/), and B is the
o calculate the
e n" sub-band.
per of texture
rk.
(4)
formula (5) to
sub-band.
(5)
tion (6), where
dt.
(6)
ks , and using
t coefficient of
7)
(8)
sform on the
k, the circular
‘hen rotate the
ninant gradient
e back to the
ith watermark
ned.
as follow:
ature points of
n the circular
and dominant
1 the image
entered on the
nark extraction
ngular image.
isform on the
select the sub-
tivity.
, and using the
(9)
Using the upper left coefficients of each block to extract the
watermark information, when w'(i,j)>T , the value of
embedding watermark is 1, when w'(i,j)) € T, the value of
embedding watermark is 0.
3.5 Assessment Criteria of Watermark Algorithm
3.5.1 Quality Indicators of Watermarked Images
In order to evaluate the impact of the watermark on the original
satellite images, the mean square error (MSE) and the peak
signal-to-noise ratio (PSNR) between the image embedded with
watermark and the original image. If the mean square error is
small or the peak signal-to-noise ratio is large, then we can
determine that the similarity of the two images is high.
1 m-1 n-1 3 (10)
MSE=| —— LTD
ra
PSNR -10log,, 223. dB (11)
MSE
,
where I;; and Ij; represents respectively the pixel values of the
original image and the image embedded with watermark.
3.5.0 Robustness Verification of Watermark
In this study, the NC value in equation (12) is calculated to
verify the robustness of the watermark. If the NC value (within
0-1) is large, then the extracted watermark has a low degree of
distortion or high livability, which can be clearly identified by
the human eyes.
m-1 m-1
Y Y w(.j)e w'.j
NZ OO EL (12)
mxm
where W and W* are respectively the original watermark and
the extracted watermark suffered from various attacks, € is
exclusive-or (XOR) operator.
4. EXPERIMENTS
The test image in this experiment is a subset of WorldView-2
with the size of 2000x2000, which is shown in figure 3(a). The
selected watermark content is the Chinese characters of
"National Taiwan University" coordinated with individual
document No., which is specified as *1001227", so as to act as
the declaration of the ownership and distinguish different users.
The contents of watermark are shown in figure 4(a), the size of
watermark image is 40x40
4.1 Quality and Robustness of Watermarked Images
Figure 3(a) shows the original image and figure 3(b) shows the
WorldView-2 image embedded with watermark. The PSNR
value of image embedded with watermark is 47.59, and the
average PSNR of the four watermarked areas is 40.7, which
mean the distortion of image embedded with watermark is not
evident. The size of the embedded watermark is 31x31. If the
image embedded with watermark doesn’t suffer from any attack.
Figure 4(b) shows the extracted watermark with the NC value of
0.998.
(a) (b)
Figure 3. (a) Contents of original image and
(b) Watermarked image
Ex 4
A
1081 1841
(a) (b) (NC=0.998)
Figure 4. (a) Original watermark and (b) Extracted watermark
Figure 5 shows the results of robust verification of watermark
after the JPEG compression, smoothing, brightness adjustment,
regulation, contrast, resizing, translation, rotation and cutting. It
can be found from the extracted watermark in figure 5 that, the
watermark algorithm proposed in this study can resist general
JPEG compression, brightness adjustment, regulation and
contrast, as well as various geometric attacks such as image
resizing, translation, rotation and cutting, the extracted
watermark can achieve very good recognizable.
T
x
: 8
JPEG(1/7) 3*3 smoothing brightness
NC=0.934 NC=0.762 adjustment 20%
NC=0.993
i
d d d
contrast adjustment resizing by 2 translation (43,25)
20% NC=0.965 NC=0.965
xi +
A, x,
d d
rotation of cutting of 51% resizing by 75%
45 degrees NC=0.965 NC=0.721
NC=0.951
Figure 5. Resistance ability of No. 4 area after various image
processing.
In order to verify the robustness of the watermark after the
geometric correction, the RST and polynomial transformation
are performed respectively on the test image using 6 ground
control points. The results are shown in figure (6) and (7).
Figure 7 (a) is the watermark extracted from the region of No. 2
using RST transformation. The NC value of the extracted
watermark is 0.899 and can be identify with ease. However, the
extracted watermark after polynomial transformation is
unidentifiable and has a small NC value of 0.307.