In this paper the robustness of a recently proposed image watermarking scheme is investigated, namely the Double Random Phase Encoding spread-space spread-spectrum watermarking (DRPE SS-SS) technique. In the DRPE SS-SS method, the watermark is in the form of a digital barcode image which 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 a low pass filter. 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, and the energy of the watermark in any spatial or spatial frequency bin is very small. The common geometric transformations and signal processing operations are performed using both the informed and the blind detections for different barcode widths and different quantization levels. The results presented indicate that the DRPE SS-SS method is robust to scaling, JPEG compression distortion, cropping, low pass and high pass filtering. It is also demonstrated that
the bigger the barcode width is, the lower the false positive rate will be.
In this paper, we propose a method for the numerical simulation of optical double random phase encoding (DRPE). This method is based on a discrete model of the DRPE system that retains the properties of its optical counterpart and takes into account the capacity of DRPE to spread a signal’s energy in both the space and the spatial frequency domains. Discrete versions of two narrowband lossless diffusers are created to simulate their analogue optical counterparts and their bandwidths control how much the energy of the input signal is spread in both the space and spatial frequency domains as it passes through the system. The limiting case, when complete aliasing (maximum overlap) takes place, is also discussed in relation to our method. In this case, we show our method reduces to a purely numerical encryption procedure which can, nonetheless, be decrypted perfectly. Simulation results are presented to demonstrate the feasibility of the proposed technique.
Proc. SPIE. 8498, Optics and Photonics for Information Processing VI
KEYWORDS: Signal to noise ratio, Image encryption, Digital image processing, Image processing, Digital watermarking, Computer programming, Digital imaging, Quantization, Signal detection, Optical image encryption
In this paper a digital invisible image watermarking technique is proposed based on the numerical simulation of optical Double Random Phase Encoding (DRPE). This technique utilizes the capability of the DRPE to spread the energy of the input information in both the space and the spatial frequency domains using two different users. The watermark is in the form of a digital barcode image which 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 a low pass filter. The results presented indicate the feasibility and robustness of the proposed method and it is demonstrated that even when using very few quantization levels, i.e. 2-levels, the watermark can still be extracted with very small errors.