Singular Sets of Minimizers for the Mumford-Shah Functional

2005
ISBN: 978-3-7643-7182-1
Verlag: Springer

Buch, Englisch, Band 233, 581 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1062 g

Reihe: Progress in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

David, Guy

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.