Probabilistic watershed

• Verfasst von: Fita Sanmartin, Enrique [VerfasserIn]
• Verfasst von: Damrich, Sebastian [VerfasserIn]
• Verfasst von: Hamprecht, Fred [VerfasserIn]
• Titel: Probabilistic watershed
• Titelzusatz: sampling all spanning forests for seeded segmentation and semi-supervised learning
• Verf.angabe: Enrique Fita Sanmartin, Sebastian Damrich, Fred A. Hamprecht
• E-Jahr: 2019
• Jahr: 6 Nov 2019
• Umfang: 19 S.
• Fussnoten: Gesehen am 13.07.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2019
• Band/Heft Quelle: (2019), Artikel-ID 1911.02921, Seite 1-19
• DOI: doi:10.48550/arXiv.1911.02921
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Computer Science - Computer Vision and Pattern Recognition
• Sach-SW: Computer Science - Data Structures and Algorithms
• K10plus-PPN: 1810090725

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.