Design and Implementation - Segmentation of Hand Bone for Bone Age Assessment - page 93

contrary, the entropy reaches its minimum value, which is 0, only when all P ( i , j )
are equal to zero. This indicates that the more occurrences of different group spa-
tial related pixel intensity, the larger the entropy. Whereas, if there is less occur-
rences of different group spatial related pixel intensity, the smaller the entropy.
This entropy concept of measuring randomness is analogous to measuring the
local variance. Therefore, instead of computing the entropy value, the local vari-
ance value obtained in previous process to increase the computational efficiency
is adopted. The only difference is that the local variance in Eq. ( 3.40 ) has been
normalized.

VI ( x , y ) = D m − 1 ( x , y )

(3.65)

The main problem that impedes this scheme of straight-forward edge detection
is the nature of hand bone image contains high variations on bone texture which
will affect this removal of pixel. Therefore, the anisotropic diffused image from
pre-processing is utilized rather than the input image. Let the ( m - 1 )-iterated dif-
fused image as D m − 1 ( x , y ) , each single pixel in the diffused image undergo an
local variance transformation using windowing technique, and let the transformed
image as VI ( x , y ) . This produced an image where the pixels inside the bone have
been transformed to low intensity value as shown in Fig. 3.24 .
After transforming to normalized local variance images, there are noises and
artifacts. To separate the spurious edges from the actual edges, k-mean clustering
on edge strength is adopted. As a result, the detected edges pixels for Fig. 3.20 a, b
after being denoised was shown in Fig. 3.25 a, b respectively.
In order to illustrate the relative position of edges and the segmented hand bone
for better understanding, the detected edges were combined with segmented hand
bone image. Figure 3.26 showed the result of the combination where Fig. 3.20 a
is combined with Figs. 3.25 a, 3.20 b is combined with Fig. 3.25 b to produce
Fig. 3.26 a, b respectively.

Fig. 3.24 Normalized local
variance transformation from
diffused bone images of
Fig. 3.20 a, b