Calculus of Variations and Geometric Measure Theory
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P. W. Dondl - M. Novaga - B. Wirth - S. Wojtowytsch

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

created by novaga on 14 Oct 2018
modified on 28 Sep 2019

[BibTeX]

Published Paper

Inserted: 14 oct 2018
Last Updated: 28 sep 2019

Journal: SIAM J. Math. Anal.
Volume: 51
Number: 5
Pages: 3902–3920
Year: 2019

ArXiv: 1810.05787 PDF

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. We prove convergence of the approximating energies and present numerical results and applications to image segmentation.


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