Watermarking for 3D polygons using wavelet transform and modified traveling salesman problem

Recent developments in computer technologies and networks have enabled the use of high-quality digital contents, such as electronic documents, images, and audio and video contents. A watermarking technique has recently been developed for the copyright protection of these digital contents. There are few watermarking techniques for three-dimensional (3D) geometric models, such as solid models or polygonal models. In the present paper, we propose an optimization problem for embedding watermarks on 3D polygon models. Then, using a genetic algorithm, we obtain the approximately optimum solutions for an original problem and a partial problem, which has an advantage with respect to security over the corresponding original problem. For embedding and extracting the watermark, we use a simplified method based on the previous study using the wavelet transform. The structure of the optimization problem examined in the present research is the same as that for the Traveling Salesman Problem, except for the objective function and the two additional constraints.