Shape watermarking based on minimizing the quadric error metric

Blind and robust watermarking of 3D object aims to embed codes into a 3D object such that the object is not visually distorted from the original shape. An essential condition is that the message should be securely extracted even after the graphical object was processed. In this paper, we propose a novel blind and robust mesh watermarking method based on the quadric error metric. The vertices are firstly grouped into bins using a secret key according to their distances to the object center. The statistics of the distances in each bin is modified when embedding the message. A novel quadric selective vertex placement scheme is proposed for finding the best location of each vertex, following watermark embedding, such that the resulting shape distortion is minimal. Experimental results show that the proposed method reduces the distortion to a minimum in the 3D shape.