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Abstract This paper concerns the spatial and intensity transformations that map one image onto another. We present a general technique that facilitates nonlinear spatial (stereotactic) normalization and image realignment. This technique minimizes the sum of squares between two images following nonlinear spatial deformations and transformations of the voxel (intensity) values. The spatial and intensity transformations are obtained simultaneously, and explicitly, using a least squares solution and a series of linearising devices. The approach is completely noninteractive (automatic), nonlinear, and noniterative. It can be applied in any number of dimensions. Various applications are considered, including the realignment of functional magnetic resonance imaging (MRI) time‐series, the linear (affine) and nonlinear spatial normalization of positron emission tomography (PET) and structural MRI images, the coregistration of PET to structural MRI, and, implicitly, the conjoining of PET and MRI to obtain high resolution functional images. © 1995 Wiley‐Liss, Inc.
Friston et al. (Sun,) studied this question.