We present a newly computationally efficient numerical scheme for
minimizing the flow formulation of the optimal 
mass transport
mapping. We consider the fluid dynamic formulation of the problem, in
which we cast the time-dependency of the mass preserving partial
differential equation as an additional (artificial) spatial dimension. We
present an algorithmic framework tailored for solution of large scale
problems using the proposed formulation. Our implementation accounts for
changes in intensity, which empowers it to function in situations where
high dynamic range (high contrast) images are involved. Lastly, we
demonstrate the effectiveness of our approach with numerical examples.