Polar Harmonic Fractional Fourier Moment and Its Application in Zero-watermarking Algorithm
As a global feature descriptor,image moment has become a powerful tool for pattern recognition and image analysis.In or-der to resist common image processing attacks and geometric attacks effectively,Polar harmonic fractional Fourier moment and quater-nion polar harmonic fractional Fourier moment are proposed to describe image features.Firstly,taking the polar harmonic polynomial as the radial function and the kernel function of the fractional Fourier transform as the angular function,the polar harmonic fractional Fourier moment is obtained,and its related properties are analyzed.Secondly,the polar harmonic fractional Fourier moment of the im-age are applied to the zero-watermarking algorithm,to calculate and extract the polar harmonic fractional Fourier moment of the im-age,randomly select the appropriate feature image,and construct the binary feature image.The obtained binary feature image is per-formed by XOR operation with the watermark image to construct the feature image as a zero-watermark.Finally,the proposed zero-watermarking algorithm is tested by noise,filtering,rotation and scaling.The experimental results show that the polar harmonic frac-tional Fourier moment proposed in this paper combines the advantages of polar harmonic polynomial and fractional Fourier transform,and can effectively resist image processing attacks and geometric attacks in zero-watermarking algorithm,and is more robust than other algorithms.
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