Sparse Iterative Closest Point

Rigid registration of two geometric data sets is essential in many applications, including robot navigation, surface reconstruction, and shape matching. Most commonly, variants of the Iterative Closest Point (ICP) algorithm are employed for this task. These methods alternate between closest point computations to establish correspondences between two data sets, and solving for the optimal transformation that brings these correspondences into alignment. A major difficulty for this approach is the sensitivity to outliers and missing data often observed in 3D scans. Most practical implementations of the ICP algorithm address this issue with a number of heuristics to prune or reweight correspondences. However, these heuristics can be unreliable and difficult to tune, which often requires substantial manual assistance. We propose a new formulation of the ICP algorithm that avoids these difficulties by formulating the registration optimization using sparsity inducing norms. Our new algorithm retains the simple structure of the ICP algorithm, while achieving superior registration results when dealing with outliers and incomplete data. The complete source code of our implementation is provided at http://lgg.epfl.ch/sparseicp.

[1]  Helmut Pottmann,et al.  Registration of point cloud data from a geometric optimization perspective , 2004, SGP '04.

[2]  Zhengyou Zhang,et al.  Iterative point matching for registration of free-form curves and surfaces , 1994, International Journal of Computer Vision.

[3]  Ghassan Hamarneh,et al.  A Survey on Shape Correspondence , 2011, Comput. Graph. Forum.

[4]  Julien Mairal,et al.  Optimization with Sparsity-Inducing Penalties , 2011, Found. Trends Mach. Learn..

[5]  Leonidas J. Guibas,et al.  Example-Based 3D Scan Completion , 2005 .

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

[7]  Emanuele Trucco,et al.  Robust motion and correspondence of noisy 3-D point sets with missing data , 1999, Pattern Recognit. Lett..

[8]  Rick Chartrand,et al.  Exact Reconstruction of Sparse Signals via Nonconvex Minimization , 2007, IEEE Signal Processing Letters.

[9]  Helmut Pottmann,et al.  Registration without ICP , 2004, Comput. Vis. Image Underst..

[10]  Jon Louis Bentley,et al.  An Algorithm for Finding Best Matches in Logarithmic Expected Time , 1977, TOMS.

[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]  Takeo Kanade,et al.  A Correlation-Based Approach to Robust Point Set Registration , 2004, ECCV.

[13]  Helmut Pottmann,et al.  Geometry of the Squared Distance Function to Curves and Surfaces , 2002, VisMath.

[14]  Mark Pauly,et al.  Realtime performance-based facial animation , 2011, ACM Trans. Graph..

[15]  Xavier Pennec,et al.  Multi-scale EM-ICP: A Fast and Robust Approach for Surface Registration , 2002, ECCV.

[16]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[17]  Daniel Cohen-Or,et al.  4-points congruent sets for robust pairwise surface registration , 2008, ACM Trans. Graph..

[18]  Brendt Wohlberg,et al.  A nonconvex ADMM algorithm for group sparsity with sparse groups , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

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

[20]  Beata Bylina,et al.  The influence of a matrix condition number on iterative methods' convergence , 2011, 2011 Federated Conference on Computer Science and Information Systems (FedCSIS).

[21]  Anand Rangarajan,et al.  A new point matching algorithm for non-rigid registration , 2003, Comput. Vis. Image Underst..

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

[23]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[24]  Naokazu Yokoya,et al.  A Robust Method for Registration and Segmentation of Multiple Range Images , 1995, Comput. Vis. Image Underst..

[25]  G. Champleboux,et al.  From accurate range imaging sensor calibration to accurate model-based 3D object localization , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[26]  Leonidas J. Guibas,et al.  Robust global registration , 2005, SGP '05.

[27]  Hidekata Hontani,et al.  Robust nonrigid ICP using outlier-sparsity regularization , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[28]  Shi-Min Hu,et al.  Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes , 2006, International Journal of Computer Vision.

[29]  N. Yokoya,et al.  A robust method for registration and segmentation of multiple range images , 1994, Proceedings of 1994 IEEE 2nd CAD-Based Vision Workshop.

[30]  Gary K. L. Tam,et al.  Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid , 2013, IEEE Transactions on Visualization and Computer Graphics.

[31]  Hao Li,et al.  Global Correspondence Optimization for Non‐Rigid Registration of Depth Scans , 2008, Comput. Graph. Forum.

[32]  Simon Flöry,et al.  Surface fitting and registration of point clouds using approximations of the unsigned distance function , 2010, Comput. Aided Geom. Des..

[33]  Kim L. Boyer,et al.  Performance evaluation of a class of M-estimators for surface parameter estimation in noisy range data , 1992, Defense, Security, and Sensing.

[34]  Yonina C. Eldar,et al.  Block-Sparse Signals: Uncertainty Relations and Efficient Recovery , 2009, IEEE Transactions on Signal Processing.

[35]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[36]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[37]  Wotao Yin,et al.  Iteratively reweighted algorithms for compressive sensing , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[38]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[39]  Robert B. Fisher,et al.  Estimating 3-D rigid body transformations: a comparison of four major algorithms , 1997, Machine Vision and Applications.

[40]  Pavel Krsek,et al.  Robust Euclidean alignment of 3D point sets: the trimmed iterative closest point algorithm , 2005, Image Vis. Comput..

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

[42]  Kwang-Ho Bae.  Automated Registration of Unorganised Point Clouds from Terrestrial Laser Scanners , 2004 .

[43]  Peihua Gu,et al.  Free-form surface inspection techniques state of the art review , 2004, Comput. Aided Des..

[44]  Goran Marjanovic,et al.  On $l_q$ Optimization and Matrix Completion , 2012, IEEE Transactions on Signal Processing.

[45]  Kari Pulli,et al.  Multiview registration for large data sets , 1999, Second International Conference on 3-D Digital Imaging and Modeling (Cat. No.PR00062).

[46]  Andrew W. Fitzgibbon,et al.  Robust Registration of 2D and 3D Point Sets , 2003, BMVC.