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Brain surface-based image registration, an important component of brain image analysis, establishes spatial correspondence between cortical surfaces. Existing iterative and learning-based approaches focus on accurate registration of folding patterns of the cerebral cortex, and assume that geometry predicts function and thus functional areas will also be well aligned. However, structure/functional variability of anatomically corresponding areas across subjects has been widely reported. In this work, we introduce a learning-based cortical registration framework, JOSA, which jointly aligns folding patterns and functional maps while simultaneously learning an optimal atlas. We demonstrate that JOSA can substantially improve registration performance in both anatomical and functional domains over existing methods. By employing a semi-supervised training strategy, the proposed framework obviates the need for functional data during inference, enabling its use in broad neuroscientific domains where functional data may not be observed. The source code of JOSA will be released to the public at https://voxelmorph.net.
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