## 3 Results  
Gaussian noise was added to the standard lung CT image acquired using data from the NLST dataset, with MMWF kernel sizes of 3 \(\times\) 3, 5 \(\times\) 5, 7 \(\times\) 7, 9 \(\times\) 9, and 11 \(\times\) 11. Figure 2 shows the MMWF applied to a lung CT image according to the kernel size, with Figure 2a as the ground-truth image and Figure 2b as the noisy image. The images from Figure 2c-g represent the application results of the MMWF with increasing kernel size.  
After applying the MMWF by kernel size, a region-growing-based segmentation algorithm was used to perform lung segmentation. The results are shown in Figure 3, with Figure 3a as the ground-truth of segmented image and Figure 3b showing that the accuracy of segmentation has significantly deteriorated due to the presence of noise. From Figure 3c-g, the images demonstrate the segmentation results as a function of increasing the MMWF kernel size.  
Figure 4 shows the accuracy, F1-score, and IoU values obtained from the lung images with the MMWF with kernel sizes of 3 \(\times\) 3, 5 \(\times\) 5, 7 \(\times\) 7, 9 \(\times\) 9, and 11 \(\times\) 11. The accuracy of the noisy image was 0.7210, whereas the accuracies for each kernel size were 0.9952, 0.9960, 0.9954, 0.9952, and 0.9949, respectively. When the kernel size was set to 5 \(\times\) 5, the accuracy increased 1.38 times compared with that of the noisy image. The F1-score of the noisy image was 0.0299, while the F1-score for each kernel size was 0.9915, 0.9928, 0.9919, 0.9914, and 0.9909, respectively. Similar to the accuracy, the kernel size of 5 \(\times\) 5 increased the F1-score 33.20-fold compared with that of the noisy image. The IoU value for the noisy image was 0.0152, whereas the values for each kernel size were 0.9831, 0.9858, 0.9839, 0.9829, and 0.9819, respectively. In line with previous evaluations, the kernel size of 5 \(\times\) 5 increased the IoU value a 64.86 times in comparison with that of the noisy image. The accuracy, F1-score and IoU values demonstrated a decreasing trend as the kernel size increased beyond 5 \(\times\) 5.  
Figure 3: Segmented lung image using region-growing-based segmentation algorithm with (a) original, (b) noisy, (c–g) 3 \(\times\) 3 MMWF, 5 \(\times\) 5 MMWE, 7 \(\times\) 7 MMWF, 9 \(\times\) 9 MMWF, and 11 \(\times\) 11 MMWF.  
Figure 2: Filtered lung CT images with (**a**) original, (**b**) noisy, (c–g) 3 \(\times\) 3 MMWF, 5 \(\times\) 5 MMWF, 7 \(\times\) 7 MMWF, 9 \(\times\) 9 MMWF, and 11 \(\times\) 11 MMWF.  
Figure 5 shows the RMSEs and PSNRs obtained from the lung images when applying an MMWF with kernel sizes of 3 \(\times\) 3, 5 \(\times\) 5, 7 \(\times\) 7, 9 \(\times\) 9, and 11 \(\times\) 11. The RMSE of the noisy image was 0.2229, whereas for each kernel size, it was 0.0292, 0.0271, 0.0285, 0.0294, and 0.0303, respectively. The kernel size of 5 \(\times\) 5 yielded the lowest RMSE value, which was 7.82 times lower than that of the noisy image. The PSNR of the noisy image was 61.1689, whereas for each kernel size, it was 78.8171, 79.4585, 79.0361, 78.7585, and 78.5779,  
Figure 4: (**a**) Accuracy, (**b**) F1-score, and (**c**) IoU results of the segmented image according to the kernel size of the applied MMWF.  
respectively. The kernel size of \(5\times 5\) generated the highest value, which was 1.30 times higher than that of the noisy image.