Efficient Global Point Cloud Alignment Using Bayesian Nonparametric Mixtures

Point cloud alignment is a common problem in computer vision and robotics, with applications ranging from 3D object recognition to reconstruction. We propose a novel approach to the alignment problem that utilizes Bayesian nonparametrics to describe the point cloud and surface normal densities, and branch and bound (BB) optimization to recover the relative transformation. BB uses a novel, refinable, near-uniform tessellation of rotation space using 4D tetrahedra, leading to more efficient optimization compared to the common axis-angle tessellation. We provide objective function bounds for pruning given the proposed tessellation, and prove that BB converges to the optimum of the cost function along with providing its computational complexity. Finally, we empirically demonstrate the efficiency of the proposed approach as well as its robustness to real-world conditions such as missing data and partial overlap.

[1]  Guy Rosman,et al.  The Manhattan Frame Model—Manhattan World Inference in the Space of Surface Normals , 2018, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Ailsa H. Land,et al.  An Automatic Method of Solving Discrete Programming Problems , 1960 .

[3]  Vladlen Koltun,et al.  Fast Global Registration , 2016, ECCV.

[4]  Barry Joe,et al.  Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision , 1996, Math. Comput..

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

[6]  Ewald von Puttkamer,et al.  Keeping track of position and orientation of moving indoor systems by correlation of range-finder scans , 1994, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'94).

[7]  L. J. Boya,et al.  On Regular Polytopes , 2012, 1210.0601.

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

[9]  Philipp Hennig,et al.  Using an Infinite Von Mises-Fisher Mixture Model to Cluster Treatment Beam Directions in External Radiation Therapy , 2010, 2010 Ninth International Conference on Machine Learning and Applications.

[10]  John W. Fisher,et al.  Parallel Sampling of DP Mixture Models using Sub-Cluster Splits , 2013, NIPS.

[11]  E. L. Lawler,et al.  Branch-and-Bound Methods: A Survey , 1966, Oper. Res..

[12]  Jiaolong Yang,et al.  Go-ICP: Solving 3D Registration Efficiently and Globally Optimally , 2013, 2013 IEEE International Conference on Computer Vision.

[13]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[14]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

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

[16]  Emin Orhan.  Dirichlet Processes , 2012 .

[17]  John J. Leonard,et al.  A Mixture of Manhattan Frames: Beyond the Manhattan World , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

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

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

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

[21]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

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

[23]  John J. Leonard,et al.  Real-time large-scale dense RGB-D SLAM with volumetric fusion , 2014, Int. J. Robotics Res..

[24]  Inderjit S. Dhillon,et al.  Clustering on the Unit Hypersphere using von Mises-Fisher Distributions , 2005, J. Mach. Learn. Res..

[25]  L. Devroye.  A Course in Density Estimation , 1987 .

[26]  David Fofi,et al.  A review of recent range image registration methods with accuracy evaluation , 2007, Image Vis. Comput..

[27]  D. Healy,et al.  Computing Fourier Transforms and Convolutions on the 2-Sphere , 1994 .

[28]  Michael Bosse,et al.  Map Matching and Data Association for Large-Scale Two-dimensional Laser Scan-based SLAM , 2008, Int. J. Robotics Res..

[29]  Inderjit S. Dhillon,et al.  Concept Decompositions for Large Sparse Text Data Using Clustering , 2004, Machine Learning.

[30]  Andrew W. Fitzgibbon,et al.  KinectFusion: Real-time dense surface mapping and tracking , 2011, 2011 10th IEEE International Symposium on Mixed and Augmented Reality.

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

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

[33]  Nicholas I. Fisher,et al.  Statistical Analysis of Circular Data , 1993 .

[34]  Michael I. Jordan,et al.  Revisiting k-means: New Algorithms via Bayesian Nonparametrics , 2011, ICML.

[35]  Andrea Torsello,et al.  Fast and accurate surface alignment through an isometry-enforcing game , 2015, Pattern Recognit..

[36]  Marc Levoy,et al.  Zippered polygon meshes from range images , 1994, SIGGRAPH.

[37]  Anders P. Eriksson,et al.  Fast Rotation Search with Stereographic Projections for 3D Registration , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[38]  Andrew E. Johnson,et al.  Surface matching for object recognition in complex three-dimensional scenes , 1998, Image Vis. Comput..

[39]  Joachim Hertzberg,et al.  Evaluation of 3D registration reliability and speed - A comparison of ICP and NDT , 2009, 2009 IEEE International Conference on Robotics and Automation.

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

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

[42]  Berthold K. P. Horn.  Some Notes on Unit Quaternions and Rotation , 2003 .

[43]  Niloy J. Mitra,et al.  Estimating surface normals in noisy point cloud data , 2003, SCG '03.

[44]  Dieter Fox,et al.  RGB-D mapping: Using Kinect-style depth cameras for dense 3D modeling of indoor environments , 2012, Int. J. Robotics Res..

[45]  Berthold K. P. Horn.  Extended Gaussian images , 1984, Proceedings of the IEEE.

[46]  Jonathan P. How,et al.  Small-variance nonparametric clustering on the hypersphere , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[47]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[48]  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).

[49]  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).

[50]  John J. Leonard,et al.  Real-time manhattan world rotation estimation in 3D , 2015, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[51]  Patrick J. Flynn,et al.  A Survey Of Free-Form Object Representation and Recognition Techniques , 2001, Comput. Vis. Image Underst..

[52]  Toshihide Ibaraki,et al.  Theoretical comparisons of search strategies in branch-and-bound algorithms , 1976, International Journal of Computer & Information Sciences.

[53]  Tom Duckett,et al.  Scan registration for autonomous mining vehicles using 3D‐NDT , 2007, J. Field Robotics.

[54]  Lars Petersson,et al.  GOGMA: Globally-Optimal Gaussian Mixture Alignment , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[55]  Nico Blodow,et al.  Fast Point Feature Histograms (FPFH) for 3D registration , 2009, 2009 IEEE International Conference on Robotics and Automation.