On Semi-implicit Splitting Schemes for the Beltrami Color Flow

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.