An Anisotropic Diffusion Algorithm with Optimized Rotation Invariance

Hanno Scharr, Joachim Weickert

Abstract: For strongly directed anisotropic diffusion filtering it is crucial to use numerical schemes with highly accurate directional behaviour. To this end, we introduce a novel algorithm for coherence-enhancing anisotropic diffusion. It applies recently discovered differentiation filters with optimal rotation invariance [10], 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). We also show that the new scheme is more than three times more efficient than common 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.