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Bioinformatics of the Brain

FIGURE 4.7

Clustering based techniques were applied on same brain MRI images. The

source image featured in this figure was selected from the dataset available as

open source on Kaggle [5].

The algorithm will terminate if maxij

u(k+1)

ij

−u^(k)

ij





< ϵ where ϵ and

k stand for the termination and iteration values, respectively [52].

Figure 4.7 depicts the resultant images obtained by employing k-means

and Fuzzy c-means clustering methods mentioned above on a sample brain

MRI image. For both methods, the number of clusters was taken as four.

4.3.3.5

Watershed Technique

A watershed is essentially the area of land that lies between two rivers. In the

realm of image processing, an image can be interpreted as a topographic sur-

face based on its gray levels [53]. Watershed lines are formed if these surfaces

are subsequently filled with water from their minimum points while being kept

apart from water originating from other sources [54].

Soille and Vincent [55] presented an adaptable algorithm for calculating

watersheds in digital images. Let I be a grayscale image and hmin and hmax are

the smallest and largest values of I, respectively. The term Th(I) represents

the threshold of I at level h. A recursion is defined with the gray level h

varying from hmin to hmax. At the beginning of the recursion, the basin set

Xh is taken to be equal to the set of points (Thmin) with the value hmin.

In Equation 4.38, Thmin represents the set of points that water reaches first

and Xhmin denotes the set of points that belong to the minima of the lowest

altitude [55].

Xhmin = Thmin(I)

(4.38)

Then, the domain (IZTh+1(I)(Xh)) of the basin cluster Xh within the

threshold cluster Th+1 is expanded sequentially [56]:

Xh+1 = minh+1 ∪IZTh+1(I)(Xh), ∀h ∈[hmin, hmax −1]

(4.39)

In Equation 4.39, minh stands for the set of points belonging to the min-

imum at height h. Xhmax obtained from this recursion process is the set of