Information Technology Reference
In-Depth Information
randomly prior to a second-layer DCT. The purpose of data shuffling, as stated above,
was to remove correlation between coefficients and make the second-layer DCT coef-
ficients in each group to possess a uniform expected energy, that is, to achieve spec-
tral equalization. Incidentally, the particular mapping corresponding to the shuffling
may be used as part of the key for prevention of unauthorized watermark extraction.
As a result of data shuffling, the second-layer DCT coefficients, except the DC
component, within each group are i.i.d. Gaussian with a zero mean and a standard
deviation associated to the rank of the group inherited from the index of the first layer
DCT. This was confirmed by a
test with a level of significance 0.10. In Table 1,
standard deviation values of the spectrum-equalized second-layer DCT coefficients of
the test image corresponding to the eight diagonal indices are listed.
χ
2
Table 1.
Standard deviation of the spectrum-equalized second-layer DCT coefficients of Lena
at diagonal frequency locations
Data group index
(1,1)
(2,2)
(3,3)
(4,4)
(5,5)
(6,6)
(7,7)
(8,8)
σ
I
368.9
57.0
25.4
14.2
10.2
6.4
4.6
4.3
It is clear from the preceding analysis that the watermark performance is closely
related to the choice of several parameters including
N
,
M
, and
α
. It is also related to
the amplitude of host data and noise.
In the experiments,
N
= 1024. Coefficients of group (4,4) were chosen as the host
data for embedding, with
σ
I
=14.23. Let
M
= 128 so that 7 bits were carried by each
orthogonal sequence, which can represent one character. Thus, a total of 16 alphanu-
meric characters were embedded into the host image.
5.2
Performance Comparison
In the experiments, the peak-signal-to-watermark power ratio (PSWR) was used to
describe invisibility, while the character-extraction error rate (CER) under the attack
of AWGN at PSNR=30 dB was used to represent robustness. From Equation (9), CER
of the single-bit-per-sequence scheme is given by
N
CER
=
m
BER
=
m
1
−
Φ
α
,
(20)
S
S
S
2
2
σ
+
σ
I
N
while CER of the proposed method can be obtained from Equation (17):
N
CER
=
M
1
−
Φ
α
.
(21)
M
M
2
2
2
(
σ
+
σ
)
I
N
PSWR can be calculated by the following equation:
2
σ
S
p
PSWR
=
10
log
,
(22)
10
E
mark
