Résumé en anglais

This paper introduces a novel and generic framework embedding statistical constraints for variational problems. We resort to the theory of Monge-Kantorovich optimal mass transport to define penalty terms depending on statistics from images. To cope with the computation time issue of the corresponding Wasserstein distances involved in this approach, we propose an approximate variational formulation for statistics represented as point clouds. We illustrate this framework on the problem of regularized color specification. This is achieved by combining the proposed approximate Wasserstein constraint on color statistics with a generic geometric-based regularization term in a unified variational minimization problem. We believe that this methodology may lead to some other interesting applications in image processing, such as medical imaging modification, texture synthesis, etc.