Toward a Unified Framework for Point Set Registration

Point set registration plays a critical role in robotics and computer vision. Early methods considered registration as a purely geometric problem, presenting excellent extensibility for various tasks due to their explicit handling of correspondences; statistical methods were later introduced to handle noise. However, the two categories of algorithms have evolved independently without sharing much in common. In this paper, we leverage the concept of information geometry to theoretically unify the two classes together by interpreting them as the same operation but in different spaces associated with respective metrics. Moreover, based on the proposed unification, we also develop a novel bandwidth estimation strategy to solve the long-standing problem of statistical registration algorithms, and demonstrate its theoretical and practical advantages over deterministic annealing, the most commonly used technique. We also present a case study to show how geometric and statistical approaches can benefit from each other.

[1]  Aleksandr V. Segal,et al.  Generalized-ICP , 2009, Robotics: Science and Systems.

[2]  Nobuaki Minematsu,et al.  A Study on Invariance of $f$-Divergence and Its Application to Speech Recognition , 2010, IEEE Transactions on Signal Processing.

[3]  Richard Sinkhorn.  A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices , 1964 .

[4]  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.

[6]  Stefan Gumhold,et al.  Feature Extraction From Point Clouds , 2001, IMR.

[7]  Vladlen Koltun,et al.  A Large Dataset of Object Scans , 2016, ArXiv.

[8]  Jihua Zhu,et al.  Robust point cloud registration based on both hard and soft assignments , 2019, Optics & Laser Technology.

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

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

[11]  Achim J. Lilienthal,et al.  Point set registration through minimization of the L2 distance between 3D-NDT models , 2012, 2012 IEEE International Conference on Robotics and Automation.

[12]  Zi Jian Yew,et al.  RPM-Net: Robust Point Matching Using Learned Features , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

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

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

[15]  Lars Petersson,et al.  An Adaptive Data Representation for Robust Point-Set Registration and Merging , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[16]  Erion Hasanbelliu,et al.  Information Theoretic Shape Matching , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Marc Levoy,et al.  A volumetric method for building complex models from range images , 1996, SIGGRAPH.

[18]  Roland Siegwart,et al.  Challenging data sets for point cloud registration algorithms , 2012, Int. J. Robotics Res..

[19]  Jian Zheng,et al.  Robust Non-Rigid Point Set Registration Using Student's-t Mixture Model , 2014, PloS one.

[20]  Junjun Jiang,et al.  Non-Rigid Point Set Registration with Robust Transformation Estimation under Manifold Regularization , 2017, AAAI.

[21]  Jiaolong Yang,et al.  Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Fernando De la Torre,et al.  Factorized Graph Matching , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Anand Rangarajan,et al.  Groupwise point pattern registration using a novel CDF-based Jensen-Shannon Divergence , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[24]  Max Q.-H. Meng,et al.  Robust Generalized Point Cloud Registration Using Hybrid Mixture Model , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[25]  Eric Mjolsness,et al.  New Algorithms for 2D and 3D Point Matching: Pose Estimation and Correspondence , 1998, NIPS.

[26]  Kok-Lim Low.  Linear Least-Squares Optimization for Point-to-Plane ICP Surface Registration , 2004 .

[27]  Michael A. Greenspan,et al.  Approximate k-d tree search for efficient ICP , 2003, Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings..

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

[29]  Gérard G. Medioni,et al.  Object modelling by registration of multiple range images , 1992, Image Vis. Comput..

[30]  Anath Fischer,et al.  3D Point Cloud Registration for Localization Using a Deep Neural Network Auto-Encoder , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[31]  Peter Biber,et al.  The normal distributions transform: a new approach to laser scan matching , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[32]  Li Xie,et al.  Robust CPD Algorithm for Non-Rigid Point Set Registration Based on Structure Information , 2016, PloS one.

[33]  Yu-Lin He,et al.  A new kernel density estimator based on the minimum entropy of data set , 2019, Inf. Sci..

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

[35]  F. Opitz.  Information geometry and its applications , 2012, 2012 9th European Radar Conference.

[36]  H. Chui,et al.  A feature registration framework using mixture models , 2000, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis. MMBIA-2000 (Cat. No.PR00737).

[37]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .