Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

Adaptive color image watermarking by the use of

quaternion image moments

E.D. Tsougenis1, G.A. Papakostas

2, D.E. Koulouriotis

1

and E.G. Karakasis1

1Democritus University of Thrace, Department of Production Engineering and

Management, 67100 Xanthi, Greece

2Human Machines Interaction (HMI) Laboratory, Department of Computer &

Informatics Engineering, Eastern Macedonia and Thrace Institute of Technology,

GR-65404 Agios Loukas, Kavala, Greece

e-mail: stsougen@pme.duth.gr, gpapak@teikav.edu.gr, jimk@pme.duth.gr,

ekarakas@pme.duth.gr

Abstract

The first adaptive moment-based color image watermarking is presented in this work.

The proposed method exploits rotation invariance, high reconstruction capability and

computation accuracy of the Quaternion Radial moments’ (QRMs), subject to the

tradeoff between robustness and imperceptibility. The current system manages to

multi-embed binary logos to color images applying QRMs as information carriers. A

novel adaptive system adjusts the watermark’s embedding strength (online) by taking

into account image’s morphology, with respect to robustness and imperceptibility.

The method manages to experimentally justify and further eliminate the attack-free

phenomenon that state-of-the-art methods suffer. The simulation results justified that

the proposed framework manages to highly secure its carrying information under

common signal processing and geometric attacking conditions. Furthermore, the

adoption of the novel adaptive process enhances the robustness and imperceptibility

requirements by reducing the Bit Error Rate even by 49% and producing even 5db

higher PSNR values, respectively.

Keywords: image watermarking, color watermarking, adaptivity, quaternion

moments, orthogonal moments, dither modulation.

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

1. Introduction

The protection of the nowadays huge information sharing/exchange in mobile

devices, computers and cyber space constitutes one of the most challenging tasks in

the security area. Although tremendous efforts have been reported during the last

decades, the researchers still cannot handle this situation preventing any unauthorized

exploitation. The media security and the corresponding establishment of their rightful

copyright information employ thousands of people working on the design of an ideal

security system. The specific problem has been partially solved by different

perspectives such as steganography / steganalysis (Abdelfattah & Mahmood, 2013) or

applied cryptography on data (Papadopoulos, Cormode, Deligiannakis & Garofalakis,

2013). However, the majority of these solutions cannot be generic due to the

environmental complexity including either populations’ ethics or even the legal

systems (laws). Watermarking constitutes one of the latest achievements in the

security area applied in all kinds of media including text, audio, image and video. The

main idea behind this achievement is to ensure the integrity, authority and authenticity

of images by incorporating significant information for further identification (Lei, Tan,

Chen, Ni, Wang & Lei, 2014; Bhatnagar, Jonathan Wu, & Atrey, 2014). According to

Hartung et al. (1999), a watermark is a non-removable digital code, robustly and

imperceptibly embedded in the original (host) data, which contains information about

the origin, status, and/or destination of the data. Watermarking manages to

successfully combine the cryptography and steganography properties leading to an

increased high level security scheme with multi-application perspectives.

The present work constitutes the first moment-based color image watermarking

framework consisting of a novel adaptive system and the recently introduced

quaternion radial moments. In Section 2 the motivation and challenges that inspired

this work are discussed. Section 3 briefly discusses a number of significant transform-

domain color image watermarking methods along with the advancement and

contribution derived from present work. Section 4 includes the main theoretical

background concerning image quaternion radial moments. In Section 5, the novel

adaptive system is presented and evaluated in terms of robustness and

imperceptibility. Section 6 presents the proposed adaptive moment-based

watermarking framework. In Section 7 the simulation results are presented and

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

analyzed along with a comparison of the proposed framework to a number of

transform-domain color image watermarking methods from the literature. Finally, a

number of conclusions and implications that could lead to future perspectives are

being presented and discussed through Section 8.

2. Motivation

This work focuses on image watermarking area where the transformation of image

moments dominates during the last decade (Tsougenis, Papakostas, Koulouriotis &

Tourassis, 2012). The pre-mentioned transformation is distortion tolerable, a property

that provides to the researchers the opportunity to incorporate their information into

the corresponding coefficients as additive data. Image moments constitute one of the

most attractive information carriers in the transform-domain image security field. This

work was mainly inspired by the following motivations which authors call as research

challenges:

Motivation #1: The ultimate scope of an advanced ideal image watermarking scheme

is the sufficient satisfaction of the basic requirements consisting of robustness,

imperceptibility, capacity and complexity. As a matter of fact, a simple implemented /

fast (low complexity) watermarking method should incorporate the maximum

allowable amount of information (high capacity) to the host image, according to the

perceptual redundancy (high imperceptibility) maintaining also under any geometric

or signal processing attacking condition (high robustness). However, the

interrelationship of the basic requirements (Fig. 1) generates the traditional tradeoff

existing in image watermarking field where uncontrollable manipulations regarding to

one requirement’s enhancement possibly leads to an alongside degradation of another

one.

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Figure 1. A tradeoff between basic watermarking requirements.

Motivation #2: Adaptivity constitutes an efficient approach to the traditional image

watermarking for handling the aforementioned tradeoff. The adaptivity challenge can

be interpreted as the selection of the most qualified candidate image portion for

hosting the watermark information or either as the calibration of watermark's

embedding strength, both of them with respect to the pre-discussed basic

requirements. A successful detection of highly textured area may lead to the

incorporation of larger amount of information without being suspected. In addition,

the detection of plain or edged areas where even small interventions can be

immediately recognizable may lead to higher visual quality results. As a matter of

fact, the adaptivity handling of information “sealing” constitutes the first challenge

during the design of an up-to-date moment-based image watermarking method.

Motivation #3: Based on the color theory (Chou & Liu, 2010) and the demands of

image watermarking, it can be easily comprehended that the calibration of separate

individual embedding strength per color plane (i.e. Red, Green and Blue) along with

the identification of the candidate area's complexity raises the adaptivity challenge to

a higher level. The fact that color provides us with extra information in contrast with

grayscale and binary images producing a more complex working environment makes

inevitable the existence of adaptivity in the forthcoming generation of transform

domain image watermarking.

As a matter of fact, the present work accepts and manages to cope with the pre-

mentioned challenges presenting a novel designed moment-based color image

watermarking framework that adapts to the host area characteristics in order to highly

satisfy the basic requirements.

3. Related work

Numerous moment-based grayscale image watermarking works have been reported in

the literature (Tsougenis, Papakostas, Koulouriotis & Tourassis, 2012). As for the

color space, a number of significant works adopt other commonly applied

transformations such as Discrete Wavelet Transform (DWT), Discrete Cosine

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Transform (DCT) and Discrete Fourier Transform (DFT) in order to use the

corresponding coefficients as watermark information carriers.

Discrete Wavelet Transform: One of the first works presented in DWT color image

watermarking area was by Caramma et al. (2000) where the RGB color channels were

exploited regarding to the adjustment of watermark embedding strength. Lately, Tsai

& Lin (2008) managed to highly satisfy the proposed system’s robustness and

imperceptibly embedding the watermark information based on HSV models. Chou &

Liu (2010) embed high-strength watermarks in DWT by taking into consideration the

corresponding perceptual redundancy. In (Peng, Wang & Wang, 2010), the

information is embedded applying the mean value modulation in multi-wavelet-

domain coefficients and blind extraction is achieved by trained support vector

machines (SVMs). Singhal et al. (2011) evaluated experimentally the performance of

various wavelet techniques for color image watermarking with respect to the basic

requirements. The latest work on this domain presented by Kalra et al. (2014) embeds

watermark information to color images combining the properties of DWT and DCT.

Discrete Cosine Transform: During the late 90s, Piva et al. (1999) presented a DCT

domain method that simulated the HVS by exploiting the correlation between signals

of different color channels. The authors calibrated the power of the watermark

strength by taking into account the working color plane. Barni et al. (2002) presented

a DCT watermarking method that detects the watermark existence based on a global

correlation measure which is calculated by taking into account the information

conveyed by the three color channels as well as their interdependency. In (Ahmidi &

Safabakhsh, 2004), a number of middle frequency DCT coefficients are selected in

order to carry the watermark image which is being incorporated with respect to Just

Noticeable Difference (JND) threshold. Lin et al. (2010) presented an improved DCT-

based image watermarking method where the watermark information is embedded

based on the concept of mathematical remainder modifying a number of low-

frequency DCT coefficients. Recently in (Su, Wang, Jia, Zhang, Liu, & Liu, 2013),

the DCT two-level strategy decomposition has been applied for embedding color

logos in color images presenting a promising robustness and imperceptibility

performance compared to similar methods.

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Discrete Fourier Transform: Bas et al. (2003) introduced the term quaternion to the

image watermarking community by their application in Fourier transform (QFT). The

adaptivity of the specific scheme lies on the calibration of quaternions’ μ parameter

regarding to an optimized watermark insertion. Tsui et al. (2008) designed an adaptive

watermarking method based on JND (Just Noticeable Distortion) that its host QFT

coefficients are calculated over the spatiochromatic CIELAB color space enhancing

the visual quality of the results. However, the method's non-blind nature constitutes a

significant drawback. On the contrary, Wang et al. (2013) embedded and extracted

blindly the watermark information from the real part of QFT coefficients.

Apart from the pre-mentioned transform-domain methods, also a number of other

transformations have been applied in color image watermarking field such as Discrete

Hadamard Transform (DHT) (Gilani, Kostopoulos, & Skodras, 2002), Principal

Component Analysis (PCA) (Lang, Zhou, Cang, Yu, & Shang, 2012) and Non-

Sampled Contourlet Transform (NSCT) (Niu, Wang, Yang & Lu, 2011) trying to

enhance the performances of the corresponding schemes.

Concerning the advancement over the latest state-of-the-art works, the proposed

framework manages to alongside deal with existing weaknesses and to further

contribute in the area. Latest work (Kalra, Talwar & Sadawarti, 2014) on DWT

domain is limited to signal processing attacking conditions in comparison to the

proposed framework that deals also with geometric attacks including a geometric

distortion recovery operation. As for the DCT domain, despite (Su, Wang, Jia, Zhang,

Liu & Liu, 2013) taking into consideration the global brightness and contrast of the

host image for incorporating the watermark information, our proposed adaptive

system functions locally providing a different embedding strength with respect to the

area complexity. The latest work functioning in QFT domain (Wang, Wang, Yang, &

Niu, 2013) completely neglects the complexity of each image embedding watermark

information to all tested images using a single pre-defined embedding strength.

Generally the multi-contribution of the present work lies on the introduction of

quaternion radial moments along with their properties’ examination in comparison to

other domains; the novel adaptive system that adjusts the watermark’s embedding

strength to host area’s characteristics based on a simple genetic algorithm which was

never done before; the elimination of the attack-free phenomenon (Section 5) existing

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in transform domain color image watermarking (Tsai & Sun, 2007); and the high

performance of the watermarking process in terms of robustness, imperceptibility and

capacity.

4. Quaternion image moments

During the last decades, the quaternion algebra has been widely applied in Discrete

Fourier transform (DFT) domain representing a variety of color spaces such as RGB

(Ell, 1993), YCbCr (Wang, Wang, Yang & Niu, 2013), CIELAB (Tsui, Zhang &

Androutsos, 2008) etc. Despite image moments' close mathematical nature to DFT,

the first quaternion moment families have been recently introduced based on Fourier-

Mellin (Guo & Zhu, 2011) and Zernike (Chen, Shu, Zhang, Chen, Toumoulin,

Dillenseger & Luo, 2012) polynomials. Recently, the radial quaternion moments

which eliminate the approximation errors of the aforementioned continuous moment

families and guarantee rotation invariance have been presented in image analysis

(Karakasis, Papakostas & Koulouriotis, 2009).

Although the fundamentals concerning the radial color moments are extensively

discussed in (Karakasis, Papakostas & Koulouriotis, 2013), a brief presentation of the

theory is presented herein. Initially, the color image f(x,y) must be represented in a

quaternion form. Having transformed the original RGB image f(x,y) , in polar

coordinates ,cf r , then the quaternion image ,qf r , is defined as:

, 0 , , ,R G B

q c c cf r f r f r f r (1)

where ,R

cf r , ,G

cf r and ,B

cf r is the red, green and blue color channels of

the original image, respectively.

The corresponding quaternion moment of order n and repetition m of the

quaternion image is defined as:

12 1

0 0

1, k

N

lm

nm q k n

r kn

Q f r P r elW

(2)

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where i,j and k are the imaginary parts, l denotes the maximum number of pixels

along the circumference (Karakasis, Papakostas & Koulouriotis, 2013), Wn is the

scaling factor relative to the used orthogonal polynomial nP r . The radius r of

image's internal circular area is defined into 0,2

N

, the angle

k defined

into 0 2k is calculated according to 2 /k l . At this point, it should be

noted that the multiplication of quaternion numbers is not commutative in contrast

with the complex numbers.

The reconstruction of a color image by a finite set of quaternion color moments

nmQ up to a maximum order maxn and repetition , is performed by applying the

following inverse formula:

max max

0 0

,n m

m

C nm n

n m

F r Q P r e

(3)

In this work the Tchebichef, Krawtchouk and dual Hahn discrete polynomials were

used in order to construct the corresponding quaternion radial moments QRTMs,

QRKMs and QRdHMs respectively. The main characteristics of these polynomials

are summarized in (Papakostas, Koulouriotis & Karakasis, 2009).

5. Adaptive system (offline/online session)

Color image watermarking constitutes a more complex procedure compared to

grayscale case if one considers the triple amount of information (the three planes of

the color space) that should be handled in order to satisfy the basic requirements. As it

was previously mentioned, the adaptive handling of watermark embedding to the

image content may constitute the ideal solution. In details, a calibration of the

embedding strength and the quantity of information with respect to the host image

area will produce the optimal balance between pre-discussed requirements. Adaptivity

has been dealt by different perspectives in moment-based grayscale image

watermarking. The first one considers the identification of the proper area where the

information can be accommodated in a more imperceptible way (Papakostas,

Tsougenis & Koulouriotis, 2010). The second perspective is strongly connected to the

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

calibration of the embedding strength depending on the specific area (Tsougenis,

Papakostas, Koulouriotis & Tourassis, 2013).

The lack of adaptivity leads to a commonly discussed phenomenon in color image

watermarking known as the attack-free case (Tsai & Sun, 2007) where the embedded

information cannot be accurately extracted even when no attacking conditions exist.

The authors’ scope is to eliminate the specific phenomenon by designing a novel

adaptive system that optimizes (offline) a generalized version of the logistic curve

based on block’s complexity. Furthermore, an appropriate adjustment of the

embedding strength (online) leads to the enhancement of the color image watermark's

basic requirements. As a matter of fact, the optimization of the parameters that define

this flexible logistic function is crucial. The form of the used generalized logistic

curve (Richard's curve) is defined as:

1/

1v

B t M

K AY t A

Qe

(4)

where A denotes the lower asymptote, K the upper asymptote, B is the growth rate,

v>0 affects near which asymptote maximum growth occurs, Q depends on the value

Y(0) and M is the time of maximum growth (Q=ν).

An optimization process handles the pre-mentioned 6 parameters (A, B, K, Q, M, v)

and produces a separate logistic function concerning the block’s nature (Plain, Edge

and Texture) where the corresponding embedding strength of the block will be

defined afterwards. Τhe “goal” of the proposed algorithm is the adjustment of three

kinds of image blocks depending on content's complexity that could be assigned with

the appropriate embedding strength based on the optimized logistic curves.

5.1 Block classification

Initially, the process that defines the complexity of every 8x8 pixels sized carrier

block should be presented. Based on a block classification method proposed in (Wei

& Ngan, 2009), the complexity of its host block is further analyzed in the moment

domain. The image should be first converted to grayscale space in order to block-

wisely apply the traditional canny edge detector. The scope of this method is to

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estimate the edginess (edgelp ) of each block based on Eq. (5) which will be used

to estimate its corresponding embedding strength in the upcoming step. Based on two

pre-defined thresholds (α,β), each block is classified according to the following

analysis:

2

edgels

edgel

block

Np

N (5)

, 0

,

,

edgel

edgel

edgel

Plane p a

Block type Edge a p

Texture p

(6)

where blockN is the size of the block and edgelsN the number of block’s edge pixels,

while the threshold values (α,β) are empirically assigned as 0.1 and 0.2, respectively

(Wei & Ngan, 2009). The presented analysis quantifies blocks’ content complexity

based on the number of contained edge pixels (edgels), a measure that is aimed to be

correlated with the blocks' embedding strength during the optimization process.

5.2 Optimization process

Genetic Algorithms (GAs) have been applied in numerous applications of the

engineering science constituting a powerful tool for optimization. A simple genetic

algorithm is a stochastic method that performs searching in wide search spaces,

depending on some probability values that mimics the evolutionary process that

characterizes the evolution of living organisms (Holland, 2001). Therefore, GA has

the ability to converge to the global minimum or maximum, depending on the specific

application skipping this way any possible local minima or maxima (Colley, 2001).

A data set of 150 image blocks of 8x8 pixels size (50 for each block category) is

provided to the GA regarding to the optimization of the generalized logistic curves.

The GA produces 18 parameter values (6 per block category / logistic curve) scoping

to minimize the Bit Error Rate (BER) and alongside maximize the Peak-Signal-to-

Ration (PSNR) enhancing the robustness and imperceptibility system’s performance,

respectively. The structure of the ith

algorithm's chromosome is defined as:

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1 1 1 1 2 2 2 2 3 3 3 3

1 2 3 6 1 2 3 6 1 2 3 6, , ,..., , , , ,..., , , , ,...,iCh f f f f f f f f f f f f

where 1 2 3 6{ , , ,..., }k k k kf f f f with k=1,2,3 (1: plane, 2: edge, 3: texture) are the six free

parameters of the kth

logistic curve. Each chromosome corresponds to a candidate

optimum set of parameter values constructing the three logistic curves (one for each

block category). The fitness function which is used to evaluate the appropriateness of

each candidate solution is defined as:

1 arg 2

1

1 T

T et jj

fitness SF PSNR PSNR SF BERT

(7)

where T is the number of attacks encountered in the procedure, SF1, SF2 are scaling

factors equal to 10 and 1 respectively, (BER)j is the BER of the jth

attacked block and

PSNRtarget is a desired PSNR value equal to 40. The incorporation of the PSNRtarget

transforms the optimization to a constrained procedure in order to ensure a minimum

of image quality that must be achieved per block. The GA’s configuration is as

follows: population size 20, maximum generations 50, crossover with probability 0.6

and 2 points, mutation probability 0.01 and Stochastic Universal Approximation

(SUS) selection method.

The derived optimized logistic curves are considered for adjusting the appropriate

embedding strength of each image block according to the following form.

, 0

,

,

Plane edgel edgel

Edge edgel edgel

Texture edgel edgel

Y p p a

Y p a p

Y p p

(8)

The Δ factor which is the quantization step of Dither Modulation (DM) (Chen &

Wornell, 2001) constitutes the embedding strength of the proposed moment-based

watermarking scheme. As a matter of fact, the curve defined Δ values are provided to

the watermarking framework in order to examine its performance. These steps

constitute an offline iterative process (Fig. 2) that terminates when all GA generations

are accomplished.

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Figure 2. Offline operational mode of the proposed adaptive system.

The best results considering BER and PSNR values indicate the optimum forms of

the logistic curves which are provided to the online part of the framework gaining

significant time.

5.3 Performance evaluation

The moment-based color image watermarking method presented extensively in the

next section is applied to the genetic algorithm regarding to the justification of

scheme's high performance applying multiple embedding strengths per block. The

results of the pre-analyzed steps are provided to the embedding strength adjustment

process. During the first part of the experiments, the GA examines iteratively the

performance of the applied watermarking method on the 150 selected blocks

constructing new logistic curves per iteration. Having optimized the set of the

parameters, the constructed curves are given as aforehand information to the system

in order to produce the block-wise Δ values.

The proposed adaptive process is evaluated by comparing the adaptive Δ case

(AΔC) to the single Δ case (SΔC) where the same Δ value is applied to each host

block ignoring the blocks' complexity factor. The quaternion radial moment families

(RTMs, RKMs and RdHMs) are applied for the specific experiment. A group of

signal processing / geometric attacks (analyzed in section 6) are applied in order to

test the robustness of the proposed system.

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Fig. 3 depicts the results of the adaptive adjustment of Δ values based on the

complexity of its block. The logistic curves differ for each applied moment family

proving their difference in magnitude values and content’s description.

A significant conclusion based on the results of the optimization process, is the

linear relationship between blocks’ complexity and Δ values in contrast to the initial

assertion about this relationship's nonlinearity. Although slightly different Δs are

produced within each complexity range, the absolute difference is close enough to

produce the corresponding illustrated lines (Fig. 3). The optimized logistic curves are

tested under attacking conditions regarding to the evaluation of the proposed adaptive

system. The performance of both tested cases (SΔC and AΔC) considering the

robustness (BER) and the imperceptibility (PSNR) requirements are presented in

Table 1.

It can be easily concluded that the proposed adaptive method manages to enhance

the performance of the traditional SΔC. The embedding strength calibration per block

achieves lower BERs alongside with higher visual quality. In details, the QRdHMs

manage to overcome the performance of the rest studied quaternion radial moment

families. Moreover, the specific family raises significantly the imperceptibility

parameter based on the PSNR value. Recall that one of the challenges behind the

construction of the proposed AΔC was the elimination of the attack-free case.

Numerous color image watermarking methods (Tsai & Sun, 2007) could not extract

intact the carried information from the transformation coefficients. Other methods

(Wang, Wang, Yang & Niu, 2013; Lu & Sun, 2000) apply the multiple insertion of

the same watermark along with the majority rule in order to overtake the specific

issue without dealing with it straightforward.

(a)

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(b)

(c)

Figure 3. The resulted Δ values based on the block complexity for (a)

QRTMs, (b) QRKMs and (c) QRdHMs.

The proposed adaptive system aims to take into consideration the properties of its

carrier blocks in order to decrease the BER (Table 1) significantly, without affecting

the visual quality. Although all applied quaternion radial moment families have

shown an enhancement to the robustness criteria, only the QRdHMs eliminate the

attack-free phenomenon.

Table 1. The performance of SΔC and AΔC under attack and attack-free conditions for the radial

discrete orthogonal moment families

SΔC AΔC

PSNR

(dB)

BER BER

Attack-free

PSNR

(dB)

BER BER

Attack-free

QRTMs 41.2890 0.0561 0.0400 41.0442 0.0442 0.0267

QRKMs 40.8936 0.0780 0.0617 40.7126 0.0345 0.0167

QRdHMs 42.8976 0.0224 0.0017 42.8168 0.0175 0.0000

It can be easily concluded (Table 1) that AΔC outperforms SΔC in terms of

robustness. The fact that different Δ values are assigned to each block proves that the

adaptivity handling of each block's complexity leads to the elimination of attack-free

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phenomenon and the enhancement of robustness performance. Moreover, the fact that

the results are produced based on random blocks of different complexity makes the

system performance stable and independent of the image content (generic). The

interesting properties of this novel proposed adaptive system motivated the authors to

incorporate it in the following moment-based color image watermarking framework

regarding to a further enhancement of the basic requirements' performance.

6. Moment-based color image watermarking framework

The proposed adaptive moment-based color image watermarking framework presents

a multi-purpose structure which is divided into five important sub-sections (pre-

processing step, insertion, attacking, geometric distortion recovery and detection),

described extensively hereafter.

6.1 Pre-processing

The proposed adaptive system is divided into offline and online operational modes.

The pre-processing sub-section is strongly connected with the offline adaptivity part

of the framework. During the offline mode the logistic curves of each blocks' category

are optimized based on a number of random selected blocks. The construction of the

specific logistic curves has to be done separately for each moment family. Afterwards,

during the online mode, the system produces the corresponding Δ values based on the

offline optimized logistic curves and provides them to the insertion / detection process

in real-time. All details concerning the implementation of the specific process are

provided in Section 5.

6.2 Insertion

The insertion process takes as inputs the host color image f and a binary logo W as the

watermark information. The original image is subdivided in 8x8 pixels sized blocks

where a pre-defined number of host coefficients/moments is calculated Eq. (2)

applying the kernel of the corresponding moment family. The proposed insertion

strategy embeds four times the same binary watermark W by splitting the image into

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four quadrants. The authors decided to sacrifice a noteworthy capacity level regarding

to the significant enhancement of the robustness and imperceptibility performance of

the system. As a matter of fact the maximum capacity of the scheme is defined as

follows:

Im Im / 4age age

Block Block

N MCapacity CapacityPerBlock

N M

(9)

where NImage, MImage, and NBlock, MBlock, are the dimensions of the host image and the

blocks respectively and the maximum CapacityPerBlock is 4 bits. Moreover, the

watermarks are scrambled by the Arnold's Catmap Transformation increasing even

more the security level of the system, according to:

1 1

mod1 2

x xN

y y

(10)

where ,x y and ,x y constitute the original and the new scrambled position of the

pixels, respectively. The watermark logo can be retrieved after specific number of

iterations Itermax specified by the frequency parameter FrWatermark. During the proposed

scheme, each embedded watermark is scrambled with different frequency increasing

the randomness of the system but resulting also in a side information increase.

Triangular numbers are adopted for maintaining the side information to the same low

level. In deatils, the frequency FrWatermark is now defined based on the

sequence of the triangular numbers. Given a frequency number as a key, the rest of

the corresponding frequencies per watermark are adjusted as it is explained in Table

2.

Table 2. Arnold's frequency based on triangular numbers

Number of Watermarks Key Triangular Sequence FrWatermark

1 1 1 1

2 3 1+2=3 1,2

3 6 (1+2)+3=6 1,2,3

4 10 (1+2+3)+4=10 1,2,3,4

All scrambled watermarks are then transformed into bit sequences in order to be

treated as single dimension signals. A number of low order color image moments

11 12 21 22ˆ ˆ ˆ ˆ, ,M M M and M are selected as candidate host coefficients.

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Each moment can be assigned with one single bit of information applying the

commonly used Dither Modulation (DM) (Chen & Wornell, 2001) which is a special

form of quantization index modulation. The corresponding conjugate

moments ˆp qM

are also dither modulated by the same bits to further improve the

reconstruction process. Eq. (11) shows the application of the DM on

the ˆi ip qM moment coefficient:

ˆ

, 1,..., 4i i

i i

p q i i

p q i i i

i

M d bM d b i

(11)

ˆ , 1,...,ˆ

i i

i i i i

i i

p q

p q p q

p q

MM M i L

M (12)

where di is the dither function for the ith

quantizer

satisfying 1 0 , 02

ii i id d d

belongs to [0 Δi] range, Δi is the quantization

step, is the modulus of the corresponding moment and [ ] is the rounding operation.

The security level of the embedded information is controlled by the calibration of Δi

parameter often referred also as embedding strength. Based on the complexity of each

block, a different Δi value is defined for each one adopting the results of the pre-

processing step. A reconstruction of the dither modulated image moments would

theoretically produce the watermarked block (Eq. (3)). However, the reconstruction

error and the computational burden in higher order values seriously affect the visual

quality and complexity of the proposed scheme, respectively. In order to avoid these

undesired conditions, a reconstruction of the isolated watermark information w (Eq

(13)) from the quantized moments i ip qM is spatially added to the original host

block ( , )Blk r (Eq. (14)) producing the watermarked block ( , )wBlk r .

,w r 2 2

1 0

ˆ q

pq pq p

p q

M M P r e

(13)

( , ) ( , ) ,wBlk r Blk r w r (14)

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

The specific iterative process is repeated for each block per quadrant until all

watermark bits are multiple incorporated to the host image.

6.3 Attacks

The watermarked color image f can be easily distorted in the outer hostile

environment of cyber space. As a matter of fact, two groups of attacks are constructed

simulating any possible manipulation during watermarked image's exchange between

users. The first group consists of the signal processing attacks that basically alter the

image intensities destroying this way the watermark information. The framework's

robustness under signal processing attacks is evaluated by applying JPEG

compression, median and average filtering, blurring, Gaussian and salt & pepper noise

addition. On the contrary, the second group consisting of geometric transformation

attacks manages to desynchronize the system by performing rotation, symmetric

cropping and size rescaling to the watermarked image. The application of the pre-

mentioned attacking conditions leads to a distorted watermark image that the

following step tries to recover based on image moments.

6.4 Geometric distortion recovery

Discrete orthogonal moments show a stable behaviour during their recalculation at the

detection side. The corresponding stability in combination with the margin of error of

DM process leads to the construction of watermarking system's defence against

common signal processing attacking conditions. However, the second group of attacks

can easily “disarm” the framework preventing the detection process from extracting

the watermark information unharmed. As a matter of fact, it seems indispensable the

addition of an extra processing step between insertion and detection tasks that will

estimate the geometric transformation parameters (rotation angle and scaling factor)

of a distorted watermarked image. Zhang et al. (2007) proposed a low complexity

effective solution where the rotation angle and the scaling factor of a geometrically

attacked image can be straightforward estimated by taking into consideration the first

three calculated TMs 00 10 01, ,T T T of the original watermarked image and the

corresponding manipulated moments 00 10 01ˆ ˆ ˆ, ,T T T of the attacked one. It should be

noted that both moment triplets are calculated after transforming the produced color

images into grayscale space. The specific moments can be either calculated based on

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

(Mukundan, Ong & Lee, 2001) or (Zhang, Qian & Xiao; 2007) equations. The

successful estimation of the geometric transformation parameters permits the user to

reverse the distorted image to its original form by rotating and rescaling it back by a

Theta angle and Alpha factor, respectively. The specific pre-process manages to

restore synchronization between the insertion and detection process regarding to an

accurate watermark extraction as described analytically by the following step.

6.5 Detection

The final sub-section of the proposed color image watermarking framework consists

of the detection process. The recovered version of the attacked watermarked image

along with all pre-mentioned side information / keys constitute the inputs to the

detection stage where the authentication of image’s originality is achieved. The

watermarked image is divided again in 8x8 pixels sized blocks where the same group

of host coefficients is calculated per block. The specific moments

are re-quantized (Eq. (15)) for both bit values {0,1} along with the same Δi value

specified by the pre-processing step. Then, the Minimum Distance Decoder (MDD)

Eq. (16) is applied to the quantized values in order to detect the carrying bit.

, 1,..., 4, 0,1

i i

i i

p q i

p q i ij

i

M d jM d j i j

(15)

2

{0,1}

argmin( )i i i ii p q p q

jj

b M M

(16)

where i ip q

jM denotes the modulus of the quantized moment of

i ip qM for the

specific value of j. The bit sequence is extracted per block constructing the watermark

bit sequence that can be reshaped into the extracted logo W'. The iterative process is

repeated based on the triangular number key (Table 2) that implies the number of the

carrying watermarks (or iterations). The Arnold transform is applied on the entire W'

with a given frequency calculated by (Itermax - FrWatermark). Having recovered all

extracted watermarks, the majority-vote decision (Tsai & Lin, 2008) rule is applied in

order to decide for the final optimal bit value.

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

The block diagram of the proposed moment-based color image watermarking

scheme is illustrated in Fig. 4.

Figure 4. The block diagram of the proposed moment-based color image

watermarking framework in online operational mode

7. Experimental results

A set of experiments were conducted in order to evaluate the proposed framework.

The software was developed in the MATLAB 2012b environment, while all

experiments were executed in an Intel i5 3.3GHz PC with 8GB RAM. A number of

common benchmark RGB images with 256x256 pixels size are applied for the

experiments, while the binary logo Rose sized as 32x32 bits (1024bits in total) is used

as the watermark information (Fig. 5).

The attacking conditions simulated for framework’s evaluation consisting of

common signal processing and geometric attacks: JPEG (90%, 70%, 50%, 40%,

30%), Median (3x3), Gaussian Noise (0.05), Average Filtering (3x3), Gaussian

Filtering (3x3), Salt & Pepper (0.01), Blurring, Rotation (5o, 15

o, 45

o, 70

o, 90

o),

Symmetric Crop (10%, 20%), Scaling (50%, 90%, 120%, 150%, 200%).

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

(a)

(b)

(c)

(d)

Figure 5. The benchmark images (a) Lena, (b) Barbara, (c) Mandrill and (d) the binary watermark

Rose.

The proposed framework is tested for the pre-mentioned benchmark images by

embedding the same watermark repeatedly for each image's quadrant. The

watermarked images produced by the QRTMs, QRKMs and QRdHMs are depicted in

Fig. 6.

Although the estimated PSNR values evaluate the imperceptibility performance of

almost all tested families, the QRdHMs constitute the ideal selection in terms of

visual quality. The specific conclusion justifies that the constructed optimized logistic

curves based on QRdHMs better handle the blocks’ complexity presenting a

satisfying adaptive behavior in contrast with the rest moment families.

PSNR=38.5647

PSNR=37.5179

PSNR=39.4322

PSNR=37.2721

PSNR=36.5488

PSNR=37.4961

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

PSNR=40.3806

PSNR=39.9316

PSNR=41.2707

Figure 6. The watermaked images for QRTMs (1st row), QRKMs (2nd

row) and QRdHMs (3rd row) moments

Generally, the proposed adaptive system seems to produce better quality results in

high texture images (i.e. Mandrill) in contrast with high plain images where the

watermark can be more detectable. However, the performance of the proposed

framework achieves high PSNR values (Fig. 6) close to 40db, which is a commonly

approved image quality by the watermarking community.

The robustness of the examined quaternion radial moment families is evaluated by

the BER values calculated under the pre-mentioned attacking conditions. A

comparison between the proposed method for the three moment types and other

methods from the literature is depicted in Table 3.

Initially, it should be highlighted that despite the non-eliminated attack-free

phenomenon of the QRTMs and QRKMs, the applied majority-vote decision rule

based on the multiple embedding watermarks manages to achieve zero BERs.

However, the QRdHMs constitute the only family that eliminates this undesired

situation, a fact that was proved experimentally in Section 5. The adaptive system has

partially adjusted with great success the embedding strength based on the results of

Table 3.

Generally, BERs of the examined moment families are in great low levels proving

a robust performance and visual quality results are satisfying concerning the PSNR

values. In details, the QRKMs presented a significant robust behavior under the

majority of the attacks but the imperceptibility requirement could not be satisfied. The

capability description of the specific moment family seems to be sensitive to the

adjustment of the embedding strength harming significantly the image content. On the

contrary, the QRTMs produce watermarked images that achieve close values to the

commonly approved 40db PSNR value securing also their carrying watermark bits.

The specific moment family would be the proper selection for the framework’s

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

information carrier module but QRdHMs manage to overcome the performance of

both pre-mentioned moment families. Despite the fact that the corresponding BERs

are the lowest comparing to the rest moment families, the visual quality of the

produced watermarked images achieves significantly high PSNR values even close to

42db. Recall also that the use of the specific moment family eliminated the attack-free

phenomenon. Conclusively, it should be noted that the high description capability of

the QRdHMs constitutes a property that is successfully adopted by the adaptive

system and the watermarking process in order to enhance significantly their

performance with respect to the basic requirements.

Table 3. Mean BER values for the three benchmark images of the proposed method (QRTMs,

QRKMs, QRdHMs) and other methods from the literature.

PROPOSED METHOD OTHER METHODS

QRTMs QRKMs QRdHMs Wang

et.al. (2013)

Tsui

et.al. (2008)

Chou & Liu

(2010)

ATTACK-FREE 0.0000 0.0000 0.0000 0.0000 0.0034 0.0117

JPEG (90) 0.0625 0.0567 0.0264 0.0000 0.0385 0.0336

JPEG (70) 0.0492 0.0462 0.0238 0.0038 0.0573 0.0594

JPEG (50) 0.0355 0.0377 0.0619 0.0333 0.0877 0.0772

JPEG (40) 0.0237 0.0264 0.0667 0.0605 0.1030 0.0947

JPEG (30) 0.0137 0.0091 0.0765 0.1160 0.1183 0.1085

MEDIAN 0.0104 0.0039 0.0137 0.0708 0.0681 0.0906

GAUSSIAN Noise 0.0466 0.0436 0.0729 0.0569 0.0680 0.2252

AVERAGE Filter 0.0101 0.0059 0.0120 0.0772 0.0607 0.0587

GAUSSIAN Filter 0.0010 0.0007 0.0000 0.0044 0.0709 0.0561

SALT & PEPPER 0.0007 0.0000 0.0003 0.0220 0.0753 0.0771

BLURRING 0.0202 0.0124 0.0322 0.0267 0.0450 0.0443

CROP (10%) 0.0173 0.0156 0.0104 0.0000 0.1263 0.0245

CROP (20%) 0.1396 0.0993 0.0778 0.0000 0.1849 0.0622

ROTATION (5) 0.0055 0.0013 0.0036 0.0243 N/A N/A

ROTATION (15) 0.0091 0.0062 0.0084 0.0387 N/A N/A

ROTATION (45) 0.0225 0.0146 0.0202 0.0478 N/A N/A

ROTATION (70) 0.0111 0.0130 0.0134 0.0408 N/A N/A

ROTATION (90) 0.0000 0.0033 0.0000 0.0000 N/A N/A

SCALING (50%) 0.0762 0.0791 0.0973 0.1461 0.0554 0.0563

SCALING (90%) 0.0059 0.0033 0.0111 0.0470 0.0355 0.0339

SCALING (120%) 0.0023 0.0013 0.0016 0.0400 0.0364 0.0260

SCALING (150%) 0.0023 0.0003 0.0023 0.0412 0.0401 0.0304

SCALING (200%) 0.0020 0.0007 0.0033 0.0408 0.0499 0.0262

MEAN 0.0236 0.0200 0.0265 0.0391 0.0697 0.0630

PSNR 38.5049 37.1057 40.5276 35.3600 32.9933 39.7833

A representative part (for the Lena image) of the extracted watermarks per

moment family is depicted in Table 4. The optimum watermark logos are

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

recognizable in the majority of the attaching conditions. However, it can be visually

evaluated that QRdHMs higher secures the watermark information.

Concerning the performance of the proposed method compared to the other

methods it is noteworthy that the elimination of the attack-free case in contrast with

the rest studied methods is the first point that should be highlighted based on the BER

results. Wang et al. (2013) method manages also to eliminate the specific

phenomenon by multiple embedding the same watermark. The proposed framework

applying the QRdHMs solves the specific problem in contrast with the rest families.

The values of the evaluation metrics justify the high performance of the proposed

framework in both terms of robustness and imperceptibility.

The significant mean BER differences between the proposed and the Tsui et al.

(2008) and Chou & Liu (2010) methods prove the significant robust behavior of the

proposed system. The adoption of the novel adaptive process has been justified that

enhances the robustness requirement reducing the Bit Error Rate (BER) by 49%

(QRKMs - on average for the three test images) compared to the most recently

published method of Wang et al. (2013). Although Wang et al. (2013) produce also

low BERs, the lack of a block-wise adaptive system leads to even 5db lower PSNR

values on average.

Table 4. The extracted Rose watermarks for all examined moment families for some attacking

conditions for the benchmark image Lena.

LENA

QRTMs QRKMs QRdHMs

ATTACK -FREE

JPEG (30)

MEDIAN

GAUSSIAN NOISE

BLURRING

CROP (20%)

ROTATION (45)

SCALING (50%)

Published in: Expert Systems with Applications, vol. 41, no. 14, pp.6408–6418, 2014.

Generally, the rotation invariance of the applied transformation is evident under

the majority of the applied rotation angles, while this superiority was expected due to

the QFT lack of this specific property. Moreover, Wang's et al. algorithm has zero

error under cropping attack, a performance that could not be achieved by the proposed

scheme. However, the current moment-based framework achieves lower BERs in

contrast with the rest state-of-the-art methods (Table 3). Conclusively, it can be easily

justified that the proposed adaptive color image watermarking framework overcomes

the performance of the methods under comparison, highly satisfying the basic

watermarking requirements.

8. Discussion And Conclusions

The first adaptive moment-based framework that highly secures color images has

been presented. Our novel and efficient block-based adaptive system carries the heavy

load of computation (training process) offline and produces online the optimized

embedding strength (Δ) for the corresponding host area gaining significant time which

was never done before. It has been also justified that the use of Richard’s curve

adjusted through the genetic algorithm for adaptivity purposes managed to enclose the

imperceptibility and robustness demands in the fitness function. Three recently

introduced quaternion radial discrete orthogonal moment families (QRTMs, QRKMs

and QRdHMs) have been examined as information carriers for the first time in the

image watermarking application.

Recalling the challenges accepted in Section 2; the need for adaptivity during a

color image watermarking process in the transform domain has been experimentally

highlighted and solved (Section 5); the high performance of QRdHMs in combination

with an adaptively provided embedded strength by the proposed system eliminated

the attack-free phenomenon existed in other frequency domains (Section 5.3);

balancing within the basic requirements satisfaction of color image watermarking, an

optimal solution has been achieved consisting of low BERs along with high PSNR

values overcoming performances of the most recent state-of-the-art algorithms

(Section 7). Generally, the proposed method manages to deal efficiently with the

multiple aforementioned issues existing in the transform domain color image

watermarking area showing a promising behaviour for the next generation algorithms.

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Although the proposed framework highly satisfies robustness, imperceptibility

and capacity requirements, a heavy load of computations strictly connected with

QRMs estimation along also with the multiple tasks (Section 6.1-6.5) lead to a

sacrifice of the complexity requirement. The block based approach followed by our

algorithm avoids estimating higher order moments which are time consuming but still

the need for faster and more efficient methods for QRMs’ computation should be

expected in the near future. As for the adaptivity system, Richard’s curve has been

selected and studied for composing our solution. However, there are multiple other

curves that future researchers can examine searching for a more convenient one that

could better fit to blocks’ nature. It should be noted also that the adaptive scheme has

been tested only for the image moment’s domain. However, there are no restrictions /

limitations applying it in different domains such as DCT, DWT and QFT; it is

believed that future transform domain watermarking algorithms may adapt this system

and benefit from its promising behaviour. From the security aspect, as previously

mentioned, a number of keys need to be transferred to the detection part for retrieving

successfully the watermark information. Another future “goal” would be a totally

blind watermarking framework that could recover the watermark information having

zero side-information eliminating this way any tracking processes of the specific keys.

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