Directional Filters for Cartoon + Texture Image Decomposition

Abstract

We present in this article a detailed analysis and implementation of the cartoon+texture decomposition algorithm proposed in [A. Buades, J.L. Lisani, 'Directional filters for color cartoon + texture image and video decomposition', Journal of Mathematical Imaging and Vision, 2015]. This method follows the approach proposed by [A. Buades, T. Le, J-M. Morel, L. Vese, 'Cartoon+Texture Image Decomposition', IPOL 2011], based on low/high-pass filtering, but replaces the isotropic filters by a bank of low-pass directional filters. The cartoon image is obtained by filtering in the direction that leads to the largest local total variation rate reduction. This permits to improve the performance of the decomposition near image discontinuities, where an halo effect was produced by the previous method.