Instead of uniform rescaling along the three cardinal axes, it is also possible to rescale anisotropically. In this case, the order in which rotations and rescaling are performed also matters. Indeed, nine-parameter affine transformations do not comprise a closed set under matrix inversion or matrix multiplication, since these operations can alter the order in which rotations are rescaling are performed. Consequently, use of the nine-parameter affine model implies an intrinsic asymmetry between two images that are being registered. For registration of images from a single subject, this model would be useful if one of the images is known to be properly calibrated, but the calibration of the other image is unknown. In this case, variable rescaling would need to be applied to the unknown image before that image is rotated to match the other image. For intersubject registration, this model is often used as part of the global Talairach transformation (see the chapter entitled "Talairach Space as a Tool for Intersubject Standardization in the Brain." In this case, the rescaling is applied after rotation of an individual brain to match an atlas target. Consequently, two different formulations may be required. The representation of the first formulation is
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