Watermarking 3D Triangular Mesh with High Visual Quality

Two common problems are usually encountered in 3D watermarking, the causality problem and the convergence problem. In order to avoid the causality problem, we have proposed an efficient technique for traversing the polygonal meshes. Our procedure also solved the convergence problem by reducing the update of the vertices in the smooth areas and increasing it in the rough areas. The roughness of an area is calculated according to the angle between each pair of triangles in that area. The base edge of the triangle is then divided into small segments. The number of the segments will be increased in rough areas and decreased in the smooth areas, so that the vertex shift (move) will be imperceptible. We referred to our procedure as the Nearest Neighbor Move or NNM, because the vertex position will be moved to the nearest neighbor segment. The results of NNM show comparatively high visual quality for the watermarked meshes