Cayley approach for 3D points registration in visual SLAM

Abstract

Abstract: An essential problem in SLAM system is to compute the 3D rigid body transformation of cameras, which aligns two sets of points when correspondences are known. The errors accumulated during the locating and mapping process result in the drift of scale for the pairs of points. The Euclidean transformation will be degraded into the similarity transformation due to the drift. A closed-form solution using Cayley transform is presented to estimate the similarity transformation between 3D corresponding points. The accuracy and robustness of the proposed Cayley approach are verified by simulation and error analysis. Apart from SLAM system, this approach is also suitable for 3D reconstruction and registration in computer vision.

Key words: SLAM, 3D registration, similarity transformation, Cayley transform

CLC Number:

TP391
V219

ZHANG Hongyan, WANG Jingyan, ZHOU Lusha, WANG Binghui. Cayley approach for 3D points registration in visual SLAM[J]. .

References

[1] HARALICKRM, JOOH, LEEC N, et al. Pose estimation from corresponding point data[J]. Machine Vision for Inspection & Measurement,1989, 19(6): 1-84.
[2] BESL P J, MCKAY N D. Method for registration of 3D shapes[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, 14(2): 239-256.
[3] HENRY P, KRAININ M, HERBST E, et al. RGB-D mapping: using Kinect-style depth cameras for dense 3D modeling of indoor environments[J]. International Journal of Robotics Research, 2012, 31(5): 647-663.
[4] HARTLEY R, ZISSERMAN A. Multiple View Geometry in Computer Vision[M]. 2nd ed. Cambridge: Cambridge University Press, 2003.
[5] 王忠立, 赵杰, 蔡鹤皋. 大规模环境下基于图优化SLAM 的图构建方法[J].哈尔滨工业大学学报, 2015, 47(1): 75-85.
[6] 顾照鹏, 刘宏.单目视觉同步定位与地图创建方法综述[J]. 智能系统学报, 2015(4): 499-507.
[7] IZADI S, NEWCOMBE R A, KIM D, et al. Kinect Fusion: Real-time Dynamic 3D Surface Reconstruction and Interaction Using a Moving depth Camera[C]//International ConferenceonComputerGraphicsand Interactive Techniques, Santa Barbara, CA, Oct 16-19, 2011: 1175-1184.
[8] RAUL MA, MONTIEL JM M, JUAN D T. ORB-SLAM: a versatile and accurate monocular SLAM system[J]. IEEE Transaction on Robotics,2015, 31(5): 1147-1163.
[9] ARUN K S, HUANG T S, BLOSTEIN S D. Least-squares fitting of two 3-D point sets[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, 9(5): 698-700.
[10] HORNBKP, HILDENHM, NEGAHDARIPOURS. Closed-form solution of absolute orientation using orthonormal matrices[J]. Journal of the Optical Society of America A, 1988, 5(7): 1127-1135.
[11] HORN B K P. Closed-form solution of absolute orientation using unit quaternions[J]. Journal of the Optical Society of America A, 1988, 4(4):629-642.
[12] WALKERMW, SHAOL, VOLZRA. Estimating 3Dlocation parameters using dual number quaternions[J]. CVGIP: Image Understanding, 1991,54(3): 358-367.
[13] EGGERT D W, LORUSSO A, FISHER R B. Estimating 3D rigid body transformations: a comparison of four major algorithms[J]. Machine Vision and Applications, 1997, 9: 272-290.
[14] WU Fuchao, WANG Zhiheng, HU Zhanyi. Cayley transformation and numerical stability of calibration equation[J]. International Journal of Computer Vision, 2009, 82(4): 156-184.
[15] CAYLEYA. Sur quelquesproprietesdes determinant gauches[J]. Journal Fur Die Reine Und Angewandte Mathematik, 1846(32): 119-123.
[16] 吴福朝. 计算机视觉: Cayley 变换与度量重构[M]. 北京: 科学出版社, 2011.
[17] 张鸿燕.基于视频图像的三维建模方法与系统———消化道三维建模方法与应用研究[D].北京: 中国科学院研究生院, 2011.
[18] 周璐莎.大尺度场景的同步定位与地图构建[D].天津:中国民航大学, 2016.
[19] ASmallProgramforRenderingaPointCloudUsingVTK[EB/OL]. [2017-06-14]. http://www.umiacs. umd.edu/~huytho/codes.htm.