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arXiv · 1810.05787

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

Patrick Dondl·Matteo Novaga·Benedikt Wirth·Stephan Wojtowytsch
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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.

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Patrick Dondl, Matteo Novaga, Benedikt Wirth, Stephan Wojtowytsch. 2018-10-13. Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields. https://arxiv.org/abs/1810.05787

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