Moo K. Chung | Search arXiv

arXiv2026

Tensor-based Brain Surface Modeling and Analysis

We present a unified computational approach to tensor-based morphometry in detecting the brain surface shape differences between two clinical groups based on magnetic resonance images. Our approach is novel in a sense that we combined surface modeling, surface data smoothing and statistical analysis in a coherent unified mathematical framework. The cerebral cortex has the topology of a 2D highly convoluted sheet. Between two different clinical groups, the local surface area and curvature of the cortex may differ. It is highly likely that such surface shape differences are not uniform over the whole cortex. By computing how such surface metrics differ, the regions of the most rapid structural differences can be localized. To increase the signal to noise ratio, diffusion smoothing based on the explicit estimation of Laplace-Beltrami operator has been developed and applied to the surface metrics. As an illustration, we demonstrate how this new tensor-based surface morphometry can be applied in localizing the cortical regions of the gray matter tissue growth and loss in the brain images longitudinally collected in the group of children.

cs.CV↗

arXiv2026

Poisson Flow of Cortical Folding in Juvenile Myoclonic Epilepsy

Cortical folding reflects coordinated neurodevelopmental processes and is increasingly recognized as a sensitive marker of neurological disease. However, most existing analyses rely on indirect scalar summaries that do not explicitly model folding geometry itself. In juvenile myoclonic epilepsy (JME), a common genetic epilepsy, cortical abnormalities are often subtle, spatially distributed, and difficult to detect using conventional morphometric measures. We introduce a Poisson-equation--based framework that models cortical folding as a geometry-driven flow derived from mean curvature on the cortical manifold. By treating folding patterns as a stationary source--sink structure, the proposed approach yields a smooth, globally balanced potential field whose surface gradient defines a physically interpretable flux. This framework enables spatially coherent analysis of sulcal--gyral folding organization and provides a principled representation of geometry-driven cortical structure in JME.

cs.CV↗