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Optik 122 (2011) 311–316

Contents lists available at ScienceDirect

Optik

journa l homepage: www.e lsev ier .de / i j leo

lind image watermarking based on discrete fractional random transform andubsampling

ao Luo, Fa-Xin Yu ∗, Zheng-Liang Huang, Zhe-Ming Luchool of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310029, PR China

r t i c l e i n f o

rticle history:eceived 11 June 2009ccepted 27 December 2009

a b s t r a c t

This paper proposes a blind watermarking scheme based on discrete fractional random transform. Thewatermark information can be a binary sequence, a gray level image or a set of decimal fractions sampledfrom a given source signal. The host image is subsampled into four subimages, and the high correlations

eywords:lind image watermarkingiscrete fractional random transform

mage subsampling

among their discrete fractional random transform coefficients are exploited for watermark embedding.Based on this self-reference strategy, the watermark can be extracted without the aid of the host image.As a fragile watermarking technique, our scheme can be used in tamper detection. Besides, it can be usedin self-embedding for a large payload is provided. Meanwhile, security of the watermark is preserveddue to the randomness of the discrete fractional random transform. Experimental results demonstrate

chem

amper detectionelf-embedding

the effectiveness of our s

. Introduction

Digital watermarking [1] plays an important role in multimedianformation security. It is a process of embedding some secret datan the host media such as images, videos, audios, 3D meshes, etc. Soar various digital image watermarking techniques have been pre-ented in literatures. These schemes can be categorized accordingo different aspects as follows.

According to the watermark perceptibility, they can be dividednto visible and invisible watermarking methods. Visible water-

arking [2,3] can be used in applications such as copyrightnnouncement and advertisement, while invisible watermark-ng [4–15] is used for covert communication, traitor tracing,tc.

According to the watermark robustness against attacks, theyan be divided into robust, semi-fragile and fragile approaches.obust watermarking [4,5,8,9,16], usually designed for copyrightrotection, can resist most intentional or unintentional attacks, e.g.,otation, scaling and translation. In contrast, fragile watermarks

11] are sensitive to any alterations on the watermarked imagencluding common image operations (e.g., JPEG compression, low-ass filtering) and malicious attacks (e.g., cropping). They can besed for content authentication, tamper detection and localiza-

∗ Corresponding author at: MinZhuGuan, HuaJiaChi Campus, Zhejiang University,o. 268 KaiXuan Road, Hangzhou 310029, PR China. Tel.: +86 571 86971612;

ax: +86 571 86971612.E-mail addresses: luohao@zju.edu.cn (H. Luo), aeeizju@gmail.com (F.-X. Yu),

yland@zju.edu.cn (Z.-L. Huang), zheminglu@zju.edu.cn (Z.-M. Lu).

030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2009.12.018

e.© 2010 Elsevier GmbH. All rights reserved.

tion, etc. Semi-fragile watermarking [15] can resist common imageoperations, while not robust to malicious attacks.

According to the watermark embedding domain, they can bedivided into spatial domain, transform domain and compres-sion domain based techniques. Generally speaking, the spatialdomain based schemes [7,10,11] have lower computational com-plexity than the other two kinds of methods. For instance, thewatermarking methods based on the least significant bitplane(LSB) modification [11,17] are such a kind of classical spatialdomain based techniques. Watermarks in the transform domainbased schemes [4–6,16] usually exhibit good robustness. The com-pression domain based techniques insert the watermark duringcompression or on compressed images. The associated com-pression techniques consist of JPEG [18], JPEG2000 [19], vectorquantization (VQ) [12–14], block truncation coding (BTC) [20], etc.

According to whether the host image is required or not inwatermark extraction, the available methods can be divided intoblind, semi-blind and non-blind techniques. In the blind ones[6,7,9–11,21], the host image is not required. On the contrary, itmust be provided in the non-blind methods [4,5]. In the semi-blind schemes [16], the host image is not required while someprior knowledge is usually supplied as auxiliary information forwatermark extraction.

According to whether the host image can be perfectly recov-ered or not after watermark extracted, they can be divided into

reversible and irreversible schemes. The host image can be per-fectly recovered in the reversible methods [10], while cannot inthose irreversible [4–7,9,11–16].

Generally a watermarking scheme may have two or more prop-erties as mentioned above. For instance, the methods in [4,5] are

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12 H. Luo et al. / Opt

ot only robust but also transform domain based, while that in [22]s a reversible method in the VQ-compressed domain.

Nowadays, most existing transform domain watermarkingchemes are based on discrete cosine transform (DCT) [6,23], dis-rete wavelet transform (DWT) [8], discrete Fourier transformDFT) [16], etc. Recently, Guo et al. [4] propose a novel transformomain watermarking method based on discrete fractional randomransform (DFRNT). The DFRNT [24] is derived from the discreteractional Fourier transform (DFrFT). In Guo et al.’s scheme, thehase shift keying (PSK) is adopted to adjust the phase of complexoefficients in the DFRNT domain with reference to the watermarkit to be embedded. This scheme is robust against some familiarttacks including cropping, noising and low-pass filtering. In 2008,nother DFRNT based watermarking scheme is proposed in [5].t further demonstrates the method maintains higher robustnesshan those based on DCT, DFT and DFrFT.

These DFRNT based watermarking methods have two commonharacteristics, i.e., both of them belong to robust and non-blindechniques. However, in many scenarios, the host image cannote released after watermark embedded. In those cases, the non-lind DFRNT based methods are no longer appropriate. In addition,s aforementioned, fragile watermarking can be widely used inamper detection and self-embedding [7]. Motivated by this, weropose a blind and fragile watermarking scheme based on DFRNT.

n it, the watermark can be accurately extracted if the water-arked image is intact, without the host image aided. Moreover,

ts utilization in tamper detection, localization and recovery is alsoemonstrated.

Our method starts from subsampling the host image into fourqual-sized subimages. Then each subimage is transformed intoFRNT domain coefficients. It is easy to understand that high corre-

ation among the spatial subimages’ pixels still exists more or lessn their corresponding DFRNT coefficients. Thus, watermark cane embedded and extracted with respect to the correlation of twoubimages’ coefficients. A high visual quality watermarked imagean be acquired even if much watermark data is hidden. As longs the watermarked image suffers alterations, the coefficient cor-elation is destroyed. Therefore, our scheme can be used in tamperetection and localization. In particular, it can be easily extendedor self-embedding. That is, if the host image content is used as aatermark, the tampered area can be recovered to some extent.

The rest part of this paper is organized as follows. Section 2riefly reviews the DFRNT transform and two non-blind water-arking methods based on it. Section 3 extensively describes theatermark embedding and extraction procedures of our scheme.

xperimental results are shown in Sections 4 and 5 concludes theaper.

. Related work

.1. DFRNT transform

In [24], Liu et al. introduced the transform named DFRNT forhe first time. It can be used for one or two-dimensional discreteignal analysis. Specially, it is effective for image encryption [24],ecret sharing [25] and watermarking [4,5]. The DFRNT of a two-imensional image I can be represented as

= R˛I(R˛)T (1)

here R˛ and ˛ denote the kernel transform matrix and the frac-ional order of DFRNT, respectively. The superscript T means matrixransposition. The output matrix C is the transform coefficientsn DFRNT domain. To construct a transform matrix R˛, we must

(2011) 311–316

generate a random matrix P in advance as

P = Q + Q T

2(2)

where Q is a real nonsingular matrix with elements randomlygenerated. Suppose (V = v1, v2, . . . , vn) denotes the normalizedeigenvector matrix of P. Obviously, any two eigenvectors (twocolumns of V) are orthonormal because P is a real symmetric matrix.Then we can obtain R˛ as

R˛ = VD˛VT (3)

where D˛ is a diagonal matrix defined as

D˛ = diag[

1, exp(

−i2�˛

t

), . . . , exp

(−i

2(N − 1)�˛

t

)](4)

where t denotes the periodicity of DFRNT.Clearly, DFRNT is a random transform due to the randomness of

R˛. In other words, different P or Q corresponds to different R˛, andfurther different DFRNT. Specifically, when ˛ = rt/2 (r is a constantinteger), the output of DFRNT is real for a real signal [24].

2.2. Non-blind watermarking based on DFRNT

The two watermarking schemes based on DFRNT are brieflyreviewed. In [4], the host image is firstly transformed into DFRNTcoefficients. Then this coefficient matrix is partitioned into a setof non-overlapping blocks. Next, in each block several coefficientswith the largest amplitudes are selected for watermark embedding.The watermark is hidden by PSK, i.e., slightly changing the phaseof selected coefficient according to the watermark bit. At last, thewatermarked coefficients are transformed into the watermarkedimage via inverse DFRNT. The watermark extraction is the inverseprocess of watermark embedding by comparing the DFRNT coef-ficients’ phases of the host image with those of the watermarkedversion.

Different from the first one, the second scheme [5] exploits thefact that when ˛ is set as half periodicity, the output of DFRNTremains real for a real signal [24]. It starts from transforming thehost image and the watermark image into coefficients in DFRNTdomain, respectively. Then similar as the scheme in [4], some coef-ficients of the host image with the largest amplitudes are selected.The watermark embedding is achieved by slightly changing theamplitudes of these selected coefficients according to the water-mark image’s coefficients. At last, the watermarked coefficientsare inverse DFRNT transformed into the watermarked image. Thewatermark extraction is also a comparison mechanism similar asthat in the first scheme [4], with the host image needed.

In these two DFRNT based schemes, the selected coefficients ofthe host image for watermark embedding are with largest ampli-tudes. This is because small variations on larger coefficients aremore likely to result in smaller distortions of the host image intro-duced by watermark embedding. In this way, the imperceptibilityof the watermark is better preserved. In addition, as the host imagemust be provided during watermark extraction, they belong to non-blind watermarking techniques.

3. Proposed scheme

The main difference between our scheme and the reportedtwo methods lies in the host image is not required in watermark

extraction. That is, some substitute reference information mustbe provided for watermark extraction. Actually, much informationredundancy exists in natural image pixels, especially in small localblocks. Thus, we can exploit this high correlation among them asreference information, namely the principle of self-reference. This

H. Luo et al. / Optik 122 (2011) 311–316 313

st

3

awlsbs

(

witbgpc

okar

vCtt

Fig. 1. Block diagram of watermark embedding.

elf-reference strategy based on subsampling is similar to that inhe blind watermarking method based on DCT [6].

.1. Watermark embedding

Suppose the host image I is a gray level image of size K1 × K2,nd the original watermark W is composed by a set of numbersith each element 0 ≤ w ≤ 1. It can be a binary sequence, a gray

evel image or some decimal fractions sampled from a given sourceignal. All these secret data are normalized to the range of [0,1]efore embedded. The block diagram of watermark embedding ishown in Fig. 1 with details described below.

Firstly, I is subsampled into four subimages I1, I2, I3, I4 of sizeK1/2) × (K2/2) with the rule given as

I1(i, j) = I(2i − 1, 2j − 1)

I2(i, j) = I(2i − 1, 2j)

I3(i, j) = I(2i, 2j − 1)

I4(i, j) = I(2i, 2j)

(5)

here (i, j) denotes the pixel’s coordinates in the subimages with= 1, 2, . . ., K1/2, j = 1, 2, . . ., K2/2. This subsampling strategy is illus-rated in Fig. 2 where I is partitioned into 2 × 2 non-overlappinglocks. To each block, the upper-left pixel (indicated by the trian-le), the upper-right pixel (indicated by the circle), the bottom-leftixel (indicated by the square) and the bottom-right pixel (indi-ated by the diamond) are assigned to I1, I2, I3, and I4, respectively.

Secondly, each subimage is partitioned into k1 × k2 non-verlapping blocks represented by B1(k), B2(k), B3(k), B4(k) with= 1, 2, . . ., L. Here L is the number of blocks of each subimage,nd B1(k), B2(k), B3(k), B4(k) denote the kth block of I1, I2, I3, I4,espectively.

Thirdly, the DFRNT is performed on B1(k), B2(k), B3(k), B4(k) indi-idually, and the corresponding DFRNT coefficient matrices C1(k),2(k), C3(k), C4(k) are obtained. In this paper, the periodicity t andhe fractional order ˛ are set as 1 and 0.5 respectively. Hence, allhe elements of C1(k), C2(k), C3(k) and C4(k) are real.

Fig. 2. Image subsampling strategy.

Fig. 3. Selection of watermark embedding positions.

Fourthly, C1(k), C2(k), C3(k) and C4(k) are classified into twogroups with each group possess two coefficient matrices. Obviouslythere are totally P2

4 = 12 combinations. The grouping mecha-nism can be fixed or randomly determined by a pseudo-randomsequence. In our case, we adopt a fixed order combination, i.e.,{C1(k), C2(k)} and {C3(k), C4(k)}. This means C1(k) and C2(k) belongto one group, and the other group is composed of C3(k) and C4(k).For description simplicity, we only select the group {C1(k), C2(k)} toexplain the watermark embedding process in detail. The operationson {C3(k), C4(k)} are exactly the same.

Now our task is reduced to select some appropriate pairs ofcoefficients from the possible k1 × k2 coefficient pairs in the samepositions of {C1(k), C2(k)}. For the current coefficient pair (ca, cb),compute its mean value as

m = ca + cb

2(6)

where a and b are integers in the range of [1, k1 × k2]. ca and cb arethe DFRNT coefficients located at the same positions of C1(k) andC2(k), respectively. In our case, the coefficient pair with a large meanvalue m is selected for watermark embedding. Thereby a relativesmall distortion is introduced to the host image and meanwhile theimperceptibility of the watermark is well preserved. If l watermarkdata are to be embedded in {C1(k), C2(k)}, the l pairs with the llargest mean values are selected.

The following rule is applied to evaluate if the current pair (ca,cb) is selected or not for watermark embedding:

(ca, cb) ={

selected m belongs to the l highest means

non-selected otherwise(7)

The selection of watermark embedding positions is illustratedin Fig. 3. Actually, this process is to compute the mean matrix M ofC1(k) and C2(k). Then several largest mean values in M are selectedfor watermark embedding. For instance, if l = 4, the four largestmean values indicated by black points are chosen.

If (ca, cb) is selected, the current watermark w (0 ≤ w ≤ 1) isembedded as Eq. (8), otherwise it is skipped and the next pairof coefficients are examined. Usually the watermark is permutedbefore embedding.

c′a = m(1 + ˇw)

c′b

= m(1 − ˇw)(8)

where ˇ denotes the watermark embedding strength. A larger ˇindicates higher watermark energy and accordingly more visualdistortion is introduced. Repeat this operation for all pairs ofselected coefficients, and thus four watermarked coefficient matri-

′ ′ ′ ′

ces C1, C2 are obtained. Similarly, C3 and C2 are also obtained.At last, the inverse DFRNT is performed on C ′

1, C ′2, C ′

3, and C ′4,

respectively, and the corresponding I′1, I′2, I′3, and I′4 are obtained.These watermarked subimages are recomposed and the water-marked image I′ is obtained.

314 H. Luo et al. / Optik 122 (2011) 311–316

3

cf

sk

BCd

t

m

dpmwF

w

t

4

iemnma

P

wtrw

iatF3mo

Fig. 5. Experimental results on embedding a binary image in Lena, (a) the host

is used, the extracted watermark as shown in Fig. 5(e) looks likerandom noise. This proves that security of the watermark contentis guaranteed because of the randomness of DFRNT.

Another five 512 × 512 images Baboon, Barbara, Boat, F16 andPeppers as shown in Fig. 6 are selected as host images to evalu-

Fig. 4. Block diagram of watermark extraction.

.2. Watermark extraction

As shown in Fig. 4, the watermark extraction is the inverse pro-ess of watermark embedding with the procedures described asollows.

Firstly, the watermarked image I’ is subsampled into four equal-ized subimages I′1, I′2, I′3, I′4, and each of them is partitioned into1 × k2 non-overlapping blocks B′

1(k), B′2(k), B′

3(k), B′4(k).

Secondly, the DFRNT is performed on B′1(k), B′

2(k), B′3(k),

′4(k) respectively, and the coefficient matrices C ′

1(k), C ′2(k),

′3(k), and C ′

4(k) are obtained. Then these coefficient matrices areivided into two groups {C ′

1(k), C ′2(k), C ′

3(k), C ′4(k)}.

Thirdly, the mean value of the current coefficient pair (ca, c′b) in

he group {C ′1(k), C ′

2(k)} is computed as

′ = c′a + c′

b

2(9)

Obviously m′ is equal to m no matter whether the watermarkata is embedded or not. In other words, the mean value of eachair is not changed. Hence the coefficient pair whose mean value′ belongs to the l largest mean values is found again. For instance,hen l = 4, the four positions indicated by black points as shown in

ig. 3 are accurately retrieved during watermark extraction.At last, the watermark bit can be extracted as

= c′a − c′

b

ˇ(c′a + c′

b)

(10)

This operation is repeated on all pairs of coefficients and untilhe entire watermark W is extracted after inverse permutation.

. Experimental results

In all the experiments, the DFRNT kernel transform matrix R˛

s generated by a uniformly random matrix Q, and the watermarkmbedding strength ˇ is set as 0.01. Each subimage’s coefficientatrix is partitioned into 8 × 8 blocks. The metric peak signal to

oise ratio (PSNR) is used to evaluate the visual quality of the water-arked image. For an 8-bit gray level image, the PSNR is defined

s

SNR = 10 log102552

1/K1 × K2

K1∑i=1

K2∑j=1

(I(i, j) − I′(i, j))2

(11)

here I(i, j) and I′(i, j) denote the gray levels of the pixel in the posi-ion of (i, j) of the K1 × K2 host image and the watermarked image,espectively. A higher PSNR indicates smaller distortions due to theatermark embedded.

The first experiment is to embed a 128 × 128 binary watermarkmage as shown in Fig. 5(c) in the 512 × 512 gray level Lena images shown in Fig. 5(a). The four 256 × 256 subimages of Lena and

heir associated DFRNT coefficients are shown in Fig. 5(f)–(i) andig. 5(j)–(m), respectively. As each coefficient matrix consists of2 × 32 blocks, there are totally 2048 groups of blocks and 8 water-ark data (in this case, 0 or 1) should be hidden in each group

f blocks. Before embedded, the watermark image is permuted by

image, (b) the watermarked image with PSNR = 90.53 dB, (c) the original watermark,(d) the watermark extracted with the correct kernel matrix R˛ , (e) the watermarkextracted with a wrong kernel matrix R˛ , (f)–(i) four subimages of Lena, and (j)–(m)the four DFRNT coefficient matrices corresponding to the four subimages.

a pseudo-random sequence. The PSNR value of the watermarkedLena as shown in Fig. 5(b) compared with the original version canbe achieved as 90.53 dB. Besides, if the watermarked image suf-fers no alterations, the watermark extracted with the correct kernelmatrix R˛ as shown in Fig. 5(d) is exactly the same as the originalone. However, if a wrong kernel matrix R˛ (randomly generated)

Fig. 6. Five 512 × 512 test images Baboon, Barbara, Boat, F16 and Peppers (from leftto right).

H. Luo et al. / Optik 122 (2011) 311–316 315

Table 1PSNR values with different watermark capacities embedded.

Images Capacity

2048 4096 8192 16384 32768 65536

Baboon 96.99 dB 94.09 dB 90.85 dB 87.94 dB 84.90 dB 81.90 dBBarbara 101.29 dB 98.21 dB 95.75 dB 92.53 dB 89.45 dB 86.47 dBBoat 102.56 dB 99.35 dB 96.46 dB 93.58 dB 90.77 dB 87.86 dB

98.60 dB 95.63 dB 92.54 dB 88.97 dB97.17 dB 94.38 dB 91.59 dB 88.20 dB

95.77 dB 92.81 dB 89.85 dB 86.68 dB

awnaicrisPct

2dwcieib

Stwttrspivqs

Fmo

F16 103.62 dB 101.42 dBPeppers 102.55 dB 99.85 dB

Average 101.40 dB 98.58 dB

te the average performance of our scheme. In this experiment, theatermarks are random number sequences produced by pseudo-umber generators. They consist of 2048, 4096, 8192, 16384, 32768nd 65536 decimal fractions, respectively, with each element liesn the range of [0,1]. Accordingly the numbers of watermark dataarried by each group of blocks correspond to 1, 2, 4, 8, 16 and 32,espectively. The PSNR values of the watermarked images are listedn Table 1. Generally speaking, human eyes cannot distinguish con-picuous visual distortions of the watermarked image when itsSNR value is larger than 30 dB. From Table 1, we can find that theomputed PSNR values are much larger than this level. This implieshe distortions introduced by watermark embedded are acceptable.

To illustrate the tamper detection ability of our scheme, a56 × 256 binary watermark image as shown in Fig. 7(d) is embed-ed in the 512 × 512 host image Bridge as shown in Fig. 7(a). Theatermarked image is shown in Fig. 7(b) with PSNR = 84.51 dB. Its

orrupted version is shown in Fig. 7(c) with the tampered positionsndicated by two white circles. Clearly, the associated areas of thextracted watermark as shown in Fig. 7(e) are also tampered. Noten this case it is unnecessary to permute the original watermarkefore embedding.

In fact, our scheme can be easily extended for self-embedding.elf-embedding [7] refers to embedding part of the host image con-ent in itself for tamper detection, localization and recovery. Theatermark in self-embedding is usually a highly compressed con-

ent of the host image, e.g., the low frequency DCT coefficients,he output of digital halftoning. This information can be used toeconstruct an approximate version of the host image. Generally,elf-embedding watermarking schemes can provide a relative large

ayload such that a high fidelity version of the host image can be

nserted and reconstructed. From Table 1, we find that a high PSNRalue of the watermarked image can be preserved when a largeuantity of secret data is embedded. Thus it is feasible to apply ourcheme in self-embedding. As the example demonstrated in Fig. 8,

ig. 7. Experimental results on tamper detection, (a) the host image, (b) the water-arked image with PSNR = 84.51 dB, (c) the tampered watermarked image, (d) the

riginal watermark, and (e) the extracted watermark.

Fig. 8. Experimental results on self-embedding, (a) the host image, (b) the water-marked image with PSNR = 89.30 dB, (c) the original watermark, (d) the tamperedwatermarked image, and (e) the extracted watermark.

the 512 × 512 host image is shown in Fig. 8(a). The 256 × 256 orig-inal watermark is shown in Fig. 8(d) with its pixel values beingthe mean values of each 2 × 2 block of Fig. 8(a). These pixel val-ues are normalized into decimal fractions between 0 and 1 beforeembedded. The watermarked image is shown in Fig. 8(b) withPSNR = 89.30 dB. The corrupted watermarked image is shown inFig. 8(c) with the tampered area indicated with a white circle, whereone of the three original trucks in the watermarked image is copiedand pasted. The extracted watermark is shown in Fig. 8(e). From theextracted watermark, the tampered area is detected, localized andits content in the original image is recovered approximately.

5. Conclusions

A blind image watermarking scheme based on DFRNT is pre-sented in this paper. Compared with the available DFRNT basedmethods, it exploits the high correlation among four subimagesof the host image as self reference information for watermarkextraction, and thus the host image is no longer required. Thisimprovement expands the application scenarios in the cases thatthe host image cannot be released or obtained. As a fragile water-marking technique, our scheme can be used for tamper detection.Furthermore, if the content of the host image is employed as thewatermark, the tampered area can be localized and recoveredapproximately. If a wrong DFRNT kernel matrix is used in water-mark extraction, no meaningful watermark information can berevealed. That is, security of our scheme is perfectly preserved bythe randomness of DFRNT kernel matrix.

Acknowledgments

The authors would like to express sincere thanks to Dr. ZhengjunLiu, Harbin Institute of Technology, PR China, for valuable discus-sions.

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