Digital watermarking of polygonal meshes with linear operators of scale functions

  • Authors:

  • Hyeong-In Choi;Tae-wan Kim;Song-Hwa Kwon;Hwan Pyo Moon;Sung Ha Park;Heon-Ju Shin;Jung-Kyo Sohn

  • Affiliations:

  • Department of Mathematics, Seoul National University, Seoul, 151-747, Republic of Korea and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea;Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea and Research Institute of Marine Systems Engineering, Seoul National University, ...;Department of Mathematics, Seoul National University, Seoul, 151-747, Republic of Korea and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea;Department of Mathematics, Dongguk University, Seoul 100-715, Republic of Korea;Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea;STX R&D Center, STX Shipbuilding Co., Republic of Korea;Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea

  • Venue:
  • Computer-Aided Design
  • Year:
  • 2010

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Abstract

Digital watermarking is already used to establish the copyright of graphics, audio and text, and is now increasingly important for the protection of geometric data as well. Watermarking polygonal models in the spectral domain gives protection against similarity transformation, mesh smoothing, and additive random noise attacks. However, drawbacks exist in analyzing the eigenspace of Laplacian matrices. In this paper we generalize an existing spectral decomposition and propose a new spatial watermarking technique based on this generalization. While inserting the watermark, we avoid the cost of finding the eigenvalues and eigenvectors of a Laplacian matrix in spectral decomposition; instead we use linear operators derived from scaling functions that are generated from Chebyshev polynomials. Experimental results show how the cost of inserting and detecting watermarks can be traded off against robustness under attacks like additive random noise and affine transformation.