A robust registration method using Huber ICP and low rank and sparse decomposition

This paper proposes a robust registration and alignment framework for multiple point clouds using low rank and sparse decomposition. A coarse registration phase utilizing Huber-ICP is firstly performed to roughly align all the point clouds to a same location, and then sparse and low rank decomposition is applied to extract the low rank subspace of all the point clouds, which is expected to be outlier and loss data free. Finally, a fine registration procedure can be carried out between each point clouds from this low rank space to not only a more accurate registration result but also a more precise correspondence. Robustness of our method for outliers contained in point clouds is verified through manufactured data and it also shows that an effective result can still be achieved even when some points in the cloud are lost.

[1]  Andrew W. Fitzgibbon Robust registration of 2D and 3D point sets , 2003, Image Vis. Comput..

[2]  Jorge J. Moré,et al.  The Levenberg-Marquardt algo-rithm: Implementation and theory , 1977 .

[3]  JianBing,et al.  Robust Point Set Registration Using Gaussian Mixture Models , 2011 .

[4]  Baba C. Vemuri,et al.  Robust Point Set Registration Using Gaussian Mixture Models , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[6]  Lisa M. Brown,et al.  A survey of image registration techniques , 1992, CSUR.

[7]  Andrea Tagliasacchi,et al.  Sparse Iterative Closest Point , 2013, Comput. Graph. Forum.

[8]  Yi Ma,et al.  The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices , 2010, Journal of structural biology.

[9]  G. Sapiro,et al.  A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography. , 2013, Journal of structural biology.

[10]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Gérard G. Medioni,et al.  Object modeling by registration of multiple range images , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[12]  Bruce A. Draper,et al.  Analyzing PCA-based Face Recognition Algorithms: Eigenvector Selection and Distance Measures , 2003 .

[13]  Frederick R. Forst,et al.  On robust estimation of the location parameter , 1980 .

[14]  Yong Yu,et al.  Robust Recovery of Subspace Structures by Low-Rank Representation , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Maarten Weyn,et al.  A Survey of Rigid 3D Pointcloud Registration Algorithms , 2014 .

[16]  Pablo A. Parrilo,et al.  Rank-Sparsity Incoherence for Matrix Decomposition , 2009, SIAM J. Optim..

[17]  Marc Levoy,et al.  Efficient variants of the ICP algorithm , 2001, Proceedings Third International Conference on 3-D Digital Imaging and Modeling.

[18]  Pablo A. Parrilo,et al.  Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization , 2007, SIAM Rev..

[19]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.