Figure 2: A zigzag scan in a block of DCT coefficients.
Coefficients equal to 1 are not used because of
the serious increase in bitrate they may cause. This
is because 1 have a special processing in the
entropy coding stage of the video codec
(Richardson, 2003). The DC coefficients are avoided
because of the high degradation they may introduce,
as well as the high frequencies coefficients because
they are mainly composed from values equal to 0
or 1.
In this case the majority of coefficients planned
for embedding the watermark would be even
coefficients. An example of a video histogram of
significant DCT coefficients of the position k = 4 is
given in figure 3.
Figure 3: Histogram of the quantized significant DCT
coefficients of position k=4 of Container sequence.
For the embedding process, simple methods are
preferred such as the Least Significant Bit (LSB)
method, in which the LSB of the coefficient is
replaced by the watermark bit. That means that the
bit 0 is preferebly embedded in an even value in
order not to change the original value of the
coefficient. However , the watermark may be
composed of bits “1” more than “0”, and because we
deal with more even coefficients than with odd ones
as mentionned previousely; it may be better to
change the embedding formula so that the LSB of
the coefficient is replaced, not by the watermark bit,
but by its complement. In this case we need to
reserve one bit during the embedding process to
know wich formula has been used.
3.2 Watermark Pre-processing
We suppose that our watermark has been encrypted
to ensure its security. Our objective is to find the
best transformation of the watermark in order to
correspond - as much as possible- the bits “0” to
even coefficients and the bits “1” to the odd ones.
To do so, we apply a rotation by one several
times to the watermark. In each rotation, the last bit
of the watermark becomes the first one and in each
time we calculate the intercorrelation coefficient
between the watermark signal (W) and the
coefficients (transformed to binary signal C).
Considering W and C two binary sequences of
the same length N:
W={W1=1, W2, .. , WN}, C={C1=1,C2,.. , CN}.
The intercorrelation function for positive delays
is given by:
(
,
)
=
∑
, = 0,1,2, … , − 1 (1)
In our case d=0.
To clarify this point an example is given:
Let’s consider the sequences of dimension N= 8.
C
4
is composed from coefficients of position k=4 in
the block and W is the Watermark.
C
4
={2, -3, 6, 4, 5, 2,-2,3}, W={0,0,1,0,1,1,0,1}.
The preprocessing consists in the following
steps:
- C
4
is replaced by the binary sequence :
C’
4
= {1,-1,1,1,-1,1,1,-1}, 1 for even coefficients
and -1 for odd coefficients.
- If we consider that the bit 0 is preferably
embedded in an even coefficient, we transform
the watermark W to W1={1,1,-1,1,-1,-1, 1,-1} ,
where the bit 1 replaces 0 and -1 replaces 1, then
we apply a rotation (N-1) times to obtain:
W2={-1,1,1,-1,1,-1,-1, 1 },
W3={1,-1,1, 1,-1,1, -1, -1},
…,
W8= {1,-1,1,-1,-1, 1,-1,1}.
The highest value of the correlation coefficient is
given for W3 or W6 (Cor = 6). The watermark
corresponding to W3 is: W’={0,1,0,0,1,0,1,1}.
After the embedding process (using the LSB
method) the watermarked DCT coefficients become
Cw
4
={2, -3, 6,4,5,2,-3,3} where only one coefficient
is modified. Besides, we can check that if we had
k=0
k=4
k=11
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