“A symmetric objective function for ICP” by Rusinkiewicz

  • ©Szymon Rusinkiewicz




    A symmetric objective function for ICP

Session/Category Title:   Scene and Object Reconstruction



    The Iterative Closest Point (ICP) algorithm, commonly used for alignment of 3D models, has previously been defined using either a point-to-point or point-to-plane objective. Alternatively, researchers have proposed computationally-expensive methods that directly minimize the distance function between surfaces. We introduce a new symmetrized objective function that achieves the simplicity and computational efficiency of point-to-plane optimization, while yielding improved convergence speed and a wider convergence basin. In addition, we present a linearization of the objective that is exact in the case of exact correspondences. We experimentally demonstrate the improved speed and convergence basin of the symmetric objective, on both smooth models and challenging cases involving noise and partial overlap.


    1. Dror Aiger, Niloy J. Mitra, and Daniel Cohen-Or. 2008. 4-Points Congruent Sets for Robust Pairwise Surface Registration. ACM Trans. Graph. 27, 3, Article 85 (Aug. 2008). Google ScholarDigital Library
    2. Paul J. Besl and Neil D. McKay. 1992. A Method for Registration of 3-D Shapes. IEEE Trans. PAMI 14, 2 (Feb. 1992), 239–256. Google ScholarDigital Library
    3. Sofien Bouaziz, Andrea Tagliasacchi, and Mark Pauly. 2013. Sparse Iterative Closest Point. In Proc. SGP. Google ScholarDigital Library
    4. Benedict Brown and Szymon Rusinkiewicz. 2007. Global Non-Rigid Alignment of 3-D Scans. ACM Trans. Graph. 26, 3, Article 21 (July 2007). Google ScholarDigital Library
    5. Yang Chen and Gérard Medioni. 1992. Object Modelling by Registration of Multiple Range Images. Image and Vision Computing 10, 3 (April 1992), 145–155. Google ScholarDigital Library
    6. Dmitry Chetverikov, Dmitry Stepanov, and Pavel Krsek. 2005. Robust Euclidean Alignment of 3D Point Sets: The Trimmed Iterative Closest Point Algorithm. Image and Vision Computing 23, 3 (March 2005), 299–309.Google ScholarCross Ref
    7. Brian Curless and Marc Levoy. 1996. A Volumetric Method for Building Complex Models from Range Images. In Proc. SIGGRAPH. Google ScholarDigital Library
    8. Yago Díez, Ferran Roure, Xavier Lladó, and Joaquim Salvi. 2015. A Qualitative Review on 3D Coarse Registration Methods. ACM Comput. Surv. 47, 3, Article 45 (Feb. 2015). Google ScholarDigital Library
    9. Chitra Dorai, Gang Wang, Anil K. Jain, and Carolyn Mercer. 1998. Registration and Integration of Multiple Object Views for 3D Model Construction. IEEE Trans. PAMI 20, 1 (Jan. 1998), 83–89. Google ScholarDigital Library
    10. David W. Eggert, Adele Lorusso, and Robert B. Fisher. 1997. Estimating 3-D Rigid Body Transformations: A Comparison of Four Major Algorithms. Machine Vision and Applications 9, 5–6 (March 1997), 272–290. Google ScholarDigital Library
    11. Andrew W. Fitzgibbon. 2001. Robust Registration of 2D and 3D Point Sets. In Proc. BMVC.Google ScholarCross Ref
    12. Natasha Gelfand, Leslie Ikemoto, Szymon Rusinkiewicz, and Marc Levoy. 2003. Geometrically Stable Sampling for the ICP Algorithm. In Proc. 3DIM.Google ScholarCross Ref
    13. Natasha Gelfand, Niloy J. Mitra, Leonidas Guibas, and Helmut Pottmann. 2005. Robust Global Registration. In Proc. SGP. Google ScholarDigital Library
    14. Maciej Halber and Thomas Funkhouser. 2017. Fine-to-Coarse Global Registration of RGB-D Scans. In Proc. CVPR.Google ScholarCross Ref
    15. Daniel F. Huber and Martial Hebert. 2003. Fully Automatic Registration of Multiple 3D Data Sets. Image and Vision Computing 21, 7 (July 2003), 637–650.Google ScholarCross Ref
    16. Shahram Izadi, David Kim, Otmar Hilliges, David Molyneaux, Richard Newcombe, Pushmeet Kohli, Jamie Shotton, Steve Hodges, Dustin Freeman, Andrew Davison, and Andrew Fitzgibbon. 2011. KinectFusion: Real-time 3D Reconstruction and Interaction Using a Moving Depth Camera. In Proc. UIST. Google ScholarDigital Library
    17. Peter Kovesi. 2015. Good Colour Maps: How to Design Them. arXiv:1509.03700.Google Scholar
    18. Stefan Leopoldseder, Helmut Pottmann, and Hongkai Zhao. 2003. The d2-Tree: A Hierarchical Representation of the Squared Distance Function. Technical Report 101. Institute of Geometry, Vienna University of Technology.Google Scholar
    19. Hiêp Quang Luong, Michiel Vlaminck, Werner Goeman, and Wilfried Philips. 2016. Consistent ICP for the Registration of Sparse and Inhomogeneous Point Clouds. In Proc. Int. Conf. on Communications and Electronics (ICCE).Google ScholarCross Ref
    20. Takeshi Masuda, Katsuhiko Sakaue, and Naokazu Yokoya. 1996. Registration and Integration of Multiple Range Images for 3-D Model Construction. In Proc. ICPR. Google ScholarDigital Library
    21. Niloy J. Mitra, Natasha Gelfand, Helmut Pottmann, and Leonidas Guibas. 2004. Registration of Point Cloud Data from a Geometric Optimization Perspective. In Proc. SGP. Google ScholarDigital Library
    22. Tomáš Pajdla and Luc Van Gool. 1995. Matching of 3-D Curves Using Semi-Differential Invariants. In Proc. ICCV. Google ScholarDigital Library
    23. Fran cois Pomerleau, Francis Colas, and Roland Siegwart. 2015. A Review of Point Cloud Registration Algorithms for Mobile Robotics. Foundations and Trends in Robotics 4, 1 (May 2015), 1–104. Google ScholarDigital Library
    24. Helmut Pottmann, Qi-Xing Huang, Yong-Liang Yang, and Shi-Min Hu. 2006. Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes. IJCV 67, 3 (May 2006), 277–296. Google ScholarDigital Library
    25. Kari Pulli. 1999. Multiview Registration for Large Data Sets. In Proc. 3DIM. Google ScholarDigital Library
    26. Szymon Rusinkiewicz and Marc Levoy. 2001. Efficient Variants of the ICP Algorithm. In Proc. 3DIM.Google ScholarCross Ref
    27. Aleksandr V. Segal, Dirk Haehnel, and Sebastian Thrun. 2009. Generalized-ICP. In Proc. RSS.Google Scholar
    28. Jürgen Sturm, Nikolas Engelhard, Felix Endres, Wolfram Burgard, and Daniel Cremers. 2012. A Benchmark for the Evaluation of RGB-D SLAM Systems. In Proc. IROS.Google ScholarCross Ref
    29. Andrea Tagliasacchi, Matthias Schroeder, Anastasia Tkach, Sofien Bouaziz, Mario Botsch, and Mark Pauly. 2015. Robust Articulated-ICP for Real-Time Hand Tracking. In Proc. SGP.Google ScholarCross Ref
    30. Anastasia Tkach, Mark Pauly, and Andrea Tagliasacchi. 2016. Sphere-Meshes for Real-Time Hand Modeling and Tracking. ACM Trans. Graph. 35, 6, Article 222 (Nov. 2016). Google ScholarDigital Library
    31. Greg Turk and Marc Levoy. 1994. Zippered Polygon Meshes from Range Images. In Proc. SIGGRAPH. Google ScholarDigital Library
    32. Jiaolong Yang, Hongdong Li, Dylan Campbell, and Yunde Jia. 2016. Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration. IEEE Trans. PAMI 38, 11 (Nov. 2016), 2241–2254. Google ScholarDigital Library

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