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Stereo Calibration from Rigid Motions
December 2000 (vol. 22 no. 12)
pp. 1446-1452

Abstract—In this paper, we describe a method for calibrating a stereo pair of cameras using general or planar motions. The method consists of upgrading a 3D projective representation to affine and to Euclidean without any knowledge, neither about the motion parameters nor about the 3D layout. We investigate the algebraic properties relating projective representation to the plane at infinity and to the intrinsic camera parameters when the camera pair is considered as a moving rigid body. We show that all the computations can be carried out using standard linear resolutions techniques. An error analysis reveals the relative importance of the various steps of the calibration process: projective-to-affine and affine-to-metric upgrades. Extensive experiments performed with calibrated and natural data confirm the error analysis as well as the sensitivity study performed with simulated data.

[1] P. Beardsley, I. Reid, A. Zisserman, and D. Murray, “Active Visual Navigation Using Non-Metric Structure,” Proc. Fifth Int'l Conf. Computer Vision, 1995.
[2] G. Csurka, D. Demirdjian, and R. Horaud, “Finding the Collineation between Two Projective Reconstructions,” Computer Vision and Image Understanding, vol. 75, no. 3, 260–268, Sept. 1999.
[3] D. Demirdjian, G. Csurka, and R. Horaud, “Autocalibration in the Presence of Critical Motions,” Proc. British Machine Vision Conf., pp. 751–759, Sept. 1998.
[4] F. Devernay and O. Faugeras, "From Projective to Euclidean Reconstruction," Proc. Conf. Computer Vision and Pattern Recognition,San Francisco, June 1996.
[5] R.I. Hartley, “In Defense of the 8-Point Algorithm,” Proc. Fifth Int'l Conf. Computer Vision, pp. 1,064-1,070, June 1995.
[6] R.I. Hartley and P. Sturm, “Triangulation,” Computer Vision and Image Understanding, vol. 68, no. 2, pp. 146-157, 1997.
[7] R.A. Horn and C.R. Johnson, Matrix Analysis. Cambridge Univ. Press, 1990.
[8] Q.-T. Luong, “Matrice Fondamentale et Autocalibration en Vision par Ordinateur,” PhD thesis, Universitéde Paris Sud, Orsay, Dec. 1992.
[9] Q.T. Luong and T. Vieville, “Canonic Representations for the Geometries of Multiple Projective Views,” Computer Vision and Image Understanding, vol. 64, no. 2, pp. 193–229, 1996.
[10] T. Moons, L. Van Gool, M. Proesmans, and E. Pauwels, “Affine Reconstruction from Perspective Image Pairs with a Relative Object-Camera Translation in Between,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 1, pp. 77-83, Jan. 1996.
[11] A. Ruf, G. Csurka, and R. Horaud, “Projective Translations and Affine Stereo Calibration,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 475–481, June 1998.
[12] A. Ruf and R. Horaud, “Visual Servoing of Robot Manipulators, Part I: Projective Kinematics,” Int'l J. Robotics Research, vol. 18, no. 11, pp. 1,101–1,118, Nov. 1999.
[13] B. Triggs, “Autocalibration and the Absolute Quadric,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 609-614, June 1997.
[14] A. Zisserman, P.A. Beardsley, and I.D. Reid, "Metric Calibration of a Stereo Rig," Workshop Representation of Visual Scenes, pp. 93-100,Cambridge, Mass., USA, June 1995.

Index Terms:
camera calibration, projective reconstruction, metric reconstruction, rigid motion, stereo vision, epipolar geometry.
Radu Horaud, Gabriella Csurka, David Demirdijian, "Stereo Calibration from Rigid Motions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 12, pp. 1446-1452, Dec. 2000, doi:10.1109/34.895977
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