Abstract:
In this paper, we consider minimizing the Mumford-Shah functional over two-valued functions in the plane, which is equivalent to minimizing over characteristic functions. Existence of minimizers is straightforward and we show that any minimizing set is essentially open, has a boundary with finitely many connected components, and each component is C 1. The relatively quick proof does not rely on quasi-minimal surface or varifold theory, but on uniform estimates on the regularity of the boundary.
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Received: 4 February 1997 / Revised version: 4 February 1998
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Larsen, C. A new proof of regularity for¶two-shaded image segmentations . manuscripta math. 96, 247–262 (1998). https://doi.org/10.1007/s002290050065
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DOI: https://doi.org/10.1007/s002290050065