Cut Pursuit: fast algorithms to learn piecewise constant functions on general weighted graphs

Loic Landrieu (1, 2) , Guillaume Obozinski (2)

1 MATIS - Méthodes d'Analyses pour le Traitement d'Images et la Stéréorestitution
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

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

Mots clés: total variation; Mumford Shah; optimization; working-set; greedy algorithm; minimal partition

Domaines: Machine Learning [stat.ML]

Loic Landrieu, Guillaume Obozinski. Cut Pursuit: fast algorithms to learn piecewise constant functions on general weighted graphs. SIAM Journal on Imaging Sciences, 2017, Vol. 10 ( No. 4 ), pp. 1724-1766. ⟨hal-01306779v4⟩