植基於計算智能之浮水印技術及其在無記憶性二階對稱通訊通道之應用

(1)

行政院國家科學委員會專題研究計畫成果報告

植基於計算智能之浮水印技術及其在無記憶性二階對稱通

訊通道之應用

計畫類別：個別型計畫計畫編號： NSC93-2213-E-151-008- 執行期間： 93 年 08 月 01 日至 94 年 09 月 30 日執行單位：國立高雄應用科技大學電子工程系計畫主持人：廖斌毅共同主持人：謝欽旭，潘正祥報告類型：精簡報告報告附件：出席國際會議研究心得報告及發表論文處理方式：本計畫涉及專利或其他智慧財產權，2 年後可公開查詢

中華民國 94 年 10 月 27 日

(2)

行政院國家科學委員會專題研究計畫成果報告

植基於計算智能之浮水印技術及

其在無記憶性二階對稱通訊通道之應用

Digital Watermarking Based on Computational Intelligences and Its

Applications of the Memoryless Binary Symmetric Channel

計畫編號：NSC 93-2213-E-151-008

執行期限：93 年 8 月 1 日至 94 年 7 月 31 日

主持人：廖斌毅

國立高雄應用科技大學電子工程系

E-mail: [email protected]

一、中文摘要本計畫提出一種植基於向量量化的浮水印最佳化技術，利用計算智能演算法來克服編碼簿中每個編碼字的索引值分配問題，使得藏入浮水印後的影像，能適合在具有通道雜訊的通道上傳輸。經由測試數個不同的影像後，實驗結顯示此技術對於通道雜訊所產生的影響，能有較佳的強健性，也可與其他藏入浮水印技術幾乎有著相同的影像品質，這也證明此技術對於保護版權有著良好的效果。關鍵詞：計算智能、數位浮水印、二階對稱通訊通道 Abstract

An innovative watermarking optimized schemes based on vector quantization (VQ) is proposed. It overcome the VQ index assignment problem with computational intelligence, which is suitable for transmitting the watermarked image over noisy channels.

It obtain better robustness of the watermarking algorithm against the effects caused by channel noise in the simulations

after inspecting the results from several test images. In addition, to compare with existing schemes in literature, the watermarked image quality in our scheme has approximately the same quality. This also proves the effectiveness of our proposed schemes in VQ-based image watermarking for copyright protection.

Key words : Computational Intelligence、 Digital Watermarking、Binary Symmetric Channel

二、緣由與目的

People easily retrieve digital images through the Internet nowadays. Ironically, because of the digital nature such as easy transferring and flexible editing, digital contents suffer from infringing upon the intellectual properties of original owners. To counteract this situation, digital watermarking offers a useful solution for copyright protection. We employ vector quantization (VQ) based schemes [1] for watermark embedding and extraction. We also make use of genetic algorithm (GA) to train VQ indices to pursue both

(3)

error-resilient transmission of watermarked image over a binary symmetric channel (BAC) [2],[3], and the robustness of extracted watermark.

In genetic algorithms (GA), parameters are represented by an encoded binary string, called the chromosome. And the elements in the binary strings, or the genes, are adjusted to minimize or maximize the fitness value. The fitness function generates its fitness value, which is composed of multiple variables to be optimized by GA. For every iteration in GA, a pre-determined number of individuals will correspondingly produce fitness values associated with the chromosomes. GA begins by defining the optimization parameters, the fitness function, and the fitness value, and it ends by testing for convergence. According to the applications for optimization, designers need to carefully define the necessary elements for training with GA. Then, the fitness function in addition to the terminating criteria are evaluated with the natural selection, crossover, and mutation operations to be described below [4]. Assuming that we employ GA to search for the largest fitness value with a given fitness function.

Let the input image be X with size . Our goal is to embed a robust watermark with VQ indices, and to have a watermarked reconstruction

(

M×N

)

'

X . In addition, '

X is resilient to channel errors for

transmitting over the binary symmetric channel (BSC).

Assuming that the binary-valued watermark to be embedded is W , having

size

(

Mw×Nw

)

. We perform the VQ

operation first [1] to train the codebook for X , and we obtain the codebook with lengthL,C =

{

Co,C1,L,CL−1

}

. The element

is called the codeword , .

i

C i∈

[

0,L−1

]

X is divided into vector x with size

w w N

N

MM × , then each finds its nearest codeword in the codebook C , and the index I is assigned to . While decoding with the VQ indices, the decoder merely performs a table look-up process on the received index to obtain , and then to get the reconstruction image

x i c x ' i c_i' ' X .

For watermark embedding purposes, is randomly split into two

sub-codebooks, C ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ = − ' 1 2 ' 1 ' 0 ' , c L , ,c _L c C and ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ = − '' 1 2 '' 1 '' 0 " , , ,c cL c C _L , before optimizing with GA. For one index in , it has a one-to-one corresponding counterpart in .

Therefore, and 0. ' C " C C C C' ∪ " = C'∩C" = In embedding the watermark, we adopt relationships between the watermark bits ‘0’ and ‘1’, and the split sub-codebooks and . Suppose we find the index of the current codeword in . Embedding procedures are: ' C " C i c C

．if the embedded bit is ‘0,’ and the index of the current codeword is in , keep the index unchanged;

i

c '

C

．if the embedded bit is ‘1,’ and the index of the current codeword is in , keep the index unchanged;

i

c "

C

．if the embedded bit is ‘0,’ and the index of the current codeword is in , replace by its corresponding index in

i

c "

C

i

(4)

'

C ;

．if the embedded bit is ‘1,’ and the index of the current codeword is in , replace by its corresponding index in

. i c C' i c " C

In extracting the watermark, because the watermarked imageX may experience ' channel errors during transmission, the receiver obtains the possibly corrupted image , X . In the receiver side, we " employ the same sub-codebooks and to extract the watermark. We use table look-up to find the VQ indices of the received image ' C " C "

X . If the index in one

codeword belongs to , we determine the extracted bit to be ‘0’; if not, the extracted bit is ‘1.’ By gathering all the extracted watermark bits, we obtain the extracted watermark .

'

C

'

W

In a memoryless binary symmetric channel (BSC), the input and output a alphabet sets consist of the binary elements, ‘0’ and ‘1.’ The bit error probabilities are symmetric, and given a channel symbol was transmitted, the probability that it is received in error is ε. We define a channel model for memoryless BSC with bit error probability ε,

(

)

(

)

( ) H(ci cj) j i c c H m i j c c P , , 1 | = −ε − ⋅ε (1)

where is the number of bits to represent the indices,

L m=log₂

(

ci cj

)

H , denotes the Hamming distance between the two indices. Suppose that m⋅ε <<1, Eq. (1) can be simplified by [3]

(

)

⎪ ⎩ ⎪ ⎨ ⎧ − = , 0 1 , | ε ε i j c c P

(

)

(

)

(

,

)

1. ; 0 , ; 1 , > = = j i j i j i c c H c c H c c H (2)

We propose a method to calculate “channel

watermarking distortion” by Eq.(3)

( )

(

) (

∑∑

− = − = ⋅ ⋅ = 1 0 1 0 , | L i L j j i i j i cw P c Pc c c c E δ

)

(3) Where

( )

groups; different the to belong , , 1 group; same the to belong , , 0 , ⎪⎩ ⎪ ⎨ ⎧ = j i j i j i c c c c c c δ (4) cw

E is a measure of expected Bit Error Rate (BER) of extracted watermark, which is calculated from received, watermarked image over a memoryless BSC. If we have smaller values, we obtain better robustness of the watermark.

cw

E

We employ GA to optimize the codeword index assignment that is suitable for VQ-Based watermarking transmitting over noisy channel . On the one hand, the goal for optimizing watermarked image is to maximize the PSNR value [1],[3]. On the other hand, the goal for optimizing the watermark robustness is to minimize the Bit Error Rate (BER) of the extracted watermark.

Considering both the received image quality and the watermark robustness, we derive a fitness function in GA for maximizing the effects by both factors

n E PSNR f cw n n , 1 ⋅ + = λ (5) where , and denote the fitness value, PSNR value, and expected BER value of the n-th iteration in GA, respectively.

n

f PSNR_n E_cw,_n

λ is the weighting factor to balance the effects caused by both effects of image quality and the robustness. By doing so , we are able to take both the conflicting factors into account by optimizing with GA. 三、結果與討論

(5)

The test image, Lena, with size 512× 512, as the original source. We have the embedded watermark with size 128×128. The original source is divided into 4×4 block for VQ compression, which also meets the number of bits to be embedded for watermarking. The codebook size is L=256. The bit error probability for BSC is set to

36 1 =

ε .

After optimization, our results have higher PSNR values. In addition, we have the lower BER in the extracted watermark. We employ two factors in the fitness function in Eq.(5). Firstly, denotes the combined effects from both source distortion and watermark embedding. And secondly, represents the distortion caused by the BSC. n PSNR n cw E ,

In addition, we use GA to optimize the fitness function. It can be suitable to deal with non-linear fitness functions, such as the case in Eq.(5).

We take the source distortion, the channel distortion, and the distortion induced by watermark embedding into account, and we use GA to search for globally optimal solutions.

To sum up, results with our proposed algorithm outperform those with existing algorithm in [1]. This means the effectiveness of the proposed algorithm. 四、計畫成果自評

We proposed an optimized scheme for VQ-based image watermarking, which is suitable for transmitting over noisy channels in this project. With GA, we can explore both the optimized index assignment for watermark embedding, and the effect caused

by channel noise. By splitting the codebook and assigning different indices for embedding watermark bits, the proposed algorithm outperforms the existing algorithm in literature. We also demonstrate the differences between our algorithm and that in [3]. Simulation results presented both the better robustness of our watermarking algorithm, and the more resilience to combat with channel noise.

五、參考文獻

[1] Z.M. Lu and S. H. Sun, “Digital image watermarking technique based on vector quantization,” Electron. Lett., vol.36, no.4, pp.303-305, 2000.

[2] V. Bozantzis and F.H. Ali, “Combined source adaptive and channel optimized vector quantization algorithm,” Electron. Lett., vol.35, no.17, pp.1455-1456, 1999.

[3] N. farvardin, “A study of vector quantization for noisy channels,”

IEEE Trans. Inf. Theory, vol.36, no.4, pp799-809, 1990.

[4] M. Gen and R. Cheng, Genetic Algorithms and engineering design, John Wiley & Sons, New York, NY, 1997.