## 4 Discussion  
LDCT is widely used for the examination of diseases such as lung cancer, owing to its low radiation dose. However, the limited number of photons used in LDCT results in increased noise, which degrades image quality. The presence of noise in LDCT leads to a deterioration in the performance of lung segmentation algorithms used for detecting and extracting lung tissue, ultimately affecting diagnostic accuracy [9]. To address this issue, various filtering techniques such as Gaussian, median, and Wiener filters have been proposed. However, conventional filtering techniques have drawbacks such as erosion and distortion of the edges of structures or blurring. To overcome these limitations, a fusion algorithm called an MMWF has been proposed [14]. In the MMWF, the kernel size is a key parameter that determines the trade-off between noise removal and preserving signal details, including boundary edges [23]. However, if the kernel size is too small, the noise removal capability is reduced. In contrast, if the kernel size is excessively large, the image may become excessively blurred. When the image is blurred, the threshold must be set defensively to prevent over-segmentation, reducing segmentation accuracy. Therefore, deriving an optimal kernel size that can optimize noise and blur reduction is crucial for the effective application of the MMWF. Figure 5: (**a**) RMSE and (**b**) PSNR results of the segmented image according to the kernel size of the MMWF. Hence, the current study aimed to determine the optimal kernel size for the MMWF to improve the performance of lung segmentation. The MMWF was modeled and applied with kernel sizes ranging from 3 \(\times\) 3 to 11 \(\times\) 11 at 2 \(\times\) 2 intervals. Figure 4 shows that a kernel size of 5 \(\times\) 5 yielded the highest accuracy, F1-score, and IoU values. RMSE and PSNR were measured to analyze the relationship between the image restoration rate and segmentation performance due to the MMWF. Figure 5 indicates that a kernel size of 5 \(\times\) 5 had the highest PSNR and lowest RMSE values. Overall, a kernel size of 5 \(\times\) 5 resulted in the best performance for all evaluation metrics. We found that the metrics of segmentation performance and similarity evaluation tends to be similar, indicating that optimizing the MMWF to remove only noise with minimal distortion is important to improve segmentation performance. Therefore, the optimal kernel size for the MMWF to achieve accurate segmentation was determined to be 5 \(\times\) 5. We observed that when the kernel size was too small, the noise removal was inadequate, leading to uneven lumen signals and a degradation in segmentation performance (Figure 6). Setting a high threshold value to overcome this problem can result in excessive tissue segmentation. Conversely, when the kernel size is too large, edge information is lost, making it difficult to distinguish the Hounsfield unit differences between tissues. Lowering the threshold value to address this problem resulted in improper tissue segmentation. Lung segmentation is a crucial initial step in image-based approaches for the early detection, diagnosis, and treatment of various respiratory diseases such as lung cancer and chronic bronchitis [24]. Numerous software tools are currently being developed for the effective detection and identification of pulmonary nodules in lung CT images [25]. Specifically, computer-aided detection (CAD) systems have significantly affected lung cancer diagnosis by improving nodule detection rates and distinguishing between benign and malignant nodules [26]. Lung segmentation serves as preprocessing step in CAD systems and influences their accuracy and precision [27]. Therefore, accurate lung segmentation is essential to improve the overall performance of CAD systems. Enhancing the accuracy of lung segmentation through denoising is vital for improving the effectiveness of CAD systems. Various non-local algorithms, such as the fast non-local means (FNLM) algorithm are currently being developed for noise removal.