## 4 Experiments and Results
### Cornea Segmentation Results
To demonstrate the effect of our proposed circle selection process, in this method the circle with the highest accumulator value is selected as the output instead of using the objective function \(F_{\alpha}(C)\). * PROPOSED with \(F_{\alpha}(C)\): This method represents the full version of the proposed cornea segmentation process, incorporating the EM-5  
In the canny edge detection process in Methods 1 and 2, the grayscale image is first blurred using a Gaussian filter. Then, the image gradients are calculated for each pixel, and only pixels with local maxima of the gradient magnitude along the gradient direction are considered as edge candidates. Double thresholding is applied to classify candidate pixels into strong and weak edges using high and low threshold values, respectively. The final edge image is obtained from strong edges and weak edges that are connected to the strong edges. In this experiment, we varied the standard deviations of the Gaussian filter across 5, 10, 15, 20, and 25. Additionally, we varied the high and low threshold values across 6, 12, 18, 24, 30, and 36, pairing each lower value with its equivalent and all higher values to create a range of threshold combinations. We selected the optimal combination of Gaussian filter standard deviation and high and low threshold values that achieved the highest average precision in cornea edge detection. In this experiment, we identified the optimal parameters for the canny edge detection process as a Gaussian filter standard deviation of 10 with both the low and high thresholds set to 12. For RANSAC-based circle detection, let \(P\) represent a set of pixels used for circle fitting, which includes either the edge pixels in Method 1 or the contour of the cornea segments in Method 4. The algorithm starts by randomly selecting three pixel positions from \(P\) and determining the circle \(C\) that best fits these points. The distance between every pixel in \(P\) and the circle \(C\) is calculated. The inlier pixels, which are those with distances less than the threshold, are counted and stored. In this experiment, the inlier threshold is set to 2. This process of random sampling, circle fitting, and inlier counting is repeated for a predetermined number of iterations \(T\), which is calculated as follows [50]:  
\[T=\frac{\log(1-p)}{\log(1-w^{n})} \tag{10}\]  
where \(p\) denotes the desired probability of success, \(w\) denotes the percentage of inliers in the dataset, and \(n\) denotes the number of points to define the model (for circle detection, \(n=3\)). After \(T\) iterations are completed, the circle with the highest inlier count is returned as the final result. In this experiment, we set the desired probability of success \(p\) to 0.95. For Method 1, the percentage of inliers \(w\) was 1.87%, which leads to a number of iterations totaling 458,117 rounds. For Method 4, where the percentage of inliers \(w\) was 13.24%, we used 1289 iterations. The results in Table 4 reveal that the proposed method provides more accurate results in cornea detection across all metrics compared to conventional methods. Examples of the circle detection process and results for each method are shown in Figure 12. The first two conventional methods, which apply canny edge detection directly to the original ocular staining images, provide low performance. This is because edge detection algorithms tend to detect many edges other than the cornea, especially the eyelid, which has a curve resembling a circular shape. These issues are illustrated in Figure 12, Method 1 and 2. Consequently, the RANSAC and HCT algorithms are unable to accurately detect the cornea area. The experimental results indicate that presegmentation of the corneal area prior to circle detection significantly improves cornea detection performance compared to direct application of circle detection algorithms on the original images.