Image Processing Reference
In-Depth Information
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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