Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

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Wang Jing
Ling Weay Ang
Sellappan Palaniappan
Bing He


This study presents a zero-watermarking algorithm that can resist rotation attacks. The algorithm uses quaternion fractional-order polar harmonic-Fourier moments (QFr-PHFMs) based on wavelet-transformation. First, the wavelet-transformation is applied to each component of the host image, which is in RGB three-channel color. The low-frequency sub-bands of each component are then extracted and represented using quaternion algebra. Multiple QFr-PHFMs are calculated, and the invariants of the QFr-PHFMs are utilized to establish the watermark system. The watermark extraction process is also simplified. The detection of the image requires a two-level wavelet transformation, followed by the calculation of multiple invariant moments of the low-frequency sub-image. The experimental results are shown and compared with similar methods. Simulations show that this method can produce high-quality visual effects and withstand noise, filtering, JPEG compression, and cropping attacks.

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