English

Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields

Analysis of PDEs 2018-10-16 v1

Abstract

We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional and the connectedness constraint of (Dondl, Lemenant, Wojtowytsch 2017). We prove convergence of the approximating energies and present numerical results and applications to image segmentation.

Keywords

Cite

@article{arxiv.1810.05787,
  title  = {Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields},
  author = {Patrick Dondl and Matteo Novaga and Benedikt Wirth and Stephan Wojtowytsch},
  journal= {arXiv preprint arXiv:1810.05787},
  year   = {2018}
}
R2 v1 2026-06-23T04:38:22.406Z