# Statistical Edge Detection and Circular Hough Transform for Optic Disk Localization
## 4 Conclusions  
In this study, a methodology for the automatic localization of the OD based on statistical edge detection and circular Hough transform was described. After the standard preprocessing steps, the average brightness value for each image was calculated, and the pixels below the mean value were eliminated from the image with a dynamically determined threshold. Then, the statistical edge  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Dataset**} & \begin{tabular}{c} **Number of** \\ **Images** \\ \end{tabular} & \
\begin{tabular}{c} **Correct** \\ **Classification** \\ \end{tabular} &
\begin{tabular}{c} **Accuracy** \\ **(\%)** \\ \end{tabular} & \multirow{2}{*}{**Distance**} \\ \hline [PERSON] et al. [13] & DRIVE & 40 & 36 & 90 & 18 \\ \hline \multirow{3}{*}{[PERSON] [41]} & DRIVE & 40 & 40 & 100 & 9.12 \\ \cline{2-6}  & DIARETDB0 & 130 & 126 & 96.92 & 11.83 \\ \cline{2-6}  & DIARETDB1 & 89 & 88 & 98.88 & 13.00 \\ \hline \multirow{3}{*}{[PERSON] and [PERSON] [46]} & DRIVE & 40 & 40 & 100 & - \\ \cline{2-6}  & DIARETDB0 & 130 & 128 & 98.5 & - \\ \cline{2-6}  & DIARETDB1 & 89 & 87 & 97.8 & - \\ \hline \multirow{3}{*}{[PERSON] and [PERSON] [47]} & DRIVE & 40 & 38 & 95 & - \\ \cline{2-6}  & DIARETDB0 & 130 & 126 & 96.9 & - \\ \cline{2-6}  & DIARETDB1 & 89 & 89 & 100 & - \\ \hline \multirow{3}{*}{**Proposed Method**} & **DRIVE** & **40** & **40** & **100** & **10.07** \\ \cline{2-6}  & **DIARETDB0** & **130** & **126** & **96.92** & **10.54** \\ \cline{1-1} \cline{2-6}  & **DIARETDB1** & **89** & **88** & **98.88** & **12.36** \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._detection framework was applied to retinal images in order to avoid performance degradation due to noise. Optic disk localization was performed by applying the circular Hough transform to the images, which has previously been used in the edge-extraction process. It has been proved in previous studies [25; 26] that the performance of the robust rank order-based statistical edge detection method is the most robust to variations in noise and performs better in all noise distributions tested than the conventional edge detection methods. Therefore, compared to the approaches proposed by the researchers given in Table 2, the proposed procedure for OD detection has the advantage that it is applicable to images contaminated with noise.  
The results show that the proposed method is able to locate the OD accurately in three public databases. According to experiments, the accuracy of the method was 100%, 96.92%, and 98.88% for the DRIVE, DIARETDB0, and DIARETDB1 databases, respectively.  
As a limitation of the proposed method, in some cases, such as when the OD region is not significantly bright compared to other regions, the circular Hough transform may be found to be unsuccessful in detecting the OD.  
In our future studies, it is planned to overcome this limitation by using a hybrid framework in which heuristic methods are used.  
The manuscript was written by Y.K. under the supervision of H.M.U. The modeling, analysis, and software process was executed by Y.K. and E.D. Technical support was provided by O.A.E., and H.M.U. helped in the review.  
This research received no external funding.  
The authors declare no conflict of interest.