A variational method for curve extraction with curvature-dependent energies

• URL: http://arxiv.org/abs/2512.01494v1
• Date: Mon, 01 Dec 2025 10:16:58 GMT
• Title: A variational method for curve extraction with curvature-dependent energies
• Abstract summary: We introduce a variational approach for extracting curves between a list of possible endpoints.<n>It is used to design a bi-level minimization approach to automatically extract curves and 1D structures from an image.
• Score: 0.15293427903448018
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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