Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm

Duval, Vincent; Aujol, Jean-François; Vese, Luminita A.

doi:10.1007/s10851-010-0203-9

Cited by 48 publications

(25 citation statements)

References 68 publications

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“…A direct proof is obtained by modifying and completing the argument in [13] and may be found in [18].…”

Section: The Algorithmsmentioning

confidence: 99%

Piecewise Linear Approximation of the Continuous Rudin--Osher--Fatemi Model for Image Denoising

Lai¹,

Messi²

2012

SIAM J. Numer. Anal.

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This paper is concerned with the numerical approximation of the minimizer of the continuous Rudin-Osher-Fatemi (ROF) model for image denoising. A new discrete total variation is proposed and the associated Hilbertian total variation denoising model is used to construct continuous piecewise linear functions that approximate the minimizer of the ROF model in the strong topology of L 2 (Ω), provided that the data function is bounded and weakly regular in the sense of Lip(α, L 2 (Ω)).

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“…A direct proof is obtained by modifying and completing the argument in [13] and may be found in [18].…”

Section: The Algorithmsmentioning

confidence: 99%

Piecewise Linear Approximation of the Continuous Rudin--Osher--Fatemi Model for Image Denoising

Lai¹,

Messi²

2012

SIAM J. Numer. Anal.

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“…It can be done with a regularized version of TV and the use of the CB or HSB spaces as in [20,7]. Another possibility is to use the definition of BV (R 3 ) and then resort to a projection scheme as in [12,29] (the mixing of the three channels is then done through the vectorial norm). For the curvelet part (J curv ) of the regularization term, the same idea can be used with a multichannel 1 -norm as in [49].…”

Section: Color Texture Processingmentioning

confidence: 99%

Locally Parallel Texture Modeling

Maurel¹,

Aujol²,

Peyré³

2011

SIAM J. Imaging Sci.

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Abstract. This article presents a new adaptive framework for locally parallel texture modeling. Oscillating patterns are modeled with functionals that constrain the local Fourier decomposition of the texture. We first introduce a texture functional which is a weighted Hilbert norm. The weights on the local Fourier atoms are optimized to match the local orientation and frequency of the texture. This adaptive model is used to solve image processing inverse problems, such as image decomposition and inpainting. The local orientation and frequency of the texture component are adaptively estimated during the minimization process. To improve inpainting performances over large missing regions, we introduce a higly non-convex generalization of our texture model. This new model constrains the amplitude of the texture and it allows one to impose an arbitrary oscillation profile. Numerical results illustrate the effectiveness of the method.

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“…• image decomposition methods: one can refer to Gilles and Meyer (2010), Buades et al (2010), Duval et al (2010), Shahidi and Moloney (2009), Aubert and Aujol (2005) for example.…”

Section: Introductionmentioning

confidence: 99%

“…Let us mention the use of Sobolev-type spaces (including Besov spaces or BMO) in the regularization term (see , Garnett et al (2011), Kim and Vese (2009), Le et al (2009), Lieu and Vese (2008), Garnett et al (2007), Le and Vese (2005), Tadmor et al (2004) for example) and/or the use of Meyer space (Meyer (2001), , Aubert and Aujol (2005), Strong et al (2006), Aujol (2009), Gilles and Meyer (2010), Duval et al (2010)). …”

Section: Introductionmentioning

confidence: 99%

Second-order Variational Models for Image Texture Analysis

Bergounioux

2014

Advances in Imaging and Electron Physics

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To cite this version:Maïtine Bergounioux. Second order variational models for image texture analysis. Advances in Imaging and Electron Physics, Elsevier, 2014, 181, pp.35-124 AbstractWe present variational models to perform texture analysis and/or extraction for image processing. We focus on second order decomposition models. Variational decomposition models have been studied extensively during the past decades. The most famous one is the Rudin-Osher-Fatemi model. We first recall most classical first order models . Then we deal with second order ones : we detail the mathematical framework, theoretical models and numerical implementation. We end with two 3D applications. Eventually, an appendix includes the mathematical tools that are used to perfom this study and Matlab c codes are provided.

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Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm

Cited by 48 publications

References 68 publications

Piecewise Linear Approximation of the Continuous Rudin--Osher--Fatemi Model for Image Denoising

Piecewise Linear Approximation of the Continuous Rudin--Osher--Fatemi Model for Image Denoising

Locally Parallel Texture Modeling

Second-order Variational Models for Image Texture Analysis

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