@article {Wolf2020,
	title = {The Mutex Watershed and its Objective: Efficient, Parameter-Free Graph Partitioning},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {43},
	year = {2020},
	pages = {3724-3738},
	abstract = {Image partitioning, or segmentation without semantics, is the task of decomposing an image into distinct segments, or equivalently to detect closed contours. Most prior work either requires seeds, one per segment; or a threshold; or formulates the task as multicut / correlation clustering, an NP-hard problem. Here, we propose a greedy algorithm for signed graph partitioning, the "Mutex Watershed". Unlike seeded watershed, the algorithm can accommodate not only attractive but also repulsive cues, allowing it to find a previously unspecified number of segments without the need for explicit seeds or a tunable threshold. We also prove that this simple algorithm solves to global optimality an objective function that is intimately related to the multicut / correlation clustering integer linear programming formulation. The algorithm is deterministic, very simple to implement, and has empirically linearithmic complexity. When presented with short-range attractive and long-range repulsive cues from a deep neural network, the Mutex Watershed gives the best results currently known for the competitive ISBI 2012 EM segmentation benchmark.},
	doi = {10.1109/tpami.2020.2980827},
	author = {Wolf, Steffen and Bailoni, Alberto and Pape, Constantin and Rahaman, Nasim and Kreshuk, Anna and K{\"o}the, Ullrich and Hamprecht, Fred A.}
}
@conference {Wolf2018,
	title = {The Mutex Watershed: Efficient, Parameter-Free Image Partitioning},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {11208 LNCS},
	year = {2018},
	month = {apr},
	pages = {571{\textendash}587},
	abstract = {Image partitioning, or segmentation without semantics, is the task of decomposing an image into distinct segments; or equivalently, the task of detecting closed contours in an image. Most prior work either requires seeds, one per segment; or a threshold; or formulates the task as an NP-hard signed graph partitioning problem. Here, we propose an algorithm with empirically linearithmic complexity. Unlike seeded watershed, the algorithm can accommodate not only attractive but also repulsive cues, allowing it to find a previously unspecified number of segments without the need for explicit seeds or a tunable threshold. The algorithm itself, which we dub {\textquotedblleft}Mutex Watershed{\textquotedblright}, is closely related to a minimal spanning tree computation. It is deterministic and easy to implement. When presented with short-range attractive and long-range repulsive cues from a deep neural network, the Mutex Watershed gives results that currently define the state-of-the-art in the competitive ISBI 2012 EM segmentation benchmark. These results are also better than those obtained from other recently proposed clustering strategies operating on the very same network outputs.},
	isbn = {9783030012243},
	issn = {16113349},
	doi = {10.1007/978-3-030-01225-0_34},
	url = {http://arxiv.org/abs/1904.12654},
	author = {Wolf, Steffen and Pape, Constantin and Bailoni, Alberto and Rahaman, Nasim and Kreshuk, Anna and Ullrich K{\"o}the and Fred A. Hamprecht}
}
