The study of brain functions using fMRI often requires an accurate alignment of cortical data across a population. Particular challenges are surface inflation for cortical visualizations and measurements, and surface matching or alignment of functional data on surfaces for group-level analyses. Present methods typically treat each step separately and can be computationally expensive. For instance, smoothing and matching of cortices often require several hours. Conventional methods also rely on anatomical features to drive the alignment of functional data between cortices, whereas anatomy and function can vary across individuals. To address these issues, we propose BrainTransfer, a spectral framework that unifies cortical smoothing, point matching with confidence regions, and transfer of functional maps, all within minutes of computation. Spectral methods decompose shapes into intrinsic geometrical harmonics, but suffer from the inherent instability of eigenbasis. This limits their accuracy when matching eigenbasis, and prevents the spectral transfer of functions. Our contributions consist of, first, the optimization of a spectral transformation matrix, which combines both, point correspondence and change of eigenbasis, and second, focused harmonics, which localize the spectral decomposition of functional data. Brain-Transfer enables the transfer of surface functions across interchangeable cortical spaces, accounts for localized confidence, and gives a new way to perform statistics directly on surfaces. Benefits of spectral transfers are illustrated with a variability study on shape and functional data. Matching accuracy on retinotopy is increased over conventional methods.
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