Abstract

We address the continuous problem of assigning multiple (unordered) labels with the minimum perimeter. The corresponding dis- crete Potts model is typically addressed with a-expansion which can gen- erate metrication artifacts. Existing convex continuous formulations of the Potts model use TV-based functionals directly encoding perimeter costs. Such formulations are analogous to ’min-cut’ problems on graphs. We propose a novel convex formulation with a continous ’max-flow’ func- tional. This approach is dual to the standard TV-based formulations of the Potts model. Our continous max-flow approach has significant nu- merical advantages; it avoids extra computational load in enforcing the simplex constraints and naturally allows parallel computations over dif- ferent labels. Numerical experiments show competitive performance in terms of quality and significantly reduced number of iterations compared to the previous state of the art convex methods for the continuous Potts model.