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Top1. Introduction
As a new means of digital image copyright protection, image digital watermarking technology is increasingly connected with various facets of society and plays a decisive role in medical images, commercial publicity, industrial production, information security, etc. The embedding domain of watermarks is generally divided into three kinds: spatial domain, frequency domain, and compression domain. The watermark embedding algorithm based on the spatial domain (Wu et al., 2021) features a low time complexity and a large watermark capacity due to its simplicity and capability to avoid changing the original image. However, as a conventional semi-fragile watermarking algorithm, it only provides adequate resistance against image compression attacks but is less robust against noise disturbances. Frequency-domain-based watermark embedding algorithms (Wu et al., 2021), such as discrete cosine transform, wavelet transform, contourlet transform, shear wave transform, vector transform, and Hadamard transform, require specific alteration of the original image before embedding the watermark, and the watermark can be embedded by modifying, replacing, or exchanging the frequency band coefficients of quality images. In general, the low-frequency section contains important contour information of the image, while the high-frequency section contains redundant details of the image. If robustness is emphasized, it would be suitable to embed the watermark into low-frequency information, while if invisibility and embedding capacity are regarded as more important, it would be suitable to embed the watermark information into the high-frequency section.