A nonlocal mean curvature flow for multi-dimensional image processing

In this paper, we propose a mean curvature flow equation with nonlocal nonlinearities for an image processing model on noisy surfaces, which corresponds to the negative L^2-gradient flow of surface energy functional in (1.4). We investigate the initial value problem mathematically. Furthermore, numerical simulations are shown, which exhibit that the model performs smoothing operation on a complicated level surface of a given image data while preserving its geometric shape feature under suitable parameters chosen.