Directional Filters for Color Cartoon+Texture Image and Video Decomposition

Abstract

The decomposition of an image in a geometrical and a textural part has shown to be a challenging problem with several applications. Since the theoretical breakthrough of Y. Meyer, many variational methods and minimization techniques have been proposed for this task. This paper uses a different approach based on low/high-pass filtering with directional filters. This approach modifies the algorithm proposed in Buades et al. (IEEE Trans Image Process 19(8):1978---1986, 2010) improving its performance near image discontinuities while keeping the simplicity and rapidity of a linear model. Comparisons with variational methods illustrate the flexibility of the proposed algorithm. We illustrate how the proposed method is the only one dealing correctly with frame-by-frame video processing.