Watermarking for 3D NURBS graphic data

In this paper, two watermarking algorithms for nonuniform rational b-spline (NURBS) are proposed. One is suitable for steganography, and the other for watermarking. Both algorithms do not directly embed data into the parameters of NURBS, but into the 2D virtual images extracted from the sampled points of 3D model. As a result, the proposed algorithm for steganography preserves the data size of the model and can embed more information than the conventional algorithm. Also, the watermarking algorithm can use any of existing 2D watermarking techniques when embedding data into the virtual 2D images. From the experiment, it is found that the algorithm is robust against the operations to knots and control points. It is also robust against the remodeling of NURBS model through approximation.