Many disorders that affect the brain can cause shape changes in subcortical structures, and these may provide biomarkers for disease detection and progression. Automatic tools are needed to accurately identify and characterize these alterations. In recent work, we developed a surface multivariate tensor-based morphometry analysis (mTBM) to detect morphological group differences in subcortical structures, and we applied this method to study HIV/AIDS, William's syndrome, Alzheimer's disease and prematurity. Here we will focus more specifically on mTBM in neonates, which, in its current form, starts with manually segmented subcortical structures from MRI images of a two subject groups, places a conformal grid on each of their surfaces, registers them to a template through a constrained harmonic map and provides statistical comparisons between the two groups, at each vertex of the template grid. We improve this pipeline in two ways: first by replacing the constrained harmonic map with a new fluid registration algorithm that we recently developed. Secondly, by optimizing the pipeline to study the putamen in newborns.