Robust Color Image Watermarking Using Geometric Invariant Quaternion Polar Harmonic Transform

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It is a challenging work to design a robust color image watermarking scheme against geometric distortions. Moments and moment invariants have become a powerful tool in robust image watermarking owing to their image description capability and geometric invariance property. However, the existing moment-based watermarking schemes were mainly designed for gray images but not for color images, and detection quality and robustness will be lowered when watermark is directly embedded into the luminance component or three color channels of color images. Furthermore, the imperceptibility of the embedded watermark is not well guaranteed. Based on algebra of quaternions and polar harmonic transform (PHT), we introduced the quaternion polar harmonic transform (QPHT) for invariant color image watermarking in this article, which can be seen as the generalization of PHT for gray-level images. It is shown that the QPHT can be obtained from the PHT of each color channel. We derived and analyzed the rotation, scaling, and translation (RST) invariant property of QPHT. We also discussed the problem of color image watermarking using QPHT. Experimental results are provided to illustrate the efficiency of the proposed color image watermarking against geometric distortions and common image processing operations (including color attacks).