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Singular Sets of Minimizers for the Mumford-Shah Functional 2005 Edition
Contributor(s): David, Guy (Author)
ISBN: 376437182X     ISBN-13: 9783764371821
Publisher: Birkhauser
OUR PRICE:   $104.49  
Product Type: Hardcover - Other Formats
Published: March 2005
Qty:
Annotation: 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 Some time is spent on the C1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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 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.
Additional Information
BISAC Categories:
- Mathematics | Linear & Nonlinear Programming
- Mathematics | Mathematical Analysis
- Mathematics | Differential Equations - General
Dewey: 515.64
LCCN: 2005043573
Series: Progress in Mathematics
Physical Information: 1.37" H x 6.36" W x 9.15" (2.47 lbs) 581 pages
 
Descriptions, Reviews, Etc.
Publisher Description:

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 Some time is spent on the C 1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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