Robust Blind Watermarking of Point-Sampled Geometry

ABSTRACT
Watermarking schemes for copyright protection of point cloud representation of 3D models operate only on the geometric data, and are also applicable to mesh based representations of 3D models, defined using geometry and topological information. For building such generic copyright schemes for 3D models, this paper presents a robust spatial blind watermarking mechanism for 3D point sampled geometry. To find the order in which points are to be encoded/decoded, a clustering approach is proposed. The points are divided into clusters, and ordering is achieved using inter-cluster and intra-cluster ordering. Inter-cluster ordering achieves local ordering of points, whereas intra-cluster ordering does it globally. Once ordered, a sequence of clusters is chosen based on nearest neighbor heuristic. An extension of quantization index of bit encoding scheme is proposed, and used to encode and decode inside the clusters. The encoding mechanism makes the technique robust against uniform affine transformations (rotation, scaling, and transformation), reordering attack and topology altering (e.g. retriangulation) attack when applied to 3D meshes as well. Replication of watermark provides robustness against localized noise addition, cropping, simplification and global noise addition attacks. Security of the scheme is analyzed, and the time complexity is estimated as O (n log n), where n is the number of 3D points. Theoretical bounds on hiding capacity are estimated, and experiments show that a high hiding capacity is high, with embedding rate greater than 3 bits/point. The bit encoding method reduces the distortions and makes the watermark imperceptible, indicated by a signal to noise ratio greater than 100 dB.