On the Consistent Normal Vector Adjustment of Point Cloud Using Surface Variation

doi:10.11947/j.AGCS.2018.20170494

Abstract

Abstract: In order to improve the efficiency and accuracy of existing normal vector adjustment algorithms,a consistent normal vector adjustment algorithm using surface variation is proposed.Firstly,the normal vector and surface variation of point cloud are calculated using principal component analysis.Then,the points on flat or uneven area are distinguished based on surface variation.In the process of adjusting normal vector,the search scope is narrowed to k-nearest neighbors and the number of adjusted normal vector is increased to improve efficiency.The propagating direction of normal vector is restrained to insure accuracy.The experiments show that the proposed algorithm can always receive accurate result on flat region,feature condition and high curvature area,meanwhile,the proposed algorithm is more efficient than the existing algorithms.

Key words: consistent normal vector adjustment, surface variation, principal component analysis, k-nearest neighbors, point cloud

CLC Number:

P237

HE Hua, LI Zongchun, YAN Rongxin, YANG Zaihua, RUAN Huanli, FU Yongjian. On the Consistent Normal Vector Adjustment of Point Cloud Using Surface Variation[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(2): 275-280.

References

[1] 陶海跻, 达飞鹏. 一种基于法向量的点云自动配准方法[J]. 中国激光, 2013, 40(8):179-184. TAO Haiji, DA Feipeng. Automatic Registration Algorithm for the Point Clouds Based on the Normal Vector[J]. Chinese Journal of Lasers, 2013, 40(8):179-184.
[2] 董震, 杨必胜. 车载激光扫描数据中多类目标的层次化提取方法[J]. 测绘学报, 2015, 44(9):980-987. DOI:10.11947/j.AGCS.2015.20140339. DONG Zhen, YANG Bisheng. Hierarchical Extraction of Multiple Objects from Mobile Laser Scanning Data[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(9):980-987. DOI:10.11947/j.AGCS.2015.20140339.
[3] 张强, 李朝奎, 李俊晓, 等. 一种改进的基于法矢方向调整的平面点云分割方法[J]. 地理与地理信息科学, 2015, 31(1):45-48. ZHANG Qiang, LI Chaokui, LI Junxiao, et al. Planar Point Cloud Segmentation Based on the Weighted Average of Adjusted Normal Vector[J]. Geography and Geo-Information Science, 2015, 31(1):45-48.
[4] 方悄云, 吕东辉, 孙九爱. 改进的物体表面重建的三角网格法[J]. 应用科学学报, 2016, 34(2):145-153. FANG Qiaoyun, LV Donghui, SUN Jiuai. Improved Triangle Mesh Method for Surface Reconstruction from Normal Field[J]. Journal of Applied Sciences, 2016, 34(2):145-153.
[5] 朱德海, 郭浩, 苏伟. 点云库PCL学习教程[M]. 北京:北京航空航天大学出版社, 2012. ZHU Dehai, GUO Hao, SU Wei. The Learning Tutorial for Point Cloud Library PCL[M]. Beijing:Beihang University Press, 2012.
[6] HOPPE H, DEROSE T, DUCHAMP T, et al. Surface Reconstruction from Unorganized Points[J]. ACM SIGGRAPH Computer Graphics, 1992, 26(2):71-78.
[7] 贺美芳. 基于散乱点云数据的曲面重建关键技术研究[D]. 南京:南京航空航天大学, 2006. HE Meifang. Research on Key Technologies of Surfaces Reconstruction Based on Scattered Point Cloud Data[D]. Nanjing:Nanjing University of Aeronautics and Astronautics, 2006.
[8] 肖天姿. 散乱点云的数据预处理及曲面重建研究[D]. 大连:大连海事大学, 2012. XIAO Tianzi. Research on Data Preprocessing and Surface Reconstruction of Scattered Point Cloud[D]. Dalian:Dalian Maritime University, 2012.
[9] 孟祥林, 何万涛, 赵灿, 等. 逆向工程中点云邻域搜索及法矢估算相关算法研究[J]. 制造技术与机床, 2009(2):44-47. MENG Xianglin, HE Wantao, ZHAO Can, et al. Point Cloud-nearest-neighbor Search and Normal Vector Estimation Relative Algorithm in Reverse Engineering[J]. Manufacturing Technology & Machine Tool, 2009(2):44-47.
[10] 何学铭. 点云模型的孔洞修补技术研究[D]. 南京:南京师范大学, 2013. HE Xueming. Research on Hole Filling Technology of Point Cloud Model[D]. Nanjing:Nanjing Normal University, 2013.
[11] 孙金虎. 点云模型分割与融合关键技术研究[D]. 南京:南京航空航天大学, 2013. SUN Jinhu. Research on Key Technologies of Point Cloud Segmentation and Fusion[D]. Nanjing:Nanjing University of Aeronautics and Astronautics, 2013.
[12] 孙金虎, 周来水, 安鲁陵. 点云模型法矢调整优化算法[J]. 中国图象图形学报, 2013, 18(7):844-851. SUN Jinhu, ZHOU Laishui, AN Luling. Optimal Algorithm for Normal Adjustment of Point Clouds[J]. Journal of Image and Graphics, 2013, 18(7):844-851.
[13] 易倩宇. 高质量鲁棒曲面重建[D]. 杭州:浙江大学, 2014. YI Qianyu. High-quality and Robust Surface Reconstruction[D]. Hangzhou:Zhejiang University, 2014.
[14] 张剑清, 李彩林, 郭宝云. 基于切平面投影的散乱数据点快速曲面重建算法[J]. 武汉大学学报(信息科学版), 2011, 36(7):757-762. ZHANG Jianqing, LI Cailin, GUO Baoyun. A Fast Surface Reconstruction Algorithm for Unorganized Points Based on Tangent Plane Projection[J]. Geomatics and Information Science of Wuhan University, 2011, 36(7):757-762.
[15] 刘健. 可修正的点云一致定向[D]. 大连:大连理工大学, 2014. LIU Jian. Mendable Consistent Orientation of Point Clouds[D]. Dalian:Dalian University of Technology, 2014.
[16] SUN Jiuai, SMITH M, SMITH L, et al. Examining the Uncertainty of the Recovered Surface Normal in Three Light Photometric Stereo[J]. Image and Vision Computing, 2007, 25(7):1073-1079.
[17] LIU Shengjun, WANG C C L. Orienting Unorganized Points for Surface Reconstruction[J]. Computers & Graphics, 2010, 34(3):209-218.
[18] 曾峰, 钟治初, 杨通, 等. 基于SOM的散乱点云法矢计算[J]. 计算机工程, 2012, 38(8):287-290. ZENG Feng, ZHONG Zhichu, YANG Tong, et al. Scattered Point Cloud Normal Vector Calculation Based on SOM[J]. Computer Engineering, 2012, 38(8):287-290.
[19] MULLEN P, GOES F D, DESBRUN M, et al. Signing the Unsigned:Robust Surface Reconstruction from Raw Pointsets[J]. Computer Graphics Forum, 2010, 29(5):1733-1741.
[20] PAULY M, GROSS M, KOBBELT L P. Efficient Simplification of Point-sampled Surfaces[C]//Proceedings of the IEEE Visualization Conference. Boston, MA, USA:IEEE, 2002.
[21] PAULY M, KEISER R, KOBBELT L P, et al. Shape Modeling with Point-sampled Geometry[J]. ACM Transactions on Graphics (TOG), 2003, 22(3):641-650.
[22] LEVIN D. The Approximation Power of Moving Least-squares[J]. Mathematics of Computation, 1998, 67(224):1517-1531.
[23] AMENTA N, BERN M. Surface Reconstruction by Voronoi Filtering[J]. Discrete & Computational Geometry, 1999, 22(4):481-504.
[24] DEY T K, GOSWAMI S. Provable Surface Reconstruction from Noisy Samples[C]//Proceedings of the 12th Annual Symposium on Computational Geometry. New York:ACM, 2004:330-339.
[25] HUANG Hui, LI Dan, ZHANG Hao, et al. Consolidation of Unorganized Point Clouds for Surface Reconstruction[J]. ACM Transactions on Graphics, 2009, 28(5):1-7.