Consistency-based rectification of nonrigid registrations

We present a technique to rectify nonrigid registrations by improving their group-wise consistency, which is a widely used unsupervised measure to assess pair-wise registration quality. While pair-wise registration methods cannot guarantee any group-wise consistency, group-wise approaches typically enforce perfect consistency by registering all images to a common reference. However, errors in individual registrations to the reference then propagate, distorting the mean and accumulating in the pair-wise registrations inferred via the reference. Furthermore, the assumption that perfect correspondences exist is not always true, e.g., for interpatient registration. The proposed consistency-based registration rectification (CBRR) method addresses these issues by minimizing the group-wise inconsistency of all pair-wise registrations using a regularized least-squares algorithm. The regularization controls the adherence to the original registration, which is additionally weighted by the local postregistration similarity. This allows CBRR to adaptively improve consistency while locally preserving accurate pair-wise registrations. We show that the resulting registrations are not only more consistent, but also have lower average transformation error when compared to known transformations in simulated data. On clinical data, we show improvements of up to 50% target registration error in breathing motion estimation from four-dimensional MRI and improvements in atlas-based segmentation quality of up to 65% in terms of mean surface distance in three-dimensional (3-D) CT. Such improvement was observed consistently using different registration algorithms, dimensionality (two-dimensional/3-D), and modalities (MRI/CT).