Minimal distortion 3-D watermarking using statistics of geodesic distances

This paper describes a statistical 3-D digital watermarking method using distributions of distances measured along mesh surfaces. The proposed method employs a mesh propagation procedure called the Fast Marching Method (FMM), which defines regions of equal geodesic distance width calculated with respect to a reference location on the mesh surface. The embedding is performed by statistically changing the normalized distribution of local geodesic distances. Vertices are moved onto the plane of triangles containing the current geodesic front line as generated by the FMM. Such vertex perturbations ensure that the resulting distortions in the 3-D graphics is minimal.