Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Watermarking Algorithms for 3D NURBS Graphic Data | EURASIP Journal on Applied Signal Processing 2004 14 2142-2152 2004 Hindawi Publishing Corporation 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 jazzon@ Nam IkCho Institute of New Media and Communications INMC School of Electrical Engineering Seoul National University Seoul 151-744 Korea Email nicho@ Sang Uk Lee Institute of New Media and Communications INMC School of Electrical Engineering Seoul National University Seoul 151-744 Korea Email sanguk@ 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. 1. 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
