Abstract
An optimization-based methodology is proposed in this paper preserving mesh surfaces in 3D watermarking. The Levenberg-Mar- quardt optimization algorithm is used for displacing the vertices according to the message to be embedded. A specific cost function is used by this method in order to ensure minimal surface distortion while the watermark would be enabled with high robustness to attacks. This cost function consists of three components representing the distance to the original surface, to the watermarked surface and the vertex displacement, respectively. The proposed methodology is statistical, blind and robust. A study of its crypto-security is provided as well in this research study.
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References
Bors, A.G.: Watermarking mesh-based representations of 3-D objects using local moments. IEEE Trans. on Image Processing 15(3), 687–701 (2006)
Cho, J.W., Prost, R., Jung, H.Y.: An oblivious watermarking for 3-D polygonal meshes using distribution of vertex norms. IEEE Trans. Signal Processing 55(1), 142–155 (2007)
Luo, M., Bors, A.G.: Surface-preserving watermarking of 3-D shapes. IEEE Trans. on Image Processing 20(10), 2813–2826 (2011)
Zafeiriou, S., Tefas, A., Pitas, I.: Blind robust watermarking schemes for copyright protection of 3D mesh objects. IEEE Trans. on Visualization and Computer Graphics 11(5), 496–607 (2005)
Liu, Y., Prabhakaran, B., Guo, X.H.: Spectral Watermarking for Parameterized Surfaces. IEEE Trans. on Information Forensics and Security 7(5), 1459–1471 (2011)
Luo, M., Bors, A.G.: Shape watermarking based on minimizing the quadric error metric. In: Proc. IEEE International Conference on Shape Modeling and Applications, Beijing, China, pp. 103–110 (2009)
Levenberg, K.: An algorithm for least-squares estimation of nonlinear parameters. The Quarterly of Applied Mathematics 2, 164–168 (1944)
Cignoni, P., Rocchini, C., Scopigno, R.: Metro: Measuring error on simplified surfaces. Computer Graphics Forum 17(2), 167–174 (1998)
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Bors, A.G., Luo, M. (2013). Watermark Optimization of 3D Shapes for Minimal Distortion and High Robustness. In: Wilson, R., Hancock, E., Bors, A., Smith, W. (eds) Computer Analysis of Images and Patterns. CAIP 2013. Lecture Notes in Computer Science, vol 8048. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40246-3_37
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DOI: https://doi.org/10.1007/978-3-642-40246-3_37
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