On Semi-implicit Splitting Schemes for the Beltrami Color Flow

Authors:
Lorina Dascal;Guy Rosman;Xue-Cheng Tai;Ron Kimmel
Affiliations:
Department of Computer Science, Technion --- Israel Institute of Technology, Haifa, Israel 32000;Department of Computer Science, Technion --- Israel Institute of Technology, Haifa, Israel 32000;Division of Mathematical Sciences, SPMS, Nanyang Technological University, Singapore 639798 and Department of Mathematics, University of Bergen, Bergen, Norway 5007;Department of Computer Science, Technion --- Israel Institute of Technology, Haifa, Israel 32000
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

The Beltrami flow is an efficient non-linear 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 small time steps and therefore require many iterations. In this paper we introduce a semi-implicit scheme based on the locally one-dimensional (LOD) and additive operator splitting (AOS) schemes for implementing the anisotropic Beltrami operator. The mixed spatial derivatives are treated explicitly, while the non-mixed derivatives are approximated in a semi-implicit manner. Numerical experiments demonstrate the stability of the proposed scheme. Accuracy and efficiency of the splitting schemes are tested in applications such as the scale-space analysis and denoising. In order to further accelerate the convergence of the numerical scheme, the reduced rank extrapolation (RRE) vector extrapolation technique is employed.