Multiscale Texture Separation
Jérôme Gilles · Multiscale Modeling and Simulation · 2012
In this paper, we investigate theoretically the behavior of Meyer's image cartoon + texture decomposition model. Our main result is a new theorem which shows that, by combining the decomposition model and a well-chosen Littlewood--Paley filter, it is possible to extract almost perfectly a certain class of textures. This theorem leads us to the construction of a parameterless multiscale texture separation algorithm. Finally, we propose extending this algorithm into a directional multiscale texture separation algorithm by designing a directional Littlewood--Paley filter bank. Several experiments show the efficiency of the proposed method on both synthetic and real images.