Total Variation in Imaging

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 its numerous applications to denoising, optical flow, stereo imaging and D 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.