Consistent Positive Directional Splitting of Anisotropic Diusion

Abstract

Anisotropic nonlinear diusion filters describe a large class of powerful image filtering operations. In order to be applicable to sampled data, the continuous diusion equations have to be discretized, e.g. using additive operator splitting scheme which approximates the continuous equation by one-dimensional processes along several chosen directions. In this paper we concentrate on one step of the separation of the continu- ous diusion into one-dimensional processes: we analyse, design and test consistent positive directional splitting on a 3 ◊ 3 window. We derive a set of formulas for directional diusivities with one free parameter, and demonstrate that the best results are obtained if the parameter is chosen from the interior of the admissible interval.