  We propose a framework for jointly modeling the geometry and functionality in
high dimensional functional surfaces. The proposed mixed effects model
characterizes effects of subject-specific covariates and exogenous stimuli on
functional surfaces while accounting for potential mutual-influence of their
geometry and functionality. This is achieved through a computationally
efficient estimation method that incorporates regularized estimation of the
precision matrix of the random effects. We perform a thorough analysis of
cerebral cortical surface structural MRI and task fMRI data from the Human
Connectome Project and discover relationships between the geometric shapes of
cortical surface and neuronal activation responding to task stimuli. Our
findings highlight new modes of correspondence between cortical surface shape
and functional activation relevant to emotion processing.
