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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Piegl, L., Tiller, W.: The NURBS Book. Springer-Verlag, Heidelberg, Germany (1997)
Ohbuchi, R., Masuada, H., Aono, M.: Watermarking Three-Dimensional Polygonal Models. ACM Multimedia 97, 261–272 (1997)
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)
Fornaro, C., Sanna, A.: Public key watermarking for authentication of CSG models. Computer Aided Design 32(12), 727–735 (2000)
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)
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)
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)
Mitrea, M., Zaharia, T., Prêteux, F.: Spread spectrum robust watermarking for nurbs surfaces. WSEAS Transactions on Communications 3(2), 734–740 (2004)
Boehm, W.: Inserting new knots into B-spline curves. Computer-Aided Design 12(4), 199–201 (1980)
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)
Farin, G.: Curves and Surfaces for CAGD: a Practical Guide, 5th edn. Morgan Kaufmann, San Francisco (2002)
Foley, J., van Dam, A., Feiner, S.K., Hughes, J.F.: Computer Graphics: Principles and Practice. Addison-Wesley, Reading (1989)
Piegl, L.: Modifying the shape of rational B-splines. Part 2: surfaces. CAD 21(9), 509–518 (1989)
Piegl, L., Tiller, W.: Geometry-based triangulation of trimmed surfaces. CAD 30(1), 11–18 (1998)
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)
Agoston, M.K.: Computer Graphics and Geometric Modeling: Implementation and Algorithms. Springer, London (2005)
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
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)