The Community for Technology Leaders
RSS Icon
Issue No.05 - May (2009 vol.31)
pp: 783-794
Carl Olsson , Lund University, Lund
Fredrik Kahl , Lund University, Lund
Magnus Oskarsson , Lund University, Lund
In this paper, we propose a practical and efficient method for finding the globally optimal solution to the problem of determining the pose of an object. We present a framework that allows us to use point-to-point, point-to-line, and point-to-plane correspondences for solving various types of pose and registration problems involving euclidean (or similarity) transformations. Traditional methods such as the iterative closest point algorithm or bundle adjustment methods for camera pose may get trapped in local minima due to the nonconvexity of the corresponding optimization problem. Our approach of solving the mathematical optimization problems guarantees global optimality. The optimization scheme is based on ideas from global optimization theory, in particular convex underestimators in combination with branch-and-bound methods. We provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data. We also give examples of where traditional methods fail due to the local minima problem.
Registration, camera pose, global optimization, branch-and-bound.
Carl Olsson, Fredrik Kahl, Magnus Oskarsson, "Branch-and-Bound Methods for Euclidean Registration Problems", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.31, no. 5, pp. 783-794, May 2009, doi:10.1109/TPAMI.2008.131
[1] E.H. Thompson, “An Exact Linear Solution of the Problem of Absolute Orientation,” vol. 15, no. 4, pp. 163-179, 1958.
[2] R.I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, second ed. Cambridge Univ. Press, 2004.
[3] Manual of Photogrammetry, C. Slama, ed., fourth ed. Am. Soc. Photogrammetry, 1984.
[4] B.K. Horn, H.M. Hilden, and S. Negahdaripour, “Closed-Form Solution of Absolute Orientation Using Ortonormal Matrices,” J.Optical Soc. Am. A, vol. 5, pp. 1127-1135, 1988.
[5] K. Kanatani, “Unbiased Estimation and Statistical Analysis of 3-D Rigid Motion from Two Views,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 1, pp. 37-50, Jan. 1993.
[6] P. Besl and N. McKay, “A Method for Registration Two 3-D Shapes,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 232-256, Feb. 1992.
[7] N. Gelfand, L. Ikemoto, S. Rusinkiewicz, and M. Levoy, “Geometrically Stable Sampling for the ICP Algorithm,” Proc. Fourth Int'l Conf. 3-D Digital Imaging and Modeling, 2003.
[8] Y. Chen and G. Medioni, “Object Modeling by Registration of Multiple Range Images,” Proc. IEEE Int'l Conf. Robotics and Automation, vol. 3, pp. 2724-2729, 1991.
[9] H. Pottman, Q. Huang, Y. Yang, and S. Hu, “Geometry and Convergence Analysis of Algorithms for Registration,” Int'l J. Computer Vision, vol. 67, no. 3, pp. 277-296, 2006.
[10] J.A. Grunert, “Das Pothenot'sche Problem in Erweiterter Gestalt; Nebst Bemerkungen über Seine Anwendung in der Geodäsie,” Grunert Archiv der Mathematik und Physik, vol. 1, no. 3, pp. 238-248, 1841.
[11] R.M. Haralick, C.N. Lee, K. Ottenberg, and M. Nolle, “Review and Analysis of Solutions of the 3-Point Perspective Pose Estimation Problem,” Int'l J. Computer Vision, vol. 13, no. 3, pp. 331-356, Dec. 1994.
[12] I.E. Sutherland, “Sketchpad: A Man-Machine Graphical Communications System,” Technical Report 296, MIT Lincoln Laboratories, 1963.
[13] L. Quan and Z. Lan, “Linear N-Point Camera Pose Determination,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 8, pp. 774-780, Aug. 1999.
[14] B. Triggs, “Camera Pose and Calibration from 4 or 5 Known 3D Points,” Proc. Eighth Int'l Conf. Computer Vision, pp. 278-284, 1999.
[15] B. Kolman and R.E. Beck, Elementary Linear Programming with Applications. Academic Press, 1995.
[16] H.S. Ryoo and N.V. Sahinidis, “Analysis of Bounds for Multilinear Functions,” J. Global Optimization, vol. 19, pp. 403-424, 2001.
[17] T. Breuel, “Implementation Techniques for Geometric Branch-and-Bound Matching Methods,” Computer Vision and Image Understanding, vol. 90, no. 3, pp. 258-294, 2003.
[18] T. Breuel, “Geometric Aspects of Visual Object Recognition,” PhD dissertation, Massachusetts Inst. of Tech nology, 1992.
[19] F. Kahl, S. Agarwal, M.K. Chandraker, D.J. Kriegman, and S. Belongie, “Practical Global Optimization for Multiview Geometry,” Int'l J. Computer Vision, vol. 79, no. 3, pp. 271-284, 2008.
[20] C. Olsson, F. Kahl, and M. Oskarsson, “The Registration Problem Revisited: Optimal Solutions from Points, Lines and Planes,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 1206-1213, 2006.
[21] C. Olsson, F. Kahl, and M. Oskarsson, “Optimal Estimation of Perspective Camera Pose,” Proc. 18th Int'l Conf. Pattern Recognition, pp. 5-8, 2006.
[22] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge Univ. Press, 2004.
[23] S. Altmann, Rotations, Quaternions and Double Groups. Clarendon Press, 1986.
[24] J.F. Sturm, Using Sedumi 1.02, a Matlab Toolbox for Optimization over Symmetric Cones, 1998.
25 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool