Optimal transport is nowadays a major statistical tool for computer vision and image processing. It may be used for measuring similarity between features, matching and averaging features or registrating images. However, a major drawback of this framework is the lack of regularity of the transport map and the robustness to outliers. The computational cost associated to the estimation of optimal transport is also very high and the application of such theory is difficult for problems of large dimensions. Hence, we are interested in the definition of new algorithms for computing solutions of generalized optimal transports that include some regularity priors.