/), 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.