An oblivious watermarking for 3-D polygonal meshes using distribution of vertex norms

Abstract—Although it has been known that oblivious (or blind) watermarking schemes are less robust than nonoblivious ones, they are more useful for various applications where a host signal is not available in the watermark detection procedure. From a viewpoint of oblivious watermarking for a three-dimensional (3-D) polygonal mesh model, distortionless attacks, such as similarity transforms and vertex reordering, might be more serious than distortion at-tacks including adding noise, smoothing, simplification, remeshing, clipping, and so on. Clearly, it is required to develop an oblivious watermarking that is robust against distortionless as well as distor-tion attacks. In this paper, we propose two oblivious watermarking methods for 3-D polygonal mesh models, which modify the dis-tribution of vertex norms according to the watermark bit to be embedded. One method is to shift the mean value of the distri-bution and another is to change its variance. Histogram mapping functions are introduced to modify the distribution. These map-ping functions are devised to reduce the visibility of watermark as much as possible. Since the statistical features of vertex norms are invariant to the distortionless attacks, the proposed methods are robust against such attacks. In addition, our methods employ an oblivious watermark detection scheme, which can extract the watermark without referring to the cover mesh model. Through simulations, we demonstrate that the proposed approaches are re-markably robust against distortionless attacks. In addition, they are fairly robust against various distortion attacks. Index Terms—Distortion attack, distortionless attack, distribu-tion of vertex norms, three-dimensional (3-D) polygonal meshes, watermarking. I