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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SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017, Vol. 10 ( No. 4 ), pp. 1724-1766. 〈http://epubs.siam.org/doi/ref/10.1137/17M1113436〉
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Loic Landrieu, Guillaume Obozinski. Cut Pursuit: fast algorithms to learn piecewise constant functions on general weighted graphs. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017, Vol. 10 ( No. 4 ), pp. 1724-1766. 〈http://epubs.siam.org/doi/ref/10.1137/17M1113436〉. 〈hal-01306779v4〉

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