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

  • François Alter

    CMLA-ENS, Cachan, France
  • Vicent Caselles

    Universitat Pompeu-Fabra, Barcelona, Spain
  • Antonin Chambolle

    Ecole Polytechnique, Palaiseau, France

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 , 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.

Cite this article

François Alter, Vicent Caselles, Antonin Chambolle, Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow. Interfaces Free Bound. 7 (2005), no. 1, pp. 29–53

DOI 10.4171/IFB/112