Robust digital watermarking for compressed 3D models based on polygonal representation

Multimedia has recently played an increasingly important role in various domains, including Web applications, movies, video game and medical visualization. The rapid growth of digital media data over the Internet, on the other hand, makes it easy for anyone to access, copy, edit and distribute digital contents such as electronic documents, images, sounds and videos. Motivated by this, much research work has been dedicated to develop methods for digital data copyright protection, tracing the ownership, and preventing illegal duplication or tampering. This paper introduces a methodology of robust digital watermarking based on a well-known spherical wavelet transformation, applied to 3D compressed model based on polygonal representation using a neural network. It will be demonstrated in this work that applying a watermarking algorithm on a compressed domain of a 3D object is more effective, efficient, and robust than when applied on a normal domain

Numerical Computation of Determinants with Additive Preconditioning ∗

Various geometric and algebraic computations (e.g., of the convex hulls, Voronoi diagrams, and scalar, univariate and multivariate resultants) boil down to computing the sign or the value of the determinant of a matrix. For these tasks numerical factorizations of the input matrix is the most attractive approach under the present day computer environment provided the rounding errors are controlled and do not corrupt the output. This is the case where the input matrix is well conditioned. Ill conditioned input matrices, however, frequently arise in geometric and algebraic applications, and this gives upper hand to symbolic algorithms. To overcome the problem, we apply our novel techniques of additive preconditioning and combine them with some nontrivial symbolic-numerical techniques. We analyze our approach analytically and demonstrate its power experimentally