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Approximation of the Mumford–Shah functional by phase fields of bounded variation.
- Source :
-
Analysis & Applications . Mar2021, Vol. 19 Issue 2, p183-217. 35p. - Publication Year :
- 2021
-
Abstract
- In this paper, we introduce a new phase field approximation of the Mumford–Shah functional similar to the well-known one from Ambrosio and Tortorelli. However, in our setting the phase field is allowed to be a function of bounded variation, instead of an H 1 -function. In the context of image segmentation, we also show how this new approximation can be used for numerical computations, which contains a total variation minimization of the phase field variable, as it appears in many problems of image processing. A comparison to the classical Ambrosio–Tortorelli approximation, where the phase field is an H 1 -function, shows that the new model leads to sharper phase fields. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02195305
- Volume :
- 19
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 148182655
- Full Text :
- https://doi.org/10.1142/S0219530520500190