An image decomposition model using the total variation and the infinity Laplacian
Christopher Elion, Luminita A. Vese · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
This paper is devoted to a recent topic in image analysis: the decomposition of an image into a cartoon or geometric part, and an oscillatory or texture part. Here, we propose a practical solution to the (BV,G) model proposed by Y. Meyer. We impose that the cartoon is a function of bounded variation, while the texture is represented as the Laplacian of some function whose gradient belongs to L(infinity). The problem thus becomes related with the absolutely minimizing Lipschitz extensions and the infinity Laplacian. Experimental results for image denoising and cartoon + texture separation, together with details of the algorithm, are also presented.