Cryptography Reference
In-Depth Information
expressed as, for 255 A > 127,
contrast =
E[y(i;j)j(i;j) 2 W
w
] E[y(i;j)j(i;j) 2 W
b
]
E[y(i;j)j(i;j) 2 W
w
]
A (2A 255)
A
255 A
A
255
A
1
=
=
(13.33)
and, for 127 A 0,
contrast =
E[y(i;j)j(i;j) 2 W
w
] E[y(i;j)j(i;j) 2 W
b
]
E[y(i;j)j(i;j) 2 W
w
]
A 0
A
= 1
(13.34)
To summarize, for any (i;j) in the right half of R that is in W
b
, the
expected value of y(i;j) is
0; 127 A 0
2A 255; 255 A > 127
E[y(i;j)]
(13.35)
The difference in average intensity of the left half and right half of R is
A; 127 A 0
255 A; 255 A > 127
intensity
(13.36)
and the contrast between the left half and right half of R is
1;
127 A 0
contrast
(13.37)
255
A
1; 255 A > 127
To verify these, we simulate DHCED using an artificial image called
tensity decreases gradually and linearly from 255 at the top row to 0 at the
bottom row. The hidden pattern to be embedded is called "Column" and is
black at the center and white on the left and right, as shown in
Figure 13.15.
spectively. The row-wise average intensity of Y
1
and Y
2
are plotted against
the average intensity of the corresponding row in X in
Figure 13.22.
As ex-
pected, the row-wise average intensity of Y
1
and Y
2
are very similar to the
corresponding intensity in X, which verifies (13.21) and (13.24).
identical to Y
1
and Y
2
, with intensity decreasing from top to bottom. In the
W
b
region, the intensity of Y is as high as X at the top. But as the intensity
of X decreases from the top to bottom, we observe that the intensity of Y
decreases at a fast pace to about the middle of the image (where intensity is
about 127), and remains low in the lower half of the image.
To show the exact behavior of Y in the W
b
region, we compute the average
intensity in the W
b
for each row of Y and plot it against the average intensity of
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