This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Motion and Structure of Four Points from One Motion of a Stereo Rig with Unknown Extrinsic Parameters
December 1995 (vol. 17 no. 12)
pp. 1222-1227

Abstract—We describe an analytical method for recovering 3D motion and structure of four or more points from one motion of a stereo rig. The extrinsic parameters are unknown. The motion of the stereo rig is also unknown. Because of the exploitation of information redundancy, the approach gains over the traditional “motion and structure from motion“ approach in that less features and less motions are required, and thus more robust estimation of motion and structure can be obtained. Since the constraint on the rotation matrix is not fully exploited in the analytical method, nonlinear minimization can be used to improve the result. We propose to estimate directly the motion and structure by minimizing the difference between the measured positions and the predicted ones in the image plane. Both computer simulated data and real data are used to validate the proposed algorithm, and very promising results are obtained.

[1] Z. Zhang,“Motion analysis from a sequence of stereo frames and its applications,” Dissertation, Univ. of Paris XI, Orsay, Paris, France, 1990, in English.
[2] Z. Zhang and O.D. Faugeras, 3D Dynamic Scene Analysis: A Stereo Based Approach. Berlin Heidelberg: Springer, 1992.
[3] C. Jerian and R. Jain,“Structure from motion—a critical analysis of methods,” IEEE Trans. Systems, Man, and Cybernetics, vol. 21, no. 5, pp. 572-588, May 1991.
[4] T. Huang and A. Netravali,“Motion and structure from feature correspondences: A review,” Proc. IEEE, vol. 82, pp. 252-268, Feb. 1994.
[5] H. Longuet-Higgins,“A computer algorithm for reconstructing a scene from two projections,” Nature, vol. 293, pp. 133-135, 1981.
[6] R. Tsai,T. Huang,, and W. Zhu,“Estimating three-dimensional motion parameters of a rigid planar patch, ii: Singular value decomposition,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 30, no. 4, pp. 525-534, 1982.
[7] O. Faugeras,F. Lustman,, and G. Toscani,“Motion and structure from motion from point and line matches,” Proc. First Int’l Conf. Computer Vision, pp. 25-34,London, 1987.
[8] J. Weng,T. Huang,, and N. Ahuja,“Motion and structure from two perspective views:Algorithms, error analysis and error estimation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 5, pp. 451-476, May 1989.
[9] S. Ullman,The Interpretation of Visual Motion.Cambridge, Mass: MIT Press, 1979.
[10] J. Koenderink and A. van Doorn,“Affine structure from motion,” J. Optical Soc. of Am. A, vol. A8, pp. 377-385, 1991.
[11] H.C. Longuet-Higgins,“A method of obtaining the relative positionsof four points from three perspective projections,” Image and Vision Computing, vol. 10, pp. 266-270, June 1992.
[12] J. Aloimonos,I. Weiss,, and A. Bandopadhay,“Active vision,” Int’l J. Computer Vision, vol. 1, no. 4, pp. 333-356, 1988.
[13] R. Sharma and J. Aloimonos,“Robust detection of independent motion: An active and purposive solution,” Technical Report CAR-TR-534, Center for Automation Research, Univ. of Maryland, College Park, 1991.
[14] T. Huang and O. Faugeras,“Some properties of the E matrix in two-view motion estimation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 12, pp. 1,310-1,312, Dec. 1989.
[15] S. Maybank,Theory of Reconstruction from Image Motion.Berlin, Heidelberg: Springer-Verlag, 1993.
[16] H. Longuet-Higgins,“The reconstruction of a scene from two projections—configurationsthat defeat the 8-point algorithm,” Proc. First Conf. Artificial Intelligence Applications, pp. 395-397,Denver, 1984.
[17] H. Longuet-Higgins,“Multiple interpretations of a pair of images of a surface,” Proc. Royal Soc. London A., vol. 418, pp. 1-15, 1988.
[18] O.D. Faugeras and M. Hebert,“The representation, recognition, and locating of 3D objects,” Int’l J. of Robotics Research, vol. 5, no. 3, pp. 27-52, Fall 1986.
[19] B. Horn,“Closed-form solution of absolute orientation using unit quaternions,” J. Optical Soc. of Am. A, vol. 7, pp. 629-642, Apr. 1987.
[20] M. Spetsakis and J. Aloimonos,“Optimal computing of structure from motion using point correspondences in two frames,” Proc. Second Int’l Conf. Computer Vision, pp. 449-453,Florida, Dec. 1988.
[21] O. Faugeras and G. Toscani,“The calibration problem for stereo,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 15-20,Miami, June 1986.
[22] Z. Zhang, R. Deriche, O. Faugeras, and Q.T. Luong, “A Rubust Technique for Matching Two Uncalibrated Images through the Recovery of the Unknown Epipolar Geometry,” Artificial Intelligence J., vol. 78, pp. 87-119, 1995.
[23] A. Netravali,T. Huang,A. Krishnakumar,, and R. Holt,“Algebraic methods in 3-D motion estimation from two-view point correspondences,” Int. J. Imaging Systems Technology, vol. 1, pp. 78-99, 1989.
[24] Q.-T. Luong,“Matrice fondamentale et calibration visuelle sur l’environnement: Vers uneplus grande autonomie des systèmes robotiques,” Dissertation, Univ. of Paris XI, Orsay, Paris, Dec. 1992.
[25] Z. Zhang,Q.-T. Luong,, and O. Faugeras,“Motion of an uncalibrated stereo rig: Self-calibration and metric reconstruction,” Proc. 12th Int’l Conf. Pattern Recogition, vol. I, pp. 695-697,Jerusalem, Oct. 1994. To appear in IEEE Trans. Robotics Automation.

Index Terms:
Motion analysis, uncalibrated stereo, structure from motion, four-points algorithm, minimization criteria.
Citation:
Zhengyou Zhang, "Motion and Structure of Four Points from One Motion of a Stereo Rig with Unknown Extrinsic Parameters," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 12, pp. 1222-1227, Dec. 1995, doi:10.1109/34.476516
Usage of this product signifies your acceptance of the Terms of Use.