Introduction to algorithms
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Digital watermarking
IEEE Transactions on Visualization and Computer Graphics
Geometry-Based Watermarking of 3D Models
IEEE Computer Graphics and Applications
Robust Watermarking and Affine Registration of 3D Meshes
IH '02 Revised Papers from the 5th International Workshop on Information Hiding
Robust Watermarking of Point-Sampled Geometry
SMI '04 Proceedings of the Shape Modeling International 2004
Wavelet-based blind watermarking of 3D models
Proceedings of the 2004 workshop on Multimedia and security
Watermarking a 3D Shape Model Defined as a Point Set
CW '04 Proceedings of the 2004 International Conference on Cyberworlds
Blind Robust Watermarking Schemes for Copyright Protection of 3D Mesh Objects
IEEE Transactions on Visualization and Computer Graphics
Robust blind watermarking mechanism for point sampled geometry
Proceedings of the 9th workshop on Multimedia & security
Progressive compression invariant semi-fragile watermarks for 3d meshes
Proceedings of the 9th workshop on Multimedia & security
Three-dimensional meshes watermarking: review and attack-centric investigation
IH'07 Proceedings of the 9th international conference on Information hiding
Data hiding on 3-D triangle meshes
IEEE Transactions on Signal Processing
An Oblivious Watermarking for 3-D Polygonal Meshes Using Distribution of Vertex Norms
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Watermarking three-dimensional polygonal models through geometric and topological modifications
IEEE Journal on Selected Areas in Communications
Watermarking mesh-based representations of 3-D objects using local moments
IEEE Transactions on Image Processing
A robust spectral approach for blind watermarking of manifold surfaces
Proceedings of the 10th ACM workshop on Multimedia and security
A blind image copyright protection scheme for e-government
Journal of Visual Communication and Image Representation
Double watermarks of 3D mesh model based on feature segmentation and redundancy information
Multimedia Tools and Applications
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Digital watermarking for copyright protection of 3-D meshes cannot be directly applied to point clouds, since we need to derive consistent connectivity information, which might change due to attacks, such as noise addition and cropping. Schemes for point clouds operate only on the geometric data and, hence, are generic and applicable to mesh-based representations of 3-D models. For building generic copyright schemes for 3-D models, this paper presents a robust blind watermarking mechanism for 3-D point-sampled geometry. The basic idea is to find a cluster tree from clusters of 3-D points. Using the cluster tree, watermarks can be embedded and extracted by deriving an order among points at global (intracluster) and local levels (intercluster). The multiple bit watermarks are encoded/decoded inside each cluster based on an extension of the cluster structure-based 3-D quantization index modulation. The encoding mechanism makes the technique robust against uniform affine transformations (rotation, scaling, and transformation), reordering, cropping, simplification, and noise addition attacks. The technique when applied to 3-D meshes also achieves robustness against retriangulation and progressive compression techniques. Customization of the bit-encoding scheme achieves high hiding capacity with embedding rates that are equal to 4 b/point, while maintaining the imperceptibility of the watermark with low distortions. The estimated time complexity is O(n log n), where n is the number of 3-D points.