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Cortical surface registration plays a crucial role in aligning corticalfunctional and anatomical features across individuals. However, conventionalregistration algorithms are computationally inefficient. Recently,learning-based registration algorithms have emerged as a promising solution,significantly improving processing efficiency. Nonetheless, there remains a gapin the development of a learning-based method that exceeds the state-of-the-artconventional methods simultaneously in computational efficiency, registrationaccuracy, and distortion control, despite the theoretically greaterrepresentational capabilities of deep learning approaches. To address thechallenge, we present SUGAR, a unified unsupervised deep-learning framework forboth rigid and non-rigid registration. SUGAR incorporates a U-Net-basedspherical graph attention network and leverages the Euler angle representationfor deformation. In addition to the similarity loss, we introduce fold andmultiple distortion losses, to preserve topology and minimize various types ofdistortions. Furthermore, we propose a data augmentation strategy specificallytailored for spherical surface registration, enhancing the registrationperformance. Through extensive evaluation involving over 10,000 scans from 7diverse datasets, we showed that our framework exhibits comparable or superiorregistration performance in accuracy, distortion, and test-retest reliabilitycompared to conventional and learning-based methods. Additionally, SUGARachieves remarkable sub-second processing times, offering a notable speed-up ofapproximately 12,000 times in registering 9,000 subjects from the UK Biobankdataset in just 32 minutes. This combination of high registration performanceand accelerated processing time may greatly benefit large-scale neuroimagingstudies.

SUGAR: Spherical Ultrafast Graph Attention Framework for Cortical Surface Registration