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Using Points at Infinity for Parameter Decoupling in Camera Calibration
February 2005 (vol. 27 no. 2)
pp. 265-270
The majority of camera calibration methods, including the Gold Standard algorithm, use point-based information and simultaneously estimate all calibration parameters. In contrast, we propose a novel calibration method that exploits line orientation information and decouples the problem into two simpler stages. We formulate the problem as minimization of the lateral displacement between single projected image lines and their vanishing points. Unlike previous vanishing point methods, parallel line pairs are not required. Additionally, the invariance properties of vanishing points mean that multiple images related by pure translation can be used to increase the calibration data set size without increasing the number of estimated parameters. We compare this method with vanishing point methods and the Gold Standard algorithm and demonstrate that it has comparable performance.

[1] A.S. Aguado, E. Montiel, and M.S. Nixon, “Invariant Characterization of the Hough Transform for Pose Estimation of Arbitrary Shapes,” Proc. British Machine Vision Conf., vol. 2, pp. 785-794, 2000.
[2] K.S. Arun, T.S. Huang, and S.D. Blostein, “Least-Squares Fitting of Two 3-D Point Sets,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 5, pp. 698-700, Sept. 1987.
[3] A. Bartoli, R. Hartley, and F. Kahl, “Motion from 3D Line Correspondences: Linear and Nonlinear Solutions,” Proc. IEEE Int'l Conf. Computer Vision and Pattern Recognition (CVPR '03), pp. 477-484, 2003.
[4] P. Beardsley and D. Murray, “Camera Calibration Using Vanishing Points,” Proc. British Machine Vision Conf., pp. 416-425, 1992.
[5] T. Buchanan, “The Twisted Cubic and Camera Calibration,” Computer Vision, Graphics and Image Processing, vol. 42, pp. 130-132, 1988.
[6] B. Caprile and V. Torre, “Using Vanishing Points for Camera Calibration,” Int'l J. Computer Vision, vol. 4, no. 2, pp. 127-140, 1990.
[7] W. Chen and B.C. Jiang, “3-D Camera Calibration Using Vanishing Point Concept,” Pattern Recognition, vol. 24, no. 1, pp. 57-67, 1991.
[8] R. Cipolla, D.P. Robertson, and E.G. Boyer, “Photobuilder— 3 Models of Architectural Scenes from Uncalibrated Images,” Proc. IEEE Int'l Conf. Multimedia Computing and Systems (ICMCS '99), vol. 1, pp. 25-31, 1999.
[9] K. Daniilidis and J. Ernst, “Active Intrinsic Calibration Using Vanishing Points,” Pattern Recognition Letters, vol. 17, no. 11, pp. 1179-1189, 1996.
[10] F. Devernay and O.D. Faugeras, “Straight Lines Have to Be Straight,” Machine Vision and Applications, vol. 13, no. 1, pp. 14-24, 2001.
[11] T. Echigo, “A Camera Calibration Technique Using Three Sets of Parallel Lines,” Machine Vision and Applications, vol. 3, no. 3, pp. 159-167, 1990.
[12] O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, 1993.
[13] R.M. Haralick, “Propagating Covariance in Computer Vision,” Int'l J. Pattern Recognition and Artificial Intelligence, vol. 10, no. 5, pp. 561-572, 1996.
[14] C. Harris and M. Stephens, “Combined Corner and Edge Detector,” Proc. Alvey Vision Conf., pp. 147-151, 1988.
[15] R.I. Hartley, “In Defense of the Eight-Point Algorithm,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 6, pp. 580-593, June 1997.
[16] R.I. Hartley, “Lines and Points in Three Views and the Trifocal Tensor,” Int'l J. of Computer Vision, vol. 22, no. 2, pp. 125-140, 1997.
[17] R.I. Hartley, “Minimizing Algebraic Error in Geometric Estimation Problems,” Proc. Int'l Conf. Computer Vision, pp. 469-476, 1998.
[18] R.I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision. Cambridge Univ. Press, 2000.
[19] D.J. Heeger and A.D. Jepson, “Subspace Methods for Recovering Rigid Motion I: Algorithm and Implementation,” Int'l J. Computer Vision, vol. 7, no. 2, pp. 95-117, 1992.
[20] D. Liebowitz, A. Criminisi, and A. Zisserman, “Creating Architectural Models from Images,” Proc. Eurographics Conf. '99, vol. 18, pp. 39-50, 1999.
[21] Y. Liu and T.S. Huang, “A Linear Algorithm for Determining Motion and Structure from Line Correspondences,” Computer Vision, Graphics, and Image Processing, vol. 44, no. 1, pp. 35-57, 1988.
[22] W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, The Art of Scientific Computing. Cambridge Univ. Press, second ed., 1992.
[23] J.H. Reiger and D.T. Lawton, “Processing Differential Image Motion,” J. Optical Soc. of Am. A, vol. 2, pp. 354-359, 1985.
[24] J.A. Shufelt, “Performance Evaluation and Analysis of Vanishing Point Detection Techniques,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 3, pp. 282-288, Mar. 1999.
[25] C.C. Slama, Manual of Photogrammetry. Am. Soc. of Photogrammetry, fourth ed., 1980.
[26] G.P. Stein and A. Shashua, “On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 3, pp. 244-251, Mar. 1999.
[27] D. Stevenson and M. Fleck, “Robot Aerobics: Four Easy Steps to a More Flexible Calibration,” Proc. Int'l Conf. Computer Vision, pp. 34-39, 1995.
[28] B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, “Bundle Adjustment— A Modern Synthesis,” Vision Algorithms: Theory and Practice, W. Triggs, A. Zisserman, and R. Szeliski, eds., Lecture Notes in Computer Science, pp. 298-375, 2000.
[29] R.Y. Tsai, “A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses,” IEEE J. Robotics and Automation, vol. RA-3, no. 4, pp. 323-344, 1987.
[30] T. Viéville, A Few Steps Towards 3D Active Vision. Springer Verlag, 1998.
[31] L.L. Wang and W.H. Tsai, “Computing Camera Parameters Using Vanishing-Line Information from a Rectangular Parallelepiped,” Machine Vision and Applications, vol. 3, no. 3, pp. 129-141, 1990.
[32] L.L. Wang and W.H. Tsai, “Camera Calibration by Vanishing Lines for 3-D Computer Vision,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 370-376, Apr. 1991.
[33] J. Weng and T. Huang, “Motion and Structure from Line Correspondences: Closed-Form Solution, Uniqueness, and Optimization,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 3, pp. 318-335, Mar. 1992.

Index Terms:
Computer vision, camera calibration, invariants.
Jean-Yves Guillemaut, Alberto S. Aguado, John Illingworth, "Using Points at Infinity for Parameter Decoupling in Camera Calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 2, pp. 265-270, Feb. 2005, doi:10.1109/TPAMI.2005.41
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