Symmetric Completion of Deformable Registration via Bi-Residual Inversion
Deformable image registration is fundamental and critical to both diagnostics and therapeutics in precision and personalized medicine. Existing software packages for deformable registrations either provide only a forward deformation vector field (DVF), or render both forward and backward DVFs with time-intensive computation. The latter has multiple advantages in medical image analysis and processing. However, its latency, which is substantially longer than clinical time windows, hinders the transition of its benefits to clinical applications. This study aims at facilitating the transition with algorithmic innovation. We introduce a novel registration approach, which substantiates a significant shift of the conventionally perceived tradeoff boundary between efficiency on the one side and functionality and accuracy on the other.
In the new approach, we utilize efficient existing methods for forward DVF estimation. We complete symmetric registration with a backward DVF estimation, at high computation speed comparable to the forward DVF generation, and at high accuracy in inverse consistency as well as in registration. The forward DVF is possibly refined also in the symmetric augmentation or completion process. The efficacy of our approach is supported by theoretical analysis and empirical results. The key conceptual and algorithmic innovation is adaptive use of forward and backward inverse consistency (IC) residuals as feedbacks to refining DVF estimation. The forward IC residual was used heuristically in earlier work. We give a theoretical explanation and conditions on when non-adaptive feedback succeed or fail. We provide furthermore a framework of algorithm design for DVF inversion with a simple adaptive feedback control mechanism. The use of backward IC residuals is original. The iteration with backward IC residuals as updates may be seen as an implicit Newton iteration, by convergence rate analysis. It has great advantages in simplicity, efficiency and robustness over the explicit Newton iteration, for DVF inversion. The algorithm framework is completed with convergence analysis, controllability condition, pre-evaluation of the initial forward DVF data, and post-evaluation of DVF estimates. Experiment results with our approach on synthetic data and real thoracic CT images show significant improvements in both registration and inverse-consistency errors. They are also in a remarkable agreement with the analysis-based predictions.