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Directional Filters for Color Cartoon+Texture Image and Video Decomposition

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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.

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Notes

  1. A grayscale (resp. color) image is represented by a function\(f:(x,y) \rightarrow {\mathbb {R}}\) (resp. \({\mathbb {R}}^3\)), where \(\Omega \) is an open subset of \({\mathbb {R}}^2\), typically a rectangle or square. The image is defined on a continuous domain by interpolation of the values on a discrete set of pixels.

  2. Web address: https://sites.google.com/site/thunsukeono/.

  3. On a 3.2GHz Intel Core i5 processor (4 cores) with 8GB of RAM memory

  4. Excerpt from “San Francisco Zoo” video, http://vimeo.com/365747, Eugenia Loli, CC BY 3.0.

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Authors and Affiliations

  1. Universitat Illes Balears, Palma, Spain

    A. Buades & J. L. Lisani

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  1. A. Buades
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  2. J. L. Lisani
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Correspondence to J. L. Lisani.

Additional information

This paper has supplementary downloadable material provided by the authors (http://dmi.uib.es/~lisani/JMIVcartoon/). The material includes eight videos associated to Figs. 8, 9 and 10 of the manuscript, in mp4 format. Contact joseluis.lisani@uib.es for further questions about this work.

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Buades, A., Lisani, J.L. Directional Filters for Color Cartoon+Texture Image and Video Decomposition. J Math Imaging Vis 55, 125–135 (2016). https://doi.org/10.1007/s10851-015-0617-5

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