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This work presents a novel cortical surface registration framework by using the whole anatomical atlas structures as correspondence constraints, which are extracted as atlas graphs (nodes are the junctions and edges are the intersecting curves of regions). The focus of this work is on the geometric registration category of cortical surfaces, i.e., brains are registered only using structural information without any functional information. We aim to innovate the geometric registration framework by utilizing the prominent anatomical features, atlas, to drive the registration. Intuitively, we convert the 3D cortical surfaces to 2D disks by special geometric mappings, where the curvy atlas regions become straight and convex polygonal regions; then registration is achieved between 2D domains such that curvy constrains become linear constraints and are solvable in linear time. The mappings generated are intrinsic and have …