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Spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences, thereby allowing for group analysis to be carried out. The work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold. The geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework. A multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain, creating the desired normalization. The partial differential equation that carries out the warping is implemented in a Euclidean framework in order to facilitate a multiresolution strategy, thereby permitting large deformations between the two surfaces. The technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces. A quantitative comparison between our proposed surface-based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface-based spatial normalization performs better in matching homologous cortical anatomies.