Fractional-Order Image Moments and Applications

Image moments, as a global feature descriptor for images, have become a powerful tool for pattern recognition and image analysis. Most of the currently existing fractional-order image moments are polynomial-based. Three novel moments, namely Zernike fractional Fourier moment, Merlin fractional Fourier moment, and exponential fractional Fourier moment, combined with classical moments and fractional Fourier transform, are introduced based on angular functions. Additionally, we propose a zero watermarking algorithm based on these moments. We present robustness and comparative analysis experiments, including the effects of noise, filtering, rotation, and scaling. The experimental results demonstrate that the zero watermarking algorithm utilizing fractional-order moments can effectively withstand image processing attacks and geometric attacks. In both cases, their performance surpasses that of their corresponding integer-order image moments.