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Linear Pose Estimation from Points or Lines
May 2003 (vol. 25 no. 5)
pp. 578-589

Abstract—Estimation of camera pose from an image of n points or lines with known correspondence is a thoroughly studied problem in computer vision. Most solutions are iterative and depend on nonlinear optimization of some geometric constraint, either on the world coordinates or on the projections to the image plane. For real-time applications, we are interested in linear or closed-form solutions free of initialization. We present a general framework which allows for a novel set of linear solutions to the pose estimation problem for both n points and n lines. We then analyze the sensitivity of our solutions to image noise and show that the sensitivity analysis can be used as a conservative predictor of error for our algorithms. We present a number of simulations which compare our results to two other recent linear algorithms, as well as to iterative approaches. We conclude with tests on real imagery in an augmented reality setup.

[1] Y.I. Abdel-Aziz and H.M. Karara, “Direct Linear Transformation Into Object Space Coordinates in Close-Range Photogrammetry,” Proc. Symp. Close-Range Photogrammetry, pp. 1-18, 1971.
[2] R.T. Azuma, “A Survey of Augmented Reality,” Presence: Teleoperators and Virtual Environments, vol. 7, pp. 355-385, 1997.
[3] D. Dementhon and L. Davis, "Model-Based Object Pose in 25 Lines of Code," Int'l J. Comp. Vision, vol. 15, pp. 123-141, 1995.
[4] M. Dhome, M. Richetin, J.T. Lapreste, and G. Rives, “Determination of the Attitude of 3D Objects from a Single Perspective View,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 12, pp. 1,265-1,278, Dec. 1989.
[5] R.M. Haralick, H. Joo, C.-N. Lee, X. Zhuang, and M.B. Kim, “Pose Estimation from Corresponding Point Data,” IEEE Trans. Systems, Man, and Cybernetics, vol. 19, no. 6, p. 1426, 1989.
[6] O.D. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint.Cambridge, Mass.: MIT Press, 1993.
[7] P.D. Fiore, “Efficient Linear Solution of Exterior Orientation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, pp. 140-148, 2001.
[8] M.A. Fischler and R.C. Bolles, “Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography,” Graphics and Image Processing, vol. 24, no. 6, pp. 381–395, June 1981.
[9] S. Ganapathy, “Decomposition of Transformation Matrices for Robot Vision,” Proc. IEEE Int'l Conf. Robotics and Automation, pp. 130-139, 1984.
[10] J. Huang, J.A. Stankovic, K. Ramamritham, D. Towsley, and B. Purimetla, “On Using Priority Inheritance in Real-Time Databases,” Special Issue of Real-Time Systems J., vol. 4. no. 3, Sept. 1992.
[11] R. Horaud, B. Conio, O. Leboulleux, and B. Lacolle, “An Analytic Solution for the Perspective 4-Point Problem,” Computer Vision, Graphics, and Image Processing, vol. 47, pp. 33–44, 1989.
[12] B.K.P. Horn, “Closed-Form Solution of Absolute Orientation Using Quaternions,” J. Optical Soc. Am. A, vol. 4, pp. 629-642, 1987.
[13] B.K.P. Horn, “Relative Orientation,” Int'l J. Computer Vision, vol. 4, pp. 59-78, 1990.
[14] B.K.P. Horn, H.M. Hilden, and S. Negahdaripour, “Closed-Form Solution of Absolute Orientation Using Orthonormal Matrices,” J. Optical Soc. Am. A, vol. 5, pp. 1127-1135, 1988.
[15] T.S. Huang, A.N. Netravali, and H.H. Chen, “Motion and Pose Determination Using Algebraic Methods,” Time-Varying Image Processing and Moving Object Recognition, Elsevier Science Publication, V. Cappellini, ed., no. 2, pp. 243-249, 1990.
[16] R. Kumar and A.R. Hanson, “Robust Methods for Estimating Pose and a Senitivity Analysis,” Computer Vision and Graphic Image Processing: Image Understanding, vol. 60, no. 3, pp. 313-342, 1994.
[17] R.K. Lenz and R.Y. Tsai, “Techniques for Calibration of the Scale Factor and Image Center for High Accuracy 3D Machine Vision Metrology,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 713-720, Sept. 1988.
[18] Y. Liu, T.S. Huang, and O.D. Faugeras, “Determination of Camera Location from 2D to 3D Line and Point Correspondences,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 28-37, Jan. 1990.
[19] D.G. Lowe, "Fitting Parameterized Three-Dimensional Models to Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 5, pp. 441-450, May 1991.
[20] C.P. Lu, G.D. Hager, and E. Mjolsness, Fast and Globally Convergent Pose Estimation from Video Images IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 6, pp. 610-622, June 2000.
[21] S. Maybank, Theory of Reconstruction from Image Motion. Springer-Verlag, 1993.
[22] N. Navab and O.D. Faugeras, “Monocular Pose Determination From Lines: Critical Sets and Maximum Number of Solutions,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 254-260, June 1993.
[23] W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, second ed. Cambridge Univ. Press, 1992.
[24] L. Quan and Z. Lan, “Linear N-Point Camera Pose Determination,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, pp. 774-780, 1999.
[25] G.W. Stewart and J.-G. Sun, Matrix Perturbation Theory. Boston, Mass.: Academic Press, Inc., 1990.
[26] E.H. Thompson, “Space Resection: Failure Cases,” Photogrammetric Record, pp. 201-204, 1966.
[27] B. Triggs, “Camera Pose and Calibration from 4 or 5 Known 3D Points,” Proc. Int'l Conf. Computer Vision, pp. 278-284, Sept. 1999.
[28] S. Yi, R.M. Haralick, and L.G. Shapiro, “Error Propagation in Machine Vision,” Machine Vision and Applications, vol. 7, pp. 93-114, 1994.

Index Terms:
Pose estimation, exterior orientation, absolute orientation, camera localization.
Adnan Ansar, Kostas Daniilidis, "Linear Pose Estimation from Points or Lines," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 5, pp. 578-589, May 2003, doi:10.1109/TPAMI.2003.1195992
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