Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions

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