Image Processing Reference

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TABLE 2.2 Performance of Different C-Means Algorithms

DataSet Algorithms DBIndex DunnIndex β Index

HCM 0.16 2.13 12.07

I-20497761 FCM 0.14 2.26 12.92

RCM 0.15 2.31 11.68

RFCM 0.13 2.39 13.06

HCM 0.18 1.88 12.02

I-20497763 FCM 0.16 2.02 12.63

RCM 0.15 2.14 12.59

RFCM 0.11 2.12 13.30

HCM 0.18 1.17 8.11

I-20497774 FCM 0.16 1.50 9.08

RCM 0.17 1.51 9.10

RFCM 0.15 1.64 9.68

HCM 0.17 2.01 8.68

I-20497777 FCM 0.16 2.16 9.12

RCM 0.15 2.34 9.28

RFCM 0.14 2.39 9.81

In this section, the feature extraction methodology for segmentation of brain MR images

is first described. Next, the methodology to select initial centroids for different c-means

algorithms is provided based on the concept of maximization of class separability (Maji and

Pal, 2008).

Statistical texture analysis derives a set of statistics from the distribution of pixel val-

ues or blocks of pixel values. There are different types of statistical texture, first-order,

second-order, and higher order statistics, based on the number of pixel combinations used

to compute the textures. The first-order statistics, like mean, standard deviation, range,

entropy, and the qth moment about the mean, are calculated using the histogram formed by

the gray scale value of each pixel. These statistics consider the properties of the gray scale

values, but not their spatial distribution. The second-order statistics are based on pairs of

pixels. This takes into account the spatial distribution of the gray scale distribution. In the

present work, only first- and second-order statistical textures are considered.

A set of 13 input features is used for clustering the brain MR images. These include gray

value of the pixel, two recently introduced features (first order statistics) - homogeneity and

edge value of the pixel (Maji and Pal, 2008), and 10 Haralick's textural features (Haral-

ick, Shanmugam, and Dinstein, 1973) (second order statistics) - angular second moment,

contrast, correlation, inverse difference moment, sum average, sum variance, sum entropy,

second order entropy, difference variance, and difference entropy. They are useful in charac-

terizing images, and can be used as features of a pixel. Hence these features have promising

application in clustering based brain MRI segmentation.

Homogeneity

If H is the homogeneity of a pixel I
m,n
within 3×3 neighborhood, then

H = 1−
1

6(I

)
{|I
m−1,n−1

+ I
m+1,n+1

−I
m−1,n+1

−I
m+1,n−1

|+

−I

max

min

|I
m−1,n−1
+ 2I
m,n−1
+ I
m+1,n−1
−I
m−1,n+1
−2I
m,n+1
−I
m+1,n+1
|}

where I
max
and I
min
represent the maximum and minimum gray values of the image. The

region that is entirely within an organ will have a high H value. On the other hand, the

regions that contain more than one organ will have lower H values (Maji and Pal, 2008).

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