Robust and Blind Watermarking of Polygonal Meshes Based on Volume Moments

This paper describes a robust and blind watermarking algorithm for polygonal meshes, dedicated to copyright protection. The watermark primitives are intrinsic 3D shape descriptors: the analytic and continuous geometric volume moments. The mesh is first normalized by using its global moments, and decomposed into patches by discretizing its cylindric domain. Then, one bit is inserted in each candidate patch by quantizing its local zero-order moment, through a modified scalar Costa scheme. The patch is then deformed by an iterative process, so as to reach the target quantized moment value; a smooth deformation mask is used to avoid introducing visible distortion. A global moment compensation post-processing is carried out after bit insertion so as to recover the normalized mesh pose; thus, the causality problem is resolved. The watermarking security is ensured by the key-dependent scalar Costa quantization. The blind watermark extraction simply consists of mesh normalization, patch decomposition and bit extraction. Experimental results and comparisons with the state-of-the-art have demonstrated the superiority of the proposed approach in terms of robustness, security and imperceptibility. Moreover, to the authors’ knowledge, it is the first attempt in the literature to tackle the robustness against 3D representation conversions (e.g. discretization of the mesh into voxels).