# Bi-Directional Point Flow Estimation with Multi-Scale Attention for Deformable Lung CT Registration
## 5 Discussion  
Our results demonstrate that the proposed point-based deformable registration framework achieves a state-of-the-art performance on the Lung250M benchmark [16]. By incorporating geometric keypoint attention at coarse resolutions, contextual flow refinement at finer scales, and bi-directional learning objectives, our method achieves a superior accuracy across all TRE metrics compared to that of the prior optimization-based and learning-based approaches. These findings validate our core hypothesis: that accurate lung CT registration requires joint modeling of the long-range structural consistency and localized deformation patterns, particularly given the large respiratory motion and anatomical variability inherent in this domain. Compared to prior point-based methods primarily developed for rigid registration or generic scene flow tasks [17; 18], our approach is the first to specifically target deformable lung CT alignment using sparse point clouds, building on the recent Lung250M dataset [16]. While voxel-based learning methods have achieved notable success in brain MRI and abdominal CT registration, their application to thoracic imaging remains limited by the computational costs and sensitivity to variations in intensity. Our method addresses these limitations by leveraging sparse geometric inputs and multi-scale feature interactions, offering a more efficient and robust alternative. Moreover, the use of bi-directional training with cycle consistency constraints across all resolution levels contributes to the deformation stability by enforcing multi-scale coherence in the flow predictions. This regularization, in combination with a coarse-to-fine refinement architecture, enhances the robustness to noisy or imperfect training correspondences. The empirical consistency of our model's performance across datasets further suggests resilience to residual noise in the pseudo-ground-truth labels without requiring additional denoising mechanisms. From a clinical standpoint, the proposed framework offers practical benefits. Its efficiency enables rapid deployment across large-scale datasets, while its anatomical interpretability--grounded in vascular keypoints--aligns with radiologists' mental models for thoracic anatomy. Such properties suggest its promising utility in workflows such as longitudinal disease monitoring and dose accumulation analyses in radiotherapy, where consistent, reliable registration is critical. Despite these advantages, our framework also has limitations. As it operates on vessel-derived point clouds, the registration accuracy in regions without clear geometric landmarks--such as homogeneous parenchymal areas--is less directly evaluated. In addi \begin{table}
\begin{tabular}{l c|c c|c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Representation**} & **Train Mem.** & **Inference Mem.** & **FLOPS** & **Time** \\  & & **(GB)** & **(GB)** & **(G)** & **(ms)** \\ \hline VoxelMorph++ & Voxel & 5.70 & 4.97 & 318.72 & 266.88 \\ Ours & Point cloud & 2.78 & 0.82 & 56.89 & 74.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Efficiency comparison between VoxelMorph++ [48] and ours. Lower is better. tion, our training supervision relies on the pseudo-ground-truth correspondences generated by corrField [15]. Although these correspondences have demonstrated high reliability, with reported mean TREs of 1.45 mm (test) and 2.67 mm (validation) against manual landmark annotations [16], a certain level of noise is inevitable. Our model mitigates the potential supervision noise through bi-directional cycle consistency regularization, but an explicit analysis of the robustness to correspondence noise remains an area for future investigation. Future work could explore hybrid architectures that fuse the voxel-level appearance with the point-based geometry, potentially enhancing the deformation estimations in texture-rich but landmark-sparse regions.