# Fundus Image Registration Technique Based on Local Feature of Retinal Vessels
## 3 Methodology
### Stage 2: Feature Extraction
#### 3.2.2 Feature Selection Module  
The feature selection module includes exclusion and selection processes. The exclusion process discards the candidate feature points associated with noises while the selection process selects the final feature points according to the strength of the retinal vessels. These processes require gradient and binary interpolated patches as input. (a) STEP 4: Preparing gradient and binary interpolated patches The initial step of the feature selection module is to extract a square patch with the size of \(s_{p}\times s_{p}\) pixels for each candidate feature point from the respective \(G_{p,q}\). The size of the patch is varied depending on the octave position (\(p\)) of the candidate feature point to  
Figure 4: Outer ring test. (a) Sixteen pixels denoted by \(b_{l},l\in[1,\dots,\ 16]\) surrounding an extremum, _e._ (b–e) Examples of outer ring patterns. Pixels with red dot are from group _low_, pixels with purple dot are from group _medium_ and pixels with green dot are from group _high_. Figure 5: Example of candidate feature point (pointed by black arrow) from feature detection module. The candidate feature point is an extremum within a curvature structure. ensure the retinal vessel can be captured within the patch despite the image size of \(G_{p,q}\). The side length \(\big{(}s_{p}\big{)}\) of the patch is an odd number computed as follows:  
\[s_{p}=s_{initial}-4(p+1) \tag{8}\]  
where, \(s_{initial}\) is the initial side length. There are three possible values for \(s_{initial}\) as defined in (9). \(s_{initial}\) is set by referring to the size of the initial Gaussian image \(G_{0,-1}\). These values are determined by observing the retinal vessels with the thickest width on the fundus images from five datasets; CHASE_DB1 [33; 34], DRIVE [35; 36], HRF [37; 38], STARE [39; 40] and Fundus Image Registration (FIRE) dataset [41]. Furthermore, by considering scale or zoom less than 1.5 [8]. The \(s_{initial}\) is suitable for input images larger than that of the largest image used to determine \(s_{initial}\) (10 megapixels). This is because hierarchical Gaussian scale space down-sampled the input image by half as the level increased and reduced the image details as the octave increased, allowing the vessels of varying sizes to fit in the square patch even for input images larger than 10 megapixels. \[s_{initial} \begin{cases}35\text{ pixels \ if }G_{0,-1}&>1000\times 1000\text{ pixels}\\ 25\text{ pixels \ if }G_{0,-1}&\leq 1000\times 1000\text{ pixels}>600\times 600\text{ pixels}\\ 21\text{ pixels \ if }G_{0,-1}&\leq 600\times 600\text{ pixels}\\ \end{cases}  \tag{9}\]  
The extracted gradient patch is up-sampled using cubic interpolation with a refinement factor of two to smooth the region around the vessel edges. Then, this interpolated patch is converted to a binary image as depicted in Figure 6(ai_i_,bi_i_). These patches are used as input for exclusion and selection processes. (b) STEP 5: Exclusion process  
The curvature structure in the local patch represents retinal vessels of various sizes as well as noises such as the retinal nerve fiber layer, underlying choroidal vessels, microaneurys and exudates. Therefore, five exclusion criteria specifying the characteristics of the retinal vessels and noises on the sum of intensity profiles are presented to discard candidate feature points on noises. The intensity profile is the intensity value of the pixels extracted from a cross-sectional line running through the patch. In this study, the intensity profiles extracted from multiple cross-sectional lines are summed to distinctively highlight the characteristics of the retinal vessels and noises in the interpolated patch. The intensity profiles are extracted from a total of \(L_{total}\) cross-sectional lines that parallel each other with \(L_{distance}\) distance between the lines. These cross-sectional lines are positioned either along or perpendicular to the main orientation of the interpolated patch.