Enhancement of image watermark retrieval based on genetic algorithms

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Abstract

A watermark hidden in an image is retrieved differently from the original watermark due to the frequently used rounding approach. The simple rounding will cause numerous errors in the embedded watermark especially when it is large. A novel technique based on genetic algorithms (GAs) is presented in this paper to correct the rounding errors. The fundamental is to adopt a fitness function for choosing the best chromosome which determines the conversion rule of real numbers into integers during the cosine transformation. Experimental results show that the dramatic improvement in reducing the errors is successful when GAs are used in decision making. Furthermore, we develop an initial chromosome by comparing the difference between the original image and the rounded watermarked image to speed up the process. In additional to correct fragile-watermarking rounding errors, our algorithm can also be applied in robust watermarking to achieve higher watermarked image quality.

Introduction

Digital images, video, and audio have revolutionized in the way of enormous data storage, friendly manipulation, and secure transmission. These give rise to a wide range of applications in electronics, entertainment, and medial industry (Berghel and O’Gorman, 1996). Digital watermarking of electronic images has gained prominence as a result of the proliferation of multimedia and the Internet, with the need to protect copyright and ensure authenticity. It places an inherent digital identity into all media content, allowing media owners or issuers to identify the source, creator, owner, distributor, or authorized consumer of a document or an image. It can also be used for tracing images that have been illegally distributed.

Two types of digital watermarking are visible and invisible. For the visible watermarking technique such as on the bills, the embedded watermark can be viewed by eyes. The advantage is that we can recognize the owner of the watermarking without any calculation, but the disadvantage is that the embedded watermark can be removed or destroyed easily. The most common example is the encoded channels in the cable TV. On the other hand, for the invisible watermarking technique, the watermark is hidden on the unknown places in the media data and cannot be viewed by eyes. If someone illegally uses the watermarked data, the embedded watermark will be used for showing the ownership. In this paper, we are concerned with the invisible watermarking technique.

Invisible watermarking can be classified into two parts, robust and fragile watermarks. Generally speaking, robust watermarks (Cox et al., 1997, Lin and Chen, 2000, Nikolaidis and Pitas, 1998) are usually designed to resist arbitrarily malicious attacks such as image scaling, bending, cropping, lossy compression, and so on. They are usually used for copyright protection to declare the rightful ownership. In contrast, for the purpose of image authentication, the fragile watermarks (Celik et al., 2002, Wong, 1998) are adopted and designed to detect any unauthorized modification. For implementation of both watermarking approaches, the watermarks are usually embedded in the LSB of a host image for the fragile watermarks; however in the perceptually significant regions of the image pixels for the robust watermarks despite the risk of potential fidelity distortions.

There are two methods of performing image watermarking, one in spatial domain and the other in frequency domain. In the spatial domain (Bruyndonckx et al., 1995, Nikolaidis and Pitas, 1998), we can simply insert watermarks into a host image by changing the gray levels of some pixels in the host image, but the inserted information may be easily detected using computer analysis. Furthermore, they can be easily removed by simple image processing, such as smooth filter and noise addition. Consequently, most current watermarking schemes are focused on the frequency domain approaches because they are more robust, invisible and stable than the spatial domain approaches.

In frequency domain (Bas et al., 2002, Huang et al., 2000, Lin and Chen, 2000), we can insert watermarks into coefficients of a transformed image, for example, using Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT) or Discrete Wavelet Transform (DWT) and that is usually difficult to detect. Cox et al. (1997) developed a spread-spectrum approach to improve robustness of watermarking by embedding watermarks into DCT domain of an image. However, there are two major defects. First, we cannot embed too much data in the frequency domain because the quality of the host image will be distorted significantly. That is, the size of watermark should be smaller than the host image. Generally, the size of watermark is 1/16 of the host image. Shih and Wu (2002) proposed a combinational image watermarking in the spatial and frequency domains to increase the watermark capacity and imperceptibility. Second, the data embedded in coefficients of a transformed image will be somewhat disturbed in the process of transforming the image from its frequency domain into its spatial domain because of deviations in converting real numbers into integers in spatial domain.

Note that, when embedding watermarks into frequency domain of a transformed image, the rounding errors are usually occurred in fragile watermarks since they are usually embedded into the LSB of coefficients of a transformed image. That is, they are so sensitive to any unauthorized modification. To reduce rounding errors, a novel technique by using genetic algorithms (GAs) is developed. Our GA-based algorithm can successfully correct the rounding errors for both robust and fragile watermarks since the rounding errors may happen on the perceptually significant bits of coefficients of a transformed image. For robust watermarks, they are usually embedded into higher bits of coefficients of a transformed image. However, it will cause large degradation of the original image. Therefore, our GA-based algorithm can also be used to achieve a higher Peak Signal-to-Noise Ratio (PSNR).

The paper is organized as follows. In Section 2, we present the overview of GAs used in reducing errors. Section 3 introduces the errors caused by deviations in translating real numbers into integers. Section 4 describes our methodology of applying GAs to solve the problem. Experimental results are shown in Section 5. Section 6 discusses further enhancement by GAs. Another implementation of our algorithm is described in Section 7. Finally, conclusions are made in Section 8.

Section snippets

Overview of genetic algorithms applied in reducing errors

Before presenting the basic concept of reducing errors by GAs, we are concerned with two primary issues:

  • (1) The embedded data should be accurate.

  • (2) The changes in order to modulate the errors should be minimal.

Note that coefficients in the frequency domain will be changed dramatically even though only one pixel in the spatial domain is changed. Moreover, changes of pixels in the frequency domain are difficult to derive intuitively. Therefore, we cannot know whether the embedded data are

The errors caused by deviations in translating real numbers into integers

Fig. 2 shows the errors caused by using the round technique in translating real numbers into integers. Fig. 2A is the original host image, an 8 × 8 gray-level image, in the spatial domain and Fig. 2B is the transformed image of Fig. 2A by DCT. Fig. 2C is a binary watermark, in which “0” and “1” denote the embedded value in its location; the minus sign “−” indicates no change in its position. We obtain Fig. 2D by embedding Fig. 2C into Fig. 2B based on LSB modification. Note that, the watermark is

Applying genetic algorithms to solve the problem

Since we cannot simply predict what the impacts will happen in the frequency domain of a host image if we change some values of pixels in the spatial domain of the host image, how to correct the rounding errors becomes a difficult task. To solve the problem, we can use the evolutionary algorithms, such as simulated annealing, hill climbing and GAs. In simulated annealing, the choice of an initial temperature and the corresponding temperature decrement strategy will affect the performance

Experimental results

Fig. 9 shows the result that corrects the errors by using GAs in translating real numbers into integers. Fig. 9A is the original host image, an 8 × 8 gray-level image, in the spatial domain and Fig. 9B is the transformed image of Fig. 9A by DCT. Fig. 9C is a binary watermark, in which “0” and “1” denote the embedded data in its location; the minus sign “−” indicates no change in its position. We obtain Fig. 9D by embedding Fig. 9C into Fig. 9B based on LSB modification. We can find three

Further enhancement by genetic algorithms

In Fig. 10, although we obtain numerous suitable solutions by GAs in order to correct the errors, many of them are useless if we consider the factor that changes in the original image should be as small as possible. That is, the PSNR should be as high as possible. The definition of PSNR isPSNR=10×log102552∑i=1N∑j=1Nh(i,j)-hGA(i,j)2.Therefore, the improved method for minimizing the changes is developed. To achieve the purpose of limited changes, we generate the first population based on an

Another implementation of our algorithm

Robust watermarks are designed to resist arbitrarily malicious attacks. Usually, they are embedded into higher bits of coefficient of a transformed image. Therefore, they do not have the rounding error problem except in some special cases. For example, the embedded watermark will be change from “0” to “1” in the 4th bit of “23” and “24.” However, it will cause large degradation of the original image.

Our GA-based algorithm can be used to achieve a higher PSNR. Fig. 15 shows an example of

Conclusions

In this paper, we present progression of correcting rounding errors based on GAs. Two primary issues that the embedded data should be extracted correctly and the changes in the watermarked images should be minimal, are considered. In general, if we want to achieve a higher PSNR (i.e., better quality in the watermarked image), NC must be lower (i.e., worse quality in the retrieved watermark). Therefore, how to choose the trade-off is an important issue in practical applications. In order to

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