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On Semi-implicit Splitting Schemes for the Beltrami Color Image Filtering

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dc.contributor.author Rosman, Guy eng
dc.contributor.author Dascal, Lorina eng
dc.contributor.author Tai, Xue-Cheng eng
dc.contributor.author Kimmel, Ron eng
dc.date.accessioned 2011-03-02T11:06:14Z
dc.date.available 2011-03-02T11:06:14Z
dc.date.issued 2011 eng
dc.identifier.citation Journal of Mathematical Imaging and Vision 1-15 en_US
dc.identifier.uri http://hdl.handle.net/1956/4541
dc.description.abstract The 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.language.iso eng eng
dc.publisher Springer en
dc.rights Copyright The Author(s) 2011. This article is published with open access at Springerlink.com eng
dc.rights.uri http://creativecommons.org/licenses/by-nc/2.5/ eng
dc.subject Splitting methods eng
dc.subject Beltrami flow eng
dc.subject Image denoising eng
dc.subject Diffusion eng
dc.title On Semi-implicit Splitting Schemes for the Beltrami Color Image Filtering en_US
dc.type Peer reviewed eng
dc.type Journal article eng
dc.subject.nsi VDP::Mathematics and natural science: 400 eng
dc.rightsHolder The Author(s) 2011 eng
dc.type.version publishedVersion eng
bora.peerreviewed Peer reviewed eng
bibo.doi http://dx.doi.org/10.1007/s10851-010-0254-y eng
dc.identifier.doi http://dx.doi.org/10.1007/s10851-010-0254-y


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Copyright The Author(s) 2011. This article is published with open access at Springerlink.com Except where otherwise noted, this item's license is described as Copyright The Author(s) 2011. This article is published with open access at Springerlink.com

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