contourlet-based image adaptive...

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Signal Processing: Image Communication 23 (2008) 162–178

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Contourlet-based image adaptive watermarking

Haohao Song�, Songyu Yu, Xiaokang Yang, Li Song, Chen Wang

The Institute of Image Communication and Information Processing, Shanghai Jiao Tong University, Shanghai, PR China

Received 23 May 2006; received in revised form 8 January 2007; accepted 5 January 2008

Abstract

In the contourlet transform (CT), the Laplacian pyramid (LP) decomposes an image into a low-frequency (LF) subband

and a high-frequency (HF) subband. The LF subband is created by filtering the original image with 2-D low-pass filter.

However, the HF subband is created by subtracting the synthesized LF subband from the original image but not by 2-D

high-pass filtering the original image. In this paper, we propose a contourlet-based image adaptive watermarking (CIAW)

scheme, in which the watermark is embedded into the contourlet coefficients of the largest detail subbands of the image.

The transform structure of the LP makes the embedded watermark spread out into all subbands likely in which the LF

subbands are included when we reconstruct the watermarked image based on the watermarked contourlet coefficients.

Since both the LF subbands and the HF subbands contain watermarking components, our watermarking scheme is

expected to be robust against both the LF image processing and the HF image processing attacks. The corresponding

watermarking detection algorithm is proposed to decide whether the watermark is present or not by exploiting the unique

transform structure of LP. With the new proposed concept of spread watermark, the watermark is detected by computing

the correlation between the spread watermark and the watermarked image in all contourlet subbands fully. The proposed

CIAW scheme is particularly superior to the conventional watermarking schemes when the watermarked image is attacked

by some image processing methods, which destroy the HF subbands, thanks to the watermarking components preserved in

the LF subbands. Experimental results show the validity of CIAW in terms of both the watermarking invisibility and the

watermarking robustness. In addition, the comparison experiments prove the high-efficiency of CIAW again.

r 2008 Elsevier B.V. All rights reserved.

Keywords: Image watermarking; Watermarking detection; Laplacian pyramid; Contourlet

1. Introduction

Copyright protection of digital image is one ofchallenging issues imposed in ubiquitous media.Digital watermarking for images has been identifiedas a possible solution to this challenge, and hasbecome an area of increased research activity over thelast decade. Image watermarking is the process ofembedding the owner’s mark into image data so that

e front matter r 2008 Elsevier B.V. All rights reserved

age.2008.01.005

ing author.

ess: [email protected] (H. Song).

intellectual property rights can be identified. Ingeneral, a watermarking scheme shall satisfy twoproperties. First, the embedded watermark does notvisually distort the image. The second property is thatthe watermark is difficult for an attacker to remove. Itshould be robust to common signal processing andgeometric distortions, such as low-pass filtering,compression, noise, affine, and rotation.

Watermarking may be performed in either imagedomain or transform domain, such as discreteFourier transform (DFT), discrete wavelet trans-form (DWT), and discrete cosine transform (DCT).

.

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ARTICLE IN PRESSH. Song et al. / Signal Processing: Image Communication 23 (2008) 162–178 163

Schyndel et al. [1] proposed to insert a watermarkby changing the least significant bit of some pixels inan image. Bender et al. [2] described a watermarkingapproach by modifying a statistical property of animage. Recent contributions have shown that imageadaptive watermarking schemes can be successfullyimplemented using image transforms with spatial-frequent local properties. Kang et al. [3] embeddedwatermark in the coefficients of the LL subband inthe DWT domain while a template is embedded inthe middle frequency components in the DFTdomain to achieve the robustness to both affinetransform and JPEG compression. The approachimplemented as a DCT–DWT dual domain algo-rithm and applied for the protection and compres-sion of cultural heritage imagery is proposed byZhao et al. [4]. In order to guarantee the quality of awatermarked image not to degrade visually, water-mark should be embedded in high-frequency (HF)components. However, it makes the scheme vulner-able to attacks such as compression and low-passfiltering. Performance gain can be obtained byexploiting the characteristics of the human visualsystem (HVS) in the watermarking scheme [5,6].They compensated for the lack of robustness in theHF components by increasing the watermarkstrength to its maximum, while preserving theimperceptibility thanks to the visual masks.

Conventional watermarking schemes embedwatermark into a certain scale subbands in trans-form domain (either HF subbands or low-frequency(LF) subbands), thus they can only resist the attackof a particular kind of image processing. Consider-ing a watermarking scheme that embeds watermarkinto HF subbands, the watermark will be removedeasily when the watermarked image is attacked byimage processing methods which destroy the HF ofthe image, although it is robust to the LF filtering.Therefore, most of conventional watermarkingschemes are semi-robust in general.

In this paper, we propose a contourlet-basedimage adaptive watermarking (CIAW) scheme. Inthe CIAW scheme, although the watermark isembedded into the largest detail subbands (thehighest-frequency subbands), it is likely to be spreadout into all subbands when we reconstruct thewatermarked image, due to the special transformstructure of Laplacian pyramid (LP) [7]. Because theLF subbands of the watermarked image contain thewatermarking components, the proposed CIAWscheme is very robust against various HF attacks,such as low-pass filtering, quantization, and com-

pression, which will destroy the HFs of the image.On the other hand, some watermarking componentscan be preserved at the HF subbands. Thus, theCIAW scheme is expected to be also robust to theLF attacks, such as gamma correction, histogramequalization, and cropping, which will destroy theLFs of the image. Consequently, the proposedCIAW watermarking scheme is robust to the widelyspectral attacks resulting from both the LF imageprocessing and the HF image processing.

The watermarking detection algorithm corre-sponding is proposed to decide whether the water-mark is present or not by exploiting the uniquetransform structure of LP. It checks the correlationbetween the watermarked image and the spread

watermark in all subbands of contourlet domain.Our detection algorithm is superior to the conven-tional detection algorithms because it can exploitthe correlation of the watermark and all water-marking components in different subbands of thewatermarked image fully.

The rest of this paper is organized as follows. Innext section, the contourlet transform (CT) isdescribed in detail and the characteristic of LP isanalyzed from the viewpoint of watermarkingembedding. Section 3 presents our CIAW schemetogether with its corresponding watermarking de-tection algorithm. In Section 4, the simulationresults are presented. Lastly, Section 5 concludesthis paper.

2. Contourlet transform and characteristic analysis

2.1. Contourlet transform

Contourlet was proposed by Do and Vetterli in2001 [8,9]. It can efficiently represent contours andtextures of an image. Contourlet is a double filterbank (FB) structure for obtaining sparse expansionsfor typical images with smooth contours, where theLP is used to capture the point discontinuitiesfirstly, then followed by a directional filter bank(DFB) to link the point discontinuities into linearstructures. The overall result is an image expansionusing basic elements like contour segments, andthus named contourlet [9].

Fig. 1 shows the flowchart of CT for a 512� 512image. The HF subband images from the LP are fedinto a DFB so that the directional information canbe captured. The scheme can be iterated the LFsubband image over. The CT decomposes the imageinto directional subbands at multiple scales.

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Fig. 1. Flowchart of contourlet transform for a 512� 512 image.

Fig. 2. Contourlet representation of ‘‘Lena’’ image: (a) contourlet coefficient image; (b) frequency partitioning with four real wedge-

shaped frequency bands; and (c) corresponding sequence numbers of four directional subbands.

H. Song et al. / Signal Processing: Image Communication 23 (2008) 162–178164


The CT has several distinguishing properties [9]as follows: (1) seamless translation to the discreteworld; (2) 2-D frequency partition on centricsquares; (3) fast FB algorithms and convenient treestructures; (4) compactly supported contourletframes; and (5) flexible refinements for the spatialresolution and the angular resolution.

Fig. 2(a) shows the example of contourletrepresentation on 512� 512 ‘‘Lena’’ image. Forclear visualization, the image is only decomposedinto three pyramidal levels, which are then trans-formed into four directional subbands. Here, smallcoefficients are shown in black while large coeffi-cients are shown in white. We noticed that only thecontourlets, which match both location and direc-tion of image contours produce the significantcoefficients. Fig. 2(b) illustrates the frequencypartitioning with four real wedge-shaped frequencybands of each scale of contourlet representation, inwhich 01, 301, 601, and 901 subbands are signedsequence numbers as 1, 2, 3, and 4 as shown inFig. 2(c).

2.2. Characteristic analysis of LP for watermarking

embedding

Burt and Adelson [10] introduced the LP as amultiresolution representation for images in 1983.Do and Vetterli studied the LP using the frametheory, and revealed that the LP with orthogonalfilters is a tight frame. In 2003, they proposed anefficient FB for the reconstruction of the LP usingprojection that leads to a proved improvement overthe conventional method in the presence of noise.Setting up the LP as an oversampled FB, theyoffered a complete parameterization of all synthesisFBs that provide perfect reconstruction for the LP.

Fig. 3 shows the LP scheme. Here, H and G arethe analysis filter and the synthesis filter of LP,respectively; I is the original image, c and r are thecoarse approximation (LF subband) and the differ-ence (HF subband), respectively. The process canbe iterated by decomposing the coarse versionrepeatedly.

By analyzing the scheme of LP, we find that theHF subband r is created by subtracting theG-filtered LF subband c from the original image I,rather than by filtering the original image with a2-D high-pass filter as wavelet transform (WT) does.In this case, if we change the HF coefficients, the LFcoefficients will be affected likely. We explain itbriefly as follows. Here, I0 is the modified image; c0

and r0 are the LF and the HF subband of I0,respectively.

c ¼ HðIÞ r ¼ I �GðcÞ ‘I ¼ GðcÞ þ r

‘c ¼ HðIÞ ¼ HðGðcÞ þ rÞ¼ HðGðcÞÞ þ HðrÞ.

The bi-orthogonal filters are normallyused for LP filtering. Therefore,H(G(c)) ¼ cH(r) ¼ 0.

‘r is orthogonal with H.It is noticeable that c and H(r) have been

down-sampled here, and 0 is zero matrix.When r is changed to rw randomly,

I0 ¼ G(c)+rw which is decomposed by LPagain.

c 0 ¼ HðI 0Þ ¼ HðGðcÞ þ rw Þ¼ HðGðcÞÞ þ Hðrw Þ ¼ c þ Hðrw Þ.Only if rw is orthogonal with H, i.e. the

difference of rw and r is orthogonal with H,H(rw) would be zero matrix. But becausethe change from r to rw is random, it ishardly possible that rw is orthogonal withH.

‘H(rw) is likely to not equal to zeromatrix, ‘c0 is likely to be different from c.

The phenomenon that the change of HF coeffi-cients likely affects the LF coefficients can bedemonstrated by an experiment below, where azero-coefficients image is tested and 3-level LP isconducted. It is easy to know that the contourletcoefficients of the zero-coefficients image are allzeros. We change the largest detail subbands of thezero-coefficients image by embedding the matriceswith pseudo-random binary values {�100, 100} intothem. Fig. 4(a) shows the contourlet coefficientsafter we embed the random matrices into the largestdetail subbands of the zero-coefficients image. Here,the largest detail subbands are made up of non-zerocoefficients while the other two levels are made upof zero coefficients. Fig. 4(b) shows the contourletcoefficients after the image in Fig. 4(a) is recon-structed and then is decomposed with the CT again.It is seen that not only the largest detail subbands,but the subbands in the other two levels also containnon-zero coefficients. The experimental result isconsistent with our proposition. If we regard theprocess of randomly changing from r to rw as the

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Fig. 3. Laplacian pyramid scheme: (a) analysis and (b) synthesis.

Fig. 4. Comparison of contourlet coefficients. (a) The contourlet coefficients after we embed the random matrices into the largest detail

subbands of the zero-coefficients image. (b) The contourlet coefficients after the image in (a) is reconstructed and then is decomposed with

contourlet transform again.


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Fig. 5. The construction of the simplified DFB.

H. Song et al. / Signal Processing: Image Communication 23 (2008) 162–178 167

process of watermarking embedding, the phenom-enon that the change of HF coefficients affects theLF coefficients likely occurs in the watermarkingscheme based on contourlet.

Because of the characteristic of LP, the CT isevidently different from the WT. In the WT, the HFsubband is created by filtering the original imagewith high-pass filter. Therefore, the change of HFcoefficients does not affect the LF coefficients.Because the WT does not have the spreading effectas the LP, the embedded watermark is susceptible tothe attacks such as low-pass filtering, quantization,and compression that destroy the HF coefficients ofthe image seriously. In contrast, if the watermark isembedded into the largest detail subbands of CT, itis likely to be spread out into all subbands when wereconstruct the watermarked image. Thus, thewatermarking scheme in CT domain may be robustto the widely spectral attacks resulting from bothLF image processing and HF image processing.

Furthermore, we found that the embedded water-mark just is spread to the lower-frequency sub-bands, but not to the higher-frequency subbands byanalyzing the characteristic of LP. In other words, ifthe watermark is embedded into ith scale subbands,it is likely to be spread out into (i+1)th, (i+2)th?subbands, but not into (i�1)th, (i�2)th? sub-bands. In order to ensure the highest-frequencysubbands have watermark components to resistthe HF image processing, we should embed thewatermark into the highest-frequency subbands atbeginning.

2.3. Characteristic analysis of DFB for

watermarking embedding

In 1992, Bamberger and Smith [11] constructed a2-D DFB that can be maximally decimated whileachieving perfect reconstruction. The DFB is effi-ciently implemented via an s-level binary tree decom-position that leads to 2s subbands with wedge-shapedfrequency partitioning. In [12], Do and Vetterliproposed a new construction for the DFB that avoidsmodulating the input image and has a simpler rule forexpanding the decomposition tree. The simplifiedDFB is intuitively constructed from two buildingblocks shown in Fig. 5. The first building block is atwo-channel quincunx FB with fan filters that dividesa 2-D spectrum into two directions: horizontal andvertical. The second building block of the DFB is ashearing operator, which amounts to just reorderingof image samples [9].

We desire that the visual quality of the image isnot declined after the watermark is embedded intothe image. The sensitivity of human eyes varies withthe direction. Based on the property of human eyes,the strength of watermark to be embedded shouldbe different in different directions (i.e. the differentdirection subbands). The direction subbands can beacquired easily by implementing the DFB ofcontourlet. By the DFB, the HF subbands outputby the LP can be decomposed into 2s directionalsubbands. It is more favorable for the imageanalysis and the watermarking embedment com-pared with three direction subbands by wavelet.

3. Contourlet-based image adaptive watermarking

(CIAW) scheme

The watermark W to be embedded can bearranged as a set of matrices Ws,d(i, j) with the sizeMW�NW and the pseudo-random binary values{�1, 1}. The indices s and d indicate the scale andthe direction of contourlet subband being embeddedby watermark, respectively. Embedding watermarkinto the contourlet subbands of an image isaccomplished according to

C0s;dði; jÞ ¼ Cs;dði; jÞ þ aMs;d ði; jÞW s;dði; jÞ, (1)

where Cs,d(i, j) and C0s,d(i, j) are the originalcontourlet coefficient and the watermarked con-tourlet coefficient at a resolution scale s andfrequency direction d, respectively. Here, se{0, 1,2?S}, in which S is the coarsest resolution scale,and de{1, 2, 3, 4}, illustrated as Fig. 2(b). The factora is a strength control parameter, and Ms,d(i, j) is awatermark visual mask used to adapt the level ofwatermark strength and the invisibility according tothe local characteristics of the image for a givenresolution scale and frequency direction. In addi-tion, we define the size of images to be watermarkedas M�N.

3.1. Watermark visual mask

To adapt the watermark to the local properties ofthe image, we incorporate the perceptual weighting

ARTICLE IN PRESSH. Song et al. / Signal Processing: Image Communication 23 (2008) 162–178168

in [6] and the quantization model based on the HVS[13] into the calculation of the watermark visualmask for the given image in contourlet domain. Theperceptual sensitivity to noise and brightness varia-tions as well as the presence of significant imagefeatures (textures and edges) are taken into con-sideration in this method. For a given resolutionscale s and frequency direction d of the contourletrepresentation, Ms,d(i, j) is created as

Ms;dði; jÞ ¼ Ys;dLsði; jÞs;d ði; jÞ0:2. (2)

Here

Ys;d ¼1 if d ¼ 1; 3ffiffiffi2p

if d ¼ 1; 4

( )�

1:00 if s ¼ 0

0:32 if s ¼ 1

0:16 if s ¼ 2

0:10 if s ¼ 3

8>>><>>>:

9>>>=>>>;,

(3)

Lsði; jÞ ¼ 1:5þ 0:5j � Lsði; jÞ�� (4)

and

Xs;dði; jÞ ¼XS�s

k¼1

1

16k

X1x¼0

X1y�0

Csþk;di

2k

� �þ x;

i

2k

� �þ y

� ��

� Var Csi

23�s

� �þ x;

i

23�s

� �þ y

� � �x¼0;1y¼0;1

.

(5)

In (4)

Lsði; jÞ ¼1

256Cs

i

23�s

� �;

j

23�s

� �� . (6)

Human eye is less sensitive to noise in high-resolution subbands and the subbands havingorientation of 301 (subband 2) and 601 (subband4). Both of these effects are considered in Ys,d. Ls

takes the local brightness of the low-pass version ofthe image into account. Xs,d measures the textureactivity in the neighborhood of the given pixel.

The HF subbands are all decomposed into threedirection subbands (HL, LH, and HH) by waveletin [6,13]. In contrast, each HF subband is decom-posed into four direction subbands by the DFB inour CIAW scheme. There are the different subbandstructure between wavelet and contourlet. There-fore, we modified (4) in [6] into the first term givenby (3) in order to adapt to the subband structure ofcontourlet. It is noticeable that the last term givenby (5) is different from (8) in [6] when calculatingVar. In [6], the top-left corner of the current 2� 2square is oriented at 1þ i=23�s

� ; 1þ j=23�s

� � �

when calculating Var at (i, j). However, we orientthe top-left corner of the current 2� 2 square at

i=23�s�

; j=23�s� � �

Our term can orient fathercoefficients more precisely than the correspondingterm in [6].

3.2. The watermark detection algorithm for CIAW

The conventional watermark detection algo-rithms, such as that proposed in [6], only calculatethe correlation of the watermark and the water-marked wavelet subbands. Thus, these algorithmscannot work well in our watermark scheme, wherethe watermark is likely to be spread out into allsubbands. The experiment in Section 4 proves ourstatement. We therefore propose a new watermarkdetection algorithm for CIAW. The new watermarkdetection algorithm is based on the comparison of acorrelation value R to a threshold T. The value R isan average measure of the correlation between allcontourlet subbands of spread watermark and thecorresponding contourlet subbands of a givenimage. Here, we define the spread watermark asthe contourlet representation with regard to thewatermark. It can be constructed by embedding thegenuine watermark into the largest detail subbandsof a zero-coefficients image (the contourlet coeffi-cients of the zero-coefficients image are all zeros).

Contourlet coefficients of the spread watermarkcan be created by

CWs;dði; jÞ ¼W s;dði; jÞ; s ¼ 0;

0; otherwise:

((7)

Subsequently, the correlation value R is calcu-lated by

R ¼2ffiffiffi2p

TOT

XS

s¼0

X4d¼1

XMi¼1

XN

j¼1

C00s;d ði; jÞCW0s;d ði; jÞ: (8)

Here C00s,d(i, j) might be either the original or theattacked version of the watermarked image. CW0s,dis the contourlet representation of the imagereconstructed from CWs,d, CW

0s,d, and CWs,d might

be different from each other due to the spreadingeffect in special transforming of LP as analyzed inSection 2.2. The relationship between CW0s,d andCWs,d is described as

CW0 ¼ CTðICTðCWÞÞ. (9)

Moreover, TOT is the number of all contourletcoefficients of the given image, and can be


calculated by

TOT ¼ 1þXS

s¼1

1

4

� �s" #

MN, (10)

where M and N are the height and the width of theoriginal image, respectively.

Fig. 6. Comparison between original images (left) and their correspond

and the watermarked image with PSNR ¼ 36.65 dB. (b) The orig

PSNR ¼ 35.25 dB. (c) The original image of ‘‘Peppers’’ and the waterm

In (8), the coefficients of all scales have beenexploited since the watermark may propagateinto the high scales (the LF subbands) due tothe spreading effect of LP. Note that in contrast, theWT does not have the spreading effect and thewatermarked wavelet subbands contain all water-mark information, so calculating the correlation

ing watermarked images (right). (a) The original image of ‘‘Lena’’

inal image of ‘‘Barbara’’ and the watermarked image with

arked image with PSNR ¼ 34.98 dB.

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Fig. 7. Difference images between the watermarked images and

their corresponding original images: (a) ‘‘Lena’’, (b) ‘‘Barbara’’,

and (c) ‘‘Peppers’’.


between the watermark and the attacked image inthe highest-frequency subbands is sufficient todetect the watermark.

The threshold T depends on the variance of thecontourlet coefficients of the watermarked imageand can be calculated according to

T ¼1

100TOT

XS

s¼0

X4d¼1

XMi¼1

XN

j¼1

C00s;d ði; jÞ2: (11)

3.3. Analysis of spreading effect and robustness

By analyzing the characteristic of contourlet, wefound that the LP spreads the watermark to otherbands, and it is more difficult to control. Thespreading effect and the robustness are affected bymany factors such as the property of the embeddedwatermark, the content of the original image andthe filter characteristic of the CT. Here, we analyzethe relationship among them simply.

Based on the analysis in Section 2.2, we knowthat only if rw is orthogonal with H, i.e. thedifference of rw and r is orthogonal with H,H(rw)would be a zero matrix when r is changed torw randomly. In our CIAW scheme, the differenceof rw and r is the embedded watermark, H(rw) ¼ 0

shows the spreading effect does not happen. There-fore, the above condition can be rewritten as onlywhen the embedded watermark is orthogonal withH, the LP does not spread the embedded watermark

Table 1

Experimental results of watermarking detection

Image Lena Barbara Peppers

Strength factor a 0.04 0.04 0.04

PSNR (dB) 36.65 35.25 34.98

Threshold T 1.68 6.67 2.41

R 22.08 28.62 27.53

R0 0.63 1.06 0.85

Table 2

Detecting results when the watermarked image ‘‘Lena’’ is

attacked by various low-pass filtering

Low-pass filtering Threshold T R R0

Median filtering 3� 3 0.90 6.69 0.47

Median filtering 5� 5 0.62 2.16 0.40

Gaussian filtering 3� 3 1.05 14.53 0.17

Gaussian filtering 5� 5 1.05 14.50 0.23

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Fig. 8. The compressed watermarked image of ‘‘Lena’’ by JPEG

with quality factor 5.

Table 3

Detecting results when the watermarked image ‘‘Lena’’ is

attacked by JPEG and SPIHT compressions

Compression algorithm Threshold T R R0

JPEG 75 1.53 12.27 0.63

JPEG 50 1.38 8.70 0.55

SPIHT 0.2 bpp 0.89 3.23 0.13

SPIHT 0.1 bpp 0.62 1.36 0.08


into the other subbands. But the randomicity of theembedded watermark make the above conditiondifficult to exist. Further, the watermark is strength-ened by the watermark visual mask before embed-ding watermark. The watermark visual mask iscalculated based on the content of the originalimage. In conclusion, how much the watermarkingcomponents spread into the other subbands areaffected by the property of the embedded water-mark, the content of the original image and the filtercharacteristic of the CT. In our CIAW scheme, weembed the watermark into the highest-frequencysubbands. When the watermarking components arespread into the lower-frequency subbands by thespreading effect, the robustness of the CIAWscheme is enhanced. It is easy to understand thatthe more watermarking components are spread, thestronger the robustness of our CIAW scheme is.

4. Experimental results

To validate the invisibility and the robustness ofthe CIAW scheme, we conducted the experimentson the different images (‘‘Lena’’, ‘‘Barbara’’, and‘‘Peppers’’ images of size 512� 512) and simulatedsome image processing operations, which mayremove the inserted watermark. The 5/3 bi-ortho-gonal filters are used for both the multiresolutionpyramidal filtering and the directional decomposi-tion. Firstly, we transform the image into contourletrepresentation with S ¼ 3. Subsequently, we embedthe watermark into four largest detail subbands byadjusting their strength based on the calculatedwatermark visual mask.

It is deemed that the watermark at the HFsubbands of an image is sensitive to many imageprocessing methods such as low-pass filtering, lossycompression, noise, and geometrical distortion. Onthe other hand, the watermark at LF subbands ofan image is sensitive to other image processingmethods such as gamma correction, histogramequalization, and cropping. We attempt to checkthe robustness of our watermarking scheme and thevalidity of our detection algorithm for both the HFand the LF signal processing.

4.1. Invisibility of watermark

Fig. 6 gives the comparison between originalimages and their corresponding watermarkedimages. The watermark invisibility can be guaran-teed by our scheme at the PSNR values of around

35 dB for all three test images. Fig. 7 shows theabsolute difference between the watermarkedimages and their original images, where the water-mark tends to appreciate the regions with strongedges and extreme brightness.

4.2. Validity of watermark detection algorithm

For the evaluation of the performance of theproposed watermark detection algorithm, we collectits responses to 1000 different watermarks includingthe genuine (embedded) one. The experimentalresults of one correct detection (for the genuinewatermark) and 999 false detections (for all otherfake watermarks) demonstrate the high effectivenessof our detection algorithm to recognize the genuinewatermark. Table 1 shows the experimental results

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0 100 200 300 400 500 600 700 800 900 1000-1

-0.5

0

0.5

1

1.5

2

2.5

Watermark

Det

ectin

g R

espo

nse

Detecting ResponseThreshold

Fig. 9. The detecting responses of ‘‘Lena’’ attacked by JPEG compression with quality factor 5 for 999 randomly generated watermarks

and the embedded one. Only the detecting response of the genuine watermark (no. 500) is higher than threshold.

0 100 200 300 400 500 600 700 800 900 1000-5

0

5

10

15

20

25

Watermark

Det

ectin

g R

espo

nse


Fig. 10. The detecting responses of ‘‘Lena’’ attacked by ‘Gaussian’ noise with zero mean and 0.01 variance for 999 randomly generated

watermarks and the embedded one. Only the detecting response of the genuine watermark (no. 500) is higher than threshold.



of watermarking detection. Here, R is the detectingresponse to the embedded one and R0 is the highestdetecting response to 999 fake watermarks. More-over, these results demonstrate the validity of aposteriori threshold calculated based on (11) asshown in Table 1.

The watermark at HF subbands of an image issensitive to many image processing methods such aslow-pass filtering, lossy compression, noise, andgeometrical distortion. On the other hand, thewatermark at LF subbands of an image is sensitiveto other image processing methods such as gammacorrection, histogram equalization, and cropping.In this paper, we prove the robustness of ourwatermarking scheme and the validity of ourdetection algorithm for both the HF signal proces-sing and the LF signal processing.

4.3. Robustness to low-pass filtering

To assess the robustness of our watermarkingscheme to low-pass filters, median filtering, andGaussian filtering with 3� 3 and 5� 5 window size,respectively, are used to attack the watermarkedimages. A total of 1000 different watermarksincluding the genuine one are tested. Table 2 showsthe experimental results of ‘‘Lena’’. In all cases, the

0 100 200 300 400 5-5

0

5

10

15

20

25

Wate

Det

ectin

g R

espo

nse

Fig. 11. The detecting responses of ‘‘Lena’’ attacked by ‘Salt and Pe

watermarks and the embedded one. Only the detecting response of the

genuine watermark can be detected successfully,consequently demonstrating an excellent robustnessof our watermarking scheme and a high validity ofour detection algorithm.

4.4. Robustness to JPEG and SPIHT compressions

JPEG compression with quality factor 75, 50, and5, and SPIHT compression with the compressionrates 0.2 and 0.1 bpp were applied on the water-marked images to evaluate robustness of ourwatermarking scheme and the validity of detectionalgorithm (Fig. 8). A total of 1000 different water-marks including the genuine one are tested. Table 3gives the detecting results when the watermarkedimage ‘‘Lena’’ is attacked by JPEG and SPIHTcompressions. Fig. 9 illustrates that when thequality factor of JPEG compression is 5 (i.e. thecompression ratio is very high, shown is Fig. 8), ourdetection algorithm still can judge the genuinewatermark successfully.

4.5. Robustness to ‘Gaussian’ and ‘Salt and Pepper’

noises

It is very possible that the image is disturbed byvarious noises when it is transmitted on the internet.

00 600 700 800 900 1000

rmark


pper’ noise with 0.01 noise density for 999 randomly generated

genuine watermark (no. 500) is higher than threshold.


Fig. 10 shows the detecting responses of ‘‘Lena’’attacked by ‘Gaussian’ noise with zero mean-valueand 0.01 variance. Fig. 11 shows the detectingresponses of ‘‘Lena’’ attacked by ‘Salt and Pepper’noise with 0.01 noise density. Both are commonnoises in internet transmission. Experimental resultsdemonstrate the robustness of our watermarkingscheme and the validity of detection algorithmagain.

4.6. Robustness to affine transform and rotation

We attack the watermarked images using affinetransform and rotation. Fig. 12 shows the affinedimage with a StirMark test function [14]: line-ar_1.010_0.013_0.009_1.011 and rotated image of

Fig. 12. The attacked watermarked image of ‘‘Lena’’: (a) the

affined image with linear_1.010_0.013_0.009_1.011 and (b) the

rotated image of ‘‘Lena’’ with angle 0.51.

‘‘Lena’’ with angle 0.51, respectively. Figs. 13 and14give the detecting responses to them, whichannounce the success of our watermarking schemeand detection algorithm.

4.7. Robustness to gamma correction

We process the watermarked images usinggamma correction. Fig. 15 gives the detectingresponses of ‘‘Lena’’, which announces the successof our watermarking scheme and detection algo-rithm again.

4.8. Robustness to histogram equalization

We process the watermarked images usinghistogram equalization. Fig. 16 gives the detectingresponses of ‘‘Lena’’. In all cases, the genuinewatermark can be detected successfully, conse-quently demonstrating an excellent robustness ofour watermarking scheme and a high validity of ourdetection algorithm.

4.9. Robustness to cropping

We process the watermarked images by cropping.Fig. 17 gives the detecting responses of ‘‘Lena’’.Here, the cropped portion with size 128� 128 istested. It proves the excellent robustness of ourwatermarking scheme and the high validity of ourdetection algorithm again.

4.10. Comparison

In the last experiment, we adopt the water-marking scheme in [6] to detect the existence ofthe embedded watermark. The above various imageattacks is implemented to test the robustness of thewatermarking scheme in [6]. The comparison ofexperimental results between the watermarkingscheme in [6] and our watermarking scheme areshown in Table 4. When the watermarked image‘‘Lena’’ is compressed by JPEG with the qualityfactor 5 and SPIHT with the compression rate0.1 bpp, the detection algorithm in [6] cannot detectthe embedded watermark successfully. The detec-tion result is shown in Table 5. In contrast, thewatermarking components are included at the LFsubbands due to the spreading effect of the LP inour CIAW scheme. Consequently, the proposedalgorithm can detect the embedded watermarksuccessfully in the same condition. The experimental

ARTICLE IN PRESS

0 100 200 300 400 500 600 700 800 900 1000-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Watermark

Det

ectin

g R

espo

nse


Fig. 13. The detecting responses of ‘‘Lena’’ attacked by affine transform with a StirMark test function: linear_1.010_0.013_0.009_1.011

for 999 randomly generated watermarks and the embedded one. Only the detecting response of the genuine watermark (no. 500) is higher

than threshold.

0 100 200 300 400 500 600 700 800 900 1000-0.5

0

0.5

1

1.5

2

2.5

Watermark

Det

ectin

g R

espo

nse


Fig. 14. The detecting responses of ‘‘Lena’’ attacked by rotation with angle 0.51 for 999 randomly generated watermarks and the

embedded one. Only the detecting response of the genuine watermark (no. 500) is higher than threshold.


ARTICLE IN PRESS

0 100 200 300 400 500 600 700 800 900 1000-5

0

5

10

15

20

Watermark

Det

ectin

g R

espo

nse


Fig. 15. The detecting responses of ‘‘Lena’’ processed by gamma correction for 999 randomly generated watermarks and the embedded

one. Only the detecting response of the genuine watermark (no. 500) is higher than threshold.

0 100 200 300 400 500 600 700 800 900 1000-5

0

5

10

15

20

25

30

35

Watermark

Det

ectin

g R

espo

nse


Fig. 16. The detecting responses of ‘‘Lena’’ processed by histogram equalization for 999 randomly generated watermarks and the

embedded one. Only the detecting response of the genuine watermark (no. 500) is higher than threshold.


ARTICLE IN PRESS

0 100 200 300 400 500 600 700 800 900 1000-1

-0.5

0

0.5

1

1.5

2

Watermark

Det

ectin

g R

espo

nse


Fig. 17. The detecting responses of ‘‘Lena’’ processed by cropping for 999 randomly generated watermarks and the embedded one. Only

the detecting response of the genuine watermark (no. 500) is higher than threshold.

Table 4

The comparison of experimental results between the watermark

detection algorithm in [6] and our detection algorithm

Attack Success?

The watermarking

scheme in [6]

Our watermarking

scheme

Median filter

3� 3

Yes Yes

Median filter

5� 5

Yes Yes

Gaussian filter

3� 3

Yes Yes

Gaussian filter

5� 5

Yes Yes

JPEG 75 Yes Yes

JPEG 50 Yes Yes

JPEG 5 No Yes

SPIHT 0.2 Yes Yes

SPIHT 0.1 No Yes

‘Gaussian’ noise Yes Yes

‘Salt and Pepper’

noise

Yes Yes

Affine transform Yes Yes

Rotation Yes Yes

Gamma

correction

Yes Yes

Histogram

equalization

Yes Yes

Cropping Yes Yes

Table 5

The comparison of detecting results when the watermarked image

‘‘Lena’’ is attacked by JPEG and SPIHT compressions

Compression

algorithm

The watermarking

scheme in [6]

Our watermarking

scheme

Threshold T R Threshold T R

JPEG 5 0.033 0.018 1.36 2.40

SPIHT

0.1 bpp

0.025 0.018 0.62 1.36


results confirm the validity of our proposed water-marking scheme again.

5. Conclusion

We have proposed the new watermarking scheme,namely CIAW, which enjoys both the invisibilityand the robustness. Correspondingly, a new water-mark detection algorithm has been proposed for theCIAW by fully exploiting the characteristic of CT,which can detect the watermark efficiently from thewatermarked image under severe attacks. Experi-mental results have shown that the proposed schemeis very robust to common attacks such as low-passfiltering, compression, noise, affine, and rotation.


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