Recurrent Amortized Solvers for Deformable Image Registration

Deformable image registration aligns anatomical structures across medical images, enabling comparison across subjects, modalities, and time points. It is commonly formulated as a regularized optimization problem balancing image alignment against deformation regularity. A central difficulty, shared by many regularized optimization problems, is choosing the regularization strength \(\lambda\) in advance: different choices induce different accuracy–regularity trade-offs. Current learning-based registration methods amortize this optimization across image pairs, but typically fix \(\lambda\) during training or use a single value throughout each prediction. We introduce the Recurrent Amortized Solver (RAS), a meta solver that can condition unrolled optimization with flexible \(\lambda\) scheduling. RAS enables \(\lambda\) to be controlled throughout the unrolling process without retraining the model. On each of three public 3D image registration benchmarks, we show that our RAS solver reaches competitive accuracy–regularity fronts with a single trained model. Furthermore, we introduce a per-case Pareto framework that evaluates the trade-offs available to each image pair, extending registration evaluation beyond cohort averages. RAS therefore provides a general formulation for learning iterative solvers with inference-time regularization control, applicable to regularized optimization problems beyond image registration.