Linear algorithm for motion estimation: How to handle degenerate cases

  • T. S. Huang
  • Y. S. Shim
Motion And Depth Analysis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 301)


For determining motion/structure of a 3-D rigid object from point correspondences over two perspective views, a linear algorithm was developed in Refs. 1 and 2. This algorithm fails when the 3-D points under observation satisfy certain geometrical constraints, as demonstrated in Refs. 3 and 4. In the present paper, we show that the linear algorithm can be resurrected in these degenerate cases.


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  1. 1.
    H.C. Longuet-Higgins, A Computer Program for Reconstructing a Scence From Two Projections, Nature, Vol. 293, pp. 133–135, 1981.CrossRefGoogle Scholar
  2. 2.
    R.Y. Tsai and T.S. Huang, Uniqueness and Estimation of 3-D Motion Parameters of Rigid Bodies with Curved Surfaces, IEEE Trans. PAMI, Vol. 6, No. 1, pp. 13–27, 1984.Google Scholar
  3. 3.
    H.C. Lonquet-Higgins, The Reconstruction of a Scene From Two Projections — Configurations That Defeat the 8-Point Algorithm, Proc. 1st Conf. AI Applications, Dec 5–7, 1984, Denver, CO., pp. 395–397.Google Scholar
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    X. Zhuang and R.M. Haralick, Two-View Motion Analysis, Proc. Int. Conf. ASSP., March 1985, Tampa, FL.Google Scholar
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    T.S. Huang, Determining Three-Dimensional Motion and Structure From Two Prospective Views, in "Handbook of Pattern Recognition and Image Processing," ed. by T.Y. Young and K.S. Fu, Academic Press, 1986; pp. 333–354.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • T. S. Huang
    • 1
  • Y. S. Shim
    • 1
  1. 1.Coordinated Science LaboratoryUniversity of IllinoisUrbanaU.S.A.

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