Approximation of the Mumford-Shah Functional by Phase Fields of Bounded Variation

Sandro Belz; Kristian Bredies

doi:10.1142/s0219530520500190

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arXiv · 1903.02349

Approximation of the Mumford-Shah Functional by Phase Fields of Bounded Variation

Sandro Belz·Kristian Bredies

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Abstract

In this paper we introduce a new phase field approximation of the Mumford-Shah functional similar to the well-known one from Ambrosio and Tortorelli. However, in our setting the phase field is allowed to be a function of bounded variation, instead of an $H^1$-function. In the context of image segmentation, we also show how this new approximation can be used for numerical computations, which contains a total variation minimization of the phase field variable, as it appears in many problems of image processing. A comparison to the classical Ambrosio-Tortorelli approximation, where the phase field is an $H^1$-function, shows that the new model leads to sharper phase fields.

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Sandro Belz, Kristian Bredies. 2019-03-06. Approximation of the Mumford-Shah Functional by Phase Fields of Bounded Variation. https://doi.org/10.1142/s0219530520500190

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