Item description for Singular Sets of Minimizers for the Mumford-Shah Functional (Progress in Mathematics) by Guy David...
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 Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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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Est. Packaging Dimensions: Length: 9.1" Width: 6.3" Height: 1.4" Weight: 2.45 lbs.
Release Date Aug 5, 2005
Publisher Birkhäuser Basel
ISBN 376437182X ISBN13 9783764371821
Availability 89 units. Availability accurate as of Jan 19, 2017 12:53.
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More About Guy David
Guy David was born in 1957 and has an academic affiliation as follows - Institut Universitaire de France.