Reversible watermarking of 3D mesh models by prediction-error expansion

In this paper, a reversible watermarking algorithm is proposed for 3D mesh models based on prediction-error expansion. Firstly, we predict a vertex position by calculating the centroid of its traversed neighbors. Then the prediction error, i.e. the difference between the predicted and real positions, is expanded for data embedding. So only the vertex coordinates are modified to embed a watermark into the mesh content without changing the topology. We further reduce the distortion by adaptively choosing a threshold so that the prediction errors with too large magnitude will not be expanded. The chosen threshold value and critical location information should be saved in the watermarked mesh to guide the recovery process. The experiments show that the original mesh can be exactly recovered and consequently our algorithm can be used for symmetric or public key authentication of 3D mesh models.