The utilization of consistency metrics for error analysis in deformable image registration

The aim of this study was to investigate the utility of consistency metrics, such as inverse consistency, in contour-based deformable registration error analysis. Four images were acquired of the same phantom that has experienced varying levels of deformation. The deformations were simulated with deformable image registration. Using calculated deformation maps, the inconsistencies within the algorithm were investigated. This can be done, for example, by calculating deformation maps both in forward and reverse directions and applying them subsequently to an image. If the algorithm is not inverse consistent, then this final image will not be the same as the original, as it should be. Other consistency tests were done, for example by comparing different algorithms or by applying the deformation maps to a circular set of multiple deformations, whereby the original and final images are in fact the same. The resulting composite deformation map in this case contains a combination of the errors within those maps, because if error free, the resulting deformation map should be zero everywhere. We have termed this the generalized inverse consistency error map (Σ-vector(x-vector)). The correlation between the consistency metrics and registration error varied considerably depending on the registration algorithm and type of consistency metric. There was also a trend for the actual registration error to be larger than the consistency metrics. A disadvantage of these techniques is that good performance in these consistency checks is a necessary but not sufficient condition for an accurate deformation method.