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The field which is associated with this problem is uniformly referred to in the literature as ``non-rigid registration''. The subject is broad and for deeper understanding of alternative approaches, there are useful textbooks [].
Given a collection of images, all of which depict the same type of object, one wishes to transform these images so that the correspondingly transformed objects within the images now appear as similar as possible to one another. The solution to this problem is never a unique one as there will be infinitely many transformations that lead to similar results. Since such images may not contain precisely the same elements, there is rarely an absolute one-to-one correspondence between imaged objects. Absence or reappearance of finer elements, for example, mean that no unique point-to-point correspondence can exist, so good solutions need be approximated instead.
The aim of non-rigid registration of medical images is to properly identify 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.
Typical registration algorithms proceed by optimising an objective function, which depends on the similarity of the images after alignment, wrt 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. The three components of an NRR algorithm are:
Roy Schestowitz 2010-04-05
