Inserted: 25 oct 2012
Last Updated: 11 nov 2018
Journal: in Handbook of Mathematical Methods in Imaging, Springer
The use of total variation as a regularization term in imaging problems was motivated by its ability to recover the image discontinuities. This is at 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, 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.