Watermarking 3D Polygonal Meshes in the Mesh Spectral Domain

Digital watermarking embeds a structure called watermark into the target data, such as image and 3D polygonal models. The watermark can be used, for example, to enforce copyright and to detect tampering. This paper presents a new robust watermarking method that adds watermark into a 3D polygonal mesh in the mesh's spectral domain. The algorithm computes spectra of the mesh by using eigenvalue decomposition of a Laplacian matrix derived only from connectivity of the mesh. Mesh spectra can be obtained by projecting coordinates of vertices onto the set of eigenvectors. A watermark is embedded by modifying the magnitude of the spectra. Watermarks embedded by using this method are resistant to similarity transformation, random noise added to vertex coordinates, mesh smoothing, and partial resection of the meshes.