This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Motion and Structure from Line Correspondences; Closed-Form Solution, Uniqueness, and Optimization
March 1992 (vol. 14 no. 3)
pp. 318-336

This work discusses estimating motion and structure parameters from line correspondences of a rigid scene. The authors present a closed-form solution to motion and structure parameters from line correspondences through three monocular perspective views. The algorithm makes use of redundancy in the data to improve the accuracy of the solutions. The uniqueness of the solution is established, and necessary and sufficient conditions for degenerate spatial line configurations are given. Optimization has been employed to further improve the accuracy of the estimates in the presence of noise. Simulations have shown that the errors of the optimized estimates are close to the theoretical lower error bound.

[1] G. Adiv, "Determining three-dimensional motion and structure from optical flow generated by several moving objects,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-7, pp. 348-401, 1985.
[2] O. Bottema and B. Roth,Theoretical Kinematics, New York: North-Holland, 1979.
[3] T. Broida and R. Chellappa, "Estimation of object motion parameters from noisy images,"IEEE Trans. Pattern Anal. Machine Intell, vol. PAMI-8, no. 1, Jan. 1986.
[4] J. Burns, A. Hanson, and E. Riseman, "Extracting straight lines,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, no. 4, pp. 425-455, July 1986.
[5] H. Cramér,Mathematical Methods of Statistics. Princeton NJ: Princeton, Univ. Press, 1946.
[6] L. Davis, Z. Wu, and H. Sun, "Contour based motion estimation",Comput. Vision Graphics Image Processing, vol. 23, pp. 313-326, 1983.
[7] L. Dreschler and H.-H. Nagel, "Volumetric model and 3-D trajectory of a moving car derived from monocular TV frame sequences of a street scene,"Comput. Graphics Image Processing, vol. 20, pp. 199-228, 1982.
[8] O. D. Faugeras and M. Hebert, "A 3-D recognition and positioning algorithm using geometric matching between primitive surfaces,Proc. 8th Int. Joint Conf. Artificial Intell.(Karlsruhe, W. Germany), Aug. 1983, pp. 996-1002.
[9] O. D. Faugeras, F. Lustman, and G. Toscani, "Motion and structure from point and line matches," inProc. First Int. Conf. Comput. Vision, (London, England), June, 1987.
[10] A. A. Giordano and F. M. Hsu,Least Squares Estimation with Applications to Digital Signal Processing, New York: Wiley, 1985.
[11] D. G. Luenberger, Optimization byVector Space Methods. New York: Wiley, 1969.
[12] Y. Liu and T. S. Huang, "Estimation of rigid body motion using straight line correspondences, further results," inProc. Int. Conf. Patt. Recog.(Paris, France), Oct. 27-31, 1986, pp. 306-307.
[13] Y. Liu and T. S. Huang, "A linear algorithm for determining motion and structure from line correspondences,Comput. Vision Graphics Image Processing, vol. 44, no. 1, pp. 35-57, 1988.
[14] H. C. Longuet-Higgins, "A computer program for reconstructing a scene from two projections,"Nature, vol. 293, pp. 133-135, Sept. 1981.
[15] H. C. Longuet-Higgins, "The reconstruction of a scene from two projections - configurations that defeat the 8-point algorithm,"Proc. 1st Conf. Artificial Intell. Applications, (Denver, CO), Dec. 5-7, 1984, pp. 395-397.
[16] J. H. McIntosh and K. M. Mutch, "Matching straight lines,"Comput. Vision Graphics Image Processing, vol. 43, no. 3, pp. 386-408, 1988.
[17] A. Mitiche, S. Seida, and J. K. Aggarwal, "Interpretation of structure and motion using straight line correspondences," inProc. Int. Conf. Patt. Recog.(Paris, France), Oct. 27-31, 1986, pp. 1110-1112.
[18] C. R. Rao,Linear Statistical Inference and Its Applications, 2nd Ed., New York: Wiley, 1973.
[19] M. D. Shuster, "Approximate algorithms for fast optimal attitude computation,"Proc. AIAA Guidance Cont. Spec. Conf., (Palo Alto), Aug. 1978, pp. 88-95.
[20] H. W. Sorenson,Parameter Estimation: Principles and Problems, New York: Marcel Dekker, 1980.
[21] M. Spetsakis and J. Aloimonos, "Closed form solution to the structure from motion problem from line correspondences," inProc. Sixth AAAI Nat. Conf. Artificial Intell.(Seattle, WA), July 1987, pp. 738-743.
[22] R. Y. Tsai and T. S. Huang, "Uniqueness and estimation of 3-D motion parameters of rigid bodies with curved surfaces,IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, no. 1, pp. 13-27, 1984.
[23] A. M. Waxman and K. Wohn, "Contour evolution, neighborhood deformation, and global image flow: Planar surfaces in motion,"Int. J. Robotics Res.vol. 4, pp. 95-108, 1985.
[24] A. M. Waxman, B. Kamgar-Parsi, and M. Subbarao, "Closed-form solutions to image flow equations for 3D structure and motion,"Int. J. Comput. Vision, vol. 1, pp. 239-258, 1987.
[25] J. Weng, N. Ahuja, and T. S. Huang, "Error analysis of motion parameter estimation from image sequences," inProc. First Int. Conf. Comput. Vision(London, England), June 1987, pp. 703-707.
[26] J. Weng, N. Ahuja, and T. S. Huang, "Closed form solution + maximum likelihood: A robust approach to motion and structure estimation," inProc. IEEE Conf. Computer vision and Pattern Recognition, June 1988.
[27] J. Weng, T. S. Huang, and N. Ahuja, "Motion from images: Image matching, parameter estimation, and intrinsic stability," inProc. IEEE Workshop Visual Motion, (Irvine, CA), Mar. 20-22, 1989, pp. 359-366.
[28] J. Weng, T. S. Huang, and N. Ahuja, "Motion and structure from two perspective views: Algorithm, error analysis, and error estimation,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 5, pp. 451-476, 1989.
[29] B. L. Yen and T. S. Huang, "Determining 3-D motion and structure of a rigid body using straight line correspondences,"Image Sequence Processing and Dynamic Scene Analysis. Heidelberg, Germany: Springer-Verlag, 1983.
[30] X. Zhuang and R. M. Haralick, "Rigid body motion and the optical flow image," inProc. 1st Conf. Artificial Intell. Applications, (Denver, CO), Dec. 1984, pp. 366-375.
[31] X. Zhuang, T. S. Huang, and N. Ahuja, "A simplified linear optical flowmotion algorithm,"Compt. Vision Graphics, Image Processing, vol. 42, pp. 334-344, 1988.

Index Terms:
motion parameters; parameter estimation; necessary conditions; picture processing; pattern recognition; line correspondences; closed-form solution; uniqueness; optimization; rigid scene; structure parameters; sufficient conditions; optimisation; parameter estimation; pattern recognition; picture processing
Citation:
J. Weng, T.S. Huang, N. Ahuja, "Motion and Structure from Line Correspondences; Closed-Form Solution, Uniqueness, and Optimization," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 3, pp. 318-336, March 1992, doi:10.1109/34.120327
Usage of this product signifies your acceptance of the Terms of Use.