Skip to main content
SpringerLink
Log in

Robust and efficient image watermarking via EMD and dimensionality reduction

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

In the past decades, bi-dimensional empirical mode decomposition (BEMD) algorithms have been developed for the image watermarking task with good robustness and imperceptibility; however, the non-negligible algorithm efficiency has received little attention at the same time. In this paper, we devise a robust and efficient image watermarking algorithm based on 1D empirical mode decomposition (EMD) and dimensional reduction via Hilbert curve. Converting the problem of two-dimensional image watermarking into the problem of one-dimensional signal watermarking promises to enhance the efficiency and the robustness of the proposed algorithm. Specifically, host image is first reduced into one-dimensional signal by the Hilbert curve. Our key insight is a dimensionality reduction strategy based on the Hilbert curve that preserves the spatial local relationship to the greatest extent possible. Second, the one-dimensional signal is segmented into several short signal intervals, and each of them is decomposed into several intrinsic mode functions (IMFs) and a residue by 1D EMD, which is much faster than BEMD. Third, the maximum or minimum points of the first IMF are chosen as the watermark embedding positions. For the watermark image, it is first encrypted by Arnold transform, which improves the security of the algorithm. And then, it is also transformed into one-dimensional signal correspondingly. A repeated embedding strategy is used in the embedding process to improve the algorithm’s robustness. The final watermarked image can be reconstructed by the inverse Hilbert curve transform after integrating the modified first IMF, the remaining IMFs, and the residual. To improve the security and reduce the length of the key, Arnold transform and Huffman coding are adopted. The watermark extraction is the inverse of the embedding process without using the host image and watermark image. Comprehensive experimental results confirm that our new algorithm exhibits good robustness, efficiency, and high imperceptibility. Compared with the actual watermarking algorithms, the newly proposed watermarking algorithm not only reduces the computational expense, but also shows better performance in combating the cropping attacks, Gaussian noise, median filter, image enhancement attacks, etc.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Abbas, N.H., Ahmad, S.M.S., Parveen, S., Wan, W.A., Ramli, A.R.B.: Design of high performance copyright protection watermarking based on lifting wavelet transform and bi empirical mode decomposition. Multimed. Tools Appl. 77(19), 24593–24614 (2018)

    Article  Google Scholar 

  2. Ahmadi, S.B.B., Zhang, G., Wei, S., Boukela, L.: An intelligent and blind image watermarking scheme based on hybrid SVD transforms using human visual system characteristics. Vis. Comput. 37, 385–409 (2020)

    Google Scholar 

  3. Ali, H., Hariharan, M., Yaacob, S., Adom, A.H.: Facial emotion recognition using empirical mode decomposition. Expert Syst. Appl. 42(3), 1261–1277 (2015)

    Article  Google Scholar 

  4. Ali, M., Ahn, C.W., Pant, M., Siarry, P.: An image watermarking scheme in wavelet domain with optimized compensation of singular value decomposition via artificial bee colony. Inf. Sci. 301, 44–60 (2015)

    Article  Google Scholar 

  5. Amira Biad, S., Bouden, T., Nibouche, M., Elbasi, E.: A bi-dimensional empirical mode decomposition based watermarking scheme. Int. Arab J. Inf. Technol. 12(1), 24–31 (2015)

    Google Scholar 

  6. An, L., Gao, X., Li, X., Tao, D., Deng, C., Li, J.: Robust reversible watermarking via clustering and enhanced pixel-wise masking. IEEE Trans. Image Process. 21(8), 3598–3611 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Barni, M., Bartolini, F., Cappellini, V., Piva, A.: A DCT-domain system for robust image watermarking. Signal Process. 66(3), 357–372 (1998)

    Article  MATH  Google Scholar 

  8. Begum, M., Uddin, M.S.: Implementation of secured and robust DFT-based image watermark through hybridization with decomposition algorithm. SN Comput. Sci. 2(3), 1–13 (2021)

    Article  Google Scholar 

  9. Bi, N., Sun, Q., Huang, D., Yang, Z., Huang, J.: Robust image watermarking based on multiband wavelets and empirical mode decomposition. IEEE Trans. Image Process. 16(8), 1956–1966 (2007)

    Article  MathSciNet  Google Scholar 

  10. Boudraa, A.O., Cexus, J.C.: Emd-based signal filtering. IEEE Trans. Instrum. Meas. 56(6), 2196–2202 (2007)

    Article  Google Scholar 

  11. Butz, A.R.: Convergence with Hilberts space filling curve. J. Comput. Syst. Sci. 3(2), 128–146 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chang, C.C., Hu, Y.S., Lu, T.C.: A watermarking-based image ownership and tampering authentication scheme. Pattern Recogn. Lett. 27(5), 439–446 (2006)

    Article  Google Scholar 

  13. Chen, B., Coatrieux, G., Chen, G., Coatrieux, J.L., Shu, H.: Full 4-D quaternion discrete Fourier transform based watermarking for color images. Digit. Signal Process. 28, 106–119 (2014)

    Article  Google Scholar 

  14. Chen, Z., Li, L., Peng, H., Liu, Y., Yang, Y.: A novel digital watermarking based on general non-negative matrix factorization. IEEE Trans. Multimed. 20(8), 1973–1986 (2018)

    Article  Google Scholar 

  15. Chu, W.C.: DCT-based image watermarking using subsampling. IEEE Trans. Multimed. 5(1), 34–38 (2003)

    Article  Google Scholar 

  16. Cox, I., Kilian, J., Leighton, F., Shamoon, T.: Secure spread spectrum watermarking for multimedia. IEEE Trans. Image Process. 6(12), 1673–1687 (1997)

    Article  Google Scholar 

  17. Di, C., Yang, X., Wang, X.: A four-stage hybrid model for hydrological time series forecasting. PLoS ONE 9(8), e104663 (2014)

    Article  Google Scholar 

  18. Ernawan, F., Kabir, M.N.: A block-based RDWT-SVD image watermarking method using human visual system characteristics. Vis. Comput. 36(1), 19–37 (2020)

    Article  Google Scholar 

  19. Fallahpour, M., Shirmohammadi, S., Semsarzadeh, M., Zhao, J.: Tampering detection in compressed digital video using watermarking. IEEE Trans. Instrum. Meas. 63(5), 1057–1072 (2014)

    Article  Google Scholar 

  20. Hamidi, M., Haziti, M.E., Cherifi, H., Hassouni, M.E.: Hybrid blind robust image watermarking technique based on DFT-DCT and Arnold transform. Multimed. Tools Appl. 77(20), 27181–27214 (2018)

    Article  Google Scholar 

  21. Hernandez, J.R., Amado, M., Perez-Gonzalez, F.: DCT-domain watermarking techniques for still images: detector performance analysis and a new structure. IEEE Trans. Image Process. 9(1), 55–68 (2000)

    Article  Google Scholar 

  22. Hilbert, D.: Über die stetige abbildung einer linie auf ein flächenstück. In: Dritter Band: Analysis Grundlagen der Mathematik. Physik Verschiedenes, pp. 1–2. Springer (1935)

  23. Hu, J., Wang, X., Qin, H.: Improved, feature-centric EMD for 3D surface modeling and processing. Graph. Models 76(5), 340–354 (2014)

    Article  Google Scholar 

  24. Hu, J., Wang, X., Qin, H.: Novel and efficient computation of Hilbert–Huang transform on surfaces. Comput. Aided Geom. Des. 43, 95–108 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  25. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. 454(1971), 903–995 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  26. Islam, M., Laskar, R.H.: Geometric distortion correction based robust watermarking scheme in LWT-SVD domain with digital watermark extraction using svm. Multimed. Tools Appl. 77(11), 14407–14434 (2017)

    Article  Google Scholar 

  27. Jagadish, H.V.: Analysis of the Hilbert curve for representing two-dimensional space. Inf. Process. Lett. 62(1), 17–22 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  28. Kang, X., Zhao, F., Lin, G., Chen, Y.: A novel hybrid of DCT and SVD in DWT domain for robust and invisible blind image watermarking with optimal embedding strength. Multimed. Tools Appl. 77(11), 13197–13224 (2017)

    Article  Google Scholar 

  29. Lee, Y., Nah, J., Kim, J.: Digital image watermarking using bidimensional empirical mode decomposition in wavelet domain. In: IEEE International Symposium on Multimedia, pp. 583–588 (2009)

  30. Li, C., Zhang, Z., Wang, Y., Ma, B., Huang, D.: Dither modulation of significant amplitude difference for wavelet based robust watermarking. Neurocomputing 166, 404–415 (2015)

    Article  Google Scholar 

  31. Li, Z., Zhang, H., Liu, X., Wang, C., Wang, X.: Blind and safety-enhanced dual watermarking algorithm with chaotic system encryption based on RHFM and DWT-DCT. Digital Signal Process. 115, 103062 (2021)

    Article  Google Scholar 

  32. Luo, Y., Li, L., Liu, J., Tang, S., Cao, L., Zhang, S., Qiu, S., Cao, Y.: A multi-scale image watermarking based on integer wavelet transform and singular value decomposition. Expert Syst. Appl. 168, 114272 (2021)

    Article  Google Scholar 

  33. Makbol, N.M., Khoo, B.E.: A new robust and secure digital image watermarking scheme based on the integer wavelet transform and singular value decomposition. Digit. Signal Process. 33, 134–147 (2014)

    Article  Google Scholar 

  34. Makbol, N.M., Khoo, B.E., Rassem, T.H., Loukhaoukha, K.: A new reliable optimized image watermarking scheme based on the integer wavelet transform and singular value decomposition for copyright protection. Inf. Sci. 417, 381–400 (2017)

    Article  Google Scholar 

  35. Nazari, M., Mehrabian, M.: A novel chaotic IWT-LSB blind watermarking approach with flexible capacity for secure transmission of authenticated medical images. Multimed. Tools Appl. 80(7), 10615–10655 (2021)

    Article  Google Scholar 

  36. Nunes, J.C., Niang, O., Bouaoune, Y., Delechelle, E., Bunel, P.: Bidimensional empirical mode decomposition modified for texture analysis. In: Scandinavian conference on image analysis, pp. 171–177 (2003)

  37. Sayood, K.: Introduction to Data Compression. Newnes, London (2012)

    MATH  Google Scholar 

  38. Singh, S.P., Bhatnagar, G.: A new robust watermarking system in integer DCT domain. J. Vis. Commun. Image Represent. 53, 86–101 (2018)

    Article  Google Scholar 

  39. Solachidis, V., Pitas, I.: Watermarking polygonal lines using Fourier descriptors. IEEE Comput. Graphics Appl. 24(3), 44–51 (2004)

    Article  Google Scholar 

  40. Subr, K., Soler, C., Durand, F.: Edge-preserving multiscale image decomposition based on local extrema. ACM Trans. Graph. 28(5), 1–9 (2009)

    Article  Google Scholar 

  41. Taghia, J., Doostari, M.A., Taghia, J.: An image watermarking method based on bidimensional empirical mode decomposition. In: Congress on Image and Signal Processing, pp. 674–678 (2008)

  42. Tao, P., Eskicioglu, A.: A method for image recovery in the DFT domain. In: IEEE Consumer Communications and Networking Conference, pp. 1134–1138 (2006)

  43. Tsui, T.K., Zhang, X.P., Androutsos, D.: Color image watermarking using multidimensional Fourier transforms. IEEE Trans. Inf. Forensics Secur. 3(1), 16–28 (2008)

    Article  Google Scholar 

  44. Verma, V.S., Bhardwaj, A., Jha, R.K.: A new scheme for watermark extraction using combined noise-induced resonance and support vector machine with PCA based feature reduction. Multimed. Tools Appl. 78(16), 23203–23224 (2019)

    Article  Google Scholar 

  45. Wang, H., Su, Z., Cao, J., Wang, Y., Zhang, H.: Empirical mode decomposition on surfaces. Graph. Models 74(4), 173–183 (2012)

    Article  Google Scholar 

  46. Wang, X., Hu, J., Guo, L., Zhang, D., Qin, H., Hao, A.: Feature-preserving, mesh-free empirical mode decomposition for point clouds and its applications. Comput. Aided Geom. Des. 59, 1–16 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  47. Wang, X., Hu, J., Zhang, D., Guo, L., Qin, H., Hao, A.: Multi-scale geometry detail recovery on surfaces via empirical mode decomposition. Comput. Graph. 70, 118–127 (2018)

    Article  Google Scholar 

  48. Wang, X., Hu, J., Zhang, D., Qin, H.: Efficient EMD and Hilbert spectra computation for 3D geometry processing and analysis via space-filling curve. Vis. Comput. 31(6), 1135–1145 (2015)

    Article  Google Scholar 

  49. Wang, X., Hu, K., Hu, J., Du, L., Anthony, T., Qin, H.: Robust and blind image watermarking via circular embedding and bidimensional empirical mode decomposition. Vis. Comput. 36, 2201–2214 (2020)

    Article  Google Scholar 

  50. Wang, Y., Doherty, J.F., Van Dyck, R.E.: A wavelet-based watermarking algorithm for ownership verification of digital images. IEEE Trans. Image Process. 11(2), 77–88 (2002)

    Article  Google Scholar 

  51. Xie, X.: Illumination preprocessing for face images based on empirical mode decomposition. Signal Process. 103, 250–257 (2014)

    Article  Google Scholar 

  52. Xu, G., Wang, X.T., Xu, X.G.: Improved bi-dimensional EMD and Hilbert spectrum for the analysis of textures. Pattern Recogn. 42(5), 718–734 (2009)

  53. Zainol, Z., Teh, J.S., Alawida, M., et al.: A new chaotic image watermarking scheme based on SVD and IWT. IEEE Access 8, 43391–43406 (2020)

    Article  Google Scholar 

  54. Zang, Y., Huang, H., Zhang, L.: Efficient structure-aware image smoothing by local extrema on space-filling curve. IEEE Trans. Visual Comput. Graph. 20(9), 1253–1265 (2014)

    Article  Google Scholar 

  55. Zhang, D., Wang, X., Hu, J., Qin, H.: Interactive modeling of complex geometric details based on empirical mode decomposition for multi-scale 3D shapes. Comput. Aided Des. 87, 1–10 (2017)

    Article  Google Scholar 

  56. Zhou, N.R., Hou, W.M.X., Wen, R.H., Zou, W.P.: Imperceptible digital watermarking scheme in multiple transform domains. Multimed. Tools Appl. 77(23), 30251–30267 (2018)

    Article  Google Scholar 

  57. Zhu, X., Ho, A.T., Marziliano, P.: A new semi-fragile image watermarking with robust tampering restoration using irregular sampling. Signal Process. Image Commun. 22(5), 515–528 (2007)

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the anonymous reviewers for their helpful comments. This work is supported in part by National Science Foundation of USA (IIS-1812606, IIS-1715985); National Natural Science Foundation of China (No. 61532002, 61672149, 61602341, 61602344, 61802279); The Science & Technology Development Fund of Tianjin Education Commission for Higher Education (Grant No.2018KJ222). The Open Project Program of the State Key Lab of CAD&CG (Grant No. A2105), Zhejiang University.

Author information

Authors and Affiliations

  1. University of Chinese Academy of Sciences, 100049, Beijing, China

    Kun Hu

  2. School of Mathematical Sciences at Tiangong University, Tianjin, 300387, China

    Xiaochao Wang

  3. School of Sciences at Northeast Electric Power University, Jilin, 132012, China

    Jianping Hu

  4. School of Computer Science and Technology at Tiangong University, Tianjin, 300387, China

    Danyang Li & Ling Du

  5. Key Laboratory of Space Utilization, Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, 100094, Beijing, China

    Hongfei Wang

  6. Department of Computer Science, Stony Brook University (State University of New York), Stony Brook, NY, 11794-2424, USA

    Hong Qin

Authors
  1. Kun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaochao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianping Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Danyang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ling Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hongfei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Hong Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaochao Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, K., Wang, X., Hu, J. et al. Robust and efficient image watermarking via EMD and dimensionality reduction. Vis Comput 38, 2153–2170 (2022). https://doi.org/10.1007/s00371-021-02275-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-021-02275-3

Keywords

Search

Navigation