三维网格模型特征向量水印嵌入

Eigenvector-Based Watermarking for 3D Mesh Models

为了保证在一定鲁棒性的基础上提高三维网格模型水印算法的水印容量,提出一种基于网格拉普拉斯矩阵特征向量的三维网格模型半盲水印算法。在水印嵌入阶段,计算Tutte拉普拉斯矩阵,然后对其进行特征值分解进而得到特征向量,扰动拉普拉斯矩阵的特征向量以实现水印的嵌入。为了使水印引起的模型失真尽可能的小,在水印算法优化阶段,设计了对应特征向量矩阵的选中矩阵,并启发式地计算出水印嵌入的具体特征向量分量。在水印提取阶段,用扰动后的特征向量与水印模型的特征向量相减以实现水印信息的提取。对于规模较大的模型,先用谱聚类算法分割成较小的子网格,然后在每个子网格中逐一嵌入水印。该算法在水印提取阶段不需要原始网格模型,但需要记录更改后的特征向量,实现了水印算法的半盲检测。实验结果表明,该算法能抵抗仿射变换、随机噪声、平滑、均匀量化、裁剪等常见攻击,具有较强的鲁棒性,同时极大提升了水印负载容量。

In order to embed a high capacity of the watermarks into a3D mesh model,this paper proposes a novel semi-blind watermark algorithm based on Tutte Laplacian eigenvectors.In the process of embedding watermarks,it first computes the Tutte Laplacian matrix and then obtains eigenvectors of the matrix.A watermark is then embedded into these eigenvectors.To reduce the distortion of the embedded models,we formulate the selection of entries of the eigenvector matrix to be modified as an optimization issue and then design a heuristic method to solve the problem.During the extraction process,we detect the watermark information by using the modified eigenvectors minus the corresponding eigenvectors calculated from the watermarked model.As for models with large number of vertices,the spectral cluster algorithm is used by cutting those mesh models into sub-meshes.The watermark is repeatedly embedded into each sub-mesh.The proposed method can semi-blindly detect the watermark in the sense that it doesn't need the original model in the extracting process.The experimental results show that the proposed method can not only resist attacks such as affine transformation,random additive noise,mesh smoothing,uniform quantization as well as cropping but also outperform state-of-the-art approaches in embedding capacity.