# Fundus Image Registration Technique Based on Local Feature of Retinal Vessels
## 3 Methodology
### Stage 2: Feature Extraction
#### 3.2.2 Feature Selection Module
The first factor of the entropy (\(EG\)) [43] defines the texture of the grayscale grid image. The grid image with high contrast retinal vessels, regardless of the sizes, will yield a large entropy value and vice versa. However, the entropy value presents a minimal distinction between the grid image with low contrast retinal vessels and with only noises or retinal surface. Therefore, peak deviation nonuniformity (\(UG\)) [44] is included as the second factor. This factor is sensitive to the changes in the grayscale level. Thus, it is beneficial in distinguishing between the grid image containing low contrast vessels and the grid image with only noises. In the coarser grid image, particularly at the higher octave, fewer candidate feature points are detected compared to the finer grid image. However, the values of the entropy and peak deviation nonuniformity measured from the coarser and finer grid images only show a minimal difference. To compensate for these factors, the total candidate feature points detected in the grid image (\(TG\)) is considered as the third factor. The distribution coefficient \(DC_{u}\) for a grid image \(u\) can be expressed as the combination of the three factors:  
Figure 6:3  
where, \(W_{EG}\) is the weight factor for the entropy, \(W_{UG}\) is the weight factor for the peak deviation nonuniformity, \(W_{TG}\) is the weight factor for the total candidate feature points, \(u\) is the index of the grid image with \(u\in[1,\ \cdots,U]\) and \(U\) is the total grid in a Gaussian image \(G_{p,q}\). The weight factors are empirically set to \(W_{EG}=0.3,\ W_{UG}=0.3\) and \(W_{TG}=0.4\) to give a distinctive representation in describing the grid image. * STEP 6(b): Selection weightage  
The selection process is continued by computing selection weightage for each candidate feature point. The selection weightage highlights the strength of the retinal vessels indicated by entropy, area of the intersected region and the mean histogram of gradient orientation at the vessel edges. The entropy (\(EP\)) is computed as in [43] to describe the texture in the gradient interpolated patch. Next, the area of the intersected region (\(AP\)) is determined between the sums of intensity profiles from the gradient and binary interpolated patches in STEP 5(e), as depicted in Figure 6:4 The lowest intersection point on the \(y\)-axis is used as the reference level to approximate the area of the intersected region using the trapezoidal rule. The area of the intersected region expresses the strength of the retinal vessels in terms of size and contrast. For example, the intersected region has a larger area for a thicker and high contrast retinal vessel. The area decreases as the size and contrast of the retinal vessel decreases. Figure 6:5 Area of intersected region between the sums of the intensity profiles from _exclusion criterion 5_. The mean histogram of the gradient orientation at the vessel edges (\(HP\)) is estimated using both gradient and binary interpolated patches. Initially, the partial derivative is performed on the gradient interpolated patch to obtain gradient orientation for each pixel. The partial derivative is approximated using the central difference as it gives a more accurate approximation compared to other techniques, such as forward and backward approximations. Then, the binary interpolated patch is used to obtain the vessel edges by performing binary dilation to increase the thickness of the edges. Once the pixels on the vessel edges are identified, the gradient orientation is extracted. The gradient orientation for these pixels is organized into a histogram of 36 bins, as shown in Figure 6:6 In this histogram, the non-zero frequencies are averaged to represent the mean histogram of the gradient orientation at the vessel edges. The mean histogram will yield a high value for a high contrast retinal vessel as the edges are thicker and the gradient orientation is more uniform.