Methods for Inverting Dense Displacement Fields: Evaluation in Brain Image Registration

In medical image analysis there is frequently a need to invert dense displacement fields which map one image space to another. In this paper we describe inversion techniques and determine their accuracy in the context of 18 inter-subject brain image registrations. Scattered data interpolation (SDI) is used to initialise locally and globally consistent iterative techniques. The inverse-consistency error, E(IC) is computed over the whole image and over 10 specific brain regions. SDI produced good results with mean (max) E(IC) approximately 0.02mm (2.0mm). Both iterative method produced mean errors of approximately 0.005mm but the globally consistent method resulted in a smaller maximum error (1.9mm compared with 1.4mm). The largest errors were in the cerebral cortex with large outlier errors in the ventricles. Simple iterative techniques are, on this evidence, able to produce reasonable estimates of inverse displacement fields provided there is good initialisation.