Design and Implementation - Segmentation of Hand Bone for Bone Age Assessment - page 73

are named offset at times and different value of offset will give different indication
for the texture of image. Gray scale levels used in this topic is divided into four in
order to increase the algorithm computing speed:

1, if 0 ≤ I ( x , y ) ≤ argmax columnrow

I ( x , y )

xy

4

argmax columnrow
xy

≤ I ( x , y ) ≤ argmax columnrow

I ( x , y ) I ( x , y )

xy

2, if

4 2

(3.48)

I ( x , y ) =

3, argmax columnrow ≤ I ( x , y ) ≤ argmax columnrow

I ( x , y ) I ( x , y )

xy xy

2

4
3

argmax columnrow
xy

I ( x , y )

≤ I ( x , y ) ≤ argmax columnrow
xy

4, if I ( x , y )

4
3

where I ( x , y ) represents pixels gray level intensity at coordinate ( x , y ) , x represents
column and y represents row. The second order statistical measure that relevant in
this topic is shown in Eqs. ( 3.49 ) and ( 3.50 ).

N − 1

P i , j ( i − j ) 2 C ontrast = (3.49)

i , j = 0

N − 1

P i , j
1 + ( i − j ) 2

Homogeneity = HOM = (3.50)

i , j = 0

where P i , j represents the probability a group of spatial related pixel intensity occur
in the image. Among the twelve statistical equations proposed by Haralicks [ 19 ],
homogeneity is a suitable one for the purpose in the segmentation framework in
order to choose a uniform region of image. Homogeneity, also called 'Inverse
Difference Moment' is an inversion to the contrast. While computing the contrast,
the weight of element increases when distance of element from diagonal of the
GLCM increases. Inversely, the weight of element decreases as the distance of ele-
ments from diagonal increases. In short, the weight of contrast is ( i − j ) 2 , on the
other hand, the weight of Homogeneity is

1

1 +( i − j ) 2 .
The texture analysis in the proposed ACR k-means clustering method will be
conducted twice. First the texture analysis implemented on selecting the number
of k in k-means clustering, both images for k equals to two and k equals to three
will be computed, however only one of them will be used in reconstruction step,
the criteria is based on the homogeneity value. The concept is that between every
set of two resultant segmented images in each block, the one with higher homoge-
neity will be selected.

B ( i ) = B ( i , k )
where k = argmax k ∈ 2 ,3 ( HOM ( B ( i , k ))

(3.51)

where B(i) represents the i i-th quadruple divided block of the image, HOM(B(i,k))
represents homogeneity value in B(i,k) . All the blocks are then combined using