Zero-watermarking method for resisting rotation attacks in 3D models

It is challenging to relocate the embedded positions of the watermark when 3D models are subjected to rotation attacks, because the vertex data of 3D models has no implicit order. This paper proposes a zero-watermarking scheme for 3D models, using the Beamlet transform method. First, the area of the 1-ring neighbourhood of each vertex is calculated. Then, the 1-ring neighbourhoods of the vertices with moderate areas are projected onto the tangent planes; the X-axis of each tangent plane corresponds to the mesh line with the maximum curvature in the 1-ring neighbourhood. The Beamlet dictionary is constructed by recording the line segments on both sides of the X-axis; thus, a zero-watermarking image which protects the copyright of the model is produced. Simulations and experiments show that the proposed watermarking scheme exhibits a robust resistance to common signal-processing attacks, especially rotation attacks, and can protect the copyrights of 3D models reliably without distorting the content in any manner.