Robust Zero Watermarking for 3D Triangular Mesh Models Based on Spherical Integral Invariants

  • Chenchen Cui
  • Rongrong NiEmail author
  • Yao Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10431)


At present, zero-watermarking algorithms can well resist geometric attacks and signal attacks. However, most of them are not robust to resampling attack. To solve the problem, this paper presents a robust zero-watermarking algorithm for copyright protection of 3D triangular mesh models. The watermark information is constructed by spherical integral invariants and a new computing method based on spherical crown for the invariants is proposed. CPCA(Continues Principle Component Analysis) is introduced to normalize the input mesh, while Ray-Based method is introduced to decompose the normalized mesh into ordered patches. On one hand, for the model to be protected, once the watermark is constructed, it needs to be registered in a trusted third-party IPR(Intellectual Property Rights) database together with a timestamp. On the other hand, for the model to be detected, the constructed watermark should be matched with all watermarks to recognize whether its original model is in the database. Experimental results prove that it is robust against common geometric attacks, signal processing attacks and uniform resampling attack.


3D triangular mesh models Zero-watermark Robust Spherical integral invariants CPCA Ray-Based Resampling attack 



This work was supported in part by National NSF of China (61672090, 61332012). The National Key Research and Development Program of China (2016YFB0800404), Fundamental Research Funds for the Central Universities (2015JBZ002).


  1. 1.
    Ohbuchi, R., Masuda, H., Aono, M.: Watermaking three-dimensional polygonal models. In: ACM International Conference on Multimedia 1997, vol. 16, pp. 261–272 (1997)Google Scholar
  2. 2.
    Benedens, O.: Geometry-based watermarking of 3D models. IEEE Comput. Graph. Appl. 19(1), 46–55 (1999)CrossRefGoogle Scholar
  3. 3.
    Cho, J., Prost, R., Jung, H.: An oblivious watermarking for 3-D polygonal meshes using distribution of vertex norms. IEEE Trans. Signal Process. 55(1), 142–155 (2007)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Liu, Y., Prabhakaran, B., Guo, X.: Spectral watermarking for parameterized surfaces. IEEE Trans. Inf. Forensics Secur. 7(5), 1459–1471 (2012)CrossRefGoogle Scholar
  5. 5.
    Bors, A., Luo, M.: Optimized 3D watermarking for minimal surface distortion. IEEE Trans. Image Process. 22(5), 1822–1835 (2013)CrossRefGoogle Scholar
  6. 6.
    Wen, Q., Sun, T., Wang, S.: Based zero-watermark digital watermarking technology. In: The Third China Information Hiding and Multimedia Security Workshop (CIHW). Xidain University Press, Xi’an (2001)Google Scholar
  7. 7.
    Yang, S., Li, C.H., Sun, F., Sun, Y.: Study on the method of image non-watermark in DWT domain. J. Image Graph. 8(1), 664–669 (2003)Google Scholar
  8. 8.
    Wang, C., Li, D.: Image zero-watermarking utilizing wavelet zerotree structure and PCA. Opto Electron. Eng. 32(41), 75–77 (2005)Google Scholar
  9. 9.
    Lu, J., Huang, Q., Wang, M., Li, L., Dai, J., Chang, C.-C.: Zero-watermarking based on improved orb features against print-cam attack. In: Shi, Y.-Q., Kim, H.J., Pérez-González, F., Yang, C.-N. (eds.) IWDW 2014. LNCS, vol. 9023, pp. 187–198. Springer, Cham (2015). doi: 10.1007/978-3-319-19321-2_14 CrossRefGoogle Scholar
  10. 10.
    Dhoka, M.S.: Robust and dynamic image zero watermarking using Hessian Laplace detector and logistic map. In: IEEE International Advance Computing Conference (IACC), Bangalore, pp. 930–935 (2015)Google Scholar
  11. 11.
    Xu, T., Zhang, Y.: Zero-watermarking technique of three-dimensional meshes. J. Jilin Univ. (Eng. Technol. Ed.) 37(4), 901–904 (2007)Google Scholar
  12. 12.
    Gao, L.: A zero watermarking scheme for 3D meshes based on affine invariant. In: The 2011 Asia-Pacific Youth Conference of Youth Communication and Technology (2011)Google Scholar
  13. 13.
    Du, S., Zhan, Y.Z., Wang, X.Y.: A zero watermarking algorithm for 3D mesh models based on shape diameter function. J. Comput. Aided Des. Comput. Graph. 25(5), 653–665 (2013)Google Scholar
  14. 14.
    Manay, S., Hong, B.-W., Yezzi, A.J., Soatto, S.: Integral invariant signatures. In: Pajdla, T., Matas, J. (eds.) ECCV 2004, Part IV. LNCS, vol. 3024, pp. 87–99. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-24673-2_8 CrossRefGoogle Scholar
  15. 15.
    Pottmann, H., Huang, Q., Yang, Y.: Integral invariants for robust geometry processing. Technical report, Vienna University of Technology (2005)Google Scholar
  16. 16.
    Wang, Y.P.: Research on 3D Model Watermark Embedding Method. Tsinghua University, Beijing (2008)Google Scholar
  17. 17.
    Molaei, A., Ebrahimnezhad, H., Sedaaghi, M.: Robust and blind 3D mesh watermarking in spatial domain based on faces categorization and sorting. 3D Res. 7(2), 1–18 (2016)CrossRefGoogle Scholar
  18. 18.
    Vranic, D.: 3D Model Retrieval. Universitat Leipzig, Leipzig, Germany Saxony (2003)Google Scholar
  19. 19.
    Papadakis, P., Pratikakis, I., Perantonis, S., Theoharis, T.: Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation. Pattern Recogn. 40(9), 2437–2452 (2007)CrossRefzbMATHGoogle Scholar
  20. 20.
    Vranic, D., Saupe, D., Richter, J.: Tools for 3D-object retrieval: Karhunen-Loeve transform and spherical harmonics. In: Fourth Workshop on Multimedia Signal Processing, pp. 293–298. IEEE (2001)Google Scholar
  21. 21.
    Liu, H., Zhang, Z.H., Wen, J.: A DCT domain zero-watermark scheme based on time stamping. Comput. Technol. Dev. 19(9), 143–145 (2009)Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Information ScienceBeijing Jiaotong UniversityBeijingChina
  2. 2.Beijing Key Laboratory of Advanced Information Science and Network TechnologyBeijingChina

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