Cryptography Reference
In-Depth Information
descriptions for one block X
k
are received, then the resulting index decoded
by MDSQ can be uniquely determined, and the watermark bit is extracted by
taking out the last bit. Because of the error concealment capability for index
assignment, when only one description is received, the block can be partly
reconstructed, and the watermark bit needs to be determined from several
possible indices assigned in the MDSQ row or column matrix [27]. We first
use a majority vote to determine the watermark bit 0 or 1. If there are
equal numbers of 0s and 1s obtained in MDSQ decoding process, we assign
the watermark bit randomly. If none of the description is received, the water-
mark bit is randomly assigned. By gathering all the extracted watermark bits
W
′
k
, we obtain the extracted watermark W
′
.
12.5 The MDC-Based Multiple Watermarking
Algorithm
The multiple watermarking algorithm is derived and implemented based on
the single watermarking algorithm described in Sec. 12.4.
12.5.1 The Multiple Watermarks Embedding Algorithm
We propose our watermarking algorithm for embedding two watermarks with
VQ and MDC in this section. The structure for our proposed watermarking
system is demonstrated in Fig. 12.6. It is an extension to Fig. 12.5. That is,
the multiple watermarks embedding algorithm is based on the single water-
mark embedding algorithm. Our goal is to focus on using MDVQ to incorpo-
rate with robust watermarking techniques to provide both an error-resilient
transmission of watermarked image over different channels with independent
breakdown probabilities, and to provide ownership protection.
Similar to the notations used in Sec. 12.4.1, let the input image be X with
asizeMN . VQ operation is performed [16] and the codebook has a length
L, C =c
0
,c
1
,,c
L−1
is obtained. X is divided into non-overlapping
M
M
W
N
W
,0≤k≤M
W
blocks X
k
with a size
−1. Each X
k
finds its
nearest codeword c
i
in the codebook C, and the index i is assigned to X
k
.
Let the watermarks for embedding be W
1
=W
1,0
,W
1,1
,W
1,M
W
N
W
−1
N
W
and W
2
=W
2,0
,W
2,1
,W
2,M
W
N
W
−1
, both having sizes M
W
N
W
.Each
element in W
1
and W
2
represents one watermark bit to be embedded into X
k
.
Embedding of the two watermarks will now be described.
Embedding the First Watermark
When embedding the first watermark W
1
, we split C into two sub-codebooks
C
. This is known as the
codeword selection portion in Fig. 12.6. We can see that C
c
′′
′
c
′
0
,c
′
1
,c
′
′′
0
,c
′′
1
,c
′′
=
and C
=
L
2
L
2
−1
−1
′
′′
C
= C and
