## 4 Discussion  
3D brain MRI alignment is important in observing structural brain lesions and performing brain health treatments. Traditional deformation alignment algorithms take a significant amount of time to align image pairs and require several manual adjustments of parameters to achieve optimal results. In addition, the optimal alignment parameters are different from one image to another, so the traditional methods are highly dependent on manual operation, which is both troublesome and time-consuming. With the improvement of hardware performance and the increase of network model size, the traditional methods gradually become unsatisfactory in terms of alignment time and accuracy. In contrast, the model proposed in this paper can learn the best parameters for predicting deformations through continuous optimization and can be directly applied to unseen images, completing the alignment at near real-time speed without human involvement. The network can automatically complete the deformation prediction based on the features of the input image, which is efficient and accurate. Although some traditional algorithms still have an advantage in deformation smoothing, FAIM and MCANet have made great strides in this area as well. When the weights of the regularization terms are large enough, they can achieve very smooth deformation without unnecessary sacrifices. While VoxelMorph has been a benchmark for unsupervised alignment due to its alignment accuracy, speed, and robustness, MCANet introduces several key architectural improvements. Specifically, MCANet incorporates attention gates to focus on critical anatomical regions and employs dilated convolutions to expand the receptive field without increasing computational complexity. These enhancements significantly improve deformation smoothness, reduce voxel folding, and enable more precise alignment of complex anatomical structures. Additionally, MCANet's multi-scale context aggregation mechanism further refines the deformation field, making it particularly effective in scenarios requiring high-precision registration.When the model has a large receptive field and can focus on key areas of deformation, its deformation of deformed images will become more natural and accurate. As can be seen from the data of the ablation experiments in Table 2, the addition of attention gates and regularization terms significantly reduces voxel folding, a common issue in learning-based methods. When combined with dilated convolutions, the proportion of folded voxels decreases by 0.3%, and the smoothness of the deformation field improves by 38%. Bending energy regularization further enhances these improvements by reducing voxel folding, though with a slight decrease in alignment accuracy (as shown in Table 3). This trade-off is justified as it leads to more biologically plausible deformations, which are critical in medical imaging. FAIM, a lightweight unsupervised network model that directly incorporates the value of a non-orthonormal comparable determinant as part of the loss function, has also made some progress. Although MCANet is larger than FAIM in terms of network architecture and number of parameters, it is significantly better than the latter in terms of alignment accuracy, which remains one of the most important metrics for evaluating models and algorithms. Compared to Transmorph, another advanced deep-learning-based registration method, MCANet demonstrates superior performance in deformation smoothness and voxel folding reduction. While Transmorph achieves competitive registration accuracy, MCANet excels in generating more natural and interpretable deformation fields, which is crucial for medical applications. MCANet's ability to balance alignment precision with computational efficiency makes it a standout choice for image registration tasks, particularly in scenarios where high-precision and biologically plausible deformations are required.