Watermarking Algorithms for 3D NURBS Graphic Data
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Watermarking Algorithms for 3D NURBS Graphic Data Jae Jun Lee Institute of New Media and Communications (INMC), School of Electrical Engineering, Seoul National University, Seoul 151-744, Korea Email: [email protected]
Nam Ik Cho Institute of New Media and Communications (INMC), School of Electrical Engineering, Seoul National University, Seoul 151-744, Korea Email: [email protected]
Sang Uk Lee Institute of New Media and Communications (INMC), School of Electrical Engineering, Seoul National University, Seoul 151-744, Korea Email: [email protected] Received 14 March 2003; Revised 10 June 2004 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 and phrases: watermark, 3D image, nonuniform rational B-spline (NURBS), steganography, data hiding.
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INTRODUCTION
With the development of computing environments, 3D models became widely used and are being produced in great numbers. 3D models are usually represented by mesh, nonuniform rational B-spline (NURBS), or voxel. Among these models, mesh is quite widely used because many studies on the mesh have already been performed, and also because the scanned 3D data are naturally the sampling points of surfaces. However, the mesh representation has drawbacks in that it requires large amount of data, and it cannot represent mathematically rigorous curves and surfaces. Unlike mesh, the NURBS describes 3D models by using mathematical formula. The data size for the NURBS is remarkably smaller than that for the mesh because the surface can be represented by only a few parameters. Also, the NURBS is smooth in nature so that the smoothness of NURBS is restricted only by hardware resolution. Hence, the NURBS is used in CAD and other areas which need high precision, and it is also used in animation because the motion of an object can be realized by successively adjusting some of the parameters.
Although the amount of 3D multimedia data is dramatically increasing, there has not been much discussion on the watermarking of 3D models, especially on the 3D NURBS models. For example, Ohbuchi et al. proposed an algorithm that embeds information into the knot equations by knot reparameterization [1]. This algorithm has merits that the resulting NURBS model has exactly the same shape as the original one, and that
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