Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow

Abstract

In this paper we compute the explicit evolution of the Minimizing Total Variation flow when the initial condition is the characteristic function of a convex set in ${\mathbb{R}}^2$, or a finite number of them which are sufficiently separated. We shall also obtain some explicit solutions of the Total Variation formulation of the denoising problem in image processing. We illustrate these results with some experiments.