Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 937432, 13 pages

http://dx.doi.org/10.1155/2015/937432

## A Novel Scrambling Digital Image Watermark Algorithm Based on Double Transform Domains

^{1}School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, China^{2}School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

Received 21 January 2015; Accepted 20 August 2015

Academic Editor: Konstantinos Karamanos

Copyright © 2015 Taiyue Wang and Hongwei Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Digital watermark technology is a very good method for protecting copyright. In this paper, in terms of requisition of imperceptibility and robustness of watermarking, the multidirectional, multiscale, and band-pass coefficient features of Curvelet transform are introduced and a novel image watermark scheme based on Curvelet and human visual system is proposed. Digital watermark information is embedded into the first 16 directions with larger energy in the fourth layer. Experimental results indicate that the proposed watermark scheme is feasible and simple. Simultaneously, the embedded watermark images just have tiny difference with the original images and the extracted watermark is accurate. Moreover, it is imperceptible and robust against various methods of signals processing such as cropping, noise adding, and rotating and altering.

#### 1. Introduction

With the development of multimedia technology and network communications, digital products are increasingly popular. Due to illegal copying and tampering of digital product, traditional encryption technology is not sufficient to protect legitimate rights of digital media copyright. Digital watermarking which is hidden in digital products can play an important role. Recently, the digital watermarking has become one of research hotspots in the field of signal processing and information security. Its key is to embed the unremovable watermarking into the protected original signal without affecting data availability. Simultaneously, the watermarking can be completely and exactly extracted or detected, to satisfy solving the copyright disputes such as piracy tracking, and so forth. Therefore, the embedded digital watermarking must possess the following characteristics [1, 2]: imperceptibility: embedded watermarking should not lead to obvious visual difference and hidden information cannot be perceived easily; robustness: the carrier image is attacked or processed; the embedded digital watermark information also can be extracted exactly; maximum of information: the embedded watermark information should be capacity as much as possible in the digital products to achieve the largest hidden information volume of carrier object; determinacy: the copyright of digital watermark information could uniquely determine the owner of the digital products even via certain damage.

According to the difference of embedding watermark technology, the algorithms were divided into watermarking in spatial domain and watermarking in transform domain [3]. For watermarking in spatial domain, the amplitude of sample points of original image was changed directly and its representative algorithm was the Least Significant Bit algorithm [4]. Changing coefficients of carrier image via embedding watermark information was called watermarking in transform domain. In general, the main idea of watermark algorithm in transform domain is changing the image transform domain coefficients to embed watermarking which adopts the spread spectrum communication principle. Digital watermark technology in transform domain has obvious advantages [5, 6]: The watermark information can be distributed into all pixels of spatial domain and ensure the imperceptibility of watermarking. Centralization of energy distribution can embed large quantity of watermark data and guarantee better imperceptibility, stronger robustness, and higher security. It is compatible with the existed image compression method and can embed watermarking into the compressed image. It is compatible with human visual system and can hide the watermarking easily. The existed watermark algorithms in transform domain mainly include Discrete Fourier Transform (DFT) [7], Discrete Cosine Transform (DCT) [8], and Discrete Wavelet Transform (DWT) [9]. They can effectively represent point singularity and deficiency for linear or curve singularity of natural images. Recently, with the development of the multiscale geometric transform, the approximation abilities of signal and image are continually enhanced, which is gradually correspondent to the human visual system and has been widely applied in many fields. There are plenty of researches in the field of information security, such as watermark algorithm based on Ridgelet Domain [10] and Curvelet Domain [11]; they can further improve the imperceptibility and robustness of watermark algorithm. According to various transforms and HVS, the capacity of the watermark insertion was introduced in some literatures [12–14].

In this paper, we study an algorithm in transform domain. According to the requirement of digital watermarking robustness and imperceptibility, the multidirectional, multiscale, and band-pass coefficient features of Curvelet transform are introduced and a novel image watermark scheme based on Curvelet and human visual system is proposed. At first, the scrambling digital watermark image via a layer of wavelet decomposition. Then, the original carrier image is transformed via Curvelet. At last, we embed low frequency components of watermark image into the larger 16-directional coefficient matrix of fourth layer of carrier image. Experimental results show that the proposed algorithm is simple and effective. The difference between the original image and the embedded watermark image is tiny. Simultaneously, the embedded watermarking can be extracted easily and accurately. Moreover, the algorithm has good imperceptivity and robustness for various attacks such as cropping, noise adding, and rotating and altering.

#### 2. Curvelet Transform

##### 2.1. The Theory of Curvelet Transform

Wavelet theory emerged in the mid-1980s. The good capability of time and frequency analysis is the important reason for its rapid development. However, wavelet transform cannot ideally achieve the optimal approximation order of signal for two-dimensional or higher “line of singularity.” So, Ridgelet theory was arisen at the historic background of theory. The basic theories of Ridgelet transform are given by Candès in 1998 [15]. It transforms “line of singularity” in the two-dimensional function into “point of singularity,” and then wavelet transform can obtain the optimal nonlinear approximation order for the “line of singularity” of two-dimensional or high dimensional function. Monoscale Ridgelet transform [16] and Curvelet transform [17] are developed based on the Ridgelet transform. They derive from function localization and frequency band splitting, respectively, and both can approximately represent line and curve singularity. Differently, the basic scale of monoscale Ridgelet transform is fixed; the basic scale of Curvelet transform is arbitrary and can be decomposed in any possible scale. Curvelet transform is a mixture of special filter process and multiscale Ridgelet transform as follows. Achieving Curvelet transform requires a series of filters: , . The filter maps the function as follows: The coefficients of Curvelet transform are as follows:

Curvelet transform maps arbitrary mean square integrable function as transform coefficient , where the parameter set of is and is called Curvelet. The set of Curvelet constitutes a compact framework of and can be decomposed asSupport interval of Curvelet bases is the most core relationship of Curvelet transform and satisfies the following:

It denotes anisotropy scaling relationship. Curvelet is a kind of directional basis atom and Curvelet transform is a kind of multidirectional, multiresolution, and band-pass function analysis method. USFFT and WRAP algorithm for Curvelet transform are presented by Candès [18].

##### 2.2. Analysis of Curvelet Coefficients Characteristics

The coefficients of structure can be obtained via Curvelet transform, where , , and denote scale, direction, and th direction matrix coordinate in scale layer , respectively. Lena image (Figure 1) with the size of , for example, is divided into six-scale layer via Curvelet transform. Its innermost layer, namely, the first layer, is called Course scale layer, which is a matrix made up of low frequency coefficient and occupies the vast majority of energy of the coefficients, including the general picture of image. The outermost layer, namely, the 6th layer, is called fine scale layer, which is a matrix composed of high frequency coefficient, and shows image edges and details. The 2~5 layer in the middle is called the detail scale layers. Coefficient of each layer is stratified into four broad directions and each broad direction is divided into 8, 8, 16, and 16 small directions. Each small direction is a matrix composed of medium and high frequency coefficients and the matrix is called subband coefficients matrix. Figure 2 shows coefficient matrix images of the first five layers; Figure 3 shows the coefficient matrix image of different directions in the 4th layer. Figure 4 is the outermost layer coefficient matrix image. The transform coefficient format of matrix coordinate in th direction of th layer is shown in Table 1.