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Singular Sets of Minimizers for the Mumford-Shah Functional by Guy David (Englis

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ISBN-13
9783764371821
Book Title
Singular Sets of Minimizers for the Mumford-Shah Functional
ISBN
9783764371821
Subject Area
Mathematics
Publication Name
Singular Sets of Minimizers for the Mumford-Shah Functional
Item Length
9.2 in
Publisher
Springer Basel A&G
Subject
Differential Equations / General, Geometry / Differential, Functional Analysis, Calculus, Differential Equations / Partial, Optimization
Series
Progress in Mathematics Ser.
Publication Year
2005
Type
Textbook
Format
Hardcover
Language
English
Item Height
1.4 in
Author
Guy David
Item Width
6.4 in
Item Weight
37.5 Oz
Number of Pages
Xiv, 581 Pages

關於產品

Product Information

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 Some time is spent on the C 1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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

Product Identifiers

Publisher
Springer Basel A&G
ISBN-10
376437182x
ISBN-13
9783764371821
eBay Product ID (ePID)
20038669316

Product Key Features

Author
Guy David
Publication Name
Singular Sets of Minimizers for the Mumford-Shah Functional
Format
Hardcover
Language
English
Subject
Differential Equations / General, Geometry / Differential, Functional Analysis, Calculus, Differential Equations / Partial, Optimization
Series
Progress in Mathematics Ser.
Publication Year
2005
Type
Textbook
Subject Area
Mathematics
Number of Pages
Xiv, 581 Pages

Dimensions

Item Length
9.2 in
Item Height
1.4 in
Item Width
6.4 in
Item Weight
37.5 Oz

Additional Product Features

LCCN
2005-043573
Intended Audience
Scholarly & Professional
Series Volume Number
233
Number of Volumes
1 Vol.
Lc Classification Number
Qa402.5-402.6
Reviews
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), 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), From the reviews: a?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 a? and the book is therefore a useful source for mathematicians working in this field.a?(MATHEMATICAL REVIEWS)
Table of Content
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.
Copyright Date
2005
Dewey Decimal
515/.64
Dewey Edition
22
Illustrated
Yes

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