Image Digitl Watermarking Based On The Fractional Fourier Transform

Based on fractional Fourier transform, this paper presents four digital watermarking algorithms. The watermarked images are little degraded and the algorithms have good robustness.In gray image watermarking, a watermark of 32 X 32 gray image is embedded into the secondary visual important part of the original image. And in another gray image watermarking, the watermark is transformed with different orders for four times and the four watermarks in different FRFT domain can be gained. They are added to four different places of original image in DFRFT domain. The original image in DFRFT domain added with watermarks was inversely transformed and the watermarked image is obtained. The average value of the four extracted watermarks is viewed as the extracted watermark to balance the distortion of the watermark signals.Linear Frequency Modulation signal will present energy centralization when it is transformed with some order to some FRFT domain. A 128×128 2D Chirp signal is used. First transform the Chirp signal with different order from 0 to 1 and then search the maximum...