## 4 Experimental Results
### Data and Evaluation Indicators  
For the **dataset**, the first dataset used in this study is the Brats 2019 dataset provided by Brats, which uses MRI scans of patients' pre-operation brain conditions from multiple institutions, focusing on heterogeneous segmentation (appearance, shape, and tissue) of brain tumors, which in this case mainly refer to gliomas. Data are obtained from scanners at different institutions with different treatment regimens, and these MRI scans contain four modes of data: T1-weighted (T1), contrast-enhanced T1-weighted (T1 ce), T2-weighted (T2), and T2 fluid-attenuated inversion recovery (T2-FLAIR) volumes. All datasets were manually segmented by 1-4 professional and experienced radiologists according to the same protocol standards. The segmented labels included enhancing tumor (ET-label 4), peritumoral edematous/invaded tissue (ED), and necrotic tumor core (NCR), for a total of three tumor regions. The Brats 2019 dataset contains two preoperative MRI sequence datasets: the training set, including 335 multimodal MRI cases and the corresponding brain-tumor labeling, and the validation set, containing 125 cases without any public labeling. These images have been preprocessed, including stripping the skull, co-registering all MRI volumes to the same anatomic template, and resampling at an isotropic resolution of 1 mm\({}^{3}\), resulting in a 128 \(\times\) 128 \(\times\) 128 brain-tumor image. The second dataset adopted in this study is the Brats 2021 dataset, which is consistent with the Brats 2019 dataset except for the number of cases, including the mode, output size, etc. Brats 2021 contains 8160 MRI scans of 2040 patients, among which 1251 cases are used as training sets and publicly labeled. A total of 219 cases of data were classified as validation sets, with the  
Figure 3: Overall architecture of the Swin Transformer encoder. The 3D feature map was sliced along the axial plane, coronal plane, and sagittal plane and was fused after the training. corresponding annotations not disclosed, and another 570 cases were classified as test datasets, with undisclosed data. For **dataset preprocessing**, the BraTS dataset contains MRI images of multiple modalities (T1, T1 Gd, T2, and T2-FLAIR). We integrate the data from these different modalities to effectively utilize multi-modal information for brain-tumor segmentation. However, we standardize these data, as the dataset provided by BraTS is composed of sequences acquired by different institutions using devices from various manufacturers, thus resulting in inconsistent intensities of MRI volumes. After removing background pixels, the images are cropped to a fixed patch size of 128 \(\times\) 128 \(\times\) 128. The four sequence images are then placed in the same dimension, resulting in each processed sample image having dimensions of (4, 128, 128, 128). The mask images undergo the same processing during training. To prevent overfitting, this study employs data-augmentation techniques, which are crucial in the training process. These techniques ensure that the model possesses a degree of invariance to specific natural transformations, effectively enhancing the model's generalization capabilities. 1. The background region was clipped, considering the proportion of tumor region and non-tumor region, and 128 \(\times\) 128 \(\times\) 128 feature blocks were extracted. 2. The scaling coefficient is 0.8-1.2; the probability is 0.15. 3. Gaussian N(0, 0.01) noise is added. 4. Gaussian smoothing is performed with \(\alpha\in\) [0.5, 1.15]. 5. The probability of random flipping on the axial, coronal, and sagittal planes is 0.5. For the **training details**, the dual-path encoder brain-tumor segmentation model proposed in this study is implemented in PyTorch. It is trained from scratch using six NVIDIA RTX 3090 GPUs (each with 24 GB of memory) with a batch size of 12 and trained for 7000 iterations.