We apply the proposed affine model for registering rat brain functional images. We applied 6 studies (dataset 1) containing 270 samples for training and test. To train the model, we initially created a training dataset by randomly selecting 80% of the data, reserving the remaining 20% for final performance testing. During the training phase, an additional 80% of the data were randomly sampled from the training dataset, leaving the remaining 20% for validating the training of the model. This training-validation process was repeated five times to ensure an unbiased data distribution. Subsequently, the model with the highest averaged validation accuracy was chosen as the final model for testing. To evaluate the model's generalization ability, we applied one study (dataset 2), containing 10 subjects which has not been applied for training.

Data preprocessing before affine registration is critical for enhancing the model's robustness and generalization. We apply a standard preprocessing steps, including denoising, motion correction, and skull stripping. In our affine registration method, we align the fMRI scans to a standardized 256 × 256 × 64 atlas (Wang et al., 2025; Fuini et al., 2025). This atlas, developed by Ekam Imaging (Boston, MA, USA), provides a consistent anatomical reference that facilitates accurate spatial normalization across subjects. By registering all scans to this common space, we ensure comparability in subsequent analysis steps, enabling robust group-level statistical studies and downstream applications in functional neuroimaging. It should be noted that this step performs only affine (global) alignment rather than deformable (non-linear) registration. The proposed MsDCSwinT model estimates affine parameters (translation, rotation, scaling, and shearing) to bring each subject's fMRI volume into coarse correspondence with the standardized atlas space. This affine transformation provides a globally aligned reference frame for downstream group analyses. Deformable or non-linear alignment, which refines local anatomical correspondence, is beyond the current scope and remains part of our planned future work.

fMRI data are inherently noisy due to physiological, hardware-related, and external artifacts, making denoising a critical preprocessing step. As shown in Figure 1, we apply our 3D U-WGAN (Soltanpour et al., 2025a), a structure-preserving denoising method based on a 3D Wasserstein GAN with a 3D dense U-Net discriminator. This approach processes 4D fMRI data to retain both spatial and temporal features while effectively mitigating noise. The 3D dense U-Net discriminator captures both global and local patterns, and the inclusion of adversarial and perceptual losses helps prevent oversmoothing and preserve structural integrity. This denoising step enhances downstream processing, including affine registration, by providing cleaner and more reliable fMRI data.

Motion correction is an essential preprocessing step in fMRI analysis to reduce the impact of subject movement during image acquisition. In our pipeline, we applied AFNI's rigid-body motion correction method (Cox, 1996) prior to skull stripping to ensure temporal alignment of the brain volumes and improve the accuracy of subsequent steps.

Prior to affine registration, skull stripping as illustrated in Figure 1 is applied to remove non-brain tissues and improve anatomical alignment. Manual skull stripping is time-consuming and prone to variability, especially in preclinical fMRI data, which present challenges such as low resolution, varying slice sizes, and anatomical differences. To address these issues, we incorporate our recently developed SST-DUNet method (Soltanpour et al., 2025b), which combines a dense U-Net architecture with a Smart Swin Transformer-based feature extractor (Fu et al., 2024). The Smart Shifted Window Multi-Head Self-Attention (SSW-MSA) module enables robust feature learning by focusing on channel-wise dependencies within brain structures. Additionally, a hybrid loss function combining Focal and Dice loss mitigates class imbalance, resulting in more accurate skull extraction. This automated approach ensures reliable brain masking, which is essential for accurate affine registration.

For the fixed and moving images with the size of H×W×D, where H, W, and D are the image spatial dimension, we calculate the patch embeddings. In the first stage, where the input images have smaller resolution, we use a window of size 2 × 2 × 2. In the next stages, by increasing the resolutions, windows of size 4 × 4 × 4 and 8 × 8 × 8 are used to capture the larger patches. For the data with size H×W×D, we obtain vectors with the same number of features but with various feature lengths. In this way, for both F_i and M_i, we extract patches with length h×w×d×8, h×w×d×64, and h×w×d×512 for three different stages. We employ fully connected layers to convert the variable-length feature representations into fixed-size vectors of dimension C, ensuring uniformity in the output dimensions. Consequently, the general feature map is defined by ZFi∈ℝh×w×d×C, and ZMi∈ℝh×w×d×C for the fixes and moving images.

The patch merging operation, applied after each patch embedding and within each SwinT block, follows the same approach used in ViT. This mechanism is employed to create connections between non-overlapping image patches. Initially, the patch merging layer combines the features of adjacent 2 × 2 patches, resulting in a 4C-dimensional representation. This aggregated feature set is then passed through a linear layer, which not only reduces the number of tokens by a factor of four, equivalent to a twofold decrease in spatial resolution, but also transforms the feature representation accordingly. In this way, ZFi and ZMi are transformed to the same dimension as ℝ^{h/2 × w/2 × d/2 × 2C}

To further enhance the affine registration performance, we integrate the dilated convolutional block, as proposed by Gao et al. (2022), into our model. This design combines dilated convolutions with the SwinT architecture, enabling the model to capture both local and global contextual information across images. By leveraging dilated convolutions, we expand the receptive field without increasing computational complexity, which allows for more accurate localization of features in both the fixed and moving images. This is particularly advantageous for preclinical fMRI data, where image resolution and variability in structural features present significant challenges. Additionally, the SwinT's window-based self-attention mechanism facilitates capturing long-range dependencies, further improving the registration accuracy. Integrating the dilated convolutional block provides a robust approach to handling complex variations in brain geometry and resolution, ultimately enhancing the precision and reliability of the affine registration process.

In our affine Swin Transformer framework, we incorporate dilated convolution to effectively expand the receptive field across multiple stages without reducing spatial resolution. Dilated convolution proposed by Yu and Koltun (2015), enables wider spatial context modeling compared to traditional convolutions. For example, while a standard 3 × 3 × 3 kernel captures local features within a limited 3 × 3 × 3 region, a 2-dilated convolution with the same kernel expands the receptive field to 7 × 7 × 7. This expansion is particularly advantageous in our model, where 3D inputs are processed through three hierarchical stages. By using dilated convolution at each stage, we enhance the model's ability to capture global affine transformations and structural dependencies across the full 3D volume, while maintaining spatial detail and resolution.

Considering that the data flow in SwinT uses vectors instead of feature maps, as in traditional CNNs, the dilated convolution block first reshapes a group of vector features into a spatial feature map. For instance, a set of tokens with dimensions hp×wp×dp is reshaped into a feature map of size hp×wp×dp×C where p is the patch size. Following this, two dilated convolutional layers with Batch Normalization (Ioffe and Szegedy, 2015) and ReLU activation are applied to capture large-range spatial features.Finally, the feature map is re-transformed back into the original token dimensions hp×wp×dp and passed to the next stage in the model. This integration of dilated convolutions with SwinT allows the model to capture both local and global spatial features, improving the overall accuracy and robustness of affine registration, particularly in challenging preclinical fMRI datasets.

The hierarchical self attention mechanism of the SwinT (Liu et al., 2021) is highly effective to model long range dependencies within sequences of embeddings. In our algorithm, the misalignment between fixed and moving images is captured through two consecutive SwinT blocks including W-MSA and SW-MSA which are multi-head self attention modules with regular and shifted windowing configurations, respectively. The structure of SwinT block has been shown in Figure 3.

The formula to represent the SwinT block is as follows:

where Ẑ^l and Z^l denote the output of block l. LN (LayerNorm) represents a regularization. MLP denotes multi-layer preceptron. W_MSA and SW_MSA represent the window self-attentive mechanism and the shifted window self-attentive respectively. Finally, the attention head's output is input to the dilated convultional block and the output is passed through a multi-layer linear network, which generates the corresponding affine transformation matrix A_i.

The transformer encoders in MsDCSwinT use the similarity between projected query-key pairs to capture misalignment and global relationships between the fixed and moving images, generating attention scores for each patch embedding. The query (Q), key (K), and value (V) are linearly projected from the patch embeddings (tokens).

Considering that the number of attention heads in the SwinT block is h′, the linear projection matrices are WjQ,WjK,WjV∈ℝD×Dh′, and Dh′=D/h′. Attention operation for attention head j is calculated as follows:

where Dh′ is the embedding dimension and B_P denotes the relative position encoding. In this study, we employ h′=2 attention heads for all the transformer encoders. Finally, the attended embeddings from all attention heads are concatenated and passed through a linear projection matrix.

We incorporate a multiresolution approach into our architecture. Specifically, each stage of MsDCSwinT includes a classification head, which consists of two consecutive MLP layers with a hyperbolic tangent (Tanh) activation function. This classification head processes the averaged patch-wise embeddings and generates a set of affine parameters. At each intermediate stage i, the resulting affine matrix is applied to progressively transform the moving image M_i+1 via a warping operation using a spatial transformer (Jaderberg et al., 2015). The warped image M_i+1 is then concatenated with the fixed image F_i+1 and passed to the next stage, i+1. This progressive transformation strategy allows for initial misalignments to be corrected at lower resolutions, enabling higher-level transformers to focus on more complex misalignments, thus simplifying the problem at later stages.

Rather than directly estimating the affine transformation matrix, our model predicts a set of geometric transformation parameters. Specifically, the affine registration problem is reformulated as:

We parameterize the affine transform with [t, r, s, h]∈ℝ¹², where t=(t_x, t_y, t_z), r=(r_x, r_y, r_z), s=(s_x, s_y, s_z), and h=(h_xy, h_xz, h_yz). Using homogeneous coordinates, the overall affine matrix A is the ordered product:

where T, R, S, and H represent translation, rotation, scaling, and shearing matrices, respectively.

Translation (T):

Rotation (R): The overall rotation matrix is defined as:

Rotation about x-axis:

Rotation about y-axis:

Rotation about z-axis:

Scaling (S):

Shearing (H):

To reduce the search space and enforce meaningful transformations, we constrain the predicted parameters during training as follows: rotation and shearing values are limited to the range [−π, π], translation values are constrained within ±50% of the image resolution, and scaling values are restricted to the range [0.5, 1.5]. Additionally, we apply the center of mass of the image c_I (Mok and Chung, 2022) computed as:

where Ω represents the spatial domain of the image and p denotes the voxel position.

Our affine registration method is based on unsupervised learning. This is primarily because generating manual segmentation maps for fMRI data is extremely time-consuming and impractical. Additionally, creating manual maps using the mean of fMRI data often results in inconsistent segmentation, particularly due to the low resolution of the data, which can lead to varying numbers of detected regions across different samples. Given these challenges and the unavailability of reliable ground truth labels, we opted for an unsupervised approach that does not rely on manually annotated data. Instead, the model learns to align the input image with an atlas by optimizing a similarity measure between them, allowing for robust and automated registration even in the absence of labelled training data.

The affine registration problem is parametrized as a learning problem to minimize the following equation:

where θ represents the learning parameters in the MsDCSwinT model, F is the atlas, and M is the moving image from the training dataset D. The loss function L measures the similarity between the atlas F and the affine transformed moving image M(ϕ(A)). We use the negative Normalized Cross-Correlation (NCC) (Mok and Chung, 2020b) similarity measure to quantify the distance between F and M(ϕ(A)) as follows:

where L represents the number of image pyramid levels, NCC_w denotes the local normalized cross-correlation with window size w×w, and (F_i, M_i) are the atlas and moving images in the image pyramid.

The overall loss function is inspired by the energy-based formulation used in traditional image registration. It consists of two components: a similarity loss between the fixed image (atlas) and the affine-transformed moving image, and a regularization term that constrains the affine parameters to prevent implausible transformations. The total loss is defined as:

where F is the fixed image (atlas), M is the moving image, and ϕ denotes the affine transformation predicted by the network. The similarity term Lsim quantifies alignment quality, for which we use a multi-resolution negative normalized cross-correlation (NCC) as described in Equation 8.

The regularization term R(ϕ) penalizes overly large or unrealistic affine transformations to maintain stable optimization. In our work, we regularize the rotation and shearing parameters by constraining them within [−π, +π], translation within [−0.5R, +0.5R], and scaling between [0.5, 1.5], where R denotes the spatial resolution of the input image. This encourages the model to learn physically plausible transformations while maintaining registration accuracy. Here, λ is a regularization weighting parameter that balances the contribution of the similarity loss and the regularization term. A higher value of λ enforces stronger constraints on the transformation parameters, while a lower value focuses more on image similarity. In our experiments, we empirically set λ=0.01 to achieve a good balance between accuracy and stability.

We applied the mean of fMRI scans to create 3D MRI data. We resampled and padded all scans to 96 × 96 × 48 with the same resolution (0.3mm × 0.3mm × 0.4mm). The input voxel values were adjusted to fall within the range of 0.0–1.0 through normalization. The model was implemented using the PyTorch framework and trained on an Nvidia GeForce RTX 4090 GPU with CUDA support. We used the Adam optimizer with a fixed learning rate of 0.0001 and a batch size of 1. The value of λ=0.01 was selected based on validation performance to ensure optimal registration accuracy without overfitting the transformation parameters.

All fMRI datasets were preprocessed using AFNI (https://afni.nimh.nih.gov/). Each image volume was smoothed using a Gaussian kernel with a full width at half maximum (FWHM) of 0.1 mm. The data were then cropped using a previously generated brain mask, aligned to a down-sampled rat 96 × 96 × 48 template space, and band-pass filtered within the frequency range of 0.01–0.1 Hz to remove physiological and low-frequency noise artifacts. These steps follow established preprocessing protocols (Lupinsky et al., 2025; Sourty et al., 2024b,a; Nasseef et al., 2021; Karatas et al., 2021).

Post-processing included seed-based functional connectivity (FC) analysis, one of the most widely adopted methods in rodent fMRI studies (Lupinsky et al., 2025; Sourty et al., 2024a,b; Nasseef et al., 2021; Karatas et al., 2021; Nasseef et al., 2019). Seed-to-seed correlation analysis was conducted on datasets from eight rats, all of which underwent identical preprocessing pipelines, except for the registration methods. Based on these methods, five registration groups were established including MsDCSwinT (ours), ANTS, C2FViT, C2FGALF, and ConvNet.

To define anatomical brain regions, we utilized a previously generated, in-house high-resolution rat brain atlas (Wang et al., 2025; Fuini et al., 2025), initially composed of 176 brain regions at a spatial resolution of 256 × 256 × 64. To ensure compatibility between the lower-resolution functional imaging data and the high-resolution rat brain atlas, the atlas was down-sampled to a spatial resolution of 96 × 96 × 48, yielding a total of 159 functional brain regions.

Seed regions were defined based on the down-sampled atlas. The mean time series for each seed region was extracted, and pairwise Pearson correlations were computed and Fisher's Z transformation was applied to generate the seed-to-seed FC matrix. Statistical significance of connectivity differences between groups was assessed using two-sample t-tests with False Discovery Rate (FDR) correction (Nasseef et al., 2021, 2019, 2018). Statistical significance of connectivity differences between groups was assessed using two-sample t-tests with False Discovery Rate (FDR) correction (Nasseef et al., 2021, 2018, 2019)). MATLAB-based Multiple Testing Toolbox (https://www.mathworks.com/matlabcentral/fileexchange/70604-multiple-testing-toolbox) was used for circular plotting and FDR correction. All computations were carried out using an in-house developed MATLAB script, following our previously validated pipeline (Lupinsky et al., 2025; Nasseef et al., 2021, 2019).

To evaluate the performance of our affine registration algorithm, we align each subject's image to the atlas. The registration accuracy is assessed using the Dice Similarity Coefficient (DSC) (Dice, 1945), which quantifies the overlap between the transformed moving image and the atlas. This provides a measure of segmentation accuracy. In addition to DSC, we compute the 95% percentile of the Hausdorff Distance (HD95) (Huttenlocher et al., 1993), which measures the distance between the boundaries of the transformed moving image and the atlas. Together, these metrics offer a comprehensive view of the registration's precision and reliability.

The Dice Similarity Coefficient (DSC) for the subcortical segmentation map can be formulated as:

where SM(ϕ)k represents the set of voxels of structure k in the registered moving image, and SFk represents the set of voxels of structure k in the fixed image (atlas).

Additionally, we evaluate the 95th percentile of the Hausdorff distance (HD95) between segmentation maps to assess the robustness of the registration algorithm. The calculation can be formulated as:

where

and ||·||₂ denotes the Euclidean distance.

In addition to reporting the traditional overall Dice Similarity Coefficient (DSC) to evaluate our model's performance, we further assessed the registration accuracy by analyzing the distribution of results. Specifically, we computed the 30% lowest DSC of all cases (DSC30), based on the registration accuracy ranking across the 159 segmented structures in the test set. To provide a more complete analysis, we also reported the DSC for unregistered data (moving data). Together, these evaluations offer a comprehensive understanding of the registration accuracy and robustness of the proposed method.

The overall experimental results are summarized in Table 1. Our proposed method, MsDCSwinT, achieves a DSC of 0.9286 and 0.9214 on the CTNI dataset1 and dataset 2, demonstrating the best registration performance among all methods compared. The most competing conventional method, ANTS, achieves a DSC of 0.9159 and 0.9082 on dataset 1 and dataset 2 respectively. Other learning-based methods, including ConvNet, C2FViT, and C2FGALF achieve DSCs of 0.7469, 0.8408, and 0.8638 for dataset 1, and 0.7294, 0.8231, and 0.8469 for dataset 2 respectively. In comparison, our model, MsDCSwinT, not only achieves an overall registration accuracy of 0.93 but also obtains the highest DSC30 and lowest HD95 outperforming all competing methods on both datasets.

Figure 4 presents a qualitative comparison for the test set of fMRI dataset 1, highlighting the visual differences between the moving (unregistered) image, the registered images using different methods, and the atlas across representative slices and time points. As shown in Figure 4, example coronal, axial, and sagittal slices from the test dataset 1 illustrate the visual alignment performance of various registration methods, including ANTS, ConvNet, C2FViT, C2FGALF, and our proposed MsDCSwinT model. The figure displays the fixed image (Atlas), unregistered images, and the corresponding warped outputs produced by each method. Color-coded overlays help visualize registration quality, green indicates atlas-only regions, red shows registered-only regions, and yellow highlights overlapping areas, which represent perfect alignment. Visually, our proposed MsDCSwinT achieves the highest degree of overlap with the atlas, indicated by more extensive yellow regions. While the performance of MsDCSwinT is very close to ANTS, a widely regarded traditional method, it clearly outperforms other deep learning-based approaches. These results demonstrate that our model effectively combines the robustness of traditional methods with the efficiency and automation of deep learning, achieving accurate registration while maintaining anatomical integrity. The distribution of evaluation metrics for CTNI fMRI test sets is shown in Figure 5. All results have been computed as the mean ± standard deviation over all slices and time points of the fMRI test sets.

Table 2 presents the average inference times for all methods. We report the average registration time to register the mean of fMRI data to the atlas. As the table shows our method is the fastest among the methods evaluated, mainly due to GPU acceleration and efficient learning-based design. ConvNet, C2FViT, and C2FGALF are also significantly faster than ANTS. ANTS shows variable runtimes depending on the level of initial misalignment.Our model reduces the inference time to just 0.12 s, making it much more suitable for the practical demands of preclinical image registration.

To provide a complete view of the computational efficiency, we report the total preprocessing time for each subject, which includes denoising, skull stripping, and affine registration. The full proposed pipeline requires approximately 24.85 s per subject, consisting of 24.18 s for denoising, 0.55 s for skull stripping, and about 0.12 s for affine registration. For comparison, ANTs registration alone takes about 33.38 s, which is already longer than the entire runtime of our full preprocessing workflow. These results show that our proposed registration method contributes less than 1% of the total processing time and that the overall pipeline remains substantially faster than ANTs-based preprocessing approaches.

To facilitate group-level interpretation, the results were visualized using MATLAB's built-in plotting tools. Visualization formats included scatter plots, and box plots. For circular plotting, the CircularGraph (https://www.mathworks.com/matlabcentral/fileexchange/48576-circulargraph) toolkit was applied. These representations provided intuitive insights into group-wise variability, inter-regional correlation patterns, and overall data distribution, thereby enhancing the interpretability of the findings.

Resting-state fMRI (rs-fMRI) data from all eight rats, preprocessed through five different automated registration methods (including the proposed MsDCSwinT), were analyzed across 159 functional brain regions. For each dataset, mean time series were extracted from each region based on the corresponding registration. This hypothesis-driven, atlas-based approach allowed for a comprehensive whole-brain investigation of connectivity differences between the MsDCSwinT method and the five other registration strategies. To evaluate inter-group connectivity patterns, symmetric Pearson's correlation coefficients (CC) were first computed for all pairs of the 159 regions within each rat and automated registration group. The results were visualized through scatter plots comparing each method with MsDCSwinT (Figure 6A), box plots of mean CC distributions across methods (Figure 6B), and scatter plots comparing each method with the classical ANTS method (Figure 6C). The box plot analysis revealed a striking similarity in mean, quartiles, and outlier patterns between the proposed MsDCSwinT method and the classical ANTS method (Figure 6B). Similarly, scatter plots with fitted regression lines (Figure 6A, first panel) demonstrated a high degree of correlation between MsDCSwinT and ANTS, reinforcing the consistency of these findings. In contrast, comparatively lower similarity was observed between MsDCSwinT and the other three existing deep learning powered methods: C2FViT, C2FGALF, and ConvNet as shown in both scatter plots (Figure 6A, second to fourth panels) and box plots (Figure 6B). Interestingly, a similar pattern of reduced similarity was also observed when comparing ANTS with C2FViT, C2FGALF, and ConvNet (Figures 6B, C), suggesting consistent differentiation across methods.

To further assess group-level differences, a pairwise t-test (p = 0.05, two-tailed, FDR-corrected, n = 8 per group) was conducted to compare the proposed MsDCSwinT method with each of the four other automated registration methods respectively across all 1,256 seed-to-seed correlation coefficient (CC) values (Figure 7). Notably, very few statistically significant differences were observed between the MsDCSwinT method and the classical ANTS method (Figure 7A), indicating a high degree of similarity in their resulting connectivity patterns. In contrast, a substantially greater number of connectivity differences were identified when MsDCSwinT was compared to the other three AI-powered methods: C2FViT, C2FGALF, and ConvNet (Figure 7B), suggesting more variability in their alignment outcomes. To contextualize these results, additional comparisons between gold standard ANTS and each of the three AI methods were performed independently (Figure 7C). Visual inspection suggests that the patterns of differences for C2FGALF and ConvNet were comparable to those observed in the MsDCSwinT vs. ANTs analysis (Figures 7B, C, middle and bottom panels), while ANTS appeared to outperform MsDCSwinT slightly in the comparison with C2FViT(Figures 7B, C, top panels). Collectively, these findings reinforce that MsDCSwinT achieves connectivity profiles closely aligned with those of the widely recognized ANTS method, supporting its reliability, robustness, and suitability as a fully automated solution for preprocessing in rodent resting-state fMRI studies. Consequently, the results underscore the potential of MsDCSwinT for fully automated and more accurate rs-fMRI preprocessing and analysis.

Despite its promising results, our proposed method has several limitations. It is currently tailored for affine registration and has not been extended to deformable registration tasks. Furthermore, this study was conducted using data acquired from a single institute with consistent imaging parameters. Because MRI contrast is highly dependent on scanner settings such as TR and TE, the generalizability of MsDCSwinT to data acquired using different MRI sequences or substantially different scan parameters has not yet been evaluated. In practical applications, additional training or fine-tuning may be required when deploying the model across sites with different acquisition protocols. Future work will include multi-center validation to assess performance across varied scanning environments. In this study, the test Dataset 1 was selected from the training dataset using cross-validation, while Dataset 2 comprised independent subjects from other studies and experimental conditions. This design supports intra-center generalization, and future work will focus on inter-center validation to evaluate robustness across imaging platforms and acquisition protocols. We also did not include comparisons with manual registration due to its time-consuming nature and reliance on expert interpretation. Nevertheless, incorporating such comparisons in future work could provide valuable insights into the method's performance in preclinical imaging studies.

For simplicity and clarity, we have taken the advantage of using h-values from the pairwise t-tests (p = 0.05, two-tailed, FDR-corrected, n = 8 per group) to highlight statistically significant differences in functional connectivity (Figure 7). Importantly, our primary aim was to identify the presence or absence of significant differences, rather than to assess the magnitude or strength of those differences in the form of p-values or tstat-values, which are more commonly interpreted in the context of biological or functional meaning (Lupinsky et al., 2025; Nasseef et al., 2021; Karatas et al., 2021; Nasseef et al., 2019; Boulos et al., 2019; Hamida et al., 2018; Charbogne et al., 2017). In this context, the binary nature of h-values (1 = significant vs. 0 = not significant) effectively serves our objective of comparing the different registration methods from a methodological perspective. Therefore, we deliberately chose not to present the associated p-values, as our interest lies in the existence of statistically significant differences, not in their relative quantification (Lupinsky et al., 2025; Nasseef et al., 2021, 2019; Boulos et al., 2019) or degree (Wang et al., 2025; Fuini et al., 2025) or effect size (Nasseef et al., 2018) or dynamic functional connectivity (Sourty et al., 2024a,b). Additionally, we did not perform further analysis such as hypothesis free independent component analysis (ICA) (Lupinsky et al., 2025; Nasseef et al., 2021; Karatas et al., 2021; Nasseef et al., 2019; Hamida et al., 2018; Charbogne et al., 2017) or directed (model based/model free) functional connectivity (Hamida et al., 2018; Charbogne et al., 2017) as these methods fall outside the primary scope of our current investigation. Given that our objective was to find the benchmark automated registration methods using atlas-based seed-to-seed correlation analysis, additional exploratory or directional techniques were deemed unnecessary. Equally, these alternative approaches are unlikely to provide further insights relevant to our methodological comparison and may instead introduce confounding variability unrelated to the core aim of evaluating registration performance.