中文摘要：

3维点模型与传统的三角网格模型相比，更适合处理外形非常复杂并且不规则的几何体，但基于点模型的数字水印算法却屈指可数。为了对3维点模型进行有效的保护，提出了一种新的基于几何特征分布的3维点模型数字水印算法。该算法首先根据所需嵌入的水印信息来修改主元分析后3维点模型中各个点到模型中心的距离值，然后通过移动整个模型点距离分布的平均值来达到嵌入水印的目的。该算法在嵌入水印时，并不需要对点模型进行网格化的预处理，是一种真正的直接面向点模型的数字水印算法；另外，为验证算法的有效性，还分析了原始点模型和嵌入水印后的点模型之间的几何失真程度，并讨论了强度系数和水印长度对算法鲁棒性的影响。实验证明，该算法在遭受仿射攻击、重排序攻击，提取水印时，不需要原始点模型信息，并且该点模型水印算法对于仿射攻击、重排序攻击、简化、剪切、噪声和局部几何失真的各种变形攻击具有较强的鲁棒性。

英文摘要：

Compared with traditional triangle meshes, point models are suitable to represent irregular objects with complex geometry. However, there are few digital watermarks algorithm based on point models. In order to protect effectively 3D point model, a new method for digital watermarking of a 3D model defined as a set of un-oriented points based on geometrical property is proposed in this paper. Our approach is to modify the distance between each point and the center of the model after principle component analysis according to the watermarking bits. At last, embed watermarking by shifting the mean value of the distance distribution. Mesh pre-processing doesn＇ t need before watermarking is embedded into the point model in the algorithm. In addition, geometrical distortion degree between the original and the tested model is analyzed, and two parameters of watermark strength factor and the size of bin that affect the robustness of the proposed methods are discussed. After conducting the affine transformation and vertex reordering attacks, the original model is not needed during the watermarking extraction. Experiments show that this approach is greatly robust against attacks, such as affine transformation, resorting, simplification, cropping, nosing and various distortion ones with local geometric alterations.