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Mumford-Shah minimizers on thin plates

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Abstract

We show that limits of Mumford-Shah minimizers in product domains Ω = Ω′× (0,t), t small, are Mumford-Shah minimizers in one less dimension. The main ingredient of the proof is a symmetry argument from Dal Maso, Morel, and Solimini.

Résumé

On montre que les limites de segmentations minimales pour la fonctionnelle de Mumford-Shah dans des domaines produits \( \Omega = \Omega'\times (0,t)\), avec t petit, sont des segmentations minimales de Mumford-Shah dans \(\Omega '\). La démonstration repose sur un argument de symétrie de Dal Maso, Morel, et Solimini.

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Authors and Affiliations

  1. Mathématiques, Bâtiment 425, Université de Paris-Sud, 91405, Orsay Cedex, France

    Guy David

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  1. Guy David
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Correspondence to Guy David.

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AMS classification 49K99, 49Q20

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David, G. Mumford-Shah minimizers on thin plates. Calc. Var. 27, 203–232 (2006). https://doi.org/10.1007/s00526-006-0018-0

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  • DOI: https://doi.org/10.1007/s00526-006-0018-0

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