Transformation Model and Constraints Cause Bias in Statistics on Deformation Fields

This work investigates the effects of nonrigid transformation model and deformation constraints on the results of deformation-based morphometry (DBM) studies. We evaluate three popular registration algorithms: a B-spline algorithm with several different constraint terms, Thirion's demons algorithm, and a curvature PDE-based algorithm. All algorithms produced virtually identical overlaps of corresponding structures, but the underlying deformation fields were very different, and the Jacobian determinant values within homogeneous structures varied dramatically. In several cases, we observed bi-modal distributions of Jacobians within a region that violate the assumption of gaussianity that underlies many statistical tests. Our results demonstrate that, even with perfect overlap of corresponding structures, the statistics of Jacobian values are affected by bias due to design elements of the particular nonrigid registration. These findings are not limited to DBM, but also apply to voxel-based morphometry to the extent that it includes a Jacobian-based correction step ("modulation").