  We propose a new method with $\mathcal{L}_2$ distance that maps one
$N$-dimensional distribution to another, taking into account available
information about correspondences. We solve the high-dimensional problem in 1D
space using an iterative projection approach. To show the potentials of this
mapping, we apply it to colour transfer between two images that exhibit
overlapped scenes. Experiments show quantitative and qualitative competitive
results as compared with the state of the art colour transfer methods.
