A Relaxed Wasserstein Distance Formulation for Mixtures of Radially Contoured Distributions

Abstract: Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the same family and satisfy marginal consistency. In this paper, we propose a simple relaxed Wasserstein distance for identifiable mixtures of radially contoured distributions whose components can come from different families. We show some properties of this distance and that its definition does not require marginal consistency. We apply this distance in color transfer tasks and compare its performance with the Wasserstein-type distance for Gaussian mixture models in an experiment. The error of our method is more stable and the color distribution of our output image is more desirable.