Riemannian Shape Analysis of the Corpus Callosum in Kendall Space: Aging and Alzheimer's Disease
Abstract
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 \cite{fletcher2013geodesic-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 ($0.67$).
Related
- The exact region determined by Blomqvist's beta, Spearman's footrule and Kendall's tau
- Propagation of opinions on a network. Convergence, spreading speed and patterns in the Daley-Kendall model
- Handwriting-based Alzheimer’s disease classification on the DARWIN dataset: Repeated nested validation, task-level reduction, and cross-validated explainability
- Multimodal Three-Class Alzheimer's Disease Classification: The MCI Bottleneck
- Predicting Long-Term ADAS-Cog Change From Early Response After Repetitive Transcranial Magnetic Stimulation in Alzheimer Disease
BibTeX
@misc{abawonse2026riemannian,
title = {{Riemannian Shape Analysis of the Corpus Callosum in Kendall Space: Aging and Alzheimer's Disease}},
author = {Olakunle S. Abawonse and Fatou Fall},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05326},
eprint = {2610.05326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05326},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Riemannian Shape Analysis of the Corpus Callosum in Kendall Space: Aging and Alzheimer's Disease
AU - Olakunle S. Abawonse
AU - Fatou Fall
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.05326
UR - https://arxiv.org/abs/2610.05326
AB - 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 \cite{fletcher2013geodesic-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 (R^2 = 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 ($0.67$).
ER -