Cut Pursuit: fast algorithms to learn piecewise constant functions on general weighted graphs
Abstract
We propose working-set/greedy algorithms to efficiently solve problems penalized respectively by the total variation on a general weighted graph and its L0 counterpart the Mumford Shah total level-set boundary size when the piecewise constant solutions have a small number of distinct level-sets; this is typically the case when the total level-set boundary size is small, which is encouraged by these two forms of penalization. Our algorithms exploit this structure by recursively splitting the level-sets of a piecewise-constant candidate solution using graph cuts. We obtain significant speed-ups over state-of-the-art algorithms for images that are well approximated with few level-sets
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