A variational method for curve extraction with curvature-dependent energies
Computer Vision and Pattern Recognition
2025-12-02 v1
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.
Keywords
Cite
@article{arxiv.2512.01494,
title = {A variational method for curve extraction with curvature-dependent energies},
author = {Majid Arthaud and Antonin Chambolle and Vincent Duval},
journal= {arXiv preprint arXiv:2512.01494},
year = {2025}
}