  Brain pathologies often manifest as partial or complete loss of tissue. The
goal of many neuroimaging studies is to capture the location and amount of
tissue changes with respect to a clinical variable of interest, such as disease
progression. Morphometric analysis approaches capture local differences in the
distribution of tissue or other quantities of interest in relation to a
clinical variable. We propose to augment morphometric analysis with an
additional feature extraction step based on unbalanced optimal transport. The
optimal transport feature extraction step increases statistical power for
pathologies that cause spatially dispersed tissue loss, minimizes sensitivity
to shifts due to spatial misalignment or differences in brain topology, and
separates changes due to volume differences from changes due to tissue
location. We demonstrate the proposed optimal transport feature extraction step
in the context of a volumetric morphometric analysis of the OASIS-1 study for
Alzheimer's disease. The results demonstrate that the proposed approach can
identify tissue changes and differences that are not otherwise measurable.
