PC-Reg: A pyramidal prediction–correction approach for large deformation image registration

Deformable image registration plays an important role in medical image analysis. Deep neural networks such as VoxelMorph and TransMorph are fast, but limited to small deformations and face challenges in the presence of large deformations. To tackle large deformations in medical image registration, we propose PC-Reg, a pyramidal Prediction and Correction method for deformable registration, which treats multi-scale registration akin to solving an ordinary differential equation (ODE) across scales. Starting with a zero-initialized deformation at the coarse level, PC-Reg follows the predictor–corrector regime and progressively predicts a residual flow and a correction flow to update the deformation vector field through different scales. The prediction in each scale can be regarded as a single step of ODE integration. PC-Reg can be easily extended to diffeomorphic registration and is able to alleviate the multiscale accumulated upsampling and diffeomorphic integration error. Further, to transfer details from full resolution to low scale, we introduce a distillation loss, where the output is used as the target label for intermediate outputs. Experiments on inter-patient deformable registration show that the proposed method significantly improves registration not only for large but also for small deformations.