  Analysis of longitudinal changes in imaging studies often involves both
segmentation of structures of interest and registration of multiple timeframes.
The accuracy of such analysis could benefit from a tailored framework that
jointly optimizes both tasks to fully exploit the information available in the
longitudinal data. Most learning-based registration algorithms, including joint
optimization approaches, currently suffer from bias due to selection of a fixed
reference frame and only support pairwise transformations. We here propose an
analytical framework based on an unbiased learning strategy for group-wise
registration that simultaneously registers images to the mean space of a group
to obtain consistent segmentations. We evaluate the proposed method on
longitudinal analysis of a white matter tract in a brain MRI dataset with 2-3
time-points for 3249 individuals, i.e., 8045 images in total. The
reproducibility of the method is evaluated on test-retest data from 97
individuals. The results confirm that the implicit reference image is an
average of the input image. In addition, the proposed framework leads to
consistent segmentations and significantly lower processing bias than that of a
pair-wise fixed-reference approach. This processing bias is even smaller than
those obtained when translating segmentations by only one voxel, which can be
attributed to subtle numerical instabilities and interpolation. Therefore, we
postulate that the proposed mean-space learning strategy could be widely
applied to learning-based registration tasks. In addition, this group-wise
framework introduces a novel way for learning-based longitudinal studies by
direct construction of an unbiased within-subject template and allowing
reliable and efficient analysis of spatio-temporal imaging biomarkers.
