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.
Highlights
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
We have proposed two algorithms for the watermarking of 3D NURBS surface
One is suitable for the steganography, and the other for the watermarking. These algorithms extract 2D images from 3D NURBS model, the pixels of which represent the coordinates of surfaces for the given parameters
Summary
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. 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 because the scanned 3D data are naturally the sampling points of surfaces. The mesh representation has drawbacks in that it requires large amount of data, and it cannot represent mathematically rigorous curves and surfaces. 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. The NURBS is used in CAD and other areas which need high precision, and it is used in animation because the motion of an object can be realized by successively adjusting some of the parameters
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