Reversible Watermarking in Digital Image Using PVO and RDWT

Introduction

Digital watermark has been widely used in the copyright protection of digital image. By whether the algorithm could reverse the cover image to the original state, digital watermarking schemes could be divided into reversible and irreversible schemes. Reversible watermarking scheme is more preferred than irreversible scheme because of the highly demand on the perceptional quality of the image, especially in some special area, such like medical or military usage. Based on the algorithm used to achieve reversible embedding, the reversible watermarking scheme could be categorized into three types: lossless compression based schemes, difference expansion (DE) based schemes and histogram shifting / histogram modifying (HS/HM) based schemes.

The lossless compression based schemes first compressed the cover image using lossless compressing scheme (Kountchev, Todorov, Kountcheva, & Milanova, 2006; Maxwell, Handel, & Bradley, 1998; Shih & Wu, 2005). Then the watermark could be embedded into the image by exploit the space generated by the compression. During the extraction process, the watermark was extract from the image, then the cover image was reverse to the original state by decompressing the compressed image using the lossless compression algorithm.

Lossless compression based schemes are easily to achieve. However, the performance of these schemes highly effected by the performance of the lossless compression algorithm. The drawback of lossless compression based scheme are robustness and perceptional quality. This kind of scheme usually vulnerable against tampering attack. Moreover, since the cover image had been compressed, the visual quality of the stego-image is significantly deduced. This drawback made the lossless compression based scheme not suitable for the usage of reversible watermarking.

Difference expansion based scheme was first proposed by Tian (2003). The main idea of Tian’s scheme is as follows: For an 8-bit grayscale image, a pixel pair (x, y) is used to embed a secret bit S,. In the embedding phase, the difference value h and the integer average value l are defined as:

The inverse transform is

Next, the new difference is obtained as follows:

Finally, the stego-pixel pair is obtained by the following transform:

In order to prevent underflow and overflow, the absolute of new difference after a secret bit S has been embedded must satisfy the following condition:

DE based scheme was initially proposed and used in spatial domain embedding. Since it is easy to achieve, lots of researches had been done and several improvements have been made based on Tian's scheme. For example, Alattar et al. introduced DE scheme into quad of pixels (2004). By expanding pairs to quads, Alattar's scheme improved the embedding capacity from 0.5 bpp to 0.75 bpp at best case. Other researches using the same method including Lee's (2008) and Chang's (2006) scheme. These schemes tried to expand pairs of pixels to quads or even more pixels. These improved schemes could generate more differences than original DE scheme, which means higher embedding capacity.