Volume 12, Issue 12 (December 2025), Pages: 9-18

----------------------------------------------

 Original Research Paper

A reversible watermarking algorithm based on complementary embedding of diamond pixel pairs

 Author(s): 

 Zhengwei Zhang *, Fenfen Li, Shenghua Jin

 Affiliation(s):

 Faculty of Computer and Software Engineering, Huaiyin Institute of Technology, Huai’an, China

 Full text

    Full Text - PDF

 * Corresponding Author. 

   Corresponding author's ORCID profile:  https://orcid.org/0000-0002-3207-0586

 Digital Object Identifier (DOI)

  https://doi.org/10.21833/ijaas.2025.12.002

 Abstract

To improve both invisibility and embedding capacity, this study proposes a reversible watermarking algorithm based on diamond pixel pairs with complementary embedding. To avoid pixel value overflow, the carrier image is first preprocessed and divided into blocks. Each block is then separated into two half-planes, gray and white. The watermark is embedded in both horizontal and vertical directions. In the horizontal direction, the target pixel in a smooth block is compared with four reference pixels in its cross-shaped neighborhood to calculate their difference values and construct a histogram. The first embedding is carried out in the gray half-plane using the histogram shifting method, followed by a second embedding in the white half-plane. The same process is applied in the vertical direction to reduce the distortion introduced by horizontal embedding. Experimental results indicate that, under the same embedding capacity, the proposed method achieves an average PSNR (Peak Signal-to-Noise Ratio) that is 6.92 dB higher than that of the non-complementary embedding scheme. Moreover, compared with other related algorithms, this approach demonstrates superior embedding performance for the same PSNR value.

 © 2025 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 Reversible watermarking, Complementary embedding, Diamond pixel pairs, Histogram shifting, Image distortion reduction

 Article history

 Received 7 July 2025, Received in revised form 3 November 2025, Accepted 9 November 2025

 Acknowledgment

This work is supported by the National Statistical Science Research Project (2018LY12). At the same time, this work is also supported by the Huaian natural science research program (HAB202363). 

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Zhang Z, Li F, and Jin S (2025). A reversible watermarking algorithm based on complementary embedding of diamond pixel pairs. International Journal of Advanced and Applied Sciences, 12(12): 9-18

  Permanent Link to this page

 Figures

  Fig. 1  Fig. 2  Fig. 3  Fig. 4  Fig. 5  Fig. 6  Fig. 7  Fig. 8 

 Tables

  Table 1  Table 2  Table 3  Table 4

----------------------------------------------   

 References (22)

1. Alattar AM (2004). Reversible watermark using the difference expansion of a generalized integer transform. IEEE Transactions on Image Processing, 13(8): 1147-1156.  https://doi.org/10.1109/TIP.2004.828418    [Google Scholar] PMid:15326856
2. Arham A and Nugroho HA (2024). Enhanced reversible data hiding using difference expansion and modulus function with selective bit blocks in images. Cybersecurity, 7: 61.  https://doi.org/10.1186/s42400-024-00251-7    [Google Scholar]
3. Cao X, Zhou Y, and Guo JM (2020). Guest editorial introduction to special section on modern reversible data hiding and watermarking. IEEE Transactions on Circuits and Systems for Video Technology, 30(8): 2297-2299.  https://doi.org/10.1109/TCSVT.2020.3002109    [Google Scholar]
4. Chidirala B and Acharya B (2024). Prediction error expansion based reversible watermarking scheme in higher order pixels. Sādhanā, 49: 227.  https://doi.org/10.1007/s12046-024-02569-x    [Google Scholar]
5. Das S and Sunaniya AK (2022). FPGA implementation of high-fidelity hybrid reversible watermarking algorithm. Microprocessors and Microsystems, 89: 104442.  https://doi.org/10.1016/j.micpro.2022.104442    [Google Scholar]
6. Gao G, Tong S, Xia Z, and Shi YQ (2023). A universal reversible data hiding method in encrypted image based on MSB prediction and error embedding. IEEE Transactions on Cloud Computing, 11(2): 1692-1706.  https://doi.org/10.1109/TCC.2022.3155744    [Google Scholar]
7. Jia Y, Yin Z, Zhang X, and Luo Y (2019). Reversible data hiding based on reducing invalid shifting of pixels in histogram shifting. Signal Processing, 163: 238-246.  https://doi.org/10.1016/j.sigpro.2019.05.020    [Google Scholar]
8. Krishnamoorthi N and Chinnababu VK (2022). Hash and prediction-error-based reversible watermarking for medical images. Fluctuation and Noise Letters, 21(1): 2250007.  https://doi.org/10.1142/S0219477522500079    [Google Scholar]
9. Lee CF and Chen HL (2012). Adjustable prediction-based reversible data hiding. Digital Signal Processing, 22(6): 941-953.  https://doi.org/10.1016/j.dsp.2012.05.015    [Google Scholar]
10. Lee CF, Weng CY, and Kao CY (2019). Reversible data hiding using Lagrange interpolation for prediction-error expansion embedding. Soft Computing, 23: 9719-9731.  https://doi.org/10.1007/s00500-018-3537-7    [Google Scholar]
11. Li YC, Yeh CM, and Chang CC (2010). Data hiding based on the similarity between neighboring pixels with reversibility. Digital Signal Processing, 20(4): 1116-1128.  https://doi.org/10.1016/j.dsp.2009.10.025    [Google Scholar]
12. Ni Z, Shi YQ, Ansari N, Su W, Sun Q, and Lin X (2008). Robust lossless image data hiding designed for semi-fragile image authentication. IEEE Transactions on Circuits and Systems for Video Technology, 18(4): 497-509.  https://doi.org/10.1109/TCSVT.2008.918761    [Google Scholar]
13. Tai WL, Yeh CM, and Chang CC (2009). Reversible data hiding based on histogram modification of pixel differences. IEEE Transactions on Circuits and Systems for Video Technology, 19(6): 906-910. https://doi.org/10.1109/TCSVT.2009.2017409    [Google Scholar]
14. Tanwar L and Panda J (2024). Hybrid reversible watermarking algorithm using histogram shifting and pairwise prediction error expansion. Multimedia Tools and Applications, 83: 22075-22097.  https://doi.org/10.1007/s11042-023-15508-5    [Google Scholar]
15. Tian J (2003). Reversible data embedding using a difference expansion. IEEE Transactions on Circuits and Systems for Video Technology, 13(8): 890-896.  https://doi.org/10.1109/TCSVT.2003.815962    [Google Scholar]
16. Wang N, Xu S, Qin C, Lin SJ, Shao S, and Han YS (2024). High-capacity framework for reversible data hiding using asymmetric numeral systems. IEEE Transactions on Knowledge and Data Engineering, 36(12): 8447-8461.  https://doi.org/10.1109/TKDE.2024.3438943    [Google Scholar]
17. Xiong X (2019). Novel scheme of reversible watermarking with a complementary embedding strategy. IEEE Access, 7: 136592-136603.  https://doi.org/10.1109/ACCESS.2019.2942449    [Google Scholar]
18. Yang CH and Tsai MH (2010). Improving histogram-based reversible data hiding by interleaving predictions. IET Image Processing, 4(4): 223-234.  https://doi.org/10.1049/iet-ipr.2009.0316    [Google Scholar]
19. Yang Y, Cheng M, Ding Y, and Zhang W (2023). A visually meaningful image encryption scheme based on lossless compression SPIHT coding. IEEE Transactions on Services Computing, 16(4): 2387-2401.  https://doi.org/10.1109/TSC.2023.3258144    [Google Scholar]
20. Zhang Z, Li F, Zuo X, Meng Q, and Jin S (2023). Reversible image watermarking algorithm based on reverse histogram translation. Multimedia Tools and Applications, 82(7): 11005-11019.  https://doi.org/10.1007/s11042-022-13770-7    [Google Scholar]
21. Zhang Z, Zhang M, and Wang L (2020). Reversible image watermarking algorithm based on quadratic difference expansion. Mathematical Problems in Engineering, 2020: 1806024.  https://doi.org/10.1155/2020/1806024    [Google Scholar]
22. Zheng H, Wang C, Wang J, and Xiang S (2019). A new reversible watermarking scheme using the content-adaptive block size for prediction. Signal Processing, 164: 74-83.  https://doi.org/10.1016/j.sigpro.2019.05.035    [Google Scholar]