We propose a new principle, the
variational region competition
, to simultaneously propagate multiple disjoint level-sets in a fully time-implicit manner, minimizing the total cost w.r.t. region changes. We demonstrate, that the problem of multiphase level-set evolution can be reformulated in terms of a Potts problem, for which fast optimization algorithms are available using recent developments in convex relaxation. Further, we use an efficient recently proposed duality-based continuous max-flow method  implemented using massively parallel computing on GPUs for high computational performance. In contrast to conventional multi-phase level-set evolution approaches, ours allows for large time steps accelerating the evolution procedure. Further, the proposed method propagates all regions simultaneously, as opposed to the one-by-one phase movement of current time-implicit implementations. Promising experiment results demonstrate substantial improvements in a wide spectrum of practical applications.