## 2 Materials and Methods
### Evaluation Method  
In this paper, the Dice equation was used to calculate the volume overlap of the same anatomical tissues between the fixed image and the deformed image, and the Dice scores of all labeled tissues were averaged to quantitatively evaluate the registration accuracy. The calculation equation is as follows:  
\[Dice(S_{F},S_{W})=2\frac{\mid S_{F}\cap S_{W}\mid}{\mid S_{F}\mid+\mid S_{W} \mid}, \tag{10}\]  
where \(S_{F}\) and \(S_{W}\) represent the corresponding brain anatomical tissues in the fixed image and the warped image, respectively. At the same time, in order to quantify the regularization of the DVF during registration, we also counted the number of folded voxels in the DVF, which was obtained by calculating the number of voxels with non-positive Jacobian determinant in the DVF (i.e., \(\left|J_{\varphi}\right|\leq 0\)). In order to better measure the smoothness of the deformation field, SDlogJ is also used in the study. _SDlogJ_ is an index used to evaluate the regularity of the deformation field, mainly to calculate the logarithmic standard deviation of the Jacobian determinant. The calculation formula is as follows:  
\[SDlogJ=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(\log\left|J_{\varphi}(i)\right|-\mu)^{ 2}}, \tag{11}\]  
In this formula, \(N\) represents the total number of voxels. \(\left|J_{\varphi}(i)\right|\) denotes the absolute value of the Jacobian determinant for the \(i\)-th voxel, and \(\mu\) is the mean of the logarithm of the Jacobian determinants across all voxels. Additionally, the study introduces Sensitivityto evaluate the model's ability to detect positive samples. Sensitivity is calculated using the following formula:  
\[Sensitivity=\frac{TP}{TP+FN}, \tag{12}\]  
where \(TP\) is the number of true positive samples (correctly identified as positive) and \(FN\) is the number of false negative samples (positive samples incorrectly classified as negative). This metric quantifies the proportion of actual positives that are correctly identified by the model. In order to intuitively demonstrate the performance of MCANet, this study introduced several other advanced registration methods as baselines, including SyN [33], LDDMM [34], VoxelMorph-1, VoxelMorph-2, FAIM, and Transmorph [21] DIF-VM. SyN, as an excellent representative of traditional registration algorithms, has been proven to perform effective inter-patient brain registration. We used the ANTs software package to conduct SyN experiments with cross-correlation as the similarity measure and a gradient step size of 0.2. The second traditional algorithm baseline was LDDMM, which aimed to solve large deformation image registration and can handle inter-patient registration with varying brain structures very well. In our experiment, the mean square error (MSE) was used as the objective function, the smoothing kernel size was 5, the smoothing kernel power was 2, the matching item coefficient was 4, the regular item coefficient was 8, and the number of iterations was 500. Moreover, this paper also selected VoxelMorph based on unsupervised learning as the baseline. There were two variants of this model: VoxelMorph-1 and VoxelMorph-2. In this study, it was retained according to the optimal parameters given in Ref. [15], and the registration evaluation was completed on the test dataset of this paper. FAIM is a lightweight unsupervised registration model that can achieve high-precision registration with a small number of network parameters. In addition, FAIM also incorporates a regularization term that directly penalizes folded voxels during training. According to Ref. [16], in this study, the weight coefficient of this regularization term was set to \(1\times 10^{-5}\) to ensure the balance between the registration accuracy and the smoothness of the deformation field. In addition to the above methods, two baseline methods for deep learning have been chosen for this paper.