Modern theory of numerical methods for motion by mean curvature

We analyze two finite difference schemes, the median and the morphological schemes, for numerically solving the motion by mean curvature partial differential equation. We show that these schemes satisfy sufficient conditions for convergence to the correct viscosity solution of the underlying equation. Moreover, we explore a recent link between the motion by mean curvature partial differential equation to a two-person differential game; we argue that these schemes can be interpreted as discrete approximations to this two-person differential game. Numerical results comparing the two schemes to standard finite difference discretization are also presented.