Groupwise registration makes sense when more than two images have to be aligned. In order to remove bias, none of the original images are chosen as the single target image. Instead, a group mean image is used. However, an arithmetic mean will work poorly since it tends to smooth out the features that are important for guiding the registrations. Thus, this type of work is mainly focused on approaching the mean image (population center) explicitly or implicitly.

This is the authors’ second paper about groupwise registration. Although it is more theoretical than the first, the basic idea remains the same. Two different groups presented the framework at the 23rd IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2010), indicating that there is some interest in its potential applications.

The authors’ first paper calculated the mean image by adaptively merging images that are similar enough at certain stages during an iterative process until only one image, which is the mean, is left. This paper proposes updating each input image during the iterations in a way that they will all emerge to be similar enough to the mean image in the end (a so-called graph shrink process). Both algorithms work on the manifold formed by the input images. An important question is how to measure the distance between images, especially the latter, which heavily relies on the descendent of the distance to converge. The solution here is to approximate the distance using the velocity vector from the log-demons algorithm (the theoretical convergence proof included in the paper), which implies that the transformation between the final mean image and other images can be modeled by log-demons. Users need to be aware of this implication when additional constrains on the transformation should be considered.

The final word is that the algorithm is meant to work better when the data fits the model well (please refer to figure 4 for an intuitive understanding of the model) while it has its own overhead including building a graph. For example, when dealing with 4D sequence data, a traditional pairwise registration should work fine since adjacent images are always similar enough.