It is relatively easy to make a connection between the implicit time-discrete approaches for the mean curvature flow and the "Rudin-Osher-Fatemi" total variation based approach for image denoising. This connection has interesting consequences, allowing to build explicit solutions for the flow of the total variation or study regularity issues, up to showing the existence of the crystalline curvature flow of convex sets or building up efficient algorithms. The talk will explain the relationship between all these problems. (Joint works with V. Caselles, M. Novaga, J. Darbon, T. Pock, D. Cremers).