The authors have devised, implemented, and tested a fast, spatially accurate technique for calculating the high-dimensional deformation field relating the brain anatomies of an arbitrary pair of subjects. The resulting three-dimensional (3-D) deformation map can be used to quantify anatomic differences between subjects or within the same subject over time and to transfer functional information between subjects or integrate that information on a single anatomic template. The new procedure is based on developmental processes responsible for variations in normal human anatomy and is applicable to 3-D brain images in general, regardless of modality. Hybrid surface models known as Chen surfaces (based on superquadrics and spherical harmonics) are used to efficiently initialize 3-D active surfaces, and these then extract from both scans the developmentally fundamental surfaces of the ventricles and cortex. The construction of extremely complex surface deformation maps on the internal cortex is made easier by building a generic surface structure to model it. Connected systems of parametric meshes model several deep sulci whose trajectories represent critical functional boundaries. These sulci are sufficiently extended inside the brain to reflect subtle and distributed variations in neuroanatomy between subjects. The algorithm then calculates the high-dimensional volumetric warp (typically with 3842x256x3 approximately 0.1 billion degrees of freedom) deforming one 3-D scan into structural correspondence with the other. Integral distortion functions are used to extend the deformation field required to elastically transform nested surfaces to their counterparts in the target scan. The algorithm's accuracy is tested, by warping 3-D magnetic resonance imaging (MRI) volumes from normal subjects and Alzheimer's patients, and by warping full-color 1024(3 ) digital cryosection volumes of the human head onto MRI volumes. Applications are discussed, including the transfer of multisubject 3-D functional, vascular, and histologic maps onto a single anatomic template; the mapping of 3-D brain atlases onto the scans of new subjects; and the rapid detection, quantification, and mapping of local shape changes in 3-D medical images in disease and during normal or abnormal growth and development.