Convergence of a Median filter for level set mean curvature flow

The MBO or thresholding scheme by Merriman, Bence and Osher is one of the most important approximation schemes for mean curvature flow.

In this talk, we will explain a possible extension of this scheme to level set mean curvature flow on a discrete sampled domain.

In this scheme, the function is evolved by a median filter, i.e., iterated applications of a local median. This results in a movement of the level sets according to mean curvature flow.

We prove convergence of the evolution to the viscosity solution in the limit of vanishing time-step size and growing sample size.