Riemannian Statistical Analysis of Cortical Geometry with Robustness to Partial Homology and Misalignment

Typical studies of the geometry of the cerebral cortical structure focus on either cortical folding or thickness. They rely on spatial normalization, but use cortical descriptors that are sensitive to misregistration arising from the well-known problems of partial homologies between subject brains and local optima in nonlinear registration. In contrast to these approaches, we propose a novel framework for studying the geometry of the entire cortical sheet, subsuming its folding and thickness characteristics. We propose a novel descriptor of local cortical geometry to increase robustness to partial homology and misregistration. The proposed descriptor lies on a Riemannian manifold, and we describe a method for hypothesis testing on manifolds for cross-sectional studies. Results on simulated and clinical data show the benefits of the proposed approach for detecting between-group differences with greater accuracy and consistency.