Hierarchical Blind Watermarking of 3D Triangular Meshes

An original hierarchical watermarking scheme for three-dimensional triangular meshes is proposed in this paper. A geometrically robust watermark and a high-capacity watermark are inserted in different resolution levels of the wavelet decomposition of a semi-regular mesh by modifying the norms of wavelet coefficients. Both watermarks are blind and invariant to similarity transformations. The robustness of the first watermark is achieved by synchronizing and quantizing watermark primitives according to edges lengths of the coarsest level, which are quite insensible to geometrical attacks. The high capacity of the second watermark is obtained by considering the permutation of the norms of a group of wavelet coefficients. Experiments have proven the high robustness of the first watermark under common geometrical attacks. To our knowledge, the capacity of the second method, which can attain the factorial of the candidate coefficients number, is the highest for 3D meshes in the literature.