ABSTRACT This paper presents a robust reversible watermarking algorithm based on a two‐stage embedding strategy. In the first stage, the host image is partitioned into non‐overlapping blocks. Embedding locations are selected within the inscribed circle of the host image by leveraging the Just Noticeable Distortion (JND) threshold, and copyright watermarks are embedded into the lower‐order Tchebichef Moments (TMs) at these positions. The watermark quantisation error is converted to an integer value using an enhanced Distortion‐Compensated Quantised Index Modulation (DC‐QIM) technique. In the second stage, compensation data is embedded into image blocks located outside the inscribed circle, thereby ensuring reversibility in the absence of attacks. Prior to watermark extraction, a resynchronisation method tailored to the specific type of attack is applied to realign the block positions, significantly improving robustness against geometric distortions. Compared with existing advanced methods of the same kind, the proposed algorithm effectively addresses key limitations of traditional methods, including the trade‐off between robustness and reversibility, redundancy in compensation data, and insufficient resistance to geometric attacks. The amount of compensation information is reduced by over 90%. Under comparable experimental settings, the average peak signal‐to‐noise ratio (PSNR) is improved by 0.5–2.2 dB. Extensive experiments demonstrate that, in terms of resistance to noise interference, the performance of the proposed algorithm is comparable to that of methods based on Zernike Moments (ZMs) and Pseudo‐Zernike Moments (PZMs). The algorithm achieves a bit error rate (BER) of less than 1% under Joint Photographic Experts Group (JPEG) compression, salt‐and‐pepper noise with intensity ≤ 0.017, Gaussian noise with variance ≤ 0.011, and rotation and scaling attacks under ideal resynchronisation conditions. When subjected to random cropping attacks of 128 × 128 pixels, the average BER remains below 7%. It also demonstrates robust resilience against various attacks, including filtering and translation.
Sun et al. (Thu,) studied this question.