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}
}