Adding a Noise Component To A Color Decomposition Model For Improving Color Texture Extraction

Following the recent work of J-F. Aujol and A. Chambolle, a decomposition model of grayscale images into three components (geometrical, texture and noise) has recently been proposed. Inspired by this work, J-F. Aujol and S. Ha Hung have introduced a new decomposition model for color images. This model splits an image into only two components: a geometrical component and a texture component. The major contribution of this paper is to add a noise component into the image decomposition model for color images in order to better separate texture from noise. Several numerical exemples illustrate the benefit of our approach. Introduction Decomposing an image into meaningful components is an important and challenging inverse problem in image processing. Y. Meyer has recently introduced [8] a new model to split a given image into two components: a geometrical component and a texture one. Inspired by this work, numerical models have been developed to carry out the decomposition of grayscale images. In [1], J-F. Aujol and A. Chambolle propose a decomposition model which splits a grayscale image into three components: the first one, u ∈ BV 1, containing the structure of the image, a second one, v ∈ G 2, the texture, and the third one, w ∈ E 3, the noise. In [2], J-F. Aujol and S. Ha Kang, introduce an algorithm for a color decomposition model which splits a color image into only two components: a geometrical one and a texture one. For this decomposition, they use a generalization of Meyer’s G norm applied to RGB vectorial color image, and use Chromaticity and Brightness color model with total variation minimization [4]. In this paper, an extension of the decomposition algorithm for color images is presented. More precisely, the 1BV (Ω) is the subspace of functions u ∈ L1(Ω) such that the following quantity, called the total variation of u, is finite: