Singular Sets of Minimizers for the Mumford-Shah Functional

Singular Sets of Minimizers for the Mumford-Shah Functional

By (author) 

Free delivery worldwide

Available. Dispatched from the UK in 3 business days
When will my order arrive?

Description

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. It 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.
show more

Product details

  • Hardback | 581 pages
  • 161.54 x 232.41 x 34.8mm | 1,063g
  • Basel, Switzerland
  • English
  • 2005 ed.
  • XIV, 581 p.
  • 376437182X
  • 9783764371821

Table of contents

Presentation of the Mumford-Shah Functional.- Functions in the Sobolev Spaces W1,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.
show more

Review Text

From the reviews:

"This monograph is the Ferran Sunyer i Balaguer 2004 prize winner.The book under review gives an excellent overview of a part of the work done in recent years on this problem ... and the book is therefore a useful source for mathematicians working in this field."(MATHEMATICAL REVIEWS)
show more

Review quote

From the reviews:


"This monograph is the Ferran Sunyer i Balaguer 2004 prize winner.The book under review gives an excellent overview of a part of the work done in recent years on this problem ... and the book is therefore a useful source for mathematicians working in this field."(MATHEMATICAL REVIEWS)
show more