Spectral Watermarking for Parameterized Surfaces

This paper presents a blind spectral two-way watermarking framework for 3-D models with parametric information. We introduce a spectral geometric watermarking technique based on Dirichlet Manifold Harmonic Transform to alter the geometric shape, while the spectral basis functions are computed from the parametric mesh as the analysis domain. This new geometric method embeds watermarks into small surface patches without introducing discontinuity across the patch boundary, while at the same time is robust against various spatial attacks. By manipulating part of the geometric shape on the intermediate model instead of the original model, this method gains robustness against connectivity changing and cropping attacks. By combining the new geometric method with the existing texture method into the two-way watermarking framework, we can withstand various attacks applied to either geometric mesh or parametric information. Theoretical analysis and experiments show that this new geometric method is robust against the majority of attacks and the two-way watermarking framework helps achieve better robustness.