Nonlinear diffusion filtering on extended neighborhood

A generalization to the nonlinear diffusion of digital images is proposed, taking into account an extended neighborhood as a prolongation to information derived from local, nearest-neighboring pixels. Traditionally, each iteration in nonlinear diffusion filtering is performed on a 3 × 3 window. While several iterations can propagate this local information to pixels which are further away from the center of the window, it clearly presents a limitation in some applications as compared to non-PDE based filtering approaches in which the window is larger than 3 × 3. Here, an extension is presented to describe the nonlinear diffusion equation for larger windows, thus overcoming this limitation.