Cut Pursuit: fast algorithms to learn piecewise constant functions

We propose working-set/greedy algorithms to efficiently find the solutions to convex optimization problems penalized respectively by the total variation and the Mumford Shah boundary size. Our algorithms exploit the piecewise constant structure of the level-sets of the solutions by recursively splitting them using graph cuts. We obtain significant speed up on images that can be approximated with few level-sets compared to state-of-the-art algorithms.