Inverse Consistent Mapping in 3D Deformable Image Registration: Its Construction and Statistical Properties

This paper presents a new approach to inverse consistent image registration. A uni-directional algorithm is developed using symmetric cost functionals and regularizers. Instead of enforcing inverse consistency using an additional penalty that penalizes inconsistency error, the new algorithm directly models the backward mapping by inverting the forward mapping. The resulting minimization problem can then be solved uni-directionally involving only the forward mapping, without optimizing in the backward direction. Lastly, we evaluated the algorithm by applying it to the serial MRI scans of a clinical case of semantic dementia. The statistical distributions of the local volume change (Jacobian) maps were examined by considering the Kullback-Liebler distances on the material density functions. Contrary to common belief, the values of any non-trivial Jacobian map do not follow a log-normal distribution with zero mean. Statistically significant differences were detected between consistent versus inconsistent matching when permutation tests were performed on the resulting deformation maps.