OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 11, Iss. 7 — Jul. 1, 1994
  • pp: 1976–1984

Recovery of an unknown axis of rotation from the profiles of a rotating surface

P. J. Giblin, F. E. Pollick, and J. E. Rycroft  »View Author Affiliations


JOSA A, Vol. 11, Issue 7, pp. 1976-1984 (1994)
http://dx.doi.org/10.1364/JOSAA.11.001976


View Full Text Article

Enhanced HTML    Acrobat PDF (1126 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We consider a surface (semitransparent or opaque) in space, viewed by orthogonal projection to a view plane that is rotating uniformly about an unknown axis (equivalently, a surface rotating about an unknown axis and viewed by orthogonal projection to a fixed view plane). We consider profiles of this surface (also known as apparent contours, occluding contours, and outlines), and we do not track marked points or curves nor assume that a correspondence problem has been solved. We show that, provided the angular speed is known, the location of the axis, and hence the surface, can be recovered from measurements on the profiles over an interval of time. If the angular speed is unknown, then there is a one-parameter family of solutions similar to the bas-relief ambiguity. The results are obtained by use of frontier points on the surface, which can also be viewed as points of epipolar tangency. Results of a numerical experiment showed that the performance was best with larger extents of rotation or when the axis was nearly perpendicular to the view direction.

© 1994 Optical Society of America

History
Original Manuscript: August 16, 1993
Manuscript Accepted: February 3, 1994
Published: July 1, 1994

Citation
P. J. Giblin, F. E. Pollick, and J. E. Rycroft, "Recovery of an unknown axis of rotation from the profiles of a rotating surface," J. Opt. Soc. Am. A 11, 1976-1984 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-7-1976


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Blake, R. Cipolla, “Robust estimation of surface curvature from deformations of apparent contours,” Image Vis. Comput. 9, 107–112 (1991). [CrossRef]
  2. R. Cipolla, A. Blake, “The dynamic analysis of occluding contours,” in Proceedings of the Third International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 616–623. [CrossRef]
  3. R. Cipolla, A. Blake, “Surface shape from the deformation of apparent contours,” Internat. J. Computer Vis. 9, 83–112 (1992). [CrossRef]
  4. J. Callahan, R. S. Weiss, “A model for describing surface shape,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1985), pp. 240–245.
  5. P. J. Giblin, R. S. Weiss, “Reconstruction of surfaces from profiles,” in Proceedings of the First International Conference on Computer VisionInstitute of Electrical and Electronics Engineers, New York, 1987), pp. 136–144.
  6. J. J. Koenderink, Solid Shape (MIT Press, Cambridge, Mass., 1990).
  7. J. J. Koenderink, A. J. van Doorn, “The singularities of the visual mapping,” Biol. Cybernet. 24, 51–59 (1976). [CrossRef]
  8. R. Vaillant, O. D. Faugeras, “Using extremal boundaries for 3–D object modelling,” IEEE Trans. Pat. Anal. Mach. Intell. 14, 157–172 (1992). [CrossRef]
  9. J. M. H. Beusmans, “Visual perception of solid shape from occluding contours,” Ph.D. dissertation (University of California, Irvine, Irvine, Calif., 1990)(also Tech. Rep. 90–40, Department of Information and Computer Science, University of California, Irvine, 1990).
  10. J. A. Webb, J. K. Aggarwal, “Structure from motion of rigid and jointed objects,” Artif. Intell. 19, 107–130 (1982). [CrossRef]
  11. B. M. Bennett, D. D. Hoffman, J. E. Nicola, C. Prakash, “Structure from two orthographic views of rigid motion,” J. Opt. Soc. Am. A 6, 1052–1069 (1989). [CrossRef] [PubMed]
  12. J. H. Rieger, “Three-dimensional motion from fixed points of a deforming profile curve,” Opt. Lett. 11, 123–135 (1986). [CrossRef] [PubMed]
  13. J. Porrill, S. Pollard, “Curve matching and stereo calibration,” Image Vis. Comput. 9, 45–50 (1991). [CrossRef]
  14. J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975). [CrossRef]
  15. T. S. Huang, C. H. Lee, “Motion and structure from orthographic projections,” IEEE Trans. Pat. Anal. Mach. Intell. 11, 536–540 (1989). [CrossRef]
  16. J. J. Koenderink, A. J. van Doorn, “Affine structure from motion,” J. Opt. Soc. Am. A 8, 377–386 (1991). [CrossRef] [PubMed]
  17. L. S. Shapiro, A. P. Zisserman, M. Brady, “Motion from point matches using affine epipolar geometry,” Int. J. Computer Vision (to be published).
  18. J. W. Bruce, P. J. Giblin, Curves and Singularities, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
  19. A. K. Chhabra, T. A. Grogan, “Uniqueness, the minimum norm constraint and analog networks for optical flow along contours,” in Proceedings of the Third International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 80–84. [CrossRef]
  20. E. Hildreth, The Measurement of Visual Motion (MIT Press, Cambridge, Mass., 1984).
  21. A. Movshon, “Visual processing of moving images,” in Images and Understanding, H. Barlow, C. Blakemore, M. Weston-Smith, eds. (Cambridge U. Press, Cambridge, 1990).
  22. K. Nakayama, G. Silverman, “The aperture problem—I. Perception of nonrigidity and motion direction in translating sinusoidal fines,” Vision Res. 28, 739–746 (1988). [CrossRef]
  23. K. Nakayama, G. Silverman, “The aperture problem—II. Spatial integration of velocity information along contours,” Vision Res. 28, 747–753 (1988). [CrossRef]
  24. J. E. Rycroft, “A geometrical investigation into the projections of surfaces and space curves,” Ph.D. dissertation (University of Liverpool, Liverpool, UK, 1992).
  25. P. J. Giblin, J. E. Rycroft, F. E. Pollick, “Moving surfaces,” in Design and Applications of Curves and Surfaces, R. Fisher, ed., Institute of Mathematics and Its Applications Conference Proceedings Series (Oxford U. Press, Oxford, 1994), pp. 433–453.
  26. F. E. Pollick, S. Nishida, Y. Koike, M. Kawato, “Perceived motion in structure-from-motion: pointing responses to the axis of rotation,” Percept. Psychophys. (to be published).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited