Tabu Search Based Multi-Watermarking over Lossy Networks - Intelligent Multimedia Data Hiding - page 321

C

MD Encoder MD Decoder

i 1

index
assignment

Decoder 1
β 1

p 1

X (1)
k

VQ −1

i 1

i 1

C

l 1 (•)

Channel 1

i 0

i

Decoder 0
β 0

X k

X (0)
k

VQ

VQ −1

i 2

i 2

C

C

l 2 (•)

Channel 2

i 2

p 2

Decoder 2
β 2

VQ −1 X (2)

k

Fig. 12.4. The structure for MDVQ for two descriptions over two independent
channels with mutually independent breakdown probabilities.

12.4.1 The Single Watermark Embedding Algorithm

We demonstrate the structure of our single watermarking system with MDVQ
in Fig. 12.5, by introducing the watermark embedding and extraction com-
ponents into Fig. 12.4 [18]. We modify the MDVQ algorithm and the index
assignment process in [27] and [28] for watermark embedding. Our watermark-
ing structure can be divided into three parts:
(i) MD encoder with watermark embedding,
(ii) multiple channels or lossy networks for transmission,
(iii) MD decoder with watermark extraction.

Our goal is to focus on using MDVQ and to incorporate with robust water-
marking techniques. Our scheme provides both the error-resilient transmission
of a watermarked image over different channels having independent breakdown
probabilities, and the capability for copyright protection.
Let the input image be X with size MN . In the left part of Fig. 12.5,
we perform the VQ operation first [16] to train the codebook for X.We
obtain the codebook with length L, C =c 0 ,c 1 ,,c L−1 . Each index in

C is represented by a⌈log 2 L⌉-bit binary string, where⌈•⌉denotes a ceiling
function. X is divided into non-overlapping blocks X k with a size

M
M W

N W ,

0≤k≤M W −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 watermark for embedding be W =W 0 ,W 1 ,W M W N W −1

N W

, with
asizeM W N W . Each element in W , W k ∈0, 1, k∈[0,M W N W −1],
represents one watermark bit to be embedded into the corresponding index of
X k . For watermarking purposes, the new index representing X k is generated
from two parts: This is done to shift the original index i to the left by one