Digital watermarking of 3D meshes

Despite the increasing interest in digital watermarking of multimedia data, watermarking of 3D geometrical models has received little attention by the research community. One of the main reasons is that geometric data is intrinsically complex to handle, in addition a lot of diverse attacks can be thought of that are not possible in the 2D and 1D cases. So it is very difficult to develop robust watermarking algorithms for 3D models. In order to overcome the above problems most of the systems proposed so far exploit the knowledge of the original, non marked, mesh for watermark recovery. The practical usefulness of non-blind schemes, though, is very limited, hence the need to develop new blind schemes for 3D watermarking. In this paper we propose a blind watermarking algorithm for 3D meshes. Watermarking is achieved by perturbing the position of the vertices of the model according to a spherical pseudo-random bumped surface. The pseudo-random position and amplitude of the bumps encode the watermark. In order to gain robustness while keeping the distortion to a minimum, the watermark is embedded into a low resolution version of the mesh. The coarse version of the model is obtained by a MAPS1 (Multiresolution Adaptive Parameterization of Surface) algorithm. The base domain produced by this algorithm is used to obtain the full resolution watermarked model from the coarse watermarked one. Watermark recovery is accomplished by means of a standard correlation detector. Experimental results show that the system assure high visual quality of the watermarked model, and that a good degree of robustness can be reached for models with a suffciently high number of faces.