A minimum description length objective function for groupwise non-rigid image registration

Non-rigid registration finds a dense correspondence between a pair of images, so that analogous structures in the two images are aligned. While this is sufficient for atlas comparisons, in order for registration to be an aid to diagnosis, registrations need to be performed on a set of images. In this paper we describe an objective function that can be used for this groupwise registration. We view the problem of image registration as one of learning correspondences from a set of examplar images (the registration set), and derive a Minimum Description Length (MDL) objective function. We give a brief description of the MDL approach as applied to transmitting both single images and sets of images, and show that the concept of a reference image (which is central to defining a consistent correspondence across a set of images) appears naturally as a valid model choice in the MDL approach. In this paper we demonstrate both rigid and non-rigid groupwise registration using our MDL objective function on two-dimensional T1 MR images of the human brain, and show that we obtain a sensible alignment. The extension to the multimodal case is also discussed. We conclude with a discussion as to how the MDL principle can be extended to include other encoding models than those we present here.