A New Image Watermarking Scheme using Multi-Objective Bees Algorithm

Appl. Math. Inf. Sci. 8, No. 6, 2945-2953 (2014) 2945

Applied Mathematics & Information Sciences

http://dx.doi.org/10.12785/amis/080632

A New Image Watermarking Scheme using

Multi-Objective Bees Algorithm

Jiann-Shu Lee1,∗, Jing-Wein Wang2and Kung-Yo Giang1

1_{Department of Computer Science and Information Engineering, National University of Tainan, Taiwan}

2_{Institute of Photonics and Communications, National Kaohsiung University of Applied Science, Kaohsiung, Taiwan}

Received: 15 Nov. 2011, Revised: 15 Nov. 2013, Accepted: 1 Feb. 2014 Published online: 1 Nov. 2014

Abstract: The optimization of watermarked image fidelity and watermark robustness is an attractive research topic in image watermarking. In this paper, we propose a new image watermarking scheme based on multi-objective bees algorithm to promote watermarking robustness as well as fidelity. In contrast with the existing genetic algorithms (GAs) based approaches utilizing single objective optimization, we treat the image watermarking as a multi-objective optimization problem. Based on this new perspective, the inherent conflict existing in image fidelity and watermark robustness for image watermarking can be objectively handled. The experimental study shows that our method indeed outperform the conventional GA-based approaches in both robustness and fidelity. Furthermore, the proposed watermarking method can also provide solutions with higher stability.

Keywords: Watermarking, Multi-Objective Bees Algorithm, Genetic Algorithm

1 Introduction

Because of the rapid and extensive growth of the internet and popular digital recording and storage devices, digital content can be replicated, transmitted, and distributed in an effortless way. The protection of intellectual property rights for digital media has become an important issue. In recent years, digital watermarking, proposed to protect the copyright property of the legal owners and providers [1], has become an active research area. The techniques for watermarking still images can be classified into spatial-domain approaches and frequency-domain approaches. Spatial domain approaches tend to achieve fidelity while suffering from low robustness. On the contrary, the frequency-domain approaches show greater robustness because the watermark has been spread over the whole image, thus being resistant to cropping or cutting. The most recently proposed watermarking approaches [2–11] belong to the latter. One common problem confronted by these approaches is how to decide and choose the best embedding frequencies. For watermark embedding in the discrete cosine transform (DCT) domain, if we embed the watermark in the higher frequency bands, even though the watermarked image fidelity is good, it is vulnerable to the low pass filtering

(LPF) attack. In contrast, if we embed the watermark in the coefficients in the lower frequency bands, it should be robust against common image processing attacks such as the LPF attack. However, the watermarked image fidelity greatly degrades. Hence, most recent researches choose to embed the watermarks into the middle-frequency bands to serve as a compromise between image fidelity and watermark robustness [12].

Even though the watermarks are embedded into the middle-frequency bands, the problem about how to choose the optimal embedding frequencies is still not solved [13]. Recently, artificial intelligence techniques have been applied to resolve this problem [14,15]. Those methods [14,15] treated the image watermarking problem as an optimization problem and then genetic algorithms were employed to solve that. Shieh and Huang et al. [14] proposed a DCT watermarking method based on the GA. The GA is applied to search for the locations to embed the watermark in the DCT coefficients so that the robustness and the watermarked image fidelity are simultaneously optimized. Wei et al. [15] presented an improved method to increase the speed of GA.

The image watermarking issue inherently possesses two conflicting goals, i.e. fidelity and robustness. The existing GA-based watermarking methods handle this by

∗

Corresponding author e-mail:[email protected]

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combining the two objectives into a single composite fitness function and then search for the optimal solution. Such approaches rely on the proper selection of the weights or utility functions to characterize the decision-maker’s preferences. Hence, they face a predicament that they must consider the weights among objectives, and on the other hand, small perturbations in the weights can sometimes lead to quite different solutions. In practice, it can be very difficult to precisely and accurately select these weights, even for someone familiar with the problem domain. Besides, the existing GA based methods can not handle a practical requirement from users that gives them the corresponding optimally robust watermarked image when an acceptable fidelity such as peak-signal-to-noise ratio (PSNR) is specified.

To deal with the dilemma faced by the existing GA-based approaches, we propose a new scheme by treating the image watermarking as a multi-objective optimization problem rather than a single one like the existing GA-based approaches did. Hence, we have two objectives, i.e. image fidelity and watermark robustness, needed to be optimized simultaneously. By applying the multi-objective optimization algorithm, we can obtain a set of optimal solutions from which the user can select the most suitable one according to his demand without trial-and-error procedure.

The Bees Algorithm (BA) is a new population-based search algorithm. The algorithm mimics the food foraging behavior of swarms of honey bees. The foraging process begins in a colony by scout bees being sent to search for promising flower patches. Scout bees move randomly from one patch to another. When they return to the hive, those scout bees that found a patch will pass three pieces of information regarding that flower patch: the direction in which it will be found, its distance from the hive and its quality rating through the “waggle dance” [16]. This information helps the colony to evaluate the relative merit of different patches according to both the quality of the food they provide and the amount of energy needed to harvest it [17]. Accordingly, the bee colony can dispatch its bees to flower patches precisely. In [18], the Bees Algorithm was presented and its performance was tested by means of solving functional optimization problems,

including nine benchmarking functions from

two-dimensional function to ten-dimensional function, in terms of speed of optimization and accuracy of the results obtained. These experimental results show that the Bees Algorithm produces a 100% success rate in all cases. Compared with the deterministic simplex method [19], the stochastic simulated annealing optimization procedure [19], the GA [19] and the ant colony system [19], the BA can find the optima 1.4 times, 18.4 times, and 2.4 times faster than deterministic simplex method, GA, and ant colony system, respectively, in terms of averaged iteration number. The only one exception is the stochastic simulated annealing optimization procedure, its speed is 2.5 times faster than BA. However, its success rate is lower. Generally speaking, the BA can

outperform most popular optimization techniques compared with it in terms of speed of optimization and accuracy of the results obtained.

Recently, Pham and Ghanbarzadeh [20] extended the BA to solve multi-objective optimization problems, which is denoted as MOBA (multi-objective Bees Algorithm), and achieved very good performance. A standard mechanical design problem, the design of a welded beam structure, was used to benchmark the MOBA. In comparison with the number of solution found by non-dominated sorting genetic algorithms, it can be seen that the MOBA can find more non-dominated solutions fast. Based on the good performance for the MOBA in solving multi-objective optimization problems, we model the image watermarking problem via utilizing the MOBA to develop a new watermarking scheme. The cover image is transformed into DCT domain first. Initially, the watermark embedding locations are randomly selected to embed the watermark. The image fidelity and the robustness of the watermarked image are evaluated to form two objectives for the MOBA evolution and then the embedding locations are updated. These processes are repeated until convergence and a set of optimal solutions can be acquired. Each optimal solution corresponds to a specific set of embedding locations arrangement. Finally, the user can select one of the optimal solutions according to his demand.

This paper is organized as follows. We describe the fundamental concepts of multi-objective optimization and introduce the MOBA in Section 2. Section 3 explains the algorithm for embedding and extracting the watermark in the DCT domain with the MOBA. Section 4 illustrates the experimental results, and we also show the superiority of our scheme over the results by using the existing GA-based approaches in this section. In Section 5, the proposed method’s applicability and weakness are explained and a comparison with another method which also handles conflicting requirements of watermarks is made. Finally, we conclude this paper in Section 6.

2 The MOBA

Since a minimum of a function f is a maximum of –f, the

general optimization problem may be stated

mathematically as maximize fi(x), i = 1, 2, . . . , l, subject to Eqs. (1) to (2), where x is the column vector of n independent variables, i.e. x = [x1,x2,. . . ,xn]T, fi(x) are the l objective functions, cj(x) are the p equality constraints, and hk(x) are the q inequality constraints. When fi(x) and Eqs. (1) and (2) are taken together, they are known as problem function [21].

cj(x) = 0, j = 1, 2, . . . , p (1)

hk(x) ≥ 0, k = 1, 2, . . . , q (2)

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Jiann-Shu Lee received the Ph.D. degree in electrical engineering from the National

Cheng Kung University,

Tainan, Taiwan. He is

currently a Professor with the Department of Computer

Science and Information

Engineering, National

University of Tainan, Taiwan. His current research interests include multimedia signal analysis, image processing, medical image processing, and computational intelligence. He is author or coauthor of many academic articles. Dr. Lee has engaged as a Section Chairs in many domestic and international conferences. He has also received numerous awards from organizations, such as Acer, International Association for the Engineers, Information Hiding and Multimedia Signal Processing, and Xerox.

Jing-Wein Wang

received B.S. and M.S. degrees in Electronic Engineering from National Taiwan University of Science and Technology in 1986 and 1988, respectively, and a Ph.D. degree in Electrical Engineering from National

Cheng Kung University,

Taiwan, in 1998. From 1992 to 2000 he was a principal project leader at Equipment Design Center of PHILIPS, Taiwan. In 2000, he joined the faculty of National Kaohsiung University of Applied Sciences, where he is currently a professor in the Institute of Photonics and Communications. His current research interests are combinatorial optimization, pattern recognition, wavelets, and biometric applications. He is a member of IEEE.

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Appl. Math. Inf. Sci. 8, No. 6, 2945-2953 (2014) /www.naturalspublishing.com/Journals.asp 2953

Kuang-Yu Chien

received the Master degree in Department of Computer

Science and Information

Engineering from National University of Tainan, Tainan, Taiwan, in 2009. His research interests include softwae formal methods and image processing.

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