| Hardcover ISBN: | 978-3-98547-089-1 |
| Product Code: | EMSMONO/13 |
| List Price: | $75.00 |
| AMS Member Price: | $60.00 |
| Hardcover ISBN: | 978-3-98547-089-1 |
| Product Code: | EMSMONO/13 |
| List Price: | $75.00 |
| AMS Member Price: | $60.00 |
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Book DetailsEMS Monographs in MathematicsVolume: 13; 2025; 266 ppMSC: Primary 49
This book provides a thorough and up-to-date account of the state of art of the regularity theory for minimizers of the Mumford–Shah functional of image segmentation in the 2-dimensional setting. Starting with some classical preliminary results, which settle the issue of existence of minimizing couples \((u, K)\), the structure of the set \(K\) is then analyzed by using $\varepsilon$-regularity theorems. Several consequences of the latter are also investigated, in particular, leading to different characterizations of the Mumford–Shah conjecture.
The proofs are given with full details, often revisiting the relevant literature and introducing new arguments.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipResearchers and graduate students interested in the calculus of variations and geometric measure theory.
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This book provides a thorough and up-to-date account of the state of art of the regularity theory for minimizers of the Mumford–Shah functional of image segmentation in the 2-dimensional setting. Starting with some classical preliminary results, which settle the issue of existence of minimizing couples \((u, K)\), the structure of the set \(K\) is then analyzed by using $\varepsilon$-regularity theorems. Several consequences of the latter are also investigated, in particular, leading to different characterizations of the Mumford–Shah conjecture.
The proofs are given with full details, often revisiting the relevant literature and introducing new arguments.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Researchers and graduate students interested in the calculus of variations and geometric measure theory.
