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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.01494 |
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| _version_ | 1866911296312573952 |
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| author | Arthaud, Majid Chambolle, Antonin Duval, Vincent |
| author_facet | Arthaud, Majid Chambolle, Antonin Duval, Vincent |
| contents | We introduce a variational approach for extracting curves between a list of possible endpoints, based on the discretization of an energy and Smirnov's decomposition theorem for vector fields. It is used to design a bi-level minimization approach to automatically extract curves and 1D structures from an image, which is mostly unsupervised. We extend then the method to curvature-dependent energies, using a now classical lifting of the curves in the space of positions and orientations equipped with an appropriate sub-Riemanian or Finslerian metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01494 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A variational method for curve extraction with curvature-dependent energies Arthaud, Majid Chambolle, Antonin Duval, Vincent Computer Vision and Pattern Recognition We introduce a variational approach for extracting curves between a list of possible endpoints, based on the discretization of an energy and Smirnov's decomposition theorem for vector fields. It is used to design a bi-level minimization approach to automatically extract curves and 1D structures from an image, which is mostly unsupervised. We extend then the method to curvature-dependent energies, using a now classical lifting of the curves in the space of positions and orientations equipped with an appropriate sub-Riemanian or Finslerian metric. |
| title | A variational method for curve extraction with curvature-dependent energies |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2512.01494 |