A robust logo watermarking technique in divisive normalization transform domain

A robust logo watermarking technique in divisivenormalization transform domain

Punit Pandey & Shishir Kumar & Satish K. Singh

Published online: 5 July 2013# Springer Science+Business Media New York 2013

Abstract In this paper, a novel imagewatermarking scheme has been presented, which is based onDivisive Normalization Transform, Discrete Wavelet Transform and Singular Value Decomposi-tion. Through this paper an attempt has been made to solve the problem of statically andperceptually redundant wavelet coefficients, used during watermarking with the help of divisivenormalization transform while maintaining the robustness and imperceptibility. Divisive Normali-zation Transform is an adaptive nonlinear image illustration in which all linear transform coefficientare divided by a weighted sum of coefficient amplitudes in a generalized neighbourhood. The ideaof embedding thewatermark image into singular values of divisively normalized coefficients of hostimage has been exploited. The proposed algorithm is providing the perceptually better-qualitywatermarked image and at the same time maintaining the robustness of watermarked algorithm.Thus the proposed watermarking algorithm is a semi-blind, image adaptive due to use of divisivenormalization transform and suitable for rightful ownership. Various comparative results make thealgorithm superior in terms of intentional and non-intentional attacks.

Keywords Singular Value Decomposition . Discrete wavelet transform . Divisivenormalization transform . Nonlinear image transformation

1 Introduction

Rapid expansions of the web technologies and coupled services have been amplified significantlyleads to the problem of rightful ownership and associated copyright to be protected. This has lead toa new opportunity in developing new copy prevention and enrichment mechanisms giving thedigital watermarking as an obvious solution [10, 11, 16]. Digital watermarks could have a widerange of applications in the sectors like broadcast monitoring, content authentication, owner

Multimed Tools Appl (2014) 72:2653–2677DOI 10.1007/s11042-013-1577-7

P. Pandey : S. Kumar (*)Department of CSE, Jaypee University of Engineering & Technology, Guna 473226, Indiae-mail: [email protected]

P. Pandeye-mail: [email protected]

S. K. SinghDepartment of ECE, Jaypee University of Engineering and Technology, Guna 473226, India

S. K. Singhe-mail: [email protected]

identification, defense and intelligence [30, 31]. Digital watermarking is the practice of embeddinguseful information into digital image considering the fact that embedding must be ended in such away so that, perceptual degradation is nil and at the same time non-removable by illegal parties [16].All the reportedwatermarking algorithms can be generally separated into two groups namely spatialand transform-domain. The spatial domain watermarking algorithms directly modify the pixelvalues of the host image while the transformed domain coefficients of the host images have beenmodified to embed the watermarks in transform domain routines. Unfortunately the reportedwatermarking algorithms experience from a wide range of malicious and non-malicious attacks.Spatial domain algorithms are easier to implement, however not robust, while the transformdomain techniques are relatively more reliable and robust to various attacks. The frequencydomain algorithms are resistant to filtering and compressions attacks and are generally, rotation,translation and scale invariant. Discrete Cosine Transform (DCT) [3, 8, 29] and DiscreteWavelet Transform (DWT) [2, 4, 14, 28, 29] have commonly used frequency domain tech-niques. The watermark can be embedded in various sub-bands (either low frequency or highones) after wavelet decomposition of host and/or watermark image. Watermarks inserted in thelow frequencies are robust against the attack having low pass characteristics e.g. filtering, lossycompression, and geometric distortions in contrast to high frequency embedding which isrobust to attack having high pass response like histogram equalization, gamma correction andbrightness adjustments [7].

Recently Singular Value Decomposition (SVD), a new transform for watermarking has beenintroduced and the first algorithm has been proposed by Liu et al. [23] in 2002. The main feature ofSVD-based image watermarking is the stability of singular values, which contain most of the imageenergy. In this algorithm the singular values of the host image are modified by directly adding thegray scale watermark image of the same size as of host image. SVD was again applied to theresultant matrix for finding the modified singular values. These modified singular values werecombined with the known component to get the watermarked image. Similarly for the watermarkextraction inverse process was adopted. Lai et al. [9] suggested a hybrid DWT-SVD watermarkingprocedure in which two halves of the watermark image is embedded into the two singular valuematrices of intermediate frequency sub-bands obtained while taking one level DWTof host image.After embedding the watermark, the two halves are combined to get the watermarked image. At thetime of the extraction reverse procedure is adopted to get the extracted watermark image. Thisparticular watermarking technique has shown the significant improvement over the other parallelwatermarking approaches in terms of imperceptibility and robustness under an assortment ofattacks. Lin et al. [20–22] have been proposed a blind watermarking algorithm by applying theconcept of wavelet coefficient quantization for copyright protection. In this scheme watermark hasbeen embedded into the local maximum wavelet coefficient of host image. Bhatnagar et al. [18]have proposed a new robust reference watermarking scheme based on DWT-SVD in which theoriginal image is transformed into wavelet domain. In this scheme authors have used a directcontrast of wavelet coefficients and to form a reference sub-image. Furthermore, reference imagehas been used to embed the watermark by modifying the singular values of reference image usingthe singular values of the watermark. Bhatnagar et. al. 2012 [6] have proposed a robust grayscalelogo watermarking in wavelet domain. In this scheme logo watermark has been embedded in therobust blocks of wavelet sub-bands obtained by non-overlapping segmentation using ZIG-ZIGsequence and the variance statistic. Bhatnagar et al. 2012 [16] have proposed a novel and robustlogo watermarking scheme for image authentication in context of fractional wavelet packettransform and singular value decomposition domain. Through this proposed watermarking methodauthors have provided the opportunity for user to constructing a watermarked image by using twoembedding strength value. Reddy et al. 2005 [1] have proposed a DWT based grayscale logowatermarking scheme in which watermark information has been embedded into the coefficients

2654 Multimed Tools Appl (2014) 72:2653–2677

elected on the basis of weight factors calculated by exploiting the HVS characteristics. Thisparticular scheme is pretty reliable for watermark extraction and at the same time robust againstdifferent types of image processing attacks.

It is a well known fact that discrete wavelet transform suffers from higher-order staticaldependencies between coefficients at nearby locations, orientations and scales [25, 27]. TheDWT-SVD based watermarking and its variations which have been reported through literature [1,2, 4, 6, 9, 12–14, 16, 17, 21–24, 28, 32]mainly deals with robustness and impeccability issueswhileoverlooking the problem of perceptual redundancy in wavelet coefficients. Recently there has beena notable corresponding expansion of transformations that reduce either statistical or perceptualredundancy, intiated with frequency-based representations, to local frequency or wavelet basedrepresentations, to most recent rationalization of divisively normalized transformations. DivisiveNormalization Transform (DNT) [19, 25–27] is a nonlinear transformation, aggravated by thestatistical properties of an image and the human visual system. The divisive normalize transforma-tion is a combination of a linear transform followed by a divisive normalization procedure, in whicheach linear transform coefficient is divided by a normalization factor. Divisive NormalizationTransform is an obvious solution to the statistical dependence of the coefficients in traditionaltransform coding. Recently a diversity of methods named as Independent Components Analysis(ICA), have been proposed to utilize higher-order statistics for the purpose of achieving a uniquelinear transform coefficient [19, 27]. Even though the use of ICA does not provide statisticallyindependent coefficients of an image and that included the use of divisive normalization transform.

Through this paper a novel attempt has been made to propose a watermarking scheme indivisive normalization transform (DNT) domain. The main idea is to remove the statisticalredundancies between wavelet coefficients of host image and provide the perceptual per-fection to the watermarked image by using divisive normalization transform. The proposedapproach is a hybrid one and based on DWT-DNT-SVD based image watermarking algo-rithm. The divisive normalization transforms coefficients of intermediate frequency sub-bands of host image have been used to embed a logo watermark. First the host image istransformed into discrete wavelet transform domain and then corresponding divisive nor-malization transform coefficients has been computed. Furthermore, SVD is applied to DNTcoefficients of intermediate frequency sub-bands of host image. Finally a logo watermarkhas been embedded into singular values of DNT coefficients. The proposed watermarkingalgorithm is perceptually preeminent because of the use of divisive normalization transformand its capability to reduction in statistical redundancies between wavelet coefficients.

Towards further organization, Section 2 gives the concise overview of the SVD, DWTand DNT. The proposed watermarking embedding and extraction algorithm has beenelaborated in section 3. Various experiments have been performed to make obvious robust-ness and reliability of the proposed algorithm in section 4. Section 4 also provides thegraphical representation of comparative performance analysis on the basis of robustness andimperceptibility among various existing routines. Various discussions about the obtainedresults and associated conclusion have been accounted in section 5.

2 Preliminaries of DWT, SVD and DNT

2.1 Discrete wavelet transform

In recent times DWT has established considerable attention in various signal processingapplications, including image watermarking because of its capability to supply sufficientinformation for analysis and synthesis of the original image signal, with a major diminution

Multimed Tools Appl (2014) 72:2653–2677 2655

in the required computation time. The wavelet transform decomposes the image into threespatial directions, i.e. horizontal, vertical and diagonal and reflect the anisotropic propertiesof Human Visual System (HVS) [10, 11, 17, 29]. Wavelet transforms use wavelet filters totransform the image, i.e. Haar Wavelet Filter, Daubechies Orthogonal Filters and DaubechiesBi-Orthogonal Filters. All of these mentioned filters decompose the image into severalfrequencies. Single level decomposition gives four frequency representations of the imagescalled as LL, LH, HL and HH sub-bands. The watermark can be embedded in a variety of sub-bands (either low frequency, mid frequency and high frequency) after wavelet decomposition ofhost and/or watermark image. The sizes of all sub-bands are reduced as the decomposition levelis increased. It may be observed that in DWT as well as decomposition level increases, thehuman visual system (HVS) characteristic is highly sensitive to embedded watermark. DWT iscomposed of DWT analysis and DWT synthesis in combination with low pass and high passfilters. If suppose A as an image matrix then DWT analysis can be expressed as

A xð Þ ilowpass ¼ A xð Þiþ1*lowpass −x½ ��

↓2

A xð Þ ihighpass ¼ A xð Þiþ1*highpass −x½ ��

↓2

Where * and ↓ has been used for convolution and down sampling respectively. DWTsynthesis can be expressed as

A xð Þiþ1 ¼ A xð Þ ilowpass ↑ 2Þ*lowpass x½ �� þ A xð Þ i

highpass ↑ 2Þ*highpass x½ �� Watermarks inserted in low frequency sub-bands are robust against various types of image

processing attacks but at the same time it compromises with the perceptual quality of image. Ifmid frequency sub-bands (LH and HL) of host image are used to embed the watermark then theperceptual quality of embedded watermarked is superior as well as robust against a wide rangeof attacks. Despite of its frequency localization properties, DWTsuffers from various problemssuch as shift variant causes a momentous change in the wavelet coefficients. This particularphenomenon occurs due to down sampling after each level of filtering.Wavelet coefficients alsosuffer from the problem of statical redundancy that exists in all sub bands.

2.2 Singular value decomposition

In image processing an image can be observed as a matrix with nonnegative scalar entries. SVDis an effective mathematical tool from linear algebra to decompose a rectangular matrix “A”into an orthogonal matrix U, diagonal matrix S, and the transpose of an orthogonal matrix V [2,5, 6, 8, 9, 12–16, 18, 23, 28, 29, 32]. SVD decomposes a given image A of size M × N as

A ¼ USVT

A ¼u1;1 … u1;mu2;1; ⋯ ; u2;m⋮ ⋱ ⋮um;1; ⋯ um;m;

2664

3775

σ1;1 0 00; σ2;2 ; 0⋮ ⋱ ⋮0; ⋯ σm;n;

2664

3775

v1;1 … v1;nv2;1; ⋯ ; v2;n⋮ ⋱ ⋮vn;1; ⋯ vn;n;

2664

3775T

ð1Þ

U andVare orthogonal matrices of sizeM×MandN ×N, respectively. S is a diagonal matrixof size M × N having singular values and satisfy the property σ1,1 > σ2,2 > σ3,3 >……… > σm,n.

It is well known fact that, the singular vectors of an image signify the image “geometry”and at the same time left singular vectors represent horizontal details, right singular vectorsrepresent the vertical details of an image, while the singular values denote the “luminance”(energy) of the image. Slight deviations in the singular values of an image do not affect the


visual sensitivity of the eminence of the image. Because of this property, It permits embeddingtheWatermark bits in the original image throughminor modification of the singular values of theoriginal image. Singular Value Decomposition reveals the properties of transpose, flip, rotation,scale and translation invariance, which are common geometric distortion attacks. These geo-metric invariance natures make SVD a very encouraging tool for digital image watermarking.

2.3 Divisive normalization transformation

Divisive Normalization Transform (DNT) [19, 25–27] is an invertible non linear imagetransformation technique endowwith a better perceptual sensitivity of the human visual system.Divisive Normalization Transform has been defined as a flow of two transformation stages

Image xi; y j� �h i

→linear transform→ A xi; y j� �h i

→DivisiveNormalizationTransform→ DNT x; yð Þ½ �

In Divisive Normalization Transform each coefficient of linear transform is modified withsome normalization parameter. Here in this paper wavelet transform has been considered as alinear transformation stage, owing its ability to present enough information for analysis andfusion of the original signal. Suppose if A is a matrix that represents the low frequencycomponent of wavelet transform then a divisive normalized coefficient may be considered asA1 = A/n where n is a divisive normalization factor [19].

Divisive normalization factor n is energy of cluster coefficient that is close to the originalwavelet coefficient matrix A in space, range and direction. DNT representation of an imagehas been utilized extensively because of its diminution in statistical redundancies betweenwavelet coefficients and high significance to biological vision.

There are numerous approaches subsisting to compute divisive normalization factor andthe majority of them employed a weighted sum of squared neighboring coefficients byadding some positive constant. In this paper a global model of Markov random field over thewavelet coefficient is considered to calculate the divisive normalization factor.

The conditional mean and variance of A matrix may be defined as

μi ¼X

j∈N ið ÞajA j

σ2i ¼ bþ

Xj∈N ið Þ c j A j − μ j

� �2

It can be identified from the above equations that conditional mean of wavelet coefficient is inlinear form to its neighboring coefficients, and at the same time the conditional variance is alsolinear of mean-adjusted squares of neighboring coefficients, plus a constant b. The parameters{aj, cj, b} are same for each neighborhood coefficient, apart from the absolute spatial position orscale. Furthermore, Divisive Normalization Transform [25, 26] may be defined as

DNTi ¼ Ai−μ½ �ffiffiffiffiffiσ2

p ð2Þ

DNTi ¼Ai−

Xj∈N ið ÞajA j ið Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

bþX

j∈N ið Þc j A j −X

k∈N jð ÞakAj

� �2r ð3Þ

Figure 1a shows a wavelet horizontal details of Lena image whereas (b) represent thecorresponding DNTcoefficients. It can be identified from Fig. 1c and d that DNT representationhas subsidiary distribution closer to the Gaussian than that of original wavelet coefficients. We


can easily outline that DNT coefficients are more homogenous and Gaussian nature rather thanits wavelet coefficients.

Like any other linear transformation, Divisive Normalization Transformation of an image alsorequired a method to recover the original image. The original image can be recovered by storingthe value of mean and variance of the original image matrix but at the same time it boosts thecomplexity of the system. To describe the iterative procedure of Divisive Normalization Trans-formation image matrix A = (A1, A2…….AN)

T and corresponding DNT coefficients DNTc =(DNTc1, DNTc2…….DNTcN)

T have been considered in vector form. Furthermore, b is convertedinto N-dimensional vector whose elements are all equal to parameter b used in Eq. 3 whereas Dand C represents the matrices that compute sums over the neighborhoods using weights aj and cj.The iterative procedure of Divisive Normalization Transformation may be explained asbelow

y ¼ IN −Dð ÞAz ¼ y21; y

22; y

23;………:y 2

N

� �r ¼ z⊘ bþ C zð Þ

DNTc ¼ sign y1ð Þ ffiffiffiffir1

p;…………::; sign yNð Þ ffiffiffiffiffi

rNp½ � T

ð4Þ

Where y, z, r are intermediate variables, IN represents the NxN dimension identity matrixand ⊘ indicates the element wise division operator. Now we can reverse the abovementioned steps to get the original vector A.D, C and b are

r ¼ DNTc21;DNTc22;DNTc

23;………:DNTc2N

Tz ¼ IN −Di rð ÞAð Þ−1r

y ¼ sign DNTc1ð Þ ffiffiffiffiz1

p;…………::; sign DNTcNð Þ ffiffiffiffiffiffi

zNp½ �T

A ¼ IN −Dð Þ−1y

ð5Þ

Where Di(r) represents the diagonal elements of r. Divisive Normalization Transforma-tion is an efficient way to reduce the statistical redundancies between wavelet coefficientsand at the same time it is also highly apposite to biological vision. Divisive NormalizationTransform based illustrations of images are also roughly consistent with the nonlinearproperties of human eye neurons and have been shown relevant to human perception. Oneof the main features Divisive Normalization Transform based image representation is thenormalization parameter, used for removal of redundancy between wavelet coefficients andmakes it more homogenous. Divisive Normalization Transform based nonlinear imagerepresentation has been widely used for many image analysis and processing applications,such as image restoration, synthesis, fusion, coding and compression because of its superiorstatistical features and good perceptual properties.

DNT representation of an image based on above mentioned statistical model shows that itcan efficiently reduce the visibility of errors in linear transform coefficients that are nearby inlocation, orientation, or scale. Furthermore, in this paper the perceptual relevance of DNTimage representation and its resilience to noise contagion has also been tested against imagewatermarking.


3 Proposed watermarking scheme

The proposed scheme supports the essentials and interpretation about the various DWT-SVDbased watermarking systems that reflect the resistive behavior to normal signal and imageprocessing attacks but suffers from the perceptual quality of image. It’s a well known factthat the robustness and imperceptibility are conflicting requirements for any proficientwatermarking system. The embedding strength is selected similar or same for the all typesof images, irrespective of the image contents. If the images to be inserted are different thenthey may pose perceptual distortions. Different watermark images will show totally indif-ferent performance in terms of visual transparency and robustness. Through the proposedapproach the wavelet coefficients of host image are modified with help of divisive normaliza-tion transform, hence showing a perceptually better as well as a robust watermarking scheme inthe DWT-SVD domain.

Divisive Normalization Transform has been used during watermarking because its co-efficients are homogenous, statistically independent in comparison to the discrete wavelettransforms and provide superior perceptual quality of watermarked image. In addition to thatSingular Value Decomposition has been used because of its resilience against various imageprocessing attacks. In order to survive with the fact of balancing robustness and imperceptibility,the idea of embedding the watermark image into singular values of DNT coefficients has beenexploited, because of its potential to perceptual relevance. Figures 2 and 3 has been consequentlyused to depict the block diagram of proposed watermark embedding and extraction algorithm.

The DNT coefficients have been extracted by applying the divisive normalization trans-form on wavelet coefficients of host image. The host image has been decomposed by

Fig. 1 a DWTcoefficients bDNTcoefficients cHistogram of DWTcoefficients dHistogram of DNTcoefficients


applying one level DWT to get the LL, LH, HL, HH sub-bands. Let A be the original hostimages then its corresponding DNT coefficients of LH and HL sub bands are given as,

yLH ¼ IN −Dð ÞALH

yHL ¼ IN −Dð ÞAHL

zLH ¼ yLH2

1; yLH

2

2; yLH

2

3;………:yLH

2

N

� �zHL ¼ yHL

2

1; yHL

2

2; yHL

2

3;………:yHL

2

N

� �rLH ¼ zLH⊘ V þ C zLHð ÞrHL ¼ zHL⊘ V þ C zHLð Þ

ADNTLH ¼ sign yLH1ð Þ ffiffiffiffiffiffiffiffiffi

rLH1

p;…………::; sign yLHNð Þ ffiffiffiffiffiffiffiffiffi

rLHN

p TADNT

HL ¼ sign yHL1ð Þ ffiffiffiffiffiffiffiffiffirHL1

p;…………::; sign yHLNð Þ ffiffiffiffiffiffiffiffiffi

rHLN

p TWhere ALH

DNT and AHLDNT are DNT coefficient of corresponding wavelet LH and HL sub

bands. Now the watermark image is embedded with the singular value of DNT coefficient ofLH and HL sub bands to improve perceptual quality of watermarked image. The proposedwatermarking is a semi-blind algorithm because of the requirement of watermarked image aswell as original watermark during extraction.

Fig. 3 Block diagram of proposed watermark extraction scheme

Fig. 2 Block diagram of proposed watermark embedding scheme


3.1 Watermark embedding algorithm

Input [Host Image (A), Watermark Image (W)]

Step 1. Perform 1-level haar wavelet decomposition of the host image Al(i, j) and water-mark image Wl(i, j) where l ∊ {LL, LH, HL, HH}

Fig. 4 a Host image b Watermark

Fig. 5 a Host image b DNT coefficients c Watermark logo d Watermarked DNT coefficients e Watermarkedimage f Extracted watermark


Step 2. The vertical and horizontal details of wavelet coefficients of Al(i, j) have been usedto compute the divisive normalization transform coefficients

ADNTLH ¼ sign yLH1

� � ffiffiffiffiffiffiffiffiffirLH1

p;…………::; sign yLHN

� � ffiffiffiffiffiffiffiffiffirLHN

p TADNT

HL ¼ sign yHL1

� � ffiffiffiffiffiffiffiffiffirHL1

p;…………::; sign yHLN

� � ffiffiffiffiffiffiffiffiffirHLN

p TStep 3. Perform the SVD on DNT coefficients ALH

DNT and AHLDNT of host Image,

ADNTLH i; jð Þ ¼ UDNT

LH i; jð ÞSDNTLH i; jð ÞVDNTT

LH i; jð Þ

ADNTHL i; jð Þ ¼ UDNT

HL i; jð ÞSDNTHL i; jð ÞVDNTT

HL i; jð ÞStep 4. Add the watermark (W) directly into the singular value of the host image sub-bands

(LH, HL).

S*DNTLH i; jð Þ ¼ SDNTLH i; jð Þ þ α*W i; jð ÞS*DNTHL i; jð Þ ¼ SDNTHL i; jð Þ þ α*W i; jð Þ

Where α refers to watermark strength and SLH∗DNT and SHL

∗DNT represents modifiedsingular values of two sub bands LH & HL.

Table 2 Normalized correlation coefficient of extracted watermark from various cover images

Attacks JUET logo (Type1) Y logo JUET logo(Type2)

Lena Barbara Pirate Mandril Flower

Median filter 0.9496 0.8720 0.9683 0.9625 0.9374

Histogram equalization 0.9839 0.9846 0.9211 0.9188 0.9798

Rotation(60) 0.9833 0.9819 0.9891 0.9874 0.9802

Average filter (11×11) 0.7524 0.7180 0.7973 0.8382 0.7665

Contrast adjustment 0.9931 0.9909 0.9898 0.9892 0.9912

Gaussian noise 0.9783 0.9811 0.9133 0.9163 0.9728

JPEG compression (50:1) 0.9704 0.9718 0.9717 0.9791 0.9883

Cropping(1/4) 0.9806 0.8518 0.9828 0.9788 0.9672

Salt & pepper (50 %) 0.9759 0.9768 0.8924 0.9121 0.9612

Speckle 0.9832 0.9827 0.9208 0.9202 0.9811

Zooming 0.9934 0.9841 0.9887 0.9842 0.9742

Oiling 0.9848 0.9926 0.9791 0.9779 0.9868

Shearing 0.9833 0.9818 0.9235 0.9357 0.9774

Slicing 0.8966 0.9110 0.9661 0.9549 0.9187

Spreading 0.9450 0.9506 0.9229 0.9419 0.9571

Swirl 0.9919 0.9873 0.9890 0.9904 0.9834

Table 1 Peak signal to noise ratio(dB) for each host image

Test images Lena Barbara Pirate Mandril Flower

PSNR 62.97 65.42 60.73 66.22 63.83


Step 5. Perform the SVD on SLH∗DNT and SHL

∗DNT to get,

S�DNTLH i; jð Þ ¼ WUDNTLH i; jð ÞWSDNTLH i; jð ÞWVDNTT

LH i; jð Þ

S�DNTHL i; jð Þ ¼ WUDNTHL i; jð ÞWSDNTHL i; jð ÞWVDNTT

HL i; jð ÞStep 6. Compute the watermarked DNT coefficients of horizontal and vertical details as

AWDNTLH i; jð Þ ¼ UDNT

LH i; jð ÞWSDNTLH i; jð ÞVDNTT

LH i; jð Þ

AWDNTHL i; jð Þ ¼ UDNT

HL i; jð ÞWSDNTHL i; jð ÞVDNTT

HL i; jð ÞStep 7. Compute the inverse divisive normalization transform of watermarked DNT co-

efficients by using Eq. 5.Step 8. Carry out the inverse discrete wavelet transform (IDWT) on the modified DNT

coefficients to obtain the watermarked image, Aw

Output [Watermarked Image (Aw)]

Fig. 7 a & c Watermarked Lena and Pirate Image after average filter (11×11) b & d Extracted watermark

Fig. 6 a & c Watermarked Lena and Pirate Image after adding additive Gaussian noise of density 0.1 b & dExtracted watermark


3.2 Watermark extraction algorithm

Input [Distorted Watermarked Image (Aw∗), Watermark Image (W))]

Step1. Perform 1-level discrete wavelet transform (DWT) on the watermarked imageAw

∗(i,j) to get the {LL, LH, HL, HH} sub bandsStep2. Compute possibly modified DNT coefficients by applying divisive normalization

transform on LH and HL wavelet sub bands.

ADNTwLH ¼ sign ywLH1

� � ffiffiffiffiffiffiffiffiffiffiffirwLH1

p;…………::; sign ywLHN

� � ffiffiffiffiffiffiffiffiffiffiffiffirwLHN

p TADNT

wHL ¼ sign ywHL1

� � ffiffiffiffiffiffiffiffiffiffiffirwHL1

p;…………::; sign ywHLN

� � ffiffiffiffiffiffiffiffiffiffiffiffirwHLN

p TStep3. Perform the SVD on DNT coefficients AwLH

DNT and AwHLDNT of watermarked

image,

ADNTwLH i; jð Þ ¼ UDNT

wLH i; jð ÞSDNTwLH i; jð ÞVDNTT

wLH i; jð ÞADNT

wHL i; jð Þ ¼ UDNTwHL i; jð ÞSDNTwHL i; jð ÞVDNTT

wHL i; jð Þ

Fig. 9 a & c Watermarked Lena and Pirate Image after histogram equalization b & d Extracted watermark

Fig. 8 a & c Watermarked Lena and Pirate Image after Median Filtering b & d Extracted watermark


Step4. Extract the watermark by computing

W * i; jð Þ ¼ WUDNTLH i; jð ÞSDNTwLH i; jð ÞWVDNTT

LH i; jð Þ

W * i; jð Þ ¼ WUDNTHL i; jð ÞSDNTwHL i; jð ÞWVDNTT

HL i; jð Þ

4 Results and analysis

4.1 Experimental setup

Through various experiments, attempt has been made to establish the effectiveness of theproposed watermarking algorithms.

We have performed several experiments on grayscale images “Lena” of size 512×512 and“Pirate” of size 512×512 which are used as the cover image. Figure 4a-b has been given to showthe host, watermark images and the capacity of watermark and host image are 512×512 and256×256 respectively. To show the imperceptibility of watermarked image we have used thepeak signal-to-noise ratio (PSNR) [29] given by following equations

PSNR W ;W *� � ¼ 10log10

Lmax

RMSE

� �2

Fig. 11 a & c Watermarked Lena and Pirate Image after adding salt & pepper noise b& d Extracted watermark

Fig. 10 a & c Watermarked Lena and Pirate Image after a 60° rotation b & d Extracted watermark


Where RMSE is the root mean square error defined as

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

i¼1

XM

i¼1X i; jð Þ−X * i; jð Þ� �2

N �M

s

Where X(i, j) and X*(i, j) are the luminance value for N × M pixels of the original imageand watermarked Image. Figure 5a-f has been given to present the Cover image, corre-sponding DNT coefficients, watermark logo, watermarked DNT coefficients, watermarkedimage and extracted watermark respectively. Table 1 has been provided to depict the value ofPSNR for various images used during the experiment. To verify the presence of watermark,different measures can be used to show the similarity between the original and the extractedsingular values. In our proposed algorithm, normalized correlation coefficient (NCC) [29] isused which is defined as,

NCC W ;W *� � ¼ X

I¼1

N Xj¼1

N

Wij−W� �

W *ij−W*

ij

� �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXI¼1

N Xj¼1

N

Wij−W� �2

vuut :

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXI¼1

N Xj¼1

N

W*ij−W*

ij

� �2

vuut

Fig. 13 a & c Watermarked Lena and Pirate Image after adding cropping 25 % b & d Extracted watermark

Fig. 12 a & c Watermarked Lena and Pirate Image after adding speckle noise b & d Extracted watermark


Where W is the original watermark, W* is the extracted watermark from distorted image.Normalized Correlation coefficient (NCC) is the number that lies between [−1, 1]. If thevalue of NCC is equal to 1 then the extracted watermark is just equal to the original one.Table 2 has been provided to illustrate the value of normalized correlation coefficients ofextracted watermark from noisy watermarked Lena, Barbara, Pirate and Mandril Images.

4.2 Result analysis

The proposed scheme has been demonstrated for its robustness against a variety of attacksnamely Average andMedian Filtering, Gaussian noise addition, JPEGCompression, Cropping,Resize, Rotation, Histogram Equalization, Contrast Adjustment while taking the embeddingstrength value as 0.314.

Addition of noise is a very common attack that is responsible for the degradation anddistortion of the image. The watermark information is also degraded by noise addition andresults in difficulty in watermark extraction. Robustness against additive noise is estimated byGaussian noise of density 0.1. Figure 6a & c shows the watermarked Lena & Pirate Image afteraddition of Gaussian noise and Fig. 6b & d consequently represents the extracted watermark.

Filtering is most common manipulation in digital image processing. The degraded imageand extracted watermarks, after applying 11×11 averaging filter and median filter are shownthrough the Figs. 7 and 8 respectively.

Fig. 15 a & c Watermarked Lena and Pirate Image after shearing effect b & d Extracted watermark

Fig. 14 a & cWatermarked Lena and Pirate Image after increasing 60 % contrast b & d Extracted watermark


Figure 9a & c shows the Watermarked Lena and Pirate Image after histogram equalizationand Fig. 9b & d depicts the corresponding extracted Watermark. The effect of rotation hasbeen evaluated by rotating the watermarked image up to 60° and shown through Fig. 10. Theproposed algorithm is quite resistant against rotation attack and proves superiority over theother existing algorithms.

Figure 11a & c shows the watermarked Lena & Pirate image after adding salt & peppernoise with noise density 0.1 and Fig. 11b & d represents the extracted watermark. Figure 12a& c shows the watermarked image after adding speckle noise having noise density 0.05,extracted watermark has been given through Fig. 12b & d.

Figure 13 shows the watermarked image after cropping and the corresponding extractedwatermark. Cropping an image is a lossy operation where we remove either rows orcolumns. In our approach 25 % of the watermarked image is cropped and then a watermarkis extracted and obtained NCC is 0.9806. For Contrast Adjustment, the contrast of thewatermarked image is increased by 60 % shown in Fig. 14a & c and extracted watermarkrepresented through Fig. 14b & d.

The proposed watermarking scheme has also been demonstrated for its robustness againstShearing, Spreading, Slicing, Zooming, Swirl and oiling effect. We have used Xnview softwareto simulate these effects on watermarked image and then extracted the corresponding watermark byusing the proposed method. Figure 15, 16, 17, 18, 19 and 20 has been used to reveal the attackedwatermarked image by using Xnview and extracted watermarks.

Fig. 17 a & c Watermarked Lena and Pirate Image after slicing effect b & d Extracted watermark

Fig. 16 a & c Watermarked Lena and Pirate Image after spreading effect b & d Extracted watermark


4.3 Comparative analysis

In this section proposed watermarking algorithm has been compared with the other reportedparallel algorithms (Lai et al.2010 [9], Run et al.2012 [32], Bhatnagar et al.2012 [6], Liu etal.2002 [23], Ganic et al.2004 [12]). We have implemented the aforementioned watermarkingschemes and their meticulous comparative analysis is provided through Table 3.

Addition of noise is a very common attack that is responsible for the degradation anddistortion of the image. The watermark information is also degraded by noise addition and itmakes difficult for watermark extraction. Robustness against additive noise is estimated byGaussian noise of density 0.1. Figure 21 provides a performance comparison of the proposedmethod for Gaussian noise by adjusting the value of noise variance. The performance ofproposed watermarking algorithms against the Gaussian noise attack is in close proximity ofthe Lai et al.2010 [9], and far better than the watermarking algorithm reported by Run etal.2012 [32], Bhatnagar et al.2012 [6], Liu et al.2002 [23], Ganic et al.2004 [12]. The natureof extracted watermark correlation coefficient is quite similar to Lai et al.2010 [9], becauseboth methods have used mid frequency component to embed the watermark.

The effect of rotation has been estimated and compared for changeable degrees of rotationbetween 10 and 50 and shown through Fig. 22. The proposed algorithm is quite resistant againstrotation attack and proves superiority over the other existing algorithms reported by Lai etal.2010 [9], Bhatnagar et al. 2012 [6], Liu et al. 2002 [23], Ganic et al. 2004 [12].

Fig. 19 a & c Watermarked Lena and Pirate Image after oiling effect b & d Extracted watermark

Fig. 18 a & c Watermarked Lena and Pirate Image after swirl effect b & d Extracted watermark


Figure 23 provides a performance comparison of the proposed method for JPEG com-pression attack by varying the quality factor. To verify the robustness of watermarked imagethe value of quality factor has been varied from 10 to 100. It has been derived that theperformance of the proposed algorithm is close to the algorithm proposed by Lai et al. [9]and Ganic et al. [12] while superior over the algorithm proposed by Bhatnagar et al. 2012[6], Liu et al. 2002 [23].

Figure 24 illustrates a performance comparison by adjusting the value of contrast between0.2 ≤ CA ≤ 1.2. Through comparative analysis it may be figured out that proposed method isquite robust against contrast adjustment attack and shows superior performance over thealgorithm proposed by Bhatnagar et al.2012 [6], Liu et al. 2002 [23] and Ganic et al. [12].Figure 25 demonstrate the performance comparison by altering the value of average filter

Table 3 Comparisons of proposed technique with Run et al. [32], Bhatnagar et al. [6] and Lai et al. [9]

Attacks Proposed method Run et al. [32] Bhatnagar et al. [6] Lai et al. [9]

Extraction technique Semi-blind Non-blind Semi-blind Non-blind

Embedding domain DNT+SVD DWT+SVD FRFT+SVD DWT+SVD

Size of watermark 256×256 256×256 256×256 128×128

Size of host image 512×512 512×512 512×512 256×256

Time complexity O(N3) O(N3) O(MN2) O(N3)

Median filter 13×13 Not tested 11×11 Not tested

Histogram equalization Tested Tested Tested Tested

Rotation 60° Not tested 50° 50°

Average filter 11×11 Not tested 11×11 11×11

Contrast adjustment 50 % 20 % 50 % 20 %

Gaussian noise Up to 50 % Up to 10 % Up to 100 % Up to 10 %

JPEG compression QF=1 to 100 QF=1 to 75 QF=1 to 100 QF=1 to 100

Cropping 25 % Not tested 90 % Not tested

Salt & pepper Up to 50 % Not tested Up to 100 % Not tested

Speckle Tested Not tested Not tested Not tested

Zooming Tested Not Tested Tested Not Tested

QF Quality factor

Fig. 20 a & c Watermarked Lena and Pirate Image after zooming effect b & d Extracted watermark


size. It may be observed that the proposed algorithm shows better performance over otherreported watermarking algorithms.

Tables 4 and 5 have been consequently used to compare the PSNR value and NormalizedCorrelation Coefficient of proposed watermarking algorithm with the method reported byRun et al. [32],Lai et al. [9], Bhatnagar et al. [16] and Bhatnagar et al. [6].

Fig. 21 Performance of proposed watermarking method for different Gaussian noise parameters

Fig. 22 Performance of the proposed watermarking method by varying the degree of rotation


4.4 Time complexity evaluation

The time complexity illustrates the total amount of time taken by a particular method or algorithmto solve given problem. The time complexity of the proposed watermarking method in a divisivenormalization domain has been computed as

TimeComplexity ¼ Complexityof DWTþ Complexityof DNTþ Complexityof SVD

þ Complexityof watermarkembeddingþ Complexityof InverseSVD

þ Complexityof InverseDNTþ Complexityof InverseDWT

Suppose the size of the image matrix is X xY then we may write the above equation as

T X;Yð Þ ¼ T1 X;Yð Þ þ T2 X;Yð Þ þ T3 X;Yð Þ þ T4 X;Yð Þ þ T5 X;Yð Þ þ T6 X;Yð Þþ T7 X;Yð Þ

Where

Time Complexity of DWT ¼ T 1 X;Yð Þ ¼ O XYð ÞTime Complexity of DNT ¼ T 2 X;Yð Þ ¼ O XYð ÞTime Complexity of SVD ¼ T 3 X;Yð Þ ¼ O min XY2;YX2

� �� Time Complexity of watermark embedding ¼ T4 X;Yð Þ ¼ O XYð ÞTime Complexityof InverseSVD ¼ T5 X;Yð Þ ¼ O min XY2;YX2

� �� Time Complexity of Inverse DNT ¼ T 6 X;Yð Þ ¼ O XYð ÞTime Complexity of Inverse DWT ¼ T 7 X ; Yð Þ ¼ O XYð Þ

Fig. 23 Performance of the proposed watermarking method by varying the value of quality factor


Fig. 24 Performance of the proposed watermarking method by varying the value of contrast

Fig. 25 Performance of the proposed watermarking method by varying the filter size


Now the above equation of time complexity can be written as

T X;Yð Þ ¼ O XYð Þ þ O XYð Þ þ O min XY 2;YX 2� �� þ O XYð Þ þ O min XY 2;YX 2

� �� þ O XYð Þ þ O XYð Þ

In view of above equation it has been concluded that the overall time complexity of proposedwatermarking technique in divisive normalization domain estimated to the complexity of SVDconversion and embedding a watermark into DNTcoefficients. Further if we consider the equaldimension matrix (X = Y) then the overall complexity of the proposed algorithm is O(X 3).

5 Conclusions

Through this paper, a novel hybrid wavelet based transparent image watermarking algorithmhas been presented, which is based on divisive normalized transformation and SVD. In thisscheme watermark signal is added directly on the singular values of divisive normalizedtransform coefficients of the cover image’s DWTsub bands. The idea of embedding watermarkinto divisive normalization transform domain has been exploited because of its ability toremove the statistical redundancies between wavelet coefficients and providing perceptualperfection towards the watermarked image. The proposed algorithm avoids the pitfall encoun-tered by various wavelet based watermarking method reported through literature and improves

Table 4 Comparisons of peak signal to noise ratio with existing method

Test images Proposed method Run et al.[32] Lai et al. [9] Bhatnagar et al. [6]

Lena 62.97 32.54 36.11 48.59

Barbara 65.42 31.47 36.24 47.89

Pirate 60.73 33.93 32.18 49.35

Mandril 66.22 31.72 35.86 48.91

Table 5 Comparisons of normalized correlation coefficient with existing method

Attacks Proposedmethod

Bhatnagar et al.[6]

Bhatnagar et al.[16]

Lai et al.[9]

Run et al.[32]

Median filter 0.9496 0.4838 0.4624 Not given 0.9564

Histogram equalization 0.9839 0.9320 0.9861 Not given 0.9615

Rotation(60) 0.9833 Not given 0.9025 0.4972 Not given

Average filter (11×11) 0.7524 0.3167 0.3499 0.3537 0.9530

Contrast adjustment 0.9931 −0.3416 0.5478 Not given 0.7716

Gaussian noise 0.9783 0.2848 0.3603 0.4279 0.9322

JPEG compression(50:1)

0.9704 0.9842 0.9637 0.5376 0.7566

Cropping(1/4) 0.9806 −0.9038 −0.9861 0.5156 0.9512

Salt & pepper (50 %) 0.9759 0.3100 0.4635 0.4255 Not given

Speckle 0.9832 Not given Not given 0.9202 0.9827

Zooming 0.9934 0.8382 0.9492 Not given Not given


the imperceptibility. By conducting several experiments, the conclusion has been derived; thatthe proposed method is quite robust against intentional and non-intentional attacks and at thesame time it also shows a good PSNR value as given through Tables 4 and 5. The results of theproposed technique indicate that it conserves the imperceptibility of watermarked image and therobustness under various types of image processing attacks. Various graphical comparisonssignify that the robustness of proposed algorithm is far better than the other reported parallelwatermarking algorithms.

References

1. Adhipati RA, Chatterji BN (2005) A new wavelet based logo-watermarking scheme. Pattern RecognitLett 26:1019–1027

2. Bao P, Ma X (2005) Image adaptive watermarking using wavelet domain singular value decomposition.IEEE Trans Circ Syst Video Technol 15(1):96–102

3. Barni M, Bartolini F, Piva A (1998) A DCT domain system for robust image watermarking. IEEE TransSignal Process 66:357–372

4. Barni M, Bartolini F, Piva A (2001) Improved wavelet based image watermarking through pixel wisemasking. IEEE Trans Image Process 10(5):783–791

5. Benhocine A, Laouamer L, Nana L, Pascu AC (2013) New images watermarking scheme based onsingular value decomposition. J Inf Hiding Multimed Signal Process 4(1):9–18

6. Bhatnagar G, Raman B (2009) A new robust reference logo watermarking scheme. Multimed Tools Appl52(2–3):621–640

7. Chang CC, Chuang JC, Chen TS (2002) Recognition of image authenticity using significant DCTcoefficients quantization. Informatica 26(4):359–366

8. Chang CC, Tsai P, Lin CC (2005) SVD-based digital image watermarking scheme. Pattern Recognit Lett26:1577–1586

9. Chih-Chin L, Cheng-Chih T (2010) Digital image watermarking using discrete wavelet transform andsingular value decomposition. IEEE Trans Instrum Meas 59(11):3060–3063

10. Cox I, Kilian J, Leighton T, Shamoon T (1997) Secure spread spectrum watermarking for multimedia.IEEE Trans Image Process 6(12):1673–1687

11. Cox I, Miller ML, Bloom JA (2001) Digital watermarking. Morgan Kaufmann12. Ganic E, Eskicioglu AM (2004) Robust DWT-SVD domain image watermarking: embedding data in all

frequencies. In: Proceedings of theACMMultimedia and Securityworkshop,Magdeburg, Germany, pp. 166–17413. Ganic E, Eskicioglu AM (2005) Robust embedding of visual watermarks using DWT-SVD. J Electron

Imaging 14(4):04300414. Gaurav B, Raman B (2009) A new robust reference watermarking scheme based on DWT-SVD. Comput

Stand Interfaces 31(5):1002–101315. Gaurav B, Wu QMJ, Raman B (2011) A new aspect in robust digital watermarking. Multimed Tools Appl.

doi:10.1007/s11042-011-0788-z16. Gaurav B, Wu QMJ, Raman B (2012) A new robust adjustable logo watermarking scheme. Comput Secur

31:40–5817. Kim WS, Hyung OH, Park RH (1999) Wavelet based watermarking method for digital images using

human visual system. Electron Lett 35(6):466–46818. Kundur D, Hatzinakos D (2004) Towards robust logo watermarking using multi resolution image fusion.

IEEE Trans Multimed 6:185–19719. Li Q, Wang Z (2009) Reduced-reference image quality assessment using divisive normalization-based

image representation. IEEE J Sel Top Signal Process 3(2):202–21120. Lin WH, Horng SJ, Kao T, Fan WP, Lee CL, Pan Y (2008) An efficient watermarking method based on

significant difference of wavelet coefficient quantization. IEEE Trans Multimed (SCI 12/86, 2288)10(5):746–757

21. Lin W-H, Wang Y-R, Horng S-J (2009) Awavelet-tree-based watermarking method using distance vectorof binary cluster. Expert Syst Appl (SCI 1/64, 2596) 36(6):9869–9878

22. Lin W-H, Wang Y-R, Horng S-J, Pan Y (2009) A blind watermarking method using maximum waveletcoefficient quantization. Expert Syst Appl (SCI 1/64, 2596) 36(9):11509–11516

23. Liu R, Tan T (2002) An SVD-based watermarking scheme for protecting rightful ownership. IEEE TransMultimed 4(1):121–128


http://dx.doi.org/10.1007/s11042-011-0788-z

24. Loukhaoukha K (2012) On the security of digital watermarking scheme based on singular valuedecomposition and tiny genetic algorithm. J Inf Hiding Multimed Signal Process 3(2):135–141

25. Lyu S, Simoncelli EP (2007) Statistically and perceptually motivated nonlinear image representation. In:Proceeding of SPIE Conference on Human Vision and Electronic Imaging XII, vol. 6492, San Jose, CA, Jan

26. Lyu S, Simoncelli EP (2008) Nonlinear image representation using divisive normalization. IEEE Con-ference on Computer Vision and Pattern Recognition, Anchorage, Alaska, June 24–26

27. Malo J, Epifanio I, Navarro R, Simoncelli EP (2006) Nonlinear image representation for efficientperceptual coding. IEEE Trans Image Process 15(1):68–80

28. Mohammad AA, Alhaj A, Shaltaf S (2008) An improved SVD-based watermarking scheme for protectingrightful ownership. Signal Process 88:2158–2180

29. Pandey, P, Kumar S, Singh SK (2013) Rightful ownership through image adaptive DWT-SVDwatermarking algorithm and perceptual tweaking. Multimed Tools Appl 1–26. http://link.springer.com/article/10.1007/s11042-013-1375-2

30. Podilchuk CI, Delp EJ (2001) Digital watermarking: algorithms and applications. IEEE Signal Proc Magpp. 33–46, July

31. Rosiyadi D, Horng S-J, Fan P, Wang X, Khan MK, Yi P (2012) An efficient copyright protection schemefor e-government document images. IEEE Multimed 19(3):62–73

32. Run R-S, Horng S-J, Lai J-L, Kao T-W, Chen R-J (2012) An improved SVD-based watermarkingtechnique for copyright protection. Expert Syst Appl 39(1):673–689

Punit Pandey received the B.Tech degree in Computer Science & engineering from U.P Technical University,India in 2004, the M.Tech degree in Computer Science from the BIT Mesra,Ranchi, in 2007,respectively.Currently he is pursuing Ph.D. in computer science & engineering from Jaypee University of Engineering &Technology. From July 2007 to June 2009, he was a project engineer in Wipro Technology, Hyderabad. Since2009 he has been working with Jaypee University of Engineering & Technology as a senior lecturer indepartment of computer science & engineering.


http://link.springer.com/article/10.1007/s11042-013-1375-2

http://link.springer.com/article/10.1007/s11042-013-1375-2

Shishir Kumar is currently working as Professor in Department of Computer Science and Engineering atJaypee University of Engineering and Technology, Guna, India. He has completed his PhD (ComputerScience) in 2005. He is having around 14 years of teaching experience. His current areas of interest areImage Processing & Network Communication.

Dr. Satish Kumar Singh has completed his Ph.D., M. Tech. & B. Tech in 2010, 2005 and 2003 respectively.He is having more than 08 years of experience in academic and research institutions. He has more than 15publications in international journal and conference proceedings of repute. He is member of various profes-sional societies like, IEEE, IETE, IAENG and IACSIT etc. He is serving as editorial board member andreviewer for many international journals e.g. JPRR, JICT, MIJST, COMPJ, CSSP, IET-IPR etc.


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A robust logo watermarking technique in divisive normalization transform domain