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.
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Acknowledgements
We would like to thank Cécile Louchet for providing us the experiments of Sect. 9 and Gabriele Facciolo and Enric Meinhardt for the experiments in section “Global Solutions of Geometric Problems”. V. Caselles acknowledges partial support by PNPGC project, reference MTM2006-14836, and also by “ICREA Acadèmia” for excellence in research funded by the Generalitat de Catalunya.
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Caselles, V., Chambolle, A., Novaga, M. (2015). Total Variation in Imaging. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_23
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DOI: https://doi.org/10.1007/978-1-4939-0790-8_23
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