Monotonicity enhancing nonlinear diffusion

We consider the task of filtering the noise from images and other types of inputs which are assumed to be piecewise continuous and piecewise monotone. We show that nonlinear diffusion of the data, a powerful filtering method, is too restrictive for such a case, leading to piecewise constant functions. We claim that the piecewise monotonicity can be enhanced by nonlinear diffusion of first partial derivatives of the input data. The method is developed in this paper; we introduce the algorithms and present experimental results. (C) 2002 Elsevier Science (USA).