1. 
2 
  
Figure 1. Circular areas selected by characteristic scale and 
dominant gradient orientation of keypoints (a) Overlapping 
circular areas (b) Non-overlapping circular areas 
3.3 Watermark embedding 
The steps of watermark embedding are described as follow: 
Figure 2(a) shows the circular area selected by the feature 
point and figure 2(b) shows the result of the normalization 
according to the dominant gradient orientation. To avoid the 
damage on the feature points when embedding the 
watermark, a smaller circular area around the keypoint is 
removed which is shown in figure 2(c). Figure 2(d) shows 
the rectangular image after the circular image is reorganized. 
  
Figure 2. Selection, normalization, and rectangularity of the 
circular area by feature points. 
Performing a three-layer wavelet packet transform (WPT) 
on the rectangular image, 64 sub-bands of wavelet 
coefficients can be calculated. In addition to the sub-band of 
low-frequency, the texture sensitivities of the other 63 sub- 
bands are calculated using equation (2) and (3). 
1 
T,(i, j)= >. |w(i+ p,j+q)—B| 2) 
P,Q=—1 
1 
B= > w(i+p,j+q)/9 3) 
P,Q=-1 
where w(i, j) is the WPT coefficients on (7, j), and B is the 
coefficients average adjacent to (i, j). 
Set a threshold 7, and using equation (4) to calculate the 
number of texture sensitivity N,(T) within the n^ sub-band. 
Then the sub-band with maximum number of texture 
sensitivity will be selected to embed watermark. 
N, (T) - number(T, (i,j) t, ) sy (4) 
According to the selected sub-band, using formula (5) to 
calculate the energy E, m Xn is the size of the sub-band. 
E-Y V wi(,j) (5) 
iz j=l 
Calculate the embedded intensity using equation (6), where 
d, is an empiric value for intensity adjustment. 
NT number (T, (J) >4,} | (6) 
n E m n 2 f 
YXwG)D 
i=l j=1 
  
Divide the selected sub-band into 2x2 blocks , and using 
equation (7) and (8) to modify the upper left coefficient of 
each block to embed watermark. 
if the value of embedding watermark is 1, (7) 
w'(i, j) 7 max{w(i, j) i=12;j=12} +a, 
if the value of embedding watermark is 0, (8) 
w'(ij) = min{w(i, j) 1=1,2;j=1,2}-a, 
Perform the inverse wavelet packet transform on the 
coefficients after embedding the watermark, the circular 
image containing watermark is obtained. Then rotate the 
circular image inversely according to the dominant gradient 
orientation. Finally, fill the circular image back to the 
original satellite image then an image with watermark 
embedded around the local keypoints is obtained. 
3.4 Watermark Extraction 
The steps of watermark extraction are illustrated as follow: 
1. 
Make use of SIFT algorithm to get the feature points of 
satellite image containing watermark, gain the circular 
image based on the characteristic scale o and dominant 
gradient orientation and then perform the image 
normalization, and remove annular image centered on the 
feature point, take it as the areas for watermark extraction 
and reorganize the annular image as the rectangular image. 
Perform a three-layer wavelet packet transform on the 
rectangular image and obtain 64 sub-bands, select the sub- 
bands with maximum number of texture sensitivity. 
Divide the selected sub-band into 2x2 block, and using the 
formula (9) to calculate the value of T. 
T = (max{w(i, j) i = 1,2;j =1,2} (9) 
+ min{w(i, j) i =1,2;j=1,2}}/2 
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