A Study of Point Cloud Registration with Probability Product Kernel Functions

3D point cloud registration is an essential problem in 3D object and scene understanding. In many realistic circumstances, however, because of noise during data acquisition and large motion between two point clouds, most existing approaches can hardly work satisfactorily without good initial alignment or manually marked correspondences. Inspired by the popular kernel methods in machine learning community, this paper puts forward a general point cloud registration framework by constructing kernel functions over 3D point clouds. More specifically, Gaussian mixtures Based on the point clouds are established and probability product kernel functions are exploited for the registration. To enhance the generality of the framework, SE(3) on-manifold optimization scheme is employed to compute the optimal motion. Experimental results show that our registration framework works robustly when many outliers are presented and motion between point clouds is relatively large, and compares favorably to related methods.

[1]  Tony Jebara,et al.  A Kernel Between Sets of Vectors , 2003, ICML.

[2]  Justus H. Piater,et al.  A Probabilistic Framework for 3D Visual Object Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[4]  Lei Zhang,et al.  Robust ICP Registration Using Biunique Correspondence , 2011, 2011 International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission.

[5]  Edwin R. Hancock,et al.  Spectral correspondence for point pattern matching , 2003, Pattern Recognit..

[6]  Nicholas Ayache,et al.  3D-2D Projective Registration of Free-Form Curves and Surfaces , 1997, Comput. Vis. Image Underst..

[7]  Mark D. Plumbley.  Lie Group Methods for Optimization with Orthogonality Constraints , 2004, ICA.

[8]  Siwei Lyu,et al.  A Kernel Between Unordered Sets of Data: The Gaussian Mixture Approach , 2005, ECML.

[9]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2004 .

[10]  Jose Luis Blanco,et al.  A tutorial on SE(3) transformation parameterizations and on-manifold optimization , 2012 .

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

[12]  Marc Rioux,et al.  Three-dimensional registration using range and intensity information , 1994, Other Conferences.

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

[14]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[15]  Justus H. Piater,et al.  Continuous Surface-Point Distributions for 3D Object Pose Estimation and Recognition , 2010, ACCV.

[16]  Andrew E. Johnson,et al.  Registration and integration of textured 3-D data , 1997, Proceedings. International Conference on Recent Advances in 3-D Digital Imaging and Modeling (Cat. No.97TB100134).

[17]  Tony Jebara,et al.  Probability Product Kernels , 2004, J. Mach. Learn. Res..

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

[19]  Sing Bing Kang,et al.  Registration and integration of textured 3-D data , 1997, Proceedings. International Conference on Recent Advances in 3-D Digital Imaging and Modeling (Cat. No.97TB100134).

[20]  Nico Blodow,et al.  Persistent Point Feature Histograms for 3D Point Clouds , 2008 .

[21]  Yonghuai Liu,et al.  3D shape matching using collinearity constraint , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[22]  Rüdiger Dillmann,et al.  The KIT object models database: An object model database for object recognition, localization and manipulation in service robotics , 2012, Int. J. Robotics Res..

[23]  Luc Van Gool,et al.  Matching of 3-D curves using semi-differential invariants , 1995, Proceedings of IEEE International Conference on Computer Vision.

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

[25]  Ruigang Yang,et al.  Registering, integrating, and building CAD models from range data , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

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