## 4 Experimental Results
### Robustness to Noise  
Both synthetic and real brain MRI were used to show the robustness of RC_LCI. BrainWeb [29] is a simulated brain database used to simulate brain MRI using three sequences (T1-, T2-, and PD-weighted) and a variety of slice thicknesses, noise levels, and levels of intensity inhomogeneity; the brain images used in this paper were T1-weighted and had a 1-mm slice thickness. Firstly, synthetic images with 9% noise provided by BrainWeb were used as the experimental images and RC_LCI was compared with MICO [27], BCFCM [22], and FLICM [24]. In Figure 2, the upper row shows the 67 th slice image and the lower row shows the 96 th slice image. It can be seen from the original images in the first column that WM and GM were intertwined with each other due to severe noise, which meant that it was difficult to segment them accurately without an effective model. Since MICO does not consider local information and thus is sensitive to noisy pixels, it produces incorrect results in the case of severe noise. Therefore, it can be clearly observed in the second column that there were many outliers in the segmentation results of MICO. The third column shows that noisy pixels were clearly presented in the segmentation results of BCFCM because the local spatial information was not anisotropic, so the noisy pixels in the neighborhood directly led to misclassification. FLICM utilizes the spatial Euclidean distance in the neighborhood, which easily results in oversegmentation in adjacent different areas. RC_LCI utilizes the weight of each pixel in the 8-neighborhoods to update the current central pixel, so it can easily identify the noisy pixels in the neighborhood so as to decrease the influence of noise. By comparing the segmentation results of all models with the ground truth (GT) in the sixth column, it can be seen that the segmentation results of RC_LCI were the closest to GT. From the above experimental results, the robustness of RC_LCI to noise was slightly superior to FLICM and significantly superior to MICO and BCFCM. The iterations and Central Processing Unit (CPU) time of the four models are listed in Table 1. It can be seen from the last row that RC_LCI consumed less iterations and CPU time than the other models in terms of segmentation efficiency. Figure 2: Comparison of the segmentation results of multiplicative intrinsic component optimization (MICO), bias-corrected fuzzy c-means (BCFCM), fuzzy local information c-means (FLICM), and RC_LCI: (**a**) original images; (**b**) segmentation results of MICO; (**c**) segmentation results of BCFCM; (**d**) segmentation results of FLICM; (**e**) segmentation results of RC_LCI; and (**f**) ground truth. RC_LCI was then applied to real images with skulls and compared with MICO, BCFCM, and FLICM. In Figure 3, axial-, sagittal-, and coronal-sectioned brain MRI are shown in the first, second, and third rows, respectively. As shown in Figure 3, GM and WM are also intertwined with each other in the first column and the three images are occupied by low noise. The segmentation results of MICO were still corrupted by noisy pixels. BCFCM did not clearly distinguish WM and GM in adjacent areas. FLICM did not distinguish background and CFS because of oversegmentation, so it obtained incorrect segmentation results when the background was adjacent to CFS. In real brain MRI, RC_LCI clearly classified images into four classes and effectively removed noisy pixels without being influenced by the skull. To more objectively and accurately compare the performances of these models, quantitative evaluation was used to analyze the segmentation results of synthetic brain images with noise ranging from 6% to 9%. BrainWeb also provides GT, which are the standard segmentation results of the corresponding images. The Jaccard similarity (JS) coefficient can be used to compare the similarity of two sets. It is given by  
\[JS(S_{1},\ S_{2})=\frac{|S_{1}\cap S_{2}|}{|S_{1}\cup S_{2}|}, \tag{24}\]