## 2 Methods
### Cerebral vasculature Segmentation  
The segmentation algorithm presented in this manuscript is automatic, adaptive, and accurate in delineating cerebral vasculature [10]. As shown in Figure 2, the algorithm starts with a preprocessing step to eliminate noise artifacts such as acquisition errors and image biasing that might result from the magnetic field of the MRA scanner. In this step, a bias correction algorithm was used to resolve inconsistencies of data [19]. Then, to enhance image homogeneity, the 3D Generalized Gauss-Markov Random Field (3D GGMRF) was employed. The 3D GGMRF model analyzes the spatial homogeneous pairwise interactions between each voxel and its 26 neighborhood system and minimizes differences between the voxel and its neighbors [20]. A skull stripping approach [21] was then applied on the enhanced images to remove cerebral fat tissues that usually look like cerebral blood vessels. This approach employs a Markov-Gibbs Random Field (MGRF) model and a geometric deformable (brain iso-surface) model to preserve the topology of the cerebral vasculature during the skull stripping.  
After data preprocessing, the vasculature tree was delineated in two steps. First, a Linear Combination of Discrete Gaussians (LCDG) [22] was used to produce the initial segmentation of the vascular tree by estimation of the marginal probability density of MRA voxel values for brain vessels and other cerebral tissues. This initial segmentation, however, may miss some tiny blood vessels in the vascular tree. This is why the second step in the segmentation process is very essential. In the second step, a 3D local adaptive segmentation algorithm [21] was applied to refine the initial segmented vasculature by finding any missing details, specifically the small vessels. This adaptive algorithm divides each image into a set of connected components. Then, an adaptive search window is centered over each connected component where a new threshold is calculated to separate blood vessels from other brain tissues. Cerebral segmentation using this algorithm achieved a sensitivity of 94.82%, a specificity of 99.00%, a dice similarity coefficient of 92.23%, and an average volume difference of 10.03% compared to state of the art algorithms [10]. Figures 3 and 4 present an output sample of the segmentation module. Additionally, this algorithm is fully automatic and thus, it resolves the associated problems of semi-automatic and automatic segmentation methods such as time-consuming and inter-observer variability. Unlike most vascular segmentation algorithms in the literature [23], this algorithm has no constraints regarding the linearity or the circular cross-sections of blood vessels because it can segment both healthy and unhealthy blood vessels accurately and efficiently. The algorithm is also able to delineate even tiny blood vessels (\(\leq\)1 mm) which makes it a very good fit in the proposed CAD system because it is clinically known that the impact of hypertension development mainly affects tiny blood vessels [24; 25]. In addition, the segmentation approach overcomes and handles the noise in the MRA (e.g., microscopic, or mesoscopic noisy disturbance) images through homogeneity enhancement using the 3D GGMRF model which minimizes the energy between each voxel and its 26-neighborhood to enhance the homogeneity and remove any noise.  
Figure 2: Module 1: MRA data preprocessing and segmentation.