Conceptualization, H.A.W. and A.H.; methodology, H.A.W.; software, H.A.W.; validation, H.A.W. and M.B.S.; formal analysis, H.A.W. and A.H.; investigation, H.A.W. and M.B.S.; data curation, H.A.W. and M.B.S.; writing—original draft preparation, H.A.W.; writing—review and editing, A.H., R.S. and M.B.S.; visualization, H.A.W.; supervision, A.H., R.S. and M.B.S.; project administration, A.H.; funding acquisition, A.H. All authors have read and agreed to the published version of the manuscript.

Figure 1. An example of polar coordinates in retinal image (DD: disc diameter).

Figure 1. An example of polar coordinates in retinal image (DD: disc diameter).

Figure 2. The flow of macular center point detection (OD: optic disc, ROI: region of interest).

Figure 2. The flow of macular center point detection (OD: optic disc, ROI: region of interest).

Figure 3. OD localization process, (a) input image, (b) grayscale image of I (c) Ipre1 image, (d) Ipre2 image, (e) Ic, (f) OD center area candidate (g) OD ROI (h) closing+opening result of binary OD ROI, (i) OD, (j) localization result of OD.

Figure 3. OD localization process, (a) input image, (b) grayscale image of I (c) Ipre1 image, (d) Ipre2 image, (e) Ic, (f) OD center area candidate (g) OD ROI (h) closing+opening result of binary OD ROI, (i) OD, (j) localization result of OD.

Figure 4. Temporal direction viewed from the appearance of blood vessels in the optic disc.

Figure 4. Temporal direction viewed from the appearance of blood vessels in the optic disc.

Figure 5. The extraction process of blood vessels on the optic disc; (a) optic disc on the green layer; (b) the extraction result of blood vessels on the optic disc; (c) the result of elimination of horizontal blood vessels.

Figure 5. The extraction process of blood vessels on the optic disc; (a) optic disc on the green layer; (b) the extraction result of blood vessels on the optic disc; (c) the result of elimination of horizontal blood vessels.

Figure 6. Illustration of macular ROI determination. The red box shows the macular ROI.

Figure 6. Illustration of macular ROI determination. The red box shows the macular ROI.

Figure 7. The extraction process results of the macular center point, (a) retinal image, (b) macular ROI localization result (red box), (c) macular ROI gray image, (d) macular ROI binarization result, (e) dilation + opening operation result, (f) macular center point detection result.

Figure 7. The extraction process results of the macular center point, (a) retinal image, (b) macular ROI localization result (red box), (c) macular ROI gray image, (d) macular ROI binarization result, (e) dilation + opening operation result, (f) macular center point detection result.

Figure 8. Euclidian distance distribution between the proposed method with GT. A red circle with a radius of 50 shows the acceptable distance limit for well-detected results, (a) DRIVE, (b) DiaretDB1, (c) Messidor, and (d) JOGED.com (accessed on 22 July 2022).

Figure 8. Euclidian distance distribution between the proposed method with GT. A red circle with a radius of 50 shows the acceptable distance limit for well-detected results, (a) DRIVE, (b) DiaretDB1, (c) Messidor, and (d) JOGED.com (accessed on 22 July 2022).

Figure 9. Examples of the detection results and location of the ground truth. The red ‘+’ symbol represents the detection result while the blue ‘+’ indicates the location of the ground truth.

Figure 9. Examples of the detection results and location of the ground truth. The red ‘+’ symbol represents the detection result while the blue ‘+’ indicates the location of the ground truth.

Figure 10. Macular center detection failure on image059.png of DiaretDB1.

Figure 10. Macular center detection failure on image059.png of DiaretDB1.

Table 1. Comparison of macular center detection results with other studies.

Table 1. Comparison of macular center detection results with other studies.

MethodDRIVEDiaretDB1MessidorJOGED.comAccuracyTime (s)AccuracyTime (s)AccuracyTime (s)AccuracyTime (s)Zheng [23]100%1293.3%12----Medhi [35]100%-95.51%-97.98%---Chalakkal [17]100%2595,5%2598.5%25--Sedai [10]100%0.4------Romero-oraá [24]100%0.54100%14.5599.67%27.04--Proposed method100%0.3498.78%0.5794.67%0.6493%0.78