Design and Implementation - Segmentation of Hand Bone for Bone Age Assessment - page 59

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m=2,n=3
m=2,n=4
m=2,n=5
m=2,n=6
m=2,n=7

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Relative Brightness Difference (RBD)

Fig. 3.6 Illustration of the bound property of NBPS function range when the BPS curves in
Fig. 3.5 are normalized

Firstly, we define the input of OCS which is the Relative Contrast Different
(RCD) as follows: where σ x and σ y denote Normalized Root Mean Squared
(NRMS) contrast of input image where pixel intensities are the i-th j-th element of
the two dimensional image of size by M by N , denotes an extremely small constant
for purpose of maintaining the function stability. The RCD function represents a
contrast comparison metric where the constant c is added for the sake of function
stability. This function out satisfies bound condition where the range is limited
between zero and one; function output is zero only when both input and output
images possess identical standard deviation; function output is one whenever the
output image NRMS is twice or more than NRMS of input image.Similar to BPS ,
the RCD is converted to OCS and NOCS using beta distribution function:

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β ( p , q ) RCD ( p − 1 ) ( 1 − RCD ) ( q − 1 )

(3.10)

OCS ( RCD ; p , q ) =

OCS ( p , q )
argmax ( OCS ( p , q ))

(3.11)

NOCS ( p , q ) =

This is to satisfy the new perception that distinguishable features in image of
any application should have optimum contrast which is oppose to the traditional
perception that the value of contrast should be as high as possible. The property