Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions

Loic Landrieu, Guillaume Obozinski
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:1384-1393, 2016.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v51-landrieu16, title = {Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions}, author = {Landrieu, Loic and Obozinski, Guillaume}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {1384--1393}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/landrieu16.pdf}, url = {https://proceedings.mlr.press/v51/landrieu16.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions %A Loic Landrieu %A Guillaume Obozinski %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-landrieu16 %I PMLR %P 1384--1393 %U https://proceedings.mlr.press/v51/landrieu16.html %V 51 %X 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.
RIS
TY - CPAPER TI - Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions AU - Loic Landrieu AU - Guillaume Obozinski BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-landrieu16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 1384 EP - 1393 L1 - http://proceedings.mlr.press/v51/landrieu16.pdf UR - https://proceedings.mlr.press/v51/landrieu16.html AB - 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. ER -
APA
Landrieu, L. & Obozinski, G.. (2016). Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:1384-1393 Available from https://proceedings.mlr.press/v51/landrieu16.html.

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