LDVoxelMorph: A precise loss function and cascaded architecture for unsupervised diffeomorphic large displacement registration

The traditional learning-based non-rigid registration methods for medical images are trained by an invariant smoothness regularization parameter, which cannot satisfy the registration accuracy and diffeomorphic property simultaneously. The diffeomorphic property reflects the credibility of the registration results.

To improve the diffeomorphic property in 3D medical image registration, we propose a diffeomorphic cascaded network based on the compressed loss (CL), named LDVoxelMorph. The proposed network has several constituent U-Nets and is trained with deep supervision, which uses a different spatial smoothness regularization parameter in each constituent U-Nets for training. This cascade-variant smoothness regularization parameter can maintain the diffeomorphic property in top cascades with large displacement and achieve precise registration in bottom cascades. Besides, we develop the CL as a penalty for the velocity field, which can accurately limit the velocity field that causes the deformation field overlap after the velocity field integration.

In our registration experiments, the dice scores of our method were 0.892 ± 0.040 on liver CT datasets SLIVER³⁷ , 0.848 ± 0.044 on liver CT datasets LiTS³⁸ , 0.689 ± 0.014 on brain MRI datasets LPBA³⁸ , and the number of overlapping voxels of deformation field were 325, 159, and 0, respectively. Ablation study shows that the CL improves the diffeomorphic property more effectively than increases.

Experiment results show that our method can achieve higher registration accuracy assessed by dice scores and overlapping voxels while maintaining the diffeomorphic property for large deformation.