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Motion fields are hardly ever ambiguous

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Abstract

There has been much concern with ambiguity in the recovery of motion and structure from time-varying images. I show here that the class of surfaces leading to ambiguous motion fields is extremely restricted—only certain hyperboloids of one sheet (and some degenerate forms) qualify. Furthermore, the viewer must be on the surface for it to lead to a potentially ambiguous motion field. Thus the motion field over an appreciable image region almost always uniquely defines the instantaneous translational and rotational velocities, as well as the shape of the surface (up to a scale factor).

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References

  1. A.R. Bruss and B.K.P. Horn, “Passive navigation,” Computer Vision, Graphics, and Image Processing, vol. 21, pp. 3–20, 1983.

    Google Scholar 

  2. B.K.P. Horn, Robot vision. MIT Press: Cambridge. and McGraw-Hill: New York City, 1986.

    Google Scholar 

  3. J.C. Hay, “Optical motions and space perception: An extension of Gibson's analysis,” Psychological Review, vol. 73(6), pp. 550–565, 1960.

    Google Scholar 

  4. S.J. Maybank, “The angular velocity associated with the optical flow field due to a single moving rigid plane,” in PROC. SIXTH EUROPEAN CONF. ARTIFI. INTELL., Pisa, September 5–7, 1984, pp. 641–644.

  5. H.C. Longuet-Higgins, “The visual ambiguity of a moving plane,” Proc. Roy. Soc. (London) B, vol. 223, pp. 165–175, 1984.

    Google Scholar 

  6. M. Subbarao and A.M. Waxman, “On the uniqueness of image flow solutions for planar surfaces in motion,” Third IEEE Workshop on Computer Vision; to appear in COMPUTER VISION, GRAPHICS, AND IMAGE PROCESSING, 1985.

  7. A.M. Waxman, B. Kamgar-Parsi, and M. Subbarao, “Closed-form solutions to image flow equations for 3-D structure and motion,” University of Maryland Center for Automation Research, CAR-TR-190 (S-TR-1633), 1986.

  8. S. Negahdaripour, “Direct passive navigation,” Ph.D. thesis, Department of Mechanical Engineering, MIT, 1986.

  9. B.K.P. Horn and E.J. Weldon, Jr., “Robust direct methods for recovering motion,” submitted to INT. J. COMP. VISION, vol. 1, 1987.

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

  11. S.J. Maybank, “The angular velocity associated with the optical flow field arising from motion through a rigid environment,” Proc. Roy. Soc. (London), A, vol. 401, pp. 317–326, 1985.

    Google Scholar 

  12. S. Negahdaripour and B.K.P. Horn, “Direct passive navigation,” IEEE Trans. Pami, vol. 9(1), pp. 168–176, January, 1987.

    Google Scholar 

  13. G.A. Korn and T.M. Korn, Mathematical Handbook for Engineers and Scientists. McGraw-Hill: New York City, 1972.

    Google Scholar 

  14. D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination. Chelsea Publishing Company: New York City, 1952.

    Google Scholar 

  15. H.C. Longuet-Higgins, “The reconstruction of a scene from two projections—configurations that defeat the eight-point algorithm,” in IEEE PROC. FIRST CONF. ARTIFI. INTEL. APPLI., Denver, Colo. 1984.

  16. P.R. Wolf, Elements of Photogrammetry. McGraw-Hill: New York, 1983.

    Google Scholar 

  17. S.J. Gosh, Theory of Stereophotogrammetry, The Ohio State University Bookstore: Columbus, Ohio, 1972.

    Google Scholar 

  18. K. Schwidefsky, An Outline of Photogrammetry. Translated by John Fosberry, Pitman and Sons: London, 1973.

    Google Scholar 

  19. W. Hofmann, “Das Problem der ‘Gefährlichen Flächen’ in Theorie and Praxis,” Ph.D. thesis, Technische Hochschule München, 1949. Published in 1953 by Deutsche Geodätische Kommission, München, West Germany.

  20. A. Brandenberger, “Fehlertheorie der äusseren Orientierung von Steilaufnahmen,” Ph.D. thesis, Eidgenössische Technische Hochschule, Zürich, Switzerland, 1947.

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Authors and Affiliations

  1. Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 02139, Cambridge, Mass.

    Berthold K. P. Horn

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  1. Berthold K. P. Horn
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Research for this article was conducted while the author was on leave at the Department of Electrical Engineering, University of Hawaii at Manoa, Honolulu, Hawaii 96822, and was supported by the National Science Foundation under Grant No. DMC85-11966.

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Horn, B.K.P. Motion fields are hardly ever ambiguous. Int J Comput Vision 1, 259–274 (1988). https://doi.org/10.1007/BF00127824

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