# Fundus Image Registration Technique Based on Local Feature of Retinal Vessels
## 3 Methodology
### Stage 2: Feature Extraction
#### 3.2.2 Feature Selection Module
* STEP 5(c): Exclusion criterion 3 The valleys discovered in STEP 5(b) are further examined for their depth and positioned on the \(y\)-axis. For a candidate feature point located on a retinal vessel, the valley with the maximum depth is at the lowest position of the \(y\)-axis or global minimum, as shown in Figure 9(a\(ii\),b\(ii\)). Therefore, a candidate feature point is discarded if the valley with the maximum depth is a local minimum, such as in Figure 9(c\(ii\)). * STEP 5(d): Exclusion criterion 4  
Figure 11: Exclusion criterion 5. Cross-sectional lines on (\(i\)) gradient and (\(ii\)) binary interpolated patches for (**a**) retinal vessel and (**b**) noise. (\(iii\)) The intersection between sums of intensity profiles from (\(i\)) and (\(ii\)). A candidate feature point is discarded when the overlaid sums of intensity profiles are apart from each other, as in (**b**)(\(iii\)). The valley with maximum depth and global minimum from STEP 5(c) is examined for its position on the \(x\)-axis. The sum of the intensity profiles is divided into four sections of equal size. The valley with the maximum depth is expected to be at the second or third section on the \(x\)-axis if a candidate feature point on a retinal vessel is either normal or with central light reflex as shown in Figure 10a,b Therefore, a candidate feature point is excluded if the valley with the maximum depth is located at the first and fourth sections, as in Figure 10c. * STEP 5(e): Exclusion criterion 5 This criterion overlaid the sum of the intensity profiles from gradient and binary interpolated patches. The intersection can be found when a candidate feature point is located on a retinal vessel and vice versa, as depicted in Figure 11. Thus, the candidate feature point is discarded when the overlaid sums of the intensity profiles are apart from each other. * STEP 6: Selection process The exclusion process removes the majority of the candidate feature points detected on noises. However, the remaining candidate feature points may include points detected on noises with a high structural similarity as the retinal vessels in the interpolated patches. Therefore, the selection process includes two main steps to select the final feature points, namely, distribution and selection weightage. The distribution will ensure the final feature points are selected throughout the image, while the selection weightage highlights the strength of the retinal vessel in the patch for each candidate feature point. * STEP 6(a): Distribution The distribution of the feature points all over the image is vital to ensure a high registration accuracy [42]. There are two procedures involved in distributing the feature points. First, the feature points are distributed across the hierarchical Gaussian scale space by computing the maximum number of feature points (\(N_{p,q}\)) for each Gaussian image \(G_{p,q}\). \(N_{p,q}\) is set proportionally inverse to the width of the Gaussian kernels used when building the scale space as described in [8; 11; 19]: \[N_{p,q}=N_{total}.F_{p,q}\] (11) The proportion of the feature points \(F_{p,q}\) is given by: Figure 6:0 (12) The proportion in the initial image of the scale space \(f_{0}\) and the constant factor \(\mu\) can be expressed as: Figure 6:1 (13) Figure 6:2 (14) where, \(P\) is the total octave with index \(p\in[1,\dots,P-1]\), \(Q\) is the total level with index \(q\in[-1,\dots,Q-2]\), \(n\) is the index of the images in the hierarchical Gaussian scale space and \(N_{total}\) is the total feature points in the hierarchical Gaussian scale space. In this study, \(N_{total}\) is set to 4500 points, which empirically shows to provide a reasonable amount of feature points to perform image registration. However, if the candidate feature points are detected at less than 4500 points, \(N_{total}\) is set to  
The distribution coefficient for a grid image \((DC_{u})\) represents a combination of three factors. These factors are entropy [43], peak deviation nonuniformity [44] and total candidate feature points detected in the grid image.