A New Scheme for Anisotropic Di usion: Performance Evaluation of Rotation Invariance, Dissipativity and EÆciency

For strongly directed anisotropic di usion ltering it is crucial to use numerical schemes with highly accurate directional behaviour. To this end, we introduce a novel algorithm for coherence-enhancing anisotropic di usion. It applies recently discovered di erentiation 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). We also show that the new scheme is more than three times more eÆcient 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.