{"ID":2834430,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.01494","arxiv_id":"2512.01494","title":"A variational method for curve extraction with curvature-dependent energies","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.01494","url_pdf":"https://arxiv.org/pdf/2512.01494v1","authors":"[\"Majid Arthaud\",\"Antonin Chambolle\",\"Vincent Duval\"]","published":"2025-12-01T10:16:58Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[]","has_code":false}