Information Technology Reference
In-Depth Information
By using the described technique, the hidden information can be removed from the
marked image, accompanied by a small amount of additional distortion. Taking into
account the statistical distribution of the DCT coefficients, nonetheless, this additional
distortion can be reduced, or even better, the original damage done by the watermark
embedding can be repaired to certain extent. Since each DCT component obeys a
zero-mean generalized Gaussian distribution, the probability of small magnitudes is
greater than that of large magnitudes. The marked image may even be “repaired” for
images with moderate amount of high-frequency details if half of the AC coefficients
that are relatively far from zero are perturbed by ∆/4 towards zero.
Quantizer 0
A
−∆
A
x
A
+
∆
Quantizer 1
A
−∆/2
A
A
+∆/2
x
Fig. 5.
Removing QIM watermark using discrete dithering. The shaded narrow stripes represent
the range of dithering
4.2
Detection of Watermarks Embedded with Double Transform and QIM
With double-transform/QIM embedding as illustrated in Fig. 6 (see [5]), histograms
of the first layer coefficients no longer show a discrete nature.
In this case, a different property of the block DCT coefficients is utilized. Let
C
represent the first-layer block-DCT coefficients of a host image, and
C
'
the modified
version obtained after a series of operations including scrambling, second-layer trans-
formation (e.g., DFT), QIM embedding, IDFT, and then de-scrambling. The differ-
ence between
C'
and
C
can be calculated:
′
(7)
D
=
C
−
C
.
Taking into account the statistical independence between the image and the em-
bedding-induced error, energy contained in the transform coefficients satisfies the
following relation:
[
]
2
(
)
(
)
(
)
∆
2
2
2
2
2
E
|
C
′
|
=
E
|
C
+
D
|
=
E
|
C
|
+
2
|
C
|
⋅
|
D
|
+
|
D
|
=
E
|
C
|
+
,
(8)
12
where
/12 is the mean energy of the quantization error that is uniformly distributed.
This indicates that watermark embedding in the second-layer coefficients will cause
an increase in the expected energy of the corresponding first-layer coefficients.
∆
2
