Wasserstein active contours

In this paper, we propose a novel and rigorous framework for region-based active contours that combines the Wasserstein distance between statistical distributions in arbitrary dimension and shape derivative tools. To speed-up the computation and be able to handle high-dimensional features and large-scale data, we introduce an approximation of the differential of the Wasserstein distance between histograms. The framework is flexible enough to allow either minimization of the Wasserstein distance to prior distributions, or maximization of the distance between the distributions of the regions to be segmented (i.e. region competition). Numerical results reported demonstrate the advantages of the proposed optimal transport distance with respect to point-wise metrics.