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Séparation en composantes structures, textures et bruit d'une image, apport de l'utilisation des contourlettes

Jerome Gilles

TL;DR

This paper proposes to replace the wavelet transform by the contourlet transform which better approximate geometry in images and gets an iterative algorithm which is tested on two noisy textured images.

Abstract

In this paper, we propose to improve image decomposition algorithms in the case of noisy images. In \cite{gilles1,aujoluvw}, the authors propose to separate structures, textures and noise from an image. Unfortunately, the use of separable wavelets shows some artefacts. In this paper, we propose to replace the wavelet transform by the contourlet transform which better approximate geometry in images. For that, we define contourlet spaces and their associated norms. Then, we get an iterative algorithm which we test on two noisy textured images.

Séparation en composantes structures, textures et bruit d'une image, apport de l'utilisation des contourlettes

TL;DR

This paper proposes to replace the wavelet transform by the contourlet transform which better approximate geometry in images and gets an iterative algorithm which is tested on two noisy textured images.

Abstract

In this paper, we propose to improve image decomposition algorithms in the case of noisy images. In \cite{gilles1,aujoluvw}, the authors propose to separate structures, textures and noise from an image. Unfortunately, the use of separable wavelets shows some artefacts. In this paper, we propose to replace the wavelet transform by the contourlet transform which better approximate geometry in images. For that, we define contourlet spaces and their associated norms. Then, we get an iterative algorithm which we test on two noisy textured images.

Paper Structure

This paper contains 5 sections, 1 theorem, 18 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Séparation structures, textures et bruit
  3. Séparation de composantes basée sur les contourlettes
  4. Résultats
  5. Conclusion

Key Result

Proposition 1

Soit $u\in BV$, $v\in G_{\mu}$, $w\in Co_{\delta}$ respectivement les composantes structures, textures et bruit découlant de la décomposition d'image. Alors, les minimiseurs sont donnés par où $P_{G_{\lambda}}$ est le projecteur non-linéaire de Chambolle et $CST$$(f-u-v,2\delta)$ est l'opérateur de seuillage doux, avec un seuil de $2\delta$, des coefficients de la transformée en contourlettes de

Figures (3)

  • Figure 1: Images de test Barbara et Léopard corrompues par un bruit gaussien ($\sigma=20$).
  • Figure 2: Composantes structures $+$ textures $+$ bruit issus de la décomposition de Barbara bruitée.
  • Figure 3: Composantes structures $+$ textures $+$ bruit issus de la décomposition du Léopard bruité.

Theorems & Definitions (1)

  • Proposition 1