Cryptography Reference
In-Depth Information
The Embedding Process
Before describing the proposed algorithm, we make some assumptions. Let X
be the original image with size AB.LetW R and W F be the binary robust
and semi-fragile watermarks with the size A w
B w , respectively. Here, a small
visually meaningful binary image V with size ab is replicated periodically
to obtain the binary semi-fragile watermark W F with the size A w B w .
That is a large enough size for embedding. In each stage of the proposed
algorithm, only one bit is embedded in each input image block (or vector).
The dimension of each input vector or codeword is k =(A/A w )(B/B w ).
Assume that the first stage codebook is C 1 =
c 10 , c 11 ,, c 1(N 1 −1)
with
size N 1 =2 n 1 . The second stage codebook is C 2 =
c 20 , c 21 ,, c 2(N 2 −1)
with size N 2 =2 n 2 . Here n 1 and n 2 are natural numbers. Thus a binary
number with n 1 + n 2 bits, in which the first n 1 bits stand for the index
of Stage 1 and the last n 2 bits denote the index of Stage 2, can represent
the overall index. The overall codeword can be selected from the equivalent
product codebook C =
N 2 . In other
words, if the index in codebook C 1 is i and the index in codebook C 2 is j,
then the equivalent overall index in the product codebook C is i +(jN 2 ).
In our algorithm, the robust watermark W R and the semi-fragile water-
mark W F are embedded in two stages respectively. We embed the robust
watermark in the first stage and the semi-fragile watermark in the second
stage to enhance the robustness and transparency of the proposed algorithm.
In the following, we describe the two-stage embedding process.
c 0 , c 1 ,, c (N−1)
with size N = N 1
The Robust Watermark Embedding Process:
In the proposed algorithm, we adopt the method [20] based on index proper-
ties to embed the robust watermark in the first stage as shown in Fig. 11.2.
The original watermark W R is first permuted by a predetermined key, key 1 ,
to generate the permuted watermark W RP for embedding. The polarities P
are then calculated with Eqs. (11.3)(11.6). Finally, we generate the final
embedded watermark known as the secret key, key 2 , using the exclusive-or
operation in Eq. (11.7). After the first stage of embedding, we can obtain the
reconstructed image X and the error image X 1 as follows:
−1 [VQ 1 [X]] .
X
=VQ 1
(11.9)
. (11.10)
According to Section 11.2.1, we know that this method has two problems.
However, in our algorithm, these two problems can be automatically solved,
and this will be discussed later in the extraction process.
X 1 = X−X
The Semi-Fragile Watermark Embedding Process:
To embed one bit of each index in the second stage, we can adopt the index
constrained vector quantization (ICVQ) encoding scheme shown in Fig. 11.3.
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