Blind Robust 3-D Mesh Watermarking Based on Oblate Spheroidal Harmonics

In this paper, a novel transform-based, blind and robust 3-D mesh watermarking scheme is presented. The 3-D surface of the mesh is firstly divided into a number of discrete continuous regions, each of which is successively sampled and mapped onto oblate spheroids, using a novel surface parameterization scheme. The embedding is performed in the spheroidal harmonic coefficients of the spheroids, using a novel embedding scheme. Changes made to the transform domain are then reversed back to the spatial domain, thus forming the watermarked 3-D mesh. The embedding scheme presented herein resembles, in principal, the ones using the multiplicative embedding rule (inherently providing high imperceptibility). The watermark detection is blind and by far more powerful than the various correlators typically incorporated by multiplicative schemes. Experimental results have shown that the proposed blind watermarking scheme is competitively robust against similarity transformations, connectivity attacks, mesh simplification and refinement, unbalanced resampling, smoothing and noise addition, even when juxtaposed to the informed ones.