A Multi-scale Optimization Learning Framework for Diffeomorphic Deformable Registration

Conventional deformable registration methods aim at solving a specifically designed optimization model on image pairs and offer a rigorous theoretical treatment. However, their computational costs are exceptionally high. In contrast, recent learning-based approaches can provide fast deformation estimation. These heuristic network architectures are fully data-driven and thus lack explicitly domain knowledge or geometric constraints, such as topology-preserving, which is indispensable to generate plausible deformations. To integrate the advantages and avoid the limitations of these two categories of approaches, we design a new learning-based framework to optimize a diffeomorphic model via multi-scale propagations. Specifically, we first introduce a generic optimization model to formulate diffeomorphic registration with both velocity and deformation fields. Then we propose a schematic optimization scheme with a nested splitting technique. Finally, a series of learnable architectures are utilized to obtain the final propagative updating in the coarse-to-fine feature spaces. We conduct two groups of image registration experiments on 3D adult and child brain MR volume datasets including image-to-atlas and image-to-image registrations. Extensive results demonstrate that the proposed method achieves state-of-the-art performance with diffeomorphic guarantee and extreme efficiency.