Fast dual minimization of the vectorial total variation norm and applications to color image processing

Bresson, Xavier; Chan, Tony F.

doi:10.3934/ipi.2008.2.455

Cited by 341 publications

(294 citation statements)

References 33 publications

Supporting

Mentioning

293

Contrasting

Unclassified

Order By: Relevance

“…Thanks to recent advances in color image processing ( [10] and [9]), motivating by the well known Chambolle's projection [17], we are able now to use a projected gradient algorithm computing the solution of this dual formulation problem extended to time. So we dispose of an efficient way to numerically solve the different minimization problem induced by the extended functional (3), using fixed point method: P 0 = 0, and…”

Section: Numerical Implementationmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Texture Extraction and Video Denoising

Lugiez

Ménard

El-Hamidi

2009

Advanced Concepts for Intelligent Vision Systems

View full text Add to dashboard Cite

Abstract. According to recent works, introduced by Y.Meyer [1] the decomposition models based on Total Variation (TV) appear as a very good way to extract texture from image sequences. Indeed, videos show up characteristic variations along the temporal dimension which can be catched in the decomposition framework. However, there are very few works in literature which deal with spatio-temporal decompositions. Thus, we devote this paper to spatio-temporal extension of the spatial color decomposition model. We provide a relevant method to accurately catch Dynamic Textures (DT) present in videos. Moreover, we obtain the spatio-temporal regularized part (the geometrical component), and we distinctly separate the highly oscillatory variations, (the noise). Furthermore, we present some elements of comparison between several models in denoising purpose.

show abstract

Section: Numerical Implementationmentioning

confidence: 99%

“…We only cite, among many others, most recent works which we appear like most relevant and useful papers. In this way, reader can refer to the work of Aujol et al [3] [4], Aujol and Chambolle [5], Aujol and Kang [6], Vese and Osher [7], Gilles [8] and more recently Bresson and Chan [9], Duval et al [10] and Aubert et al [11].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Texture Extraction and Video Denoising

Lugiez

Ménard

El-Hamidi

2009

Advanced Concepts for Intelligent Vision Systems

View full text Add to dashboard Cite

show abstract

“…We refer to (Godlewski & Raviart, 1996) for the finite volume approximation of hyperbolic systems and (Bresson & Chan, 2008;Bouchut et al, 2012) for the approximation of the vectorial total variation flow. However, the convergence analysis in this case seems out of reach.…”

Section: Convergence Of the Approximate Solutionsmentioning

confidence: 99%

Convection and total variation flow

Bouchut¹,

Doyen²,

Eymard³

2013

IMA Journal of Numerical Analysis

View full text Add to dashboard Cite

We deal with a nonlinear hyperbolic scalar conservation law, regularized by the total variation flow operator (or 1-Laplacian). We give an entropy weak formulation, for which we prove the existence and the uniqueness of the solution. The existence result is established using the convergence of a numerical approximation (a splitting scheme where the hyperbolic flow is treated with finite volumes and the total variation flow with finite elements). Some numerical simulations are also presented.Keywords: Bingham fluid, hyperbolic scalar conservation law, total variation flow, 1-Laplacian, entropy formulation, finite volumes, finite elements A Bingham fluid, also called rigid viscoplastic fluid, is a material that behaves as a rigid solid below a certain stress yield and as a viscous fluid above this yield; a familiar example of such a material is the tooth paste. For a d-dimensional Bingham fluid, the relation between the stress tensor σ , seen as a d × d matrix, the pressure p and the velocity u is When the viscosity becomes negligible (ν = 0), the analytical and numerical framework described above is no longer suitable -let us mention however an existence result in 2D obtained by Lions (1972). Although the study of inviscid Bingham fluids has been initiated in Bouchut et al. (2012) with the case of an unsteady flow without convection term, the presence of a nonlinear convection term is naturally issued from the inertial term in the momentum conservation equation. Unfortunately, the study of this problem seems to be out of reach in the actual state of the art, and we only consider here a simplified model of unsteady Bingham flow with convection. This simplified model is scalar and consists in †

show abstract

“…Furthermore, many efficient vector-based imaging tools have been introduced [2][3][4]7]. That being said, the vector-valued approach has some limitations when it comes to model the internal structure of certain complex data sets.…”

Section: Introductionmentioning

confidence: 99%

“…Vector-valued functions provide a quite natural representation for some types of images, for example, colour and hyperspectral (HS) images [4,11]. Furthermore, many efficient vector-based imaging tools have been introduced [2][3][4]7].…”

Section: Introductionmentioning

confidence: 99%

Image Denoising Using Euler-Lagrange Equations for Function-Valued Mappings

Otero

Torre

Vrscay

2016

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. In this paper, we consider a new method for representing complex images, e.g., hyperspectral images and video sequences, in terms of function-valued mappings (FVMs), also known as Banach-valued functions. At each (pixel) location x, the FVM image u(x) is a function, as opposed to the traditional vector approach. We define the Fourier transform of an FVM as well as Euler-Lagrange conditions for functionals involving FVMs and then show how these results can be used to devise some FVM-based methods of denoising. We consider a very simple functional and present some numerical results.

show abstract

Fast dual minimization of the vectorial total variation norm and applications to color image processing

Cited by 341 publications

References 33 publications

Dynamic Texture Extraction and Video Denoising

Dynamic Texture Extraction and Video Denoising

Convection and total variation flow

Image Denoising Using Euler-Lagrange Equations for Function-Valued Mappings

Contact Info

Product

Resources

About