Tabu search based multi-watermarks embedding algorithm with multiple description coding

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Tabu search based multi-watermarks embedding algorithm with

multiple description coding

Hsiang-Cheh Huang

a,⇑

, Shu-Chuan Chu

b

, Jeng-Shyang Pan

c

, Chun-Yen Huang

c

, Bin-Yih Liao

c

a

National University of Kaohsiung, 700 University Rd., Kaohsiung 811, Taiwan, ROC

b

School of Computer Science, Engineering and Mathematics, Flinders University of South Australia, Australia

c

National Kaohsiung University of Applied Sciences, 415 Chien-Kung Rd., Kaohsiung 807, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 5 February 2005

Received in revised form 2 April 2011 Accepted 6 April 2011

Available online 15 April 2011 Keywords:

Watermarking Error resilience

Multiple description coding Vector quantization Optimization Tabu search

a b s t r a c t

Digital watermarking is a useful solution for digital rights management systems, and it has been a popular research topic in the last decade. Most watermarking related literature focuses on how to resist deliberate attacks by applying benchmarks to watermarked media that assess the effectiveness of the watermarking algorithm. Only a few papers have concentrated on the error-resilient transmission of watermarked media. In this paper, we propose an innovative algorithm for vector quantization (VQ) based image watermark-ing, which is suitable for error-resilient transmission over noisy channels. By incorporating watermarking with multiple description coding (MDC), the scheme we propose to embed multiple watermarks can effectively overcome channel impairments while retaining the capability for copyright and ownership protection. In addition, we employ an optimization technique, called tabu search, to optimize both the watermarked image quality and the robustness of the extracted watermarks. We have obtained promising simulation results that demonstrate the utility and practicality of our algorithm.

1. Introduction

Digital watermarking[21,34,43], in conjunction with encryption[1,25], is a useful solution for digital rights management (DRM) systems. It embeds secret information into the digital contents to protect the intellectual property[20,42]or the own-ership of the original multimedia sources[4,11]. Typical watermarking schemes embed the watermark by altering coefﬁ-cients related to the original source in some speciﬁc domain, including the spatial-domain methods [39], transform-domain techniques using discrete cosine transform (DCT)[12,24], discrete wavelet transform (DWT)[19]and discrete Fou-rier transform (DFT)[40], or VQ domain schemes[27,36]. These schemes have been popular research topics in the last decade.

There are many metrics to measure the effectiveness of a watermarking algorithm. From the algorithm design viewpoint, the three most critical requirements are: watermark imperceptibility, watermark robustness, and watermark capacity. Although these requirements are all very desirable, as pointed out in the literature[3,28,30,50], they influence, or even conflict, with the remaining requirements. Fixing one dimension, the other two conflict with each other, and some tradeoff or compromise must be reached[29]. The tradeoff relationships can affect all three parameters.

⇑Corresponding author. Tel.: +886 918 952075. E-mail address:[email protected](H.-C. Huang).

Contents lists available atScienceDirect

Information Sciences

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(1) Watermark imperceptibility refers to whether the viewer can perceive the existence of an embedded watermark. To make the watermark imperceptible, two situations need to be considered.

(a) The number of watermark bits embedded must be less than a certain amount to make the watermark impercep-tible. The theoretical bound for this amount, called the watermark capacity, is described in item (3) below, and is derived in the literature[23]. Enhanced reliability can be expected by embedding multiple watermarks into the original multimedia [41]. Conversely, embedding fewer bits implies less robustness in the watermarking algorithm.

(b) Imperceptible watermarking indicates the least modification of the original media. The watermarked image quality is supposed to be within the just noticeable distortion (JND) region[17]. In this regard, the commonly employed scheme in the spatial domain is to embed the watermark into the least significant bits (LSB); in the frequency domain, including the DCT and DWT domains, people tend to embed the watermark into the higher frequency band coeffi-cients. This approach is motivated by the fact that most of the energy in the multimedia content, such as an image, is concentrated in the lower frequency band coefficients[15]. Hence, embedding the watermark bits into higher fre-quency band coefficients results in less modification to the original source. However,this technique renders the watermark vulnerable to common image processing steps such as low-pass filtering (LPF).

(2) Watermark robustness refers to the capability of the watermarked media to withstand intentional or unintentional media processing, called attacks, including filtering, transcoding, resizing, or rotation. There are benchmarks to exam-ine the watermark robustness objectively, such as Stirmark[37]. It is generally agreed that robustness plays an impor-tant role in the design of a watermarking algorithm. Heuristically, improving robustness requires embedding the watermark into the most significant bits (MSB) in the spatial domain or the lower frequency band coefficients in the transform domain. However, this process can seriously degrade the watermarked image quality and alert others about the existence of the watermark. Consequently, to satisfy the tradeoff between watermark imperceptibility and watermark robustness, the watermark is embedded into the ‘‘middle frequency bands’’ in the transform domain[13]. (3) Watermark capacity is determined by the number of bits embedded in the original media; that is, the size of the watermark. Generally speaking, when more bits can be embedded, the algorithm is supposed to be more robust; how-ever, under such a condition, the quality of watermarked media must be degraded, and hence, the existence of the watermark becomes more perceptible. Authors in[3,23]derived theoretical bounds for watermark capacity. For image watermarking, the watermark capacity is generally a constant size. Thus, only watermark imperceptibility and water-mark robustness need to be considered for the design of the algorithm.

After considering the three fundamental requirements for watermarking, techniques for optimizing non-linear functions with multiple variables[5,45]can be considered to search for the optimized outcome. In this paper, we fix the watermark capacity, and employ tabu search[9,14]to find a tradeoff between watermark imperceptibility and watermark robustness. Tabu search is an evolutionary algorithm, characterized by the use of a flexible memory. It is able to eliminate local minima and to search areas beyond a local minimum. Some research papers and applications concentrate on designing watermarking algorithms with tabu search for audio signals[44]and images[2,6,22,31], which are similar to the goal for optimization pre-sented in this paper.

Before going into more details of our proposed algorithm, we would like to brieﬂy summarize the existing methods [2,6,22,31,44]to design a watermarking algorithm with tabu search. These methods are closely related to the main theme of this paper. We also discuss common items and differences, in addition to the advantages and disadvantages, in the design of each algorithm.

In[44], the authors present a wavelet-based watermarking algorithm for audio signals with tabu search. Both[44]and this paper share similar concepts in designing the ﬁtness for optimizing the different goals. On the one hand, the audio qual-ity and the robustness of the watermarking algorithm under intentional attacks are considered in[44]. The authors use tabu search to design a robust audio watermarking algorithm that preserves good quality in the watermarked audio signal, and yields better robustness for the extracted watermark. On the other hand, we consider image quality and watermark robust-ness under unintentional attacks in this paper. The concepts for designing our ﬁtrobust-ness function with tabu search are similar to those presented in[44]. However, we introduce another major theme in this paper, called ‘‘multiple description coding’’ (MDC). In our work, image quality is enhanced by both tabu search and error-resilient coding, in the form of MDC. Back-ground knowledge of MDC will be covered in Section3.

In[2], the author proposes a wavelet-based robust watermarking algorithm for still images. The author claims that the algorithm can cope with JPEG compression and cropping attacks. Tabu search is employed to ﬁnd the region- of-interest (ROI) of the original image, and then the watermark is embedded into the ROI portion of the image with the wavelet trans-form. In comparison with our paper, both the concept for designing the ﬁtness function, and the goal for developing the watermarking algorithm are different. Though both[2]and this paper use tabu search, the goals to be optimized are signif-icantly different.

In[22], the authors propose a VQ-based robust watermarking algorithm suitable for transmitting watermarked VQ indi-ces over a binary symmetric channel (BSC). The authors integrate their watermark embedding scheme into the codebook design problem. They employ two conventional schemes for VQ codebook design with tabu search: the index assignment (IA) scheme and the energy allocation (EA) scheme. In this paper, we employ an existing codebook trained by the well-known LBG algorithm. Tabu search is employed to optimize both the watermarked image quality and the watermark

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robustness. Like our approach,[22]also use tabu search to train the parameters in the ﬁtness function. However, the meth-odologies for designing the algorithms in the two papers are dissimilar.

In[6]and[31], the authors propose a multiple watermarking scheme for embedding two watermarks: one in the spatial domain and the other in the transform domain. They employ tabu search to develop algorithms for image-based robust watermarking by embedding one visible watermark in the spatial domain and one imperceptible watermark in the trans-form domain. Both the watermarked image quality and the capability to resist the JPEG attack are optimized with tabu search. Because we use a different algorithm, VQ-based invisible watermarking with the error-resilient capability of MDC, we infer that the algorithms proposed in[6,31]are completely different from our method.

We will brieﬂy compare the existing VQ-based watermarking algorithms to the one we proposed. In this paper, we pro-pose an innovative, VQ-based image watermarking algorithm that is suitable for error-resilient transmission over noisy channels. A review of the research literature related to digital watermarking indicated that only a few authors have concen-trated on the error-resilient transmission of watermarked media[38,47]. Most watermarking related literature focuses on how to resist intentional attacks. For practical implementations with VQ-based watermarking, existing methods are com-pared to the proposed algorithm in this paper. We conduct researches in transmitting watermarked images over binary sym-metric channels (BSC)[35]and packet-loss channels[32,33]. In general, researchers use the BSC or packet-loss channel to simulate the transmission of baseband signals. In[32,33]and in this paper, algorithms for transmission over packet-loss channels are developed. Because these papers[32,33,35]focus on transmitting the watermarked image over lossy channels, this could be regarded as a new branch for watermarking research.

In light of the discussions above, we would like to point out that despite superﬁcial similarities between our proposed algorithm and prior research work, there are still signiﬁcant innovations presented in this paper. Besides using tabu search for optimization, we provide an additional method, MDC, to help protect the ownership of the original image, and simulta-neously retain the reconstructed image. Our proposed algorithm combines watermarking and error-resilient coding, and the results have led to promising results. Based on the experience of our previous works, we employ tabu search in this paper to obtain an optimized solution suitable for the transmission of watermarked images over lossy channels.

This paper is organized as follows. We describe the fundamental concepts of VQ and MDC in Section2and Section3, respectively. Section4concentrates on quantization-based MDC, which is an integration between the concepts in Sections 2 and 3. Section5and Section6present the watermark embedding and extraction algorithms. We demonstrate an example in Section7to improve understanding of our proposed algorithm. Optimization of our algorithm with tabu search is de-scribed in Section8. We also study two related algorithms published in the literature and brieﬂy describe them in Section 9. Simulation results are shown in Section10, and comparisons between our algorithm and those in Section9are presented. Finally, we conclude this paper in Section11.

2. Fundamentals of vector quantization

Vector quantization[8], one of the important techniques in multimedia compression, has received considerable attention since the 1980s. As an extension to scalar quantization, vector quantization works on vectors of raw data. A vector can be a small block of image data, for example, the grey-level values of a 4 4 pixel image block forms a 16-dimensional vector. Fig. 1gives a block diagram illustration of the operation of vector quantization compression.

The original image X is composed of the combination of all of the input vectors, Xk, "k. The codeword search process looks

for a ‘‘nearest codeword,’’ ci, from the codebook for the given input vector Xkwith the Euclidean distance measure. The

code-book C with size L is composed of L elements, or the codewords with the representation C = {c0, c1, . . . , cL1}.

The codebook size, or the number of codewords in a codebook, is a tradeoff between the reconstructed image quality and the compression rate. The codewords in the codebook decide the subsequent compression distortion. A dedicated procedure requires to generation the appropriate codebook.

3. Background of multiple description coding and its generic model

During transmissions of data, loss of data is inevitable due to channel error or packet loss in various types of transmission channels. In contrast to the conventional schemes such as progressive transmission, multiple description coding (MDC) of-fers an alternative method for the effective delivery of compressed multimedia information.

Fig. 1. A block diagram for vector quantization. All the L codewords form a codebook of size L, that is, C = {c0, c1, . . . , cL1}. Xkmeans the vector, or a small

block in the original image X, and X0

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MDC is an error-resilient coding technique, which can be referred to as a source coding method for a channel whose end-to-end performance includes uncorrected erasures. This channel is encountered in a packet communication system that has effective error detection but does not have the features that permit the retransmission of incorrect or lost packets. MDC uses diversity to overcome channel impairments so that a decoder that receives an arbitrary subset of the channels may repro-duce a useful reconstruction[16]. Information-theoretic issues of MDC have been studied extensively since the early 1980s [7,51]. In multiple description (MD) coders, the same source material is coded into several pieces of data, called descriptions, such that each description can be decoded independently to obtain minimum ﬁdelity. This information is also combined with other descriptions to achieve a better quality. The goal of MDC, and channel coding in general, is the making effective transmission of data, and MDC offers a totally different perspective from that of channel coding[26].

MDC is suitable for transmission over noisy channels with long bursts of errors. To gain robustness of the loss in spite of descriptions, MDC must sacriﬁce some compression efﬁciency while still retaining the capability for error resilience. There-fore, correlations between descriptions should be intentionally induced to achieve this goal.Fig. 2depicts the generic model for MD source coding with two channels and three decoders. The Encoder is denoted by

a

0. Decoder 0, denoted by b0, is

called the central decoder, and Decoders 1 and 2, are denoted by b1and b2respectively, are the side decoders. The Euclidean

distance between X and bXð0Þ_{is the central distortion, while the errors between X and b}_XðiÞ_;_{i ¼ 1; 2; are the side distortions. It}

suggests a situation in which there are three separate users or three classes of users, which could arise when broadcasting on two channels. The same abstraction holds if there is a single user that can be in one of three states depending on which descriptions are received. Generally speaking, if we extend the number of transmission channels inFig. 2to P, there will be (2P_{1) receivers that decode with different number of descriptions received and reconstruct the image with different}

quality levels.

In addition to theoretical research, it is also important to devise practical designs to make MDC applicable to the situation depicted inFig. 2. Practical applications and implementations of MDC emerged in the 1990s. Two major categories for MDC applications are: (i) quantization based schemes, such as Multiple Description Scalar Quantization (MDSQ)[46]and Multiple Description Vector Quantization (MDVQ)[10], and (ii) transform-domain based schemes, called Multiple Description Trans-form Coding (MDTC)[48,49]. In this paper, we focus on quantization based MD schemes for watermarking. Operations and realizations of quantization-based MDC will be described in Section4. For quantization-based MDC, redundancies induced between descriptions are controlled inherently. Thus, only the watermarked image quality and the robustness should be ta-ken care of, and this is the motivation to use MDVQ for watermarking. On the other hand, the idea for watermarking with MDTC is basically the same as that with MDVQ. For MDTC, correlations between different descriptions are controlled by the users at the encoder. After transmission, two descriptions are composed to reconstruct one 8 8 block at the decoder. Great-er correlation between descriptions leads to bettGreat-er resilience to channel Great-error in the reconstructed image, at the expense of degraded performance in compression. Taking watermark embedding into account, three parameters, including (a) the watermarked image quality, (b) the robustness, and (c) the correlation coefficient between descriptions should all be con-sidered. Because one 8 8 block in the original image corresponds to one correlation coefficient, the design of the fitness function may become a difficult task. The vast quantity of correlation coefficients may impair the convergence of the training with tabu search. Thus, watermarking with MDTC is beyond the scope of this paper because the design and implementation of the algorithm need to be performed by other means. We will concentrate on watermarking with quantization-based MDC in this paper.

4. Quantization-based multiple description coding

Applications of MDC focus on error concealment and error resilience. In this paper, we introduce the idea of applying MDC with watermarking schemes to cover both the reconstructed image quality after reception, and the ownership of the original image.

Fig. 2. The generic model for MD source coding with two channels and three receivers. The general case has P channels and (2P

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Fig. 2is the generic structure of MDC, which can also be applied to quantization based multiple-description (MD). For example, the first practical design is based on scalar quantization. Employing different quantization levels in the MD struc-ture is a straightforward solution. In addition, MDSQ is flexible in that it allows a designer to choose the relative importance of the central distortion and each side distortion. The basic structure for MDSQ with two descriptions is illustrated inFig. 3. The input X is first quantized into a scalar i, using the scalar quantization function

a

. Then, the encoder produces a pair of quantization indices (i1, i2) from each scalar sample i. This step is called ‘‘index assignment.’’ In[46], the author described in

detail how to perform quantization using an invertible function and introduced a convenient way to visualize the encoding operation. The method to turn the scalar sample into the indices by carrying out the index assignment process was also developed. The encoding is ﬁrst decomposed into two steps:

a

0¼ l

a

: ð1Þ

The initial encoder

a

is a regular scalar quantizer. That is, it partitions the real line into cells that are each intervals. The index assignment l employs the index produced by the ordinary quantizer

a

, and uses the resulting encoder

a

0to produce the pair

of indices (i1, i2). After transmission of the indices over different channels with mutually independent breakdown

probabil-ities p1and p2, the three decoders produce estimates from the received indices: ð~i1;~i2Þ for Decoder 0, ~i1for Decoder 1, and ~i2

for Decoder 2, respectively. The index assignment must be invertible in order for the central decoder to recover the output of

a

. The visualization technique is to write l1_{, forming the index assignment matrix. Therefore, the b}

1and b2decoder

map-pings are indicated by the row and column positions in the MDSQ index assignment inFig. 4. The action of b0is implicit. By

performing the inverse quantization process, the output of the central decoder, which is the reconstructed sample bXð0Þ_{, has a}

low central distortion. The side decoders output the reconstructions bXð1Þ_{and b}_Xð2Þ_{with somewhat higher side distortions.}

The breakdown probabilities for the two channels, p1and p2, should be considered as the ‘‘packet-loss’’ probabilities. The

meaning and usage of p1and p2are consistent with other MDC research papers[48,49].

Fig. 4provides a simple example of MDSQ to help visualize the encoding operation in the index assignment portion of Fig. 3. This example has a codebook size of L = 8. In the design of an MD scalar quantizer, one can optimize

a

0, b0, b1, and

b2very easily as inFig. 3. The optimization of the index assignment l is very difﬁcult. Instead of addressing the exact optimal

index assignment problem, the author in[46]presented several heuristic techniques. For example, the output for the nested index assignment is close to the best possible performance. The dimension of the matrix is denoted by P. This equals the number of descriptions, or the number of channels available for transmission inFig. 2. We will set P = 2 in this paper. Thus, for P = 2, the descriptions of the MDSQ can be interpreted as the row and column indices of a matrix, where the codewords, or respectively, their indices, are placed. The basic ideas are to number the index assignment matrix from the upper-left cor-ner to the lower-right corcor-ner and to ﬁll in from the main diagonal outward. A set of index pairs are constructed from those that lie on the main diagonal and on the 2m diagonals closest to the main diagonal. The parameter m is called spread. The index assignment, shown inFig. 4, is called the ‘‘nested index assignment,’’ where the row and column indices, i1, and i2, are

transmitted over two independent channels.

The cells of the encoder

a

are used in increasing values of i, and are numbered from j0to j7inFig. 4(a), and j0to j21in

Fig. 4(b), respectively.Fig. 4(a) is an index assignment scheme with a spread m = 0. Only eight samples, or j0, j1, . . . , j7, are

the valid scalar samples for transmission. Generally speaking, an n-bit sample can be represented by log2(n)-bit strings.

The eight samples can be represented by 3-bit strings. Thus, if j3is the scalar sample to be transmitted, then after the index

assignment step l, we obtain i1= 011 and i2= 011 represented in their binary forms. The central distortion is the quantization

error between the input and the quantized samples. This conﬁguration with a spread of m = 0 can be regarded as repetition of samples. It indicates that a total of 6 bits will be received if no channel breakdown occurs. Consequently, 6 bits need to be transmitted over two different channels to describe 3 bits of information. This produces a redundancy of 63

3

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100% ¼ 100%. In decoding the received descriptions, if both are obtained, as depicted in[46]by calculating the conditional expectation, the reconstructed image decoded from both descriptions can be obtained. The conditional probabilities for receiving both descriptions inFig. 4(a) are:

pðjtji1¼ 011; i2¼ 011Þ ¼

1; if t ¼ 3; 0; otherwise:

ð2Þ

Because the conditional probability for transmitting j3is 1.0, given the received conditions, we determine that the

transmit-ted index is j3. If one of the channels breaks down, say, Channel 1, i2= 011 is received. UsingFig. 4(a) and calculating the

conditional probability at the decoder as indicated in Eq.(2), we visualize the column containing ‘011’. We can then deter-mine that the transmitted scalar is j3with a probability of 1.0. This is equivalent to when both descriptions are received. In

this circumstance, the central distortion is the same as the side distortion at a cost of 100% redundancy when the spread is m = 0 in MDSQ.

Fig. 4(b) is an index assignment scheme with a spread of m = 1. There are only 22 samples, or j0, j1, . . . , j21, which are the

valid scalar samples for transmission. This shows that the quality of side reconstructions is represented by the small ranges of values in any row or any column depending on the received description from any one channel. An index assignment ma-trix with a higher fraction of occupied cells leads to a quantizer pair with lower redundancy. From the viewpoint of practical implementation, the 22 samples can be represented by dlog2(22)e-bit, or 5-bit strings, where de indicates a ceiling function.

If j7is the scalar sample to be transmitted, after the index assignment step l, we obtain i1= 010 and i2= 011. By doing this and

when both descriptions are received, the transmitted sample j7is determined with a probability of 1.0 withFig. 4(b). That is,

pðjtji1¼ 010; i2¼ 011Þ ¼

1; if t ¼ 7; 0; otherwise

ð3Þ

and the redundancy is reduced to 6dlog2ð22Þe

dlog2ð22Þe

100% ¼ 20:00%. If one of the channels breaks down, say, Channel 1, only i2= 011 is received. With the aid ofFig. 4(b), we visualize the column containing ‘011’ and estimate that there are three

pos-sible candidates. These are j7, j9, and j11, which may have been transmitted, with the conditional probabilities:

pðjtji2¼ 011Þ ¼ 1 2mþ1; if t ¼ 7 or 9 or 11; 0; otherwise; ( ð4Þ

where m denotes the spread. The side distortion would be larger than the central distortion, because the side distortion is the error between the transmitted j7and the conditional expectation in Eq.(4),13ðj7þ j9þ j11Þ. Comparing this to the case when

m = 0, the redundancy is greatly reduced, while the side distortion is somewhat increased.

It is a straightforward task to extend MDSQ to MDVQ, though the index assignment of MDVQ is more difﬁcult than MDSQ. Fig. 5demonstrates the MDVQ structure with two descriptions. Here, by followingFig. 1, the input Xkdenotes the small block

or code vector. For example, bXkdenotes the 4 4 block described in Section2, for VQ operation. The reconstruction bXð0Þk from

the central decoder has less distortion than that from each of the side decoders, bXð1Þ k or bX

ð2Þ

k . In this paper, we follow the

MDSQ in[46]and MDVQ algorithm in[10], and devise a robust multi-watermarking algorithm suitable for both error resil-ient transmission and ownership protection.

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5. The watermarking algorithm for embedding two watermarks

We propose our watermarking algorithm for embedding two watermarks with VQ and MDC. Embedding more than one watermark has been an interesting topic in the literature. The structure is demonstrated inFig. 6. Our goals are twofold. The ﬁrst is to contribute to the error-resilience for the transmission of a watermarked image. Our second goal is to provide own-ership protection capability with watermarking.

Let the input image be X with a size M N. We perform the VQ operation ﬁrst to train the codebook for X. The codebook has a size L. The codebook C = {c0, c1, . . . , cL1} is obtained. Each index therein is represented by a dlog2Le-bit binary string,

where de means a ceiling function. In operating the VQ procedure, X is divided into non-overlapping blocks Xkwith size M

MW

N

NW;0 6 k 6 MW NW 1, then each Xkﬁnds its nearest codeword ciin the codebook C, and the index i is assigned to

Xk. The steps above follow the conventional VQ procedures.

Let the watermarks for embedding be W1¼ fW1;0;W1;1; . . .W1;MWNW1g and W2¼ fW2;0;W2;1; . . .W2;MWNW1g, both

hav-ing sizes MW NW. Each element in W1and W2represents one watermark bit to be embedded into Xk. Embedding of the two

watermarks will now be described in Section5.1and Section5.2. 5.1. Embedding the ﬁrst watermark

When embedding the ﬁrst watermark W1, we split C into two sub-codebooks C0¼ c00;c01; . . .c0L 21 n o and C00 ¼ c00 0;c001; . . .c00L 21 n o

. We denote this in the ‘‘codeword selection’’ portion inFig. 6. We see that C0 S_C00_{= C and C}0T_C00_{= ;.}

Fig. 5. The structure for MDVQ for two descriptions over two independent channels with mutually independent breakdown probabilities.

Fig. 6. The structure for embedding two watermarks with two descriptions for transmission in MDC. The two independent channels have mutually independent breakdown probabilities.

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one watermark can be extracted with existing algorithms, and the corresponding BCR values with our algorithm are better than[27]and[36].

In summary, under a wide range of channel erasure probabilities, the results using our proposed algorithm demonstrate both the effective transmission of watermarked images, and the acceptable robustness of the extracted watermarks. Com-pared with the existing schemes, we have doubled the amount of watermark capacity embedded with our algorithm; our algorithm also performs better on imperceptibility and robustness measures.

11. Conclusions

In this paper, we proposed an innovative scheme for VQ-based image multi-watermarking with multiple description cod-ing (MDC), which is suitable for transmission over noisy channels. We modiﬁed the MDVQ and MDSQ index assignments for watermark embedding and extraction. By incorporating this with MDC, we obtained promising results. We also presented discussions and made comparisons between our algorithm and others previously published, and we point out the superiority of our algorithm. Simulation results indicate that our watermarking algorithm is more robust and more resilient with respect to combat with channel noise under both lightly and heavily erased channels. In addition, in comparison with existing VQ-based algorithms in the literature, our algorithm performed better than others in both the watermark imperceptibility, shown by PSNR, and the watermark robustness, shown by BCR. Therefore, our algorithm is not only innovative for research, but also suitable for practical implementation.

Acknowledgement

This work was supported by National Science Council (Taiwan, ROC) under Grant No. NSC 93-2219-E-009-006 and NSC 95-2221-E-390-034. The authors would also like to give their gratitude to the Editor-in-Chief and anonymous reviewers for their valuable comments.

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