GERMAN

Singular Sets of Minimizers for the Mumford-Shah Functional

By Guy David

Book information

Publisher
Birkhäuser
Year
2005
ISBN
376437182X, 9783764371821
Open Library ID
OL17176993M
Language
german
Format
PDF
Filesize
6 MB (6246739 bytes)
Series
Progress in Mathematics
Edition
1
Pages
592\592
Time added
2011-01-06 10:13:16

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 Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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

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