Abstract
In this paper, a robust and blind image watermarking algorithm via circular embedding and bidimensional empirical mode decomposition (BEMD) is developed. First, the watermark image is scrambled by Arnold transform to increase the security of the algorithm. Second, the Hilbert curve is adopted to reduce the scrambled 2D watermark image to one-dimensional watermark signal. Third, the host image is decomposed by BEMD to obtain the multi-scale representation in the forms of intrinsic mode functions (IMFs) and a residue. Then, the extreme points of the IMFs are extracted as the embedding locations. Finally, the one-dimensional watermark signal is repeatedly and cyclically embedded in the extreme locations of the first IMF according to the texture masking characteristics of the human visual system, which greatly improves the ability of our algorithm against various attacks. The final watermarked image is reconstructed by combining the modified first IMF and the residual. The watermark can be successfully extracted without resorting to the original host image. Furthermore, image correction can be applied before image watermarking extraction if there are geometric attacks in watermarked image. A large number of experimental results and thorough evaluations confirm that our method can obtain higher imperceptibility and robustness under different types of attacks, and achieve better performance than the current state-of-the-art watermarking algorithms, especially in large-scale cropping attack, JPEG compression, Gaussian noise, sharpening, Gamma correction, scaling, histogram equalization, and rotation attacks.
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29 July 2020
The publication of this article unfortunately contained mistakes. The affiliation and the biography of Ling Du were not correct. The corrected affiliation and bibliography is given below.
References
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)
Abdelouahed, S., Mohamed, K., Hamid, T., Aabdelah, A.: Image watermarking using the empirical mode decomposition. In: 5th International Conference Science Electronics, Tech. Info. Telecom., pp. 22–26 (2009)
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. Inform. Sci. 301, 44–60 (2015)
Baluja, S.: Hiding images within images. IEEE Trans. Pattern. Anal. Mach. Intell. 42(7), 1685–1687 (2019)
Barni, M., Bartolini, F., Cappellini, V., Piva, A.: A dct-domain system for robust image watermarking. Signal Process. 66(3), 357–372 (1998)
Bay, H., Ess, A., Tuytelaars, T., Gool, L.V.: Speeded-up robust features (surf). Comput. Vis. Image Underst. 110(3), 346–359 (2008)
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)
Celik, M.U., Sharma, G., Tekalp, A.M., Saber, E.: Lossless generalized-lsb data embedding. IEEE Trans. Image Process. 14(2), 253–266 (2005)
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)
Chu, W.C.: Dct-based image watermarking using subsampling. IEEE Trans. Multimed. 5(1), 34–38 (2003)
Cox, I.J., Miller, M.L.: A review of watermarking and the importance of perceptual modeling. In: Proceedings of Electronic Imaging, pp. 92–99 (1997)
Deepshikha, C., Preeti, G., Gaur, S.B., Anil, G.: Lsb based digital image watermarking for gray scale image. IOSR J. Comput. Eng. 6(1), 36–41 (2012)
Di, C., Yang, X., Wang, X.: A four-stage hybrid model for hydrological time series forecasting. PLoS ONE 9(8), e104–e663 (2014)
Fan, M.Q., Wang, H.X., Li, S.K.: Restudy on svd-based watermarking scheme. Appl. Math. Comput. 203(2), 926–930 (2008)
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)
Hernandez-Guzman, V., Cruz-Ramos, C., Nakano-Miyatake, M., Perez-Meana, H.: Watermarking algorithm based on the dwt. IEEE Lat. Am. Trans. 4(4), 257–267 (2006)
Hilbert, D.: Über die stetige abbildung einer linie auf ein flächenstück. Math. Ann. 38(3), 459–460 (1891)
Hu, J., Wang, X., Qin, H.: Improved, feature-centric emd for 3d surface modeling and processing. Graph. Models 76(5), 340–354 (2014)
Hu, J., Wang, X., Qin, H.: Novel and efficient computation of hilbert huang transform on surfaces. Comput. Aided Geom. Des. 43, 95–108 (2016)
Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. Math. Phys. Eng. Sci. 454(1971), 903–995 (1998)
Hussein, M., Bairam, M.: A survey study on singular value decomposition and genetic algorithm based on digital watermarking techniques. In: Proceedings of Firs International Conference Computer International Info., pp. 7–16 (2017)
Lai, C.C.: A digital watermarking scheme based on singular value decomposition and tiny genetic algorithm. Digit. Signal Process. 21(4), 522–527 (2011)
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)
Roy, S., Pal, A.K.: A robust blind hybrid image watermarking scheme in rdwt-dct domain using arnold scrambling. Multimed. Tools Appl. 76(3), 3577–3616 (2017)
Sagan, H.: A three-dimensional hilbert curve. Int. J. Math. Educ. Sci. Tech. 24(4), 541–545 (1993)
Seyyed, H.S., Amir, H.T., Amir, H.M.: Waca: a new blind robust watermarking method based on arnold cat map and amplified pseudo-noise strings with weak correlation. Multimed. Tools Appl. 78(14), 19163–19179 (2019)
Sharma, J.B., Sharma, K.K., Sahula, V.: Digital image dual watermarking using self-fractional Fourier functions, bivariate empirical mode decomposition and error correcting code. J. Opt. 42(3), 214–227 (2013)
Singh, S.P., Bhatnagar, G.: A new robust watermarking system in integer dct domain. J. Vis. Commun. Image R 53, 86–101 (2018)
Subr, K., Soler, C., Durand, F.: Edge-preserving multiscale image decomposition based on local extrema. ACM Trans. Graph. 28(5), 1471–1479 (2009)
Tao, P., Eskicioglu, A.M.: A method for image recovery in the dft domain. In: 3rd IEEE Cons. Comm. Network. Conf., vol. 2, pp. 1134–1138 (2006)
Torr, P., Zisserman, A.: Mlesac: a new robust estimator with application to estimating image geometry. Comput. Vis. Image Underst. 78(1), 138–156 (2000)
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)
Wang, H., Su, Z., Cao, J., Wang, Y., Zhang, H.: Empirical mode decomposition on surfaces. Graph. Models 74(4), 173–183 (2012)
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)
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)
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)
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)
Xie, X.: Illumination preprocessing for face images based on empirical mode decomposition. Signal Process. 103, 250–257 (2014)
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)
Funding
This research is supported in part by National Science Foundation of USA (IIS-1715985 and IIS-1812606), National Natural Science Foundation of China (No. 61672149, 61602341, 61672077, 61532002, 61602344, 61802279, 61872347); Natural Science Foundation of Tianjin (18JCQNJC00100). The Science & Technology Development Fund of Tianjin Education Commission for Higher Education (Grant No. 2018KJ222).
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Wang, X., Hu, K., Hu, J. et al. Robust and blind image watermarking via circular embedding and bidimensional empirical mode decomposition. Vis Comput 36, 2201–2214 (2020). https://doi.org/10.1007/s00371-020-01909-2
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DOI: https://doi.org/10.1007/s00371-020-01909-2