Singular Sets of Minimizers for the Mumford-Shah Functional

Guy David - Collection Progress in Mathematics

582 pages, parution le 19/04/2005

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Résumé

This book studies regularity properties of Mumford-Shah minimiz-ers. The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. Some time is spent on the C1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques. In particular, global minimiz-ers in the plane are studied in full detail.

The book is largely self-contained and should be accessible to graduate students in analysis. The core of the book is composed of regularity results that were proved in the last ten years and which are presented in a more detailed and unified way.

Sommaire

Foreword
Presentation of the Mumford-Shah Functional
Functions in the Sobolev Spaces W^{1, p}
Regularity Properties for Quasiminimizers
Limits of Almost-Minimizers
Pieces of C¹ Curves for Almost-Minimizers
Global Mumford-Shah Minimizers in the Plane
Applications to Almost-Minimizers (n = 2)
Quasi- and Almost-Minimizers in Higher Dimensions
Boundary Regularity
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Guy David
Collection	Progress in Mathematics
Parution	19/04/2005
Nb. de pages	582
Format	16 x 24
Couverture	Relié
Poids	1137g
Intérieur	Noir et Blanc
EAN13	9783764371821