Anisotropic diffusion and local monotonicity

This paper investigates the relationship between anisotropic diffusion and local monotonicity. A diffusion technique that has locally monotonic root signals is presented. The enhancement algorithm rapidly converges to a locally monotonic signal of the desired degree. It is shown that the diffusion coefficient used here is the only formation that guarantees idempotence for locally monotonic signals. The signals resulting from locally monotonic diffusion are closer to the original signals than the corresponding median root signals. Furthermore, the diffusion algorithm does not have a difficulty with alternating signals, as does the median filter. In contrast to other anisotropic diffusion techniques, the diffusion method given here does not preserve outliers and does not require a gradient magnitude threshold in the diffusion coefficient.