Singular Sets of Minimizers for the Mumford-Shah Functional
Ferran Sunyer i Balaguer Award winning monograph
David, Guy.
creator
author.
SpringerLink (Online service)
text
sz
2005
monographic
eng
access
XIV, 581 p. online resource.
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 Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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.
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.
by Guy David.
Mathematics
Functional analysis
Partial differential equations
Calculus of variations
Mathematics
Calculus of Variations and Optimal Control; Optimization
Functional Analysis
Partial Differential Equations
QA315-316
QA402.3
QA402.5-QA402.6
515.64
Springer eBooks
Progress in Mathematics ; 233
9783764373023
http://dx.doi.org/10.1007/b137039
http://dx.doi.org/10.1007/b137039
100301
20180115171750.0
978-3-7643-7302-3