The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with respect to its well-posedness and scale-space properties. An efficient scheme is presented which uses a stabilization by a semi-implicit additive operator splitting (AOS), and the scale-space behaviour of this method is illustrated by applying it to both 2-D and 3-D images.

ing it is crucial to use numerical schemes with highly accurate directional behaviour. To this end, we introduce a novel algorithm for coherence-enhancing anisotropic diusion. It applies recently discovered dierentiation lters with optimal rotation invariance [11], and comes down to an explicit scheme on a 5#5 stencil. By comparing it with several common algorithms we demonstrate its superior behaviour regarding rotation invariance and avoidance of blurring artifacts (dissipativity). Wealsoshow that the new scheme is more than three times more ecient than common explicit schemes on 3 # 3 stencils. It does not require to solve linear systems of equations, and it can be easily implemented in any dimension. ######### Low-level vision, diusion ltering, scale-spaces, performance evaluation, rotation invariance, fast algorithms 1 Introduction In this paper we present and evaluate a novel algorithm for coherence