تجزیه و تحلیل عملکرد بر اساس روش نهان سازی مبتنی بر روش کدگذاری فاز تصادفی دو برابر

When digital watermarking is used for piracy tracking, different watermarks are needed to be embedded into different distributions of a digital product. Based on double random phase encoding (DRPE) technique, cascaded-phases iterative algorithm and random-phase-shift algorithm, Chen et al. proposed a method to generate many different embedded watermarks from one reference watermark, while the embedded watermark can be recognized by testing the correlation between the recovered watermark and the original reference watermark. In this way, only the reference watermark instead of the embedded watermarks needs to be stored and managed. However, since the recovered watermark may be different from the embedded watermark, especially under any image processing, the correlation between the recovered watermark and the reference watermark may be different from the correlation between the embedded watermark and the reference watermark, which may result in wrong recognition. In this paper, the performance of Chen's method was analyzed with numerical simulations. The results indicated that, to correctly recognize the embedded watermark, the number of generated embedded watermarks with Chen's method is limited.

The double random phase encoding (DRPE) technique was a typical optical image encryption technique [1], which has been widely studied [2], [3] and [4] and has also been used to image hiding and watermarking [5] and [6]. Digital watermarking is mainly used to protect the copyright of digital products by embedding the copyright information, i.e., the digital watermark, into the digital products. The copyright can be proved by extracting or detecting the embedded copyright information from the digital product [7] and [8]. If the same digital watermark is embedded into many copies of a digital product for distribution, the watermark can only prove the copyright owner, while cannot tell the originality of piracy. To track the sources of illegal copies, different watermarks should be embedded into different distribution versions, which results in the requirement of generating, storing and managing many different watermarks [4], [7], [8] and [9]. To solve this problem, Chen et al. proposed a method to generate many different embedded watermarks from one reference watermark based on double random phase encoding technique, cascaded-phases iterative algorithm (CPIA) and random-phase-shift algorithm [10]. To prove the copyright and track the source of piracy, the correlation between the recovered watermark and the reference watermark is calculated to recognize the embedded watermark. Thus, only the reference watermark instead of all of the embedded watermarks needs to be stored. However, since the recovered watermark may be different from the embedded watermark due to computational errors, especially under any image processing, the correlation between the recovered watermark and the reference watermark may be different from the correlation between the embedded watermark and the reference watermark. This will influence the accuracy of watermark detection and piracy source tracking. In this paper, Chen's method is analyzed regarding the performance of watermark detection and piracy tracking. The rest of this paper is organized as follows: in Section 2, Chen's method is briefly introduced and analyzed. Section 3 performs the numerical simulations to analyze the performance of Chen's method. In Section 4, the final conclusions are presented.

The performance of the method of generating different embedded watermarks from one reference watermark proposed by Chen et al. [10] was analyzed. According to the numerical simulation results, it is found that the value of the correlation coefficient between the reference watermark and the recovered watermark may decrease significantly due to image processing. Therefore, to correctly recognize the embedded watermark, only several embedded watermarks can be generated from one reference watermark following Chen's method.