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Medical image interpretation is a difficult problem due to cross-invdividual anatomical variation. Additionally, there are factors such as image acquisition errors and soft tissue deformation. In order to perform an analysis of medical images, there needs to be a degree of commonality across these images. Above all, the images must have spatial relationships between them identified. Only by identifying these relationship, can a one-to-one pixel correspondence be obtained. This establishment of inter-image correspondences is possible owing to non-rigid registration.
NRR is a process where images get warped by the means of spatial transformations and their similarity then measured. Warps are chosen which increase this similarity. A good registration algorithm is one which is able to select and apply the 'correct' composition of warps to an image and is able to faithfully estimate similarity between images. In the medical domain, however, there is rarely a solution which is objectively correct. There is no single approach to solving the NRR problem either. The different algorithms in existence use different objective functions, which comprise the way spatial deformation fields are represented, the similarity measure, and the method for selecting deformations to maximise similarity.
Certain algorithms choose to warp one image at a time, fitting it to another arbitrary image in the set, which is known as the reference image or the template. Other algorithms rid the registration framework from bias by comparing any image with the remainder of the set (either in full or partially), directly or implicitly. The results are then not subjected to an arbitrary choice of a reference image. As many ways exist for registering images, solutions remain subjective. Each NRR algorithm will, in principle, lead to a different result, so the need to compare the algorithms becomes more apparent.