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An approach to vectorial total variation based on geometric measure theory

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2010

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Cremers, Daniel

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https://doi.org/10.1109/CVPR.2010.5540194
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2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010, San Francisco, California, USA, 13-18 June 2010; Vol. 1. Piscataway, NJ: IEEE, 2010, pp. 327-333. ISSN 1063-6919. ISBN 978-1-4244-6984-0. Available under: doi: 10.1109/CVPR.2010.5540194

Zusammenfassung

We analyze a previously unexplored generalization of the scalar total variation to vector-valued functions, which is motivated by geometric measure theory. A complete mathematical characterization is given, which proves important invariance properties as well as existence of solutions of the vectorial ROF model. As an important feature, there exists a dual formulation for the proposed vectorial total variation, which leads to a fast and stable minimization algorithm. The main difference to previous approaches with similar properties is that we penalize across a common edge direction for all channels, which is a major theoretical advantage. Experiments show that this leads to a significiantly better restoration of color edges in practice.

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CVPR 2010, 13. Juni 2010 - 18. Juni 2010, San Francisco, USA
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ISO 690GOLDLÜCKE, Bastian, Daniel CREMERS, 2010. An approach to vectorial total variation based on geometric measure theory. CVPR 2010. San Francisco, USA, 13. Juni 2010 - 18. Juni 2010. In: 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010, San Francisco, California, USA, 13-18 June 2010; Vol. 1. Piscataway, NJ: IEEE, 2010, pp. 327-333. ISSN 1063-6919. ISBN 978-1-4244-6984-0. Available under: doi: 10.1109/CVPR.2010.5540194
BibTex
@inproceedings{Goldlucke2010-06appro-40773,
  year={2010},
  doi={10.1109/CVPR.2010.5540194},
  title={An approach to vectorial total variation based on geometric measure theory},
  isbn={978-1-4244-6984-0},
  issn={1063-6919},
  publisher={IEEE},
  address={Piscataway, NJ},
  booktitle={2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010, San Francisco, California, USA, 13-18 June 2010; Vol. 1},
  pages={327--333},
  author={Goldlücke, Bastian and Cremers, Daniel}
}
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