Optimal Transport (OT) is a very popular framework for performing colour transfer in images and videos. We have proposed an alternative framework where the cost function used for inferring a parametric transfer function is defined as the robust 2 divergence between two probability density functions (Grogan and Dahyot, 2015). In this paper, we show that our approach combines many advantages of state of the art techniques and outperforms many recent algorithms as measured quantitatively with standard quality metrics, and qualitatively using perceptual studies (Grogan and Dahyot, 2017). Mathematically, our formulation is presented in contrast to the OT cost function that shares similarities with our cost function. Our formulation, however, is more flexible as it allows colour correspondences that may be available to be taken into account and performs well despite potential occurrences of correspondence outlier pairs. Our algorithm is shown to be fast, robust and it easily allows for user interaction providing freedom for artists to fine tune the recoloured images and videos (Grogan et al., 2017).