Journal of Electrical and Computer Engineering

Volume 2016, Article ID 9029745, 16 pages

http://dx.doi.org/10.1155/2016/9029745

## A New Scalar Quantization Method for Digital Image Watermarking

Computer Science, School of Information Sciences, University of Tampere, Kanslerinrinne 1, 33014 Tampere, Finland

Received 7 October 2015; Revised 18 January 2016; Accepted 24 January 2016

Academic Editor: Mazdak Zamani

Copyright © 2016 Yevhen Zolotavkin and Martti Juhola. 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

A new technique utilizing Scalar Quantization is designed in this paper in order to be used for Digital Image Watermarking (DIW). Efficiency of the technique is measured in terms of distortions of the original image and robustness under different kinds of attacks, with particular focus on Additive White Gaussian Noise (AWGN) and Gain Attack (GA). The proposed technique performance is affirmed by comparing with state-of-the-art methods including Quantization Index Modulation (QIM), Distortion Compensated QIM (DC-QIM), and Rational Dither Modulation (RDM). Considerable improvements demonstrated by the method are due to a new form of distribution of quantized samples and a procedure that recovers a watermark after GA. In contrast to other known quantization methods, the detailed method here stipulates asymmetric distribution of quantized samples. This creates a distinctive feature and is expressed numerically by one of the proposed criteria. In addition, several realizations of quantization are considered and explained using a concept of Initial Data Loss (IDL) which helps to reduce watermarking distortions. The procedure for GA recovery exploits one of the two criteria of asymmetry. The accomplishments of the procedure are due to its simplicity, computational lightness, and sufficient precision of estimation of unknown gain factor.

#### 1. Introduction

In modern communications, multimedia plays significant role. Ownership of multimedia data is important and needs to be protected [1]. As a part of nowadays popular multimedia content, digital images are an important class. A protection of digital rights of an owner is implemented by Digital Image Watermarking (DIW). A watermark that is inserted into an image has to be robust [2] as well as invisible [3].

Among the popular and efficient techniques in DIW, Quantization Index Modulation (QIM) is widely used in blind watermarking where neither original media nor watermark is known to the receiver [4, 5]. One of the aspects of robustness of QIM is evaluated by attacking a watermarked image with Additive White Gaussian Noise (AWGN). Unfortunately, all the known on practice implementations of QIM are far from achieving the channel capacity limit that was first derived in [6].

Several different QIM-related approaches are known. Some state-of-the-art realizations will be outlined briefly. According to QIM, intervals of equal length are mapped on the real number line. The oldest known approach is to replace all the original coefficients inside every interval with one of the two endpoints of that interval. The selection of the endpoint depends on a bit of a watermark [7]. The main disadvantage is that for high intensity of noise and the capacity of the oldest QIM is much lower than the theoretical limit. In a more advanced realization of DC-QIM, coefficients from every original interval are mapped into two disjoint subintervals. The gap between the subintervals is controlled by parameter , [8]. Assuming that initial distribution inside original interval and target distributions in subintervals are uniform, the mapping in accordance to DC-QIM is optimal in terms of Mean Square Error (MSE) of quantization. In order to maximize capacity for a given MSE under AWGN of different intensity, parameters , have to be adjusted. Nevertheless, the limit defined in [6] is still well above the one achievable by DC-QIM.

Not all the original coefficients in each interval need to be quantized. This idea has been explored by the authors of Forbidden Zone Data Hiding (FZDH) [9]. Another idea was proposed by the authors of Thresholded Constellation Modulation (TCM) that uses two different quantization rules to modify coefficients inside the original interval [10].

Despite sufficient robustness of QIM under AWGN, the limitation is that synchronization is required in order to reconstruct intervals that are necessary to extract (or decode) a watermark. A type of distortion which scales all the watermarked coefficients is called Gain Attack (GA). The scaling factor might be close to 1 and cause very little visual distortion, but it is unknown to the receiver which causes asynchronous extraction. Retrieval of the watermark is usually complicated by AWGN that follows GA [11].

Improvement of QIM performance under GA is the task of numerous known approaches [12]. Most of them can be classified into two groups where the main idea of the first group is to estimate the unknown factor [13] while the idea of the second is to quantize coefficients of a different kind that are invariant to scaling of original signal.

The solution proposed in [11] contributes to robustness enhancement in case of GA and a constant offset attack followed by AWGN. A pilot signal is embedded for this purpose. Fourier analysis is used during extraction to estimate the gain factor and the offset. Another method of recovery after GA and AWGN is proposed in [14]. It uses information about dither sequence and applies Maximum Likelihood (ML) procedure to estimate the scaling factor.

Watermarking that is invariant to GA demands more complex transform of original signal (e.g., nonlinear) to obtain coefficients. One of the most popular watermarking methods in that category is Rational Dither Modulation (RDM) [15]. For a particular coefficient, a ratio that depends on a norm of other coefficients is being quantized instead of a coefficient itself. In order to quantize the ratio, RDM utilizes the simplest QIM scheme. This implies that the performance of RDM under AWGN (without GA) is close to the simplest QIM. Among others recent blind watermarking methods robust to GA are, for example, detailed in [16–18].

A new scalar QIM-based watermarking method is proposed in this paper. It provides high robustness under conditions of AWGN and GA. Among the new features of the method are IDL and a new form of distribution of quantized samples.

The organization of the rest of the paper is as follows. Section 2 explains the choice of the distribution of quantized samples and contains description of the procedure of recovery after GA. Concept of IDL and quantization model are described in Section 3 using formal logic approach. The aspects of analytic-based estimation of robustness under AWGN are discussed in Section 4. Next, Section 5 contains experimental results obtained under AWGN and GA. Discussion of the details of the experiment and comparison of the performance are given in Section 6. Section 7 concludes the paper. The list of the key variables and their meaning is given in Nomenclature section.

#### 2. Distribution of Quantized Samples and Procedure for Recovery after GA

An asymmetric distribution of quantized samples is proposed and parametrized in this section. Asymmetry is the quality that can be easily expressed quantitatively. Under symmetric attack, like AWGN, such quantitative index remains sufficiently indicative. On the other hand, it can be affected by GA. Such semifragility is favorable for restoration of the right condition for decoding. The restoration is done by the procedure for recovery after GA which uses criterion of asymmetry. Compared to the known estimation procedures [14], the one proposed in this section depends on a single variable which is the unknown gain factor. This makes the technique simple and more precise.

For encoding, in our case, asymmetric distribution requires substantially more variables for description compared to common QIM methods. Because of that, it is advisable to refer to Nomenclature section.

##### 2.1. Distribution of Quantized Samples

Symbol will be used to denote a random variable whose domain is the space of original coefficients of a host. A particular realization of will be denoted as . We will further consider manipulation of original values that are in some th interval of size and its left endpoint is . Such an interval is referred further as embedding interval. For any we define and will be used to denote a random variable which represents . The value of should be small enough so that the distribution of can be considered uniform. A random variable that represents quantized coefficients inside th interval is denoted as and its realization is denoted as . Each pair of an original and corresponding quantized belongs to the same th embedding interval so that an absolute shift is never larger than . Correspondingly, a random variable that represents quantized coefficients on the whole real number line is denoted as and its realization is denoted as .

In order to provide efficient recovery after GA, we propose the following asymmetric distribution of quantized samples inside th embedding interval (Figure 1(a)):where and are two different kinds of truncated distributions defined asThe other parameters are constrained in the following way: , (see Nomenclature section). The meaning of parameters , , , will be discussed later in Section 3. In Figure 1(b) we can see the distribution of the quantized coefficients outside th embedding interval as well.