Efficient Beltrami Image Filtering via Vector Extrapolation Methods

The Beltrami image flow is an effective nonlinear filter, often used in color image processing. It was shown to be closely related to the median, total variation, and bilateral filters. It treats the image as a two-dimensional manifold embedded in a hybrid spatial-feature space. Minimization of the image surface area yields the Beltrami flow. The corresponding diffusion operator is anisotropic and strongly couples the spectral components. Thus, there is so far no implicit or operator-splitting-based numerical scheme for the partial differential equation that describes the Beltrami flow in color. Usually, this flow is implemented by explicit schemes, which are stable only for very small time steps and therefore require many iterations. At the other end, vector extrapolation techniques accelerate the convergence of vector sequences, without explicit knowledge of the sequence generator. In this paper, we propose using vector extrapolation techniques for accelerating the convergence of the explicit schemes for the Beltrami flow. Experiments demonstrate fast convergence and efficiency compared to explicit schemes.