WUJ

Vol. 11

No. 6 2006

1675-1678

Wuhan University Journal of Natural Sciences

Article ID: 1007-1202(2006)06-1675 04

Chaos.BasedMultipurposeImage Watermarking Algorithm 0 [] ZHU Congxu, LIAO Xuefeng, LI Zhihua

igital multimedia is largely distributed today over the Internet and via CD-ROM. However, the possibility of lossless and unlimited copies of digital contents is a major obstacle from the owner~ s viewpoint for entering the digital world. Copy protection, copyright protection, and content authentication have, therefore, been the three most important issues in the digital world. Digital watermarking plays an im portant role in image verification and copyright protection. Robust watermarksE137are generally used for copyright protection and ownership verification because they are robust to nearly all kinds of image processing operations. In comparison, fragile or semi fragile watermarks~4~ are mainly applied to content authentication and integrity attesta tion because they are fragile to most modifications. Most of existing watermarking schemes are designed for either copyright protection or content authentication. To fulfill multipurpose applications, several multipurpose watermarking algorithms based on wavelet transformEr~, fast Fourier transformEs?, vector quantizer (VQ) structure [9']~ , have been presented. But the computational complexity in Refs. Eg, t@~ is high, since the vector quantization in their scheme needs code book design, training and a VQ encoder, and the peak signal-to-noise ratio (PSNR) in Refs. [-9,10~ is low, too. We present a novel multipurpose digital image watermarking method based on chaotic map and block DCT, by using chaotic map to enhance security, by using a improve ment quantization method (IQM) to enhance invisibility.

D

School of Information Science and Engineering, Central South University, Changsha 410083, Hunan,China

Abstract= To

achieve the goal of image content authentica tion and copyright protection simultaneously, this paper pres ents a novel image dual watermarking method based on chaotic map. Firstly, the host image was split into many nonoverlapping small blocks, and the block wise discrete cosine transform (DCT) is computed. Secondly, the robust watermarks, shuffled by the chaotic sequences, are embedded in the I)C coefficients of blocks to achieve the goal of copyright protection. The semi-fragile watermarks, generated by chaotic map, are embedded in the AC coefficients of blocks to obtain the aim of image authentication. IMth of them can be extrac ted without the originaI image. Simulation results demonstrate the effectiveness of our algorithm in terms of robustness and fragility. Key words, copyright protection; image authentication; multipurpose watermarking; chaos theory

CkC number. TP 391.9

Received date: 2006-04-10 Foundation item: Supported by the National Natural Science Foun

dation of (;hina (60573127) Biography: ZHU Congxu( 1963 ), male, Associate professor, research direction: information security. Email : zhucongxu@ 126. corn

Wuhan Universi~

iSciences V~. 11

Introduction

:

1675

1 Proposed Watermarking Algorithm 1.1 ChaoticMap Chaotic maps have two most attractive features in information hiding, these are its extreme sensitivity to initial conditions and the outspreading of orbits over the entire space. These special characteristics make chaotic maps excellent candidates for watermarking and encryption. Logistic map is one of the simplest chaotic maps, described by x.+~ = j ~ ( 1 - x = ) , x , , ~ (0,1) (1) where 0 ~ < 4 , when 3. 569 945 6
Step 2 Generate the chaotic random sequence X 1 ~-Ix1 (n)} by the chaotic map with initial value key1, do sort transformation of the chaotic sequence {x~ (n)} to obtain the sorted sequence {x'] (n)} and a integer sequence: h , h , ' " , t i , ' " , where ti is the position order number of xl (i) in {X'l(n) }. Step 3 Transform watermark We to sequence SWR, then permute SWRwith chaotic sequence to obtain SWpR : SWpR (i) = S W R ( t i ). Transform sequence SWpR to matrix, then obtain the permuted watermark image WpR .

Step 4 Split the originat host image A into many non-overlapping small blocks with N• N pixels in a scanline order. Denote a block by subA(i,j), i=l, 2,'", LI, j = l , 2,'",L2. here, LI=M1/N,L2=M2/N. Step 5 Generate the chaotic random sequence X2 -{x2 (n) } by the chaotic map with initial value key2, and the fragile watermark image WF is obtained through mapping {&(n)} to {0,1} by qf('). Step 6 Embed WpR and W~ into each blocks subA(i,j) as follows: f=DCT2(sub A(i,j)); embed WpR(i,j) into f(0,0): f(0,0)'---- IQM(f(0,0), Q~, ql, b,WpR(i,j)); embed WF (i,j) into f ( 0 , 1 ) : f ( O , 1) ' = IQM(f(0, 1 ) , Q , q2, b,W~ (i,j)); SubA' = iDCT2

(/).

1.3 WatermarkDetection For a possible watermarked image, different from the embedding processes, extract watermark use the inverse operation to IQM. The algorithm is as follows: Step 1 Input key:, key2 ; N; Q~ ,q~ ; Qz ,q2 ;b. Step 2 Split the possible watermarked image A' into many non-overlapping small blocks with N;< N pixels in a scan-line order. Denote a block by subA'(i,j),i = 1, 2,'",LI,j=I, 2,'",L2. here, L1 =M1/N, L2=M2/

N. Step 3 Generate the chaotic random sequence X2 = (:r2 (n)} by the chaotic map with initial value keye, and the fragile watermark image WF is obtained through mapping {x2(n)} to {0,1} by qf(o). Step 4 Perform DCT operation on each block subA' (i,j), then extract W'pRand W'F as follows: f' = DCT (sub A'). extract WpR (i, j)' from f (0, o)'=,-= If(o,o)'l Nod Q1, if [r-Qx/E]>(Q]/2q])/2, then WpR(i,j)'=b; else, WpR(i,j)'=l-b. extract another fragile watermark version Ws (i, j)~ from f(0,1)' : r = [f(0,1)'lMod Q , if Ir-Q2/21>(Q2/2 - q e )/2, then WF(Z,J) ' ' ' =b; else WF(i,j)'=l-b.

Step 5 Generate the chaotic random sequence X~ = {:rl (n)} by the chaotic map with initial value key~, do sort transformation of the chaotic sequence {.r~ (n)} to obtain the sorted sequence {:r~ (n)} and a integer sequence: h, t2, "", t~, "", where t~ is the position order number of :rl (i) in {:r'l(n)}. Step 6 Transform W'H~ to sequence SW'pR, then perform inverse permutation on SW'ee with chaotic sequence to obtain SW'R : SW'R(t~) = SWpR (i). Transform sequence SW'R to matrix, then obtain the extracted robust watermark image W'R. Step 7 Having obtained the two versions of fragile watermark, Wv and W'F, we define the tamper detection matrix: T : I wF-w;. I (2) If WF =W'F then T=0. This means that the watermarked image was not tampered. Otherwise, the ' 1' elements in the tamper detection matrix denote the pixels that were tampered. Note that the size of matrix T is (M~/NXM2/N), Thus one element in the matrix denotes a corresponding N X N block in the host image. Our proposed scheme is blind because the original image is not required during the watermark detection process. Since our semi-fragile watermark scheme is designed to be robust to mild modification in all cases, it is inevitable that we do not detect all malicious attack in pixelwise. Practically, malicious attack always be applied in a certain region in host image. Thus tamper pixels are always continuous. For a certain tamper detection matrix element T ( i , j ) , if the number of tampered element in the neighboring elements of T(i,j) is greater than a given threshold, we thus consider T(i,j) to be tampered, too. The following equation is the summary of such post processing(PP) operation of tamper detection matrix: i

=

mapped in the range EO,I~. Let N=4;Q~ =0. 16, q] = 0. 022; Q = 0 . 1 2 , q2 =0. 015. The size of host image, watermark WR and WF are equal to those in Ref. E9, 101. Figure 1 shows the host image and robust watermarks. The PSNR of watermarked image is 38. 746 dB in Fig. 1. It is noted that the PSNR is only 30. 398 dB in Ref. [9~ and 30. 553 dB in Ref. ElO~. The majority bit value of robust watermark is b = 1. If the optimized em bedding is not under considering, then the PSNR is 37. 132 dB.

(a)

(b)

(c)

Fig. 1 The host images and robust watermarks (a) Original Lena image; (b) Original robust watermark; (e) Permuted robust watermark; (d) Watermarked Lena image

We employ the normalized hamming similarity (NHS) E77 and the normalized cross-correlation (NC) E~j to evaluate the effectiveness of the proposed algorithm. Results show that both the robust and fragile watermark extracted from the watermarked image without any attacks are with NHS--1.0. To check the robustness and fragility of our algorithm, we perform several attacks on the watermarked image, include JPEG compress, saltpepper noise (SPN), additive white Gaussian noise (AWGN), median filtering, etc. The extracted watermarks W'R are depicted in Fig. 2, the NHS (or NC) values of W'R and W'F are listed in Table 1, we also list the HNS or NC values in Ref. [6,91. We can see that the robust watermark is robust to general image attacks, the semi-fragile watermark is only robust to mild attacks, and our scheme has better performance than Ref. E6,91.

. . . .

(3)

u:

2

a'u:

a

To evaluate the performance of the proposed meth od, the 512 X 512 Lena image with 8 b/pixe[ resolution is used for host image A. WR is a binary image with size 128X128, WF is a 128X 128 binary matrix, which obtained by Logistic chaotic map. The pixel values of A is sci~

vol. 1t

I....................... !

I ':::"i

(a)

Experimental Results

w ~ - ~ un!vers~ty

(d)

(b)

(c)

(d)

(e)

(fi

(g)

(h)

Fig. 2 Robust watermarks extracted from attacked images (a) JPEG compress with Q F - 5 0 ~ ; (b) JPEG compress with QF 30X; (c) Adding SPN with density 0.02;(d) Adding AWGN with 02--24; (e) Median filtering with the radius of 2 pixels; (f) Blurring with radius-- 1.0 and threshold- 10.0 ; (g) Sharpening; (h) Image is cropped 256 X 256 pixels in the upper-left corner

If we consider the situation when the image is mildly modified such as severe AWGN while on the other hand 1677

Table 1 Robust against several attacks No.

NHS (WR)

NHS c< (WR)

NHS (WF)

NHS E93 NC (WF) (WF)

NC E6~ (WF)

Fig. 2(a)

0.959

0.883

0.833

0.605

0.904

0.820

Fig. 2(b)

0.855

0.850

0.667

0.420

0.792

Fig. 2(c)

0.889

0.838

Fig. 2(d)

0.934

Fig. 2(e)

0.796

0.776

0.554

0.878

0.833

0.901 0.254

0.870

O. 853

Fig. 2(f)

0.976

0.859

0.792

0.632

0.959

Fig. 2(g)

0.949

0.825

0.714

0.514

0.926

Fig. 2(h)

0.970

0.902

0.875

O. 895

1.000

it is maliciously attacked such as image content tampering attack. In our experiment, after a AWGN attack with 2 = 18, the watermarked image is maliciously attacked by adding word "Tamper" and changing the Lena's face into Elaine's face. Figure 3 shows the results of PP operation when using different parameters. It is very like the erosion operation in image processing. When a = 1, /?-- 3, we can tell the malicious attack from the mild modification very clearly. This means we define one-order neighborhood, and set the threshold in the middle of total element number. The results of above experiments show that our algorithm is capable of tamper detection with relative precise localization.

based on chaotic map and block DCT has been presented. Experimental results demonstrate that the proposed method can be used for copyright protection by extracting the robust watermark, and it can also be used for image authentication by the tamper detection matrix of semifragile watermark. The main characteristic of our scheme is as follows. @ The robust watermark robust to many mild and maliciously attacks, while the fragile watermark robust to mild modification and fragile to malicious attack; @ The fragile watermark has the ability of relative precise localization; @ By employing optimized watermark embedding method, enhanced invisibility; @ By employing chaotic sequences to shuffle the binary watermark image pixels, enhanced security. Further research can lay emphasis on theoretical analysis and optimization of watermark embedding position.

References EI~

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(c)

(d)

Fig. 3 Tampered watermarked image and PP operation on tamper detection matrix (a) Tampered watermarkedimage; (b) No PP operation; (c) a--l, fl=3; (d) a--l,fl--4

3

Conclusion An efficient multipurpose watermarking algorithm

1678

Watermarking Method Based on Mean Removed Vector Quantization~J~. Journal o f InJbrmation Assurance and Se curity, 2006,1 ( 1 ) : 33-42. [10~ [.u Z M, Xu D G, Sun S H. Multipurpose Image Water marking Algorithm Based on Multistage Vector Quantization ~J~. IEEE Trans Image Processing,2005,14(6) :822 831.

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