Geometry Invariants Based 3D Model Watermarking Techniques

In the past decades, three dimensional (3D) models have been increasingly used in the applications of industry, medical, graphics arts, entertainment, and virtual reality. Watermarking for protecting the intellectual property rights and certifying the authentication of audio signals,2D still images and video has been thoroughly studied in recent years. However, since the synchronization problem, complex geometrical and topological problems introduced by the 3D projects, watermarking technique for 3D models remains a challenging problem. In this paper, we introduce two novel geometry transform invariants, and propose two robust watermarking methods and one reversible watermarking approach, which are stated as follows:A highly adaptable capacity and invisibility 3D watermarking method:We propose a finely tunable capacity and invisibility novel blind watermarking method for 3D models with arbitrary topology in spatial domain. Our watermarking approach is based on a novel four-point set construction and selection scheme to embed watermark in the similarity-transform invariants of 3D models. Experimental results show that the capacity and invisibility of the watermarked models can be monotonically adjusted. To the best of our knowledge, our novel method can provide much better watermark invisibility than other state-of-the-art watermarking methods, while maintain large capacity and strong robustness against various typical attacks including cropping, RST transformations and local attacks. The low computational complexity of both the embedding and the extraction processes makes it suitable for copyright protection of 3D models.A new affine-transformation invariant 3D blind watermarking scheme:We propose a new blind watermarking method for 3D models with arbitrary connectivity in spatial domain based on affine invariants. Given a 3D model, a watermark is embedded as length ratios of one diagonal segment to the residing diagonal intersected by the other one in a coplanar convex quadrilateral. This ratio is an affine invariant as affine transformations preserve length ratios. In the proposed method, coplanar convex quadrilaterals are constructed by slightly disturbing the geometry of vertices located in a local neighborhood. In order to extract a watermark, we traverse all the vertices in a watermarked 3D model, computing length ratios accordingly. A watermark is then recovered by combining all the watermark pieces embedded in length ratios through majority voting. The computational complexity of our approach is as low as O(V), where V is the number of 3D points. Experimental results indicate that the proposed new approach has many significant merits in terms of robustness, tunable capacity and invisibility, and efficiency over other state-of-art watermarking methods.Similarity-transformation invariant 3D reversible watermarking:we present a reversible watermarking method for 3D models with arbitrary topology based on histogram shifting. We use similarity-transformation invariants to generate histogram such that the proposed method is invariant to similarity transformations including translation, rotation and uniform scaling. By adjusting the range of the histogram of 3D models adaptively, our proposed method provides a tunable capacity and invisibility for watermarking. The computational complexity of our proposed method is also very low. Experimental results and performance comparison with other reversible watermarking methods are presented to demonstrate the high effectiveness of our proposed algorithm.