11 Information Hiding for Spatial and Geographical Data
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– Rotation. Given an image A and its rotated A
r , both have the same singular
values.
– Translation. Given an image A and its translated A
t , both have the same singular
values.
– Scaling. Given an image A and its scaled A
s , if A has the singular values σ i , then
A
s has the singular values σ i ∗
√
L r L c with L r the scaling factor of rows and L c
Table 11.1. Robustness of the SVD watermarking scheme against attacks
attack name
parameter
correlation correlation PSNR
(Cox)
(SVD)
(SVD attacked
image)
Gaussian filter
window size = 5
0.95
0.98
29.00
median filter
window size
3
0.65
0.80
25.50
5
0.80
0.80
27.00
midpoint filter
window size
3
0.90
0.94
26.13
5
0.58
0.60
24.15
trimmed mean
window size
filter
3
0.95
0.95
29.18
5
0.82
0.89
27.77
downsampling/
upsampling
downsample factor/
upsample factor
0.75/1.33
0.87
0.98
24.00
0.50/2.00
0.74
0.77
23.05
denoising with
window size
perceptual
remodulation
3
0.88
0.90
24.28
5
0.77
0.77
24.67
hard thresholding
window size
3
0.91
0.94
24.95
5
0.90
0.93
25.82
soft thresholding
window size
3
0.90
0.90
27.00
5
0.80
0.83
27.40
JPEG compression
quality factor = 10
0.77
0.77
29.20
sharpening
window size = 3
0.77
0.76
28.50
AWGN
noise strength = 20
0.72
0.88
22.00
histogram eq.
-
0.33
0.65
20.00
intensity adjustment
intensity values/
gamma correction
[0, 0.8] → [0, 1] / 1.5
0.65
0.70
21.15
clipping
clipped portion
75%
0.31
0.55
12.78