splitting parameter, second we propose a new fast algorithm to solve the
TV − L1 minimization problem, and third we introduce the theory and design tools for the TV-Gabor model.
First online version published in February, 2006 |
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Keywords: | image decomposition restoration parameter selection BV G L1 Hilbert space projection total-variation Gabor functions |
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