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We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to adoi:10.1109/tmi.2009.2030797 pmid:19709963 pmcid:PMC2862393 fatcat:upevg52ygndo3n2hcpo5ebg6ki