The study proposed a vertex-based authentication algorithm based on spatial subdivision. A binary space partitioning tree was employed to subdivide the bounding volume of the input model into voxels. Each vertex could then be encoded into a series of binary digits, denoted as its authentication code, by traversing the constructed tree. Finally, the above authentication code was embedded into the corresponding reference vertex by modulating its position within the located subspace. Extensive experimental results demonstrated that the proposed algorithm provided high embedding capacity and high robustness. Furthermore, the proposed algorithm supported controllable distortion and self-recovery.

Abstract:Fragile watermarking algorithms for 3D models has attracted extensive research attention in recent years. Although many literatures have proposed lots of solutions on this issue, low embedding capacity and inaccurate located tampered region are still presented. Higher embedding capacity can reduce the probability of false alarms for authentication, while accurate tamper localization can detect all the modified vertices with fewer unaltered ones. This study proposes three strategies to enhance the embedding capacity and the detection accuracy of our previous algorithm. First, the modified message-digit substitution table can increase the embedding capacity by 11.5%. Second, the modified embedding ratio generation method can be integrated to raise the embedding capacity by about 47.74%. Finally, the strategy adopting a reduced number of reference vertices for authentication code generation accompanying the above two ones improves the embedding capacity up to 123.74%. Extensive experiments show that the proposed algorithm can achieve superior performance in terms of embedding capacity and tamper localization accuracy. Further, the model distortion between the original and the marked ones is small.