# Retinal Vessels Segmentation Techniques and Algorithms: A Survey
## 4 Retinal Vessels Segmentation Techniques
### Multi-Scale Techniques  
The core idea behind the multi-scale representation is to represent the image at multiple scales (levels) where the data contained in a given image are embedded into one-parameter family of derived images at multiple scales [100], as shown in Figure 13. This representation is constructed provided that the structures at coarse scales (levels) are the simplified versions of the corresponding structures at fine scales by convoluting with smoothing kernels. The only possible smoothing kernels that meet the linearity and spatial shift invariance are _Gaussian_ and its _derivatives_ kernels that have increasing widths (scales \(\sigma\)) [101]. Figure 13: Level scaling idea of multi-scale method. Originally, the scale-space is the framework of the multi-scale image representation [102]; two widely-used types of multi-scale representation are: pyramid [103; 104], and Quad-tree [105]. Most retinal vessels segmentation methodologies are built based on the pyramid multi-scale type, where the grey-level data are represented in such a way that combines sampling operations with successive smoothing steps conducted by Gaussian kernels with different scales gives rise to a response that is represented by 2D Hessian matrix [106]. The eigen values of Hessian matrix determine the vessel-likeness which, in turn, result in retinal vasculature structure enhancement. Hessian matrix processing through eigen values analysis aims to obtain the principal directions of vessels where the decomposition of local second order structures in retinal image can be performed in order to attain the direction of the smallest curvature along the retinal vessels [107]. The retinal image size decreases exponentially with scale level, as illustrated in Figure 13, and, as a consequent, the amount of required computation too. However, it shows weakness in extracting fixed-size structures such as optic disc and non-uniform structures such as retinal lesions. Thus, multiscale approaches can be best suited for structures that have varying width and length (coarse and fine) in the same image. A typical multi-scale based technique for retinal vessel segmentation was proposed by [PERSON] et al. [66]. The proposed technique composed of three major phases: (1) Gaussian pyramid generation; (2) neighborhood analysis; and (3) images fusion. After the green channel of raw retinal image was extracted, Gaussian pyramid of resolution hierarchy was generated. The hierarchy is composed of three levels (level 0, level 1, and level 2, as shown in Figure 13). The original retinal image (green channel) has the highest resolution (level 0), and the width and height of image begin reducing as we move towards further levels (fine to coarse levels). In the second phase, for each level, a \(3\times 3\) neighborhood window analysis for each pixel was analyzed by calculating Hessian matrix followed by calculation of a couple of eigenvalues \(\lambda_{l}\) and \(\lambda_{h}\) of Hessian matrix which reflect the scale of lowest curvature \(\lambda_{l}\) and the highest one \(\lambda_{h}\) in the neighborhood window of the target pixel. Then, the ratio of these values was used to calculate a vessel likeness measure \(P_{vessel}=1-\frac{\lambda_{l}}{\lambda_{h}}\); the value of \(P_{vessel}\) determines whether target pixel belongs to vessel tree or not. If \(P_{vessel}\) value is close to one, it means it is most likely a vessel pixel since \(\lambda_{l}\) and \(\lambda_{h}\) are similar to each other. This analysis was applied to each pixel at every scale (level). At the final stage, segmentation results from different levels were undergone binarization using two hysteresis thresholds, then they merged together using pixel-wise OR operation, which yielded the final segmented image. The methodology has achieved an accuracy, specificity, and sensitivity of 93.8%, 97.5% and 65.1% on STARE dataset, and 94.9%, 96.8% and 75.9% on the DRIVE dataset, respectively. [PERSON] et al. [68] proposed a two-step multi-scale retinal vessel detection algorithm.