On the relation between anisotropic diffusion and iterated adaptive filtering

Abstract

In this paper we present a novel numerical approximation scheme for anisotropic diffusion which is at the same time a special case of iterated adaptive filtering. By assuming a sufficiently smooth diffusion tensor field, we simplify the divergence term and obtain an evolution equation that is computed from a scalar product of diffusion tensor and the Hessian. We propose further a set of filters to approximate the Hessian on a minimized spatial support. On standard benchmarks, the resulting method performs in average nearly as good as the best known denoising methods from the literature, although it is significantly faster and easier to implement. In a GPU implementation video real-time performance is achieved for moderate noise levels. © 2008 Springer-Verlag Berlin Heidelberg.