Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model

We consider Alternating Direction Implicit (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. in [10] for several imaging applications. The discretised scheme is shown to preserve analogous properties to the continuous model....

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 904; no. 1; pp. 12014 - 12019
Main Authors Calatroni, L., Estatico, C., Garibaldi, N., Parisotto, S.
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.10.2017
Subjects
Alternating direction implicit methods
Implicit methods
Mathematical models
Osmosis
Physics
Splitting
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Summary:We consider Alternating Direction Implicit (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. in [10] for several imaging applications. The discretised scheme is shown to preserve analogous properties to the continuous model. The dimensional splitting strategy traduces numerically into the solution of simple tridiagonal systems for which standard matrix factorisation techniques can be used to improve upon the performance of classical implicit methods, even for large time steps. Applications to the shadow removal problem are presented.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/904/1/012014