International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004 
1) making three-level DWT of the original remote sensing 
sub-image (with the size of D XD) 
f: A A; 
2) establishing the low-frequency coefficient (LL3) matrix 
C" in the wavelet domain A of the remote sensing sub-image 
A; 
3) choosing a feature vector D={ d, Pec * from the 
low-frequency coefficient matrix; 
4) according to formula (1), embedding the watermark 
W-(W, ) into (d ,) and obtaining the new feature vector 
D={dk;e B; 
5) reconstructing the watermarked remote sensing sub-image 
B with the new transform field matrix D 
y Bp» 
In addition, we should notice that for different remote sensing 
sub-images, the watermark bits embedded in them are also 
different, namely the embedded watermark bits are based on the 
special content of each sub-image and different from each 
other. 
3. Choice of localized watermarks 
In order to guarantee robustness and security of watermarking 
algorithm, a nature choice is to combine localized watermarks 
with the feature of remote sensing sub-images. To the feature 
vector of a remote sensing sub-image D={ d y »» generally the 
corresponding watermarking space F ,, C F s orthogonal to D 
p W g 
can be found: 
Fy -(W: 9, d,w,70 kel, 2, ~K) (2) 
k 
namely, to any vector W={ W, } €F ,, we have 
D! w-o (3) 
We can see that there are countless watermarks meeting 
W-(W,)€F;,, however, in fact the establishment of 
watermarking space F,, is a controlled optimized process, 
namely 
W= arg MIN D' W| (4) 
wef" 
when D is the feature vector of the original remote sensing 
sub-image. 
194 
The ending condition of optimization is 
(5) 
ID'w| «e 
and Ó (O »0 ) is the beforehand defined threshold in the 
optimizing process. Here we choose 0-1 0:3, 
Repeating the above process for each remote sensing sub-image 
which corresponds to each feature point, we can obtain the 
watermarked remote sensing image 
4. Detection Frame of Localized Watermarks 
We exploited the Neymann-Pearson criterion to detect 
watermarks. We made edge-detection to the watermarked 
remote sensing image, chose the angle points in the edge image 
as the candidate points, then detected watermarks in each D X D 
sub-image, in the center of which is the candidate points. As 
long as in one sub-image corresponding to some feature point, 
the watermark can be detected, we think there be localized 
watermarks in the image. 
5. Results of Simulative Experiments 
In this paper, we exploited MATLAB to simulate the 
experiments and made experiments to a 600 X 800 partial 
SPOTS image of Shanghai. In order to evaluate robustness of 
the algorithm, during the experiments we exploited the testing 
software of watermark attacks-StirMark. The testing method is 
similar to COX method (Cox I J, 1997a). Firstly we exploited 
db8 wavelet and thinning algorithm of mathematic morphology 
to extract the edges of the original remote sensing image. The 
size of those local areas has an important influence on the 
robustness of watermarks: smaller areas can make watermarks 
better resist cropping, but also decrease robustness of the local 
watermarks; and bigger areas can increase robustness of the 
local watermarks but would result in no complete 
watermark-extracting areas in the remaining partial remote 
sensing image after cropping. In the experiment, we chose the 
maximum number of feature points as 20 and the size of the 
area corresponding with each feature point as 96 X 96. Then to 
each 96 X96 remote sensing sub-image we take the same 
process as follows: making three-level DWT of the remote 
sensing sub-image by  bior2.6 wavelet, establishing the 
low-frequency matrix c" (12X12) in DWT transform field, 
obtaining the feature vector D — (d k), which consisted of the 
anterior 12 coefficients in C * which had the maximum 
breadths (or the maximum angles) (not including the direct 
current weight), then according to formula (5) , making 
optimized repetition to work out the localized watermark 
W={ W, } which is a 12X 1 two-value vector orthogonal to D 
= {dk}, namely W={ W, } € { 1, -1}, i= 1, 2, »-", 12. From the 
experimental results, we can see because the watermarking