Journal of the Institute of Electronics Engineers of Korea CI (전자공학회논문지CI)

The Institute of Electronics and Information Engineers (대한전자공학회)
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3D Mesh Watermarking Using Projection onto Convex Sets

볼록 집합 투영 기법을 이용한 3D 메쉬 워터마킹

  • Lee Suk-Hwan (Dept. of Information Security, TongMyong University) ;
  • Kwon Seong-Geun (Mobile Communication Division, SAMSUNG electronics co.) ;
  • Kwon Ki-Ryong (Division of Electronics, Computer and Telecommunication Eng., Pukyong University)
  • Published : 2006.03.01
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Abstract

This paper proposes a robustness watermarking for 3D mesh model based on projection onto convex sets (POCS). After designing the convex sets for robustness and invisibility among some requirements for watermarking system, a 3D-mesh model is projected alternatively onto two constraints convex sets until the convergence condition is satisfied. The robustness convex set are designed for embedding the watermark into the distance distribution of the vertices to robust against the attacks, such as mesh simplification, cropping, rotation, translation, scaling, and vertex randomization. The invisibility convex set are designed for the embedded watermark to be invisible. The decision values and index that the watermark was embedded with are used to extract the watermark without the original model. Experimental results verify that the watermarked mesh model has invisibility and robustness against the attacks, such as translation, scaling, mesh simplification, cropping, and vertex randomization.

본 논문에서는 3D 메쉬 모델에 대한 POCS 기반의 워터마킹 방법을 제안하였다. 제안한 방법에서는 워터마킹 시스템의 조건들 중 견고성 및 비가시성에 대한 볼록 집합을 설계한 후 3D 메쉬 모델의 꼭지점들을 이 두 집합들로 수렴 조건을 만족할 때 까지 반복 교대 투영한다. 견고성 제약 조건 집합은 각 꼭지점의 거리 분포에 워터마크를 삽입하는 방법에 의하여 정의되며, 비가시성 제약 조건 집합은 꼭지점 좌표의 변화량에 의하여 정의된다. 실험 결과로부터 제안한 방법이 좌표 변환, 스케일링, 메쉬 간단화, 절단, 및 꼭지점 잡음 첨가 등의 공격에 대한 우수한 견고성 및 비가시성을 확인하였다.

Keywords

References

  1. ISO/IEC 14772-1, 'The virtual reality modeling language
  2. R. Ohbuchi, H. Masuda, and M. Aono, 'Watermarking Three-Dimensional Polygonal Models Through Geometric and Topological Modification,' IEEE Journal on Selected Areas in Communications, vol. 16, no. 4, pp. 551-560, May 1998 https://doi.org/10.1109/49.668977
  3. R. Ohbuchi, S. Takahashi, T. Miyazawa, and A. Mukaiyama, 'Watermarking 3D Polygonal Meshes in the Mesh Spectral Domain,' Proc. Graphics Interface 2001, pp. 9-17, 2001
  4. S. Kanai, H. Date, and T. Kishinami, 'Digital Watermarking for 3D Polygons using Multiresolution Wavelet Decomposition,' Proc. Sixth IFIP WG 5.2 GEO-6, pp, 296-307, Dec. 1998
  5. O. Benedens, 'Geometry-Based Watermarking of 3D Models,' IEEE Computer Graphics and Applications, vol. 19, no. 1, pp. 46-55, Jan./Feb. 1999 https://doi.org/10.1109/38.736468
  6. E. Praun, H. Hoppe, A. Finkelstein, 'Robust Mesh Watermarking,' Proc. SIGGRAPH 99, pp. 49-56, 1999 https://doi.org/10.1145/311535.311540
  7. B-L. Yeo and M. M. Yeung, 'Watermarking 3D Objects for Verification,' IEEE Computer Graphics and Applications, vol. 19, no. 1, pp. 36-45, Jan./Feb. 1999 https://doi.org/10.1109/38.736467
  8. K.-R. Kwon, S.-G. Kwon, and S.-H. Lee, '3D Watermarking Shape Recognition System Using Normal Vector Distribution Modelling,' Lecture Notes in Computer Science, vol. 3397-9743, pp. 481-490, Feb. 2005
  9. S.-H. Lee and K.-R. Kwon, 'Watermarking for 3D Mesh Model Using Patch CEGIs,' Lecture Notes in Computer Science, vol. 3481, pp, 557-566, May 2005 https://doi.org/10.1007/11424826_59
  10. S.-H. Lee, T.-S. Kim, S.-J. Kim, Y. H, K.-R. Kwon, K.-I. Lee, '3D mesh watermarking using projection onto convex sets,' International Conference on Image Processing, 2004. ICIP'04, vol. 3, pp. 1577-1580, Oct. 2004 https://doi.org/10.1109/ICIP.2004.1421368
  11. 이석환, 권기룡, '패치 CEGI를 이용한 메쉬 워터마킹,' 대한전자공학회논문지, 제42권 CI편 제1호, pp. 67-78, 2005년 1월
  12. 전정희, 호요성, '3차원 메쉬 모델의 적응형 워터마킹 방법,' 대한전자공학회논문지, 제40권 SP편 제6호, pp. 41-50, 2003년 11월
  13. Y. Yang, N. P. Galatsanos, A. K. Katsaggelos, 'Regularized Reconstruction to Reduce Blocking Artifacts of Block Discrete Cosine Transform Compressed Images,' IEEE Trans. on Circuits and Systems for Video Tech, vol. 3, no. 6, Dec. 1993 https://doi.org/10.1109/76.260198
  14. Y. Yang, and N. P. Galatsanos, 'Projection-Based Spatially Adaptive Reconstruction of Block- Transform Compressed Images,' IEEE Trans. on Image Processing, vol. 4, no. 7, July 1995 https://doi.org/10.1109/83.392332
  15. T. Kanai, MeshToSS Version 1.0.1, http://graphics.sfc.keio.ac.jp/MeshToSS/indexE.html
  16. N. Aspert, D. Santa-Cruz, and T. Ebrahimi, 'MESH: Measuring Errors Between Surfaces Using the Hausdorff Distance,' IEEE International Conference in Multimedia and Expo, 2004, ICME, vol. 1, pp. 705-708, Aug. 2002 https://doi.org/10.1109/ICME.2002.1035879