目的 基于一类三角域上定义的正交函数系——V-系统,提出一种在频域嵌入水印的3D模型水印新算法.方法 首先针对3D模型的顶点信息构造一个“伪模型”,进而对伪模型进行参数化,使之表示为在三角域上定义的一个分片线性函数;然后将这个分片线性函数在V-系统下进行正交分解,得到伪模型的V-谱;最后将水印信息通过修改V-谱嵌入到频域,得到新的V-谱,利用这些新的V-谱和V-系统基函数重构水印伪模型,将水印伪模型的顶点信息替换原3D模型的相应顶点,生成最终的水印模型.结果 本文算法水印模型保真度高,且可以在一个模型中植入多个水印依然保持较高的保真度,提取的水印误码率低、相关系数高.结论 理论上证明了本文算法具有相似变换的鲁棒性,通过实验,也表明了本文算法对噪声、剪切和平滑攻击的鲁棒性.

Objective On the basis of a new orthogonal function system called V-systemover a triangular domain, this study proposes a frequency-based watermark algorithm for 3D models. Method Vertex information is acquired to construct “pseudo model” is constructed and is then parameterized so that the pseudo model can be expressed as a piecewise linear function over a triangular domain. The linear function is then orthogonally decomposed into a V-series, which has coefficients from which the V-spectrum is obtained. Finally, the watermark is embedded into the frequency domain by modifying the V-spectrum, such that a renewed V-spectrum is formed. The pseudo model is reconstructed by using the new V-spectrum and the basis function of the V-system, and the final watermarked model is built by replacing the vertex of the original 3D model by the vertex information of the watermarked pseudo model. Result The watermarked model created by the proposed algorithm has high fidelity, which is maintained even when multiple watermarks are embedded into a model.Moreover, the bit error rate of the extracted watermark is low, and the correlation coefficient between the original watermark and the extracted watermark is high. The proposed algorithm is theoretically proven to be robust against similarity transformations. Conclusion Experiments conducted on the watermarked model show that the proposed method is robust against noise pollution, shearing, and smoothing.