  With the adoption of powerful machine learning methods in medical image
analysis, it is becoming increasingly desirable to aggregate data that is
acquired across multiple sites. However, the underlying assumption of many
analysis techniques that corresponding tissues have consistent intensities in
all images is often violated in multi-centre databases. We introduce a novel
intensity normalisation scheme based on density matching, wherein the
histograms are modelled as Dirichlet process Gaussian mixtures. The source
mixture model is transformed to minimise its $L^2$ divergence towards a target
model, then the voxel intensities are transported through a mass-conserving
flow to maintain agreement with the moving density. In a multi-centre study
with brain MRI data, we show that the proposed technique produces excellent
correspondence between the matched densities and histograms. We further
demonstrate that our method makes tissue intensity statistics substantially
more compatible between images than a baseline affine transformation and is
comparable to state-of-the-art while providing considerably smoother
transformations. Finally, we validate that nonlinear intensity normalisation is
a step toward effective imaging data harmonisation.
