Quaternion discrete fractional random transform for color image adaptive watermarking

As for the fractional transforms, to date only fractional Fourier transform (FrFT) has been applicable to color images in a holistic manner by using the quaternion algebra, yet, discrete fractional random transform (DFRNT) with the useful intrinsic randomness is still to be explored. This paper first defines quaternion DFRNT (QDFRNT) which generalizes DFRNT to efficiently process quaternion signals, and then applies QDFRNT to color image adaptive watermarking. For the QDFRNT, this paper also derives the relationship between QDFRNT of a quaternion signal and DFRNT of four components for this signal to efficiently compute QDFRNT. For the color image adaptive watermarking based on QDFRNT and SVM, in order to efficiently utilize the color information in the adaptive process, this paper also exploits the human vision system’s (HVS) masking properties of texture, edge and color tone directly from the color host image to adaptively adjust the watermark strength for each block. In addition, the constraints in watermark embedding are discussed to preserve the watermarking energy. Experimental results show that: (a) the proposed efficient computation method takes only half the computational time of the direct method; (b) the comparison of five color models (RGB, YUV, YIQ, CIEL*a*b* and YCbCr) shows that the proposed QDFRNT-based watermarking scheme using YCbCr color model has the overall best performance and can achieve a good balance between invisibility and robustness to the Checkmark attacks; (c) The proposed scheme is superior to the existing schemes respectively using DCT, DFRNT, discrete quaternion Fourier transform (DQFT), discrete fractional quaternion Fourier transform (DFrQFT), and quaternion radial moments (QRMs). Moreover, the fractional order and the random matrix of QDFRNT enhance the security of the proposed scheme.