Probabilistic Watershed: Sampling all spanning forests for seeded segmentation and semi-supervised learning
Abstract
The seeded Watershed algorithm / minimax semi-supervised learning on a graph computes a minimum spanning forest which connects every pixel / unlabeled node to a seed / labeled node. We propose instead to consider all possible spanning forests and calculate, for every node, the probability of sampling a forest connecting a certain seed with that node. We dub this approach "Probabilistic Watershed". Leo Grady (2006) already noted its equivalence to the Random Walker / Harmonic energy minimization. We here give a simpler proof of this equivalence and establish the computational feasibility of the Probabilistic Watershed with Kirchhoff's matrix tree theorem. Furthermore, we show a new connection between the Random Walker probabilities and the triangle inequality of the effective resistance. Finally, we derive a new and intuitive interpretation of the Power Watershed.
Cite
@article{arxiv.1911.02921,
title = {Probabilistic Watershed: Sampling all spanning forests for seeded segmentation and semi-supervised learning},
author = {Enrique Fita Sanmartin and Sebastian Damrich and Fred A. Hamprecht},
journal= {arXiv preprint arXiv:1911.02921},
year = {2019}
}
Comments
To be published in NeurIPS2019