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Critical surface pairs and triplets

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Abstract

In this paper, we study situations where a perspective image motion field can have multiple interpretations. We show that the ambiguity in interpretation of the three-dimensional instantaneous motion of curved surfaces is at most three-fold, and can occur only in the case of certain hyperboloids of one sheet, saddle surfaces, and hyperbolic paraboloids. We also present analytical expressions for the relationship among multiple interpretations.

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Bibliography

  • G. Adiv (1985a) “Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field,” Proc. IEEE Conf. Comp. Vision Pattern Recog., San Francisco, June.

  • G. Adiv (1985b) “Determining 3-D motion and structure from optical flow generated by several moving objects,” IEEE Trans. PAMI 7(4): July.

  • D.H. Ballard and O.A. Kimball (1983) “Rigid body motion from depth and optical flow,” “Comput. Vision, Graphics, Image Process. 22(1): April.

  • S.T. Barnard and W.B. Thompson (1980) “Disparity analysis of images,” IEEE Trans. PAMI 2(4): July.

  • A.R. Bruss and B.K.P. Horn (1983) “Passive navigation,” Comput. Vision, Graphics, Image Process. 21(1): January.

  • B.F. Buxton, H. Buxton, D.W. Murray, and N.S. Williams (1984) “3-D solution to the aperture problem,” Proc. 6th European Conf. Artif. Intell. Pisa, Italy, September.

  • J.C. Hay (1966) “Optical motion and space perceptions: An extension of Gibson's analysis,” Psychology Review 73(6).

  • D.D. Hoffman (1982) “Inferring local surface orientation from motion field,” J. Opt. Soc. Am. 72.

  • B.K.P. Horn (1987) “Motion fields are hardly ever ambiguous,” Intern. J. Comput. Vision 1(3): October.

  • C. Jerian and R. Jain (1984) “Determining motion parameters for scenes with translation and rotation,” IEEE Trans. PAMI 6(4).

  • K. Kanatani (1986) “Structure and motion from optical flow under orthographic projection,” Comput. Vision, Graphics, Image Process. 35(2).

  • K. Kanatani (1987) “Structure and motion from optical flow under perspective projection,” Comput. Vision, Graphics, Image Process. 38(2).

  • H.C. Longuet-Higgins (1984) “The visual ambiguity of a moving plane,” Proc. Roy. Soc. London, B, 223.

  • H.C. Longuet-Higgins and K. Prazdny (1980) “The interpretation of a moving retinal image,” Proc. Roy. Soc. London, ser. B, 208.

  • S.J. Maybank (1985) “The angular velocity associated with the optical flow field arising from motion through a rigid environment,” Proc. Roy. Soc. London, ser. A, 401.

  • S. Negahdaripour (1986) “Direct passive navigation,” Ph.D. thesis, Department of Mechanical Engineering, MIT, Cambridge, MA, November.

  • S. Negahdaripour (1987) “Ambiguities of a motion field,” Proc. 1st Intern. Conf. Comput. Vision, London, England, June.

  • S. Negahdaripour and B.K.P. Horn (1987) “Direct passive navigation,” IEEE Trans. PAMI 9 (1):January.

  • M. Subbarao (1987) “Solution and uniqueness of image flow equations for rigid curved surfaces in motion,” Proc. 1st Intern. Conf. Comput. Vision, London, England, June.

  • M. Subbarao and A.M. Waxman (1986) “Closed-form solutions to image flow equations for planar surfaces in motion,” Comput. Vision, Graphics, Image Process. 36.

  • K. Sugihara and N. Sugie (1984) “Recovery of rigid structure from orthographically projected optical flow,” Comput. Vision, Graphics, Image Process. 27(3).

  • R.Y. Tsai, T.S. Huang, and W.L. Zhu (1982) “Estimating three-dimensional motion parameters of a rigid planar patch, II: Singular value decomposition,” IEEE Trans. Acoustics, Speech, Signal Process. 30(4): August.

  • R.Y. Tsai, and T.S. Huang (1984) “Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces,” IEEE Trans. PAMI 6(1): January.

  • S. Ullman (1983) “Computational studies in the interpretation of structure from motion: Summary and extension,” AI Memo 706, MIT AI Lab, Cambridge, MA, March.

    Google Scholar 

  • A.M. Waxman, B. Kamgar-Parsi, and M. Subbarao (1987) “Closed-form solutions to image flow equations for 3-D structure and motion,” Intern. J. Comput. Vision 1(3): October.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 96822, Honolulu, HI

    Shahriar Negahdaripour

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  1. Shahriar Negahdaripour
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Negahdaripour, S. Critical surface pairs and triplets. Int J Comput Vision 3, 293–312 (1989). https://doi.org/10.1007/BF00132601

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  • DOI: https://doi.org/10.1007/BF00132601

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