# Statistical Edge Detection and Circular Hough Transform for Optic Disk Localization
## 3 Experimental Results and Discussion  
In this work, a method developed for OD localization is proposed. The method was tested on the DRIVE, DIARETDB0, and DIARETDB1 public datasets. The detailed specifications of these databases are given in Table 1.  
Proposed methods and all experiments and observations were carried out by the following specifications of computer and programs:  
* Operating system: Windows 10, 64-bit
* Processor: Intel(R) Core(TM) i5-2430 CPU @2.40 GHz
* Memory: 8.00 GB RAM
* Computing environment: MATLAB R2016a  
The OD center localization performance is evaluated by comparing it with ground-truth OD centers. According to [PERSON] and [PERSON]'s study [40], a distance of up to 60 pixels between the automatically detected OD center and manually detected OD center is acceptable. The proposed method for OD localization was measured and evaluated in terms of the accuracy rate and mean absolute distance of the algorithm. The accuracy rate is calculated separately for each dataset. The mean absolute distance is defined as the difference in pixels between the automatically detected and manually detected OD centers. The accuracy rate and mean absolute distance are calculated by the following equations:  
\[\text{Accuracy}=\frac{C_{0}}{N_{0}} \tag{13}\]  
N\({}_{0}\) represents the total number of retinal images present in a database. C\({}_{0}\) indicates the number of images in which OD centers are correctly detected. \[\text{Distance}=\frac{1}{N_{0}}\sum_{i=1}^{N_{0}}\frac{(|M_{ci}(x)-A_{ci}(x)|) +(|M_{ci}(y)-A_{ci}(y)|)}{2} \tag{14}\]  
The distance is the difference between the automatically detected and the manually detected OD centers. \(M_{c}(x,y)\) and \(A_{c}(x,y)\) are the manually and automatically calculated OD center points, respectively [41]. The accuracy of the proposed method was 100%, 96.92%, and 98.88% for the DRIVE, DIARETDB0, and DIARETDB1 datasets, respectively. The average absolute distance value was approximately 10 pixels for the DRIVE dataset, about 10 pixels for the DIARETDB0, and about 12 pixels for the DIARETDB1 dataset. A comparative analysis of the results and average absolute distance values of the proposed method and the state-of-the-art models in the literature is given in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Dataset**} & **Number of** & **Correct** & **Accuracy** & **Distance** \\ \cline{3-5}  & & **Images** & **Classification** & **(\%)** & **Distance** \\ \hline \multirow{3}{*}{[PERSON] et al. [16]} & DRIVE & 40 & 40 & 100 & - \\ \cline{2-5}  & DIARETDB1 & 89 & 83 & 93.25 & - \\ \cline{1-1} \cline{2-5}  & DRIVE & 40 & 39 & 97.5 & - \\ \cline{1-1} \cline{2-5}  & DIARETDB1 & 89 & 86 & 96.5 & - \\ \hline \multirow{2}{*}{[PERSON] et al. [43]} & DRIVE & 40 & 40 & 100 & 17 \\ \cline{1-1} \cline{2-5}  & DRIVE & 40 & 40 & 100 & 23.2 \\ \hline \multirow{2}{*}{[PERSON] et al. [45]} & DRIVE & 40 & 40 & 100 & 15.9 \\ \cline{1-1} \cline{2-5}  & DRIVE & 40 & 40 & 100 & 15.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A comparative analysis of the results of the proposed method and other methods in the literature. Our method was compared with nine studies in the literature, and the results are shown in Table 2. For the DRIVE dataset, it is seen that the rate of correctly detecting the OD is 100% in all other studies except three. Only one image could not be identified correctly in the study conducted by [PERSON] and [PERSON] [42]; also, [PERSON] et al. [13] failed to identify four images. The other work that could not detect all the images in the DRIVE dataset is the study of [PERSON] and [PERSON] [47]. The OD regions of all the images in the DRIVE dataset have been correctly identified by the proposed method. For the DIARETDB0 dataset, OD localization performance was 96.92% in the study of [PERSON] [41]. [PERSON] and [PERSON] [46] achieved 98.5% accuracy success in the same dataset. [PERSON] and [PERSON] [47] performed OD localization at a success rate of 96.9%.