Robustness of Double Random Phase Encoding spread-space spread-spectrum watermarking technique

• Robustness of the DRPE spread-space spread-spectrum watermarking is investigated.
• This even spreading characteristic of DRPE suggests good watermarking robustness.
• Several common geometric transformations and signal processing are performed.
• The performance of the method is compared to Cox׳s additive spread-spectrum.
• This method is robust to scaling, JPEG, cropping and low/high pass filtering.

In this paper the robustness of a recently proposed image watermarking scheme, namely the Double Random Phase Encoding spread-space spread-spectrum watermarking (DRPE SS-SS) technique, is investigated. The watermark, which is chosen to be in the form of a digital barcode image, is numerically encrypted using a simulation of the optical DRPE process. This produces a random complex image, which is then processed to form a real valued random image with a low number of quantization levels. This signal is added to the host image. Extraction of the barcode, involves applying an inverse DRPE process to the watermarked image followed by low pass filtering. This algorithm is designed to utilize the capability of the DRPE to reversibly spread the energy of the watermarking information in both the space and spatial frequency domains. In this way the energy of the watermark in any spatial or spatial frequency bin is very small. To test robustness several common geometric transformations and signal processing operations are performed using both informed and blind detections for different barcode widths and different quantization levels. The results presented indicate that while the DRPE SS-SS method is robust to scaling, and JPEG compression distortion, it is especially robust to spatial cropping and both low and high pass filtering. Both random-watermark and random-host false positive cases are examined. The uniqueness of the watermark is demonstrated, and it is shown that the DRPE SS-SS has very low false positive errors, and that the larger the barcode width, the lower the false positive rate. Finally the effects of both printing and scanning are examined.