Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions

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

Cite

Text

Landrieu and Obozinski. "Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions." International Conference on Artificial Intelligence and Statistics, 2016. doi:10.1137/17M1113436

Markdown

[Landrieu and Obozinski. "Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions." International Conference on Artificial Intelligence and Statistics, 2016.](https://mlanthology.org/aistats/2016/landrieu2016aistats-cut/) doi:10.1137/17M1113436

BibTeX

@inproceedings{landrieu2016aistats-cut,
  title     = {{Cut Pursuit: Fast Algorithms to Learn Piecewise Constant Functions}},
  author    = {Landrieu, Loïc and Obozinski, Guillaume},
  booktitle = {International Conference on Artificial Intelligence and Statistics},
  year      = {2016},
  pages     = {1384-1393},
  doi       = {10.1137/17M1113436},
  url       = {https://mlanthology.org/aistats/2016/landrieu2016aistats-cut/}
}