In the medical domain, one of the more fundamental problems is the requirement for the setting of images in a state which makes them appear collectively similar . This greatly simplifies the analysis of a group of images which bear common information, as in the case of brain slices fusion or comparison of patient data, either acquired using different modalities or collected at different time instances.
The problem is trivial if the difference is a rigid one - a difference due to rotation, scale and translation. More realistically, the problem is far more complex and images are inconsistent (primarily in the case of inter-subject registration) so affine and non-rigid transformations are required. In the case of non-rigid registration, transformation is merely unbounded. However, to avoid corruption and distortion of constituent finer parts of the image, limitations to their freedom must be forced. Clamped-plate splines (CPS), which are based on Green's function, have proven to be a useful family of warps, allowing for highly flexible manipulation of images. Their attributes are reminiscent of those developed by Lötjönen and Mäkelä .
To drive transformation in the right direction and attain convergence, minimisation of the difference perceived in the images must be pursued. To measure discrepancies, or contrariwise, the similarity between two images, mean of squared differences (MSD) or mutual information (MI) [19,12] are traditionally used as metrics although new techniques are perpetually introduced .
Overall, the process of registration comprises the transformation of images followed by similarity measures, where transformations are chosen to iteratively maximise that similarity. Conventionally, a reference is selected in the process , but our contention is that the entire groups of images should be accounted for when an optimal (correct) solution is sought.