An Oblivious Watermarking for 3-D Polygonal Meshes Using Distribution of Vertex Norms

TLDR: Two oblivious watermarking methods for 3-D polygonal mesh models, which modify the distribution of vertex norms according to the watermark bit to be embedded, are proposed, which are remarkably robust against distortionless attacks.

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 attacks 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 distortion attacks. In this paper, we propose two oblivious watermarking methods for 3-D polygonal mesh models, which modify the distribution of vertex norms according to the watermark bit to be embedded. One method is to shift the mean value of the distribution and another is to change its variance. Histogram mapping functions are introduced to modify the distribution. These mapping 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 remarkably robust against distortionless attacks. In addition, they are fairly robust against various distortion attacks