# Fundus Image Registration Technique Based on Local Feature of Retinal Vessels
## 3 Methodology
### Stage 2: Feature Extraction
#### 3.2.2 Feature Selection Module
The main orientation is the angle between the \(x\)-axis and major axis of the ellipse on the prominently connected region of the binary interpolated patch. The \(L_{total}\), \(L_{distance}\) and orientation of the cross-sectional lines are set according to the exclusion criteria as summarized in Table 1. The length of the cross-sectional lines in the  
Figure 6: Examples of the (_i_) gradient and (_ii_) binary interpolated patches extracted from (a) retinal vessel and (b) noise. Red ‘\(\times\)’ represents the position of the candidate feature point on the patch. pixel can be determined from \(L_{total}\) and \(L_{distance}\) to ensure the lines do not exceed the size of the interpolated patch in any orientation as follows:  
\[L_{length}=s_{bin}-(L_{distance}.L_{total}) \tag{10}\]  
where, \(L_{length}\) is the length of the cross-sectional lines, \(s_{bin}\) is the side length of the binary interpolated patch, \(L_{distance}\) is the distance between the parallel cross-sectional lines and \(L_{total}\) is the total cross-sectional lines. Figure 7: Exclusion criterion 1. (_i_) Cross-sectional lines and (_ii_) sum of intensity profiles for binary interpolated patch with (**a**) retinal vessel and (**b**) noise. A candidate feature point is discarded if any peak is found on the sum of intensity profiles from binary interpolated patch as in (**b**)(_ii_). Figure 8: Exclusion criterion 2. (_i_) Cross-sectional lines and (_ii_) sum of intensity profiles for gradient interpolated patch with (**a**) retinal vessel and (**b**) noise. A candidate feature point is discarded if the sum of intensity profiles from gradient interpolated patch is without any valley as in (**b**)(_ii_). Figure 10: Exclusion criterion 4. (**a,b_**) The valley with the maximum depth is on the 2 nd or 3 rd section for retinal vessels. (**c**) The valley with the maximum depth is on the 1 st or 4 th section for noise. A candidate feature point is discarded when the valley with the maximum depth is at the 1 st or 4 th section, as in (**c**). Figure 9: Exclusion criterion 3. (_i_) Cross-sectional lines and (_ii_) sum of intensity profiles for gradient interpolated patch with (**a**) normal retinal vessel, (**b**) retinal vessel with central light reflex and (**c**) noise. A candidate feature point is discarded when the valley with the maximum depth is a local minimum as in (**c**)(_ii_). \(L_{total}L_{distance}\)At\(x\)
* STEP 5(a): Exclusion criterion 1 Retinal vessel in a binary interpolated patch forms a nearly straight and wide connected region, as depicted in Figure 7(a\(i\)). This characteristic can be represented by the sum of the intensity profiles extracted from five cross-sectional lines positioned along the main orientation of the patch. The \(L_{total}\), \(L_{distance}\) and orientation for these cross-sectional lines are chosen to best express the retinal vessel of various sizes in the patch. For retinal vessels, the sum of the intensity profiles appears as a horizontal line, as depicted in Figure 7(a\(ii\)). Contrarily, the noise comprises an inconsistent connected region, as shown in Figure 7(b\(i\)), which results in the detection of peaks in the sum of intensity profiles. Therefore, a candidate feature point with peaks on the sum of intensity profiles is discarded. * STEP 5(b): Exclusion criterion 2 For the gradient interpolated patch associated with the retinal vessel as in Figure 8(a\(i\)), the cross-sectional lines with \(L_{total}=7\), \(L_{distance}=5\) and positioned perpendicular to the main orientation are fully intersected by the vessel. Therefore, the sum of the intensity profiles from these cross-sectional lines will consist of at least a valley, as depicted in Figure 8(_a\(ii\)_). In opposite, no valley can be found on the sum of the intensity profiles extracted from the patch associated with noise, as shown in Figure 8(b\(ii\)). Thus, this candidate feature point is discarded from further processing.