Watermarking Algorithms for 3D NURBS Graphic Data

Abstract

Two watermarking algorithms for 3D nonuniform rational B-spline (NURBS) graphic data are proposed: one is appropriate for the steganography, and the other for watermarking. Instead of directly embedding data into the parameters of NURBS, the proposed algorithms embed data into the 2D virtual images extracted by parameter sampling of 3D model. As a result, the proposed steganography algorithm can embed information into more places of the surface than the conventional algorithm, while preserving the data size of the model. Also, any existing 2D watermarking technique can be used for the watermarking of 3D NURBS surfaces. From the experiment, it is found that the algorithm for the watermarking is robust to the attacks on weights, control points, and knots. It is also found to be robust to the remodeling of NURBS models.

Keywords

• watermark
• 3D image
• nonuniform rational B-spline (NURBS)
• steganography
• data hiding.