Efficient symmetric and inverse-consistent deformable registration through interleaved optimization

Symmetry and inverse consistency are two important features for deformable image registration in medical imaging analysis. This work presents a novel registration method computing symmetric and inverse-consistent image alignment efficiently while preserving high accuracy and consistency of the mapping. This is achieved by optimizing a symmetric energy functional estimating forward and backward transformations constrained by the transformations being inverse to each other. In other words, this approach uses an interleaved optimization scheme borrowed from multiobjective optimization theory constrained by an inverse-consistency criterium. The new optimization scheme provides an efficient search in the space of diffeomorphisms while solving the symmetric registration problem. Moreover, it is not bound to any specific optimizer or energy functional other than to the requirement of being well-defined. In our experiments on clinical cardiac data, superior performance compared to standard, one-directional registration is achieved. The resulting inverse-consistency and symmetry errors match previously reported values while being computed more efficiently. This general approach addresses a clinical need for consistent, highly accurate image alignment achieved in a practically accepted time-frame.