A robust spectral approach for blind watermarking of manifold surfaces

This paper proposes a robust, blind, and imperceptible spectral watermarking approach for manifold surfaces represented as triangle meshes. The basic idea is to transform the original mesh into frequency domain using the Fourier-Like Manifold Harmonics Transform. The manifold harmonics basis defined on arbitrary topology surfaces is an intrinsic property of the manifold surfaces, i.e., it is only determined by the surface metric and independent of their resolution and embedding. This property makes our watermarking scheme immune to uniform affine attack (rotation, scaling, and translation) and robust against noise-addition and mesh simplification attacks. The global manifold harmonics are computed using the finite element method combined with a band-by-band algorithm that can compute thousands of eigenvectors for large meshes with up to a million triangles. The watermark data is embedded by modifying the manifold harmonics descriptors magnitude in an imperceptible way. By using global spectral analysis, the detection of such watermarks does not require mesh registration or re-sampling, and analysis of the statistics of the manifold harmonics descriptors is exploited to devise an optimal blind detector. Experimental results show the imperceptibility of the watermark with low distortions, and its robustness against the most common attacks including the uniform affine transformations, random noise addition, mesh simplification, etc.