Rotation Invariance in 2D-FRFT with Application to Digital Image Watermarking

The extraction of rotation invariant representation is important for many signal processing tasks such as image analysis, computer vision, pattern recognition and so forth. In this paper, we show that, under certain conditions, the Two-Dimensional Fractional Fourier Transform (2D-FRFT) possesses this attractive property through mathematical analysis and extensive computer simulations. Based on this property, we propose a novel digital image watermarking method which combines 2D chirp signal with the addition and rotation invariant properties of 2D-FRFT in order to improve robustness and security of digital image watermark in 2D-FRFT domain. Experimental results show that the proposed method is robust against numerous watermarking attacks including rotation geometrical transform, JPEG compression, crop, median filtering, histogram equalization, salt & pepper noise, Gaussian lowpass filter, shift, dithering and Gaussian noise, and secures against unauthorized information copying and redistribution.