A scheme with discrete maximum principle and optimized rotation invariance for coherence enhancing diffusion

Abstract

Experiments show that the widely employed 3×3 stencil schemes for the coherence enhancing diffusion neither provide acceptable rotational invariance nor do they satisfy the maximum–minimum principle at a discrete level. We address the problem of rotation invariance by proposing a new 3×3 stencil scheme. This scheme also lacks in the discrete maximum principle. An enforcement of the discrete maximum principle is presented using a repair technique. Extensive numerical simulations confirmed the advantage of the repaired scheme over the existing 3×3 stencil schemes in terms of rotational invariance and discrete maximum principle.