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dc.contributor.authorRosman, Guyeng
dc.contributor.authorDascal, Lorinaeng
dc.contributor.authorTai, Xue-Chengeng
dc.contributor.authorKimmel, Roneng
dc.PublishedJournal of Mathematical Imaging and Vision 1-15en_US
dc.description.abstractThe Beltrami flow is an efficient nonlinear filter, that was shown to be effective for color image processing. The corresponding anisotropic diffusion operator strongly couples the spectral components. Usually, this flow is implemented by explicit schemes, that are stable only for very small time steps and therefore require many iterations. In this paper we introduce a semi-implicit Crank-Nicolson scheme based on locally one-dimensional (LOD)/additive operator splitting (AOS) for implementing the anisotropic Beltrami operator. The mixed spatial derivatives are treated explicitly, while the non-mixed derivatives are approximated in an implicit manner. In case of constant coefficients, the LOD splitting scheme is proven to be unconditionally stable. Numerical experiments indicate that the proposed scheme is also stable in more general settings. Stability, accuracy, and efficiency of the splitting schemes are tested in applications such as the Beltrami-based scale-space, Beltrami denoising and Beltrami deblurring. In order to further accelerate the convergence of the numerical scheme, the reduced rank extrapolation (RRE) vector extrapolation technique is employed.en_US
dc.rightsAttribution-NonCommercial CC BY-NCeng
dc.subjectSplitting methodseng
dc.subjectBeltrami floweng
dc.subjectImage denoisingeng
dc.titleOn Semi-implicit Splitting Schemes for the Beltrami Color Image Filteringen_US
dc.typePeer reviewed
dc.typeJournal article
dc.rights.holderThe Author(s) 2011en_US
dc.rights.holderCopyright The Author(s) 2011. This article is published with open access at Springerlink.comen_US
dc.subject.nsiVDP::Mathematics and natural science: 400en_US

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