Brain Tumor Detection Using Image Processing Techniques

123

FIGURE 4.3

Histogram of an image.

3.

Ri ∩Rj = , i ̸= j

4.

P(Ri) = TRUE for i = 1, 2, ..., n

5.

P(Ri ∪Rj) = FALSE, i ̸= j, Ri adjacent Rj.

In the expressions ∩and ∪symbols denote intersection and union, re-

spectively. The first condition stands for each pixel should belong to a specific

region. Second condition specifies that regions are composed of contiguous pix-

els [34]. Third condition implies that the regions don’t intersect each other.

Fourth condition determines that each region satisfies the homogeneity predi-

cate P. Last condition implies that two adjacent regions can not be combined

into a single region [35].

Various categories exist for brain tumor segmentation techniques, includ-

ing thresholding, region growing, edge based, clustering, and watershed tech-

niques. The following sections will give an overview of these image segmenta-

tion techniques.

4.3.3.1

Thresholding Techniques

The purpose of thresholding techniques is to separate objects in the image

from the background by using an appropriate threshold value. For any pixel

(x, y) in the source image; if src(x, y) is greater than the threshold value T,

it will be a pixel belonging to the object (value 1), otherwise it will be a pixel

belonging to the background (value 0).

dst(x, y) =

1,

if src(x, y) > T

0,

if src(x, y) ≤T

(4.5)

The histogram, which shows the distributions of gray levels in the image, is

widely utilized in determining the threshold value. A suitable threshold can be

chosen if the histogram characteristics specified are narrow, tall, symmetrical,

and separated by deep valleys [36]. Assuming that we have an image with

a histogram shown in Figure 4.3 expressed by the src(x, y) function. The

figure displays gray values on the x-axis and the corresponding total number

of pixels on the y-axis. A threshold value of T can be determined between the