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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 spatial deformation field between each pair of images, so that when one image is deformed onto another, corresponding structures are brought into alignment. Such non-rigid registration of medical images is a difficult problem, due to the size and complexity of cross-individual anatomical variation.
A typical registration algorithm proceeds by optimising some objective function. The objective function depends on, for example, the degree of deformation present in the spatial deformation fields defining the correspondence, and the image similarity that remains after the deformation has been applied. Also to be defined are the representation used for the deformation fields, and the method used for finding the optimum of the objective function. Varying any of these factors produces a different registration algorithm, which in general, tends to produce a slightly different resulting correspondence.