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The aim of non-rigid registration is to find an anatomically meaningful, dense (i.e., pixel-to-pixel or voxel-to-voxel) correspondence across a set of images. This correspondence is typically encoded as a set of spatial deformation fields, one for each image, such that when the deformations are applied to the images, corresponding structures are brought into alignment.
A typical registration algorithm proceeds by optimising some objective function that depends on the similarity of the images after alignment, with respect to the set of deformations. As well as the objective function, it is necessary to define the representation used for the deformation fields and the method for finding the optimum of the objective function. Different choices lead to different registration results, and thus competing methods of NRR - hence the need for an objective and easily applied method of assessment.