Design and Implementation - Segmentation of Hand Bone for Bone Age Assessment - page 56

6

m=n=2
m=n=4
m=n=7
m=n=10
m=n=25

5

4

3

2

1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Relative Brightness DIfference (RBD)

Fig. 3.3 Illustration of the relationship between RBD and BPS when both the shape parameters
are equivalent: symmetrical with a central peak at 0.5 of RBD . The five curves in the figure dem-
onstrate the effect of five different values of equivalent shape parameters on the shape of BPS
function: as both shapes parameters increase, the curve spread and falls off evenly

normalized BPS that produces bound output values between 0 and 1; this bound
output property is of prime importance to compare other measurements which will
be defined later.
The NBPS of value 1 indicates perfect brightness preservation, whereas NBPS
value close to 0 indicates poor brightness preservation. In other words, the more
the NBPS approaches 1, the more perfect the brightness preservation. But how
large is considered as 'large'? This ambiguity is explained by m and n; different
values of m and n define different values of RBD required for favorable bright-
ness preservation. For example, as illustrated in the Fig. 3.6 , the red line, which
is formed by using m = 2, n = 3 demonstrates that, for instance, if the RBD falls
near 3.3, the histogram equalization has better performance in brightness preserv-
ing than histogram equalization algorithm that produces RBD around 3.2 or 3.8.
As the figure illustrates, the RBD is around 3.3, compared to RBD around 3.2 or
3.8, produces higher NBPS . As shown in the Figs. 3.4 and 3.6 , different values of
m and n determine the value of RBD should have in order to produce high NBPS .
In other words, the NBPS function regularizes the definition of 'good' or 'bad'
brightness preserving ability, in terms of RBD .