A short time existence/uniqueness result for a nonlocal topology-preserving segmentation model

Motivated by a prior applied work of Vese and the second author dedicated to segmentation under topological constraints, we derive a slightly modified model phrased as a functional minimization problem, and propose to study it from a theoretical viewpoint. The mathematical model leads to a second or...

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Bibliographic Details
Published in:Journal of Differential Equations 2012-08, Vol.253 (3), p.977-995
Main Authors: Forcadel, Nicolas, Le Guyader, Carole
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
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Summary:Motivated by a prior applied work of Vese and the second author dedicated to segmentation under topological constraints, we derive a slightly modified model phrased as a functional minimization problem, and propose to study it from a theoretical viewpoint. The mathematical model leads to a second order nonlinear PDE with a singularity at Du=0 and containing a nonlocal term. A suitable setting is thus the one of the viscosity solution theory and, in this framework, we establish a short time existence/uniqueness result as well as a Lipschitz regularity result for the solution.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2012.03.013