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

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


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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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