This article proposes an original method to estimate a continuous transformation that maps one N-dimensional distribution to another. The method is iterative, non-linear, and is shown to converge. Only 1D marginal distributions are used in the estimation process, hence involving low computation costs. As an illustration this mapping is applied to colour transfer between two images of different contents. The paper also serves as a central focal point for collecting together the research activity in this area and relating it to the important problem of Automated Colour Grading.