On the design of optimal derivative filters for coherence-enhancing diffusion filtering

For strongly oriented anisotropic processes such as coherence-enhancing diffusion filtering, it is crucial to use numerical schemes with highly accurate directional behavior. It is not possible in a satisfactory way when discretizations are limited to 3 × 3 stencils. We can expand discretization stencils in the first-order derivative filters scheme (J. Weickert, 2002). In 2d or 3d images, the directional behavior is correlated with first-order derivative filter. In the paper, new optimized 3-tap and 5-tap pair of first-order derivative filters with rotation-equivariant are designed in anisotropic diffusion for images with different spatial frequencies. We demonstrate the new implements have better behavior with respect to the following properties: rotation invariance, avoidance of blurring artifacts (dissipation), and more efficient.