An approach to vectorial total variation based on geometric measure theory

Goldlücke, Bastian; Cremers, Daniel

An approach to vectorial total variation based on geometric measure theory

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Date

2010

Authors

Goldlücke, Bastian

Cremers, Daniel

DOI (citable link)

10.1109/CVPR.2010.5540194

Collections

Informatik und Informationswissenschaft

Publication type

Contribution to a conference collection

Publication status

Published

Published 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

Abstract

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.

Subject (DDC)

004 Computer Science

Conference

CVPR 2010, Jun 13, 2010 - Jun 18, 2010, San Francisco, USA

Cite This

ISO 690

GOLDLÜCKE, Bastian, Daniel CREMERS, 2010. An approach to vectorial total variation based on geometric measure theory. CVPR 2010. San Francisco, USA, Jun 13, 2010 - Jun 18, 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, 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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Bibliography of Konstanz

No