Abstract
We prove that the semidiscrete schemes of a Perona-Malik type equation converge, in a long time scale, to a suitable system of ordinary differential equations defined on piecewise constant functions. The proof is based on a formal asymptotic expansion argument, and on a careful construction of discrete sub and supersolutions. Despite the equation has a region where it is backward parabolic, we prove a discrete comparison principle, which is the key tool for the convergence result.
Lingua originale | English |
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pagine (da-a) | 241-265 |
Numero di pagine | 25 |
Rivista | Mathematical Models and Methods in Applied Sciences |
Volume | 21 |
DOI | |
Stato di pubblicazione | Pubblicato - 2011 |
Keywords
- Perona-Malik
- ill-posed problems
- image segmentation
- partial differential equations