Riemannian Shape Analysis of the Corpus Callosum in Kendall Space: Aging and Alzheimer's Disease

The corpus callosum (CC) is a major white-matter structure and a well-established marker of brain aging, but most studies quantify it using scalar summaries that discard its boundary geometry. We present a Riemannian shape-space framework citefletcher2013geodesic-regression for analyzing age-related morphological change in the midsagittal CC, applied to the OASIS-1 cohort. Each contour is represented by 128 landmarks and embedded into Kendall shape space, where translation, rotation, and scale are removed. We derive a multivariate geodesic regression with exact Riemannian gradients and use the fitted age-velocity field to localize age-related deformation to five anatomical sub-regions. In the cognitively normal cohort (n = 252), geodesic regression outperforms the Euclidean linear benchmark (R2 = 0.1355 vs. 0.1216). Regional energy is anterior-dominant: the Genu carries 46.1% and the Anterior Body 23.3% of total age-related shape change, together accounting for ~ 69% despite comprising only ~ 41% of landmarks. Signed projections confirm the ordering (Genu r = 0.562; Anterior Body r = 0.507). In contrast, age explains less than 0.5% of shape variance in Alzheimer's disease (n = 88), indicating that the disease disrupts the healthy aging trajectory. A tangent-space classifier achieves an age-group AUC of 0.791 from the 2D contour alone, exceeding a recent volumetric benchmark (0.67).