Watermarking 2D vector maps in the mesh-spectral domain

The paper proposes a digital watermarking algorithm for 2D vector digital maps. The watermark is a robust, informed-detection watermark to be used to prevent such abuses as an intellectual property rights violation. The algorithm proposed in the paper embeds watermarks in the frequency-domain representation of a 2D vector digital map. Our method treats vertices in the map as a point set, and imposes connectivity among the points by using Delaunay triangulation. The method then computes the mesh-spectral coefficients (Karni, 2000) from the mesh created. Modifications of the coefficients according to the message bits, and inverse transforming the coefficients back into the coordinate domain produces the watermarked map. Our evaluation experiments showed that the watermark produced by the method is resistant against additive random noise, similarity transformation, vertex insertion and removal. It is also resistant, to some extent, against cropping. Compared to our previous algorithm (Ohbuchi, 2002), the algorithm described in this paper showed significantly improved attack resiliency.

[1]  Sushil Jajodia,et al.  Information Hiding: Steganography and Watermarking-Attacks and Countermeasures , 2000, Advances in Information Security.

[2]  Adam Finkelstein,et al.  Robust mesh watermarking , 1999, SIGGRAPH.

[3]  Oliver Benedens,et al.  Geometry-Based Watermarking of 3D Models , 1999, IEEE Computer Graphics and Applications.

[4]  Ryutarou Ohbuchi,et al.  A Frequency‐Domain Approach to Watermarking 3D Shapes , 2002, Comput. Graph. Forum.

[5]  David Zhang,et al.  Robust mesh watermarking based on multiresolution processing , 2001, Comput. Graph..

[6]  Martin F. H. Schuurmans,et al.  Digital watermarking , 2002, Proceedings of ASP-DAC/VLSI Design 2002. 7th Asia and South Pacific Design Automation Conference and 15h International Conference on VLSI Design.

[7]  Craig Gotsman,et al.  Spectral compression of mesh geometry , 2000, EuroCG.

[8]  G. de Jager,et al.  A survey of point pattern matching techniques and a new approach to point pattern recognition , 1992, Proceedings of the 1992 South African Symposium on Communications and Signal Processing.

[9]  Henri Maitre,et al.  Compression and watermarking of 3D triangle mesh geometry using spectral decomposition , 2002, SPIE Optics + Photonics.

[10]  Peter Eisert,et al.  Digital watermarking of MPEG-4 facial animation parameters , 1998, Comput. Graph..

[11]  Mark de Berg,et al.  Computational geometry: algorithms and applications, 3rd Edition , 1997 .

[12]  Hiroshi Masuda,et al.  Watermarking three-dimensional polygonal models through geometric and topological modifications , 1998, IEEE J. Sel. Areas Commun..

[13]  Herbert Süße,et al.  The Method of Normalization to Determine Invariants , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[15]  Craig Gotsman,et al.  3D Mesh Compression Using Fixed Spectral Bases , 2001, Graphics Interface.

[16]  Ingemar J. Cox,et al.  Digital Watermarking , 2003, Lecture Notes in Computer Science.

[17]  Ryutarou Ohbuchi,et al.  Robust watermarking of vector digital maps , 2002, Proceedings. IEEE International Conference on Multimedia and Expo.

[18]  S. Kanai,et al.  Digital Watermarking for 3D Polygons using Multiresolution Wavelet Decomposition , 1998 .

[19]  Ryutarou Ohbuchi,et al.  Watermarking 3D Polygonal Meshes in the Mesh Spectral Domain , 2001, Graphics Interface.

[20]  Hiroshi Masuda,et al.  Development of Digital Watermarking Technology for Vector Digital Maps , 2001 .

[21]  Christoph Busch,et al.  Towards Blind Detection of Robust Watermarks in Polygonal Models , 2000, Comput. Graph. Forum.

[22]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[23]  Boon-Lock Yeo,et al.  Watermarking 3D Objects for Verification , 1999, IEEE Computer Graphics and Applications.

[24]  Michael G. Wagner,et al.  Robust watermarking of polygonal meshes , 2000, Proceedings Geometric Modeling and Processing 2000. Theory and Applications.

[25]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[26]  Hiroshi Masuda,et al.  Watermaking three-dimensional polygonal models , 1997, MULTIMEDIA '97.