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arXiv · 1911.02921

Probabilistic Watershed: Sampling all spanning forests for seeded segmentation and semi-supervised learning

Enrique Fita Sanmartin·Sebastian Damrich·Fred A. Hamprecht
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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.

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Enrique Fita Sanmartin, Sebastian Damrich, Fred A. Hamprecht. 2019-11-06. Probabilistic Watershed: Sampling all spanning forests for seeded segmentation and semi-supervised learning. https://arxiv.org/abs/1911.02921

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