Robust mesh watermarking

Abstract

We describe a robust method for watermarking triangle meshes. Watermarking provides a mechanism for copyright protection of digital media by embedding information identifying the owner in the data. The bulk of the research on digital watermarks has focused on media such as images, video, audio, and text. Robust watermarks must be able to survive a variety of "attacks", including resizing, cropping, and filtering. For resilience to such attacks, recent watermarking schemes employ a "spread-spectrum" approach -they transform the document to the frequency domain and perturb the coefficients of the perceptually most significant basis functions. We extend this spread-spectrum approach to work for the robust watermarking of arbitrary triangle meshes.Generalizing spread spectrum techniques to surfaces presents two major challenges. First, arbitrary surfaces lack a natural parametrization for frequency-based decomposition. Our solution is to construct a set of scalar basis function over the mesh vertices using multiresolution analysis. The watermark perturbs vertices along the direction of the surface normal, weighted by the basis functions. The second challenge is that simplification and other attacks may modify the connectivity of the mesh. We use an optimization technique to resample an attacked mesh using the original mesh connectivity. Results show that our watermarks are resistant to common mesh operations such as translation, rotation, scaling, cropping, smoothing, simplification, and resampling, as well as malicious attacks such as the insertion of noise, modification of low-order bits, or even insertion of other watermarks.

Optimization approach for 3D model watermarking by linear binary programming

“…Another solution to the localization problem can be called global localization, and is employed by Praun et al (1999); Li et al (2004); Uccheddu et al (2004); Wu and Kobbelt (2005). Methods of this kind attempt to recover the order of model vertices after a reordering attack.…”

Hierarchical Blind Watermarking of 3D Triangular Meshes

“…To overcome this drawback, some algorithms propose a resampling stage on the input mesh of the watermark extraction to recover the same connectivity as the original cover mesh, but this inevitably makes the method non-blind. The second category of algorithms firstly decomposes the mesh in a transformed spectral domain, and then the watermark is inserted whether at the low, median or high frequency part [6,[10][11][12]. These methods usually provide better imperceptibility and better robustness to geometrical attacks, whereas the connectivity issue is still a problem.…”

“…These methods usually provide better imperceptibility and better robustness to geometrical attacks, whereas the connectivity issue is still a problem. For example, the Laplacian spectral analysis of 3D meshes is sensible to connectivity change [10]; the edge decimation technique to establish a multiresolution representation is also dependant to the mesh connectivity [11]; and most wavelet analysis tools require the input as semi-regular mesh, in which most vertices are of valence six [6].…”

Watermarking 2D vector maps in the mesh-spectral domain

“…By averaging the displacement of the vertices upon extraction, and by repeatedly embedding the same message many times over a map, the watermarks produced by the method are resistant against additive random noise, As a watermarking target, a three-dimensional (3D) polygonal mesh is somewhat similar to a 2D vector map; both are defined as a set of vertices (with either 2D or 3D coordinate values) and their connectivity. There are algorithms for watermarking 3D meshes [19,20,13,1,29,24,28,32,30,5,23]. These algorithms alter either vertex coordinate or vertex connectivity of the meshes for watermarking.…”

“…These algorithms alter either vertex coordinate or vertex connectivity of the meshes for watermarking. Many of the recent 3D mesh watermarking methods employed transformed-domain approaches to watermarking [13,24,21,30,5,23]. A method in this class would transform the mesh into a domain that reflects the notion of "frequency" and modify the most significant, low frequency components of the mesh shape to embed watermark messages.…”