Singular Sets of Minimizers for the Mumford-Shah Functional

  • Guy David

Part of the Progress in Mathematics book series (PM, volume 233)

About this book


Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2004.

This book studies regularity properties of Mumford-Shah minimizers. 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 Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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 minimizers 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.


Minimierungsprobleme Mumford-Shah-Funktional Randwertprobleme Sobolev space Variationsrechnung partielle Differentialgleichungen

Authors and affiliations

  • Guy David
    • 1
  1. 1.Mathématiques, Bâtiment 425Université de Paris-SudOrsay CedexFrance

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Verlag 2005
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-7182-1
  • Online ISBN 978-3-7643-7302-3
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book