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Total Variation in Imaging

In: Handbook of Mathematical Methods in Imaging

Author

Listed:
  • V. Caselles

    (DTIC, Universitat Pompeu-Fabra)

  • A. Chambolle

    (CNRS UMR 7641 Ecole Polytechnique)

  • M. Novaga

    (Dipartimento di Matematica, Università di Padova)

Abstract

The use of total variation as a regularization term in imaging problems was motivated by its ability to recover the image discontinuities. This is on the basis of his numerous applications to denoising, optical flow, stereo imaging and 3D surface reconstruction, segmentation, or interpolation, to mention some of them. On one hand, we review here the main theoretical arguments that have been given to support this idea. On the other hand, we review the main numerical approaches to solve different models where total variation appears. We describe both the main iterative schemes and the global optimization methods based on the use of max-flow algorithms. Then we review the use of anisotropic total variation models to solve different geometric problems and its use in finding a convex formulation of some non-convex total variation problems. Finally we study the total variation formulation of image restoration.

Suggested Citation

  • V. Caselles & A. Chambolle & M. Novaga, 2015. "Total Variation in Imaging," Springer Books, in: Otmar Scherzer (ed.), Handbook of Mathematical Methods in Imaging, edition 2, pages 1455-1499, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0790-8_23
    DOI: 10.1007/978-1-4939-0790-8_23
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