ENCORE: Fast geometric framework for aligning brain structural connectivity on cortical manifolds.

Brain networks are typically represented by adjacency matrices, where each node corresponds to a brain region. In traditional brain network analysis, nodes are assumed to be matched across individuals, but the methods used for node matching often overlook the underlying connectivity information. This oversight can result in inaccurate node alignment, leading to inflated edge variability. To overcome this challenge, we propose a novel framework for registering high-resolution continuous connectivity (ConCon), defined as a continuous function on a product manifold space - specifically, the cortical surface - capturing structural connectivity between all pairs of cortical points. Leveraging ConCon, we formulate an optimal diffeomorphism problem to align both connectivity profiles and cortical surfaces simultaneously. We introduce an efficient algorithm to solve this problem and validate our approach using data from the Human Connectome Project (HCP). Results show that ENCORE consistently improves inter-subject correspondence of fine-grained connectivity features and yields higher accuracy in structural pathway localization compared with existing surface-based registration methods.