A variational method for curve extraction with curvature-dependent energies
This work addresses curve extraction in image processing, which is incremental as it builds on existing variational and metric-based methods.
The authors tackled the problem of automatically extracting curves and 1D structures from images by introducing a variational approach based on discretizing an energy and using Smirnov's decomposition theorem, and extended it to handle curvature-dependent energies via a lifting technique in a sub-Riemannian or Finslerian metric space.
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.