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Robust 3D mesh zero-watermarking based on spherical coordinate and Skewness measurement

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Abstract

As the great advance in technology, 3D models are commonly used in multiple fields such as healthcare, filmdom, interactive entertainment, and construction industry. To prevent 3D data from unauthorized access and illegal tampering, we aim to propose a brand-new zero-watermarking technique based on the transformation of spherical coordinate and skewness of angle statistic. Without distorting the quality of 3D object, the main challenge in zero-watermarking is the robust feature selection and target construction. Since we have adopted the skewness measure of the spherical angle to be the resilient feature, the robustness can be highly enhanced. According to experimental results, the new method can stay stable under common signal processing operations such as translation, vertex reordering, uniform scaling, noise addition, smoothing, simplification, and cropping. This has demonstrated that the new method is suitable for the applications which need highly accurate 3D models.

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References

  1. Borah S, Borah B (2020) Prediction error expansion (PEE) based reversible polygon mesh watermarking scheme for regional tamper localization. Multimed Tools Appl 79:11437–11485

    Article  Google Scholar 

  2. Bors AG, Luo M (2013) Optimized 3D watermarking for minimal surface distortion. IEEE Trans Image Process 22(5):1822–1835

    Article  Google Scholar 

  3. Cho JW, Prost R, Jung HY (2007) An oblivious watermarking for 3D polygonal meshes using distribution of vertex norms. IEEE Trans Signal Process 55(1):142–155

    Article  MathSciNet  Google Scholar 

  4. Choi HY, Jang HU, Son J, Lee HK (2017) Blind 3D mesh watermarking based on cropping-resilient synchronization. Multimed Tools Appl 76(24):26695–26721

    Article  Google Scholar 

  5. Cox I, Miller M, Bloom J, Fridrich J, Kalker T (2007) Digital watermarking and steganography. Morgan Kaufmann Publishers, Burlington, pp 1–591

    Google Scholar 

  6. Garland M, Heckbert PS (1997) Surface simplification using quadric error metrics. Proceedings of the 24th annual conference on Computer graphics and interactive techniques, pp. 209–216

  7. Kashida N, Hasegawa K, Uto T (2020) 3-D mesh watermarking based on optimized multiple histograms. 2020 the 35th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC), pp. 363–366, Nagoya, Japan, Jul. 3–6

  8. Konstantinides JM, Mademlis A, Daras P, Mitkas PA, Strintzis MG (2009) Blind robust 3D mesh watermarking based on oblate spheroidal harmonics. IEEE Trans Multimedia 11(1):23–38

    Article  Google Scholar 

  9. Liu Y, Prabhakaran B, Guo X (2012) Spectral watermarking for parameterized surfaces. IEEE Trans Inf Forensic Secur 7(5):1459–1471

    Article  Google Scholar 

  10. Liu J, Wang Y, Li Y, Liu R, Chen J (2017) A robust and blind 3D watermarking algorithm using multiresolution adaptive parameterization of surface. Neurocomputing 237:304–315

    Article  Google Scholar 

  11. Medimegn N, Belaid S, Werghi N (2015) A survey of the 3D triangular mesh watermarking techniques. Int J Multimedia 1(1). https://doi.org/10.16966/ijm.102

  12. Mouhamed M, Soliman M, Darwish A, Hassanien A (2019) A robust 3D mesh watermarking approach based on genetic algorithm. 2019 the Ninth International Conference on Intelligent Computing and Information Systems, Cairo, Egypt, Dec. 8–10

  13. Narendra M, Valarmathi v, Anbarasi LJ (2020) Optimization of 3D triangular mesh watermarking using ACO-weber’s law. KSII Trans Internet Inf Syst 14(10):4042–4048

  14. Ohbuchi R, Mukaiyama A, Takahashi S (2002) A frequency domain approach to watermarking 3D shapes. Comput Graph Forum 21(3):373–382

    Article  Google Scholar 

  15. von Hippel PT (2005) Mean, median, and skew: correcting a textbook rule. J Stat Educ 13(2):965–971

    Google Scholar 

  16. Wang X, Zhan Y (2019) A zero-watermarking scheme for three-dimensional mesh models based on multi-features. Multimedia Tools Appl 78:27001–27028

  17. Wang K, Lavoué G, Denis F, Baskurt A (2008) A comprehensive survey on three-dimensional mesh watermarking. IEEE Trans Multimedia 10(8):1513–1527

    Article  Google Scholar 

  18. Wang K, Lavoué G, Denis F, Baskurt A, He X (2010) A benchmark for 3D mesh watermarking. Proceeding of the Shape Modeling International Conference (SMI), pp. 231–235

  19. Weisstein EW (2004) Spherical coordinates, MathWorld, Online Available: http://mathworld.wolfram.com/SphericalCoordinates.html.

  20. Wen Q, Sun TF, Wang SX (2003) Concept and application of zero-watermark. Acta Electron Sin 31(2):214–216

    Google Scholar 

  21. Zhan YZ, Li YT, Wang XY, Qian Y (2014) A blind watermarking algorithm for 3D mesh models based on vertex curvature. J Zhejiang Univ Sci C 15(5):351–362

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Information Engineering and Computer Science, Feng-Chia University, Taichung, 40724, Taiwan, Republic of China

    Jung-San Lee, Chieh Liu, Ying-Chin Chen & Wei-Che Hung

  2. Department of Computer Science, University of Illinois, Urbana-Champaign, Champaign, IL, USA

    Bo Li

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  1. Jung-San Lee
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  2. Chieh Liu
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  3. Ying-Chin Chen
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  4. Wei-Che Hung
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  5. Bo Li
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Correspondence to Bo Li.

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Lee, JS., Liu, C., Chen, YC. et al. Robust 3D mesh zero-watermarking based on spherical coordinate and Skewness measurement. Multimed Tools Appl 80, 25757–25772 (2021). https://doi.org/10.1007/s11042-021-10878-0

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  • DOI: https://doi.org/10.1007/s11042-021-10878-0

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