A new method for the registration of three-dimensional point-sets: The Gaussian Fields framework

In this paper, we present a 3D automatic registration method based on Gaussian Fields and energy minimization. A continuously differentiable energy function is defined, which is convex in a large neighborhood of the alignment parameters. We show that the size of the region of convergence can be significantly extended reducing the need for close initialization and overcoming local convergence problems of the standard Iterative Closest Point (ICP) algorithms. Moreover, the Gaussian criterion can be applied with linear computational complexity using Fast Gauss Transform methods. Experimental evaluation of the technique using synthetic and real datasets demonstrates the usefulness as well as the limits of the approach.

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

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

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

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

[5]  Mongi A. Abidi,et al.  Automatic registration of 3D datasets using Gaussian fields , 2005, IEEE International Conference on Image Processing 2005.

[6]  Larry S. Davis,et al.  Efficient Kernel Density Estimation Using the Fast Gauss Transform with Applications to Color Modeling and Tracking , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  L. Greengard.  The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

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

[9]  Robert B. Fisher,et al.  Special Issue on Registration and Fusion of Range Images , 2002, Comput. Vis. Image Underst..

[10]  Babak Taati,et al.  Automatic Registration for Model Building using Variable Dimensional Local Shape Descriptors , 2007, Sixth International Conference on 3-D Digital Imaging and Modeling (3DIM 2007).

[11]  Mongi A. Abidi,et al.  Gaussian fields: a new criterion for 3D rigid registration , 2004, Pattern Recognit..

[12]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

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

[14]  Ernest L. Hall,et al.  Three-Dimensional Moment Invariants , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Adrian Hilton,et al.  Registration of multiple point sets , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[16]  Diego A. Murio,et al.  The Mollification Method and the Numerical Solution of Ill-Posed Problems , 1993 .

[17]  Sang Wook Lee,et al.  ICP Registration Using Invariant Features , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using unit quaternions , 1987 .

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

[20]  Olivier D. Faugeras,et al.  Shape metrics, warping and statistics , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[21]  Soon-Yong Park,et al.  Automatic 3D model reconstruction based on novel pose estimation and integration techniques , 2004, Image Vis. Comput..

[22]  Chitra Dorai,et al.  Optimal Registration of Object Views Using Range Data , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

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

[24]  M. Hebert,et al.  The Representation, Recognition, and Locating of 3-D Objects , 1986 .

[25]  Gérard G. Medioni,et al.  Structural Indexing: Efficient 3-D Object Recognition , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Mi-Suen Lee,et al.  A Computational Framework for Segmentation and Grouping , 2000 .

[27]  Katsushi Ikeuchi,et al.  A Spherical Representation for Recognition of Free-Form Surfaces , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Mongi A. Abidi,et al.  Gaussian energy functions for registration without correspondences , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

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

[30]  Martial Hebert,et al.  Fully automatic registration of multiple 3D data sets , 2003, Image Vis. Comput..

[31]  Yi-Ping Hung,et al.  RANSAC-Based DARCES: A New Approach to Fast Automatic Registration of Partially Overlapping Range Images , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  Emanuele Trucco,et al.  Robust motion and correspondence of noisy 3-D point sets with missing data , 1999, Pattern Recognit. Lett..

[33]  Patrick J. Flynn,et al.  Pair-Wise Range Image Registration: A Study in Outlier Classification , 2002, Comput. Vis. Image Underst..

[34]  Helmut Pottmann,et al.  Registration without ICP , 2004, Comput. Vis. Image Underst..

[35]  Heinrich Niemann,et al.  A refined ICP algorithm for robust 3-D correspondence estimation , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[36]  Martial Hebert,et al.  Efficient multiple model recognition in cluttered 3-D scenes , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[37]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

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

[39]  Leslie Greengard,et al.  The Fast Gauss Transform , 1991, SIAM J. Sci. Comput..

[40]  Larry S. Davis,et al.  Improved fast gauss transform and efficient kernel density estimation , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[41]  Robert Bergevin,et al.  Towards a General Multi-View Registration Technique , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[42]  Jean-Philippe Thirion,et al.  New feature points based on geometric invariants for 3D image registration , 1996, International Journal of Computer Vision.