Image Forensics Using Generalised Benford's Law for Improving Image Authentication Detection Rates in Semi-Fragile Watermarking

Introduction

Nowadays, the popularity and affordability of advanced digital image editing tools, allow users to manipulate images relatively easily and professionally. Consequently, the proof of authenticity of digital images has become increasingly challenging and difficult. Moreover, image authentication and forensics techniques have recently attracted much attention and interest from the Police, particularly in law enforcement applications such as crime scene investigation and traffic enforcement applications.

Semi-fragile watermarking has been used to authenticate and localise malicious tampering of image content, while permitting some non-malicious or unintentional manipulations. These manipulations can include some mild signal processing operations such as those caused by transmission and storage of JPEG images. In the literature, a significant amount of research has been focused on the design of semi-fragile algorithms that could tolerate JPEG compression and other common non-malicious manipulations (Lin & Chang, 2000; Lin et al., 2000; Zou et al., 2006; Zhu et al., 2007a; Zhu et al., 2007b; Yu et al., 2000; Kundur & Hatzinakos, 1999). However, watermarked images could be compressed by unknown JPEG QFs. As a result, in order to authenticate the images, these algorithms have to set a pre-determined threshold that could allow them to tolerate different QF values when extracting the watermarks.

The art of determining the threshold values for semi-fragile watermarking schemes has been extensively documented by several researchers. In this paper, we review three common approaches. The first approach uses a threshold for authenticating each block of the image (Lin et al., 2000; Zhu et al., 2007a). In this scheme, if a block of correlation coefficients (between the extracted watermark and its corresponding original watermark ) is smaller than threshold, this block is classified as a tampered block, and vice versa. This is represented in Equation (1):, (1) where is the maximum threshold value with , and is the JPEG compression tolerance margin. We discuss this approach in more detail in the next section. The second approach uses a threshold, which has been pre-determined during the watermark embedding process (Zou et al., 2006; Zhu et al., 2007a). An example is illustrated in Figure 1, where the watermarks are embedded into each side of threshold according to the watermark value (e.g., 0 or 1), by shifting or substituting the corresponding coefficient. The value of and controls the perceptual quality of the watermarked image. Thresholdis determined empirically to detect the watermark while extracting the watermarks. is the JPEG compression tolerance margin. If then, otherwise (Zhu et al., 2007a).