An improved blind watermarking scheme for color image copyright protection using Hahn moments

Why hiding messages in pictures matters

Every day, people share countless photos online, from vacation snapshots to medical scans. While this makes life more convenient, it also makes it easy for others to copy, edit, or misuse those images without permission. This article explores a new way to quietly “sign” color images with an invisible digital mark that proves who owns them. The method aims to survive heavy editing, compression, and even malicious tampering, all while keeping the picture looking exactly the same to the human eye.

Protecting ownership in a copy‑and‑paste world

Digital watermarking works by hiding extra information inside an image in such a way that viewers do not notice it, but computers can later recover it to verify ownership or authenticity. Many schemes exist, but they often face a tough trade‑off: if you make the watermark strong enough to survive attacks such as resizing, filtering, or noise, you risk degrading visual quality; if you keep the image pristine, the watermark may be lost. Another practical hurdle is that many methods need the original, unmarked image during verification, which is rarely available in real‑world disputes. The work presented here tackles these issues by designing a “blind” watermarking scheme that can recover the hidden mark without ever seeing the original picture.

Using mathematical fingerprints inside images

The authors build their approach on a family of mathematical tools called Hahn moments. In simple terms, these moments act like compact, structured fingerprints of how colors and intensities are arranged in an image. Instead of editing raw pixels, the method first transforms the red color channel into a grid of small blocks, then computes Hahn moment values for each block. A modified formulation and a clever recurrence rule allow these fingerprints to be computed and inverted quickly and stably, even for high‑detail images. The team first demonstrates that they can reconstruct full‑color images from these moments with extremely low error and near real‑time speed, confirming that the transform is both accurate and efficient enough to serve as a watermarking backbone.

Hiding and recovering the invisible mark

To embed a watermark, the scheme starts with a small black‑and‑white logo and scrambles its pixels using a geometric shuffle known as the Arnold transform. This makes the mark visually meaningless unless you know the secret keys needed to undo the process. Each scrambled bit is then inserted into the magnitude of a selected Hahn moment coefficient within an 8×8 image block using a precise quantization rule. This rule nudges the chosen coefficient toward one of two nearby values, depending on whether the bit represents a 0 or a 1, while leaving the rest of the block—and all other color channels—essentially untouched. During extraction, the algorithm re‑computes the Hahn moments of the received image, inspects those same coefficients, decides which side of the quantization boundary each one lies on, and thus reconstructs the scrambled bit pattern. Applying the inverse Arnold transform finally reveals the original watermark, all without needing the original host image.

Putting the method to the test

The researchers tested their scheme on three broad types of color images: everyday scenes, aerial views, and medical images such as brain scans and breast images. They used several standard measures to judge performance. Peak signal‑to‑noise ratio (PSNR) and structural similarity index (SSIM) quantify how close the watermarked image is to the original; higher values mean the viewer sees essentially no difference. Normalized cross‑correlation (NCC) and bit error rate (BER) describe how faithfully the watermark is recovered; an NCC near 1 and a BER near 0 indicate almost perfect retrieval. Under normal conditions, the method achieved PSNR values above 55–60 dB and SSIM values essentially equal to 1, meaning the watermarked images were visually indistinguishable from the originals. At the same time, the watermark was recovered with NCC of 1 and BER of 0—perfect reconstruction.

Standing up to noise, edits, and attacks

Real‑world images rarely remain pristine, so the team subjected the watermarked pictures to a battery of attacks: adding noise, applying median and average filters, sharpening and blurring, compressing with JPEG, equalizing the brightness distribution, cropping, rescaling, rotating, shifting, and even combinations of these operations. Across twelve single‑attack types and several combined attacks, the proposed scheme consistently recovered high‑quality watermarks, usually with almost zero bit errors. In many cases it outperformed or matched several recent state‑of‑the‑art methods that rely on more complex optimization routines or heavier transforms. The method proved especially strong against sharpening, blurring, scaling, rotation, cropping, and compression, though it remained somewhat more sensitive to strong median filtering and Gaussian noise.

What this means for everyday images

In plain terms, the article shows that it is possible to hide a robust, invisible ownership mark in color images—especially in sensitive content such as medical scans—without sacrificing visual quality or needing to store original files for comparison. By encoding the watermark in carefully chosen mathematical features rather than raw pixels, and by adding an extra scrambling step for security, the proposed approach offers a practical tool for copyright protection and authenticity checking in a world of effortless copying and sharing. While further refinements are needed to handle certain types of extreme noise, the work points toward faster, more reliable watermarking systems that can quietly safeguard our digital pictures behind the scenes.

Citation: Elbatawy, N.I., Karawia, A.A., El-Gayar, M.M. et al. An improved blind watermarking scheme for color image copyright protection using Hahn moments. Sci Rep 16, 13027 (2026). https://doi.org/10.1038/s41598-026-42088-9

Keywords: digital watermarking, image copyright, color images, Hahn moments, multimedia security