Zafeiriou Stefanos, Tefas Anastasios, Pitas Ioannis
Department of Informatics, Aristotle University of Thessaloniki, Box 451, 54124 Thessaloniki, Greece.
IEEE Trans Vis Comput Graph. 2005 Sep-Oct;11(5):596-607. doi: 10.1109/TVCG.2005.71.
In this paper, two novel methods suitable for blind 3D mesh object watermarking applications are proposed. The first method is robust against 3D rotation, translation, and uniform scaling. The second one is robust against both geometric and mesh simplification attacks. A pseudorandom watermarking signal is cast in the 3D mesh object by deforming its vertices geometrically, without altering the vertex topology. Prior to watermark embedding and detection, the object is rotated and translated so that its center of mass and its principal component coincide with the origin and the z-axis of the Cartesian coordinate system. This geometrical transformation ensures watermark robustness to translation and rotation. Robustness to uniform scaling is achieved by restricting the vertex deformations to occur only along the r coordinate of the corresponding (r, theta, phi) spherical coordinate system. In the first method, a set of vertices that correspond to specific angles theta is used for watermark embedding. In the second method, the samples of the watermark sequence are embedded in a set of vertices that correspond to a range of angles in the theta domain in order to achieve robustness against mesh simplifications. Experimental results indicate the ability of the proposed method to deal with the aforementioned attacks.
本文提出了两种适用于盲三维网格物体水印应用的新方法。第一种方法对三维旋转、平移和均匀缩放具有鲁棒性。第二种方法对几何攻击和网格简化攻击都具有鲁棒性。通过对三维网格物体的顶点进行几何变形来嵌入伪随机水印信号，而不改变顶点拓扑结构。在水印嵌入和检测之前，对物体进行旋转和平移，使其质心和主成分与笛卡尔坐标系的原点和z轴重合。这种几何变换确保了水印对平移和旋转的鲁棒性。通过将顶点变形限制在相应的（r，θ，φ）球坐标系的r坐标上，实现了对均匀缩放的鲁棒性。在第一种方法中，使用一组对应于特定角度θ的顶点进行水印嵌入。在第二种方法中，将水印序列的样本嵌入到一组对应于θ域中一定角度范围的顶点中，以实现对网格简化的鲁棒性。实验结果表明了所提方法处理上述攻击的能力。
