您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (09): 166-170.doi: 10.6040/j.issn.1671-9352.0.2014.271

• 论文 • 上一篇    

基于加权PCA分析的三维点云模型对称性检测算法

王磊1, 何辰1,2, 谢江宁2   

  1. 1. 潍坊学院计算机工程学院, 山东 潍坊 261061;
    2. 山东大学计算机科学与技术学院, 山东 济南 250101
  • 收稿日期:2014-06-16 修回日期:2014-09-04 出版日期:2014-09-20 发布日期:2014-09-30
  • 作者简介:王磊（1982-），男，讲师，博士，研究方向为图形图像处理.E-mail：wanglpqpq@gmail.com

Symmetry detection of point-based 3D models algorithm based on weighted PCA

WANG Lei1, HE Chen1,2, XIE Jiang-ning2   

  1. 1. School of Computer Engineering, Weifang University, Weifang 261061, Shandong, China;
    2. Computer Science and Technology, Shandong University, Jinan 250101, Shandong, China
  • Received:2014-06-16 Revised:2014-09-04 Online:2014-09-20 Published:2014-09-30

PDF (PC)

1443

摘要： 对普通PCA（principal component analysis）算法进行了改进，使之能用来检测点云模型中存在的平面反射对称性。算法的执行过程如下：首先，使用每个点元的面积作为权重，执行一次加权PCA确定一个近似的对称平面作为初始平面；然后，采用迭代的方法逐步调整上述的对称平面，使之趋向于真正的对称平面（主对称平面）。在每次迭代过程中，算法根据一个距离度量来更新每个点元的权重，通过新的权重执行加权PCA计算来确定一个新的对称平面。如果当前的对称平面与上一次迭代中的对称平面足够接近或者迭代次数超过了给定的阈值，迭代就会终止，从而计算获得整体点云的主对称平面。实验结果表明即使对于非完美对称的模型，该算法也能精确地找出模型的主对称平面。

关键词: 点云模型, 形状分析, PCA分析, 对称性检测

Abstract: The common PCA (principal component analysis) algorithm was improved, which can be used to detect the presence of plane reflection symmetry of point-based 3D model. The iteratively re-weighted PCA process works as follows: Firstly, an initial approximate symmetry plane is computed through a weighted PCA process. Then, the area of each surfel is calculated as its weight. Thereafter, the approximate symmetry plane is refined iteratively. In each iteration, we firstly update each surfel's weight based on a distance metric at that surfel, and secondly conduct the weighted PCA to refine the approximate symmetry plane. The iteration will stop to give the final approximate symmetry plane until the new symmetry plane and the previous one are closely enough or the number of iterations goes beyond a threshold.According to the experiment results, the primary symmetry plane of the models that are not perfectly symmetric can also be found by the proposed algorithm.

Key words: shape analysis, symmetry detection, PCA analysis, point-based 3D model

中图分类号: 

  • TP391
[1] BERNER A, WAND M, MITRA N J, et al. Shape analysis with subspace symmetries[J]. Computer Graphics Forum, 2011, 30(2):277-286.
[2] MINOVIC P, ISHIKAWA S, KATO K. Symmetry identification of a 3D object represented by octree [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, 15(5):507-514.
[3] ZABRODSKY H, WEINSHALL D. Using bilateral symmetry to improve 3D reconstruction from image sequences[J]. Computer Vision and Image Understanding, 1997, 67(1):48-57.
[4] KAZHDAN M, FUNKHOUSER T, RUSINKIEWICZ S. Symmetry descriptors and 3D shape matching [C]//Proceedings of Eurographics Symposium on Geometry Processing.[S.l.]:[s.n.],2004:115-123.
[5] PODOLAK J, SHILANE P, GOLOVINSKIY A, et al. A planar-reflective symmetry transform for 3D shapes [J]. ACM Transactions on Graphics, 2006, 25(3):549-559.
[6] RUSTAMOV R M. Augmented planar reflective symmetry transforms [J]. The Visual Computer, 2008, 24(6):423-433.
[7] MARTINET A, SOLER C, HOLZSCHUCH N, et al. Accurate detection of symmetries in 3D shapes [J]. ACM Transactions on Graphics, 2006, 25(2):439-464.
[8] THRUN S, WEGBREIT B. Shape from symmetry [C]//Proceedings of IEEE International Conference on Computer Vision. Los Alamitos: IEEE Computer Society,2005:1824-1831.
[9] SIMARI P, KALOGERAKIS E, SINGH K. Folding meshes: hierarchical mesh segmentation based on planar symmetry [C]//Proceedings of the 4th Eurographics Symposium on Geometry Processing, 2006:111-119.
[10] MITRA N J, GUIBAS L J, PAULY M. Partial and approximate symmetry detection for 3D geometry[J]. ACM Transactions on Graphics, 2006, 25(3):560-568.
[11] LOY G, Eklundh J-O. Detecting symmetry and symmetric constellations of features [C]//Proceedings of ECCV'06.[S.l.]:[s.n.], 2006:508-521.
[12] MITRA N J, GUIBAS L J, PAULY M. Symmetrization [J]. ACM Transactions on Graphics, 2007, 26(3):1-8.
[13] PAULY M, MITRA N J, WALLNER J, et al. Discovering structural regularity in 3D geometry[J]. ACM Transactions on Graphics, 2008, 27(3):1-11.
[14] BOKELOH M, BERNER A, WAND M, et al. Symmetry detection using line features[J]. Computer Graphics Forum, 2009, 28(2):697-706.
[15] LIU Shenglan, MARTIN R, LANGBEIN F C, et al. Segmenting periodic reliefs on triangle meshes [C]//Proceedings of the 12th IMA International Conference. Berlin-Heidelberg: Springer-Verlag, 2007:290-306.
[16] YEH Y-T, MECH R. Detecting symmetries and curvilinear arrangements in vector art [J]. Computer Graphics Forum (Special Issue of Eurographics), 2009, 28(2):707-716.
[17] BEN-CHEN M, BUTSCHER A, SOLOMON J, et al. On discrete killing vector fields and patterns on surfaces [J]. Computer Graphics Forum (Special Issue of SGP), 2010, 29(5):1701-1711.
[18] RAVIV D, BRONSTEIN A M, BRONSTEIN M M, et al. Symmetries of non-rigid shapes [C]//Proceedings of IEEE 11th International Conference on Computer Vision. Washington: IEEE Computer Society, 2007:1-7.
[19] RUSTAMOV R M. Laplace-beltrami eigenfunctions for deformation invariant shape representation [C]//Proceedings of Eurographics Symposium on Geometry Processing. [S.l.]:[s.n.], 2007:225-233.
[20] OVSJANIKOV M, SUN J, GUIBAS L. Global intrinsic symmetries of shapes [J]. Computer Graphics Forum, 2008, 27(5):1341-1348.
[21] CHERTOK M, KELLER Y. Spectral symmetry analysis [J]. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2010, 32(7):1227-1238.
[22] KIM V, LIPMAN Y, CHEN X, et al. Mobius transformations for global intrinsic symmetry analysis [J]. Computer Graphics Forum, 2010, 29(5):1689-1700.
[23] BRONSTEIN A M, BRONSTEIN M M, BRUCKSTEIN A M, et al. Partial similarity of objects, or how to compare a centaur to a horse [J]. International Journal of Computer Vision, 2009, 84(2):163-183.
[1] 龚双双,陈钰枫,徐金安,张玉洁. 基于网络文本的汉语多词表达抽取方法[J]. 山东大学学报（理学版）, 2018, 53(9): 40-48.
[2] 余传明,左宇恒,郭亚静,安璐. 基于复合主题演化模型的作者研究兴趣动态发现[J]. 山东大学学报（理学版）, 2018, 53(9): 23-34.
[3] 严倩,王礼敏,李寿山,周国栋. 结合新闻和评论文本的读者情绪分类方法[J]. 山东大学学报（理学版）, 2018, 53(9): 35-39.
[4] 原伟,唐亮,易绵竹. 基于本体的俄文新闻话题检测设计与实现[J]. 山东大学学报（理学版）, 2018, 53(9): 49-54.
[5] 廖祥文,张凌鹰,魏晶晶,桂林,程学旗,陈国龙. 融合时间特征的社交媒介用户影响力分析[J]. 山东大学学报（理学版）, 2018, 53(3): 1-12.
[6] 余传明,冯博琳,田鑫,安璐. 基于深度表示学习的多语言文本情感分析[J]. 山东大学学报（理学版）, 2018, 53(3): 13-23.
[7] 张军,李竞飞,张瑞,阮兴茂,张烁. 基于网络有效阻抗的社区发现算法[J]. 山东大学学报（理学版）, 2018, 53(3): 24-29.
[8] 庞博,刘远超. 融合pointwise及深度学习方法的篇章排序[J]. 山东大学学报（理学版）, 2018, 53(3): 30-35.
[9] 陈鑫,薛云,卢昕,李万理,赵洪雅,胡晓晖. 基于保序子矩阵和频繁序列模式挖掘的文本情感特征提取方法[J]. 山东大学学报（理学版）, 2018, 53(3): 36-45.
[10] 王彤,马延周,易绵竹. 基于DTW的俄语短指令语音识别[J]. 山东大学学报（理学版）, 2017, 52(11): 29-36.
[11] 张晓东,董唯光,汤旻安,郭俊锋,梁金平. 压缩感知中基于广义Jaccard系数的gOMP重构算法[J]. 山东大学学报（理学版）, 2017, 52(11): 23-28.
[12] 孙建东,顾秀森,李彦,徐蔚然. 基于COAE2016数据集的中文实体关系抽取算法研究[J]. 山东大学学报（理学版）, 2017, 52(9): 7-12.
[13] 王凯,洪宇,邱盈盈,王剑,姚建民,周国栋. 一种查询意图边界检测方法研究[J]. 山东大学学报（理学版）, 2017, 52(9): 13-18.
[14] 张帆,罗成,刘奕群,张敏,马少平. 异质搜索环境下的用户偏好性预测方法研究[J]. 山东大学学报（理学版）, 2017, 52(9): 26-34.
[15] 杨艳,徐冰,杨沐昀,赵晶晶. 一种基于联合深度学习模型的情感分类方法[J]. 山东大学学报（理学版）, 2017, 52(9): 19-25.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发