基于Clifford代数的3D点云模型数字水印算法

摘要/Abstract

摘要：

引入Clifford代数，在G3空间中建立了不依赖于特定坐标系的、多维统一的3D点云数据几何表征与计算模型.介绍了Clifford代数空间中的Fourier变换及其计算公式，进而提出了基于Clifford-Fourier变换的3D点云模型数字水印算法.该方法将点云模型映射为相应的Clifford几何空间域系数，并对其进行水印信息的嵌入和提取.实验分析表明，所提出的方法对平移、旋转、均匀缩放、重排序、简化和噪声等各种攻击均具有较好的鲁棒性.

关键词: 数字水印, Clifford代数, CliffordFourier变换, 3D点云

Abstract:

In this paper, the generalized geometric representation of the 3D Point Cloud data was proposed based on Clifford algebra, where the expressions of 3D Point Cloud data were unified without losing their geometric meaning, and the geometric operation was coordinate-free for different dimensional spaces. The Clifford Fourier Transform was introduced into the digital watermarking algorithm for the 3D Point Cloud model, where point cloud models were mapped to the corresponding domain coefficients in space G3. Then the watermark was embedded or extracted based on these coefficients. The experimental results show that the algorithm has very good performance in affine transformation, reordering, simplification and noise, and is robust against attacks.

Key words: digital watermarking, Clifford algebra, Clifford Fourier transform, 3D point cloud

中图分类号:

TP 391

王瑞，金林波，陶磊，郭水林，万旺根. 基于Clifford代数的3D点云模型数字水印算法[J]. 上海交通大学学报（自然版）, 2013, 47(12): 1863-1869.

WANG Rui,JIN Linbo,TAO Lei,GUO Shuilin,WAN Wanggen. Digital Watermarking Algorithm for 3D Point Cloud Model Based on Clifford Algebra[J]. Journal of Shanghai Jiaotong University, 2013, 47(12): 1863-1869.

参考文献

［1］Liu Wei, He Yuanjun, Zhou Xionghui. Voxelizating 3D mesh models with gray levels［J］. Journal of Shanghai Jiaotong University (Science)， 2009, 14(5):513517.

［2］Ryutarou O, Hiroshi M, Masaki A.Watermarking three dimensional polygonal models through geometric and topological modifications［J］. IEEE Journal on Selected Areas in Communication,1998,16(4):55l560.

［3］Praun E, Hoppe H, Finkelstein A. Robust mesh watermarking［C］∥Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. New York, USA: ACM Press,1999: 4956.

［4］Uccheddu F, Corsini M, Barni M. Wavelet based blind watermarking of 3D models［C］∥Proc of Workshop on Multimedia and Security.New York,USA:ACM Press, 2004: 143154.

［5］刘旺,赵春晖.三维网格模型盲提取水印算法［J］.仪器仪表学报, 2009,30(12):26352639.

LIU Wang, ZHAO Chunhui. Blind watermarking algorithm for threedimensional mesh model［J］.Chinese Journal of Scientific Instrument, 2009,30(12):26352639.

［6］Cotting D, Weyrich T, Pauly M.Robust watermarking of point sampled geometry［C］∥Shape Modeling Applications, 2004. Proceedings.Genova, Italy:IEEE Press, 2004: 233242.

［7］冯小青, 李黎, 潘志庚. 一种强壮的基于几何特征分

布的3维点模型数字水印算法［J］. 中国图象图形学报， 2009, 14(8): 15351541.

FENG Xiaoqing, LI Li, PAN Zhigeng. A robust watermarking scheme for 3D point model based on geometrical property ［J］. Journal of Image and Graphics, 2009, 14(8): 15351541.

［8］吴颖斌, 耿国华, 贺毅岳. 基于DWT 的 3D 点云模型数字水印算法［J］. 计算机工程， 2012, 38(6): 151155.

WU Yingbin, GENG Guohua, HE Yiyue. Digital watermark algorithm based on DWT for 3D point cloud model ［J］. Computer Engineering, 2012, 38(6): 151155.

［9］王新宇, 詹永照. 面向三维点云模型的鲁棒零水印技术［J］. 计算机工程与应用， 2011, 47(28): 711.

WANG Xinyu, ZHAN Yongzhao. Robust zero watermarking scheme for 3D point model［J］. Computer Engineering and Applications， 2011, 47(28): 711.

［10］张义宽,张晓鹏,査红彬, 等.3维点云的拓扑结构表征与计算技术［J］.中国图象图形学报，2008,13(8):15761587.

ZHANG Yikuan, ZHANG Xiaopeng, ZHA Hongbin, et al. A surveyof topologically structural representationand computationof 3D pointcloud data［J］.Journal of Image and Graphics，2008,13(8):15761587.

［11］曹文明, 冯浩. 仿生模式识别与信号处理的几何代数方法［M］. 深圳: 科学出版社, 2010: 161182.

［12］Yuan Linwang, Yu Zhaoyuan, Luo Wen. Geometric algebra for multidimensionunified geographical information system, advances in applied clifford algebras ［J］. Advances in Applied Clifford Algebras，2013, 23(2): 497518.

［13］Ebling J, Scheuermann G. Clifford Fourier transform on vector fields［J］. IEEE Transactions on Visualization and Computer Graphics, 2005, 11(4): 469479.

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