For strongly directed anisotropic processes such as coherence-enhancing diffusion filtering it is crucial to use numerical schemes with highly accurate directional behavior. We show that this is not possible in a satisfactory way when discretizations are limited to 3 x 3 stencils. As a consequence, we investigate a novel algorithm based on 5 x 5 stencils. It utilizes recently discovered differentiation filters with optimized rotation invariance. By juxtaposing it with several common algorithms we demonstrate its superior behavior with respect to the following properties: rotation invariance, avoidance of blurring artifacts (dissipativity), and accuracy. The latter one is evaluated by deriving an analytical solution for coherence-enhancing diffusion filtering of images with circular symmetry. Furthermore, we show that the new scheme is 3 to 4 times more efficient than explicit schemes on 3 x 3 stencils. It does not require to solve linear systems of equations, and it can be easily implemented in any dimension.
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