# Retinal Vessels Segmentation Techniques and Algorithms: A Survey
## 4 Retinal Vessels Segmentation Techniques
### Mathematical Morphology-Based Techniques  
Originally, mathematical morphology belongs to set theory of _mathematics_ science, where it is considered an application of lattice theory to spatial structures. Mathematical morphology concerns the shapes that exists inside the image frame instead of pixels' intensities. That means it ignores the details that regard image content where the pixel intensities are viewed as topographical highs, as shown in Figure 12. Typically, mathematical morphology was used in binary images, and then it extended to grey and colored ones, as a general processing framework, through morphological operators. In terms of mathematical morphology, the image \(I\) is represented as a set \(I\subseteq\Re^{2}\), where foreground pixels are the members that belong to \(I\), whereas the background ones belong to the complement \(I^{c}\). The image \(I\) undergoes a transformation by another set known as structuring element. Typically, the morphological operations can be applied to binary images and then can be extended to grey images. Morphological operations can be divided into: erosion, dilation, opening and closing operations. Erosion operation is used to lessen the objects in the image, whereas the dilation one is used to boost them. Morphological openings are used to remove unwanted structures in the image by applying an erosion followed by a dilation, whereas, in the case of morphological closing, some of structures in image are filled or merged by applying dilation operation followed by erosion one. In aim of retinal vessel segmentation, a Morphological Angular Scale-Space (MASS) technique was proposed by [70]. The basic idea of the proposed technique was to rotate a varying length (multiscale) linear structuring element at different angles to determine the connected components and assure the connectivity across vessels where the scale-space is created through the variation in the length of linear structuring elements. Gradual evolution to higher scales lessens the non-vessel like elements out of the processed retinal image, where the extracted information from lower scales is used to build the retinal image of higher scales. At a certain scale (determined by authors experimentally), and using a vessel-ness measure proposed by [97], the method reported a lowest mean square error value of 0.0363, which was averaged over 50 retinal images taken from DRIVE dataset. In addition to morphological operations, morphological tools are used in retinal vessel segmentation tasks including: gradient, watershed transform, top-hat transform, distance function and geodesic distance. Watershed transform was developed in the framework of mathematical  
Figure 12: Topographic highs of retinal vessels. morphology by [PERSON] and [PERSON] [98]. The principal idea underlying this method was inspired from geography when a landscape is flooded by water, then watersheds appear as dividing lines of the domains of rain falling over the entire region [99]. A watershed-based segmentation algorithm was used by [PERSON] et al. [71] to segment retinal vasculature structure. The proposed algorithm combines watershed transform and both contrast and directional information extracted from retinal image. First, watershed transform was used to segment the image into multi-regions. Then, a unique grey-level value was assigned to each single region. A contrast value was computed for each region through calculating the difference in grey-level with respect to its adjacent regions. A \(9\times 9\) window was applied to each pixel to attain the directional map composed of 16 directions. The standard deviation of pixels' grey levels is aligned along these directions. Then, based on the occurrences of directions within watershed region, pixels locating in same region are assigned same direction.