# Exudates as Landmarks Identified through FCM Clustering in Retinal Images
## 4 Experimental Results and Discussion
In Figure 9, two regions are affected by the extension: the lower part of the segmented portion of the image which overlaps the GT by 2 pixels from a total region of 5 pixels, making a ratio \(\sigma=\frac{2}{8}\geq 0.2\); conversely, the same part of the GT overlaps a portion of the relevant segmented image; this intersection is constructed of 2 pixels out of a total region of 4 pixels representing the GT, making a ratio of \(\sigma=\frac{2}{4}\geq 0.2\). As the criteria are satisfied in both cases, the connected pixels of this portion of the segmented image, as well as the GT, are estimated as TP. On the other hand, the upper-left part similarly achieved the criteria, and, hence, it is considered as TP (the upper-left segmented portion intersects the GT with a ratio of \(\sigma=\frac{4}{4}\geq 0.2\); the GT intersects the relevant segmented part with a ratio of \(\sigma=\frac{4}{8}\geq 0.2\)). Hybrid validation techniques (pixel by pixel and extendedtechnique [32]) were implemented here to evaluate and compare our methodology with others under the same circumstances. _Sensitivity (\(Se=\frac{TP}{TP+FN}\))_ evaluates the ability of the methodology to properly detect exudates. _Specificity (\(Sp=\frac{TN}{TN+FP}\))_ evaluates the ability to properly detect non-exudates. _Accuracy (\(Acc=\frac{TP+TN}{TP+TN+FN+FP}\))_ evaluates the ability to properly detect exudates and non-exudates. _Positive Predictive Value (\(PPV=\frac{TP}{TP+FP}\))_ is the correctness degree to detect exudate pixels out of all detected exudate pixels. FCM was selected as the clustering tool because fundus image properties are not unified and standard: Variations in colors, the presence of noise, and a fuzzy look due to the eye spherical shape are drawbacks that complicate the task. The common dataset DIARETDB0/1, expressly made for exudate detection, was considered the benchmark. The preliminary exclusion of the optic disc and the vessels reduces/prevents false detection of the exudates. A brute-force approach indicated the best feature set, considering the 77 features shown in Table 1. We kept the following four features: hue, entropy, and standard deviation for both the intensity in the HSI color space and the Y channel from the XYZ color space (Figure 10). Standard deviation of intensity, with various window sizes of 3 \(\times\) 3, 7 \(\times\) 7, 11 \(\times\) 11, 15 \(\times\) 15, and 17 \(\times\) 17 pixels, was convolved with the expected exudate binary images. Results showed that the highest TP values were obtained for a standard deviation window of 3 \(\times\) 3 pixels. As the window size increased, small exudate areas were not properly detected; consequently, this loss of exudates reduces the sensitivity of the system. In the case of FP, the value of FP acted in an opposite way to TP; as the standard deviation window size increased, the number of FP values decreased, which negatively affected the  
Figure 10: Output of each step of features phase: hue (**a**), std_intensity (**b**), standard deviation of intensity (**c**), and Y channel (**d**). Figure 9: Example of expanded true positive (TP): ground truth (GT) (**a**); segmented pixels (**b**); TP (**c**), false negative (FN) (**d**), false positive (FP) (**e**), and true negative (TN) (**f**). specificity. To show the effect of variant window size on detecting the exudates, an example is introduced in Figure 11.  
As in the case of standard deviation of intensity, entropy was implemented with different window sizes, from 3 \(\times\) 3 to 17 \(\times\) 17 pixels. Increasing the size of the window affected small exudate areas that started to disappear, so the TP value was decreasing and had a negative influence on sensitivity. The FP value decreased as the size got larger, which means the misclassification data decreased. Again, TP and FP contradicted each other. Since TP is more influential on the performance of the method, it is convenient to keep the TP as high as possible, by choosing the smallest window size.