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Reversible Watermarking of NURBS-Based CAD Models

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Information Hiding (IH 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4437))

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Abstract

We present an algorithm for embedding robust reversible watermarks into CAD models that are represented by a collection of NURBS (Non Uniform Rational B-Spline) surface patches.

Changes to the geometry of the surface representation are introduced by moving one control point per surface patch. This approach provides robustness against converting the model into the mesh representation. The information needed to restore the original control point location is added to the knot vectors of the patch, thus enabling recovery of the original model from the watermarked NURBS representation.

We exploit the properties of the NURBS representation for preserving the continuity between adjacent patches. Continuity is the major criterion of designers for assessing the quality of surface models.

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References

  1. Piegl, L., Tiller, W.: The NURBS Book. Springer-Verlag, Heidelberg, Germany (1997)

    Google Scholar 

  2. Ohbuchi, R., Masuada, H., Aono, M.: Watermarking Three-Dimensional Polygonal Models. ACM Multimedia 97, 261–272 (1997)

    Article  Google Scholar 

  3. Ohbuchi, R., Masuda, H., Aono, M.: A Shape-Preserving Data Embedding Algorithm for NURBS Curves and Surfaces. In: Werner, R. (ed.) Proceedings of the 1999 International Conference on Computer Graphics, Canmore, Alberta, Canada, pp. 180–187. IEEE Press, Los Alamitos (1999)

    Chapter  Google Scholar 

  4. Fornaro, C., Sanna, A.: Public key watermarking for authentication of CSG models. Computer Aided Design 32(12), 727–735 (2000)

    Article  Google Scholar 

  5. Ko, K.H., Maekawa, T., Patrikalakis, N.M., Masuda, H., Wolter, F.E.: Shape Intrinsic Watermarks for Free-Form Objects. In: Proceedings of the 2004 NSF Design, Service and Manufacturing Grantees and Research Conference, Dallas, Texas (2004)

    Google Scholar 

  6. Nagahashi, H., Mitsuhashi, R., Morooka, K.: A method for watermarking to bézier polynomial surface models. Transactions of the Institute of Electronics, Information and Communication Engineers E87-D(1), 224–232 (2004)

    Google Scholar 

  7. Lee, J.J., Cho, N.I., Lee, S.U.: Watermarking for 3d nurbs graphic data. EURASIP Journal on Applied Signal Processing 14, 2142–2152 (2004)

    Article  Google Scholar 

  8. Mitrea, M., Zaharia, T., Prêteux, F.: Spread spectrum robust watermarking for nurbs surfaces. WSEAS Transactions on Communications 3(2), 734–740 (2004)

    Google Scholar 

  9. Boehm, W.: Inserting new knots into B-spline curves. Computer-Aided Design 12(4), 199–201 (1980)

    Article  Google Scholar 

  10. Benedens, O.: Robust Watermarking and Affine Registration of 3D Meshes. In: Petitcolas, F.A.P. (ed.) IH 2002. LNCS, vol. 2578, pp. 177–195. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Farin, G.: Curves and Surfaces for CAGD: a Practical Guide, 5th edn. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  12. Foley, J., van Dam, A., Feiner, S.K., Hughes, J.F.: Computer Graphics: Principles and Practice. Addison-Wesley, Reading (1989)

    Google Scholar 

  13. Piegl, L.: Modifying the shape of rational B-splines. Part 2: surfaces. CAD 21(9), 509–518 (1989)

    MATH  Google Scholar 

  14. Piegl, L., Tiller, W.: Geometry-based triangulation of trimmed surfaces. CAD 30(1), 11–18 (1998)

    Google Scholar 

  15. Uccheddu, F., Corsini, M., Barni, M.: Wavelet-Based Blind Watermarking of 3D Models. In: Proceedings of the Multimedia and Security Workshop, Magdeburg, Germany, pp. 143–154. ACM, New York (2004)

    Chapter  Google Scholar 

  16. Agoston, M.K.: Computer Graphics and Geometric Modeling: Implementation and Algorithms. Springer, London (2005)

    MATH  Google Scholar 

  17. Katayama, J.: Rhino 3D Modelling: Rhino Car Design School Data and Commen- tary (last accessed August 18, 2006), http://www.rhino3d.co.jp/seminar/seminarcarstylinge.html

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Jan L. Camenisch Christian S. Collberg Neil F. Johnson Phil Sallee

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© 2007 Springer-Verlag Berlin Heidelberg

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Funk, W. (2007). Reversible Watermarking of NURBS-Based CAD Models. In: Camenisch, J.L., Collberg, C.S., Johnson, N.F., Sallee, P. (eds) Information Hiding. IH 2006. Lecture Notes in Computer Science, vol 4437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74124-4_12

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  • DOI: https://doi.org/10.1007/978-3-540-74124-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74123-7

  • Online ISBN: 978-3-540-74124-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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