Design and Implementation - Segmentation of Hand Bone for Bone Age Assessment - page 78

cluster validity begins on TR-2.0 and decides that TR-2.0 needs to be further
quadrisected to achieve better result. In Fig. 3.10 d, each of the TR-2.1, TR-2.2,
TR-2.3, TR-2.4 remains according to the result of cluster validity and therefore
proceed to BL-3.0. In Fig. 3.10 e, BL-3.1 and BL-3.3 remain whereas BL-3.2
and BL-3.4 are quadrisected according to the cluster validity; all sub-blocks of
BL-3.2 and BL- 3.4 which are BL-3.2.1, BL-3.2.2, BL-3.2.3, BL-3.2.4, BL-3.4.1,
BL-3.4.2, BL-3.4.3, BL-3.4.4 remain as decided in accordance to cluster validity
on each of them and therefore proceed to BR-4.0. In Fig. 3.10 f, BR-4.1, BR-4.2,
BR-4.3 remain whereas BR-4.4 is quadrisected according to the result of cluster
validity; each sub-blocks of BR-4.4 undergoes cluster validity and result in BR-
4.4.2, BR-4.4.3, BR-4.4.4 remain as they are whereas BR-4.4.1 have to be further
quadrisected. Finally, all of the sub-blocks of BR-4.4.1 remain and hence com-
plete the process of quadruple block's division algorithm.

3.4.2.2 The Mechanism of the Automated Fuzzy Quadruple Division
Scheme

After performing the ACR clustering on each block, a series of analysis were
then performed to determine whether to further dividing the block or remain as
it is. The central concept of the proposed method is to provide best 'environment'
for the previous ACR algorithm to optimize the result. The decision is based on
a large amount of a priori knowledge: (1) the nature of the pixel intensity distri-
bution, (2) number of pixel in each partition, (3) the location in histogram. Four
simple metrics were defined to describe the nature of pixels. These metrics were
designed so that they made use of the 'by-product' of previous unsupervised clus-
tering in the proposed ACR algorithm to give some clues in order to predict the
pattern in the blocks. All these clues are crucial to play the role. Human a priori
knowledge is inserted into the algorithm of automated block division to govern the
dividing process. This a priori knowledge determines when to keep dividing and
when to stop dividing.
Firstly, we defined the Normalized Difference Expectation, NDE between two
clusters, as the difference between the expectation pixel intensity of the clus-
ters C 1 and C 2 from Sect. 3.4.1 when k = 2. The expectation value is defined by
Eq. ( 3.53 ). Let c ij ∈ C j , where j = 1,2, i = 1 to total members number of C j
, denoted as max ( n ( C j ) ). This metric as follows is to measure the distance rela-
tion between two clusters, where M( I ) represents the maximum grey level in input
block, I , in this context, the M( I ) is 256:

max ( n ( C j ))

1
max ( n ( C j ))

(3.53)

E C j = C ij

i = 1

= E ( C 1 ) − E ( C 2 )
M ( I )

(3.54)

NDE C 1, C 2