Riemannian Patch Assignment Gradient Flows
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908332875317248 |
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| author | Gonzalez-Alvarado, Daniel Schlindwein, Fabio Cassel, Jonas Steingruber, Laura Petra, Stefania Schnörr, Christoph |
| author_facet | Gonzalez-Alvarado, Daniel Schlindwein, Fabio Cassel, Jonas Steingruber, Laura Petra, Stefania Schnörr, Christoph |
| contents | This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments across the graph, entirely encoded by a dictionary of competing labeled patches and mediated by patch assignment variables. Maximal consistency of patch assignments is achieved by geometric numerical integration of a Riemannian ascent flow, as critical point of a Lagrangian action functional. Experiments illustrate properties of the approach, including uncertainty quantification of label assignments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Riemannian Patch Assignment Gradient Flows Gonzalez-Alvarado, Daniel Schlindwein, Fabio Cassel, Jonas Steingruber, Laura Petra, Stefania Schnörr, Christoph Computer Vision and Pattern Recognition This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments across the graph, entirely encoded by a dictionary of competing labeled patches and mediated by patch assignment variables. Maximal consistency of patch assignments is achieved by geometric numerical integration of a Riemannian ascent flow, as critical point of a Lagrangian action functional. Experiments illustrate properties of the approach, including uncertainty quantification of label assignments. |
| title | Riemannian Patch Assignment Gradient Flows |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2504.13024 |