Entropic Regularisation of Robust Optimal Transport

Grogan et al [11,12] have recently proposed a solution to colour transfer by minimising the Euclidean distance L2 between two probability density functions capturing the colour distributions of two images (palette and target). It was shown to be very competitive to alternative solutions based on Optimal Transport for colour transfer. We show that in fact Grogan et al's formulation can also be understood as a new robust Optimal Transport based framework with entropy regularisation over marginals.