Music score copyright protection based on mixed low-order quaternion Franklin moments

Due to the rapid growth of the digital music industry, music copyrights have become valuable intangible assets for businesses, offering exclusivity and profitability. This article takes music copyrights as an example and designs a copyright protection method for music score digital images. The zero-watermarking algorithm offers an effective and lossless means of copyright protection. Owing to their geometric invariance, orthogonal moments exhibit superior robustness, positioning them as one of the mainstream methods in the research of zero-watermarking algorithms. The current zero-watermarking algorithms based on orthogonal moments face a trade-off between robustness and discriminability. In this paper, we propose a mixed low-order moments method based on quaternion-type fractional-order moments (QTFM), which balances the global information and texture details of color image contained in QTFM. Experimental results show that the mixed low-order moments method based on QTFM exhibits superior performance in terms of robustness. In the context of using mixed low-order moment features for image analysis, Franklin moments achieve higher average structural similarity (SSIM) values than other QTFMs.