Go-ICP: Solving 3D Registration Efficiently and Globally Optimally

Registration is a fundamental task in computer vision. The Iterative Closest Point (ICP) algorithm is one of the widely-used methods for solving the registration problem. Based on local iteration, ICP is however well-known to suffer from local minima. Its performance critically relies on the quality of initialization, and only local optimality is guaranteed. This paper provides the very first globally optimal solution to Euclidean registration of two 3D point sets or two 3D surfaces under the L2 error. Our method is built upon ICP, but combines it with a branch-and-bound (BnB) scheme which searches the 3D motion space SE(3) efficiently. By exploiting the special structure of the underlying geometry, we derive novel upper and lower bounds for the ICP error function. The integration of local ICP and global BnB enables the new method to run efficiently in practice, and its optimality is exactly guaranteed. We also discuss extensions, addressing the issue of outlier robustness.

[1]  Andriy Myronenko,et al.  Point Set Registration: Coherent Point Drift , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  David M. Mount,et al.  Efficient algorithms for robust feature matching , 1999, Pattern Recognit..

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

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

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

[6]  Fredrik Kahl,et al.  Optimal correspondences from pairwise constraints , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[7]  Kostas Daniilidis,et al.  Fully Automatic Registration of 3D Point Clouds , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[8]  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.

[9]  Christoph Schnörr,et al.  Model-Based Multiple Rigid Object Detection and Registration in Unstructured Range Data , 2011, International Journal of Computer Vision.

[10]  Richard I. Hartley,et al.  Global Optimization through Rotation Space Search , 2009, International Journal of Computer Vision.

[11]  Adrien Bartoli,et al.  3D Shape Registration , 2012, 3D Imaging, Analysis and Applications.

[12]  Hongdong Li,et al.  Consensus set maximization with guaranteed global optimality for robust geometry estimation , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[13]  Daniel P. Huttenlocher,et al.  Comparing Images Using the Hausdorff Distance , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Hongdong Li,et al.  Motion estimation for multi-camera systems using global optimization , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Jacek M. Zurada,et al.  An approach to multimodal biomedical image registration utilizing particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

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

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

[18]  Allen R. Tannenbaum,et al.  Point Set Registration via Particle Filtering and Stochastic Dynamics , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Andrew E. Johnson,et al.  Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

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

[21]  Dieter Fox,et al.  A large-scale hierarchical multi-view RGB-D object dataset , 2011, 2011 IEEE International Conference on Robotics and Automation.

[22]  N. Mitra,et al.  4-points congruent sets for robust pairwise surface registration , 2008, SIGGRAPH 2008.

[23]  Hongdong Li,et al.  The 3D-3D Registration Problem Revisited , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[24]  Baba C. Vemuri,et al.  A robust algorithm for point set registration using mixture of Gaussians , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[25]  Richard I. Hartley,et al.  Global Optimization through Searching Rotation Space and Optimal Estimation of the Essential Matrix , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[26]  Jitendra Malik,et al.  Shape matching and object recognition using shape contexts , 2010, 2010 3rd International Conference on Computer Science and Information Technology.

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

[28]  Thomas M. Breuel,et al.  Implementation techniques for geometric branch-and-bound matching methods , 2003, Comput. Vis. Image Underst..

[29]  Pavel Krsek,et al.  The Trimmed Iterative Closest Point algorithm , 2002, Object recognition supported by user interaction for service robots.

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

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

[32]  Marc Pollefeys,et al.  Globally Optimal Consensus Set Maximization through Rotation Search , 2012, ACCV.

[33]  Carl Olsson,et al.  Branch-and-Bound Methods for Euclidean Registration Problems , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[34]  Kathrin Klamroth,et al.  Discrete and geometric Branch and Bound algorithms for medical image registration , 2012, Ann. Oper. Res..

[35]  Tomás Pajdla,et al.  Globally optimal hand-eye calibration , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[36]  Fredrik Kahl,et al.  Optimal Geometric Fitting under the Truncated L2-Norm , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.