Digital image watermarking capacity and detection error rate
Introduction
Watermarking techniques have recently become important in a number of application areas. The watermarking capacity of digital image is the number of bits that can be embedded in a given host image. The performance of watermarking detection is measured by the bit error rate (BER) or probability of error PB. The bit error rate is the number of error bits in the total length of information messages bits. The detection reliability of watermarking closely correlates to two other parameters, which are the watermarking capacity and robustness. The robustness denotes the performance towards intentional and unintentional attacks. The main requirement of robustness is to resist different kind of distortions introduced by common processing and/or malicious attacks while satisfying the imperceptibility criteria.
The watermarking can be considered as a communication process, and the Gaussian probability distribution is a popular model for the watermarking channel. This model gives rise to closed form solutions for the watermarking capacity. The image in which the watermark messages are embedded is the communication channel. The watermark messages are transmitted over the channel (Cox et al., 1999, Cox et al., 2001). The watermarking capacity corresponds to the communication capacity of the “watermarking channel”.
Recently, a few models on the watermarking capacity have been proposed. Servetto et al. (1998) considers each pixel in the image as an independent communication channel and calculates the capacity according to the theory of Parallel Gaussian Channels (PGC). Barni et al.’s (1999) research focuses on the watermarking capacity in the DCT and the DFT domain. A game-theoretic approach for the evaluation of watermarking capacity is introduced by Moulin, 2001, Moulin and Mihcak, 2002. Lin and Chang (2001) presents zero-error information hiding capacity analysis in the JPEG compression domain using the adjacency-reducing mapping technique. There are also some other works, such as the references Choo and Kim, 2003, Alexandre et al., 2003, Frank and Scott, 2003, Anelia and Neri, 2004, which have been presented in recent years.
The content of image influence the watermarking capacity in two aspects. The content of image are the carrier of watermarking, but in the blind watermarking, they become the obstacles in the watermark detection or extraction. Obviously, more watermark can be embedded in the complex images than in the flat images, such as a pure white image. We suggest that the watermarking capacity should be associated with the content of image. The watermarking capacities of images differ from each other. However, in some previous works on the watermarking capacity, the capacity is calculated using a given power signal-to-noise ratio (PSNR), and the same watermarking capacity is designated to different images with the same size.
This paper discusses the watermarking capacity of digital images in the spatial domain and wavelet domain. Most of these works discuss watermarking in the spatial domain. Recently, the wavelet transform became widely applied in watermarking research due to its excellent property of multi-resolution analysis. Watermarking algorithms based on the wavelet transform became the major direction of watermarking research. In these algorithms, watermark is embedded and extracted in the wavelet transform domain. The content of image in the wavelet domain differs from that in the spatial domain. It would be proper to discuss the watermarking capacity in wavelet domain. The capacity and reliability are two important properties of the digital watermarking. The research on the relation between watermarking capacity and reliability will help us find ways to transmit more watermark information while keeping an acceptable watermark detection bit error rate.
The rest of this paper is organized as follows. In Section 2, a watermark algorithm is introduced. In Section 3, the watermarking capacity of digital images are discussed in the spatial domain and wavelet domain. In Section 4, we analyze the relationship between the watermarking capacity and the watermark detection error rate, and derive the relation between the capacity and the bounds of error rate. When the channel coding is used, the relationship between the watermarking payload capacity and the watermark detection error rate is discussed in Section 5. The experimental results are shown in Section 6. The conclusions of this paper are drawn in Section 7.
Section snippets
Spatial domain
The Human Vision System (HVS) models have been studied for many years. These works describe the human vision mechanism such as the spatial frequency orientation, the sensitivity on local contrast and the masking. Noise Visibility Function (NVF) is the function that characterizes local image properties. It identifies the texture and the edge regions of an image where the watermark should be more strongly embedded (Voloshynovskiy et al., 1999, Voloshynovskiy et al., 2001). It can be used in
Watermarking capacity
In the watermarking schemes, the process of watermarking can be considered as a communication problem. The image is the channel in which the watermark messages are transmitted. The watermarking capacity corresponds to the communication capacity of the “watermark channel”. The Gaussian probability distribution is a popular model for the watermarking channel. This model gives rise to closed solutions for the watermarking capacity.
A block diagrams is shown in Fig. 1 to illustrate the process of
Relation between the watermarking capacity and detection error rate
In this section, we analyze the relation between the watermarking capacity and the watermark detection error rate, and derive the relation between the capacity and the bounds of detection error rate.
Detection error and payload capacity
The watermarking capacity is the number of bits that can be hidden in a given host image. In spite of the definition is simple, we have to distinguish between two different concepts of the watermarking capacity:
- 1.
Payload capacity CPL. It is the size (in bits) of the watermark messages actually embedded, associated to a certain decoding error rate.
- 2.
Theoretical capacity C. It is a theoretical limit on the amount of error-free emendable watermark messages, or inversely, on the minimum probability of
Experimental results
In the experiments, 256 × 256 test image Peppers, Lena and Fishingboat are used. A bi-orthogonal 9/7 DWT is used to decompose the host image into four levels. The NVF is computed in 3 × 3 image windows. The noises are assumed to be the white Gaussian noises.
According to Eq. (4), we can calculate the maximum allowable watermark amplitude of each pixel while keeping watermark’s invisibility. Fig. 2 shows Lena’s Maximum Watermark Image. Fig. 3 shows original Lena image and its stego image (PSNR is
Conclusion
Because of the requirements of robustness and invisibility, watermarking has some properties different from the traditional communication. We suggest that the watermark power constraint should be associated with the content of image. In this article, we combine Watson quantization matrix and the Noise Visibility Function to determine the watermark amplitude, and propose an adaptive watermarking capacity analysis method in the wavelet domain. The experimental results show that the watermarking
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant No. 60075002 and the National 863 Program of China under Grant No. 2003AA144080.
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