{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/probabilistic-watershed-sampling-all-spanning","title":"Probabilistic Watershed: Sampling all spanning forests for seeded segmentation and semi-supervised learning","arxiv_id":"1911.02921","date":"2019-11-06","proceeding":"NeurIPS 2019 12","authors":["Enrique Fita Sanmartin","Sebastian Damrich","Fred A. Hamprecht"],"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.","url_abs":"https://arxiv.org/abs/1911.02921v1","url_pdf":"https://arxiv.org/pdf/1911.02921v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"probabilistic-watershed-sampling-all-spanning","repo_url":"https://github.com/hci-unihd/Probabilistic_Watershed","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"all","task_name":"All"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1911.02921","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}