The neurons of the human cerebral cortex are arranged in a highly folded sheet, with the majority of the cortical surface area buried in folds. Cortical maps are typically arranged with a topography oriented parallel to the cortical surface. Despite this unambiguous sheetlike geometry, the most commonly used coordinate systems for localizing cortical features are based on 3-D stereotaxic coordinates rather than on position relative to the 2-D cortical sheet. In order to address the need for a more natural surface-based coordinate system for the cortex, we have developed a means for generating an average folding pattern across a large number of individual subjects as a function on the unit sphere and of nonrigidly aligning each individual with the average. This establishes a spherical surface-based coordinate system that is adapted to the folding pattern of each individual subject, allowing for much higher localization accuracy of structural and functional features of the human brain.