  We present a generic method for assessing the quality of non-rigid
registration (NRR) algorithms, that does not depend on the existence of any
ground truth, but depends solely on the data itself. The data is a set of
images. The output of any NRR of such a set of images is a dense correspondence
across the whole set. Given such a dense correspondence, it is possible to
build various generative statistical models of appearance variation across the
set. We show that evaluating the quality of the registration can be mapped to
the problem of evaluating the quality of the resultant statistical model. The
quality of the model entails a comparison between the model and the image data
that was used to construct it. It should be noted that this approach does not
depend on the specifics of the registration algorithm used (i.e., whether a
groupwise or pairwise algorithm was used to register the set of images), or on
the specifics of the modelling approach used.
  We derive an index of image model specificity that can be used to assess
image model quality, and hence the quality of registration. This approach is
validated by comparing our assessment of registration quality with that derived
from ground truth anatomical labeling. We demonstrate that our approach is
capable of assessing NRR reliably without ground truth. Finally, to demonstrate
the practicality of our method, different NRR algorithms -- both pairwise and
groupwise -- are compared in terms of their performance on 3D MR brain data.
