@article{Chambolle2012ACA,
title={A Convex Approach to Minimal Partitions},
author={Antonin Chambolle and Daniel Cremers and Thomas Pock},
journal={SIAM J. Imaging Sciences},
year={2012},
volume={5},
pages={1113-1158}
}

We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically, we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solution: we give some arguments to explain why it should be so, and also discuss some situation where it fails.