Journal
JOURNAL OF MATHEMATICAL IMAGING AND VISION
Volume 40, Issue 2, Pages 199-213Publisher
SPRINGER
DOI: 10.1007/s10851-010-0254-y
Keywords
Splitting methods; Beltrami flow; Image denoising; Diffusion
Categories
Funding
- United States-Israel Binational Science Foundation [2004274]
- ISF [1551/09]
- ONR [N00014-06-1-0978]
- Ministry of Science [3-3414]
- Rubin Scientific and Medical Fund
- Elias Fund for Medical Research
- MOE (Ministry of Education) [T207N2202]
- IDM [NRF2007IDMIDM002-010]
- Direct For Social, Behav & Economic Scie
- SBE Off Of Multidisciplinary Activities [2004274] Funding Source: National Science Foundation
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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.
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